A lifetime-prognosis model has been implemented for the case of generator ...... the direct maintenance costs, e.g. for spare parts, technicians, transportation and ...... service provider in good time before the wind turbine is stopped automati- ...... Lloyd (2007)] Germanischer Lloyd (2007): Guideline for the Certification of.
Maintenance Management of Wind Power Systems by means of Reliability-Centred Maintenance and Condition Monitoring Systems
Final project report February 2012
Dr.-Ing. Katharina Fischer Division of Electric Power Engineering Department of Energy and Environment Chalmers University of Technology
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Abstract Wind power plays a central role for the development of a sustainable electric power supply system. In view of climate change and limited primary energy resources, ambitious goals have been set to promote a strong increase of wind energy utilization. While the cost of onshore wind power is already today comparable to that from conventional power generation sources, the cost is higher for wind power from offshore and remote onshore wind parks. A considerable portion of 20-30% of the life-cycle cost of wind turbines is constituted by the cost for operation and maintenance (O&M), required to ensure the technical availability of the turbines. To reach cost-efficient maintenance for wind power plants by means of data-based, quantitative methods is the main objective for research in the Wind Power Asset Management (WindAM) group at the Division of Electric Power Engineering, Chalmers. In the WindAM-RCM project, funded by the research foundation of Göteborg Energi AB, the concept of Reliability-Centred Maintenance (RCM) has been applied to wind turbines. In a workgroup involving Göteborg Energi AB as a wind-turbine owner and operator, Triventus Service AB as a maintenance service provider, SKF as a provider of condition-monitoring services and a wind-turbine component supplier, as well as the WindAM group at Chalmers, an RCM analysis of the wind turbines Vestas V44-600kW and V90-2MW has been carried out. The study has identified the most critical subsystems, their dominant failures modes, the underlying failure causes and suitable preventive measures. In this way, it provides the basis for the development of quantitative models for the comparison and optimization of maintenance strategies for wind-turbine components, e.g. in the context of the Reliability-Centred Asset Maintenance (RCAM) method. In the second part of the project, approaches for optimally using information from condition-monitoring systems (CMS) in the maintenance process have been investigated. The main focus has been set on developing a methodology to predict the residual life of wind-turbine components based on their age and data from online-CMS. A lifetime-prognosis model has been implemented for the case of generator bearings in wind turbines using vibration data in order to investigate the applicability of the approach.
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Sammanfattning Vindkraft spelar en central roll för utvecklingen av ett hållbart elförsörjningssystem. Ambitiösa mål har satts med tanke på klimatförändringar och begränsade primära energiresurser för att främja en kraftig ökning av vindkraftsanvändning. Medan kostnaden för landbaserad vindkraft redan idag är jämförbar med den från konventionella kraftverk, är kostnaden högre för vindkraft från havsbaserade och avlägsna landbaserade vindkraftsparker. En betydande del av livscykelkostnaden för vindkraftverk, 20-30%, utgörs av kostnaden för drift och underhåll (O&M) som krävs för att säkerställa teknisk tillgänglighet för vindturbinerna. Målet för forskningen inom Wind Power Asset Management (WindAM) gruppen vid Avdelningen för elteknik, Chalmers, är att nå kostnadseffektivt underhåll av vindkraftverk med hjälp av databaserade, kvantitativa metoder är I WindAM-RCM-projektet, som finansieras av Göteborgs Energis forskningsstiftelse, har konceptet Reliability-Centred Maintenance (RCM) tillämpats på vindkraftverk. I en arbetsgrupp med Göteborg Energi AB som ägare och operatör av vindkraftverk, Triventus Service AB som underhålls-serviceleverantör, SKF som leverantör av tillståndsövervakningstjänster och vindturbinkomponenter, liksom WindAM-gruppen på Chalmers, har en RCManalys av vindturbinerna Vestas V44-600kW och V90-2 MW utförts. Studien har identifierat de mest kritiska delsystemen, deras dominerande felmoder, de bakomliggande orsakerna och lämpliga förebyggande åtgärder. På detta sätt ger studien en grund för utveckling av kvantitativa modeller för jämförelse och optimering av underhållsstrategier för vindturbinkomponenter, t.ex. i samband med Reliability-Centred Asset Maintenance (RCAM) metoden. I den andra delen av projektet har metoder för optimal användning av information från tillståndsövervakning system (Condition-Monitoring Systems, CMS) i underhållsprocessen undersökts. Huvudfokus har satts på att utveckla en metod för att förutsäga den återstående livslängden för vindturbinkomponenter baserade på deras ålder och data från online-CMS. En livstidsprognosmodell har skapats för fallet av generatorlager i vindkraftverk, baserande på vibrationsdata från CMS, för att undersöka tillämpbarheten av metoden för vindturbiner.
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Table of contents Abstract ........................................................................................................................................................... 2 Sammanfattning .............................................................................................................................................. 3 Table of contents ............................................................................................................................................. 4 Preface ............................................................................................................................................................. 7 List of abbreviations ......................................................................................................................................... 8 1
2
3
Introduction ............................................................................................................................................ 9 1.1
Background ............................................................................................................................................... 9
1.2
Report outline ......................................................................................................................................... 10
Methodology and state of the art ......................................................................................................... 12 2.1
Reliability-Centred Maintenance (RCM) ................................................................................................. 12
2.2
Quantitative maintenance optimisation techniques .............................................................................. 12
2.3
Reliability-Centred Asset Maintenance (RCAM) ..................................................................................... 14
2.4
RCM, QMO, and RCAM – State of the art with respect to application in wind power ........................... 16
2.5
Condition-Monitoring Systems (CMS) – Facilitators for condition based maintenance......................... 19
2.6
CMS for wind turbines - State of the art ................................................................................................. 20
2.6.1
Data acquisition, processing and analysis techniques .................................................................. 22
2.6.2
CMS utilisation in the maintenance process ................................................................................. 27
2.6.3
Failure prognosis ........................................................................................................................... 28
Reliability-Centred Maintenance study ................................................................................................. 30 3.1
Implemented RCM process..................................................................................................................... 30
3.2
Results and discussion: V44-600kW wind turbine .................................................................................. 32
3.2.1
System description ........................................................................................................................ 32
3.2.2
Subsystem selection based on statistical analysis and practical experience ................................ 34
3.2.3
Electrical system ............................................................................................................................ 36
3.2.4
Generator ...................................................................................................................................... 40
3.2.5
Gearbox ......................................................................................................................................... 43
3.2.6
Hydraulic system ........................................................................................................................... 48
3.3
Results and discussion: V90-2MW wind turbine .................................................................................... 50
3.3.1
System description ........................................................................................................................ 50
3.3.2
Subsystem selection ...................................................................................................................... 51
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3.3.3
Gearbox ......................................................................................................................................... 53
3.3.4
Generator ...................................................................................................................................... 54
3.3.5
Converter ...................................................................................................................................... 55
3.3.6
Yaw system .................................................................................................................................... 57
3.3.7
Pitch system .................................................................................................................................. 57
3.3.8
Rotor.............................................................................................................................................. 58
3.4
3.4.1
Service maintenance ..................................................................................................................... 59
3.4.2
Corrective maintenance ................................................................................................................ 59
3.4.3
Condition-based maintenance ...................................................................................................... 60
3.4.4
Inspections .................................................................................................................................... 60
3.4.5
Identified challenges ..................................................................................................................... 60
3.5 4
Wind turbine service and maintenance practices today ........................................................................ 59
A quantitative model for maintenance strategy assessment ................................................................. 62
CMS-data based prognosis of the residual life of wind-turbine components......................................... 63 4.1
Data acquisition and signal processing ................................................................................................... 63
4.2
Component selection and analysed data ............................................................................................... 65
4.3
Main assumptions................................................................................................................................... 68
4.4
Factors influencing the vibration level.................................................................................................... 69
4.4.1
Ambient temperature ................................................................................................................... 70
4.4.2
Rotational speed ........................................................................................................................... 70
4.5
Data reduction ........................................................................................................................................ 71
4.6
Mathematical reliability modelling ......................................................................................................... 74
4.6.1
Basic equations and terminology .................................................................................................. 74
4.6.2
Univariate models ......................................................................................................................... 75
4.6.3
Multivariate models ...................................................................................................................... 77
4.6.4
Proportional Hazards Model ......................................................................................................... 77
4.6.5
Maximum-likelihood based parameter estimation....................................................................... 79
4.6.6
Goodness-of-fit test for the PHM .................................................................................................. 80
4.6.7
Prediction of covariate behaviour ................................................................................................. 81
4.6.8
Residual-life prognosis .................................................................................................................. 85
4.6.9
Quality measures for the prognosis model ................................................................................... 86
4.7
Results and discussion ............................................................................................................................ 88
4.7.1
Lifetime prognosis results in case of a turbine with bearing failure ............................................. 88
4.7.2
Aspects investigated during model development ......................................................................... 90
4.7.3
Potential and limitations of the final prognosis model ................................................................. 95
5
Summary and conclusions ................................................................................................................... 100
6
Related work....................................................................................................................................... 103
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7
Publications and communication ........................................................................................................ 105 7.1
Publications and reports ....................................................................................................................... 105
7.2
Conferences and seminars.................................................................................................................... 106
7.3
Study visits ............................................................................................................................................ 107
Appendix ...................................................................................................................................................... 108 A.1 Relevant terminology ............................................................................................................................... 108 A.2 Example of an event report ..................................................................................................................... 110 A.3 Failure report sheet ................................................................................................................................. 111 A.4 Test for equality of life distributions by means of the proportional-hazards model ............................... 112 References ................................................................................................................................................... 114
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Preface The post-doc project “Maintenance management of wind power systems by means of Reliability-Centred Maintenance (RCM) and Condition-Monitoring Systems” (Swedish: “Underhållsmanagement för vindkraftverk med RCM och CMS”, project number 09-11, acronym WindAM-RCM) has been carried out by Katharina Fischer at the Division of Electric Power Engineering, Chalmers, during February 2010 to January 2012. It has been conducted within the Wind Power Asset Management (WindAM) group led by Lina Bertling Tjernberg and in close cooperation with Göteborg Energi AB, SKF and Triventus Service AB. The project has been funded by the Research Foundation of Göteborg Energi AB, which the author gratefully acknowledges. The author would like to thank the project partners for their active and valuable involvement in the project. In particular, these are •
the members of the RCM workgroup Inge Aasheim (SKF Renewable Energy), Ulf Halldén (Triventus Service AB), Björn Mathiasson (SKF Sweden), Peter Schmidt (SKF Denmark) and Thomas Svensson (Göteborg Energi AB), for their comprehensive contributions to the RCM study; and
•
Michael Wika and Erwin Weis (SKF WISC), for supporting this project with CMS data and valuable discussions.
Within the RCM study, failure data of the V44-600kW system has been provided by courtesy of Swedpower / Vattenfall Power Consultant. Failure data of the V90-2MW has been used for statistical analysis with kind permission of Vattenfall. The project has been followed by a reference group, the support of which is gratefully acknowledged. The reference group involved: Inge Aasheim and Olle Bankeström (SKF); Thomas Svensson and Per Carlson (Göteborg Energi AB); Maria Danestig, Linus Palmblad and Angelica Pettersson (STEM); Solgun Furnes (EBL); Jørn Heggset (SINTEF); Gunnar Olsson Sörell (Fortum / Triventus); Thomas Stalin and Fredrik Carlsson (Vattenfall). Finally, thanks to Lina Bertling for the opportunity to carry out this work, and to the colleagues in the Optimization group (Mathematics Department, Chalmers) and the WindAM group, in particular to François Besnard, for the valuable discussions.
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List of abbreviations ALCA
Asset Life-Cycle Analysis
CBM
Condition-Based Maintenance
CMS
Condition-Monitoring System
DS
Drive side of a generator
DTMM
Delay-Time Maintenance Model
EMS
Engine Management System
HUMS
Health and Usage Management System
MSF
Modelling System Failures
FMECA
Failure Mode, Effects and Criticality Analysis
NDS
Non-drive side of a generator
O&M
Operations and Maintenance
PHM
Proportional-Hazards Model
RCAM
Reliability-Centred Asset Management
RCC
Rotor Current Control
RCM
Reliability-Centred Maintenance
RPN
Risk Priority Number
QMO
Quantitative Maintenance Optimization
WindAM
Wind Power Asset Management
hc
high rotational-speed class
lc
low rotational-speed class
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1 Introduction 1.1 Background Wind power plays a central role for the development of a sustainable power supply system. Ambitious goals have been set to promote the strong increase of wind energy utilisation which is required in view of climate change and limited primary energy resources: From 84 GW installed wind power capacity in Europe at the end of 2010, an increase to 230 GW by 2020 is targeted, of which a minimum of 40 GW is supposed to be installed offshore. [EWEA (2010), EWEA (2011)] The cost for operations and maintenance (O&M) of wind turbines presently constitutes a considerable portion of the life-cycle cost (LCC) and thus of the cost of wind energy: approximately 20-30% onshore and up to 30% of the – in this case considerably higher – LCC in offshore installations. A reduction of maintenance cost and therefore a reduction of the cost of wind energy can be achieved by further improvements in wind turbine design leading to improvement of its inherent reliability, but also by systematic solutions for maintenance management. Previous research has shown that the present maintenance, in both on- and offshore installations, is not optimised and that there are large potential savings by reducing (a) the cost for maintenance activities and component failure, and (b) cost due to production losses. The selection of the most suitable maintenance strategies for the wind turbine components and their optimal implementation are important steps towards achieving cost-effective maintenance of wind turbines. Figure 1 gives an overview over the different types of maintenance strategies. In contrast to the conventional maintenance strategies of (a) running to failure and subsequently performing repair (so-called corrective maintenance) or (b) doing preventive maintenance in a predetermined way, e.g. in fixed time intervals, (c) condition-based maintenance (CBM) is based on the information collected by means of condition monitoring.
Figure 1: Maintenance strategies, adopted from [SS-EN 13306]
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Figure 2 illustrates the influence of the three different maintenance strategies on the condition of a system. Among the advantages of CBM over the former approaches are: •
Developing faults can be identified before they reach a critical level. Unexpected failures, which are typically afflicted with a long downtime, can be avoided
•
Unnecessary maintenance is avoided by carrying out maintenance only when there is evidence of abnormal behaviour of a component.
Figure 2: Impact of maintenance strategies on component condition, adopted from Faulstich et al. (2009)
In case of gradually deteriorating systems for which the cost of corrective replacement exceeds the cost for preventive replacement (e.g. due to secondary damage caused by component failure or due to longer downtime in case of unexpected failure), CBM is often the most cost-effective maintenance strategy.
1.2 Report outline The WindAM-RCM project has covered two main topic areas: the application of the concept of Reliability-Centred Maintenance (RCM) to wind turbines, and the optimal utilisation of data from condition-monitoring systems (CMS) in the wind-turbine maintenance process. The project report is therefore structured in the following way: Chapter 2 provides an introduction to the two topic areas RCM and CMS and the related methodology. It summarises the results of a literature study on the key topics and focuses in particular on the respective state of the art in wind power. Chapter 3 covers the work on first main topic area of this project: It presents the RCM analysis of two wind turbines, including the implemented analysis process, the system descriptions, the comprehensive results obtained and their utilisation for the development of quantitative models for maintenance strategy selection and optimisation. Subsequently, Chapter 4 covers the second main topic area. It presents a methodology for CMS-data based prognosis of the residual life of wind-turbine components and its
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implemented for the case of generator bearings monitored by means of a vibration-based CMS. Chapter 5 provides a summary of the overall performed work, the key results and the conclusions. Three thesis projects, which have been carried out within the WindAM-RCM project and are complementing the described work, are summarised in Chapter 6. Chapter 7 provides a compilation of the publications and reports as well as the conference presentations through which the results from the present project have been disseminated. The Appendix contains a list of the relevant terminology as well as material complementing the main part of the report. A bibliography covering all references given in the text constitutes the final part of the report.
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2 Methodology and state of the art 2.1 Reliability-Centred Maintenance (RCM) The Reliability-Centred Maintenance method is a risk-based qualitative approach for maintenance strategy selection, which aims at preserving the functions of a system or, using another common term, of a physical asset. Rausand and Høyland (2004) summarise RCM as a systematic analysis of system functions and the way these functions can fail as well as a priority-based consideration of safety and economics that identifies applicable and effective preventive maintenance tasks. A comprehensive introduction to the RCM method is given in a book by Moubray (1991) with the same title. In the SAE standard JA1011 (“Evaluation Criteria for Reliability-Centered Maintenance (RCM) Processes”), the key attributes of RCM are summarised using seven questions: 1. What are the functions and associated desired standards of performance of the asset in its present operating context? 2. In what ways can it fail to fulfil its functions? 3. What causes each functional failure? 4. What happens when each failure occurs? 5. In what way does each failure matter? 6. What should be done to predict or prevent each failure? 7. What should be done if a suitable proactive task cannot be found? The working process incorporated in the RCM method originates in the civil aircraft industry where it was developed and applied to the Boeing 747 in the late 1960s. A first full description and publication under the present name Reliability-Centred Maintenance was provided by Nowlan and Heap in 1978 on behalf of the US Department of Defense [Quinlan (1987)]. Since that time, the approach has been applied in several industrial sectors with considerable success, including e.g. the railway, offshore oil & gas and manufacturing sectors [Andrawus (2008)]. However, a significant limitation of RCM as a purely qualitative method is its capability of determining which maintenance strategies are the most cost effective options available.
2.2 Quantitative maintenance optimisation techniques Quantitative maintenance optimisation (QMO) techniques are characterized by the utilization of mathematical models which quantify both the cost and the benefit of maintenance and determine an optimum balance between these [Dekker (1996)]. As illustrated in Figure 3, the optimisation objective is often to find the minimum total cost consisting of •
the direct maintenance costs, e.g. for spare parts, technicians, transportation and equipment, which increase with the maintenance effort, and
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•
the indirect costs of not performing maintenance as required, i.e. due to loss of production and due to additional labour and material after component breakdowns [Andrawus (2008)].
Figure 3: Basic concept of quantitative maintenance optimisation, adopted from Andrawus (2008)
The main purpose of quantitative maintenance optimisation is to assist the management in decision making, by utilising available data and thus reducing reliance on subjective judgement of experts [Jardine and Tsang (2006)]. In the context of maintenance optimisation, it is important to note that a maintenance strategy being optimal at one point in time might no longer be appropriate in the near future. Due to the variable nature of the input variables to the optimisation problem (including e.g. interest rate, component cost or failure behaviour), maintenance optimisation is not a one-time procedure but a continuous process which requires periodic evaluation [Andrawus (2008)]. A central limitation of quantitative maintenance optimisation techniques to be aware of is that these alone do not ensure that the maintenance efforts are targeted on the critical components and the practically most relevant issues of a system.
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2.3 Reliability-Centred Asset Maintenance (RCAM) The Reliability-Centred Asset Maintenance approach (RCAM) is a quantitative approach of RCM relating preventive maintenance on the component level to system reliability and total cost. As illustrated in Figure 4, it merges the concepts of RCM and QMO and in this way overcomes the drawbacks of the two separate approaches.
Figure 4: Interrelation of RCM, QMO and RCAM
The method was originally proposed for power distribution systems by Bertling (2002) and published under the name RCAM in Bertling et al. (2005). Figure 5 gives a logic diagram of the RCAM method. The figure illustrates the different stages and steps in the method as well as the systematic process for analysing the system components and their failure causes. The three main stages of the RCAM approach are the following [Bertling et al. (2005)]: Stage 1:
System reliability analysis; definition of the system and identification of critical components
Stage 2:
Component reliability modelling; detailed analysis of the components and, based on appropriate input data, definition of the quantitative relationship between their reliability and preventive maintenance measures
Stage 3:
System reliability and cost/benefit analysis; places the results of the componentlevel analysis (Stage 2) in a system perspective and evaluates the effect of component maintenance on system reliability and cost
By merging the concept of RCM with quantitative methods, the RCAM method provides an instrument for the quantitative assessment and comparison of maintenance strategies.
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Figure 5: Reliability-Centred Asset Maintenance method (RCAM), adopted from Bertling et al. (2005)
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2.4 RCM, QMO, and RCAM – State of the art with respect to application in wind power A literature study concerning the application of RCM, QMO, and the more recent RCAM method within the field of wind power has revealed that there are only few publications documenting work on this topic. Relevant contributions, some of them being limited to a partial application of the methods of interest, are summarised in the following. An early paper presenting the logical process of RCM and its application to an example wind park was published by P.J. Quinlan in the USA in 1987 [Quinlan (1987)]. Based on statistical studies of failures in wind parks by Lynette [Lynette (1985), Lynette (1986)] as well as operational experience gathered at Southern California Edison [Scheffler et al. (1986)], the RCM logic was applied and examined for each component of a horizontal-axis based wind power system. For a relatively low level of differentiation between components (e.g. foundation, gearbox, generator), failure consequences are classified (hidden, safety, operational, and non-operational) and the maintenance strategies resulting from the RCM process are listed. Due to the considerable growth and further development of wind power technology during the past decades, the outcomes of this early work are of limited validity for the O&M of wind turbines today. A pre-study on reliability-centred maintenance for wind power systems with focus on the effect of CMS on the maintenance process was carried out at KTH in 2005-2006 [Bertling et al. (2006)]. Within this work, two master’s theses were accomplished as initial steps towards the application of the RCAM method to wind power systems: In the master’s thesis of J. Ribrant, titled “Reliability performance and maintenance – A survey of failures in wind power systems” [Ribrant (2006)] and a resulting publication [Ribrant and Bertling (2007)], failure data from >95% of all Swedish wind turbines (19972005) was analysed and compared with German and Finnish failure statistics. By studying system and component reliability and answering the question which components were most critical in wind turbines regarding the number of failures and the resulting downtime caused by these failures, the thesis contributed to the stages 1 and 2 of the RCAM method. The results revealed that the gearbox was most critical to the availability of wind turbines and that the majority of gearbox failures were caused by wear, indicating that this component was suitable for the application of condition monitoring systems. Among the results of the statistical analysis was the observation that turbines with rated capacities >1MW, being state of the art technology today, suffer from higher failure rates than smaller turbines (0. For the purpose of illustration, a univariate Weibull distribution is fitted to the bearing failure data introduced in Section 4.2. The Weibull analysis is based on both failures and suspensions together with the corresponding component age. Figure 37 (left) shows the Weibull probability plot for the data. The approximate alignment of the data points along the straight line
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confirms the suitability of the Weibull distribution to characterise the reliability behaviour of the component under consideration. The scale parameter η and the shape parameter β in Equations (9)-(12) is estimated by means of the maximum-likelihood method. The obtained estimate of the shape parameter β = 2.3 indicates that the hazard function of the analysed bearings increases over time, as it is typically the case in presence of accumulating damages and ageing (see also Chapter 3).
Figure 37: Weibull probability plot of the bearing failure data including suspensions (left); Weibull cumulative distribution function of the bearing lifetime (right)
Figure 37 (right) displays the resulting distribution of the probability of failure over the bearing age, based on the estimated Weibull parameters. From this, the expected lifetime is calculated to 12.8 years. The 95% confidence interval shown in the graph reveals that 95% of the bearings are expected to fail between the age of 3.0 and 25.3 years. The high width of the confidence interval of more than 22 years obtained in the present case clearly shows the strong limitations of the univariate model in the context of maintenance planning. Obviously, lifetime predictions with significantly higher levels of certainty and therefore with considerably narrower confidence interval are required in order to base maintenance-planning decisions upon them.
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4.6.3 Multivariate models The limitations of univariate models discussed above can be overcome by means of multivariate lifetime models which include the effect of covariates. Covariates can be stress factors that influence the life of the monitored component (socalled external covariates), e.g. quantities related to the mechanical stress on a wind-turbine component or environmental conditions like ambient temperature. Alternatively, covariates can be quantities related to the technical condition of a component, like e.g. the vibration signals or the debris particle concentration in lubricant provided by CMS (internal covariates). Multivariate lifetime models which include the effect of covariates are e.g. the Accelerated Failure Time Model, the Proportional Hazard Model, the Additive Hazard Model, the Proportional Odds Model and the Prentice William Peterson Model. See Vlok (1999) for a concise overview and Gorjian et al. (2009) for a more detailed review and comparison of these models.
4.6.4 Proportional Hazards Model Among the multivariate models named above, the Proportional Hazard Model (PHM) originally developed for biomedical applications by Cox stands out by having been most comprehensively investigated and very widely used. Among the areas within which PHM has been applied in the past are e.g. aircraft engines [Jardine and Anderson (1985)], nuclear reactor cooler pumps [Montgomery et al. (2006)], brake discs in high-speed trains [Bendell et al. (1986)], machine tools [Mazzuchi and Soyer (1989)] and power-supply cables [Kumar and Klefsjö (1994)]. Vlok applied the PHM in a context having some similarity with the task in this project, for prognosis of the remaining lifetime of water-pump components including bearings using vibration-CMS data [Vlok (1999)]. Cox showed that the hazard rate of a component can be expressed by the product of an arbitrary (and possibly even unspecified) baseline hazard function h0(t) and a functional term being a function of the covariate vector &̅. In reliability applications, a common and widely applied form is the exponential form of the functional term in combination with a Weibull baseline hazard function:
; ) ∙ exp-.̅ ∙ &̅/
∙
!
%$∙ exp0.% ∙ &% .1 ∙ &1 ⋯ 3
(13)
Herein, β, η and γi are the model parameters, which are summarised in vector of unknowns ). While t denotes the time (calendar age, working age or another usage parameter of the component under consideration, see Section 4.6.2), &̅ is the vector of covariates.
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In the present work, the PHM is applied in its fully-parametric form given by Equation (13) with t denoting the calendar age of the generator DS bearings and the CMS trend data as a single time-dependent internal covariate. In the following, the covariate z(t) is thus considered a scalar quantity. Consequently, the PHM contains three unknown parameters (, η and γ) which are to be estimated from the failure data and the CMS data histories. Note that there is no distinction between different failure modes of the considered bearings, as the provided data does not allow this level of detail in analysis. Due to the immensely large amount of data that would be required for reliability modelling on the level of detail of different bearing failure modes, it is neither considered to be of interest for the practical application of the prognosis methodology. The choice of suitable covariates requires expert knowledge. In the present case, this choice has been made the monitoring experts at the project partner SKF who selected for this work the CMS trend data as a well-proven indicator of bearing damage. In cases where covariates have to be chosen among a variety of potential condition indicators, statistical hypothesis testing can be used to verify that a covariant is significant and thus is in fact related to the lifetime of a component. In the present report, the description of the theory underlying the PHM is mainly limited to the aspects that are required for applying the model in practice. For an in-depth introduction to the PHM including the mathematical derivation of its key equations, please refer to [Banjevic et al. (2001)]. In contrast to the univariate lifetime models presented in the previous section, the multivariate PHM model offers the potential of providing bearing-specific predictions of the residual life which are continuously updated during the monitoring process when new condition information is provided by the CMS. In the following sections, the different steps required for the implementation of the prognosis method are presented, including the key equations. The following nomenclature is used, which follows to a large extent the nomenclature in [Banjevic, et al. (2001)]: • • •
• •
): vector of PHM model parameters (, , . z(t): time-dependent covariate; here: CMS trend data 0 5 5% ⋯ 567 5 : the covariate observation points for the ith component history; here: the bearing age in the moment of measurement of a certain CMS trend data point, with Ti denoting the age at failure or suspension 5 &9 & 5 59 with j = 0,1,…,ki: observed covariate values in the component history i;
here: the jth data point in the (possibly reduced) CMS trend history of bearing i (Ti, Ci, z(i)(s); s ≤ Ti) with i = 1,2,…,n: sample of n independently observed (component) histories, where Ci is the censoring indicator
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4.6.5 Maximum-likelihood based parameter estimation The method of maximum likelihood is applied to estimate the unknown parameters of the PHM model (, η and γ). For right-censored data and independent censoring, the likelihood is (see e.g. [Banjevic et al. (2001)], [Lawless (2003)]): :∝
5?@ABC DE?F
5 , & 5 5 ; ) ∙
?? G5CDA5BC
9 , & 9 9 ; )
(14)
In this, the hazard function is given by Equation (13). The non-conditional reliability function for history i can be calculated using (see e.g. [Banjevic et al. (2001)]) 67
%$-5 , & ; )/ H I J. 5
9M
5 ∙ &9 K
59L% ∙
!
59
!
"N
(15)
with the covariate value between two data points being either equal to the mean of the previous and the next data point according to & 5 0.5 ∙ Q&9 &9L% R for 59 59L% 5
5
(16)
or assuming a constant value at the level of the previous data point according to & 5 &9
5
for 59 59L% .
(17)
Equation (15) is a discrete approximation of the continuous equation
-, & / , ) " 5
!
%$ J. ∙ & 5 K "
exp -. ∙ & 5 /
!
"
which relates the reliability function and the hazard function. For the likelihood function follows, by substituting Eqs. (13 ) and (18) into Eq. (14):
(18)
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(19)
The parameter set maximising this likelihood function, , is the one representing the historical reliability behaviour of the given sample and its relation to the covariate values in the best way. It is therefore this parameter estimate which is used in the PHM model in order to make predictions about the future reliability.
Figure 38: Example of the log-likelihood distribution over β and η for optimal γ. The red circle marks the optimum parameter set which maximizes the likelihood function.
4.6.6 Goodness-of-fit test for the PHM A review over different graphical and analytical goodness-of-fit tests suitable for the PHM is provided by Vlok (1999). Out of these, one graphical and one analytical method have been applied in the present work and are thus shortly presented in the following.
4.6.6.1 Residual plots Residual plots are constructed using the Cox-generalized residuals for the PHM. These are defined by
(20)
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with i=1,2,…, n and the ui being calculated according to: 67
%$59L% 5 S5 I J. ∙ &9 K ∙ 9M
!
59
!
"
(21)
By ordering the Cox-generalized residuals ri and plotting the ordered residuals r1*≤ r2*≤ … ≤rn against their expected values T5 T5,E
1 1 1 ⋯ U U1 UV 1
(22)
the fit of the Weibull-PHM can be assessed. A distribution of the resulting data points (Ei; ri*) along the line y=x indicates a good fit of the model. The visual assessment is facilitated by a transformation of the data points (Ei; ri*) to (1-exp(Ei); 1-exp(ri*)), see [Vlok (1999)], which results in an approximately equally spaced distribution of the data points along the horizontal axis. Again, for a Weibull PHM fitting the underlying data well, the residual plots will be distributed along the line y=x.
4.6.6.2 Z test A statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution is called a Z-test. In the present case, the null hypothesis to be tested is H0: The estimated model parameters (, η and γ) are equal to the true values describing the reliability behaviour of the modelled bearings, i.e. the model fits the data. For the PHM model, the Z-test is implemented by calculating, from the ordered residuals r1*≤ r2*≤ … ≤rn, the Z-score W
∑[\] 7^] Y7 $.ZE$% _.ZE$%
A∗
with W5 A7∗ . [
(23)
The p-value corresponding to the obtained value of Z (based on a normal distribution) can be used to make inference about rejecting or not rejecting the null hypothesis. The null hypothesis is usually rejected if the p-value is smaller than or equal to the significance level α.
4.6.7 Prediction of covariate behaviour Once the parameters of the proportional-hazards model have been estimated from the failure and suspensions events and the CMS data histories, and the goodness-of-fit has been confirmed, a model is available which quantitatively relates the probability of failure with
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the corresponding covariate (here: vibration-CMS data) history. However, because covariates obtained from CMS signals are per se time-dependent, it is necessary to predict their future behaviour in order to allow a prognosis of the residual life. Vlok (2011) discusses stochastic and non-stochastic covariate behavior as well as techniques to predict future covariate behavior in both cases. In the stochastic case, covariates can only be predicted to lie within certain confidence bounds while an exact prediction is not possible. A situation to which this applies and for which a stochastic covariate would obviously be most appropriate is the example of using wind speed as an (external) covariate. In the non-stochastic case, it is assumed that the future covariate behavior can be predicted with reasonable accuracy beyond the present time t, based on the covariate history up to this point in time. In the context of condition monitoring where CMS signals related to the (often gradually deteriorating) component condition are used as covariates, this is usually the case. In case of a developing damage, often clear trends are visible in the data history, which allow a reasonably accurate extrapolation into the future (see Figure 39 for an illustrating example). To capture the variability of the CMS data is of less interest, but the covariate prediction model should be capable of properly representing the trend in the data. Due to this reasoning and the higher appeal to maintenance practitioners pointed out by [Vlok (2001)], covariates are considered non-stochastic in the present work. They are modelled by means of polynomial or exponential functions, the parameters of which are obtained through non-linear regression using the Levenberg-Marquardt algorithm (“nlinfit” command in MATLAB).
Covariate history
Covariate prediction
Figure 39: Example of history-based covariate prediction by means of a regression function
For the prediction of future covariate behaviour, it is recommendable to choose a regression function which is as closely as possible related to the monitored physical phenomenon, i.e. in the present case the defect growth in metallic components. According to Figure 40, this is usually characterized by an increasing defect-growth rate towards failure. An additional property of interest in this context is the fact that a defect will either remain constant in size or will grow, but will not become smaller over time. Note that service maintenance applied
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to a bearing by means of re-greasing might temporarily reduce the vibration level at that bearing, that this will, however, not reduce an already present defect. To constrain the regression functions to either constant or positive slopes is thus a reasonable approach even for components subject to preventive maintenance (excluding any preventive replacements).
Figure 40: Damage growth characteristics of metals and composites (left, [Jones (1999)]) and of corrosion vs. crack-like defect growth (right, [Isaksson and Dahlgren (2011)])
For the prediction of covariates representing CMS signals closely related to component condition, regression functions with the following properties are considered most suitable: • • •
exclusion of negative values constant or positive slope for all future points in time a growth-rate increasing with the covariate level (corresponding to the defect-growth rate increasing with the size of a defect)
These properties are fulfilled by exponential regression approaches, while polynomial regression functions usually have the significant drawback of providing physically implausible predictions in many cases. Both 2nd-order polynomials as well as different exponential regression functions have been investigated in the scope of this project. According to this, the best covariate representation and prediction has been achieved with the multi-step approach described in the following. Besides the long-term horizon covering the whole available CMS data history of a component, a short-term horizon of e.g. 1-6 months is used for regression in order to capture also recent trends with faster damage-growth dynamics in the data. (1) Having defined a suitable short-term horizon, the regression function z(t)=exp(at)+b is fitted both to the whole CMS data history of a bearing and to the selected number of most recent months (the short-term horizon named above) in the CMS data.
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(2) Of the two parameter sets obtained, the one with the steeper slope (corresponding to the larger value of a, i.e. showing the faster dynamics) is chosen in order to provide a conservative prediction of the future covariate behaviour. Note that for DS trend values z ≤ 1, always the long-term horizon is used for covariate prediction, with the purpose of avoiding unrealistically short residual-life prognoses which can result from trend data variations at irrelevantly low levels. (3) If the procedure described above provides negative coefficients a for both the long-term and the short-term regression, the data is approximated by means of a horizontal line, fitted to the data in the short-term horizon.
Figure 41: History-based covariate prediction obtained using the implemented multi-step exponential approach; “6m” indicates the length of the short-term horizon of 6 months chosen in this case; the red data points are those the plotted regression line is based upon.
Figure 41 illustrates the results of this multi-step prediction approach using the trend data histories of four bearings: In the case of turbine WT24 shown in the top left figure, the highest positive slope was obtained from the long-term horizon covering the whole data history. The DS bearing in turbine WT38 displays an apparently random variation of the vibration level, with a minor decreasing trend. In accordance with the reasoning described above, it is approximated by a horizontal line representing the average value from the short-term hori-
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zon. The cases of turbines WT12 and WT38 show faster dynamics in the short-term horizon than in the long-term horizon. The covariate prediction is thus based on the data from the most recent 6 months in both cases. Summarising, the described multi-step covariate-prediction approach based on the regression functions & a
b c V b 0 c V b 0
outperforms polynomial regression approaches with respect to physical plausibility and is capable of representing both short- and long-term trends in the CMS data in an accurate way.
4.6.8 Residual-life prognosis Based on the optimal parameter set for the Weibull PHM determined according to Section 4.6.5 (being valid for the entirety of considered components of comparable type) and on the prediction of the future covariate development z(t) (being specific for every individual windturbine generator bearing), the hazard function of this individual component can be calculated for future points in time:
∙
!
%$∙ exp. ∙ &
(24)
The non-conditional reliability functions for t>Ti (with Ti the present time) is given by:
, & 5 ∙ exp . ∙ & d7
!
"
(25)
The conditional expectation of the residual life can be calculated using: e5 T0 5 | 5 3
fd 7
5
(26)
Based on the present age of the component and its extrapolated CMS data history, this is the expected value of the remaining lifetime. Obviously, the expected age at failure texp.fail. equals the sum of the present age and the expected residual life μ: Bgh.=>5?. T0| 5 3 5 e5
(27)
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The conditional probability of failure F(t)=P(T≤t|T>Ti) of a failure occurring until a future time t, knowing that the component has survived until the present time Ti, is obtained using: 1
5
(28)
Finally, the 95%- confidence bounds for the age at failure, i.e. the lower bound t0.025 and the upper bound t0.975) correspond to the time in the future at which the cumulative distribution function takes on values of 0.025 and 0.975, respectively: .1Z 1 .jkZ 1
.1Z 0.025 5 .jkZ 0.975 5
(29)
(30)
It is important to note that the obtained confidence bounds are based on the implicit assumptions that (a) the estimated Weibull-PHM parameters , , . are the true parameters and not afflicted with any uncertainty, and (b) that the future covariate behaviour is predicted without any error. As also discussed by Vlok (2001), this is questionable in case of the limited sample size and the strongly variable covariate behaviour often found in practical cases like the present one. When assessing the results, it must therefore be kept in mind that the confidence bounds calculated here can only represent the spread of the considered components’ reliability behaviour resulting from the estimated optimal Weibull-PHM. In analogy with Eqs. (29) and (30) above, the recommended time of replacement (sometimes also called “Just-in-time point”) for a chosen level of risk r of unexpected failure, which a CMS analyst would be willing to accept, can be calculated. This is given by: -ABh?>nB / 1
A5C6 ?BoB? p 5
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4.6.9 Quality measures for the prognosis model In order to assess the quality of the prognosis model (comprising the PHM as well as the covariate prediction model), two measures are introduced: The model accuracy is quantified using the average of the squared errors on the residual-life estimates compared to the real times of failure:
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qrrs
v u 1 u 1 1 ∙ I ∙ I - / Bgh.=>5?. =>5?@AB uw U5 hABx. u >?? hADyEDCBC >?? =>5?Bx u nDhDEBEC z5G5E Bo>?@>5DE E7 GDA5{DE |}~. t
(32)
The lower the measure MSSE of an assessed prognosis model, the higher is its prognosis accuracy in the evaluation horizon. The uncertainty of the model is measured by the summed widths of the residual-life confidence intervals according to:
q@En
v u 1 u 1 .jkZ .1Z ∙ I ∙ I u U5 whABx. u >?? hADyEDCBC >?? =>5?Bx u nDhDEBEC z5G5E Bo>?@>5DE E7 GDA5{DE |}~. t
(33)
Therefore, the lower the measure Munc, the lower is its prognosis uncertainty in the evaluation horizon. Due to the fact that in the condition-monitoring context, the importance of a good prediction accuracy and low uncertainty is highest during the time close to failure, an evaluation horizon of 2 months before observed failure is used for the calculation of the above two quality measures.
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4.7 Results and discussion The prognosis model developed in the present project is capable of predicting the residual life of a generator bearing based on its age and its CMS trend data history. While the preceding chapter summarised the theory underlying the different parts of the prognosis model, the present chapter aims to provide an understanding of the results obtained from this model, to highlight different aspects investigated during its development together with the best identified solution, and to discuss the potential and limitations of the final model.
4.7.1 Lifetime prognosis results in case of a turbine with bearing failure For the purpose of illustration and discussion of the results provided by the prognosis model, the case of one specific wind turbine with a failure of the DS generator bearing is considered: For turbine WT144, Figure 42a shows the CMS trend data history (after reduction to 2-week maximum values) from the beginning of the monitoring period at a component age of 3 months until the failure of the bearing at an age of 1074 days. For three points in time which correspond to a component age of 600, 815 and 1020 days, respectively, the Figure 42a to c illustrate the residual-life prognoses the developed method would have provided based on the CMS data measured until that time. At the age of 600 days, the absolute vibration level is low. The regression analysis of the data history until that time indicates an only slightly increasing trend level, which is extrapolated into the future for the purpose of lifetime prediction (see the dark-green line in Figure 42a. Figure 42b shows the resulting expected residual life of µ(t = 600 days)=734 days together with the 95%-confidence bounds (71 days…1490 days), to which Figure 42c provides the corresponding conditional probability density distribution of the residual life over the bearing age. Note the flat, wide shape of the conditional pdf and the high width of the confidence interval of almost 4 years resulting from this. At the age of 815 days, a significantly increased CMS trend level (hc) of 4.9 gE is observed, together with an further increasing trend (see the green regression line in Figure 42a). Correspondingly, the expected residual life is reduced to 340 days, with the 95%-confidence interval spanning a still wide period of 27...646 days. At the third marked point on the time axis, at a bearing age of 1020 days, a further rise in the considered vibration level to 8.7 gE together with an increasingly steep trend slope is observed (light-green line in Figure 42a). The expected residual is estimated to 147 days, with a considerably narrower conditional pdf and a corresponding 95%-confidence interval ranging from 11 to 284 days. At a component age of 1074 days, 54 days later, the bearing is considered failed and the turbine is stopped for replacement.
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(a)
(b)
(c)
Figure 42: CMS data history and prediction (a), predicted residual life incl. confidence intervals (b) and predicted conditional lifetime pdf for the drive-side generator bearing in wind turbine WT144
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The case exemplarily discussed here illustrates well the significantly enhanced certainty in lifetime prediction compared to that obtained from the only univariate Weibull-model discussed in Section 4.6.2. In addition, the lifetime prognosis provided by the developed method is dynamically updated when new CMS data becomes available while the prediction was static in the univariate case. Finally, the case discussed here illustrated well how the certainty of the prognosis improves with an increasing CMS trend level and therefore usually provides increasing certainty towards the time of failure.
4.7.2 Aspects investigated during model development 4.7.2.1 Data basis for PHM parameter estimation In Sections 4.6.4 and 4.6.5 of the foregoing chapter, the equations underlying the PHM model and the maximum-likelihood based estimation of its parameters have been introduced in a generally valid form. In particular, the likelihood function given in Eq. (19) is formulated in a way that allows to include both exactly observed lifetimes (i.e. component histories ending with failure) and right-censored data (component histories in which no failure had occurred until the end of observation) in the estimation of the PHM parameters. The inclusion of censored histories in the parameters estimation is, however, subject to controversial statements in the literature. While Montgomery et al. (2006) state that both failure-terminated and censored component histories should be included, Vlok et al. (2004) claim that the inclusion of not yet failed components in the construction of the lifetime model leads to biased coefficients. The latter authors thus recommend basing the lifetime model solely on histories with failures. Due to the fact that both approaches apparently have been capable of providing useful models in the past, in the present project the two alternatives have been implemented and compared. Based on this, the approach yielding the better model quality has been chosen for the final model. Figure 43 shows the results of the graphical goodness-of-fit test described in Section 4.6.6.1. The figures on the left display the residual plots for the case in which the Weibull PHM parameters are estimated based on all 211 valid component histories, thus including both failure-terminated and censored histories. The figures on the right show the corresponding residual plots for the case in which the model parameter estimation is based on the 9 failure-terminated component histories only. The residual plots clearly indicate a major difference in the goodness-of-fit of the two models: The model fit obtained based on both failure- and suspension-terminated histories (left) is poor. In particular, the model fails to represent the histories including failure as the large number of outliers below the 10%-confidence bound at a residual level of 0.1 shows, all of which are residuals corresponding to failure-terminated histories. Due to the fact that the
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intended utilisation of the model in wind-turbine condition-monitoring in the present project requires good model accuracy in particular in the case of impending failure, the PHM obtained based on all component histories is considered insufficient. On the contrary, the PHM determined solely based on failure-terminated histories represents the data well: With the exception of a single outlier (related to history 1, WT3), the residuals spread around the level of the horizontal line r=1 in the top right figure and are clearly aligned with the straight line y=x in the lower right figure.
Figure 43: Residual plots for Weibull PHM constructed based on all component histories (left; o suspension, x - failure) and based on solely failure-terminated histories (right)
The Z-test as an analytical goodness-of-fit test introduced in Section 4.6.6 confirms the graphical results in Figure 43. Recall that the null hypothesis to test is “H0: The model fits the data”, which implies that the Z-score of its residuals would be normally distributed. In the first case described above, which is based on failure- and suspension-terminated component histories, the Z-score calculated using Eq. (23) (see Section 4.6.6.2) is Z=1.23, corresponding to a (two-sided) p-value of p=0.22. In the second case based only on failure-terminated histories, Z=-0.59 and therefore a p-value of p=0.56 is obtained. A small p-value indicates that the null hypothesis is rejected with high confidence. Accordingly, the significantly larger pvalue obtained in the second case supports the model fit to be considerably better when the censored histories are not taken into account.
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All PHM models discussed in the following are thus constructed with parameters estimated from the 9 failure-terminated bearing histories.
4.7.2.2 Covariate selection The developed Weibull-PHM includes CMS-data as an internal covariate. Out of the four CMS signals provided for analysis in this project (see Section 4.2), the generator DS-bearing specific ones of interest in this context are “trend DS hc” and “trend DS lc”, i.e. CMS trend data measure in the high-rotational-speed class (hc) and in the low-rotational-speed class (lc), respectively. The most straightforward modelling option is to use these absolute CMS trend values as covariates in the PHM. However, the fact that different wind turbines (also of identical type) can show very different base levels of vibration in good technical condition suggests that an alternative to this is worth being investigated as well: the utilisation of relative trend values as covariates, which are obtained by means of normalizing the absolute trend data with a reference level measured at the beginning of the monitoring period. On this background, the following four potential covariates have been tested and the quality of the resulting prognosis models has been compared: 1) &% pU
2) &1 pU
3) &
ABEx r Gn
>oBA>yB ABEx r Gn ?BoB?C =AD GB =5AC DEG D= DE5DA5Ey
4) & >oBA>yB ABEx r Gn ?BoB?C =AD GB =5AC DEG D= DE5DA5Ey ABEx r ?n
Table 4 summarises the measures of model accuracy MSSE and model uncertainty Munc which have been defined in Section 4.6.9. It is found that the use of CMS trend data from high rotational speeds as covariate (z1, z3) yields the better prognosis models than the use of data from low rotational speeds (z2, z4).
Table 4: Comparison of the prognosis-model quality (quantified in terms of the inaccuracy measure MSSE and the uncertainty measure Munc) resulting from different covariate choices
Absolute trend level Normalised trend level
DS trend data, hc (data from high rotat. speeds) MSSE = 5.91e+4 days² Munc = 354 days MSSE = 6.04e+4 days² Munc = 419 days
DS trend data, lc (data from low rotat. speeds) MSSE = 7.93e+4 days² Munc = 479 days MSSE = 7.38e+4 days² Munc = 554 days
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A comparison of the suitability of absolute vs. normalised hc trend values reveals that the use of the absolute DS hc trend data as covariate provides the best prognosis model, both with respect to the accuracy and the certainty of the residual-life prediction (corresponding to the lowest values of MSSE and Munc in Table 4). Consequently, this option has been selected for the final model. The choice of CMS data from high rotational speeds is additionally supported by the observation by CMS analysts that some damages are detectable only at higher rotational speed [Heintz (2010)]. This stresses the importance of using hc data in order to obtain the best possible lifetime prognosis. The normalisation of data with a reference value can only provide useful results if the monitoring of the bearing under consideration started while it was still in good condition. In the present data, this seems not to be the case for at least one wind turbine (WT147), at which increased CMS trend levels were observed already from the beginning of the monitoring period. The bad performance of the normalised covariates concluded here might thus to some extent be caused by the analysed data set. If the abovementioned prerequisite is fulfilled in future analyses using different data sets, the performance of lifetime prediction based on normalised trend values might thus be better than the present case suggests. Based on the data analysed here, however, the procedure of data normalization is not recommended. Only absolute levels of DS hc trend data are used as covariate in the following.
4.7.2.3 Data-reduction intervals As discussed in Section 4.5, a reduction of the original CMS data to its maximum values in intervals of a predefined length has the benefits of reducing the amount and variation of the input data to the prognosis and of enhancing the comparability of the data. Data reduction intervals of 1 week, 2 weeks and 1 month have been tested in the present work in order to identify the most suitable procedure for application in the final prognosis model. The choice of data-reduction scheme influences the lifetime-prognosis calculation in different steps: On the one hand, it has an impact on the optimal parameter set obtained for the Weibull-PHM; on the other hand it determines the data history (and data density) based on which the future covariate behavior is predicted. Figure 44 shows the prognosis results obtained for wind turbine WT144 based on datareduction to maximum values using the three different interval lengths (a) 1 week, (b) 2 weeks and (c) one month. The upper plot of each subfigure shows the reduced data history together with the covariate predictions based on the data up to that time. Note that the cases (a) and (b) allow the use of a short-term horizon of only 1 month for the covariate prediction procedure (see Section 4.6.7), while this needed to be set to 2 months in case (c) in order to have sufficient data points in the short-time horizon to allow a prediction.
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(a) 1-week data-reduction intervals
(b) 2-week data-reduction intervals
(c) 1-month data-reduction intervals
Figure 44: Prognosis results for wind turbine WT144 obtained using data-reduction to maximum values in intervals of (a) 1 week, (b) 2 weeks and (c) 1 month
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The lower plots display the corresponding predicted lifetimes and their 95%-confidence bounds for each of the points in the CMS data history. Note that the earliest prognosis is provided upon availability of three data points in the history. Due to this, the first prognosis in case (c) is obtained approx. 2 months later than in case (a). A reduction of the data to maximum values in longer intervals has the advantage of providing less rotational-speed related variation in the data, which can be expected to be a better indicator of the technical component condition. A drawback of reducing the original CMS data to only one value per month is that single outliers (as e.g. in Figure 44 the single data point with a particularly high trend level measured at a component age of 900 days) have a higher weight in the parameter estimation process in this case. As such outliers are very unlikely to be related to component condition, this is an undesired effect, which is diminished in case of a higher data density. Another disadvantage of using the 1-month-based datareduction procedure, which becomes obvious from Figure 44c, is the resulting less frequent update of the lifetime prognosis. In addition to this mainly qualitative reasoning, the model quality measures introduced in Section 4.6.9 have been utilized for a quantitative assessment of the three options. The results are summarised in Table 5. Note that due to the short computing time of the developed model, which does not exceed several seconds to a few minutes in any of the three cases, the computational effort does not need to be taken into account in the choice to be made. Table 5: Comparison of the prognosis-model quality (quantified in terms of the inaccuracy measure MSSE and the uncertainty measure Munc) resulting from different options of data-reduction
1-week data-reduction intervals (case a) MSSE = 6.62e+4 days² Munc = 398 days
2-week data-reduction intervals (case b) MSSE = 5.91e+4 days² Munc = 354 days
1-month data-reduction intervals (case c) MSSE = 9.68e+4 days² Munc = 418 days
Based on the discussion above and the quantitative performance of the different resulting models indicated in Table 5, the best-performing 2-week data-reduction scheme is found to be the most suitable one, which is therefore applied in the developed final model.
4.7.3 Potential and limitations of the final prognosis model As presented in the previous sections, different influential factors have been investigated and the options providing the best prognosis quality with respect to the occurred failures have been included in the final prognosis model. Its properties are summarized once again in the following list: •
The parameters of the Weibull-PHM are estimated based on the failure-terminated histories.
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•
The absolute DS hc trend values are used as covariate.
•
The original vibration data is reduced to maximum values over intervals of 2 weeks.
•
A short-term horizon of 1 month is used for covariate prediction, while the long-term horizon includes the whole CMS history.
The results discussed in the following have been obtained using the final prognosis with the above properties. Figures 45(a-d) and 46 show five different cases, which are suitable to discuss both the potential and the present limitations of the developed prognosis model. Figure 45a illustrates the case of wind turbine WT145, the generator DS bearing of which showed outstandingly high vibration levels before it was replaced at an age of 742 days. A significantly increasing trend level at the age of 300 days leads to a low predicted residual life. The subsequent stabilization of the trend level suggests that the underlying damage is not further developing at the same rate, which is reflected by higher and similarly stable values of the predicted residual life in the age range of 380…700 days. An extraordinary increase in the trend level in the weeks preceding failure correctly relates to a very short predicted residual life. In the case of wind turbine WT189 shown in Figure 45b, the generator DS bearing failed at a still significantly increased vibration level at an age of 1888 days. The case illustrates well how the predicted residual life decreases with increasing trend level and trend slope, while the certainty of the prediction increases at the same time. A comparison of the true remaining lifetime represented by the red line in Figure 45b with the predicted lifetime intervals reveals the good performance of the prognosis model in this case. The prediction capabilities of the present model are, however, limited by the wide range of vibration levels at which bearings have been replaced and thus are considered to have failed. A major source of uncertainty lies in the fact that any information about the true bearing condition at the time of replacement is missing. A consequence of this is observed in in the case of wind turbine WT3 shown in Figure 45c: Herein, a step-increase in the trend level at the age of approx. 220 days is followed by stable trend values around 1.5gE. After an initially low remaining-life prognosis related to the stepincrease in vibration, the observed stabilisation of the vibration level from t=230 days results in an increasing expectation for the remaining life. At a trend level as low as 1.6gE and a bearing age of only 350 days, the considered bearing is replaced, while this would not have been expected based on the high residual-life prognosis at this time. It may be suspected that in this case the bearing has been replaced already at an early stage of damage and that it would have reached a critical condition not before a later point in time.
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Figure 45: Prognosis results in four different cases; (a) failure at high vibration level, (b) failure at intermediate vibration level, (c) failure at low vibration level, (d) a bearing with a developing damage that had not failed yet at the end of observation; red line in (a-c): true remaining life
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Figure 46: Prognosis results in the case of a bearing without indication of damage
The case of WT3 discussed here shows that the present data basis used for development of the prognosis model is to some extent subject to subjective factors: While an operator with a higher risk appetite may initiate bearing replacement not before very strong indicators of damage (as e.g. in case of WT145), a precautious operator would order a replacement already at the first sign of developing damage (as assumably occurred in the case of WT3). Due to the abovementioned lack of information about the true bearing condition at replacement, the bearings are simply classified as “failed” in both cases. Not surprisingly, this has a negative impact on the accuracy and certainty of the mathematical model based upon this data. To overcome this problem and improve the quality of quantitative residual-life predictions for a potential future application, it is recommended to collect, together with every replacement event, information about the true component condition and to classify as a failure only the cases with a confirmed critical level of damage. Figure 45d illustrates the case of wind turbine WT199 containing a bearing with a developing damage that had not failed yet at the end of observation (i.e. at the end of the available CMS history). However, according to the most recent residual-life prognosis, this bearing can be expected to fail within the next two years with a confidence of 95%. Figure 45d provides a suitable example for discussing the impact of the covariate-prediction procedure on the prognosis result: The majority of expected-lifetime values and the corresponding confidence bounds show a systematic, uniform decrease with increasing component age and trend level. However repetitively in between, significantly lower residual-life predictions are obtained
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(see the lower plot in Figure 45d). A comparison with the covariate prediction functions (plotted green in the upper plot in Figure 45d) shows that all outstandingly low values of the predicted residual life correspond to cases in which a recent strong increase in the trend level forced a pessimistic (steep) extrapolation of the trend-level history (based on the shortterm evaluation horizon, see Section 4.6.7). Although the use of long-term and short-term based covariate predictions causes some variation in the prognosis results over time, it is considered the most suitable approach, as in every instance with an observed steep increase in the trend levels, it should be conservatively assumed that this steep trend increase is going to continue into the future. Finally, the case of a bearing in WT213 with low vibration levels over the whole monitored time is shown in Figure 46. After a slight initial increase in the trend level until t=600 days, the trend values stabilize at a level as low as 0.7 gE. An interesting effect to be discussed by means of this case is the fact that the corresponding residual-life estimates decrease steadily in spite of the constant trend levels. The effect of decreasing life predictions can therefore only be assigned to the impact of the component age. However, is it plausible that bearings of different age but with identical vibration levels have different risks of failure? Although the degree of this impact is surprising, it is considered possible: It could be explained e.g. in the way that an aged bearing has suffered from material fatigue, so that an existing defect of a certain size could be expected to grow faster than in non-aged material. Besides the fact that the data analysed in the present work clearly reveals this impact of component age on the failure risk, also results obtained from analogous cases of Weibull-PHM application, e.g. by Montgomery et al. (2006), confirm this effect to be existent. However, the degree to which the predicted residual life decreases only due to increasing component age but in spite of constant vibration values (see Figure 46) appears questionable. A possibly overestimated impact of age in the prognosis model could be explained by the fact that suspended histories were not taken into account in the parameter-estimation procedure for the final model. As discussed in Section 4.6.6, this choice was made based on the very limited capability of the Weibull-PHM to appropriately represent the complete set of data of failure-terminated and censored histories. In a potential future development of the methodology presented here into a practical application it is therefore recommended to investigate also the suitability of alternative multivariate lifetime models (see also Section 4.6.3) to represent the full set of data.
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5 Summary and conclusions The WindAM-RCM project has covered two main topic areas: the application of the concept of Reliability-Centred Maintenance (RCM) to wind turbines, and the optimal utilisation of data from condition-monitoring systems (CMS) in the wind-turbine maintenance process. During the initial phase of the WindAM-RCM project, a state-of-the-art study has been carried out. The subject of this study has been closely aligned with the abovementioned focus areas in the project: The concepts of Reliability-Centred Maintenance, quantitative maintenance optimization (QMO) and Reliability-Centred Asset Maintenance as a combination of the former are subject of the first part of this study; the second part is focused on conditionmonitoring systems and their utilisation in the maintenance process. For each of these topics, the present report has provided a general introduction, summarised previous research and presented the state of the art concerning the application in wind power systems. In addition, relevant terminology for this project has been compiled together with the definitions provided in standards. The literature study has revealed that the methods of interest - RCM, QMO, and RCAM – have been applied to wind power plants only in a few single projects until today. Regarding CMS for wind turbines, a large number of publications has been found that deal with data acquisition and data processing for condition monitoring as well as with diagnosis, while the literature focusing on failure prognosis for wind turbines was very sparse. Within the project part on Reliability-Centred Maintenance, a limited-scope RCM analysis of the wind turbines Vestas V44-600kW and V90-2MW has been carried out. The executing RCM workgroup included Göteborg Energi AB as an owner of the analysed wind turbines, Triventus Service AB as a maintenance service provider, SKF as a provider of conditionmonitoring services and a wind-turbine component supplier, as well as the WindAM research group at Chalmers. Combining the results of failure statistics and assessment of expert judgement, the analysis has been focused on the most critical subsystems with respect to failure frequencies and consequences: the gearbox, the generator, the electrical system and the hydraulic system, the pitch system and the rotor. For these subsystems, the RCM analysis has identified the most relevant functional failures and their failure causes as well as suitable measures to prevent either the failure itself or to avoid critical secondary damage. It has been found that a considerable number of preventive measures proposed by the RCM workgroup for the V44-600kW turbine are implemented in the V90-2MW series. This reflects the learning curve in wind-power technology development and indicates an increasing focus on reliability and maintainability. A highly interesting result of the RCM analysis is the identified central role that vibration plays as a failure cause for mechanical failure of a variety of components. From this it can be concluded that measures for prevention or early detection of bearing damages and other sources of excessive vibration, like e.g. vibration-monitoring, are particularly effective to enhance the overall reliability of the system. In addition to the analysis of wind-turbine subsystem specific failures and appropriate countermeasures, comprehensive background information regarding the current maintenance practices has been obtained during the RCM study. Challenges which are currently impeding
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the operation and maintenance of wind turbines from becoming more cost-effective have been identified and solutions have been proposed. Component standardization, enhanced training of maintenance personnel, and the utilisation of data-based quantitative methods for decision support in wind-turbine maintenance are concluded to be important steps to improve the reliability, availability and profitability of wind turbines. The results of the RCM study form the basis for the development of quantitative models for maintenance strategy selection and optimization within the framework of the ReliabilityCentred Asset Maintenance (RCAM) approach. A first quantitative model for maintenance strategy assessment has been developed in a thesis project supervised within the WindAMRCM project. In addition, the results of the RCM study are utilised in the PhD student project of P. Bangalore titled “Load- and risk-based maintenance of wind turbines”, which is carried out within the Swedish Wind Power Technology Centre (SWPTC) at Chalmers since autumn 2011. In addition to providing the basis for quantitative maintenance management models, the results of the RCM study can also be used as a feedback of field experience for further improvement of wind-turbine design. The second main part of the WindAM-RCM project was dedicated to approaches for optimally utilising CMS data in the maintenance process. Based on the outcome of the literature study and discussions with the project partners, the CMS-data based prognosis of the residual life of wind-turbine components has been identified as main focus in this part of the project. This has been carried out in close cooperation with the SKF Wind Industry Service Centre in Hamburg, from which over 600 CMS-equipped wind turbines are being monitored. The frequently failing generator bearings were selected as the wind-turbine component for which the prognosis methodology was implemented and tested. Vibration and failure data from over 200 turbines of identical type has been used for this purpose. So far, lifetime models of wind-turbine components had been limited to univariate, usually purely age-based reliability models, which did not take into consideration information from CMS and which are of very limited use for maintenance planning due to their usually very high uncertainty in the prediction of failure times. Alternatively for wind-turbine maintenance planning, the visual or mathematical extrapolation of trends in the vibration data is being used for a subjective assessment of the risk of failure. In contrary to this, the proportional-hazards model (PHM) used in the present work is capable of integrating failure and CMS data, which is a prerequisite for quantitatively assessing the risk of failure and predicting the residual component life. Using the CMS and failure history of a fleet of turbines as input data, the prognosis model provides the distribution of the residual life of the monitored component based on its age and its CMS vibration levels. In this way, a turbine-specific prediction is provided, which is continuously updated when new CMS data becomes available. The accuracy and certainty of the lifetime prediction increase with increasing vibration levels and thus usually in vicinity of failure. The certainty of prediction is significantly higher than that obtained from univariate reliability models (compare Figure 37 and Figure 44).
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At present, the prediction accuracy of the developed prognosis model is limited (a) by the variation in bearing condition and vibration levels at failure, which is closely related to a lacking clear definition of bearing “failure”, (b) by lack of CMS-data from the initial operating phase of wind turbines, and (c) by the lack of data from wind turbines of an age exceeding 8 years. However, these limitations can in principle be overcome by means of more comprehensive data collection in the future. The presented lifetime-prognosis method provides a promising option for the optimal utilisation of wind-turbine CMS data in the maintenance process. While in the present work, the method has been implemented and tested for the specific case of generator bearings of a selected wind-turbine type, it is in principle applicable to any CMS-monitored wind-turbine component. In light of this, the method offers the opportunity to introduce residual-life based warning and alarm procedures in the monitoring process, being either an alternative or a complement to the present use of manually set alarm thresholds and the mainly subjective assessment of the failure risk of a monitored component. In this way, the conditionbased maintenance of wind turbines could be optimised. As a concluding remark, it shall be noted that the broad practical application of quantitative methods in maintenance decision-support tools will require the structured and automated collection of in-depth failure and maintenance data of wind turbines. Thus, further and intensified efforts towards such systematic data collection and management, as e.g. using the RDS-PP component designation structure combined with the EMS designation structure for maintenance activities (see VGB PowerTech (2007), VGB PowerTech (2003)) as well as Computerised Maintenance Management Systems (CMMS), are strongly needed. This is a prerequisite for tapping the full potential of quantitative maintenance optimisation for a further cost-reduction of wind energy. In summary, the following main contributions have been achieved in the WindAM-RCM project: •
a presentation of the state of the art in Reliability-Centred Maintenance and related quantitative approaches for maintenance management, of Condition-Monitoring Systems and procedures as well as of current practices in wind-turbine maintenance, providing a basis for the present and future work on these topics;
•
the application of the concept of Reliability-Centred Maintenance to wind turbines, based on both statistical failure-data analysis and the experience of maintenance practitioners, which has demonstrated the potential of the RCM method and provides a broad knowledge base regarding the dominating failures, their causes and suitable remedial measures in wind turbines; and
•
the development of quantitative, data-based models for (a) maintenance strategy selection and optimisation and (b) enhanced condition-based maintenance, which offer the potential to overcome the presently dominant reliance on subjective expert judgement in maintenance management in the future.
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6 Related work In parallel to the post-doc project described in the present report, two PhD student projects have been on-going within the WindAM group at Chalmers during the project period, which are closely related to the WindAM-RCM project and have offered a variety of opportunities for discussion and collaboration: •
The project “Reliability modelling and optimal maintenance management for wind power systems” is carried out by PhD student Francois Besnard in cooperation with Vattenfall Wind Power and funded within Vindforsk III. The main subjects and selected results from this work have been summarised in Section 2.4 of the present report.
•
The project “Load- and risk-based maintenance of wind turbines” is carried out by Pramod Bangalore in cooperation with Göteborg Energi AB, SKF and Triventus Service AB and funded through the Swedish Wind Power Technology Centre (SWPTC) hosted at Chalmers. The research application for this PhD student project was developed within the WindAM-RCM project, based upon the outcomes of the RCM study. The main subject of the project is to investigate the dependency of wind-turbine failures on environmental factors e.g. like wind speed, wind turbulence, humidity or grid disturbances. With the overall objective to achieve cost-efficient wind-turbine maintenance, it aims at developing a method for flexibly adapting the maintenance of certain wind-turbine components based on the stress these components have been subjected to in the history.
In addition, three student thesis projects have been supervised within the WindAM-RCM project, which are complementing the present work: •
Malin Sallhammar: “Reliability Analysis of Wind Power Systems - A statistical analysis of failures in Swedish wind turbines”, master’s thesis at Chalmers in cooperation with LTH Lund, 2011 M. Sallhammar carried out a statistical analysis of failure data from wind turbines located in Sweden for the periods 1989-2005 and 2006-2009. She investigated the failure rates and resulting downtime of wind turbines from different classes of rated capacity, the seasonal variation of failure rate and downtime, and in particular the reliability characteristics of the most relevant wind turbine subsystems (i.e. identification of a decreasing, constant or increasing failure rate over time).
•
Bertrand Kerres: “A comparison of wind turbine life-cycle costs and profits resulting from different maintenance strategies”, project thesis at Chalmers in cooperation with RWTH Aachen and Göteborg Energi AB, 2011 Bertrand Kerres analysed the revenues and costs from a wind turbine, and developed an application capable of calculating and comparing the total cost of different maintenance strategies over the lifetime. This was applied in a case study for the Vestas V44-600kW system. The work has been carried out in close collaboration with Göteborg Energi which
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supported the work with access to maintenance reports and cost data for the V44600kW turbine, with wind data and with valuable discussions. •
Nelly Forsman: ”An analytical tool for the evaluation of wind power generation”, master’s thesis at Göteborg Energi AB / Chalmers, 2011 Nelly Forsman developed a methodology for a SCADA-data based tool for detecting deviations and degradations in wind-turbine performance by comparison with turbinespecific historic data. Using the data histories of wind speed, wind direction, air density and generated power, normalized power curves are derived for each wind turbine, which represent the reference signature. The present performance data is compared to this reference signature and deviations above a predefined threshold range generate an alarm. The method has been implemented for Göteborg Energi’s V44-600kW turbines located in the harbour of Göteborg. It provides a tool capable of detecting changes in wind-turbine performance as a potential indicator of maintenance need as well as of identifying measurement errors.
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7 Publications and communication The results and knowledge created in this project have continuously been disseminated and externally communicated - through presentations at conferences and seminars, scientific publications, but also through the involvement of master’s thesis students as described above. In the following, a compilation of the publications and reports created during the WindAM-RCM project is given; in addition, the visited conferences and seminars (with presentations of WindAM-RCM work as stated) carried out during the project period are listed. Finally, the last section summarises the study visits undertaken within the project.
7.1 Publications and reports •
Fischer, K.; Besnard, F.; Bertling, L.: "Reliability-Centered Maintenance for Wind Turbines Based on Statistical Analysis and Practical Experience", IEEE Transactions on Energy Conversion, In press, available online since December 2011, DOI 10.1109/TEC.2011.2176129. (related to Chapter 3 of the present report)
•
Besnard, F.; Patriksson, M.; Strömberg, A.-B.; Wojciechowski, A.; Fischer, K.; Bertling, L. (2011): “A Stochastic Model for Opportunistic Service Maintenance Planning of Offshore Wind Farms”, Proceedings of the IEEE PES PowerTech 2011, Trondheim, Norway, 19 - 23 June 2011.
•
Fischer, K.; Besnard, F.; Bertling, L.: ”A Limited-Scope Reliability-Centred Maintenance Analysis of Wind Turbines“, Proceedings of the European Wind Energy Conference EWEA 2011, Brussels, Belgium, 14-17 March 2011. (related to Chapter 3 of the present report)
•
Fischer, K.; Bertling, L.: “RCM analysis of the wind turbines Vestas V44-600kW and V902MW”, Report at the Division of Electric Power Engineering, Department of Energy and Environment, Chalmers University of Technology, Göteborg, Sweden, January 2011. (related to Chapter 3 of the present report)
•
Besnard, F.; Fischer, K.; Bertling, L.: “Reliability-Centred Asset Maintenance – A step towards enhanced reliability, availability, and profitability of wind power plants”. In Proceedings of the IEEE PES Conference on Innovative Smart Grid Technologies Europe, Göteborg, Sweden, 10-13 October 2010. (related to Chapter 2 of the present report)
•
Fischer, K.: “Maintenance Management of Wind Power Systems by means of ReliabilityCentred Maintenance (RCM) and Condition Monitoring Systems (CMS): Results of the State of the Art Study”, Report at the Division of Electric Power Engineering, Department of Energy and Environment, Chalmers University of Technology, Göteborg, Sweden, June 2010.
Two further publications are currently under preparation. These will present •
the model for maintenance strategy assessment developed in the thesis work of B. Kerres (see Section 3.5 and Chapter 6 in the present report), and
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•
the CMS-based residual life prognosis model described in Chapter 4 of this report.
7.2 Conferences and seminars •
Conference ”Vindkraftsforskning i fokus 2011” (Vindforsk/Vindval/SWPTC), Chalmers, 18-19 January 2012: Oral presentations (Pramod Bangalore, Francois Besnard, Katharina Fischer)
•
Forskningsdagen (Research day) at Göteborg Energi, Göteborg, 7 December 2011: Oral presentation (Katharina Fischer)
•
SKF Wind Farm Management Conference, Barcelona, Spain, 11-12 May 2011: Oral presentation (Katharina Fischer)
•
Seminar ”Statistical reliability 20 April 2011 (Katharina Fischer)
•
IEA Topical Expert Meeting “International Statistical Analysis on Wind Turbine Failures”, Kassel, Germany, 30-31 March 2011: Oral presentations (Francois Besnard, Katharina Fischer)
•
European Wind Energy Conference EWEA 2011, Brussels, Belgium, 14-17 March 2011: Paper and oral presentation (Katharina)
•
Conference ”Vindkraftsforskning i fokus 2010”, Chalmers, 24-25 November 2010 (Katharina Fischer)
•
IEEE Innovative Smart Grid Technologies (ISGT) Europe, Gothenburg, 11-13 October 2010: Oral presentation of joint article (Francois Besnard, Katharina Fischer, Lina Bertling)
•
Vind2010, Gothenburg, 15-17 September 2010: Oral presentation and poster (Katharina Fischer)
•
Vindforsk Seminar on Operations and Maintenance, Stockholm, 15 June 2010: Oral presentation (Katharina Fischer)
•
SKF Wind Farm Management Conference, Copenhagen, 9-10 June 2010: Poster presentation of the projects WindAM-RCM and WindAM-Opt (Katharina Fischer, Francois Besnard)
•
Nordic Wind Power Conference O&M, Stockholm, 25 May 2010: Oral presentation (Katharina Fischer, Lina Bertling)
•
ELKRAFTDAGEN, Göteborg, 25 March 2010: Poster presentation of the projects WindAMRCM and WindAM-Opt (Francois Besnard, Katharina Fischer)
•
VGB Conference "Maintenance of Wind Power Plants", Bremen, Germany, 24-26 February 2010, (Katharina Fischer)
and
lifetime
data
analysis”,
London,
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7.3 Study visits •
Lillgrund Offshore Wind Farm, Öresund, Sweden, 1 February 2010
•
SKF ERC, Nieuwegein, The Netherlands, 19 May 2010
•
Kenersys K82-2MW turbine in Gårdsten, Göteborg, during Vind2010 conference, 17 September 2010
•
SKF Wind Industry Service Centre (WISC), CMS-monitoring centre, Hamburg, 1 September 2010 and 17 June 2011
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Appendix A.1 Relevant terminology Reliability is defined as “the ability of an item to perform its required function under given conditions for a given time interval”. [SS-EN 13306] Availability is defined as “the ability of an item to be in a state to perform a required function under given conditions at a given instant of time or during a given time interval, assuming that the required external resources are provided”. [SS-EN 13306] Note: The term Availability is not used consistently in the context of wind power and should thus be specified in detail to avoid ambiguity. Within the present project, the most common and straightforward definition will be used, describing availability as the ratio of operational time divided by the nominal time, the latter usually being a period of one year: Availability =
Nominal time - Downtime Nominal time
In this definition, downtime due to external causes like failures of the grid or absence of wind is not eliminated and is thus included in the same way as downtime after wind turbine failures or due to preventive maintenance. [Ribrant (2006)] Maintenance describes the combinations of all technical and corresponding administrative actions, including supervision actions, intended to retain an entity in, or restore it to, a state in which it can perform its required function. [IEC 50(191)] Corrective maintenance is defined as “maintenance carried out after fault recognition and intended to put an item into a state in which it can perform a required function”. [SS-EN 13306] Preventive maintenance is defined as “maintenance is carried out at predetermined intervals or according to prescribed criteria and intended to reduce the probability of failure or the degradation of functioning of an item.” [SS-EN 13306] Scheduled maintenance is defined as “preventive maintenance carried out in accordance with an established time schedule or established number of units of use”. [SS-EN 13306]
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Condition based maintenance is defined as “preventive maintenance based on performance and/or parameter monitoring and the subsequent actions. Performance and parameter monitoring may be scheduled on request or continuous”. [SS-EN 13306] Repair describes the part of corrective maintenance in which manual actions are performed on an entity. [IEC 50(191)] Failure is the event when a required function is terminated (or exceeding the acceptable limits). [IEC 50(191)] Fault is defined as “abnormal condition that may cause a reduction in, or loss of, the capability of a functional unit to perform a required function”. [IEC 61508] Note: According to [NASA (2002)], the term “fault” describes a defect, imperfection, mistake, or flaw of varying severity that occurs within some hardware or software component or system. It is a general term and can range from a minor defect to a failure.
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A.2 Example of an event report
Figure 47: Example of an event report provided to the wind turbine operator by the conditionmonitoring centre. Source: Kjellberg (2009)
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A.3 Failure report sheet
Figure 48: Failure report sheet including component categorization, by courtesy of Swedpower / Vattenfall Power Consultant
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A.4 Test for equality of life distributions by means of the proportional-hazards model As described in Section 4.2, the analysed data comprises 211 component (DS generator bearing) histories from a fleet of 202 wind turbines. All turbines in the fleet are of identical model, but the sample comprises turbines with • • •
two different rotor diameters (denoted Type A and B), two different generator manufacturers (Type C and D) and two different bearing dimensions (Type E and F).
Table 6 summarises the representation of the different rotor, generator and bearing types in the total of 211 component histories, as well as the number of failures in each class. Table 6: Representation of turbine types (i.e. rotor diameter), generator manufacturers and bearing types in the component histories (in brackets: number of component histories ending with failure) Wind turbine Type A BearingType E F Total
Wind turbine Type B
Total
Generator Type C
Generator Type D
Gen.unknown (Type C or D)
Generator Type C
Generator Type D
Gen.unknown (Type C or D)
0 4(0) 4
87(4) 7(0) 94
7(1) 4(0) 11
0 74(4) 74
27(0) 0 27
0 1(0) 1
121 90 211
As described by Lawless (2003), the semi-parametric form of the proportional-hazards model can be used for testing the equality of distributions. In the present work, this model has been used to test if the hypothesis that the monitored bearings have identical lifetime distributions even if they are operated in the turbines of type A and B, in generators of manufacturers C or D and have the dimensions E or F (thus, to test the assumption (1) stated in Section 4.3: “All DS bearings in the sample have identical lifetime distribution and can thus be described by a single reliability model”). The three null hypotheses to test in the present context are: : 0 :
0 : T
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For this purpose, the semi-parametric PHM ; . ∙ exp.̅ ∙ &̅
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is utilized, in which the baseline-hazard function h0(t) covers the impact of time and internal covariates and can remain unspecified.
The covariate vector & consists of constant, binary indicator-covariates taking on the value 0 or 1 according to whether an individual is associated with the first or the second distribution (A or B, C or D, E or F). A test of γ=0 is a test of the corresponding hypothesis. According to Lawless (2003), the hypothesis testing can be carried out by fitting the PHM and using the Wald statistic for evaluation. For the present case of constant covariates, the parameters γ and their standard errors can be determined using the “coxphfit” function available in MATLAB. High values for all obtained p-values indicate that none of the null hypotheses formulated above can be rejected. Based on the limited amount of available failure data, none of the indicator covariates related to the rotor diameter, the generator manufacturer or the bearing size is found to be statistically significant. It is thus justified to assume that all analysed bearings have identical lifetime distributions and to fit a single parametric PHM with solely time-dependent internal covariates to the whole data sample as it is done in the present work.
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References [Agrolager (2012)]: Agrolager, Website, accessed January 2012, http://www.agrolager.de/popup_image.php?pID=12060796&osCsid=2a7a2fd137534d16745 44cb44aa52c64 [Andrawus et al. (2006a)] Andrawus, J.A.; Watson, J.; Kishk, M.; Adam, A. (2006a): Determining an Appropriate Condition-based Maintenance Strategy for Wind Turbines. 2nd Joint International Conference on Sustainable Energy and Environment (SEE 2006), B-027 (O), Bangkok, Thailand, 21-23 November 2006. [Andrawus et al. (2006b)] Andrawus, J.A.; Watson, J.; Kishk, M. (2006b): The selection of a suitable maintenance strategy for wind turbines. International Journal of Wind Engineering, Vol. 30(6), pp. 471-486. [Andrawus et al. (2006c)] Andrawus, J.A.; Watson, J.; Kishk, M. (2006c): Asset Management Processes in the Wind Energy Industry. Proceedings of the 2nd Joint International Conference on “Sustainable Energy and Environment (SEE 2006)” 21-23 November 2006, Bangkok, Thailand, p. 269-274. [Andrawus et al. (2007a)] Andrawus, J.A.; Watson, J.; Kishk, M. (2007a): Modelling System Failures to Optimise Wind Turbine Maintenance. International Journal of Wind Engineering, Vol. 31(6), 2007, pp. 503-522. [Andrawus et al. (2007b)] Andrawus, J.A.; Watson, J.; Kishk, M. (2007b): Wind Turbine Maintenance Optimisation: principlesof quantitative maintenance optimisation. Wind Engineering, Vol. 31(2), 2007, pp. 101–110. [Andrawus et al. (2008)] Andrawus, J.; Watson, J.; Kishk, M.; Gordon, H. (2008): Optimisation of Wind Turbine Inspection Intervals. Wind Engineering , Vol. 32 (5), p. 477-490. [Andrawus (2008)] Andrawus, J.A. (2008): Maintenance optimisation for wind turbines. PhD thesis, Robert Gordon University, Aberdeen, UK, April 2008. [Anjar et al. (2011)] Anjar, B.; Dalberg, M.; Uppsäll, M. (2011): Feasibility study of thermal condition monitoring and condition based maintenance in wind turbines. Elforsk report 11:19, Stockholm, May 2011. [Amirat et al. (2009)] Amirat, Y.; Benbouzid, M.E.H.; Al-Ahmar, E.; Bensaker, B.; Turri, S. (2009): A brief status on condition monitoring and fault diagnosis in wind energy conversion systems. Renewable and Sustainable Energy Reviews, Vol. 13 (2009), p. 2629–2636. [Balschuweit (2009)] Balschuweit, R.: Beanspruchungs- und Schadensanalyse von Windenergieanlagen am Beispiel der Vestas V90-2MW. Diplomarbeit, TFH Berlin in cooperation with Vattenfall, Germany, 2009.
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