A Fault Detection and Health Monitoring Scheme for Ship Propulsion

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2018.2812207, IEEE Access

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000. Digital Object Identifier 10.1109/ACCESS.2017.DOI

A Fault Detection and Health Monitoring Scheme for Ship Propulsion Systems using SVM Technique JING ZHOU1 , YING YANG1 , (SENIOR MEMBER, IEEE), STEVEN X. DING2 , YANYANG ZI3 , AND MUHENG WEI4 1

State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, CO 100871, China (e-mail: [email protected]) 2 Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, CO 47057, Germany 3 State Key Laboratory for Manufacturing and Systems Engineering, Xi’an Jiaotong University, Xi’an, CO 710049, Shaanxi, China 4 Oceanic Intelligent Technology Innovation Center, CSSC Systems Engineering Research Institute, Beijing, CO 100070, China

Corresponding author: Ying Yang (e-mail: [email protected]). This work has been supported by the National Natural Science Foundation of China under grants 61633001, 61473004 and U1713223.

ABSTRACT Both the model-based and data-driven techniques for fault detection have their merits and drawbacks. The fault detection systems are usually laid out separately with the health monitoring systems in practice. In this paper, the well-established observer-based residual generator is formulated to construct multiple evaluation functions, which are employed as the classification features of the support vector machine (SVM) for fault detection. It can be regarded as a tentative approach to combine the model-based and data-driven methods to enhance the fault detection performance. The standard SVM is modified for fault detection to achieve the quantitative trade-off between false alarm rate (FAR) and fault detection rate (FDR). Additionally, this paper also provides a unified framework for fault detection and health monitoring based on SVM. Simulations on the ship propulsion system show the effectiveness of the proposed method. INDEX TERMS Fault Detection, Health Monitoring, Support Vector Machine, Ship Propulsion Systems

I. INTRODUCTION

AULT detection and health monitoring are very essential for complex equipments in the coming era of Industrial 4.0. Model-based and data-driven methods are two main research issues dealing with fault detection problems. In the model-based framework, a residual signal is first formulated then the evaluation function and a threshold are constructed to indicate the occurence of faults [1], such as the case of the fault detection for a DC motor [2]. While in the datadriven framework, the massive historical data is collected for model training. If an emerging sample deviates from the nominal pattern, the system is deemed to be operating in the abnormal condition [3]–[5]. The data-driven methods are usually combined with the multivariate statistical analysis methods such as principle component analysis (PCA) and partial least square (PLS). The applications can be found in the key performance indicator (KPI) prediction and diagnosis [6] and nolinear process monitoring [7]. Both the modeland data-based methods have their merits and demerits. The former approach can reveal the intrinsical features of system-

F

VOLUME 4, 2016

s, but the fault detection performance is heavily influenced by model uncertainties and disturbances. The latter one is more appropriate for monitoring the complex industrial processes, but it requires the representative training sets. The combination of these two methods remains to be an important research topic [8]. The standard SVM is an efficient solution dealing with fault detection problems [9], [10]. In practice there is often a difference between the cost of false alarm and miss detection, such as in the medical imaging processing a sick person being wrongly diagnosed as healthy will delay the treatment and cause fatal consequences, but on the contrary the patient only needs to have more medical examinations. A miss-detected fault in nuclear power stations may lead to huge disasters, which cost much more than the maintenance fee caused by a false alarm. Nowadays the cost-sensitive SVM has been proposed to handle the difficulty by assigning different weights to training samples [11], [12], or by oversampling techniques [13]. However, the training samples from different classes are unbalanced since the training set is obtained from historical 1

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2018.2812207, IEEE Access J Zhou et al.: Fault Detection and Health Monitoring based on SVM

operating data, where the nominal data is much more than the faulty one. Beyond that, the fault detection performance can only be verified by the receiver operating characteristic (ROC) curve after the fault detection system is put into service [14], [15]. It is a more reasonable solution to design a fault detection system which can guarantee some quantitative fault detection performance before implementation. With the consideration of these limitations, we can utilize the information contained in the residual signal to generate features for classification. The training set comes from the model-based residual generator and the quantitative fault detection performance is considered in the design process. The machine learning based techniques for health monitoring have been employed in many applications [16]–[19]. Some commercial softwares for health monitoring of wind turbines can be found in [20], but there are still few papers addressing the fault detection and health monitoring in an integrated framework. In this paper, the observer-based residual generator is utilized to build classification features of SVM thus the two methods can be integrated to solve the fault diagnosis problems. We propose a modified version of standard SVM for fault detection which can achieve the quantitative fault detection performance in the design process. Additionally, this paper has combined the SVM technique with the health monitoring issue. We have defined three levels of health condition by counting the numbers of sampling points entering the different regions of feature space in a time period. Thus the fault detection and health monitoring issues can be handled in a unified framework. The paper is organized as follows. In section II, the modelbased fault detection strategies and standard SVM technique are addressed. Section III has proposed the modified SVM and health monitoring approach to achieve quantitative fault detection performance. Simulation on the ship propulsion system is illustrated in section IV. The conclusions are given in section V. II. PRELIMINARIES AND PROBLEM FORMULATION A. THE MODEL BASED FAULT DETECTION

Consider the following linear time invariant (LTI) system affected by faults and uncertainties, where f is the additive fault, ∆B is the multiplicative fault, d is the model uncertainty and ω is the measurement noise.

Define an evaluation function as J(r), the threshold Jth is set as the maximal value of J(r) under the influence of uncertainties [1]. The fault detection logic can be written as J ≥ Jth , f aulty J < Jth , f ault f ree In the norm-based threshold setting, a single norm of the residual signal is often regarded as the evaluation function. A fault is detected if the evaluation function exceeds the predetermined threshold. However, a single norm of residual vector contains much less information than the original signal. Fault detection is in fact a pattern recognition problem, the more information we obtain form residual, the more reliable the detection result is. Therefore, we can make the utmost of residual vector to establish multi-dimensional features to enhance the fault detection performance. Let r denote the model-based residual signal, some commonly-used standard evaluation functions are such RMS value The root mean square value of residual is often used instead of l2 norm for residual evaluation. The RMS for discrete-time system is defined by ||r||RM S = (

l+N 1 1 X T r (k)r(k)) 2 N

(1)

k=l

Peak Norm By introducing an evaluation window, the peak norm is modified as a residual evaluation function for fault detection. Let ψ = [k1 , k2 ], the peak norm for discretetime system is defined by 1

||r||peak,ψ = sup(rT (k)r(k)) 2

(2)

k∈ψ

Additionally, the peak value of r˙ can be used to reformulate the trend analysis. The average value evaluation function can be adopted as alternative of RMS. The detailed description of evaluation functions is given in [1]. In the practical applications, those variables which have specific physical meanings such as the vibration, temperature, noise and pressure signals are frequently used to solve the fault detection problems. Apart from these signals, the variables obtained from residual can also serve as the features of classification. This is a tentative approach to combine the aforementioned two methods to enhance the capability of fault detection. B. THE GENERAL SVM FOR FAULT DETECTION

(

x(t) ˙ = Ax(t) + (B + ∆B)u(t) + F f (t) + Dd(t) y(t) = Cx(t) + ω

The observer is formulated as ( x ˆ˙ (t) = Aˆ x(t) + Bu(t) + L(ˆ y (t) − y(t)) yˆ(t) = C x ˆ(t) The residual signal is defined as r = R(ˆ y (t) − y(t)) 2

The general SVM is widely used in the data-driven framework of fault detection [21], [22]. Nowadays the one-class SVM technique has been proposed to deal with the problem of lack of faulty data in the training process [23]–[25]. In this paper, we assume that the abnormal state of the system to be monitored can be simulated by injecting the faulty parameters into the mathematical model. Suppose the data set L which contains N1 nominal operation data and N2 faulty data is available for model training. L = {(x1 , y1 ), (x2 , y2 ), ..., (xN , yN )} N = N1 + N2 VOLUME 4, 2016



where xi ∈ Rn denotes the classification features and yi is the corresponding label. we have 1 i ∈ I+ = {1, 2, ..., N1 } yi = −1 i ∈ I− = {N1 + 1, ..., N1 + N2 }

J2

C B

By introduction of the slack vector ξ, the general support vector machine is formulated in the following optimization form [26]

A

N

X 1 ξi min ||ω||2 + C ω,b,ξ 2 i=1

Faulty

Hyperplane

(3) Norminal

s.t. yi (ω T xi + b) ≥ 1 − ξi , i = 1, 2, ....N

Margin boundary

ξi ≥ 0, i = 1, 2, ....N

J1

As for the linearly non-separable data, the kernel function K(xi , xj ) is adopted to address the original problem in feature space in which the new problem can be handled as a standard linearly separable one [27]. The new problem is formulated as min α

N N N X 1 XX αi αj yi yj K(xi , xj ) − αi 2 i=1 j=1 i=1

s.t.

N X

(4)

α i yi = 0

0 ≤ αi ≤ C, i = 1, 2, ....N The optimal margin hyperplane only achieves qualitative trade-off between FAR and FDR. There is no specific limitations on the fault detection performance. For some safetycritical equipments such as nuclear power plant, the fault detection system must guarantee a high fault detection rate since an undetected fault will cause severe damage. On the other side, the false alarm rate for the equipments with precious downtime must be limited under some level to reduce the maintenance cost. Thus, we propose a method to minimize the FAR while restrict the FDR above some given level or maximize the FDR on the condition that the FAR is limited below some level. III. FAULT DETECTION AND HEALTH MONITORING BASED ON MODIFIED SVM A. FAULT DETECTION BASED ON MODIFIED SVM

The framework of fault detection and health monitoring system can be found in Fig.2. The model-based residual generator is firstly constructed to generate residual signal. Then the data-based state monitor is formulated to supervise the operating state. The measurement variables are the outputs of process. Suppose the evaluation vector is given as (5)

where Ji is the ith evaluation function defined by L2 , L∞ norm or RMS value of residual. In this paper, we propose to utilize the multidimensional features instead of a single norm of residual to enhance the fault detection performance. VOLUME 4, 2016

J serves as the classification features of the support vector machine. The design objective is to find a hyperplane defined by ω and b, such that for an emerging sample J (i) , the following decide logic can determine whether the sample is from faulty system operation. 1 f ault f ree T (i) D = sign(ω J + b) = (6) −1 f aulty Thus, the definition of fault detection performances in the probabilistic sense are

i=1

J = [J1 , J2 , ..., Jm ]T

FIGURE 1. Linear Support Vector Machine

F DR = P r(D = −1|f 6= 0) F AR = P r(D = −1|f = 0)

(7)

Where P r(·) denotes the probability. As Fig.1 shows, we need to obtain a hyperplane to separate the two data sets corrupted by outliers. In the model training process, it is not the objective to separate the two sets as much as possible. Instead, it must be guaranteed that at least a predetermined portion of faulty samples is classified in the right side. In other word, the FDR needs to be restricted above some given level. The hyperplane obtained in this way can distinguish the emerging faulty samples more easily, thus a fault is more likely to be detected. On the assumption of sufficient training data, the FDR and FAR in SVM can be approximatively obtained by calculating the ratio of faulty and nominal samples that are labeled as −1, respectively [14]. ie 1 X φi F DR ≈ 1 − N2 i∈I− (8) 1 X F AR ≈ ϕi N1 i∈I+

φi , ϕi are the functions that indicate whether the samples are on the right side with the form 1 ω T J (i) + b = ξi − 1 > 0 φi = (9) 0 ω T J (i) + b = ξi − 1 ≤ 0 ϕi =

0 1

ω T J (i) + b = 1 − ξi ≥ 0 ω T J (i) + b = 1 − ξi < 0

(10) 3



Input

Output

Process

J

f r 

J

Fault Detection

1

1

Residual

Process Model

f r 

m

SVM Classifier

Health Monitoring

m

Model-based Residual Generator

Data-based State Monitor

FIGURE 2. The Framework of Fault Detection and Health Monitoring System.

As is well-known, the slack variable in standard SVM can be classified into four classes. Each ξi stands for the location of the corresponding xi . If ξi = 0, xi is on the margin boundary. If 0 < ξi < 1, xi lies between the margin boundary and hyperplane. If ξi = 1, xi is on the hyperplane. If ξi > 1, then xi is classified in the wrong side. The slack variable serves as the criterion of whether the samples are rightly classified. In the above analysis it can be concluded that both for nominal and faulty samples, ξi < 1 indicates the sample is properly classified and ξi > 1 means it is classified in the wrong side. We assume when ξi = 1, namely xi is on the hyperplane, it is also rightly classified, since these points are much fewer compared with other samples. The larger the ξi is, the more likely the xi is on the wrong side. Hence the sum of slack variables for those nominal data must be minimized to minimize FAR, and the sum of slack variables for those faulty data must be restricted to satisfy the FDR requirements. To this end, the following optimization problem is addressed X 1 ξi (11) min ||ω||2 + C ω,b,ξ 2

Compared with (3), the optimization problem (11) is a slightly modified version of standard SVM. The slack variables for nominal data is the function to be minimized while those for faulty data is expressed in the constrains. Similar to the solution of standard SVM, the Lagrange multiplier method is adopted to solve the constrained quadratic programming problem. The Lagrange function of (11) is N X X 1 2 L(ω, b, ξ, α, µ, κ) = ||ω|| + C µi ξi − ξi − 2 i=1 i∈I+

N X

(13)

1 X αi [yi (ω xi + b) − 1 + ξi ] + κ( ξi − β) N2 i=1 T

i∈I−

where αi ≥ 0, µi ≥ 0 (i = 1, ..., N ) and κ ≥ 0 are the Lagrange multipliers. For optimality, the derivative of Lagrange function respect to primal variables ω, b and ξ should be equal to zero, ie

i∈I+

T

s.t. yi (ω xi + b) ≥ 1 − ξi , i = 1, 2, ....N ξi ≥ 0, i = 1, 2, ....N 1 X ξi < β N2 i∈I−

Theorem 3.1: Given data set L, the hyper-plane obtained by the optimization problem (11) guarantees that the fault detection rate is greater than 1−β, meanwhile the false alarm rate is minimized . Proof: Note in (9) , if 0 < ξi ≤ 1, φi = 0. if ξi > 1, φi = 1. Then φi ≤ ξi holds for all the faulty samples. Hence we have 1 X F DR ≈ 1 − φi N2 i∈I− 1 X ≥ 1− ξi > 1 − β (12) N2 i∈I−

4

N X ∂L =ω− αi yi xi = 0 ∂ω i=1 N X ∂L =− αi yi = 0 ∂b i=1

∂L = C − αi − µi = 0 i ∈ I+ ∂ξi ∂L κ = −αi − µi + = 0 i ∈ I− ∂ξi N2 We obtain

ω=

N X

αi yi xi

i=1

αi + µi = C κ αi + µi = N2

N X i=1

i ∈ I+

αi yi = 0 (14)

i ∈ I− VOLUME 4, 2016



0 ≤ αi ≤ C, i ∈ I−

Substituting (14) into (13) to get 1 2

min L(ω, b, ξ, α, µ, κ) = −

ω,b,ξ

+

N X N X

N X

κ≥0

αi αj yi yj K(xi , xj )

i=1 j=1

(15)

αi − κβ

i=1

Thus the dual problem is given as

min α,κ

N N N X 1 XX αi αj yi yj K(xi , xj ) − αi + κβ 2 i=1 j=1 i=1

s.t.

N X

0 ≤ αi ≤

(16)

αi yi = 0

i=1

κ , i ∈ I+ N1

Theorem 3.2: Given data set L, the hyper-plane obtained by the optimization problem (19) guarantees that the false alarm rate is less than η, meanwhile the fault detection rate is maximized. Proof: Note in (10), if 0 < ξi ≤ 1, ϕi = 0. if ξi > 1, ϕi = 1. Then ϕi ≤ ξi holds for all the nominal samples. Hence we have 1 X 1 X ϕi ≤ ξi < η (21) F AR ≈ N1 N1 i∈I+

i∈I+

0 ≤ αi ≤ C, i ∈ I+ κ≥0 κ , i ∈ I− 0 ≤ αi ≤ N2 Comparing (16) with (4), the Lagrange multipliers are divided into two groups which have different bound limitations. The commonly-used optimization methods such as sequential minimal optimization (SMO) can be adopted to solve this problem [28]. The “kernel trick” can also be applied if the data sets in input space is not linear separable. The hyperplane is obtained by ω? =

N X

αi yi xi

(17)

i=1

?

b = yj −

N X

αi yi K(xi , xj )

(18)

i=1

It is worth to mention that in other applications where FAR is the more important index, we can also get a similar optimization problem to guarantee the FAR is below some given level while the FDR is maximized. ie X 1 min ||ω||2 + C ξi (19) ω,b,ξ 2 i∈I−

s.t.

yi (ω T xi + b) ≥ 1 − ξi , i = 1, 2, ....N ξi ≥ 0, i = 1, 2, ....N 1 X ξi < η N1 i∈I+

The dual problem is such min α,κ

N N N X 1 XX αi αj yi yj K(xi , xj ) − αi + κη 2 i=1 j=1 i=1

s.t.

N X i=1

VOLUME 4, 2016

α i yi = 0

(20)

There exit many other techniques such as the artificial neural network (ANN) [29]–[31] and cost-sensitive SVM [32]– [34] to handle the similar problems where we have different limitations on the classification errors of different classes. However, these methods just assign unbalanced weights to training samples from different classes. There is no quantitative limitation on FAR and FDR in the objective function and constraints. The fault detection performance can only be verified by ROC curve after the system is installed since both the training and test sets are from the actual running data. In our method, we have integrated the model-based and data-driven techniques to enhance the fault detection ability. The training set is obtained from the residual signal and we have given explicit constraints on FAR and FDR. Thus in the training process, we can guarantee that the fault detection performance can meet our safety requirements. Compared with ANN, the margin boundaries in SVM naturally divide the feature space into three regions. As the following subsection shows, the number of samples in each region can serve as the criterion of health state. B. HEALTH MONITORING BASED ON MODIFIED SVM

The health monitoring is another important issue in practice. In [35], the prognosis problem is regarded as a hierarchy of four levels which are as detection, localization, assessment and prediction. In the modified SVM, we define ω T J +b = 0 as the optimal hyperplane and ω T J + b = ±1 as the margin boundaries. As Fig.1 indicates, the two margin boundaries divide the space into three regions A, B, and C. Hence, if the system is in heathy condition, the majority of residual points will locate beneath the first margin boundary (region A). While the system is in the faulty state, the massive samples will locate above the second margin boundary (region C). In real applications, the faults often evolve from incipient failure into severe damage. As the fault evolves, more residual points will go into the region C. Thus we can regard the number of residual points in each region per time as the health index of dynamic system. The index is defined 5



k P

A Isum =

IiA

C Isum =

i=k−l

where IiA = IiC

=

1 0 1 0

k P

IiC

(22)

i=k−l

ω T J (i) + b > 1 else ω T J (i) + b < −1 else

We define three health levels to monitor the health state of systems. Level I The system is in the healthy state if there are more then Nth1 samples within the region A in a time period. Level II The system is in the sub-healthy state if there are less than Nth1 samples within the nominal region (A) meanwhile there are less than Nth2 samples lying in the faulty region (C) in a time period. Level III The system is in the faulty state if more than Nth2 samples locate in region C. The health monitoring is achieved by counting the number of samples entering the margin boundary in a time period. In real applications it can be conducted online. Once the incipient faults occur, the health state will degrade from Level I to Level III gradually. Immediate actions can be taken to avoid severe consequences.

x = [n V ]T is the state variables. u = [uθ Y ] is the control input. d = [Qf Te ] is the extern disturbance. W = diag(∆1 , ∆2 ) is the actuator faults. n, V, Im , m donate shaft speed, ship speed, shaft inertia and total mass, respectively. Ke is the gain of diesel engine with six cylinders. In this paper, we assume that one cylinder’s gain has dropped 50% due to less fuel or air inlet. The total gain has dropped 8%. In nominal state W = I2×2 , while in faulty case W = diag(1, 0.92). We consider two evaluate functions for classification. ie J1 (k) = (

t∈[k−5,k]

A. FAULT DETECTION SCHEME

For SVM training, we inject fault parameters into the Simulink model and record the corresponding nominal and faulty data. Define J(k) = [J1 (k) J2 (k)]T , the simulink model is running for 2000 seconds both in nominal and faulty condition. We record J(i) per second, the training data is scattered in Fig.3. 4.5 -1 1 Support Vectors

TABLE 1. Health monitoring strategy

3.5 The optimal plane obtained by standard SVM

3

State Healthy Sub-healthy Faulty

A Isum

1

sup (rT (t)r(t)) 2

J2 (k) =

4

Level I II III

k 1 1 X T r (t)r(t)) 2 5 t=k−5

J2

as

Symbol A Isum ≥ Nth1 C < Nth1 and Isum < Nth2 C Isum ≥ Nth2

2.5 FDR>0.5 2

FDR>0.7

1.5

The thresholds Nth1 and Nth2 are empirical values which are determined by the safety requirements. The critical equipments demand a larger Nth1 and smaller Nth2 . As is A can demonstrated in the following section, the curve of Isum serve as the degradation indictor of ship propulsion systems when incipient fault occurs. IV. IMPLEMENTATION AND SIMULATION

The proposed method is applied to the fault detection of ship propulsion system. The propulsion system is the most vital subsystem in vessels thus detecting faults in time is of great importance in the safety operation. The ship propulsion system model is given in [36], [37] x(t) ˙ = Ax(t) + BW u(t) + Ed(t) y(t) = Cx(t) where an A=

Im bn m

aV Im bV m

aθ B=

Im bθ m

1 1 0 C= E = Im 0 1 0 6

Ke Im

0 1 m

0

(23)

1 The norm-based threshold

FDR>0.9

0.5 0 0

0.5

1

1.5

2

2.5

3

3.5

J1

4

FIGURE 3. Hyperplanes with different requirements

Since an undetected fault in ship propulsion systems will cause severe damage, in the simulation we seek to guarantee that the FDR is above some level meanwhile minimize the FAR. The β value is chosen as 0.1, 0.3 and 0.5 respectively. The corresponding hyper-planes are illustrated in Fig.3. Compared with the hyperplane obtained by the standard SVM, the three planes obtained by the modified SVM can guarantee that the FDR is greater than 0.9, 0.7 and 0.5, respectively. Meanwhile, the FAR is minimized. The higher the FDR requirement is, the more the plane deflects to the nominal region. Additionally, if only a single norm J1 (k) is adopted for fault detection, the norm-based threshold is a vertical curve in Fig.3. The threshold is the maximal value of J1 (k) which can guarantee a zero-FAR in the fault-free case. But obviously the single-norm based threshold is more conservative and performs worse than the two-feature based VOLUME 4, 2016



B. HEALTH MONITORING SCHEME

To show the effectiveness of the proposed method in the health monitoring, we assume the ship propulsion system has an incipient fault. The engine gain is gradually dropping form 100% to 92%, ie Kef = [K1 + ρ(t)K2 (1 − e

−

t−t0 τ

)]Ke

300

sub-Healthy

Number of Samples in Each Region

classification. J1 (k) only reflects the one-dimensional characteristics of residual thus cannot distinguish the nominal and faulty data effectively. It seeks to achieve a zero-FAR, hence there is no quantitative trade-off between FAR and FDR. The simulation results show that the modified SVM is a more efficient solution in fault detection than the model-based fault detection.

250 N th1 200

150

Faulty

Healthy N th2

100

50

0 0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Time

FIGURE 5. Monitoring curve with incipient fault

(24)

where K1 = 1, K2 = −0.08, τ = 20, ρ(t) indicates the time the fault occurs. Let β = 0.1, the hyperplane and margin boundaries are illustrated in Fig. 4.

The combination of model-based and data-driven methods will definitely achieve better fault detection results than the single approach. V. CONCLUSION

J2

4.5 4 3.5 3 2.5 2

Faulty state

1.5 1

Incipient fault evolves Nominal state

0.5 0 0

0.5

1

1.5

2

2.5

3

3.5

J1

4

This paper studies the SVM-based fault detection and health monitoring issues and tries to solve the original problems by combining the model-based and data-driving methods. The standard SVM is modified to achieve quantitative fault detection performance. In real applications, the SVM is often used as a post-implementation method to achieve fault detection, while the method proposed in this paper can be regard as a pre-implementation method since only the model-based residual is used for classification. The more comprehensive research of fault detection using both model- and data-based methods, such as the combination with cost-sensitive ANN will be our further direction.

FIGURE 4. Samples with incipient fault.

REFERENCES

We set the thresholds as Nth1 = 210,Nth2 = 110. The health state curve of the ship propulsion system is given in Fig.5. We count the number of points locate in region A and C in 300 seconds. The fault occurs at 1650s. The red curve indicates that the number of samples locate in the nominal region decreases as the fault evolves, while the green curve shows that more and more samples will go into the faulty region as the fault evolves. Once the curves cross the thresholds, the system state is assumed to degrade to a lower level. In Fig.5, the ship propulsion system degrades to subhealthy state at 1850s and to faulty state at 2800s. The time delay is about 200s. Hence in real applications, immediate steps can be taken to handle the abnormal conditions if the system is in sub-healthy state and severe damage can be avoided. The proposed method proves to be efficient in health monitoring of industrial equipments. To better apply the proposed methods in the real processes, we can utilize more evaluation functions rather than two to enhance the fault detection performance. Besides, we can also construct more residual signals, not only the observation of output, to collect more information for pattern recognition. VOLUME 4, 2016

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