Hybrid-Knowledge-Models-Based Intelligent Fault ...

Key Engineering Materials Vols. 245-246 (2003) pp. 149-157 online at http://www.scientific.net © (2003) Trans Tech Publications, Switzerland Online available since 2003/07/15

5th International Conference on Damage Assessment of Structures, 1-3 July 2003 Copyright by Trans Tech Publications

Hybrid-Knowledge-Models-Based Intelligent Fault Diagnosis Strategies for Liquid-propellant Rocket Engines Jianjun Wu1, Honggang Liu and Qizhi Chen Department of Astronautical Engineering, School of Aerospace and Material Engineering, National University of Defense Technology, Changsha, Hunan 410073, P.R.China 1 Email: [email protected] Keywords: Fault diagnosis, Knowledge, Qualitative model, Liquid-propellant rocket engine

Abstract: This paper focuses on a qualitative fault diagnosis method based on the integration and fusion of shallow and deep knowledge for liquid-propellant rocket engines (LRE). The paper firstly clarifies the concept and the types of LRE diagnosis knowledge. Later, from the isomorphic transform point of view, the paper analyses the correlation of different knowledge and knowledge representation, and formulate the LRE fault diagnosis. Then, the ways of acquisition, representation and organization for knowledge-based hybrid models constructed by signed directed graphs, rules, prepositional logic models, and qualitative deviation models are given. The intelligent diagnosis strategies for LRE, which reason and make a decision by multiple and synthetically utilizing all kinds of diagnosis knowledge such as experience, causality, system structure, and models, are presented. Introduction Significant progresses have been made towards the development of formal intelligent fault diagnosis methods for dynamic systems since 1980s. Such methods offer the prospect of improving system reliability and providing the basis for health monitoring in a large range of applications. In particular, modeling (qualitative or quantitative) methods and reasoning strategies form the heart of automated diagnosis systems. However, a number of important technical problems remain to be solved to make intelligent fault diagnosis techniques viable for real industrial applications [1]. For a dynamic system, if its diagnostic knowledge is complete, then all of its faults can be strictly diagnosed. But, because of the complexity of practical systems, it is often impossible to construct a complete diagnostic knowledge base for a problem. So, at present the limitations of intelligent fault diagnosis can fall into one main class: the incompleteness of diagnostic knowledge. In qualitative reasoning such as qualitative simulation [2,3], this means the generation of numerous spurious behaviors except the true. There are three approaches to solve the above problem as following: the first one is the development of more qualitative representations that allow more detailed information on the system, e.g., qualitative curvature [4] and fuzzy membership functions [5,6], or additional knowledge from other sources, e.g., observations [7], to be incorporated into qualitative reasoning, thereby reducing the qualitative ambiguity. The second is the integration of qualitative reasoning and quantitative simulation, in which qualitative reasoning is used to produce primitive solutions and quantitative simulation is then used as a filtering technique to eliminate ambiguous

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behaviors [8,9]. The third is the development of model-based diagnostic reasoning [10,11,12], which uses the system’s models and observations to reason and produce the set of components that may be abnormal. However, in these methods two problems, which are important to construct a complete knowledge base for an intelligent fault diagnosis system, are obviously neglected:(1) In fault diagnosis, what kind of knowledge is needed and how deep the knowledge should be; (2) How to acquire the knowledge required and how to represent, manage and coordinate between the acquired knowledge in diagnosis. This paper, based on the earlier work reported by the authors [13], presents an intelligent fault diagnosis method that utilizes a hybrid knowledge model and reasoning strategy. It includes two main aspects: one is the diagnostic knowledge strategy that comprises the acquisition, representation, and organization of different knowledge and information such as shallow and deep knowledge, qualitative and quantitative knowledge, fuzzy knowledge and time information. Another is the intelligent diagnostic reasoning strategy based on the integration of different knowledge with different depth. Firstly, besides the correlation of different knowledge, the concept and the types of diagnostic knowledge are systematically described. Secondly, the graphic and modeling ways of different knowledge acquisition, are discussed and studied. Thirdly, the objectoriented way of knowledge representation for causality, structure, and behavior is presented, and an integrated knowledge model based on the component structure and in the form of node knowledge base is given. Finally, the intelligent fault diagnostic strategy, which utilizes synthetically different knowledge and multiple reasoning methods, such as rule-based, model-based, fuzzy-knowledge -based, and dynamic-knowledge-based, are discussed and developed. The results verified with simulated fault samples and test-firing data of the LRE show that the method studied can be available for reference in constructing automated fault diagnostic systems. The problem statement Diagnosis knowledge strategy focuses on the acquisition, representation and organization of diagnosis knowledge. It is one of the aims in the diagnosis strategy to construct a complete knowledge base. However, it is also difficult in the way of shallow or deep knowledge. Meantime, in almost all diagnosis methods for dynamic systems, a similar knowledge description is usually utilized in the idea of the following mapping principle. Definition1 Define the fault diagnosis problem of a physical system as an original problem P0. Definition2 Let U be the domain, Xi=(X1i,…,Xni) be the vector of fault parameters in the i-th (i=1,…,m) component of the system (denote as Componenti), and n=dimension(Xi) be the dimension of the vector Xi, then define a vector space with n´1dimension (1) Spacei={(X1i,…,Xni)|XjiÎU, j=1,…,n} as the fault space of Componenti, and define the product Space= Space1´Space2 ´…´Spacem (2) as the fault space of the system. Definition3 Define as an abstract expression of the fault diagnosis problem, where K is the constructed knowledge base, R is the set of reasoning methods which utilize K to diagnose. If K and R is given in a fault diagnosis problem P: , then P is called a given diagnosis problem. Definition4 Let the original problem P0=and a given problem P1= are two descriptions for fault diagnosis problem, if there exists a full mapping from K0 to K1: h1: K0®K1 (3) if and only if there also exists a full mapping from R0 to R1:

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h2: R0®R1 (4) then P1 is called a homomorphic problem of P0, denoted as PT, and h1 is called a homomorphic mapping from P0 to P1, denoted as hT. If h1 is a one to one and full mapping, then P1 is called an isomorphic problem of P0, denoted as PG, and h1 is called an isomorphic mapping, denoted as hG. Definition5 Let S be the fault space of a system, and SPÍS, if for a given problem P: , there exist k1,k2,…,kmÎK, r1,r2,…,rnÎR and a mapping f, such that f(k1,k2,…,km,r1,r2,…,rn)=SP, (5) then SP is called a solution of P. Theorem1 The following propositions are true: (a) Isomorphic mapping is the specialization of homomorphic mapping; (b) The solutions of an isomorphic problem is equal to the solutions of the original problem; The solutions of the homomorphic problem contain the solutions of the original problem. Proof : (a) is obviously true. (b) Let PT: is an isomorphic problem of the original problem P0 : , S0 is a solution of P0. In the following S0 will only be proved to be a solution of PT, but the other propositions can be proved in the similar way. At first, there exist k10, k20, …, km0ÎK0, r10,r20,…,rn0ÎR0,and a mapping f, such that f(k10,k20,…,km0, r10,r20,…,rn0)=S0, (6) At the same time, from definition4, there exists one to one and full mappings h1 and h2, and T k1 ,k2T,…,kmTÎKT, r1T,r2T,…,rnTÎ RT, such that h1(k10)= k1T,…, h1(km0)= kmT, h2(r10)= r1T,…, h2(rn0)= rnT (7) then, from equation (6), f(h1-1(k1T), h1-1(k2T),…, h1-1(kmT),h2-1(r1T),…, h2-1(rnT))=S0, (8) that is, there exists a mapping g, such that g(k1T,k2T,…,kmT,r1T,r2T,…,rnT)=S0 (9) Thus, S0 is a solution of PT. Following the principle given above, it will make the diagnosis problem explicit and convenient to solve. For example, in the mathematical models based diagnosis, if the models are accurate and perfect, the description of the diagnosis problem is an isomorphic problem (denoted as PMG, see Fig.1) of the original problem P0. So, the solutions of P0(denoted as S0)is equal to the solutions of PMG(denoted as SMG). However, for the complexity of the systems, the models constructed are usually not accurate enough. The original problem is then transformed into a homomorphic problem (denoted as PMT), and its solutions (denoted as SMT) give an approximation to S0. Easy to solve PMT

SMT

Homomorphic transition

Implicate

Difficult to solve

P0

Isomorphic transition

S0 Equivalent

Convenient to solve PMG

SMG

Fig.1 Model based diagnosis following the mapping principle

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The diagnosis strategies In the common sense, for the given diagnosis problem, there exist different methods of knowledge description with different difficulty in solving the diagnosis problem. It is critical to make efforts in the most suitable organizing and representing way for the knowledge. Therefore, in the paper, the experience, structural knowledge and model knowledge will be effectively integrated for the fault diagnosis based on the hybrid knowledge model and reasoning strategy (See Fig.2). By this way, the experience and structural knowledge will be integrated with quantitative information to form the qualitatively and quantitatively integrated knowledge base (denoted as “QQKB” in Fig.2). The model knowledge will be integrated with time information and fuzzy information to form the dynamic knowledge base (denoted as “Dynamic” in Fig.2) and the fuzzy knowledge base (denoted as “Fuzzy” in Fig.2), respectively. Then, a tree-like graph will be used to describe the membership relation between the system and its components by decomposing the system into several levels like system level, sub-system level and component level. This decomposition describes structural knowledge of the system and the fault propagation property between the system and its components, and it makes the integrated expression of shallow and deep knowledge easy. For example, a part of the tree-like graph for a liquid-propellant rocket engine is shown in the Fig.3. In this figure, the LRE is decomposed into the engine level, the sub-system level which comprises pipeline, turbo-pump and thrust chamber, and the component level which includes valve, nozzle, gas generator, and so on. Quantitative information Shallow QQKB Experience Structure Model

Experience and structure Structure and model

Dynamic Fuzzy

Deep Fuzzy information

Time information

Fig.2 Integration of diagnosis knowledge LRE

Engine Level Sub-system Level

Pipeline Sub-System Turbo-pump Sub-system Thrust Chamber Sub-System

Nozzle

Combustion

Chamber

Injector Head

Gas Generator

Oxidizer Pump

Fuel Pump

Turbine

Valve

Tie-in

Duct

Component Level

Combustion

Chamber

Injector

Powder Starter

Impeller

Inducer

Gas Nozzle

Bearing

Rotating Blade

Inlet pipe

Seal

…

……

Fig.3 Hierarchy Decomposition of Engine’s Structure

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After the above decomposition of system structure, mathematical models of components in the system will be used as the source for knowledge acquisition by the following ways (See Fig.4). Mathematical model Qualitative Qualitative analysis calculation SDG Concision Time information Dynamic knowledge base

Qualitative constraint model

Qualitative diagnosis rule base Quantitative knowledge Fuzzy Quantitative rule knowledge

Fuzzy knowledge base

Model knowledge base

Diagnosis knowledge base

Fig.4 Acquisition of diagnosis knowledge

First, models of components will be qualitatively analyzed in the way of signed directed graphs (SDG), and will be simplified to form the diagnosis rule base of system qualitative knowledge. In addition, by integration with quantitative information of measurable parameters, shallow rule knowledge can be used to form the qualitatively and quantitatively integrated diagnosis rules, called as deep rule knowledge. The shallow rule knowledge and deep rule knowledge will be used as shallow knowledge in the diagnosis strategy. Second, models of components will be qualitatively calculated to acquire system qualitative model knowledge in the way of qualitative deviation model (QDM), and are described in the form of qualitative constraint equations. This kind of knowledge will be used as deep knowledge in the diagnosis strategy when diagnosis reasoning cannot be completed by only the shallow knowledge. Third, dynamic diagnosis knowledge base and fuzzy diagnosis knowledge base will be formed by the integration of shallow knowledge with time information and fuzzy information respectively. In the diagnosis strategy, this kind of knowledge will be used in online diagnosis and to solve the uncertainty included in the measurable parameters. The fig.5 gives the integrated organizing model of knowledge. In this figure, all the sub-systems and components of the system will be dealt with as a node and the system knowledge base will be organized in three levels. The system is in level 1, every sub-system is in level 2, and every component is in level 3. Then, by regarding every node in the figure as a diagnosis object in which diagnosis knowledge is included, the system can be described as a “tree”, and each node of the tree is a knowledge unit including shallow, deep knowledge and diagnosis reasoning procedure. Diagnosis Knowledge Base

Level 1 Level 2

Sub-System Knowledge Base 1 … Sub-System Knowledge Base N Level 3 Component Knowledge Base 1 … Component Knowledge Base M

Fig.5 Integrated organizing model of diagnosis knowledge

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Then, according to the variety of the knowledge base, a hybrid diagnosis reasoning strategy is proposed (See Fig.6) by the integration of RBR (Rule-Based Reasoning), MBR (Model-Based Reasoning), DBR (Dynamic-knowledge-Based Reasoning) and FBR (Fuzzy-logic-Based Reasoning). For offline fault analysis, the FBR based reasoning will be used for fault diagnosis if there exists the measured data to be uncertain and fuzzy information in the form of language and sign. Otherwise, the RBR based reasoning will be used with the shallow rule knowledge to give the primitive solutions firstly. Then if the solutions are inaccurate, deep rule knowledge will be used in diagnosis reasoning. Similarly, if the solutions are still inaccurate, diagnosis will go to MBR based reasoning. On the other hand, for online fault detection and diagnosis, DBR based reasoning will be used to diagnosis with dynamic knowledge. Begin Online fault detection

Diagnosis type

Time variant measured data

and diagnosis

Offline fault analysis Dynamic knowledge

Measured data Yes

Including Uncertainty

Fuzzy knowledge

DBR

FBR

End

End

No RBR

Shallow rule knowledge

Result

Exact

Yes

End

No RBR

Result

Deep rule knowledge

No Exact Yes

Model knowledge

MBR

Result End

End

Fig.6 Structure of engine’s node knowledge base

Case Study The diagnosis sample in the paper is a certain large liquid-propellant rocket engine. Its simple structure is shown in Fig.7. The solution space of the diagnosis problem is noted as S0=(Mode1, Mode2, Mode3, Mode4, Mode5, Mode6, Mode7, Mode8), where Mode3=Mode1ÇMode2. Oxidizer GG OP

T

Fuel FP

CC

: Duct OP: Oxidizer Pump FP: Fuel Pump

Fig.7

CC: Combustion Chamber TB: Turbine GG: Gas Generator

System structure of the engine

In the offline fault analysis of test-firing data, shallow rule knowledge was first used in the

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diagnosis reasoning, and the result is shown in Fig.8, in which fault origins Mode1, 2, 6 and 7 are diagnosed exclusively, but not for fault origins Mode4, 5, 8. Then, deep rule knowledge was then used and the result is as Fig.9, in which fault origins are all diagnosed exclusively. Furthermore, by defining fuzzy regions and fuzzy membership functions of variables, and constructing quantitative rule knowledge base, consistency degrees of fault origins to the elements in solution space can then be computed. For example, for the fault origin Mode4, the computed result is as Fig.10. From this, not only the occurrence possibility is computed, but also it can be concluded that the descending sequence of occurrence possibility is {4,2,7,1}. Meantime, for the fault mode of descending efficiency in the component of pump, the above method based on shallow knowledge can not distinguish whether efficiency is descended in the component of oxidizer pump or of fuel pump. Moreover, faults occurred in the components of turbine can not be diagnosed by this method, either. Herein, deep model knowledge is then used to reason further, and the result is shown in Fig.11, where all the above problems are solved.

Mode(diagnosis results)

Mode(diagnosis results)

Mode(to be diagnosed)

Mode(to be diagnosed)

Fig.8 Result based on shallow rule knowledge

Fig.9 Result based on deep rule knowledge

Fault parameters

Consistency degree Mode(to be diagnosed)

Fig.10 Consistency degree to Mode4

Mode(to be diagnosed)

Fig.11 Diagnosis result based on model knowledge

Conclusions The techniques such as qualitative modeling, qualitative reasoning, integration and transform of qualitative and quantitative knowledge are discussed systematically in the paper. Then, focusing on the unified treatment of system knowledge, such as rules, facts, graphs and models, the diagnosing methods based on hybrid knowledge model and reasoning strategy based are proposed. Firstly, the principles of intelligent fault diagnosis are studied in the view of homomorphic and isomorphic mapping, by which the difficulty of knowledge representation can be decreased.

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Secondly, by proposing an integrated way of knowledge acquisition, representation and management, a hybrid-diagnosis-knowledge model is developed. Then the hybrid-reasoningstrategy based diagnosing method is developed, in which several reasoning methods are integrated to improve diagnosing efficiency and veracity. In spite of all these developments, there are still a large amount of work needed to be done. For example, unified treatment of more types of knowledge will be one of our research in the future such as oral sentences, pictures, images, and so on. Furthermore, the automatic learning of knowledge from cases, automatic maintenance of knowledge base and high reliability of the practical diagnosis software will also be the aspects to be studied. Acknowledgement The authors gratefully acknowledge the support of this work by the National Natural Science Foundation (NNSF), China, by granting the projects No. 50276068, 59806014. References [1] Honggang Liu:Studies on Theory and Strategy of Intelligent Fault Diagnosis for Liquidpropellant Rocket Engine, Ph.D. dissertation, National University of Defense Technology, China, 2002. [2] Daniel J.Clancy: Solving Complexity and Ambiguity Problems within Qualitative Simulation, Ph.D. dissertation, University of Texas at Austin, 1997. [3] Daniel J.Clancy, Benjamin J.Kuipers. Qualitative Simulation As A Temporally-Extended Constraint Satisfaction Problem. Proceedings of the 15th National Conference on Artificial Intelligence(AAAI-98). 1998 [4] Abul Hossain, Kumar S.Ray. An entension of QSIM with qualitative curvature. Artificial Intelligence, 1997:303-350 [5] Qiang Shen, Roy Leitch. Fuzzy Qualitative Simulation. IEEE Transactions on Systems, Man, and Cybernetics. 1993, 23(4) [6] Qiang Shen, Roy Leitch. Diagnosing continuous systems with qualitative dynamic models. Artificial Intelligence in Engineering. 1995(9) [7] Daniel Berleant, Benjamin Kuipers. Qualitative and Quantitative Simulation: Bridging the Gap. Artificial Intelligence. 1995(2):215-255 [8] Bernhard Rinner, Benjamin Kuipers. Monitoring Piecewise Continuous Behaviors by Refining Semi-Quantitative Trackers. In Proceedings of the 16th International Joint Conference on Artificial Intelligence(IJCAI-99). Stockholm, Sweden, 1999 [9] Herbert Kay. SQSIM:A Simulator for Imprecise ODE Models.Computers and Chemical Engineering. 1998, 23(1):27-46 [10] Martin Sachenbacher, Andress Malik, Peter Struss. From Electrics to Emissions: Experience in Applying Model-based Diagnosis to Real Problems in Real Cars. 9th International Workshop on Principles on Diagnosis(DX-98). Cape Cod, USA, 1998 [11] Cascio F., Sanseverino M., IDEA(Integrated Diagnostic Expert Assistant) model-based diagnosis in the car repair centers. IEEE Expert, 1997, 12(6) [12] Williams B., Nayak P. A model-based approach to reactive self-configuring systems. Proc.AAAI96: 971- 978, 1996 [13] Huang Weidong, Wang Kechang. Rocket Engine Diagnostics Using the Signed Directed Graph. AIAA-95-2436, 1995

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Contact author and full address: Dr. Jianjun Wu Department of Astronautical Engineering School of Aerospace and Material Engineering National University of Defense Technology Changsha, Hunan 410073 P.R.China Tel:86-731-4556611(O), 4573175(O), 2219923(H) Fax:86-731-4512301 E-mail:[email protected]

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