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Experimental Application on a Mechanical Transmission System of Integrated Fault Diagnosis and Fault Prognosis method
10th IFAC Symposium on Fault Detection, 10th IFAC Symposium Detection, Supervision and Safetyon forFault Technical Processes 10th IFAC IFAC Symposium Symposium on Fault Detection, 10th on Fault Detection, Available online at www.sciencedirect.com Supervision and Safety for Technical Processes Warsaw, Poland, August 29-31, 2018 10th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes Supervision and Safety Technical Warsaw, Poland, Augustfor 29-31, 2018 Processes Supervision and Safety for Technical Processes Warsaw, Poland, August 29-31, 2018 Warsaw, Poland, August 29-31, 2018 Warsaw, Poland, August 29-31, 2018
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IFAC PapersOnLine 51-24 (2018) 1016–1023
Experimental Application on a Mechanical Experimental Application on a Mechanical Experimental Application on a Mechanical Transmission System of Integrated Fault Experimental Application on a Mechanical Transmission System of Integrated Fault Transmission System of Integrated Fault Diagnosis and Fault Prognosis method. Transmission System of Integrated Fault Diagnosis and Fault Prognosis method. Diagnosis and Fault Prognosis method. Diagnosis and Fault Prognosis method. S. BENMOUSSA ∗∗ M.A. DJEZIRI ∗∗ ∗∗ S. ∗∗ S. BENMOUSSA BENMOUSSA ∗∗ M.A. M.A. DJEZIRI DJEZIRI ∗∗ S. BENMOUSSA ∗ M.A. DJEZIRI ∗∗ ∗ S. BENMOUSSA M.A. DJEZIRI ∗ LASA, Badji-Mokhtar Annaba University, BP 12, 23000 Annaba, ∗ LASA, Badji-Mokhtar Annaba University, BP 12, 23000 Annaba, ∗ LASA,Algeria Badji-Mokhtar Annaba University, University, BP BP 12, 12, 23000 23000 Annaba, Annaba, (e-mail: [email protected]). LASA, Badji-Mokhtar Annaba ∗∗∗ (e-mail: [email protected]). LASA,Algeria Badji-Mokhtar Annaba University, BPNormandi 12, 23000 Niemen, Annaba, Algeria [email protected]). UMR (e-mail: CNRS 7296, Avenue Escadrille Algeria (e-mail: [email protected]). ∗∗ LSIS, UMR CNRS 7296, Avenue Escadrille Normandi Niemen, ∗∗ Algeria (e-mail: [email protected]). ∗∗ LSIS, LSIS, UMR CNRS 7296, Avenue Escadrille Normandi Niemen, 13397 Marseille, France (e-mail: [email protected]) CNRSFrance 7296, Avenue Normandi Niemen, ∗∗ LSIS, 13397UMR Marseille, (e-mail:Escadrille [email protected])
LSIS, CNRSFrance 7296, Avenue Normandi Niemen, 13397UMR Marseille, France (e-mail:Escadrille [email protected]) 13397 Marseille, (e-mail: [email protected]) 13397 Marseille, France (e-mail: [email protected]) Abstract: In this paper, integrated fault diagnosis and fault prognosis approach, applied on Abstract: In paper, integrated fault diagnosis and prognosis approach, applied on Abstract: In this this paper, integrated faultgoal diagnosis and fault fault prognosis approach, appliedand on aAbstract: mechatronic system is presented . The is to assess the health status of the system In this paper, integrated fault diagnosis and fault prognosis approach, applied on aAbstract: mechatronic system is presented . The goal is to assess the health status of the system and In this paper, integrated fault diagnosis and fault prognosis approach, applied on a mechatronic mechatronic system is presented presented . The The goal goal is to to assess the the health status status ofpresented the system system and to predict the system remaining useful lifetime before observing a failure. In theof paper, a is . is assess health the and to predict the remaining useful lifetime before observing aa failure. In the presented paper, a mechatronic system is presented . The goal is to assess the health status of the system and to predict the remaining useful lifetime before observing failure. In the presented paper, the detection of the degradation beginning, the isolation of the faulty component, and the to predict the ofremaining useful lifetime before observing a failure. In the presentedand paper, the detection the degradation beginning, the isolation of the faulty component, the to the useful lifetime a failure. In the paper, the detection of the degradation beginning, the isolation of the component, and the estimation of the degradation profile are before performed in an integrated way bypresented using the Bond thepredict detection ofremaining the degradation beginning, theobserving isolation of the faulty faulty component, and the estimation of the degradation profile are performed in an integrated way using the Bond by the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation degradation profileuseful are performed performed in an integrated integrated way by using using the the Bond Graph tool.of Regarding the remaining lifetime, itin is predicted fromway the considered dynamic estimation the profile are an by Bond Graph tool. Regarding the remaining useful lifetime, it is predicted from the considered dynamic estimation of the degradation profile are performed in an integrated way by using the Bond Graph tool. Regarding the remaining useful lifetime, it is predicted from the considered dynamic of parametric degradation ordinary differential equations. the proposed Graph tool. Regarding the described remainingby useful lifetime, it is predicted fromTo thevalidate considered dynamic of parametric degradation by ordinary differential equations. the proposed Graph tool. the described remaining useful lifetime, it isapredicted fromTo thevalidate considered dynamic of parametric degradation described by ordinary differential equations. To validate the proposed method, an Regarding experimental implementation is done on mechatronic system. The prediction of parametric degradation described by ordinary differential equations. To validate the proposed method, an implementation is on system. The of parametric degradation ordinary differential equations. To validate theprediction proposed method, an experimental experimental implementation is done done on aaa mechatronic mechatronic system. The prediction performances are evaluateddescribed by usingby universal metrics. method, an experimental implementation is done on mechatronic system. The prediction performances are by metrics. method, an experimental is done on a mechatronic system. The prediction performances are evaluated evaluatedimplementation by using using universal universal metrics. performances are evaluated by using universal metrics. © 2018, IFAC (International Federation ofuniversal Automaticmetrics. Control) Hosting by Elsevier Ltd. All rights reserved. performances are evaluated by using Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. Keywords: Keywords: Fault Fault Diagnosis, Diagnosis, Fault Fault Prognosis, Prognosis, Mechatronic Mechatronic System, System, Modeling, Modeling, Bond Bond graph. graph. Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. 1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified 1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified 1. 13381-1: Three main approaches could be (Byington et al. (2002); Jardine et al. (2006); Gucik1. INTRODUCTION INTRODUCTION 13381-1: 2004); 2004); Three mainJardine approaches could be identified identified (Byington et al. (2002); et al. (2006); Gucik1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified The main goal of condition-based maintenance (CBM) is (Byington et al. (2002); Jardine et al. (2006); GucikDerigny (2011)): Data-based approach, Experience-based (Byington et al. Data-based (2002); Jardine et al.Experience-based (2006); GucikThe main goal of condition-based maintenance (CBM) is Derigny (2011)): approach, (Byington et al. (2002); Jardine et al.Experience-based (2006); GucikThe main of is to guarantee a high availability of maintenance a system and(CBM) to avoid Data-based approach, approach, and Model-based one. Theguarantee main goal goal of condition-based condition-based maintenance (CBM) is Derigny Derigny (2011)): (2011)): Data-based approach, Experience-based to a high availability of a system and to avoid approach, and Model-based one. The main goal of condition-based maintenance (CBM) is Derigny (2011)): Data-based approach, Experience-based to guarantee a high availability of a system and to avoid unnecessary or excessive maintenance actions. This is approach, Model-based one. to guarantee or a high availability of a system and to avoid approach, and and unnecessary excessive maintenance actions. This is Depending on Model-based the type of one. the used model, Data-based to guarantee a high availability of a system andregarding to avoid approach, and Model-based one. unnecessary or excessive actions. This is ensured by scheduling the maintenance actions Depending on the type of the used model, Data-based unnecessary or excessive actions. This is ensured by scheduling the maintenance actions regarding Depending on the type of the used model, Fault prognosis methods can be classified into three Depending on the type of the be usedclassified model, Data-based Data-based unnecessary or excessive maintenance actions. This is ensured by scheduling the actions regarding the health status of a system and the predicted Remaining prognosis methods can into three ensured bystatus scheduling the maintenance actionsRemaining regarding Fault Depending on the type of the used model, Data-based the health of a system and the predicted Fault prognosis methods can be classified into three categories: trend analysis-based fault prognosis, machine Fault prognosis methods can be classified into three ensured by scheduling the maintenance actions regarding the health status of aa system the predicted Remaining Useful Lifetime (RUL) beforeand observing a failure. So, the categories: trend analysis-based fault prognosis, machine the health status of system and the predicted Remaining Fault prognosis methods canand be classified into three Useful Lifetime (RUL) before observing a failure. So, the categories: trend analysis-based fault prognosis, machine learning-based fault prognosis, state estimation based categories: trend analysis-based fault prognosis, machine the health status of a system and the predicted Remaining Useful Lifetime (RUL) before observing a failure. So, the fault diagnosis module and the fault prognosis one are learning-based fault prognosis, and state estimation based Usefuldiagnosis Lifetimemodule (RUL) and before observing a failure. So, the categories: trend analysis-based fault prognosis, machine fault the fault prognosis one are the learning-based fault prognosis, and state estimation based fault prognosis. Trend analysis-based fault prognosis uses learning-based fault prognosis, and state estimation based Useful Lifetime (RUL) and before a failure. fault the fault one are main keys in a module CBM. prognosis. Trend analysis-based fault prognosis uses fault diagnosis diagnosis module and theobserving fault prognosis prognosis one So, are the the fault learning-based fault prognosis, andare state estimation based main keys in a CBM. fault prognosis. Trend analysis-based fault prognosis uses statistical models, the most used the PCA (Li et al. fault prognosis. Trend analysis-based fault prognosis uses fault diagnosis module and the fault prognosis one are the main statistical models, the most used are the PCA (Li et al. main keys keys in in aa CBM. CBM. fault prognosis. Trend analysis-based fault prognosis uses statistical models, the most used are the PCA (Li et al. (2010)), linear quadratic discrimination (Azam et statistical models, the most used are the PCA (Li et al. main keys in a CBM. linear quadratic (Azam al. statistical models, the mostdiscrimination used are models the PCA (Li et et al. Several works have been developed to assess the health (2010)), (2010)), linear quadratic discrimination (Azam et (2002)) and Auto Regressive (AR) (Yan et al. (2010)), linear quadratic discrimination (Azam et Several works have been developed to assess the health (2002)) and Auto Regressive (AR) models (Yan et al. Several works have been developed to assess the health (2010)), linear quadratic (Azam et monitoring of have dynamic systems. Based on thethe available Auto Regressive models (Yan et al. Several works beensystems. developed to assess health (2002)) (2002)). Methods based on discrimination the(AR) Euclidean metric are de(2002)) and and Auto Regressive (AR) models (Yanare et deal. monitoring of dynamic Based on the available Methods on the Euclidean metric Several works beensystems. developed to are assess the health (2002)). monitoring of dynamic Based on the available (2002)) and Autobased Regressive (AR) models (Yanare et al. information on have the system, two families distinguished: (2002)). Methods based on the Euclidean metric demonitoring of dynamic systems. Based on the available veloped in (Benmoussa and Djeziri (2017); Djeziri et al. (2002)). Methods based on the Euclidean metric are deinformation on the system, two families are distinguished: veloped in (Benmoussa and Djeziri (2017); Djeziri et al. monitoring of dynamic systems. Based on the available information on the system, two families are distinguished: (2002)). Methods based on the Euclidean metric are deData-based methods and Model-based methods. Dataveloped in (Benmoussa and Djeziri (2017); Djeziri et al. information on the system, two families are distinguished: (2018)) and used to characterize the(2017); distance and speed veloped and in (Benmoussa and Djeziri Djeziri et al. Data-based methods and Model-based methods. Dataused to characterize the distance and speed information on the system, two families are distinguished: Data-based methods and Model-based methods. Dataveloped in (Benmoussa and Djeziri (2017); etMaal. based methods consist in the use of historical data on (2018)) (2018)) and used to characterize the distance and speed Data-based methods and Model-based methods. Dataof the degradation process to predict theDjeziri RUL. (2018)) and used to characterize the distance and speed based methods consist in the use of historical data on of the degradation process to predict the RUL. MaData-based methods Model-based methods. Databased methods consist in the use of historical on (2018)) and used to characterize theisdistance and speed the system and expertand knowledge to build FDI data module. of the degradation process to predict the RUL. Mabased methods consist in the use of historical data on chine learning-based fault prognosis based on artificial of the degradation process to predict the RUL. Mathe system and expert knowledge to FDI module. fault prognosis is based on artificial based methods in theone usecan of build historical on chine the and expert knowledge to build FDI module. of thelearning-based degradation process to predict the RUL. MaAmong data-based methods, find: neuronal netchine learning-based fault is on artificial the system system and consist expert knowledge to build FDI data module. intelligence techniques as prognosis neural network (Schwabacher chine learning-based fault prognosis is based based on artificial Among data-based methods, one can find: neuronal netintelligence techniques as neural network (Schwabacher the system and expert knowledge to build FDI module. Among data-based methods, one can find: neuronal chine learning-based fault prognosis is based on artificial work (Frank and Koppen-Seliger (1997)), Bayesian net- intelligence techniques as neural network (Schwabacher Among data-based methods, one can find: neuronal and Goebel (2007)) and support vector regression (SVR) intelligence techniques assupport neuralvector network (Schwabacher work (Frank and Koppen-Seliger (1997)), Bayesian netGoebel (2007)) and regression (SVR) Among data-based methods, one can find: neuronal network (Frank and Koppen-Seliger (1997)), Bayesian intelligence techniques assupport neural network (Schwabacher (Yongli et al. (2006)), statistical models basedneton and and Goebel (2007)) and vector regression (SVR) work (Yongli (Frank and Koppen-Seliger (1997)), Bayesian (Samanta and Natara (2009)). However, fault prognosis and Goebel (2007)) and support vector regression (SVR) work et al. (2006)), statistical models based on (Samanta and Natara (2009)). However, fault prognosis (Frank and Koppen-Seliger (1997)), Bayesian network (Yongli et al. (2006)), statistical models based on and Goebel (2007)) and support vector regression (SVR) principal component analysis (PCA) (Tharrault et al. (Samanta and Natara (2009)). However, fault prognosis work (Yongli et al. (2006)), statistical models based on methods based on state estimators are used when a fault (Samanta and Natara (2009)). However, fault prognosis principal component analysis (PCA) (Tharrault et al. methods based on state estimators are used when a fault work (Yongli et al. (2006)), statistical models based on principal component analysis (PCA) (Tharrault et al. (Samanta and Natara (2009)). However, fault prognosis (2008)). Model-based methods are based on the physical methods based on state estimators are used when a fault principal component analysis (PCA) (Tharrault et al. diagnosis by pattern recognition is implemented beforemethods based on state estimators are used when a fault (2008)). Model-based methods are based on the physical by pattern recognition is implemented principal component analysis (PCA) (Tharrault et al. diagnosis (2008)). methods based on the methods based on state estimators are used when beforeaisfault knowledge on the system and itsare structure. Among modeldiagnosis by pattern recognition is implemented before(2008)). Model-based Model-based methods are based on the physical physical hand, where the evolution of the pattern trajectory prediagnosis by pattern recognition is implemented beforeknowledge on the system and its structure. Among modelhand, where the evolution of the pattern trajectory is pre(2008)). Model-based are based(Gertler on the physical knowledge on the system and its structure. Among modeldiagnosis by pattern recognition is implemented beforebased methods, one canmethods find: parity space (1997)), hand, where the evolution of the pattern trajectory is preknowledge on the system and its structure. Among modeldicted by means of Kalman filters (Swanson (2001)). Datahand, where the of evolution offilters the pattern trajectory isDataprebased methods, one can find: parity space (Gertler by means Kalman (Swanson (2001)). knowledge on the system and its structure. Among(1997)), model- dicted based one can find: parity space (Gertler (1997)), hand, the of evolution offilters thedo pattern trajectory isDatapreobserver (Patton and Chen (1997)), and Analytical Redundicted by Kalman (Swanson (2001)). based methods, methods, one can find: parity space (Gertler (1997)), based fault prognosis methods not require a detailed dicted where by means means of Kalman filters (Swanson (2001)). Dataobserver (Patton and Chen (1997)), and Analytical Redunbased fault prognosis methods do not require a detailed based methods, one can find: parity space (Gertler (1997)), observer (Patton and Chen (1997)), and Analytical Redundicted by means of Kalman filters (Swanson (2001)). Datadancy Relations (ARRs) (Blanke et al. (2003)). Modelbased methods do aa detailed observer (Patton and Chen(Blanke (1997)), et andal.Analytical Redunknowledge ofprognosis system dynamics. However, their implemenbased fault faultof prognosis methods However, do not not require require detailed dancy Relations (ARRs) (2003)). Modelsystem dynamics. their implemenobserver (Patton and Chen(Blanke (1997)), andal. Analytical dancy Relations (ARRs) (2003)). Modelbased fault prognosis methods do on notthe require a detailed based FDI is advantageous when et the prior data Redunon the knowledge knowledge system dynamics. However, their implemendancy FDI Relations (ARRs) (Blanke et al.prior (2003)). Modeltation and of their accuracy depend availability and knowledge of system dynamics. However, their implemenbased is advantageous when the data on the tation and their accuracy depend on the availability and dancy Relations (ARRs) but (Blanke et al.prior (2003)). Modelbased FDI is advantageous when the data on the knowledge of system dynamics. However, their implemensystem are not available, it presents some difficulties tation and their accuracy depend on the availability and based FDI is advantageous when the prior data on the quality of available data on the normal and on the faulty tation and their accuracy depend on theand availability and system are not available, but it presents some difficulties of available data on the normal on the faulty based FDI is advantageous when the prior data on the quality system are not available, but it presents some difficulties tation their accuracy oncase theand availability and when the system is complex to model. quality of on the normal on faulty systemthe aresystem not available, butto itmodel. presents some difficulties operation, which is data not always the especially in the qualityand of available available data ondepend the the normal and on the the in faulty when is complex operation, which is not always case especially the system are not available, but it presents some difficulties when the system is complex to model. quality of available data on the normal and on the faulty operation, which is not always the case especially in the when the system is complex to model. risky industrial plants. operation, which is not always the case especially in the risky industrial when the system is complex to model. operation, whichplants. is not always the case especially in the industrial plants. risky industrial plants. Regarding the fault prognosis which is defined as the risky Experience-based fault prognosis aims to model the deteRegarding the fault prognosis which is defined as the risky industrial plants. fault prognosis aims to model the deteRegarding fault prognosis defined as the estimation of the RUL or the which End ofis Life (EoL), and Regarding the the fault prognosis which isLife defined as and the Experience-based Experience-based fault aims model rioration of components by the mean ofto reliability lawdeteand Experience-based fault prognosis prognosis aimsof to model the the deteestimation of the RUL or the End of (EoL), rioration of components by the mean reliability law and Regarding the fault prognosis which is defined as the estimation of the RUL or the End of Life (EoL), and the estimation of RUL the risk of subsequent development Experience-based fault aimsof to model athe deteestimation of the or the End of Life development (EoL), and rioration of components by reliability law and expert knowledge. Zhouprognosis et the al. mean (2010) proposed Hidden rioration of components by the mean of reliability law and the estimation of the risk of subsequent knowledge. Zhou et al. (2010) proposed Hidden estimation of ofthe RUL or the End ofmode Life development (EoL), ISO and expert the estimation of the of subsequent or existence one or risk more faulty (Norm rioration of components reliabilitya and the existence estimation of theor risk of faulty subsequent development expert Zhou et al. (2010) aa law Hidden expert knowledge. knowledge. Zhou by et the al. mean (2010)ofproposed proposed Hidden or of one more mode (Norm ISO the estimation of the risk of subsequent development or or existence existence of of one one or or more more faulty faulty mode mode (Norm (Norm ISO ISO expert knowledge. Zhou et al. (2010) proposed a Hidden or existence of IFAC one (International or more faulty mode (Norm Control) ISO Hosting by Elsevier Ltd. 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Copyright © 2018 IFAC 1016 Copyright 2018 IFAC 1016Control. Peer review© under responsibility of International Federation of Automatic Copyright © 2018 IFAC 1016 Copyright © 2018 IFAC 1016 10.1016/j.ifacol.2018.09.713 Copyright © 2018 IFAC 1016
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Markov Model (HMM) associated with a Belief Rule Base (BRB) to predict hidden faults in a reactor, and that in the presence of disturbances. To take into account the effect of the environment on the system, Peng and Dong (2011) proposed a Hidden Semi-Markov Model (HSMM) for fault prognosis of a hydraulic pump, based on the calculation of a risk functions. The experience-based fault prognosis is not requested for some plants since it is conducted with the prior knowledge on the system and expert judgment.
experimental results of the developed methodology applied on a mechatronic system are presented in section 4. The paper ends with general synthesis and conclusions.
Model-based fault prognosis is performed by adopting the mathematical representation of the dynamic system, and carried out by the estimation of the component degradation and the RUL evaluation based on the considered degradation model. Among model-based methods, Yang (2002) provide a method of fault prognosis of direct current (DC) motor faults by state estimation. The latter is performed by a Kalman filter. In (Li and Lee (2005)), a dynamic model of crack propagation in the gear reduction part of the engine is used in combination with a dynamic model of the gear to estimate the RUL. Gucik-Derigny (2011) has proposed a method of fault prognosis of uncertain nonlinear systems based on interval observers, and has been applied to an electrical system. Djeziri et al. (2016) used a stochastic model based on Wiener Process to perform RUL prediction, The Kalman filter is used to estimate and update the drift parameter. The main advantage of the model-based fault prognosis is the no need of databases on the earlier operations of the system.
2.1 Test bench description
The BG tool proposed by Karnopp and Rosenberg (1975) can be an alternative for system modeling and fault prognosis since it is based on the physical modeling of the system’s components. The BG describes the power transfer between the passive and active components of multiphysical systems. It is considered as the interface between the physical system and its mathematical model. Danwei et al. (2013) used this tool to generate Augmented and Generalized Analytical Redundancy Relation (AGARR), for fault diagnosis and prognosis of the steering system of an electric vehicle called CyCab. However, Medjaher and Zerhouni (2009) used BG for system modeling and residuals generation in which degradation model is injected to predict the RUL of the system. This paper presents an integrated fault diagnosis and fault prognosis method based on the physical behavior of the system. By using the BG tool, the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation profile are performed. While the RUL is predicted from the dynamic of considered parametric degradation, described by ordinary differential equations (ODEs). The degradation beginning detection is ensured by the FDI module based on the generated ARRs and the adaptive thresholds. While, the degradation profile estimation is carried out by using the notion of the bicausality. All, these steps are achieved by using the unified tool which is BG.
2. SYSTEM DESCRIPTION AND BG MODELING In this section, the used test bench mechatronic system (Fig.1) is described and its corresponding BG model is presented.
The system illustrated by the Fig.1 is a mechatronic system composed of : an acquisition card NI-USB-6343 (1), a Variable-Frequency Drive Elmo Bassoon (2), a brushless motor Metronix of 400 Watt (3) with an embedded encoder, two stepper motors (4) used to introduce a progressive faults, a reducer composed of two pulleys connected by a belt (5), a gear mechanism to introduce mechanical backlash (6), a load composed of small masses to manually change its value and homogeneity (7), an incremental encoder at the load level (8), and two potentiometer which measure the position of the stems of the two stepper motors (9), an emergency stop button (10), and one security detector which prevents starting when the safety cover is not closed (11).
Fig. 1. Overview of the mechatronic system. A progressive fault can be introduced by varying the position of the belt tensioner by a stepper motor as shown in Fig.2, changing thus the stiffness of the mechanical transmission. To emulate a belt breaking, the maximum retraction of the motor’s shaft is considered: in this case, the belt is completely relaxed. The backlash can be increased gradually using the stepper motor, which increases gradually the distance between the two gears of the backlash mechanism as shown in Fig.3. 2.2 BG model of the considered system Fig.4 shows the word BG model of the mechatronic system where the global architecture of the system is described. Three parts can be distinguished: brushless motor part, transmission part, and load part:
This paper is structured as follows: in section 2, the detection and isolation of the degradation beginning is presented. The estimation of the degradation trend and RUL prediction are described in section 3. The obtained 1017
• The brushless motor part is a three phase motor. The electrical part corresponds to three RL circuits. It is composed of an input voltage source Uj with j = 1..3, an electrical resistance Rej , an inductance Lj , and an electromotive force feedback EMF (with a constant kej ), which is linear to the angular velocity of the rotor. The mechanical part is characterized by the rotor inertia Je, and a viscous friction parameter f e.
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Fig. 2. Mechanism varying the stiffness of the mechanical transmission.
Fig. 5. Bond graph model of the mechatronic system. part is estimated. The simplified BG model of the system is illustrated by the Fig.6.
Fig. 6. BG model of the monitorable part of the system. Fig. 3. Mechanism varying the backlash.
3. THE INTEGRATED BG-BASED METHOD
Fig. 4. Word bond graph model of the mechatronic system. • The transmission part concerns the belt which links the mechanical part to the load part. It is character1 ized by the belt rigidity K . The reduction between the velocities of the motor and the pulley is represented on BG model with a transformer element (TF) of a reduction constant N . • The load part of the mechatronic system is a pulley, characterized by its inertia Js , and a viscous friction parameter fs . The BG model of the mechatronic system in preferred integral causality, is given in Fig.5. The instrumentation architecture of this system is composed of: the angular position of the rotor (θe ), and the angular position of the pulley (θs ). Since the position is not a flux variable neither an effort one, the velocities θ˙e and θ˙s are represented using a Df element on the BG model. They are obtained by differentiating the position information. The BG model of the electrical part of the motor (Fig.5) can be represented in a more compact form with a single R element and single I element crossed by the measured average current. The set-point applied to the motor being known, and by using the model of the electrical part, the engine torque Γin applied to the mechanical transmission
This section is devoted to the developed integrated BGbased method for fault diagnosis and fault prognosis tasks. The Fig.7 illustrates the schema of the proposed method. The degradation beginning detection is ensured by the FDI module based on the generated ARRs and the adaptive thresholds. While, the degradation profile estimation is carried out by using the notion of the bicausality.
Fig. 7. Schema of the proposed integrated method for RUL prediction. 3.1 Robust degradation detection In this work, the detection of the degradation beginning and the isolation of the faulty component are based on the BG approach. It reposes on the generation of ARRs which are obtained in a systematic way by exploiting the causal and structural properties of the BG model. The output of a numerical evaluation of a candidate ARR is a residual which characterizes the energy balance in the considered subsystem. Thus, in normal operating, residuals should close to zero. However, when a parametric degradation begins to appear, the value of its corresponding parameter
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(identified in normal operation and implemented previously) will change by deviating from its initial value. In this case, the residual should also deviate from its normal operating envelope. Thus the beginning of degradation will be detected long before the total failure of the component. To isolate the faulty component by using the BG approach, a Boolean matrix; called Fault Signature Matrix (FSM) is constructed from the structure of ARRs. Both system modeling errors and measurement uncertainties are considered to generate adaptive thresholds for degradation detection. In fact, by using BG in its LFT (Linear Fractional Transformation) form robust ARRs can be generated (Djeziri et al. (2009); Touati et al. (2012)). The latter is composed of two perfectly separate parts: a nominal part (ARRn ) and an uncertain part (α). The nominal part is used to calculate residuals (fault indicators) while the uncertain part is exploited for threshold α computations. ARR = ARRn + α
a1 a 2
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˙ ˙ = −ζθ˙e − δK K θe dt − δN N θs dt − δN K θ˙e dt = −δN N θ˙e dt − N δN K θ˙e dt + N ζθ˙e (7) −N K ζθ˙s dt − N 2 K ζθ˙s dt
To build the FSM, the following assumptions are taken into account: • The torque and measured outputs are fault-free; • The reduction constant N cannot be faulty.
The FSM; presented by the Table 1, is obtained from Eq.2. From this FSM, one can point out that all the faults are detectable and a fault on the gear subsystem is detectable and isolable since it presents a single fault signature. Table 1. Fault Signature Matrix (FSM)
(1)
Part Mech part Gear par Load part
Comp. fe Je
Elect. subsystem r1 r2 1 0 1 0
Mb − 1 1
Ib − 0 0
The Fig.8 illustrate the LFT-BG model in derivative causality of the mechatronic system considering both parameter and measurement uncertainties. Since the initial conditions are known at t = 0, ARRs can be generK 1 1 1 1 fs 0 1 1 0 ated even if one dynamic element (C) remains in integral Js 0 1 1 0 causality. They are given by: d ARR1 = Γin − fe θ˙e − Je θ˙e − K θ˙e − N θ˙s dt + α1 3.2 RUL prediction and evaluation dt d (2) ARR2 = fs θ˙s + Js θ˙s − N K θ˙e − N θ˙s dt + α2 The fault prognosis module aims to predict the RUL before dt observing a failure given the current system condition, and the past operation profile. The developed fault prognosis The residuals are obtained by evaluating the ARRs of the method is based on the BG tool as stated previously and will be carried out as follow: Eq.2. They are given by: d • Model the faulty element(s), θ˙e − N θ˙s dt = 0 r1 : Γin − fe θ˙e − Je θ˙e − K • Estimate the degradation profile by using the bidt (3) d ˙ causality notion, ˙ ˙ ˙ r2 : f s θ s + J s θ s − N K θe − N θs dt = 0 • Predict the RUL. dt While, α1 and α2 represent the uncertain part of these residuals. They are given by: α1 = |Wfe | + Wfe /θ˙e + |WJe | + WJe /θ˙e + |a 1 | (4) α2 = |Wfs | + Wfs /θ˙s + |WJs | + WJs /θ˙s + |a 2 |
where |Wfe | , |WJe | , |Wfs | , |WJs | are the fictitious inputs that represent the modeling uncertainties. They are given by : Wfe = −δfe · fe · θ˙e WJe = −δJe · Je · θ¨e (5) Wf = −δf · fs · θ˙s WJ = −δJ · Js · θ¨s s
s
s
s
Moreover Wfe /θ˙e , WJe /θ˙e , Wfs /θ˙s and WJs /θ˙s are defined as follows : Wfe /θ˙e = f˜e ζθ˙e f˜e = fe (1 + δfe ) dζθ˙e J˜e = Je (1 + δJe ) WJe /θ˙e = J˜e dt (6) f˜s = fs (1 + δfs ) Wfs /θ˙s = f˜s ζθ˙s dζ ˙ J˜s = Js (1 + δJs ) WJs /θ˙s = J˜s θs dt
In this work, the goal of the fault prognosis module is to predict the RUL before observing the belt breaking, emulated in the test bench by a maximum relaxation of the belt. The fault on the belt is characterized by a variation on the belt rigidity M C : 1/K. The LFT-BG of the mechatronic system in the presence of the belt fault is illustrated by Fig.9. To estimate the degradation profile (the fault) F , the bicausality concept (Gawthrop (1995)) is applied on the LFT-BG model. The main idea of bicausality notion is to suppose that two power variables in the same direction are known or fixed. This idea is used in this paper to generate the mathematical equations that relate the residuals to the faults, which will permit to estimate the fault value. To this end, by replacing the source associated with fault variable M Se : WF/K and the sink associated with the output variable respectively by DeDf and SeSf elements, and by applying the bicausality through the fault-output causal path, the Bicausal-BG model for fault estimation is obtained (Fig.10). From the latter, one can point out that all dynamic elements are in derivative causality, and the
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Fig. 8. LFT-BG model in derivative causality of the mechatronic system.
Fig. 9. LFT-BG of the mechatronic system in the presence of the belt fault. 1 K
fault is causally linked to the output. So, a fault on C : is estimable. The mathematical expression for this fault is given by: FK = −
WF/K ZF/K
(8)
where WF/K is obtained from the second ARR as follow : d θ˙s − N θ˙s dt + WF/K = 0 (9) fs θ˙s + Js θ˙s − N K dt Thus, WF/K
dθ˙s − N K ∫ θ˙s − N θ˙s dt = − fs θ˙s + Js dt
(10)
Fig. 10. Bicausal BG model for fault estimation. Regarding the term ZF/K , it is the gain of the causal path that links SeSf : θ˙s to Df ∗ : ZF/K in the Bicausal-BG (Fig.10). It is given by: (11) θ˙s − N θ˙s dt ZF/K = N K So, the fault variable is given by: d ˙ θ˙s − N θ˙s dt fs θ˙s + Js dt θs − N K FK = N θ˙s − N θ˙ dt
(12)
s
The estimated fault value will be then used to predict the RUL. For the latter, the considered degradation model follows an ordinary differential equation of the form F˙ = βF where β = 0, 05 represents the degradation model constant which is identified experimentally. To generate
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the degradation profile, the stepper motor is used. The breaking elongation (ebrk ) is chosen by using Hooke’s law for belt deformation and it corresponds to Fv = 4Fn where Fn refers to the nominal maximal admissible force. The breaking elongation value is chosen experimentally. The RUL formula used in this paper is expressed by Eq.13. brk ln 1−e ˆ 1−FK − N Ts (13) RU L = β where : N represents the sample data and Ts is the sampling time. 4. EXPERIMENTAL RESULTS In this section, the obtained experimental results are exposed in order to show the effectiveness of the proposed approach. Two scenarios are considered:
Fig. 11. Torque and system’s outputs in normal and faulty operation.
• The mechatronic system under healthy conditions ; • The mechatronic system subjects to a parametric and a progressive fault on the belt. The parameters of the mechatronic system; which are given in Table 2, were identified off-line. The identified values vary slightly around an average. Thus the average is taken as the nominal value of the parameters, and the standard deviation is taken as the value of the uncertainty expressed in percentage. The values found in all parameters varied between 1.5% and 2%. So, all the values have been rounded up of 2% to avoid false alarms. Table 2. Specification of the mechatronic system fe Je K N fs Js
Nominal values 0.015 0.01 2.01 1.25 0.02 0.0002
Unit (N.m.s.rad−1 ) (Kg.m2 ) (N.m.rad−1 ) − (N.m.s.rad−1 ) (Kg.m2 )
Fig. 12. Residuals evolution under healthy situation.
Uncertainties 0.02 · fen 0.02 · Jen 0.02 · Kn 0.02 · Nn 0.02 · fsn 0.02 · Jsn
The experimental results for torque and measured outputs under healthy and faulty situations are given by the Fig.11. One can notice that when a fault occurs at t = 20s, there is a fluctuation of the pulley velocity (θ˙s ) for 5s : the belt is relaxed but it adheres to the motor shaft and the load one. In other words, the transmission of motion is always 1 ensured but not with the same stiffness ( K ). The pulley’s velocity backs to its desired value, which is due to the PI action. Regarding the residuals, from the Fig.12 and Fig.13, the following conclusion are given : • Healthy situation: both residuals are near to zero. • Faulty situation: both residuals are triggered.
Notice that the belt fault signature is (1 1) (from the Table 1), which result that r1 and r2 are both sensitive to this fault. Also, the residual takes 2s to across the thresholds, that is due to the dynamic of the considered degradation model.
Fig. 13. Residuals evolution under faulty situation. The estimated fault and the estimation error are given by the Fig.14 and 15 respectively. As it can be observed, the estimated fault tracks the considered degradation profile and converges after 10s. The mean of estimation error is on the order of 0, 01. The maximal of the error is observed at t = 23s. The RUL prediction is enabled by a controlled trigger. The latter is set to the Boolean value 1 when the residual cross the adaptive threshold, otherwise it is fixed to the Boolean value 0. The Fig.16 shows the reference RUL and the predicted one. The predicted RUL is equal to
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Fig. 14. Fault estimation. Fig. 17. α − λ performance.
Fig. 15. Fault estimation error. Fig. 18. The relative prediction accuracy. converges after 5 seconds inside the interval (α − λ) and the relative prediction accuracy increase progressively to reach a minimum of 0.7 at time t = 40s. From the latter, one can conclude that the performances of the proposed fault prognosis method are in the latter stage of system life with higher accuracy when approaching the end of life. 5. CONCLUSION
Fig. 16. Remaining useful lifetime before observing the belt breaking. 13s which means that it remains 13s before observing the belt breaking. Nevertheless, the reference RUL is on the order of 30s. The difference between these two RULs can be explained by the introduced degradation profile by the stepper motor. When the estimation error converges to the degradation profile, the predicted RUL and the reference one share the same rate. Fig.17 and 18 illustrate respectively the performance and the accuracy of the RUL prediction by using the proposed method. We note that at the beginning of the prediction (t = 23s), the estimated RUL is outside the interval (α−λ) (Fig.17) and the relative accuracy is equal to 0.4 ( Fig.18). The predicted RUL
The present paper proposes an experimental application on a mechatornic system of an integrated method for fault diagnosis and prognosis based on the bond graph tool. In fact, by using the tool properties, the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation profile are performed. The RUL is predicted from the considered fault degradation model. The developed methodology is applied on a mechatronic system to predict the remaining useful lifetime before observing a belt breaking. The obtained results supported by universal metrics demonstrate the effectiveness and the higher performances of the proposed method. REFERENCES Azam, M., Tuc, F., and Pattipati, K. (2002). Condition based predictivemaintenance of industrial power
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Samanta, B. and Natara, C. (2009). Prognostics of machine condition using soft computing. Expert Systems with Applications, 36, 9378–9387. Schwabacher, M. and Goebel, K. (2007). A survey of artificial intelligence for prognostics. In AAAI Fall Symposium. Swanson, D. (2001). A general prognostic tracking algorithm for predictive maintenance. In IEEE International Conference on Aerospace, 2971–2977. Tharrault, Y., Mourot, G., and Ragot, J. (2008). Fault detection and isolation with robust principal component analysis. In Control and Automation, 2008 16th Mediterranean Conference on, 59 –64. doi: 10.1109/MED.2008.4602224. Touati, Y., Merzouki, R., and Ould-Bouamama, B. (2012). Robust diagnosis to measurement uncertainties using bond graph approach: Application to intelligent autonomous vehicle. Mechatronics, 22, 1148–1160. Yan, T., Lee, T., , and Ko, M. (2002). Predictive algorithm for machine degradation detection using logistic regression. In Managing innovative manufacturing ”eManufacturing and e-Business integration”. Yang, S. (2002). An experiment of state estimation for predictive maintenance using kalman filter on a dc motor. Reliability Engineering and System Safety, 75, 103–111. Yongli, Z., Limin, H., and Jinling, L. (2006). Bayesian networks-based approach for power systems fault diagnosis. IEEE Transactions on Power Delivery, 21(2), 634 – 639. Zhou, Z.J., Hua, C.H., Xu, D.L., Chen, M.Y., and Zhou, D.H. (2010). A model for real-time failure prognosis based on hidden markov model and belief rule base. European Journal of Operational Research, 207, 269– 283.
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Experimental Application on a Mechanical Experimental Application on a Mechanical Experimental Application on a Mechanical Transmission System of Integrated Fault Experimental Application on a Mechanical Transmission System of Integrated Fault Transmission System of Integrated Fault Diagnosis and Fault Prognosis method. Transmission System of Integrated Fault Diagnosis and Fault Prognosis method. Diagnosis and Fault Prognosis method. Diagnosis and Fault Prognosis method. S. BENMOUSSA ∗∗ M.A. DJEZIRI ∗∗ ∗∗ S. ∗∗ S. BENMOUSSA BENMOUSSA ∗∗ M.A. M.A. DJEZIRI DJEZIRI ∗∗ S. BENMOUSSA ∗ M.A. DJEZIRI ∗∗ ∗ S. BENMOUSSA M.A. DJEZIRI ∗ LASA, Badji-Mokhtar Annaba University, BP 12, 23000 Annaba, ∗ LASA, Badji-Mokhtar Annaba University, BP 12, 23000 Annaba, ∗ LASA,Algeria Badji-Mokhtar Annaba University, University, BP BP 12, 12, 23000 23000 Annaba, Annaba, (e-mail: [email protected]). LASA, Badji-Mokhtar Annaba ∗∗∗ (e-mail: [email protected]). LASA,Algeria Badji-Mokhtar Annaba University, BPNormandi 12, 23000 Niemen, Annaba, Algeria [email protected]). UMR (e-mail: CNRS 7296, Avenue Escadrille Algeria (e-mail: [email protected]). ∗∗ LSIS, UMR CNRS 7296, Avenue Escadrille Normandi Niemen, ∗∗ Algeria (e-mail: [email protected]). ∗∗ LSIS, LSIS, UMR CNRS 7296, Avenue Escadrille Normandi Niemen, 13397 Marseille, France (e-mail: [email protected]) CNRSFrance 7296, Avenue Normandi Niemen, ∗∗ LSIS, 13397UMR Marseille, (e-mail:Escadrille [email protected])
LSIS, CNRSFrance 7296, Avenue Normandi Niemen, 13397UMR Marseille, France (e-mail:Escadrille [email protected]) 13397 Marseille, (e-mail: [email protected]) 13397 Marseille, France (e-mail: [email protected]) Abstract: In this paper, integrated fault diagnosis and fault prognosis approach, applied on Abstract: In paper, integrated fault diagnosis and prognosis approach, applied on Abstract: In this this paper, integrated faultgoal diagnosis and fault fault prognosis approach, appliedand on aAbstract: mechatronic system is presented . The is to assess the health status of the system In this paper, integrated fault diagnosis and fault prognosis approach, applied on aAbstract: mechatronic system is presented . The goal is to assess the health status of the system and In this paper, integrated fault diagnosis and fault prognosis approach, applied on a mechatronic mechatronic system is presented presented . The The goal goal is to to assess the the health status status ofpresented the system system and to predict the system remaining useful lifetime before observing a failure. In theof paper, a is . is assess health the and to predict the remaining useful lifetime before observing aa failure. In the presented paper, a mechatronic system is presented . The goal is to assess the health status of the system and to predict the remaining useful lifetime before observing failure. In the presented paper, the detection of the degradation beginning, the isolation of the faulty component, and the to predict the ofremaining useful lifetime before observing a failure. In the presentedand paper, the detection the degradation beginning, the isolation of the faulty component, the to the useful lifetime a failure. In the paper, the detection of the degradation beginning, the isolation of the component, and the estimation of the degradation profile are before performed in an integrated way bypresented using the Bond thepredict detection ofremaining the degradation beginning, theobserving isolation of the faulty faulty component, and the estimation of the degradation profile are performed in an integrated way using the Bond by the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation degradation profileuseful are performed performed in an integrated integrated way by using using the the Bond Graph tool.of Regarding the remaining lifetime, itin is predicted fromway the considered dynamic estimation the profile are an by Bond Graph tool. Regarding the remaining useful lifetime, it is predicted from the considered dynamic estimation of the degradation profile are performed in an integrated way by using the Bond Graph tool. Regarding the remaining useful lifetime, it is predicted from the considered dynamic of parametric degradation ordinary differential equations. the proposed Graph tool. Regarding the described remainingby useful lifetime, it is predicted fromTo thevalidate considered dynamic of parametric degradation by ordinary differential equations. the proposed Graph tool. the described remaining useful lifetime, it isapredicted fromTo thevalidate considered dynamic of parametric degradation described by ordinary differential equations. To validate the proposed method, an Regarding experimental implementation is done on mechatronic system. The prediction of parametric degradation described by ordinary differential equations. To validate the proposed method, an implementation is on system. The of parametric degradation ordinary differential equations. To validate theprediction proposed method, an experimental experimental implementation is done done on aaa mechatronic mechatronic system. The prediction performances are evaluateddescribed by usingby universal metrics. method, an experimental implementation is done on mechatronic system. The prediction performances are by metrics. method, an experimental is done on a mechatronic system. The prediction performances are evaluated evaluatedimplementation by using using universal universal metrics. performances are evaluated by using universal metrics. © 2018, IFAC (International Federation ofuniversal Automaticmetrics. Control) Hosting by Elsevier Ltd. All rights reserved. performances are evaluated by using Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. Keywords: Keywords: Fault Fault Diagnosis, Diagnosis, Fault Fault Prognosis, Prognosis, Mechatronic Mechatronic System, System, Modeling, Modeling, Bond Bond graph. graph. Keywords: Fault Diagnosis, Fault Prognosis, Mechatronic System, Modeling, Bond graph. 1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified 1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified 1. 13381-1: Three main approaches could be (Byington et al. (2002); Jardine et al. (2006); Gucik1. INTRODUCTION INTRODUCTION 13381-1: 2004); 2004); Three mainJardine approaches could be identified identified (Byington et al. (2002); et al. (2006); Gucik1. INTRODUCTION 13381-1: 2004); Three main approaches could be identified The main goal of condition-based maintenance (CBM) is (Byington et al. (2002); Jardine et al. (2006); GucikDerigny (2011)): Data-based approach, Experience-based (Byington et al. Data-based (2002); Jardine et al.Experience-based (2006); GucikThe main goal of condition-based maintenance (CBM) is Derigny (2011)): approach, (Byington et al. (2002); Jardine et al.Experience-based (2006); GucikThe main of is to guarantee a high availability of maintenance a system and(CBM) to avoid Data-based approach, approach, and Model-based one. Theguarantee main goal goal of condition-based condition-based maintenance (CBM) is Derigny Derigny (2011)): (2011)): Data-based approach, Experience-based to a high availability of a system and to avoid approach, and Model-based one. The main goal of condition-based maintenance (CBM) is Derigny (2011)): Data-based approach, Experience-based to guarantee a high availability of a system and to avoid unnecessary or excessive maintenance actions. This is approach, Model-based one. to guarantee or a high availability of a system and to avoid approach, and and unnecessary excessive maintenance actions. This is Depending on Model-based the type of one. the used model, Data-based to guarantee a high availability of a system andregarding to avoid approach, and Model-based one. unnecessary or excessive actions. This is ensured by scheduling the maintenance actions Depending on the type of the used model, Data-based unnecessary or excessive actions. This is ensured by scheduling the maintenance actions regarding Depending on the type of the used model, Fault prognosis methods can be classified into three Depending on the type of the be usedclassified model, Data-based Data-based unnecessary or excessive maintenance actions. This is ensured by scheduling the actions regarding the health status of a system and the predicted Remaining prognosis methods can into three ensured bystatus scheduling the maintenance actionsRemaining regarding Fault Depending on the type of the used model, Data-based the health of a system and the predicted Fault prognosis methods can be classified into three categories: trend analysis-based fault prognosis, machine Fault prognosis methods can be classified into three ensured by scheduling the maintenance actions regarding the health status of aa system the predicted Remaining Useful Lifetime (RUL) beforeand observing a failure. So, the categories: trend analysis-based fault prognosis, machine the health status of system and the predicted Remaining Fault prognosis methods canand be classified into three Useful Lifetime (RUL) before observing a failure. So, the categories: trend analysis-based fault prognosis, machine learning-based fault prognosis, state estimation based categories: trend analysis-based fault prognosis, machine the health status of a system and the predicted Remaining Useful Lifetime (RUL) before observing a failure. So, the fault diagnosis module and the fault prognosis one are learning-based fault prognosis, and state estimation based Usefuldiagnosis Lifetimemodule (RUL) and before observing a failure. So, the categories: trend analysis-based fault prognosis, machine fault the fault prognosis one are the learning-based fault prognosis, and state estimation based fault prognosis. Trend analysis-based fault prognosis uses learning-based fault prognosis, and state estimation based Useful Lifetime (RUL) and before a failure. fault the fault one are main keys in a module CBM. prognosis. Trend analysis-based fault prognosis uses fault diagnosis diagnosis module and theobserving fault prognosis prognosis one So, are the the fault learning-based fault prognosis, andare state estimation based main keys in a CBM. fault prognosis. Trend analysis-based fault prognosis uses statistical models, the most used the PCA (Li et al. fault prognosis. Trend analysis-based fault prognosis uses fault diagnosis module and the fault prognosis one are the main statistical models, the most used are the PCA (Li et al. main keys keys in in aa CBM. CBM. fault prognosis. Trend analysis-based fault prognosis uses statistical models, the most used are the PCA (Li et al. (2010)), linear quadratic discrimination (Azam et statistical models, the most used are the PCA (Li et al. main keys in a CBM. linear quadratic (Azam al. statistical models, the mostdiscrimination used are models the PCA (Li et et al. Several works have been developed to assess the health (2010)), (2010)), linear quadratic discrimination (Azam et (2002)) and Auto Regressive (AR) (Yan et al. (2010)), linear quadratic discrimination (Azam et Several works have been developed to assess the health (2002)) and Auto Regressive (AR) models (Yan et al. Several works have been developed to assess the health (2010)), linear quadratic (Azam et monitoring of have dynamic systems. Based on thethe available Auto Regressive models (Yan et al. Several works beensystems. developed to assess health (2002)) (2002)). Methods based on discrimination the(AR) Euclidean metric are de(2002)) and and Auto Regressive (AR) models (Yanare et deal. monitoring of dynamic Based on the available Methods on the Euclidean metric Several works beensystems. developed to are assess the health (2002)). monitoring of dynamic Based on the available (2002)) and Autobased Regressive (AR) models (Yanare et al. information on have the system, two families distinguished: (2002)). Methods based on the Euclidean metric demonitoring of dynamic systems. Based on the available veloped in (Benmoussa and Djeziri (2017); Djeziri et al. (2002)). Methods based on the Euclidean metric are deinformation on the system, two families are distinguished: veloped in (Benmoussa and Djeziri (2017); Djeziri et al. monitoring of dynamic systems. Based on the available information on the system, two families are distinguished: (2002)). Methods based on the Euclidean metric are deData-based methods and Model-based methods. Dataveloped in (Benmoussa and Djeziri (2017); Djeziri et al. information on the system, two families are distinguished: (2018)) and used to characterize the(2017); distance and speed veloped and in (Benmoussa and Djeziri Djeziri et al. Data-based methods and Model-based methods. Dataused to characterize the distance and speed information on the system, two families are distinguished: Data-based methods and Model-based methods. Dataveloped in (Benmoussa and Djeziri (2017); etMaal. based methods consist in the use of historical data on (2018)) (2018)) and used to characterize the distance and speed Data-based methods and Model-based methods. Dataof the degradation process to predict theDjeziri RUL. (2018)) and used to characterize the distance and speed based methods consist in the use of historical data on of the degradation process to predict the RUL. MaData-based methods Model-based methods. Databased methods consist in the use of historical on (2018)) and used to characterize theisdistance and speed the system and expertand knowledge to build FDI data module. of the degradation process to predict the RUL. Mabased methods consist in the use of historical data on chine learning-based fault prognosis based on artificial of the degradation process to predict the RUL. Mathe system and expert knowledge to FDI module. fault prognosis is based on artificial based methods in theone usecan of build historical on chine the and expert knowledge to build FDI module. of thelearning-based degradation process to predict the RUL. MaAmong data-based methods, find: neuronal netchine learning-based fault is on artificial the system system and consist expert knowledge to build FDI data module. intelligence techniques as prognosis neural network (Schwabacher chine learning-based fault prognosis is based based on artificial Among data-based methods, one can find: neuronal netintelligence techniques as neural network (Schwabacher the system and expert knowledge to build FDI module. Among data-based methods, one can find: neuronal chine learning-based fault prognosis is based on artificial work (Frank and Koppen-Seliger (1997)), Bayesian net- intelligence techniques as neural network (Schwabacher Among data-based methods, one can find: neuronal and Goebel (2007)) and support vector regression (SVR) intelligence techniques assupport neuralvector network (Schwabacher work (Frank and Koppen-Seliger (1997)), Bayesian netGoebel (2007)) and regression (SVR) Among data-based methods, one can find: neuronal network (Frank and Koppen-Seliger (1997)), Bayesian intelligence techniques assupport neural network (Schwabacher (Yongli et al. (2006)), statistical models basedneton and and Goebel (2007)) and vector regression (SVR) work (Yongli (Frank and Koppen-Seliger (1997)), Bayesian (Samanta and Natara (2009)). However, fault prognosis and Goebel (2007)) and support vector regression (SVR) work et al. (2006)), statistical models based on (Samanta and Natara (2009)). However, fault prognosis (Frank and Koppen-Seliger (1997)), Bayesian network (Yongli et al. (2006)), statistical models based on and Goebel (2007)) and support vector regression (SVR) principal component analysis (PCA) (Tharrault et al. (Samanta and Natara (2009)). However, fault prognosis work (Yongli et al. (2006)), statistical models based on methods based on state estimators are used when a fault (Samanta and Natara (2009)). However, fault prognosis principal component analysis (PCA) (Tharrault et al. methods based on state estimators are used when a fault work (Yongli et al. (2006)), statistical models based on principal component analysis (PCA) (Tharrault et al. (Samanta and Natara (2009)). However, fault prognosis (2008)). Model-based methods are based on the physical methods based on state estimators are used when a fault principal component analysis (PCA) (Tharrault et al. diagnosis by pattern recognition is implemented beforemethods based on state estimators are used when a fault (2008)). Model-based methods are based on the physical by pattern recognition is implemented principal component analysis (PCA) (Tharrault et al. diagnosis (2008)). methods based on the methods based on state estimators are used when beforeaisfault knowledge on the system and itsare structure. Among modeldiagnosis by pattern recognition is implemented before(2008)). Model-based Model-based methods are based on the physical physical hand, where the evolution of the pattern trajectory prediagnosis by pattern recognition is implemented beforeknowledge on the system and its structure. Among modelhand, where the evolution of the pattern trajectory is pre(2008)). Model-based are based(Gertler on the physical knowledge on the system and its structure. Among modeldiagnosis by pattern recognition is implemented beforebased methods, one canmethods find: parity space (1997)), hand, where the evolution of the pattern trajectory is preknowledge on the system and its structure. Among modeldicted by means of Kalman filters (Swanson (2001)). Datahand, where the of evolution offilters the pattern trajectory isDataprebased methods, one can find: parity space (Gertler by means Kalman (Swanson (2001)). knowledge on the system and its structure. Among(1997)), model- dicted based one can find: parity space (Gertler (1997)), hand, the of evolution offilters thedo pattern trajectory isDatapreobserver (Patton and Chen (1997)), and Analytical Redundicted by Kalman (Swanson (2001)). based methods, methods, one can find: parity space (Gertler (1997)), based fault prognosis methods not require a detailed dicted where by means means of Kalman filters (Swanson (2001)). Dataobserver (Patton and Chen (1997)), and Analytical Redunbased fault prognosis methods do not require a detailed based methods, one can find: parity space (Gertler (1997)), observer (Patton and Chen (1997)), and Analytical Redundicted by means of Kalman filters (Swanson (2001)). Datadancy Relations (ARRs) (Blanke et al. (2003)). Modelbased methods do aa detailed observer (Patton and Chen(Blanke (1997)), et andal.Analytical Redunknowledge ofprognosis system dynamics. However, their implemenbased fault faultof prognosis methods However, do not not require require detailed dancy Relations (ARRs) (2003)). Modelsystem dynamics. their implemenobserver (Patton and Chen(Blanke (1997)), andal. Analytical dancy Relations (ARRs) (2003)). Modelbased fault prognosis methods do on notthe require a detailed based FDI is advantageous when et the prior data Redunon the knowledge knowledge system dynamics. However, their implemendancy FDI Relations (ARRs) (Blanke et al.prior (2003)). Modeltation and of their accuracy depend availability and knowledge of system dynamics. However, their implemenbased is advantageous when the data on the tation and their accuracy depend on the availability and dancy Relations (ARRs) but (Blanke et al.prior (2003)). Modelbased FDI is advantageous when the data on the knowledge of system dynamics. However, their implemensystem are not available, it presents some difficulties tation and their accuracy depend on the availability and based FDI is advantageous when the prior data on the quality of available data on the normal and on the faulty tation and their accuracy depend on theand availability and system are not available, but it presents some difficulties of available data on the normal on the faulty based FDI is advantageous when the prior data on the quality system are not available, but it presents some difficulties tation their accuracy oncase theand availability and when the system is complex to model. quality of on the normal on faulty systemthe aresystem not available, butto itmodel. presents some difficulties operation, which is data not always the especially in the qualityand of available available data ondepend the the normal and on the the in faulty when is complex operation, which is not always case especially the system are not available, but it presents some difficulties when the system is complex to model. quality of available data on the normal and on the faulty operation, which is not always the case especially in the when the system is complex to model. risky industrial plants. operation, which is not always the case especially in the risky industrial when the system is complex to model. operation, whichplants. is not always the case especially in the industrial plants. risky industrial plants. Regarding the fault prognosis which is defined as the risky Experience-based fault prognosis aims to model the deteRegarding the fault prognosis which is defined as the risky industrial plants. fault prognosis aims to model the deteRegarding fault prognosis defined as the estimation of the RUL or the which End ofis Life (EoL), and Regarding the the fault prognosis which isLife defined as and the Experience-based Experience-based fault aims model rioration of components by the mean ofto reliability lawdeteand Experience-based fault prognosis prognosis aimsof to model the the deteestimation of the RUL or the End of (EoL), rioration of components by the mean reliability law and Regarding the fault prognosis which is defined as the estimation of the RUL or the End of Life (EoL), and the estimation of RUL the risk of subsequent development Experience-based fault aimsof to model athe deteestimation of the or the End of Life development (EoL), and rioration of components by reliability law and expert knowledge. Zhouprognosis et the al. mean (2010) proposed Hidden rioration of components by the mean of reliability law and the estimation of the risk of subsequent knowledge. Zhou et al. (2010) proposed Hidden estimation of ofthe RUL or the End ofmode Life development (EoL), ISO and expert the estimation of the of subsequent or existence one or risk more faulty (Norm rioration of components reliabilitya and the existence estimation of theor risk of faulty subsequent development expert Zhou et al. (2010) aa law Hidden expert knowledge. knowledge. Zhou by et the al. mean (2010)ofproposed proposed Hidden or of one more mode (Norm ISO the estimation of the risk of subsequent development or or existence existence of of one one or or more more faulty faulty mode mode (Norm (Norm ISO ISO expert knowledge. Zhou et al. (2010) proposed a Hidden or existence of IFAC one (International or more faulty mode (Norm Control) ISO Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2018, Federation of Automatic
Copyright © 2018 IFAC 1016 Copyright 2018 IFAC 1016Control. Peer review© under responsibility of International Federation of Automatic Copyright © 2018 IFAC 1016 Copyright © 2018 IFAC 1016 10.1016/j.ifacol.2018.09.713 Copyright © 2018 IFAC 1016
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Markov Model (HMM) associated with a Belief Rule Base (BRB) to predict hidden faults in a reactor, and that in the presence of disturbances. To take into account the effect of the environment on the system, Peng and Dong (2011) proposed a Hidden Semi-Markov Model (HSMM) for fault prognosis of a hydraulic pump, based on the calculation of a risk functions. The experience-based fault prognosis is not requested for some plants since it is conducted with the prior knowledge on the system and expert judgment.
experimental results of the developed methodology applied on a mechatronic system are presented in section 4. The paper ends with general synthesis and conclusions.
Model-based fault prognosis is performed by adopting the mathematical representation of the dynamic system, and carried out by the estimation of the component degradation and the RUL evaluation based on the considered degradation model. Among model-based methods, Yang (2002) provide a method of fault prognosis of direct current (DC) motor faults by state estimation. The latter is performed by a Kalman filter. In (Li and Lee (2005)), a dynamic model of crack propagation in the gear reduction part of the engine is used in combination with a dynamic model of the gear to estimate the RUL. Gucik-Derigny (2011) has proposed a method of fault prognosis of uncertain nonlinear systems based on interval observers, and has been applied to an electrical system. Djeziri et al. (2016) used a stochastic model based on Wiener Process to perform RUL prediction, The Kalman filter is used to estimate and update the drift parameter. The main advantage of the model-based fault prognosis is the no need of databases on the earlier operations of the system.
2.1 Test bench description
The BG tool proposed by Karnopp and Rosenberg (1975) can be an alternative for system modeling and fault prognosis since it is based on the physical modeling of the system’s components. The BG describes the power transfer between the passive and active components of multiphysical systems. It is considered as the interface between the physical system and its mathematical model. Danwei et al. (2013) used this tool to generate Augmented and Generalized Analytical Redundancy Relation (AGARR), for fault diagnosis and prognosis of the steering system of an electric vehicle called CyCab. However, Medjaher and Zerhouni (2009) used BG for system modeling and residuals generation in which degradation model is injected to predict the RUL of the system. This paper presents an integrated fault diagnosis and fault prognosis method based on the physical behavior of the system. By using the BG tool, the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation profile are performed. While the RUL is predicted from the dynamic of considered parametric degradation, described by ordinary differential equations (ODEs). The degradation beginning detection is ensured by the FDI module based on the generated ARRs and the adaptive thresholds. While, the degradation profile estimation is carried out by using the notion of the bicausality. All, these steps are achieved by using the unified tool which is BG.
2. SYSTEM DESCRIPTION AND BG MODELING In this section, the used test bench mechatronic system (Fig.1) is described and its corresponding BG model is presented.
The system illustrated by the Fig.1 is a mechatronic system composed of : an acquisition card NI-USB-6343 (1), a Variable-Frequency Drive Elmo Bassoon (2), a brushless motor Metronix of 400 Watt (3) with an embedded encoder, two stepper motors (4) used to introduce a progressive faults, a reducer composed of two pulleys connected by a belt (5), a gear mechanism to introduce mechanical backlash (6), a load composed of small masses to manually change its value and homogeneity (7), an incremental encoder at the load level (8), and two potentiometer which measure the position of the stems of the two stepper motors (9), an emergency stop button (10), and one security detector which prevents starting when the safety cover is not closed (11).
Fig. 1. Overview of the mechatronic system. A progressive fault can be introduced by varying the position of the belt tensioner by a stepper motor as shown in Fig.2, changing thus the stiffness of the mechanical transmission. To emulate a belt breaking, the maximum retraction of the motor’s shaft is considered: in this case, the belt is completely relaxed. The backlash can be increased gradually using the stepper motor, which increases gradually the distance between the two gears of the backlash mechanism as shown in Fig.3. 2.2 BG model of the considered system Fig.4 shows the word BG model of the mechatronic system where the global architecture of the system is described. Three parts can be distinguished: brushless motor part, transmission part, and load part:
This paper is structured as follows: in section 2, the detection and isolation of the degradation beginning is presented. The estimation of the degradation trend and RUL prediction are described in section 3. The obtained 1017
• The brushless motor part is a three phase motor. The electrical part corresponds to three RL circuits. It is composed of an input voltage source Uj with j = 1..3, an electrical resistance Rej , an inductance Lj , and an electromotive force feedback EMF (with a constant kej ), which is linear to the angular velocity of the rotor. The mechanical part is characterized by the rotor inertia Je, and a viscous friction parameter f e.
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Fig. 2. Mechanism varying the stiffness of the mechanical transmission.
Fig. 5. Bond graph model of the mechatronic system. part is estimated. The simplified BG model of the system is illustrated by the Fig.6.
Fig. 6. BG model of the monitorable part of the system. Fig. 3. Mechanism varying the backlash.
3. THE INTEGRATED BG-BASED METHOD
Fig. 4. Word bond graph model of the mechatronic system. • The transmission part concerns the belt which links the mechanical part to the load part. It is character1 ized by the belt rigidity K . The reduction between the velocities of the motor and the pulley is represented on BG model with a transformer element (TF) of a reduction constant N . • The load part of the mechatronic system is a pulley, characterized by its inertia Js , and a viscous friction parameter fs . The BG model of the mechatronic system in preferred integral causality, is given in Fig.5. The instrumentation architecture of this system is composed of: the angular position of the rotor (θe ), and the angular position of the pulley (θs ). Since the position is not a flux variable neither an effort one, the velocities θ˙e and θ˙s are represented using a Df element on the BG model. They are obtained by differentiating the position information. The BG model of the electrical part of the motor (Fig.5) can be represented in a more compact form with a single R element and single I element crossed by the measured average current. The set-point applied to the motor being known, and by using the model of the electrical part, the engine torque Γin applied to the mechanical transmission
This section is devoted to the developed integrated BGbased method for fault diagnosis and fault prognosis tasks. The Fig.7 illustrates the schema of the proposed method. The degradation beginning detection is ensured by the FDI module based on the generated ARRs and the adaptive thresholds. While, the degradation profile estimation is carried out by using the notion of the bicausality.
Fig. 7. Schema of the proposed integrated method for RUL prediction. 3.1 Robust degradation detection In this work, the detection of the degradation beginning and the isolation of the faulty component are based on the BG approach. It reposes on the generation of ARRs which are obtained in a systematic way by exploiting the causal and structural properties of the BG model. The output of a numerical evaluation of a candidate ARR is a residual which characterizes the energy balance in the considered subsystem. Thus, in normal operating, residuals should close to zero. However, when a parametric degradation begins to appear, the value of its corresponding parameter
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(identified in normal operation and implemented previously) will change by deviating from its initial value. In this case, the residual should also deviate from its normal operating envelope. Thus the beginning of degradation will be detected long before the total failure of the component. To isolate the faulty component by using the BG approach, a Boolean matrix; called Fault Signature Matrix (FSM) is constructed from the structure of ARRs. Both system modeling errors and measurement uncertainties are considered to generate adaptive thresholds for degradation detection. In fact, by using BG in its LFT (Linear Fractional Transformation) form robust ARRs can be generated (Djeziri et al. (2009); Touati et al. (2012)). The latter is composed of two perfectly separate parts: a nominal part (ARRn ) and an uncertain part (α). The nominal part is used to calculate residuals (fault indicators) while the uncertain part is exploited for threshold α computations. ARR = ARRn + α
a1 a 2
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˙ ˙ = −ζθ˙e − δK K θe dt − δN N θs dt − δN K θ˙e dt = −δN N θ˙e dt − N δN K θ˙e dt + N ζθ˙e (7) −N K ζθ˙s dt − N 2 K ζθ˙s dt
To build the FSM, the following assumptions are taken into account: • The torque and measured outputs are fault-free; • The reduction constant N cannot be faulty.
The FSM; presented by the Table 1, is obtained from Eq.2. From this FSM, one can point out that all the faults are detectable and a fault on the gear subsystem is detectable and isolable since it presents a single fault signature. Table 1. Fault Signature Matrix (FSM)
(1)
Part Mech part Gear par Load part
Comp. fe Je
Elect. subsystem r1 r2 1 0 1 0
Mb − 1 1
Ib − 0 0
The Fig.8 illustrate the LFT-BG model in derivative causality of the mechatronic system considering both parameter and measurement uncertainties. Since the initial conditions are known at t = 0, ARRs can be generK 1 1 1 1 fs 0 1 1 0 ated even if one dynamic element (C) remains in integral Js 0 1 1 0 causality. They are given by: d ARR1 = Γin − fe θ˙e − Je θ˙e − K θ˙e − N θ˙s dt + α1 3.2 RUL prediction and evaluation dt d (2) ARR2 = fs θ˙s + Js θ˙s − N K θ˙e − N θ˙s dt + α2 The fault prognosis module aims to predict the RUL before dt observing a failure given the current system condition, and the past operation profile. The developed fault prognosis The residuals are obtained by evaluating the ARRs of the method is based on the BG tool as stated previously and will be carried out as follow: Eq.2. They are given by: d • Model the faulty element(s), θ˙e − N θ˙s dt = 0 r1 : Γin − fe θ˙e − Je θ˙e − K • Estimate the degradation profile by using the bidt (3) d ˙ causality notion, ˙ ˙ ˙ r2 : f s θ s + J s θ s − N K θe − N θs dt = 0 • Predict the RUL. dt While, α1 and α2 represent the uncertain part of these residuals. They are given by: α1 = |Wfe | + Wfe /θ˙e + |WJe | + WJe /θ˙e + |a 1 | (4) α2 = |Wfs | + Wfs /θ˙s + |WJs | + WJs /θ˙s + |a 2 |
where |Wfe | , |WJe | , |Wfs | , |WJs | are the fictitious inputs that represent the modeling uncertainties. They are given by : Wfe = −δfe · fe · θ˙e WJe = −δJe · Je · θ¨e (5) Wf = −δf · fs · θ˙s WJ = −δJ · Js · θ¨s s
s
s
s
Moreover Wfe /θ˙e , WJe /θ˙e , Wfs /θ˙s and WJs /θ˙s are defined as follows : Wfe /θ˙e = f˜e ζθ˙e f˜e = fe (1 + δfe ) dζθ˙e J˜e = Je (1 + δJe ) WJe /θ˙e = J˜e dt (6) f˜s = fs (1 + δfs ) Wfs /θ˙s = f˜s ζθ˙s dζ ˙ J˜s = Js (1 + δJs ) WJs /θ˙s = J˜s θs dt
In this work, the goal of the fault prognosis module is to predict the RUL before observing the belt breaking, emulated in the test bench by a maximum relaxation of the belt. The fault on the belt is characterized by a variation on the belt rigidity M C : 1/K. The LFT-BG of the mechatronic system in the presence of the belt fault is illustrated by Fig.9. To estimate the degradation profile (the fault) F , the bicausality concept (Gawthrop (1995)) is applied on the LFT-BG model. The main idea of bicausality notion is to suppose that two power variables in the same direction are known or fixed. This idea is used in this paper to generate the mathematical equations that relate the residuals to the faults, which will permit to estimate the fault value. To this end, by replacing the source associated with fault variable M Se : WF/K and the sink associated with the output variable respectively by DeDf and SeSf elements, and by applying the bicausality through the fault-output causal path, the Bicausal-BG model for fault estimation is obtained (Fig.10). From the latter, one can point out that all dynamic elements are in derivative causality, and the
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Fig. 8. LFT-BG model in derivative causality of the mechatronic system.
Fig. 9. LFT-BG of the mechatronic system in the presence of the belt fault. 1 K
fault is causally linked to the output. So, a fault on C : is estimable. The mathematical expression for this fault is given by: FK = −
WF/K ZF/K
(8)
where WF/K is obtained from the second ARR as follow : d θ˙s − N θ˙s dt + WF/K = 0 (9) fs θ˙s + Js θ˙s − N K dt Thus, WF/K
dθ˙s − N K ∫ θ˙s − N θ˙s dt = − fs θ˙s + Js dt
(10)
Fig. 10. Bicausal BG model for fault estimation. Regarding the term ZF/K , it is the gain of the causal path that links SeSf : θ˙s to Df ∗ : ZF/K in the Bicausal-BG (Fig.10). It is given by: (11) θ˙s − N θ˙s dt ZF/K = N K So, the fault variable is given by: d ˙ θ˙s − N θ˙s dt fs θ˙s + Js dt θs − N K FK = N θ˙s − N θ˙ dt
(12)
s
The estimated fault value will be then used to predict the RUL. For the latter, the considered degradation model follows an ordinary differential equation of the form F˙ = βF where β = 0, 05 represents the degradation model constant which is identified experimentally. To generate
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the degradation profile, the stepper motor is used. The breaking elongation (ebrk ) is chosen by using Hooke’s law for belt deformation and it corresponds to Fv = 4Fn where Fn refers to the nominal maximal admissible force. The breaking elongation value is chosen experimentally. The RUL formula used in this paper is expressed by Eq.13. brk ln 1−e ˆ 1−FK − N Ts (13) RU L = β where : N represents the sample data and Ts is the sampling time. 4. EXPERIMENTAL RESULTS In this section, the obtained experimental results are exposed in order to show the effectiveness of the proposed approach. Two scenarios are considered:
Fig. 11. Torque and system’s outputs in normal and faulty operation.
• The mechatronic system under healthy conditions ; • The mechatronic system subjects to a parametric and a progressive fault on the belt. The parameters of the mechatronic system; which are given in Table 2, were identified off-line. The identified values vary slightly around an average. Thus the average is taken as the nominal value of the parameters, and the standard deviation is taken as the value of the uncertainty expressed in percentage. The values found in all parameters varied between 1.5% and 2%. So, all the values have been rounded up of 2% to avoid false alarms. Table 2. Specification of the mechatronic system fe Je K N fs Js
Nominal values 0.015 0.01 2.01 1.25 0.02 0.0002
Unit (N.m.s.rad−1 ) (Kg.m2 ) (N.m.rad−1 ) − (N.m.s.rad−1 ) (Kg.m2 )
Fig. 12. Residuals evolution under healthy situation.
Uncertainties 0.02 · fen 0.02 · Jen 0.02 · Kn 0.02 · Nn 0.02 · fsn 0.02 · Jsn
The experimental results for torque and measured outputs under healthy and faulty situations are given by the Fig.11. One can notice that when a fault occurs at t = 20s, there is a fluctuation of the pulley velocity (θ˙s ) for 5s : the belt is relaxed but it adheres to the motor shaft and the load one. In other words, the transmission of motion is always 1 ensured but not with the same stiffness ( K ). The pulley’s velocity backs to its desired value, which is due to the PI action. Regarding the residuals, from the Fig.12 and Fig.13, the following conclusion are given : • Healthy situation: both residuals are near to zero. • Faulty situation: both residuals are triggered.
Notice that the belt fault signature is (1 1) (from the Table 1), which result that r1 and r2 are both sensitive to this fault. Also, the residual takes 2s to across the thresholds, that is due to the dynamic of the considered degradation model.
Fig. 13. Residuals evolution under faulty situation. The estimated fault and the estimation error are given by the Fig.14 and 15 respectively. As it can be observed, the estimated fault tracks the considered degradation profile and converges after 10s. The mean of estimation error is on the order of 0, 01. The maximal of the error is observed at t = 23s. The RUL prediction is enabled by a controlled trigger. The latter is set to the Boolean value 1 when the residual cross the adaptive threshold, otherwise it is fixed to the Boolean value 0. The Fig.16 shows the reference RUL and the predicted one. The predicted RUL is equal to
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Fig. 14. Fault estimation. Fig. 17. α − λ performance.
Fig. 15. Fault estimation error. Fig. 18. The relative prediction accuracy. converges after 5 seconds inside the interval (α − λ) and the relative prediction accuracy increase progressively to reach a minimum of 0.7 at time t = 40s. From the latter, one can conclude that the performances of the proposed fault prognosis method are in the latter stage of system life with higher accuracy when approaching the end of life. 5. CONCLUSION
Fig. 16. Remaining useful lifetime before observing the belt breaking. 13s which means that it remains 13s before observing the belt breaking. Nevertheless, the reference RUL is on the order of 30s. The difference between these two RULs can be explained by the introduced degradation profile by the stepper motor. When the estimation error converges to the degradation profile, the predicted RUL and the reference one share the same rate. Fig.17 and 18 illustrate respectively the performance and the accuracy of the RUL prediction by using the proposed method. We note that at the beginning of the prediction (t = 23s), the estimated RUL is outside the interval (α−λ) (Fig.17) and the relative accuracy is equal to 0.4 ( Fig.18). The predicted RUL
The present paper proposes an experimental application on a mechatornic system of an integrated method for fault diagnosis and prognosis based on the bond graph tool. In fact, by using the tool properties, the detection of the degradation beginning, the isolation of the faulty component, and the estimation of the degradation profile are performed. The RUL is predicted from the considered fault degradation model. The developed methodology is applied on a mechatronic system to predict the remaining useful lifetime before observing a belt breaking. The obtained results supported by universal metrics demonstrate the effectiveness and the higher performances of the proposed method. REFERENCES Azam, M., Tuc, F., and Pattipati, K. (2002). Condition based predictivemaintenance of industrial power
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