- Email: [email protected]
Combining Qualitative & Quantitative Reasoning - A Hybrid Approach to Failure Diagnosis of Industrial Systems
Copyright @ IF AC Fault Detection, Supervision and Safety for Technical Processes, Budapest, Hungary. 2000
COMBINING QUALITATIVE & QUANTITATIVE REASONING - A HYBRID APPROACH TO FAILURE DIAGNOSIS OF INDUSTRIAL SYSTEMS Meera Sampath Ashok Godambe Eric Jackson Edward Mallow
Joseph C. Wilson Center for Research and Technology, Xerox Corporation
Abstract: This paper presents a hybrid approach to failure diagnosis of industrial syst.ems. The proposed diagnostic system integrates the qualitative discrete event systems diagnostic met.hodology with quantitative analysis based techniques. The primary motivation for this hybrid approach is to achieve failure diagnosis in systems with limited sensor availability. The proposed scheme has the following key advantages : (i) it integrates a variety of diagnostic technologies in one unified framework; (ii) it combines the relative advantages of the quantitative and the qualitative diagnostic schemes; and (iii) it provides the ability to study the diagnosability properties of the resulting hybrid system using existing theory of diagnosis developed for discrete event systems. The proposed approach is illustrated using the paper feeder system of a digital copier as an example. Copyright @20001FAC Keywords: Fault Diagnosis, Hybrid Systems, Discrete Event Systems, Diagnosers, Signature Analysis, Analytical Redundancy, Fault Detection and Isolation, Model based Diagnosis, Copiers, Printers
1. INTRODUCTION
in the automobile industry, motivate the need for accurate diagnostic systems.
Reliability, availability, and maintainability are key vectors of differentiation of an industrial product in its marketplace. A machine that is broken when needed results not only in loss of customer productivity, but also in increased service costs. Thus, diagnostics and service play an increasingly important role in determining the success of an industrial product. In addition, safety and integrity, not only of industrial systems and processes, but also of data and stored information, call for the development of advanced diagnostic technologies. Finally, health regulations, such as for example
This paper deals with the design of intelligent self-diagnosing systems. A variety of technologies have been proposed to date for the design of such systems. An overview of these technologies can be found in Pouliezos and Stavrakakis (1994), Sampath et al. (1996), and references therein. Some popular approaches are (i) the analytical redundancy based fault detection and isolation (FDI) schemes (see for example, Frank (1990), and Gertler (1998)); (ii) non-model based approaches such as those based on statistical hypothesis testing and signature analysis (see Pouliezos and Stavrakakis (1994) and references therein); (iii) the artificial intelligence based model-based reasoning schemes (see, for example, Hamscher et al. (1992), B.Williams and Nayak (1996), and the papers in Proc.DX (1999)); and (iv) the discrete
1 Corresponding Author: Meera Sampath, 800 Phillips Road, 147-15A, Webster, NY-14580; EMail:[email protected]; Phone:716-422-4058; Fax:716-265-5666
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niques are used for generating an initial candidate diagnosis and parameter estimation and data fitting techniques are used to refine the diagnosis.
event systems (DES) approaches (see Sampath et al. (1995) , Sampath et al. (1996), Debouk et al. (1998) , Roze and Laborie (1998) , and Zad et al. (1998)) . The FDI schemes and the non-model based approaches are based primarily on quantitative anlaysis of signals, whereas the AI based approcahes and the DES approaches are based on qualitative reasoning.
The rest of this paper is organized as follows . In Section 2 we provide an overview of the DES diagnostic methodology, and then present the proposed hybrid scheme. In the subsequent sections, we will discuss the application of the proposed scheme to failure diagnosis of the paper feeder system in a digital copier. In Section 3 we provide a brief description of the paper feeder system. In Section 4 we present the details of the diagnostic scheme for this system. A highlight of the results to date and our conclusions are presented in Section 5.
In this paper, we propose a hybrid scheme in which the qualitative DES methodology is used in conjunction with quantitative analysis for failure diagnosis in dynamic systems. The concept of a "virtual sensor" is introduced to cover the quantitative analysis schemes. Such a hybrid scheme is applicable in cases where (i) the system of interest could be adequately described by qualitative models such as discrete event models for the purpose of failure diagnosis; (ii) the design of the diagnostic inference engine is not a trivial task; and (iii) the system is limited in the number of actual sensors available, so that , it becomes necessary to exploit the information content of readily available signals to achieve dignosability. The proposed scheme combines some of the key advantages of the DES scheme such as (i) simple, easy-to-develop models; (ii) automated design of the diagnostic inference engine; (iii) the ability to handle multiple sensor information and multiple failures, and the main advantage tof the quantitative analysis based schemes,namely, the ability to exploit inherent system redundancy. Other key advantages of the proposed hybrid scheme are that it provides a unified framework to incorporate a number of diagnostic technologies, and it allows one to formally study the diagnosability properties of systems using the existing theory of diagnosability developed for discrete event systems.
2. THE PROPOSED HYBRID DIAGNOSTIC SCHEME 2.1 The DES Diagnostic Methodology
In Sampath et al. (1995) and Sampath et al. (1996), the authors propose a discrete event systems approach to the problem of failure diagnosis. Here, the system is modeled as a DES in which the failures are treated as unobservable events; diagnosis is the process of detecting occurrences of these events from observed event sequences. A systematic approach for on-line diagnosis of failures using diagnosers is presented in Sampath et al. (1995). Also presented therein are a definition of diagnosability, in the framework of formal languages, and necessary and sufficient conditions for diagnosability of systems. We provide here a brief summary of the main results of the above papers. The system of interest is represented by a finite state machine (FSM) G = (X,~, 15, xo) where X denotes the state space, ~ denotes the event set, 15 denotes the transition function (that specifies the next state, given the current state and the next event), and Xo represents the initial state. The event set ~ is partitioned into the set of observable events ~o, and the set of un observable events ~uo. The set of failure events that are to be diagnosed, ~f ' is assumed to be a subset of ~uo, since an observable failure event can be trivially diagnosed. ~ f is further partitioned into distinct failure types ~f = ~fl U .. . U ~fm . Simply speaking, the system represenetd by the state machine G is said to be diagnosable if it is possible to detect with a finite delay occurrences of failures of any type using the record of observed events. Here, finite delay is taken to mean a finite number of event occurrences following the failure.
The motivation for such a hybrid scheme derives from practical considerations. While diagnostics is a key requirement for most industrial systems today, economic considerations, often impose the need to design and develop schemes that can achieve accurate failure diagnosis with a minimal, cost effective set of sensors, and often with no additional sensors beyond those required for normal operation of the system. Hybrid approaches to failure diagnosis similar in spirit to the one we present have been proposed in Frank (1990), Passino and Antsaklis (1988), and Pomeroy et al. (1990). In the first two papers, the author propose a combination of analytical redundancy methods and expert systems, whereas in the third paper, the authors propose the use of model based reasoning algorithms and FDI schemes. An alternate approach to diagnosis of hybrid systems has been proposed in McIlraith et al. (1999), where qualitative diagnostic tech-
A systematic procedure to derive the system model G is presented in Sampath et al. (1996). This modeling procedure takes as input FSM
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models (that capture both normal and failure modes) of the various system components, and fault symptom tables that associate failure modes with sensor outputs. The global system model G is generated algorithmically from these inputs.
DIAGNOS[R
Given a DES represented by a FSM G, the diagnoser G d for the system is a deterministic FSM and can be thought of as an extended observer for G which gives (i) an estimate of the current state of the system after the occurrence of every observable event; and (ii) information on potential past failure occurrences in the form of failure labels attached to the state estimates. The diagnoser performs diagnostics when it observes on-line the behavior of G. Failures are diagnosed by simply checking the labels associated with the state estimates. The diagnoser G d is used not only to perform on-line diagnostics but also to verify off-line the diagnosability of the system.
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Fig. l. Conceptual architecture of proposed hybrid diagnostic scheme sensors and virtual sensors are passed to an event generator module. The purpose of the event generator module is to translate these outputs into discrete "events" recognized by the diagnoser. As seen from the figure, the proposed hybrid system consists of a "low-level" analytical module to generate the necessary data, and a "high-level" reasoning module to interpret the data.
A formal description of the diagnoser, the algorithm to generate the diagnoser from the system model, and the necessary and sufficient conditions for diagnosability can be found in Sampath et al. (1995).
The following points are to be noted with regard to the proposed scheme. First, the concept of an "event" in our hybrid framework is more general than that presented in Sampath et al. (1996). In addition to control signals, and sensor changes, events could include state estimates, system parameters, outputs of statistical analysis, and so on. Next, in spite of the hybrid nature of the diagnostic system, the diagnostic engine itself is still the DES diagnoser. Hence, the diagnosability properties of the hybrid system could still be analyzed using the results of Sampath et al. (1995). Finally, it is to be noted that though this paper focusses on the DES diagnostic methodology, the proposed approach and conceptual architecture apply for other qualitative reasoning methodologies, as well, such as the aritifical intelligence based model-based diagnostic technologies.
2.2 Virtual Sensors and The Hybrid Diagnostic Scheme In this section, we introduce the notion of a "virtual sensor", and present the hybrid diagnostic scheme. Virtual sensors are used to augment the diagnostic information provided by the "real" sensors in the system, such information being derived by analytical means. The purpose of a virtual sensor is to enable unique failure diagnosis with minimal sensor requirements, by exploiting the information content of readily available signals. The virtual sensor can encompass a variety of analytical techniques. In the simplest cases, the virtual sensor could be a threshold analyzer that performs limit checking on actuator and sensor signals. Alternatively, the virtual sensor could be based on signal processing techniques, such as signature analysis, spectrum analysis, vibration, and noise analysis. Statistical techniques such as means and variance analysis are also candidates for virtual sensor technologies. The virtual sensor could also be a state estimator such as a Kalman filter or a failure detection filter. In addition to the above quantitative schemes, the virtual sensor may also based on qualitative techniques such as qualitative calculus, and systems of logical equations.
We will now present a specific example to illustrate the main ideas of this paper. The diagnostic approach that we propose has been successfully applied for diagnosing failures of a paper feeder system in a digital copier. The subsequent sections deal with the design and development of this system.
3. THE PAPER FEEDER SYSTEM AND ITS FAILURES In this section, we present a brief description of the paper feed system in a digital copier. We also list the failure modes that the diagnostic system is required to identify.
Figure 1 shows the conceptual architecture of the proposed hybrid diagnostic scheme. In this architecture, the outputs of the system controllers,
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Fig. 2. Paper Feed System Drive Plate & Feed Roll Cartridge The paper feed system consists of the following components: the feed roll cartridge, the feed motor, the acquisition solenoid, and the elevator motor. The paper transportation process begins at the feed roll cartridge which serves the following functions: (i) it separates the top sheet from the rest of the stack; (ii) it prevents multiple sheet feeds; (iii) it feeds paper to the waiting area; and (iv) it drives the paper into the paper path. The feed motor, a 24 V DC servo motor, provides the drive to the feed roll cartridge via a mechanical clutch and a feed roll coupling. The acquisition solenoid controls the feeding of paper by lowering or lifting the nudger roll (which is part of the feed roll assembly) onto or from the top of the paper stack; when it is energized, it lowers the nudger roll, which in turn causes the top sheet to be nudged to a feed nip; when it de-energizes, the nudger roll is lifted back, thereby preventing more than one sheet from feeding. The elevator motor serves to move the paper stack up, as and when needed. All feeder drive components are located on a "drives plate"; also, all drive plate components share a common ground return line.
Fig. 3. Conceptual Architecture of the Diagnostic Scheme for the Paper Feeder System between a real failure and this situation, we also included a fifth "failure", namely, "tray-out-ofpaper". The requirement that we imposed on the diagnostic system was that it should be able to uniquely identify the occurrences of any of these five failures.
4. A HYBRID DIAGNOSTIC SCHEME FOR THE PAPER FEEDER SYSTEM Figure 3 shows the conceptual architecture of the diagnostic scheme that we have proposed for real time diagnosis of the paper feeder system. Note that the generic virtual sensor module of Figure 1 has been instantiated by (i) a feature extraction and discriminant analysis module and (ii) a set of counters. Note also that no additional "real" sensors beyond those used for normal control of the system, namely, the wait station sensor, and the stack height sensor, are being used for diagnosis.
Figure 2 shows a drive plate and a feed roll cartridge. The paper feed system has two sensors: a wait station sensor and a stack height sensor. The wait station sensor is used to sense the arrival of paper at the wait station (where the paper waits until further commands are issued), and to control the feeding of subsequent sheets. The stack height sensor determines the position of the paper stack and is used to control the operation of the elevator motor.
In the following sections, we will discuss the main modules in Figure 3.
4.1 The Virtual Sensor Module Recall, from Section 3, that the paper feeder system consists of only two sensors: a wait station sensor and a stack height sensor. All of the five failures that were listed in Section 3 result in paper not being fed, and hence, they have the same effect on the wait station sensor. Further, the stack height sensor reflects only the status of the elevator motor, and not that of the other components. Therefore, it is obvious that the paper feed system with these two sensors alone is non-diagnosable.
The following four failures of the paper feeder system were included within the scope of the diagnostic system: (i) stalled feed motor; (ii) stalled elevator motor; (iii) broken nudger solenoid; and (iv) broken feed roll cartridge. Since all of these failures have the same effect on the system as an "out-of-paper" situation, and since it is necessary for the diagnostic system to be able to distinguish
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Fig. 5. Clusters in the "Peak Current - Peak Power Spectral Amplitude" Feature Space are widely used in areas such as pattern recognition and analysis, for problems related to data classification. For details, we refer the reader to Anderson (1984), Morrison (1976), and Duda and Hart (1973). Here, we use these techniques to classify the feature values resulting from a diagnostic run, into one of a number of predetermined clusters (or regions) in the feature space, based on a classification algorithm . The clusters correspond to the various failure modes of the system and the name (or number of this cluster) becomes the output of the virtual sensor.
Fig. 4. Sample Plot of Ground Return Line Current & Power Spectrum In this regard, we propose the use of the following three virtual sensors: a stack height counter, a feed counter, and a feature extraction and discriminant analysis module. The stack height sensor counter keeps track of changes of the stack height sensor reading over consecutive sheet feeds. The feed counter keeps track of the number of sheets fed during a diagnostic run (which was chosen to correspond to twelve sheet feeds) by monitoring the wait station sensor.
The notion of feature extraction based diagnosis that we have adopted here, has been motivated in part by the work of Azzoni et al. (1996), and by Coleman (1997). In Azzoni et al. (1996), the authors present an approach to misfire detection in high performance engines based on feature extraction and principal component analysis.
The feature extraction and discriminant analysis module is based on analyzing the ground return line current drawn by the paper feed system components. Recall, from Section 3, that all of the paper feeder system components share the same ground return line. Since these devices draw different amounts of current, and further, since this current differs significantly in the normal and failed states of the components, analysis of the ground return line current can provide critical diagnostic information.
As the first step in the design of the classification algorithm, we conducted a series of experiments and recorded the two features of interest, namely, the peak current and the power spectral amplitudes, for several job runs corresponding to the normal mode and the various failure modes. The data collected was then analyzed using the statistical analysis package MINITAB to determine the best classification algorithm for three different choice of features, namely, the peak current alone, the power spectral amplitudes alone, and a combination of the above two. Both linear classifiers and quadratic classifiers were tested.
Now, detailed analysis of the time domain current profile can be time-consuming and computationally intensive. The approach that we have taken in this regard, is to extract out key "features" from the ground return line current and then perform statistical discriminant analysis on the extracted features. The features that we chose are the peak current and the highest power spectral amplitudes of the ground return current over a diagnostic run. Figure 4 shows a sample ground return line current plot and the corresponding power spectral amplitudes for the case of a broken solenoid.
The analysis revealed that best results, in terms of fewer misclassified samples, were obtained when the peak current alone, or a combination of the peak current and the highest power spectral amplitudes, were used. Figure 5 depicts the feature space for the latter case.
The purpose of the discriminant analysis module is to account for the statistical variations in the feature values that occur from run to run of the machine. Discriminant analysis techniques
A comparison of the two choices of feaures mentiond above, showed that they differ in the num-
491
ber of distinct clusters, and in the uniqueness of these clusters to the various failure modes. With the peak current alone as the feature, the resulting one-dimensional feature space had three distinct clusters, where two of the clusters mapped to unique failure modes, and the third cluster corresponded to all of the remaining failures as well as the normal case (see Figure 5). In the case where both the peak current and the highest power spectral amplitude were used as features, four distinct clusters were observed in the twodimensional feature space. However, none of the clusters corresponded to unique failure modes. More specifically, the normal case, the stalled feed motor, the broken solenoid, and the broken feed roll cartridge mapped to unique clusters (see Figure 5), but the case of the broken elevator motor, and the out-of-paper failure fell into any of the above four clusters, depending on the conditions of a particular diagnostic run.
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The question that arises then , is, which of these two choices of features, would result in better overall system diagnosability? When the diagnosers (see Section 4.3) were built for these two choices, it was discovered that use of the peak current alone provided better overall diagnosability results. More specifically, when both the peak current and the power spectral amplitudes were used, the resulting diagnoser could not distinguish between a broken solenoid failure and an out-ofpaper failure. This situation did not arise when the peak current alone was used. This brings to light an important point, namely, that more information doesn't necessarily mean better diagnosis, and the right choice of sensors is critical in the design of diagnostic systems.
Peak Current, Peak Current High"; "Check Stack Height Counter, Stack Height Counter High"; "Check Feed Counter, Feed Counter Low"; and "End Diagnostics".
4.3 The Diagnoser Module In this section, we describe the diagnoser module, which is the heart of the proposed diagnostic system. The primary function of the diagnoser module is to determine the status of the paper feeder system and its components, given the set of discrete events output by the event generator module. The status information should indicate if the machine is normal, or, if certain failures have occurred, or if some failures are suspected.
4.2 The Event Generator Module
The design of the diagnoser is based on the results of Sampath et al. (1995) and Sampath et al. (1996), reviewed in Section 2.1. In Figure 6, we present some sample FSM models of the paper feed system components.
As mentioned earlier, the primary functions of the event generator module are (i) to acquire the digital signals corresponding to the control commands and the sensor outputs; (ii) to acquire the outputs of the virtual sensor module; and (iii) to translate the above two sets of signals into "events" recognizable by the diagnoser module. In our implementation, data is collected for twelve paper feeds, which is roughly 15 sec, and then the collected data is anlayzed for specific event sequences. Upon completion of this analysis, an event list capturing the sequence of events that happened during the current run is generated and fed to the diagnoser module.
Note that these models are simple, and easy-togenerate, given the failure modes of the components. In Figure 7, we present a part of the FSM model of the paper feed system controller (augmented appropriately with the virtual sensor events). Part of the fault symptom table is shown in Table 1. The UMDES-LIB software tool developed at the University of Michigan was used to build the system models and to generate the diagnoser. The diagnoser has around a hundred states under the single fault assumption. A part of the diagnoser is shown in Figure 8. Each box in the figure represents a state of the diagnoser. For simplicity, only the failure attributes of the state estimates
Consider for example the case of a broken feed roll cartridge. The sequence of events arising from a diagnostic run in this case will be: "Start Diagnostics"; "Solenoid On"; "Feed Motor On"; "Solenoid Off";"Feed Motor off, Wait Sensor Low"; "Check
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and an out-of-paper situation. However, from the point of view of the utility of the system, this is not a serious concern since an out-of-paper situation is something that can be easily verified by the user of the machine.
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5. CONCLUSION In this paper, we have presented a hybrid approach to failure diagnosis of dynamic systems . The proposed diagnostic system integrates the qualitative DES diagnostic methodology with a variety of quantitative analysis based techniques, in one unified framework. This scheme combines the relative advantages of the quantitative and the qualitative schemes. The proposed approach is motivated by the practical need , in most industrial systems, to achieve diagnosis with minimal sensor requirements. This approach also provides the ability to study the diagnosability properties of the resulting hybrid system, using existing theory of diagnosis developed for discrete event systems. A special case of the proposed scheme involving the use of statistical discriminant analysis as the virtual sensor has been successfully implemented for real time failure diagnosis of a paper feeder system in a digital copier. We have shown how unique component level diagnosis can be achieved in this case, with no additional hardware sensors beyond those used for normal control. Finally, it is to be noted that though the focus of this paper is the DES diagnostic methodology, the proposed approach and conceptual architec-
Table 1. Part of the Fault-Symptom Table for the Paper Feed System and not the estimates themselves, are shown in the figure. These attributes form the output of the diagnoser; the attribute "N" indicates normal, "F1" indicates failure 1, and so on. The appearance of more than one failure type in a box indicates that either of those two failures are possible in that state. The diagnoser was implemented as a simple look up table in our system.
4.4 On Diagnosability of the Paper Feeder System
The diagnosability of the paper feeder system was analyzed using the UMDES_LIB software tool, and was verified via experimentation. It was found that the proposed diagnostic system can provide unique failure diagnosis of the paper feeder system for all failure situations, except one. Under certain conditions, the diagnoser was found to be unable to distinguish between a broken feed roll cartridge
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M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis. Diagnosability of discrete event systems. IEEE Trans. A utomatic Control, 40(9):1555- 1575, September 1995. M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis. Failure diagnosis using discrete event models. IEEE Trans. Control Systems Technology , 4(2) :105124, March 1996. S.H. Zad, R. H. Kwong, and M. Wonham . Failure diagnosis in discrete event systems- framework and model reduction. Proc. IEEE Conf. Decision and Control, pages 3769- 3774, 1998.
ture apply for other qualitative reasoning methodologies, as well, such as the aritifical intelligence based model based diagnostic technologies.
References T. W. Anderson. An Introduction to Multivariate Statistical Analysis. John Wiley & Sons, 1984. P. Azzoni, D. Moro, C. Porceddu-Cilione, and G. Rizzoni. Misfire detection in highperformance engine by the principal component analysis approach. Society of automotive Engineers, 1996. B.Williams and P. Nayak. A model-based approach to reactive self-configuring systems. Proc. of the AAAI, 1996. C. Coleman. Private communication, 1997. R. Debouk, S. Lafortune, and D. Teneketzis. A coordinated decentralized protocol for failure diagnosis of discrete event systems. In Proc. Wodes, Fourth Int. Workshop on Discrete Event Systems, pages 138-143. lEE, London, 1998. R. Duda and P. Hart. Pattern Classification and Scene Analysis. John Wiley & Sons, 1973. P. Frank. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - a survey and some new results. A utomatica, 26:459- 474, 1990. J . Gertler. Fault Detection and Diagnosis in Engineering Systems. Marcel Dekker, 1998. W. Hamscher, L. Console, and J. de Kleer, editors. Readings in Model-based Diagnosis. Morgan Kaufmann Publishers, San Mateo, CA, 1992. S. McIlraith, G. Biswas, D. Clancy, and V. Gupta. Towards diagnosing hybrid systems. In Working Papers, Tenth Int. Workshop on Principles of Diagnosis, DX99, pages 193- 203. Loch Awe, Scotland, 1999. D. Morrison. Multivariate Statistical Methods. McGraw Hill, 1976. K. M. Passino and P. J. Antsaklis. Fault detection and identification in intelligent restructurable controller. Journal of Intelligent f3 Robotic Systems, 1:145- 161 , 1988. B. D. Pomeroy, A. Spang, and M. E. Dausch. Event based architecture for diagnosis in control advisory systems. Artificial Intelligence in Engineering, 5-4:174-181, 1990. A.D. Pouliezos and G. S. Stavrakakis. Real Time Fault Monitoring of Industrial Processes. Kluwer Academic Publishers, 1994. Proc.DX. Tenth Int. Workshop on Principles of Diagnosis, DX99. Loch Awe, Scotland, 1999. L. Roze and P. Laborie. Supervision of telecommunication network: Extending the classical diagnoser approach. Working Papers, Ninth Int . Workshop on Principles of Diagnosis, DX98, pages 233- 239, 1998.
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COMBINING QUALITATIVE & QUANTITATIVE REASONING - A HYBRID APPROACH TO FAILURE DIAGNOSIS OF INDUSTRIAL SYSTEMS Meera Sampath Ashok Godambe Eric Jackson Edward Mallow
Joseph C. Wilson Center for Research and Technology, Xerox Corporation
Abstract: This paper presents a hybrid approach to failure diagnosis of industrial syst.ems. The proposed diagnostic system integrates the qualitative discrete event systems diagnostic met.hodology with quantitative analysis based techniques. The primary motivation for this hybrid approach is to achieve failure diagnosis in systems with limited sensor availability. The proposed scheme has the following key advantages : (i) it integrates a variety of diagnostic technologies in one unified framework; (ii) it combines the relative advantages of the quantitative and the qualitative diagnostic schemes; and (iii) it provides the ability to study the diagnosability properties of the resulting hybrid system using existing theory of diagnosis developed for discrete event systems. The proposed approach is illustrated using the paper feeder system of a digital copier as an example. Copyright @20001FAC Keywords: Fault Diagnosis, Hybrid Systems, Discrete Event Systems, Diagnosers, Signature Analysis, Analytical Redundancy, Fault Detection and Isolation, Model based Diagnosis, Copiers, Printers
1. INTRODUCTION
in the automobile industry, motivate the need for accurate diagnostic systems.
Reliability, availability, and maintainability are key vectors of differentiation of an industrial product in its marketplace. A machine that is broken when needed results not only in loss of customer productivity, but also in increased service costs. Thus, diagnostics and service play an increasingly important role in determining the success of an industrial product. In addition, safety and integrity, not only of industrial systems and processes, but also of data and stored information, call for the development of advanced diagnostic technologies. Finally, health regulations, such as for example
This paper deals with the design of intelligent self-diagnosing systems. A variety of technologies have been proposed to date for the design of such systems. An overview of these technologies can be found in Pouliezos and Stavrakakis (1994), Sampath et al. (1996), and references therein. Some popular approaches are (i) the analytical redundancy based fault detection and isolation (FDI) schemes (see for example, Frank (1990), and Gertler (1998)); (ii) non-model based approaches such as those based on statistical hypothesis testing and signature analysis (see Pouliezos and Stavrakakis (1994) and references therein); (iii) the artificial intelligence based model-based reasoning schemes (see, for example, Hamscher et al. (1992), B.Williams and Nayak (1996), and the papers in Proc.DX (1999)); and (iv) the discrete
1 Corresponding Author: Meera Sampath, 800 Phillips Road, 147-15A, Webster, NY-14580; EMail:[email protected]; Phone:716-422-4058; Fax:716-265-5666
487
niques are used for generating an initial candidate diagnosis and parameter estimation and data fitting techniques are used to refine the diagnosis.
event systems (DES) approaches (see Sampath et al. (1995) , Sampath et al. (1996), Debouk et al. (1998) , Roze and Laborie (1998) , and Zad et al. (1998)) . The FDI schemes and the non-model based approaches are based primarily on quantitative anlaysis of signals, whereas the AI based approcahes and the DES approaches are based on qualitative reasoning.
The rest of this paper is organized as follows . In Section 2 we provide an overview of the DES diagnostic methodology, and then present the proposed hybrid scheme. In the subsequent sections, we will discuss the application of the proposed scheme to failure diagnosis of the paper feeder system in a digital copier. In Section 3 we provide a brief description of the paper feeder system. In Section 4 we present the details of the diagnostic scheme for this system. A highlight of the results to date and our conclusions are presented in Section 5.
In this paper, we propose a hybrid scheme in which the qualitative DES methodology is used in conjunction with quantitative analysis for failure diagnosis in dynamic systems. The concept of a "virtual sensor" is introduced to cover the quantitative analysis schemes. Such a hybrid scheme is applicable in cases where (i) the system of interest could be adequately described by qualitative models such as discrete event models for the purpose of failure diagnosis; (ii) the design of the diagnostic inference engine is not a trivial task; and (iii) the system is limited in the number of actual sensors available, so that , it becomes necessary to exploit the information content of readily available signals to achieve dignosability. The proposed scheme combines some of the key advantages of the DES scheme such as (i) simple, easy-to-develop models; (ii) automated design of the diagnostic inference engine; (iii) the ability to handle multiple sensor information and multiple failures, and the main advantage tof the quantitative analysis based schemes,namely, the ability to exploit inherent system redundancy. Other key advantages of the proposed hybrid scheme are that it provides a unified framework to incorporate a number of diagnostic technologies, and it allows one to formally study the diagnosability properties of systems using the existing theory of diagnosability developed for discrete event systems.
2. THE PROPOSED HYBRID DIAGNOSTIC SCHEME 2.1 The DES Diagnostic Methodology
In Sampath et al. (1995) and Sampath et al. (1996), the authors propose a discrete event systems approach to the problem of failure diagnosis. Here, the system is modeled as a DES in which the failures are treated as unobservable events; diagnosis is the process of detecting occurrences of these events from observed event sequences. A systematic approach for on-line diagnosis of failures using diagnosers is presented in Sampath et al. (1995). Also presented therein are a definition of diagnosability, in the framework of formal languages, and necessary and sufficient conditions for diagnosability of systems. We provide here a brief summary of the main results of the above papers. The system of interest is represented by a finite state machine (FSM) G = (X,~, 15, xo) where X denotes the state space, ~ denotes the event set, 15 denotes the transition function (that specifies the next state, given the current state and the next event), and Xo represents the initial state. The event set ~ is partitioned into the set of observable events ~o, and the set of un observable events ~uo. The set of failure events that are to be diagnosed, ~f ' is assumed to be a subset of ~uo, since an observable failure event can be trivially diagnosed. ~ f is further partitioned into distinct failure types ~f = ~fl U .. . U ~fm . Simply speaking, the system represenetd by the state machine G is said to be diagnosable if it is possible to detect with a finite delay occurrences of failures of any type using the record of observed events. Here, finite delay is taken to mean a finite number of event occurrences following the failure.
The motivation for such a hybrid scheme derives from practical considerations. While diagnostics is a key requirement for most industrial systems today, economic considerations, often impose the need to design and develop schemes that can achieve accurate failure diagnosis with a minimal, cost effective set of sensors, and often with no additional sensors beyond those required for normal operation of the system. Hybrid approaches to failure diagnosis similar in spirit to the one we present have been proposed in Frank (1990), Passino and Antsaklis (1988), and Pomeroy et al. (1990). In the first two papers, the author propose a combination of analytical redundancy methods and expert systems, whereas in the third paper, the authors propose the use of model based reasoning algorithms and FDI schemes. An alternate approach to diagnosis of hybrid systems has been proposed in McIlraith et al. (1999), where qualitative diagnostic tech-
A systematic procedure to derive the system model G is presented in Sampath et al. (1996). This modeling procedure takes as input FSM
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models (that capture both normal and failure modes) of the various system components, and fault symptom tables that associate failure modes with sensor outputs. The global system model G is generated algorithmically from these inputs.
DIAGNOS[R
Given a DES represented by a FSM G, the diagnoser G d for the system is a deterministic FSM and can be thought of as an extended observer for G which gives (i) an estimate of the current state of the system after the occurrence of every observable event; and (ii) information on potential past failure occurrences in the form of failure labels attached to the state estimates. The diagnoser performs diagnostics when it observes on-line the behavior of G. Failures are diagnosed by simply checking the labels associated with the state estimates. The diagnoser G d is used not only to perform on-line diagnostics but also to verify off-line the diagnosability of the system.
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Fig. l. Conceptual architecture of proposed hybrid diagnostic scheme sensors and virtual sensors are passed to an event generator module. The purpose of the event generator module is to translate these outputs into discrete "events" recognized by the diagnoser. As seen from the figure, the proposed hybrid system consists of a "low-level" analytical module to generate the necessary data, and a "high-level" reasoning module to interpret the data.
A formal description of the diagnoser, the algorithm to generate the diagnoser from the system model, and the necessary and sufficient conditions for diagnosability can be found in Sampath et al. (1995).
The following points are to be noted with regard to the proposed scheme. First, the concept of an "event" in our hybrid framework is more general than that presented in Sampath et al. (1996). In addition to control signals, and sensor changes, events could include state estimates, system parameters, outputs of statistical analysis, and so on. Next, in spite of the hybrid nature of the diagnostic system, the diagnostic engine itself is still the DES diagnoser. Hence, the diagnosability properties of the hybrid system could still be analyzed using the results of Sampath et al. (1995). Finally, it is to be noted that though this paper focusses on the DES diagnostic methodology, the proposed approach and conceptual architecture apply for other qualitative reasoning methodologies, as well, such as the aritifical intelligence based model-based diagnostic technologies.
2.2 Virtual Sensors and The Hybrid Diagnostic Scheme In this section, we introduce the notion of a "virtual sensor", and present the hybrid diagnostic scheme. Virtual sensors are used to augment the diagnostic information provided by the "real" sensors in the system, such information being derived by analytical means. The purpose of a virtual sensor is to enable unique failure diagnosis with minimal sensor requirements, by exploiting the information content of readily available signals. The virtual sensor can encompass a variety of analytical techniques. In the simplest cases, the virtual sensor could be a threshold analyzer that performs limit checking on actuator and sensor signals. Alternatively, the virtual sensor could be based on signal processing techniques, such as signature analysis, spectrum analysis, vibration, and noise analysis. Statistical techniques such as means and variance analysis are also candidates for virtual sensor technologies. The virtual sensor could also be a state estimator such as a Kalman filter or a failure detection filter. In addition to the above quantitative schemes, the virtual sensor may also based on qualitative techniques such as qualitative calculus, and systems of logical equations.
We will now present a specific example to illustrate the main ideas of this paper. The diagnostic approach that we propose has been successfully applied for diagnosing failures of a paper feeder system in a digital copier. The subsequent sections deal with the design and development of this system.
3. THE PAPER FEEDER SYSTEM AND ITS FAILURES In this section, we present a brief description of the paper feed system in a digital copier. We also list the failure modes that the diagnostic system is required to identify.
Figure 1 shows the conceptual architecture of the proposed hybrid diagnostic scheme. In this architecture, the outputs of the system controllers,
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Fig. 2. Paper Feed System Drive Plate & Feed Roll Cartridge The paper feed system consists of the following components: the feed roll cartridge, the feed motor, the acquisition solenoid, and the elevator motor. The paper transportation process begins at the feed roll cartridge which serves the following functions: (i) it separates the top sheet from the rest of the stack; (ii) it prevents multiple sheet feeds; (iii) it feeds paper to the waiting area; and (iv) it drives the paper into the paper path. The feed motor, a 24 V DC servo motor, provides the drive to the feed roll cartridge via a mechanical clutch and a feed roll coupling. The acquisition solenoid controls the feeding of paper by lowering or lifting the nudger roll (which is part of the feed roll assembly) onto or from the top of the paper stack; when it is energized, it lowers the nudger roll, which in turn causes the top sheet to be nudged to a feed nip; when it de-energizes, the nudger roll is lifted back, thereby preventing more than one sheet from feeding. The elevator motor serves to move the paper stack up, as and when needed. All feeder drive components are located on a "drives plate"; also, all drive plate components share a common ground return line.
Fig. 3. Conceptual Architecture of the Diagnostic Scheme for the Paper Feeder System between a real failure and this situation, we also included a fifth "failure", namely, "tray-out-ofpaper". The requirement that we imposed on the diagnostic system was that it should be able to uniquely identify the occurrences of any of these five failures.
4. A HYBRID DIAGNOSTIC SCHEME FOR THE PAPER FEEDER SYSTEM Figure 3 shows the conceptual architecture of the diagnostic scheme that we have proposed for real time diagnosis of the paper feeder system. Note that the generic virtual sensor module of Figure 1 has been instantiated by (i) a feature extraction and discriminant analysis module and (ii) a set of counters. Note also that no additional "real" sensors beyond those used for normal control of the system, namely, the wait station sensor, and the stack height sensor, are being used for diagnosis.
Figure 2 shows a drive plate and a feed roll cartridge. The paper feed system has two sensors: a wait station sensor and a stack height sensor. The wait station sensor is used to sense the arrival of paper at the wait station (where the paper waits until further commands are issued), and to control the feeding of subsequent sheets. The stack height sensor determines the position of the paper stack and is used to control the operation of the elevator motor.
In the following sections, we will discuss the main modules in Figure 3.
4.1 The Virtual Sensor Module Recall, from Section 3, that the paper feeder system consists of only two sensors: a wait station sensor and a stack height sensor. All of the five failures that were listed in Section 3 result in paper not being fed, and hence, they have the same effect on the wait station sensor. Further, the stack height sensor reflects only the status of the elevator motor, and not that of the other components. Therefore, it is obvious that the paper feed system with these two sensors alone is non-diagnosable.
The following four failures of the paper feeder system were included within the scope of the diagnostic system: (i) stalled feed motor; (ii) stalled elevator motor; (iii) broken nudger solenoid; and (iv) broken feed roll cartridge. Since all of these failures have the same effect on the system as an "out-of-paper" situation, and since it is necessary for the diagnostic system to be able to distinguish
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Fig. 5. Clusters in the "Peak Current - Peak Power Spectral Amplitude" Feature Space are widely used in areas such as pattern recognition and analysis, for problems related to data classification. For details, we refer the reader to Anderson (1984), Morrison (1976), and Duda and Hart (1973). Here, we use these techniques to classify the feature values resulting from a diagnostic run, into one of a number of predetermined clusters (or regions) in the feature space, based on a classification algorithm . The clusters correspond to the various failure modes of the system and the name (or number of this cluster) becomes the output of the virtual sensor.
Fig. 4. Sample Plot of Ground Return Line Current & Power Spectrum In this regard, we propose the use of the following three virtual sensors: a stack height counter, a feed counter, and a feature extraction and discriminant analysis module. The stack height sensor counter keeps track of changes of the stack height sensor reading over consecutive sheet feeds. The feed counter keeps track of the number of sheets fed during a diagnostic run (which was chosen to correspond to twelve sheet feeds) by monitoring the wait station sensor.
The notion of feature extraction based diagnosis that we have adopted here, has been motivated in part by the work of Azzoni et al. (1996), and by Coleman (1997). In Azzoni et al. (1996), the authors present an approach to misfire detection in high performance engines based on feature extraction and principal component analysis.
The feature extraction and discriminant analysis module is based on analyzing the ground return line current drawn by the paper feed system components. Recall, from Section 3, that all of the paper feeder system components share the same ground return line. Since these devices draw different amounts of current, and further, since this current differs significantly in the normal and failed states of the components, analysis of the ground return line current can provide critical diagnostic information.
As the first step in the design of the classification algorithm, we conducted a series of experiments and recorded the two features of interest, namely, the peak current and the power spectral amplitudes, for several job runs corresponding to the normal mode and the various failure modes. The data collected was then analyzed using the statistical analysis package MINITAB to determine the best classification algorithm for three different choice of features, namely, the peak current alone, the power spectral amplitudes alone, and a combination of the above two. Both linear classifiers and quadratic classifiers were tested.
Now, detailed analysis of the time domain current profile can be time-consuming and computationally intensive. The approach that we have taken in this regard, is to extract out key "features" from the ground return line current and then perform statistical discriminant analysis on the extracted features. The features that we chose are the peak current and the highest power spectral amplitudes of the ground return current over a diagnostic run. Figure 4 shows a sample ground return line current plot and the corresponding power spectral amplitudes for the case of a broken solenoid.
The analysis revealed that best results, in terms of fewer misclassified samples, were obtained when the peak current alone, or a combination of the peak current and the highest power spectral amplitudes, were used. Figure 5 depicts the feature space for the latter case.
The purpose of the discriminant analysis module is to account for the statistical variations in the feature values that occur from run to run of the machine. Discriminant analysis techniques
A comparison of the two choices of feaures mentiond above, showed that they differ in the num-
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ber of distinct clusters, and in the uniqueness of these clusters to the various failure modes. With the peak current alone as the feature, the resulting one-dimensional feature space had three distinct clusters, where two of the clusters mapped to unique failure modes, and the third cluster corresponded to all of the remaining failures as well as the normal case (see Figure 5). In the case where both the peak current and the highest power spectral amplitude were used as features, four distinct clusters were observed in the twodimensional feature space. However, none of the clusters corresponded to unique failure modes. More specifically, the normal case, the stalled feed motor, the broken solenoid, and the broken feed roll cartridge mapped to unique clusters (see Figure 5), but the case of the broken elevator motor, and the out-of-paper failure fell into any of the above four clusters, depending on the conditions of a particular diagnostic run.
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The question that arises then , is, which of these two choices of features, would result in better overall system diagnosability? When the diagnosers (see Section 4.3) were built for these two choices, it was discovered that use of the peak current alone provided better overall diagnosability results. More specifically, when both the peak current and the power spectral amplitudes were used, the resulting diagnoser could not distinguish between a broken solenoid failure and an out-ofpaper failure. This situation did not arise when the peak current alone was used. This brings to light an important point, namely, that more information doesn't necessarily mean better diagnosis, and the right choice of sensors is critical in the design of diagnostic systems.
Peak Current, Peak Current High"; "Check Stack Height Counter, Stack Height Counter High"; "Check Feed Counter, Feed Counter Low"; and "End Diagnostics".
4.3 The Diagnoser Module In this section, we describe the diagnoser module, which is the heart of the proposed diagnostic system. The primary function of the diagnoser module is to determine the status of the paper feeder system and its components, given the set of discrete events output by the event generator module. The status information should indicate if the machine is normal, or, if certain failures have occurred, or if some failures are suspected.
4.2 The Event Generator Module
The design of the diagnoser is based on the results of Sampath et al. (1995) and Sampath et al. (1996), reviewed in Section 2.1. In Figure 6, we present some sample FSM models of the paper feed system components.
As mentioned earlier, the primary functions of the event generator module are (i) to acquire the digital signals corresponding to the control commands and the sensor outputs; (ii) to acquire the outputs of the virtual sensor module; and (iii) to translate the above two sets of signals into "events" recognizable by the diagnoser module. In our implementation, data is collected for twelve paper feeds, which is roughly 15 sec, and then the collected data is anlayzed for specific event sequences. Upon completion of this analysis, an event list capturing the sequence of events that happened during the current run is generated and fed to the diagnoser module.
Note that these models are simple, and easy-togenerate, given the failure modes of the components. In Figure 7, we present a part of the FSM model of the paper feed system controller (augmented appropriately with the virtual sensor events). Part of the fault symptom table is shown in Table 1. The UMDES-LIB software tool developed at the University of Michigan was used to build the system models and to generate the diagnoser. The diagnoser has around a hundred states under the single fault assumption. A part of the diagnoser is shown in Figure 8. Each box in the figure represents a state of the diagnoser. For simplicity, only the failure attributes of the state estimates
Consider for example the case of a broken feed roll cartridge. The sequence of events arising from a diagnostic run in this case will be: "Start Diagnostics"; "Solenoid On"; "Feed Motor On"; "Solenoid Off";"Feed Motor off, Wait Sensor Low"; "Check
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and an out-of-paper situation. However, from the point of view of the utility of the system, this is not a serious concern since an out-of-paper situation is something that can be easily verified by the user of the machine.
Wait Sensor High, Low Peak Current Low Peak Current High Stack Height Counter Low
5. CONCLUSION In this paper, we have presented a hybrid approach to failure diagnosis of dynamic systems . The proposed diagnostic system integrates the qualitative DES diagnostic methodology with a variety of quantitative analysis based techniques, in one unified framework. This scheme combines the relative advantages of the quantitative and the qualitative schemes. The proposed approach is motivated by the practical need , in most industrial systems, to achieve diagnosis with minimal sensor requirements. This approach also provides the ability to study the diagnosability properties of the resulting hybrid system, using existing theory of diagnosis developed for discrete event systems. A special case of the proposed scheme involving the use of statistical discriminant analysis as the virtual sensor has been successfully implemented for real time failure diagnosis of a paper feeder system in a digital copier. We have shown how unique component level diagnosis can be achieved in this case, with no additional hardware sensors beyond those used for normal control. Finally, it is to be noted that though the focus of this paper is the DES diagnostic methodology, the proposed approach and conceptual architec-
Table 1. Part of the Fault-Symptom Table for the Paper Feed System and not the estimates themselves, are shown in the figure. These attributes form the output of the diagnoser; the attribute "N" indicates normal, "F1" indicates failure 1, and so on. The appearance of more than one failure type in a box indicates that either of those two failures are possible in that state. The diagnoser was implemented as a simple look up table in our system.
4.4 On Diagnosability of the Paper Feeder System
The diagnosability of the paper feeder system was analyzed using the UMDES_LIB software tool, and was verified via experimentation. It was found that the proposed diagnostic system can provide unique failure diagnosis of the paper feeder system for all failure situations, except one. Under certain conditions, the diagnoser was found to be unable to distinguish between a broken feed roll cartridge
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M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis. Diagnosability of discrete event systems. IEEE Trans. A utomatic Control, 40(9):1555- 1575, September 1995. M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis. Failure diagnosis using discrete event models. IEEE Trans. Control Systems Technology , 4(2) :105124, March 1996. S.H. Zad, R. H. Kwong, and M. Wonham . Failure diagnosis in discrete event systems- framework and model reduction. Proc. IEEE Conf. Decision and Control, pages 3769- 3774, 1998.
ture apply for other qualitative reasoning methodologies, as well, such as the aritifical intelligence based model based diagnostic technologies.
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