Scholarly article on topic 'A novel approach of testability modeling and analysis for PHM systems based on failure evolution mechanism'

A novel approach of testability modeling and analysis for PHM systems based on failure evolution mechanism Academic research paper on "Mechanical engineering"

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Chinese Journal of Aeronautics
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{"Design for testability" / "Failure evolution mechanism" / "Failure-symptom dependency" / "Prognostics and health management" / "Symptom-test dependency" / "Testability modeling and analysis" / "Unit under test"}

Abstract of research paper on Mechanical engineering, author of scientific article — Xiaodong Tan, Jing Qiu, Guanjun Liu, Kehong Lv, Shuming Yang, et al.

Abstract Prognostics and health management (PHM) significantly improves system availability and reliability, and reduces the cost of system operations. Design for testability (DFT) developed concurrently with system design is an important way to improve PHM capability. Testability modeling and analysis are the foundation of DFT. This paper proposes a novel approach of testability modeling and analysis based on failure evolution mechanisms. At the component level, the fault progression-related information of each unit under test (UUT) in a system is obtained by means of failure modes, evolution mechanisms, effects and criticality analysis (FMEMECA), and then the failure-symptom dependency can be generated. At the system level, the dynamic attributes of UUTs are assigned by using the bond graph methodology, and then the symptom-test dependency can be obtained by means of the functional flow method. Based on the failure-symptom and symptom-test dependencies, testability analysis for PHM systems can be realized. A shunt motor is used to verify the application of the approach proposed in this paper. Experimental results show that this approach is able to be applied to testability modeling and analysis for PHM systems very well, and the analysis results can provide a guide for engineers to design for testability in order to improve PHM performance.

Academic research paper on topic "A novel approach of testability modeling and analysis for PHM systems based on failure evolution mechanism"

Chinese Journal of Aeronautics, 2013,26(3): 766-776

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics

cja@buaa.edu.cn www.sciencedirect.com

JOURNAL OF

AERONAUTICS

A novel approach of testability modeling and analysis for PHM systems based on failure evolution mechanism

Tan Xiaodong, Qiu Jing *, Liu Guanjun, Lv Kehong, Yang Shuming, Wang Chao

Laboratory of Science and Technology on Integrated Logistics Support, College of Mechatronics and Automation, National University of Defense Technology, Changsha 410073, China

Received 20 December 2011; revised 14 May 2012; accepted 29 June 2012 Available online 30 April 2013

KEYWORDS

Design for testability;

Failure evolution

mechanism;

Failure-symptom

dependency;

Prognostics and health

management;

Symptom-test dependency; Testability modeling and analysis; Unit under test

Abstract Prognostics and health management (PHM) significantly improves system availability and reliability, and reduces the cost of system operations. Design for testability (DFT) developed concurrently with system design is an important way to improve PHM capability. Testability modeling and analysis are the foundation of DFT. This paper proposes a novel approach of testability modeling and analysis based on failure evolution mechanisms. At the component level, the fault progression-related information of each unit under test (UUT) in a system is obtained by means of failure modes, evolution mechanisms, effects and criticality analysis (FMEMECA), and then the failure-symptom dependency can be generated. At the system level, the dynamic attributes of UUTs are assigned by using the bond graph methodology, and then the symptom-test dependency can be obtained by means of the functional flow method. Based on the failure-symptom and symptom-test dependencies, testability analysis for PHM systems can be realized. A shunt motor is used to verify the application of the approach proposed in this paper. Experimental results show that this approach is able to be applied to testability modeling and analysis for PHM systems very well, and the analysis results can provide a guide for engineers to design for testability in order to improve PHM performance.

© 2013 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

1. Introduction

With increasing performance as well as sharp rise of complexity and integration of aerospace systems, requirements of maintenance and logistic support for systems are paid more

* Corresponding author. Tel.: +86 731 84573305. E-mail addresses: xdt1010@126.com (X. Tan), qiujing16@sina.com (J. Qiu), gjliu342@qq.com (G. Liu), fhylvh@163.com (K. Lv), ysmcsu@163.com (S. Yang), zhongwangchao@163.com (C. Wang). Peer review under responsibility of Editorial Committee of CJA.

and more attention to.1 The maintenance and logistic pattern is going through a transition from the corrective maintenance, condition-based maintenance (CBM), to the predictive CBM (PCBM) and autonomic logistics (AL).2-4

Prognostics and health management (PHM) systems are being attached more and more importance to as the significant basis of AL systems adapting to high-tech local wars in the 21st Century.1 Studies on a large number of cases have shown that a PHM system is an all-around technique that can conspicuously decrease expenses on maintenance, usage, and support, and improve safety and availability of the system, so that it is worth spreading and intensively studying.1-4 PHM can be thought as an overall comprehensive management style during equipment life cycle. It utilizes a

1000-9361 © 2013 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA. http://dx.doi.org/10.1016/j.cja.2013.04.044

combination of health monitoring data and model-based techniques to track the failure evolution process and assess the health level of the system; thus by combining all kinds of available resources with mission requests, it can trigger the best decision control behavior. Undoubtedly the perceived information and tests are the premise and basis for realizing the functions of PHM systems.

The traditional way of simply adding sensors is impractical and ultimately reduces system reliability. However, if the number of sensors is insufficient, the objective of health monitoring could not be achieved, and false alarm and missed detection could happen. In order to reduce operating and maintenance costs, and to improve availability and reliability of PHM systems, it is significant to carry out design for testability (DFT) during their initial designs.

Undoubtedly testability modeling and analysis are the fundamental premises of DFT.5'6 Since the mid-1980s, a great number of testability models and computer aided design (CAD) tools have been developed by universities and institutes. ARINC developed the system testability and maintenance program (STAMP) to provide a tool for modeling diagnostic information and assessing system testability. The portable interactive troubleshooter (POINTER), which was developed to process models from STAMP and POINTER, is called the information flow model and has been described in detail in Refs.7,8 Lin et al. introduced a testability analysis tool called automatic dependency model analyzer (ADMA) based on dependency models.9 DSI International developed a diagnostic engineering tool called express based on information flow.5 Multi-signal flow graph developed by Deb et al. is another comprehensive methodology to model cause-effect dependencies of complex systems.6 QSI developed the testability engineering and maintenance system (TEAMS) design tool based on multi-signal flow.6,10 Hess et al. introduced a software tool called maintenance aware design environment (MADe) to design, assess, and optimize PHM systems.11,12 These tools are widely used for automated test sequencing and testability analysis in industries and governments.

Besides the above models, there are many testability modeling methods. Functional fault analysis is a high-level, functional model of a system that captures its physical architecture, including physical connectivity of energy, material, and data flows.13 Furthermore, the model also contains all sensory information and failure modes associated with each component of the system. Fault tree analysis has been the most widely used technique for capturing possible event paths from failure root causes to top-level consequences. Petri nets,14 directed graph,15 signed directed graph methods,16 function-fault-behavior-test-environment model,17 and quantified directed graph (QDG),18 which are simple graphical representations of the cause-effect dependency, are also widely used.

Generally speaking, although the methods discussed above are used in many fields, they can only represent fault-test dependency clearly, and are just used for traditional testability analysis and design such as fault detectable/isolatable rate evaluation, test selection and optimization, fault injection and testability verification.

However, besides the functions mentioned above, PHM systems are also capable of tracking the fault evolution process (which is a process of fault evolution from a normal state to a total failure state) to provide information for fault prognostics and health state evaluation. Hence, PHM systems require the

testability model to have the ability to describe the failure evolution process and establish the fault progression-test dependency in the process.

To address the above problems, a novel testability modeling approach called failure evolution mechanism model (FEMM) is proposed. The task of the FEMM is to construct the dependencies of failure progression-test. The strategies of the FEMM are shown as follows:

• At the component level, in order to track the failure evolution process, the failure modes, evolution mechanism, effect and critical analysis (FMEMECA) is implemented. Thus, the function and failure evolution-related information can be derived.

• At the system level, in order to analyze the quantitative information, each unit under test (UUT) is assigned dynamic attributes by using bond graph methodology.11,12

• In order to evaluate the performance of PHM systems, this paper adds some new contents for testability analysis, such as the untrackable failure modes, the unpredictable failure modes, failure trackable rate, and failure predictable rate.

The remainder of this paper is organized as follows. The novel method for testability modeling based on failure evolution mechanism is developed in Section 2. After a set of testability performance indices is presented, the inherent testability analysis is described in Section 3. The experimental results are presented in Section 4. Finally, this paper concludes with a summary and future research direction in Section 5.

2. Failure evolution mechanism model

The testability modeling, an abstract expression for failure information and structural function, is fundamental premise of DFT and testability analysis.

In order to meet the requirements of hierarchical modeling and describe the failure evolution process, this paper improves the testability modeling approach by combining the advantages of traditional information flow models with multi-signal flow graph models.

The improved contents of FEMM which differ from traditional models are as follows:

In traditional models, a system is modeled in the failure space. These models lack fault progression-related information. In the FEMM, the fault symptoms related to fault progression in the failure evolution process are defined as the attributes of failures by means of FMEMECA.

The signals in traditional models describe how the effect of the various failure sources propagates to the monitoring tests. The ways of failure propagation suffer from incorrectness in the mechanical subsystems of complex aerospace systems. The FEMM assigns bond properties to each UUT, and the fault symptom signals propagate to each test points according to functional flow. Thus the model can correctly describe the effect of the various fault symptom signals on the test points by using the bond graph methodology.

Tradition models obtain the Boolean failure-test (FT) matrix using reachability algorithm for fault diagnostic purposes. They cannot describe the fault progression-test dependency for PHM's purposes. However, the FEMM is capable of describing the fault progression-test dependency based on failure-

symptom (FS) and symptom-test (ST) matrices derived using the bond graph methodology. The two matrices can effectively support the testability analysis for PHM's purposes.

2.1. Model description

Modern sophisticated systems consist of hundreds of individual components and subassemblies. In order to analyze the hierarchical attributes of systems, two definitions are given as follows:

Definition 1. According to the structural information or repair level, a system can have multiple levels of the hierarchy ranging from the component levels to the system levels. The hierarchy can be categorized into system level, subsystem level, standalone level, board level, component level, etc.

Definition 2. If Module is an element in the 1th level of hierarchy and ft is a failure mode of Module, then f is called the 1th hierarchy failure mode, and the total number of failure modes in the lth level is the sum of the number of failure modes for all modules in the lth hierarchy.

In this paper, the node properties of the FEMM are defined as follows:

MODULE node: A round rectangle stands for a MODULE node. It represents an element or a level of a system, and may have sub-modules or be a sub-module of a larger system. Each MODULE node corresponds to an associated repair level. It has the following properties: module name, function, bond group, bond variables, number of inputs and outputs (which are ensured by material, energy, or signal flows), mean-time-to-failure (MTTF), repair and rectification time and cost.

FAILURE MODE node: A packed round rectangle stands for a FAILURE MODE node, and its outputs represent failure symptoms related to failure evolution. The properties of the node include: failure mode name, failure type, failure rate, severity, failure symptoms, symptom related condition parameters, failure diagnosis and prognostics methods.

TEST node: A circle stands for a TEST node, which corresponds to the location (physical or logical) where measurements can be made. Each TEST node is characterized by: name, cost, and weight; signal noise rate (SNR), range, response time; environmental constraints;11 type of condition parameters that are measured.

SWITCH node: The SWITCH node is able to model dynamic and reactive systems, as well as various modes of system operations. In addition, the node can be used to functionally isolate modules or break feedback loops in testing mode to improve testability of a system.10

Lines: The lines represent functional relationships between components, which are expressed by using the functional ontology developed by Stone and Wood.11-13 According to the requirements of functional flow, lines can be classified into three types: material flow, signal flow, and energy flow. Lines

can mark breakable or unbreakable loops in feedback loop analysis.10,19

A FEMM can be described by directed graph DG = {MO, FM, TE, SW, L}, where MO denotes the MODULE node set, FM denotes the FAILURE MODE node set, TE denotes the TEST node set, SW denotes the SWITHCH node set, and L

denotes the set of directed edges specifying the functional flow propagation of the system.

2.2. Component level modeling

In an aerospace system, most components undergo a gradual performance degradation process from a normal state to total failure. Tracking the process can help designers assess the health level of the system, thus trigger the best decision behavior. Through analyzing the failure evolution mechanisms, the failure progression-related information can be obtained.

Hence, at the component level, the failure evolution mechanisms are critical for testability modeling, and they can be obtained by means of FMEMECA. The FMEMECA extends the traditional failure mode, effects and criticality analysis (FME-CA) by adding failure evolution analysis, fault diagnostics and prognostics technologies. The additional contents are described as follows:

(1) Failure evolution characteristic analysis

Failure evolution characteristics are the attributes of changes when failure happens and develops. Generally, failures can be categorized into abrupt (sudden) failures and gradual (slowly developing) failures.20

The sudden failures, also termed as hard failures, occur in a very short time. These failures can be detected by the departure of features from normal operating mode, but it is difficult to track them in advance.

The gradual failures, also called soft failures, may be predicted by one or several condition monitoring indicators. Their effects can be seen by features in advance, and their severity level increases over time.

(1) Failure symptom analysis

Failure symptoms represent those characteristics which can be observed prior to total failure or at an early stage of faults, and the failure symptom parameters are the corresponding condition parameters related to fault progression.

In the failure evolution mechanisms model, these failure symptoms are obtained by means of failure evolution mechanism analysis. For those failures whose fault progression can be calculated using physics of failure (PoF) or degradation models,21,22 we can directly define their available monitoring parameters as the failure symptom parameters related to fault progression. For example, in the hot carrier degradation (HCD) model of metallic oxide semiconductor field effect transistor (MOSFET), threshold voltage, transconductance, and collector emitter on voltage are the main symptom parameters related to MOSFET's degradation progression.23 For other failures whose PoF or degradation models are hard to build, we can obtain their failure symptoms by means of expert knowledge. For example, a spall of bearings usually grows relatively quickly producing increased amounts of oil debris, high vibration levels, and elevated temperatures that eventually lead to bearing failures, so the amounts of oil debris, acceleration parameter, and bearing temperature can be defined as the symptom parameters related to the bearing's spalling progression.

The failure symptom analysis can provide critical precursor parameters relevant to appropriate prognostics information.24

It is important to help engineers improve health monitoring for PHM systems.

(1) Sensors/sensors placement

Once the analysis of failure symptoms is completed, it is essential to monitor these failure symptoms-related condition parameters. We can then select sensors/tests to measure the corresponding condition parameters of failure symptoms and optimize the sensor placement.

(1) Fault diagnostics and prognostics

Diagnostics can be either discrete or continuous. Discrete diagnostics utilizes traditional algorithms that produce 0 or 1 depending on whether a threshold has been exceeded. The fault diagnostic method can assist in selecting appropriate sensors to monitor these related condition parameters.25-27

Prognostics is a process of predicting the reliability of a product by assessing the extent of deviation or degradation of a product from its expected normal operating condition. Health monitoring, the base for prognostics, is a process of measuring and recording the extent of deviation or degradation from a normal operating condition. The prognostic technology determines the health monitoring method.

Having implemented the FMEMECA, the fault progression-related failure symptoms or condition parameters can be assigned into the FAILURE MODE nodes.

2.3. System level modeling

In FEMM, fault dependency analysis is very important. For digital systems, fault dependencies can be obtained by FME-CA due to its good modularity and linearity which contribute to the certainty of failure propagation. However, in complex aerospace systems, the physical phenomena (mechanical, electrical, hydraulic, thermal, chemical, etc.) are strongly coupled and non-linear. The fault dependencies obtained only by FMECA are unilateral or even wrong. For these systems, fault propagation is usually accompanied with energy flow, signal flow, and material flow, so failure propagation dependencies can be analyzed by system dynamic behavior analysis combined with system structure and function.

Hence, at the system level, the focus should be kept on a system's functional requirements, and it is crucial to be able to reason at the functional level and identify what functions are likely to fail or degrade and how fault progression affects the functions of the system. This requires developing an accurate mathematical model of the system and giving a set of inputs and corresponding output measurements.

Most existing models such as Petri net, fault tree, directed graph, and functional failure design method (FFDM) can be used to describe the information. Among these models, the FFDM is most widely used because it provides a powerful representation to capture cause-effect information about a sys-tem.16 However, it does not include any quantitative information related to the system's physical attributes.

Bond graph is a powerful tool for establishing quantitative models in engineering systems, especially when different physical domains (mechanical, electrical, hydraulic, thermal, chemical, etc.) are involved.28-30

The bond graph elements are described as follows:

C: a storage element for a q-type variable, e.g., a capacitor

(for charge), spring (for displacement).

I: a storage element for a p-type variable, e.g., an inductor

(for flux linkage), mass (for momentum).

R: a resistor dissipating free energy, e.g., an electric resistor,

mechanical friction.

Se, Sf: a source, e.g., electric mains (voltage source), gravity (force source), a pump (flow source). TF: an ideal transformer which relates efforts at all ports and separately relates flows. Examples are an electric transformer, toothed wheels, and a lever.

GY: an ideal gyrator which relates the effort of one port to the flow of the other port and vice versa. Examples are an electromotor, a pump, and a turbine.

0-junction: a node at which all efforts of the connecting bonds are equal.

1-junction: a node at which all flows of the connecting bonds are equal.

For complex aerospace systems which consist of many mechanical subsystems and non-mechanical subsystems, to generate a bond-graph model starting from a physical model, a systematic method is presented as follows:28

(1) Indentify distinct velocities and angular velocities and represent them by 1-junctions for mechanical subsystems; identify distinct efforts and represent them by 0-junctions for non-mechanical subsystems, respectively.

(2) Insert C-, R-, TF- and GY-ports via a 0-junction between two 1-junctions for mechanical subsystems and insert a power port of a source, energy store, dissi-pator, transformer, or gyrator via a 1-junction between two proper 0-junctions for non-mechanical subsystems, respectively.

(3) Attach inertia 1-port elements to their respective 1-junc-tions for mechanical subsystems and attach 1-port sort sources and 1-port sinks to appropriate 1-junctions for non-mechanical subsystems, respectively.

(4) Assign a reference direction (half arrow) for the energy flow to each bond.

(5) Simplify the bond graph according to the following rules.

A junction between two bonds can be left out, if the bonds have a 'through' power direction (one bond incoming and the other outgoing).

A bond between two same junctions can be left out, and the junctions can join into one.

Two separately constructed identical effort or flow differences can join into one effort or flow difference.

For each hierarchy, the structure of the model may be represented by a bond graph. At the lowest hierarchy, bond graph nodes represent basic energetic processes as delivery or storage of energy.

2.4. Steps for FEMM

In the following, we provide a four-step procedure of modeling the FEMM, which would meet modeling needs:

(1) In order to obtain failure evolution information within the analysis object and hierarchy, the FMEMECA for the analysis object and hierarchy is executed by integrating the structural and functional information of the system. Then, these MODULE nodes, standing for system UUTs, are assigned into the corresponding hierarchy, and their functional definitions and internal flow mapping are set.

(2) Bond properties are assigned to each MODEULE node in accordance with the bond graph methodology. The failure symptom parameters related to the failure evolution process are assigned to each FAILURE MODE node.

(3) Update models with additional information. For example, identify and model the mode ofoperations using SWITCH nodes. The nodes are added to the model according to the multi-mode, physical, or loop requirements.

(4) According to the effect of failure mode on function, the FAILURE MODE node's outputs and MODULE node's outputs within a MODULE node are connected. Through the functional flow method, the interacted inputs and outputs of MODULE nodes are connected in the modeling area by lines which represent the functional flows between components. Multi-level systems can be modeled by constructing two-dimensionally within each hierarchical level and specifying the causal links between each level by mapping their inputs and outputs.

The schematic FEMM, shown in Fig. 1, consists of MODULE nodes standing for system elements connected by black lines which represent the interactions between them in terms of functional flow. A circle in the figure stands for a TEST node, which corresponds to the location (physical or logical) where measurements can be made. At the system level, system function is represented by using functional structures. A functional structure is a graphical, form-independent representation of a system that shows the decomposition of the overall system function into smaller and more fundamental sub-functions. The sub-functions are connected by energy, material, and signal flows. The functions are defined by using a standardized functional taxonomy and by assigning dynamic properties to the components in accordance with the bond graph methodology.11-13 At the component level, fault progression-related failure symptoms or condition parameters are assigned into FAILURE MODE nodes.

Those nodes are interconnected by using the functional flow propagation method, forming a hierarchical graph. The dependency information has been generated through the relationships of functional flow.

Fig. 1 Schematic of FEMM.

3. Inherent testability analysis based on FEMM

3.1. Dependency analysis

Once the FEMM is constructed, the testability analysis should be implemented based on the model's dependency information.

As the structural and functional complexity rises, the dependency information also increases. In order to improve the analysis efficiency, the testability analysis should be implemented according to the requirements of the analysis object and hierarchy.

Four related definitions about testability analysis are presented as follows.

Analysis object: it is the analysis module of testability analysis and the analysis must be limited within it.

Analysis hierarchy: it is the depth of analysis. Obviously, it must be lower than the analysis object.

Failure-symptom (FS): it is the fuzzy connection between failure modes and fault symptoms in a system. It includes failure symptom information related to fault progression in the failure evolution process and can be obtained by means of FMEMECA.

In the matrix FS = {fsj}, the rows represent failure modes and the columns represent condition parameters related to fault symptoms. In the matrix, fsj is 1, if failure f causes a symptom sj to occur, and zero otherwise.

Symptom-test (ST): it is the relationship between condition parameters related to fault symptoms and tests in a system and can be derived by using the bond graph method.

In the matrix ST = {stjk}, the rows represent condition parameters related to fault symptoms and the columns represent tests in a system. In the matrix, stjk is +1,0, and 1, representing that the response of test tk increases, fixes, and decreases, respectively, when failure symptom sj appears.

The analysis object and hierarchy determine the fields of FS and ST dependency matrices. The two matrices are the basis of inherent testability analysis.

3.2. Inherent testability analysis

Testability indices are the base for testability design, validation, and verification. Traditional testability indices are mainly used to evaluate testability level for fault detection and isola-tion,31,32 yet unable to describe testability level for PHM comprehensively. The PHM system requires not only detectable and isolatable ability, but also trackability for the failure evolution process and predictability for the failures. Hence, the traditional inherent testability analysis is further developed. The contents include detectable failures (DF) and undetectable failures (UDF), isolable failures (IF) and un-isolable failures (UIF), trackable failures (TF) and untrackable failures (UTF), predictable failures (PF) and unpredictable failures (UPF), and redundant tests (RT).

The related definitions are described as follows:

• A finite set of M failure modes is F={/1/2,...,f,...,/M}, where f (1 6 i 6 M) denotes the ith failure mode in the system, and the failure rate vector of the system is

K = {k1,k2v . .,kb. . .,kM}.

• A finite set of failure symptoms is S = {s1,s2,.. .,sjv . .,sN}, where sj (1 6 j 6 N) denotes the jth symptom of N fault symptoms in the system, and we define the mapping of one failure symptom to one condition parameter. The symptom set of failure mode f is S(f) = {s,|sj 2 S, fsj = 1}.

• A finite set of available tests is T = {t1,t2,.. .,tk,.. .,tP}, where tk (1 6 k 6 Kt) denotes the kth test of Kt tests in the system.

• A finite set of detectable failure symptoms is Sd = {sj|3stjk—0}.

• A finite set of isolatable failure symptoms is Si = {sj|sj 2 Sd, Yj1-j2, Styx ® Sj = 1}, where Stj1 and Stj2 are the j1th and j2th row vectors in the ST matrix, respectively, with 1 6 j1, j2 6 N, and '©' denotes an XOR operation.

• DF: the set of failures which can be detected by the test points in the system, DF = {fi\fi 2 F, 9sj 2 S(f), stjk-0}, and undetectable failure set UDF = F-DF.

• IF: the set of failures which can be isolated by the system, IF = {fifi 2 DF, Ysj 2 S(f), 9sj 2 Si}, and un-isolable failure set UIF = DF-IF.

• TF: the set of failures which can be tracked by the system, TF = {f|f 2 DF, Ysj 2 S(f), stjk-0}, and untrackable failure set UTF = DF-TF.

• PF: the set of failures which can be predicted by the system, PF = {f |f 2 DF, Ysj 2 S(f), Sj 2 Si}, and unpredictable failure set UPF = DF-PF.

• RT: the set of redundant tests which have the same column in the ST matrix, RT = {tk |tk 2 T, Yk1-k2, Tk1 ® Tk2 = 0}, where Tk1 and Tk2 are the k1th and k2th column vectors in the ST matrix, respectively, and 1 6 k1, k2 6 Kt.

Based on the analysis of PHM essential requirements on testability, four testability indices for PHM are proposed from failure tracking, prediction, detection, to isolation as follows.

Failure tracking rate (FTR): The percentage of failure modes which can be tracked by the PHM system.

Failure prediction rate (FPR): The percentage of failure modes which can be predicted by the PHM system.

Failure detection rate (FDR): The percentage of true sud den/gradual failures which are detected by the PHM system.

Failure isolation rate (FIR): The percentage of true sudden/ gradual failures which are isolated to a single or group of LRUs and/or to a single LRU or component by the PHM system with appropriate accuracy.

fielf fiedf

4. Case studies

A great number of motors are used in aerospace drive systems. Motors are subjected to electrical, mechanical, thermal, and environmental stresses. Thus, various kinds of electrical and mechanical degradations process gradually in a long time. Early detections of abnormalities and health monitoring of motors would help avoid expensive scheduled maintenance before catastrophic failures.33'34 Therefore, a shunt motor is taken as an example to verify the usefulness of the proposed method. Its circuit is presented in Fig. 2. By means of the bond graph method, the components in the motor system have been assigned bond-group types and their associated dynamic variables have been identified. The definitions of components are listed in Table 1. A bond graph of the motor system is shown in Fig. 3.

In the Figs. 2 and 3, E is the voltage of the voltage source; i is the current through the voltage source; ia is the current through the armature; if is the current through the field windings; Rf is the resistance of the field windings; Ra is the resistance of the armature; Rm is the resistance of external disturbance; W is the flux through the field windings; K is the self-inductance coefficient of the field windings; La is the self-inductance coefficient of the armature; rn is the angular velocity of the mechanical load; uR is the voltage of the Ra; ua is the

Fig. 2 Circuit of the shunt motor.

Table 1 Definitions of components using bond graph.

Component Input flow Output flow Bond type Value

Voltage source Stator Rotor Mechanical part Stator current Armature current Torque Supply current Flux Torque Speed Voltage source Resistor Resistor Inductor Gyrator 250 V 12 X 0.012 X 3.5 mH 1

Bearing damage: The main function of the bearing is to reduce frictional resistance between surfaces with relative motion, either linear or rotational. According to some statistical data, bearing failures account for over 41% of all motor failures.35 Most mechanical breakdowns of motors are due to bearing failures. The spectrum analysis of vibration signals and shaft current can be used to detect bearing failures, and bearing temperature measurement can provide useful information about bearing health.35 Hence, monitoring bearing temperature and shaft current are the effective ways to track the evolution process of bearing damage. The FEMM of the bearing is shown in Fig. 4.

Fig. 3 Bond graph model of the shunt motor.

induced voltage; Jm is the sum of all torques acting on the mechanical load; MR is external disturbance torque; Ma is the torque of the armature; Mload is the load torque.

The state equations obtained from the bond graph model in Fig. 3 are given by the following expressions: Dissipators

ur — ra4

if — E/Rf Mr — Rmm

Modulated gyrators

W — Kif ua — Wx Ma — Wa

Energy stores

dia 1 (j7 n

-r~ — —{E - Ur - Ua)

dt La dw 1 .

dt — T M + Mload - Mr)

(8) (9)

(11) (12)

In this paper, the motor is defined at the system level, which contains the following three parts, electrical part, mechanical dynamics, and mechanical part. The electrical part includes the grid connections, the stator windings, and the rotor bars. This part converts electrical energy from the grid to mechanical energy on the shaft. The faults identified in the part are short circuit between windings in the motor, broken rotor bar, and eccentric air gab due to bend or misaligned motor shaft. The mechanical dynamics contain the mass of rotating parts in the motor. It is introduced in the functional model to cover the conversion from torque to speed. As it is not a physical component, but a functional signal transformation, no faults are identified in this component. The mechanical part of the shunt motor contains the ball bearing and the shaft of the motor. The functionality of the part is to transfer torque produced by the electrical part of the motor to the shaft connecting the load and the motor. The faults identified in this component are: bearing damage in the motor and rub impact between the stator and the rotor due to a bend or misaligned motor shaft.

The most critical failure modes in the shunt motor are categorized as: inter-turn short circuit of stator windings, broken rotor bar, and bearing damage. The FMEMECA results of the motor are presented in Appendix by means of historical data and expert knowledge.

Fig. 4 FEMM of the bearing.

Inter-turn short circuit: Insulation degradation is the main reason of inter-turn short circuit. Many researches show that stator current and temperature are the primary condition parameters indicating insulation degradation.36'37

Therefore, monitoring stator winding temperature and stator current can track the inter-turn short circuit evolution process. Its FEMM is shown in Fig. 5.

Stator

Stator current

Motor speed

Inter-turn short circuit

Failure mode

Stator current

Stator current

Stator temperature

Magnetic flux

Stator current

N Stator temperature

Fig. 5 FEMM of the stator.

Broken rotor bar: Damage of one rotor bar can cause damages of surrounding bars and thus damage can spread, leading to multiple bars' fractures. In case of crack, which occurs in a bar, the cracked bar would overheat, and this can cause the bar to break. Accordingly, the surrounding bars would carry higher current and therefore they are subjected to even larger thermal and mechanical stresses so that they may also start to crack. Experimental results show that the temperature of the rotor and the magnitude of the supply current frequency components increase as the number of broken bars increases.38 Therefore, temperature and supply current are the most sensitive condition parameters indicating broken rotor bars. The FEMM of the rotor is shown in Fig. 6.

Fig. 6 FEMM of the rotor.

For the purpose of detecting such failure mode-related signals, many condition monitoring systems have been developed so far. Chetwani et al. introduced a condition monitoring technique for motors to detect above failures.39 Through combining functional with structural information, the FEMM of the motor is shown in Fig. 7.

In this paper, the testability analysis method introduced in Section 3.2 is coded in MATLAB, thus the testability indices for PHM's purposes can be calculated.

At the component level of the motor, the testability analysis results are listed in Table 2. The results show that the FIR, FTR, and FPR are 47.7%, 0%, and 0%, respectively. In order to improve failure isolatable, trackable, and predictable levels, the symptom parameters related to these failure modes in the UIF, UTF, and UPF must be monitored.

Table 2 Testability analysis results for fault detection.

Parameter Value

Number of failure modes 3

Number of failure symptom parameters 7

Number of tests 3

UDF {}

UIF {/1/2}

UTF {/1/2/3}

UPF {/1/2/3}

FDR 100%

FIR 47.7%

Through analyzing the critical failure evolution mechanisms of the motor, a new FEMM is constructed in Fig. 8. By means of the reachability analysis algorithm and bond graph methodology, the FS and ST matrices are listed in Tables 3 and 4, respectively.

Similarly, the testability indices can be derived by using the testability analysis method introduced in Section 3.2 and the analysis results are listed in Table 5. Results show that the FEMM of the motor, which can describe the PHM-related information, would provide a guide for designers to evaluate the testability level of PHM systems, and optimize the DFT according to the inherent testability analysis results.

Shunt motor

Test on temparature

G2>.....

Rotor current

Load torque

Mechanical dynamics Bearing

Test on stator current

Test on bearing vibration

Load torque

Fig. 7 FEMM of the motor for fault detection.

Shunt motor

Supply current

Test on temparature 0*

Test on supply current

...........r<y

Load torque

Rotor current

Stator Stator current ]— M

Mechanical dynamics

Bearing

Torque

Test on stator temparature

Motor speed

Test on stator current

Load torque

.....i 'X ©

— Test on sh

Test on bearing Test on bearing current

vibration

temparature

Fig. 8 FEMM of the motor for health monitoring.

Table 3 FS matrix.

Failure mode Failure symptom parameters

s1 s2 s3 s4 s5 s6 s7

Stator Stator Rotor Supply current Bearing vibration Bearing temperature Shaft current

temperature current temperature

Inter-turn short circuit f 1 1 0 0 0 0 0

Broken rotor-bar f2 0 1 1 1 0 0 0

Bearing damage f3 0 0 0 0 1 1 1

Table 4 ST matrix.

Failure symptom parameters Tests

t1 t2 t3 t4 t5 t6 t7

Stator temperature s1 0 0 0 +1 0 0 0

Stator current s2 + 1 + 1 +1 +1 +1 0 + 1

Rotor temperature s3 0 + 1 0 0 0 0 0

Supply current s4 + 1 + 1 0 +1 + 1 + 1 + 1

Bearing vibration s5 0 0 + 1 0 0 0 0

Bearing temperature s6 0 0 0 0 0 + 1 0

Shaft current s7 0 0 0 0 0 + 1 + 1

Table 5 Results of testability analysis.

Parameter Value

Number of failure modes 3

Number of failure symptom parameters 7

Number of tests 7

UDF {}

UIF {}

UTF {}

UPF {}

FDR 100%

FIR 100%

FTR 100%

FPR 100%

5. Conclusions

For new requirements of testability modeling for PHM systems, this paper develops a novel approach of testability modeling based on failure evolution mechanisms, which is critical to improve the ability of health monitoring for PHM systems, improve system reliability, and reduce the cost of system operations. Compared with the traditional modeling methods, the main advantages of the FEMM proposed in this paper are as follows:

(1) Due to the lack of the information related to fault progression in a failure evolution process, traditional models cannot describe the fault progression-test dependency. In the FEMM, the fault symptom parameters related to fault progression are used to describe it by means of FMEMECA. Obviously, the FEMM includes more information related to fault progression which is important for accurate fault prognosis and health state evaluation.

(2) For mechanical subsystems in complex aerospace systems, the Boolean FT matrix of traditional dependency models suffers from inaccuracy. The FEMM describes the fault progression-test dependency based on FS and

ST matrices. The FS matrix presents the dependency of failures and fault symptom parameters related to fault progression which can provide a guide for health monitoring in order to track the fault evolution process prior to total failure. The ST matrix analyzes the effects of system level parameters on fault symptoms of component level. The two matrices can assist in analyzing the fault trackability of systems.

(3) Traditional testability indices such as FDR and FIR which aim at guiding DFT for fault diagnosis cannot meet the requirements of failure prognosis and health state evaluation of PHM systems. In this paper, some new testability indices based on the FEMM such as FTR and FPR are developed to describe the trackability for the failure evolution process and failure predictability, respectively. The analysis results can help to optimize the DFT in order to improve PHM performance.

The experimental results show that the FEMM and testability analysis for PHM's purposes provide a guide for designers to improve PHM performance. At the same time, the FEMM is the base of health-state evaluations and can assist in optimizing sensor placement for minimizing test cost and time.

At present, a software toolbox called testability analysis and design software (TADS) which is targeted at realizing the modeling technique of FEMM and the testability analysis method proposed in this paper is developed. The future study will focus on applying TADS in complex aerospace systems and improving the technique for other engineering systems. Moreover, we will develop the functions of the model by adding applicable prognostics methods, such as data-driven methods (e.g., artificial neural networks, hidden Markov model, and support vector machine), PoF-based methods, for critical failures or UUTs. The outcomes of tests corresponding to failure symptom parameters of each critical failure in the FEMM and historical data could be input into the corresponding prognostic models, and then the failure prognostics could be realized.

Table A1 FMEMECA of the shunt motor.

Code Component name Function Basic information of failure mode Failure effects

Failure mode Severity Occurrence

fi Stator Generates magnetic field In-turn Short circuits II 1.0 x 106 Oscillations in the length

of the pack transform

current

f2 Rotor Transforms electrical Broken rotor bar II 3.5 x 106 Higher harmonic torque

signals to torque 4.1 x 106 oscillations

f3 Bearing Reduces frictional Bearing damage I Increase bearing

resistance temperature, increased

higher harmonic

vibration

Failure evolution analysis Failure diagnostics Failure prognostics

Failure type Failure symptoms Condition parameters Sensor placement method method

fi Gradual failure Current abnormity, Stator current and Stator circuit Signal-based Model-based

increased temperature temperature

inside the motor

f2 Gradual failure Current abnormity, Stator current and Rotor circuit Signal-based Model-based

torque oscillations torque

f3 Gradual failure Bearing temperature Bearing temperature, Bearing Signal-based Model-based

increase, higher vibration, shaft current

harmonic vibration

increase

Acknowledgement

This research is partially supported by the National Natural Science Foundation of China (No. 51175502).

Appendix A. The FMEMECA of the shunt motor

References

1. Hess A, Fila L. The joint strike fighter (JSF) PHM concept: potential impact on aging aircraft problems. In: IEEE proceedings of aerospace conference; 2002. p. 3021-6.

2. Kalgren PW, Byington CS, Roemer MJ, Watson MJ. Defining PHM, a lexical evolution of maintenance and logistics. In: Systems readiness technology conference; 2006. p. 353-8.

3. Orsagh RF, Brown DW, Kalgren PW, Byington CS, Hess AJ, Dabney T. Prognostic health management for avionic systems. In: Proceedings of the IEEE aerospace conference; 2006. p. 1-7.

4. Vichare N, Pecht M. Prognostics and health management of electronics. IEEE Trans Compon Packag Technol 2006;29(1):222-9.

5. Sheppard JW. Maintaining diagnostic truth with information flow models. In: Conference record of test technology and commercialization; 1996. p. 447-54.

6. Deb S, Pattipati KR, Raghavan V, Shakeri M, Shrestha R. Multisignal flow graphs: a novel approach for system testability analysis and fault diagnosis. Aerosp Electron Syst Mag 1995;10(5):14-25.

7. William RS, Harold SB. The ARINC research system testability and maintenance program (STAMP). In: Proceedings of the IEEE AUTOTESTCON conference; 1982. p. 88-95.

8. William RS, Sheppard JW, Unkle CR. POINTER-an intelligent maintenance aid. In: Proceeding of the IEEE AUTOTESTCON conference; 1989. p. 26-31.

9. Lin CJ, Hayes L, Malais A, Kelley B, Prasad P. A new dependency model based testability analyzer. In: Proceeding of the IEEE AUTOTESTCON conference; 1998. p. 187-91.

10. Pattipati KR, Raghavan V, Shakeri M, Deb S, Shrestha R. TEAMS: testability engineering and maintenance system. In: Proceeding of the American control conference; 1994. p. 198995.

11. Hess A, Stecki JS, Rudov-Clark SD. The maintenance aware design environment: development of an aerospace PHM software tool. In: Proc. PHM08; 2008.

12. Rudov-Clark S D, Stecki JS. The language of FMEA: on the effective use and reuse of FMEA data. In: AIAC-13 thirteenth Australian international aerospace congress; 2009.

13. Stone RB, Wood KL. Development of a functional basis for design. J Mech Des 2000;122(4):359-70.

14. Dugan JB, Sullivan KJ, Coppit D. Developing a low cost high-quality software tool for dynamic fault-tree analysis. IEEE Trans Reliab 2000;49(1):49-59.

15. Wu YF, Wei ZX. Fuzzy petri net for fault diagnosis. Chin J Aeronaut 1995;8(4):305-12.

16. Kurtoglu T, Tumer IY. A graph-based fault identification and propagation framework for functional design ofcomplex system. J Mech Des 2008;130(5):1-8.

17. Zhang Y, Qiu J, Liu GJ, Yang P. Integrated function-fault-behavior-test-environment model for virtual testability verification. Acta Aeronaut Astronaut Sin 2012;33(2):273-86 [Chinese].

18. Yang SM, Qiu J, Liu GJ, Yang P. A hierarchical modelbased approach to testability modeling and analysis for PHM of aerospace systems. J Aerosp Eng 2012, in press.

19. Shakeri M. Advances in system fault modeling and diagnosis dissertation. Storrs: University of Connecticut; 1996.

20. Kacprzynski GJ, Roemer MJ, Hess AJ, Bladen KR. Extending FMECA-health management design optimization for aerospace applications. In: IEEE proceedings of aerospace conference; 2001. p. 3105-12.

21. Gu J, Pecht M. Prognostics and health management using physics-of-failure. In: Reliability and maintainability symposium annual; 2008. p. 481-7.

22. Gorjian N, Ma L, Mittinty M, Yarlagadda P, Sun Y. A review on degradation models in reliability analysis. In: Proceedings of the 4th world congress on engineering asset management; 2009. p. 36984.

23. Doyle BS, Mistry KR. A lifetime prediction method for hot-carrier degradation in surface-channel p-MOS devices. IEEE Trans Electron Devices 1990;37(5):1301-7.

24. Rudov-Clark S, Ryan A, Stecki C, Stecki J, Hess A. Extending advanced failure effects analysis to support prognostics and health management. In: 2010 Prognostic & system health management conference; 2010.

25. Kumar S, Dolev E, Pecht M. Parameter selection for health monitoring of electronic products. Microelectron Reliab 2010;50(2): 161-8.

26. Gu J, Lau D, Pecht M. Health assessment and prognostics of electronic products. In: 8th International conference on reliability, maintenance and safety; 2009.

27. Shi JY, Ji C. Study on enhanced FMECA method application. Meas Control Technol 2011;30(5):110-4 [Chinese].

28. Borutzky W. Bond graph modeling and simulation of mechatronic systems: an introduction into the methodology. In: 20th European conference on modeling and, simulation; 2006.

29. Broenink J F. Introduction to physical systems modeling with bond graphs. Technical report, University of Twente; 1999.

30. Chang BL, Danwei W, Shai A, Ming L. Quantitative hybrid bond graph-based fault detection and isolation. IEEE Trans Autom Sci Eng 2010;7(3):558-69.

31. Tian Z, Shi JY. System testability design, analysis and verification. Beijing: Beihang University Press; 2003 [Chinese].

32. Shi JY. Testability design analysis and verification. Beijing: National Defense Industry Press; 2010 [Chinese].

33. Schoen RR, Lin BK, Habetler TG, Schlag JH, Farag S. An unsupervised, on-line system for induction motor fault detection using stator current monitoring. IEEE Trans Ind Appl 1995;31(6): 1280-6.

34. Frederic CT, Sottile J, Kohler JL. Online condition monitoring of induction motors. IEEE Trans Ind Appl 2002;38(6):1627-32.

35. Martin B, Pierre G, Bertrand R. Models for bearing damage detection in induction motors using stator current monitoring. IEEE Trans Ind Electron 2004;55(4):1-6.

36. Thomson WT. On-line MCSA to diagnose shorted turns in low voltage stator windings of three-phase induction motors prior to failure. In: Proceedings of IEEE international electric machines and drives conference; 2001. p. 891-8.

37. Siddique A, Yadava GS, Singh B. A review of stator fault monitoring techniques of induction motors. IEEE Trans Energy Convers 2005;20(1):106-14.

38. Zhang R, Wang XH. On-line broken-bar fault diagnosis system of induction motor. Trans Tianjin Univ 2008;14(2):144-7.

39. Chetwani SH, Shah MK, Ramamoorty M. Online condition monitoring of induction motors through signal processing. In: Proceedings of the eighth international conference on electrical machines and systems, vol. 3; 2005. p. 2175-9.

Tan Xiaodong received his B.S. degree in mechanical engineer from Northeast University, Shenyang, China, in 2006, and M.S degree from National University of Defense Technology (NUDT), Changsha, China, in 2009. Since 2009, he has worked toward a Ph.D. degree in the College of Mechatronics Engineering and Automation. His research interests include design for testability, prognostics and health management, etc.

Qiu Jing received his B.S. degree in mechanical engineer from Beihang University, Beijing, China, in 1985, M.S and Ph.D. degrees from NUDT, in 1988 and 1998, respectively. Since 2000, he has been with NUDT, where he is a professor of mechanical engineering. He has published over 100 articles, primarily on condition monitoring, fault diagnosis techniques, and technologies of decreasing false alarms. His current research interests include fault diagnosis, reliability, testability, maintenance for complex systems, etc.

Liu Guanjun received his B.S. and Ph.D. degrees in mechanical engineer from NUDT in 1994 and 2000, respectively. Since 2000, he has been with NUDT, where he is an associate professor of Mechanical Engineering. He has published over 100 articles, primarily on condition monitoring, fault diagnosis techniques, and technologies of decreasing false alarms. His research interests include fault diagnosis, testability, maintenance, etc.

Lv Kehong received his B.S. degree in 2001 from Xi'an Jiaotong University, Xi'an, China, M.S. and Ph.D. degrees from National University of Defense Technology in 2003 and 2008, respectively. His research interests include condition monitoring, fault diagnosis techniques, technologies of decreasing false alarms, etc.

Yang Shuming received his B.S. degree in 2005 from Central South University. He is a Ph.D. student at National University of Defense Technology. His research interests include testability, design for testability, prognostics and health management, etc.

Wang Chao received his B.S. degree in 2007 from Zhengzhou University, Zhengzhou, China, and M.S degrees from National University of Defense Technology in 2009. His research interests include fault diagnosis techniques and Bayesian Theory and Application.