Robust Fault Detection with Interval Valued Uncertainties 

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Background, Tools and Techniques

This chapter introduces the concept of condition based maintenance, diagnostics and prognostics. Emphasis is laid upon the suitability and relation of prognostics with diagnostics techniques. Diagnostic approaches are reviewed and special emphasis is laid upon BG based diagnostic techniques, for which extensive literature review is provided. BG-LFT enabled robust diagnosis is discussed in a detailed manner and the associated limitations are also highlighted. Additionally, the bounding approaches and interval based approaches are reviewed. This way, the motivations for integration of the benefits of BG LFT method and interval based approaches is highlighted. Thereafter, the concept of prognostics is disused and an extensive review is provided for prognostics related works. In particular, model based prognostic approaches and hybrid prognostics are reviewed in detail. Prognostics based upon Bayesian techniques is discussed. Moreover, the existing approaches of prognostics in BG framework are provided and significant limitations are discussed. As such, the motivations for development of efficient prognostics in BG framework are highlighted and justified.

Condition Based Maintenance

Traditionally, two kinds of maintenance philosophies have been employed over critical equipment or component of a system; preventive or corrective. Preventive measures refer to approaches that use time based intervals to schedule the maintenance activities. On the contrary, corrective measures translate to such actions that are applied to restore the health of the critical component after it has failed, or functions outside the prescribed functionality limits. As such, the use of preventive approaches often lead to conservative estimates regarding the likelihood of equipment failure and result in their replacement long before they may fail in reality. The common characteristic of both the approaches remains in non-consideration of the ―actual‖ condition of the component, for planning the maintenance actions. Due to the associated limitations, both the approaches are costly for the industries as the systems become more and more complex and expensive, as shown in Fig. 1.1. As such, the need to reduce maintenance costs, minimize the risk of catastrophic failures, and maximize system availability has led to a new maintenance philosophy.
Condition-based maintenance (CBM), or predictive maintenance, represents a new maintenance philosophy, where maintenance activities are only performed when there is objective evidence of an impending fault or failure condition, whilst also ensuring safety, reliability, and reducing overall total life costs (Bengtsson, 2004).
The goal of a CBM approach remains in optimization of the overall maintenance and logistic costs by performing the maintenance actions only in case of abnormal behavior of the component or system. As such, there is a huge shift in the maintenance approach towards CBM which provides reduced number of scheduled preventative actions, minimized requirement and cost of inventory maintenance of spare parts, whilst also avoiding, potentially catastrophic, in-service equipment failures (Vachtsevanos, George et al., 2007).
Fig. 1.1 Cost associated with different maintenance approaches (Lebold et al., 2003)
CBM is a maintenance strategy whereby equipment is maintained according to its condition, rather than on an elapsed time or running hour’s basis and thus, involves monitoring of system data to provide an accurate assessment of the health, or state, of a component/system. It is followed by maintenance activities based on its observed health. It involves using real-time system monitoring and data processing. A CBM program consists of three key steps (Jardine et al., 2006), as shown in :
1. Data acquisition step (collection of information), to obtain data relevant to the system health.
2. Data processing step to handle and analyze the data or signals collected in Step 1 for better understanding of the data.

Maintenance decision-making step to recommend efficient maintenance policies.

Fig. 1.2. Three basic steps of BBM program (Jardine et al., 2006).
The two main pillars of condition based maintenance strategy are diagnostics and prognostics. Diagnostics involves identifying the root cause of a problem whereby the problem has already occurred and Prognostics involves predicting the future health of the equipment either before or after a problem occurred (Jardine et al., 2006). Moreover, as stated in Sikorska et al. (Sikorska et al., 2011), diagnostics involves identifying and quantifying the damage that has occurred (and is thus retrospective in nature), while prognostics is concerned with prediction of the damage that is yet to occur.
Irrespective of the objectives of any CBM program, the three key steps of CBM given in Fig. 1.2 are always followed to accomplish the goals of Diagnostics and Prognostics. The three basic steps are discussed in very brief here. They can be found detailed in Jardine et al. (Jardine et al., 2006) and the references therein.
• Data acquisition is a process of collecting and storing useful data (information) and forms an essential step in implementation.
• A CBM program for machinery fault (or failure, which is usually caused by one or more machinery faults) diagnostics and prognostics. Data collected can be categorized into two main types: the event data and condition monitoring data. The former includes the information on what happened (e.g., installation, breakdown, overhaul, etc., and what the causes were) and/or what was done (e.g., minor repair, preventive maintenance, oil change, etc.) to the component/system. Such data is useful in assessing the performance of current health indicators and can even be used either as feedback to the system designer for consideration of system redesign or improvement of condition indicators. Condition monitoring data are the measurements related to the health condition/state of the component/system (Jardine 11 et al., 2006), which include but not limited to vibration data, acoustic data, oil analysis data, temperature, pressure, moisture, humidity, weather or environment data, etc.
• Data processing comprises of cleaning, processing and potentially outlier data reduction in the data collected in raw format, before any informed decision can be made based on this data. Cleaning includes removing wrongly assigned failure modes to certain events data, removing NaNs (Not a Number Values), outliers etc. Sophisticated statistical and signal processing techniques can also be utilized to extract useful information from the data that are otherwise hidden within.
• Decision Making step is about issuing a recommendation over the over-all health of the component/system. It generally involves an intrusive or nonintrusive actions (Vachtsevanos, George et al., 2007). For instance, a data set reflecting that the system is operating outside the recommended limits of functionalities would call for change of its operating routines, whereas at the later stage of fault development it would result in its replacement.

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The foundation of a CBM approach is based upon robust and reliable fault diagnostic capabilities. Fault diagnostic algorithms are designed to detect system performance, monitor degradation levels, and identify faults (failures) based on physical property changes, through detectable phenomena (Vachtsevanos, George et al., 2007).
The term fault diagnostics is typically used to describe a broad range of capabilities that include, generally, the following three kinds of basic tasks (Vachtsevanos, George et al., 2007):
• Fault detection: This step involves identifying the occurrence of a fault, or failure, in a monitored system, or the identification of abnormal behavior which may indicate a fault condition.
• Fault isolation: This step involves identifying which component/subsystem/system has a fault condition, or has attained the failure state.
• Fault identification: It involves determining the nature and extent of the fault.
In the context of CBM, following questions should be answered by the diagnostic process involved (Sikorska et al., 2011):
1. Whether the component/system is in degraded state?
2. Which failure mode has initiated the degradation?
3. How severe is the degradation?
Compared to prognostic methods, there is a vast amount of available literature that throws light upon various kinds of diagnostic methods, including theory and practical applications. The different approaches of diagnostics are described in Section 1.4, laying major main emphasis on model based approaches, which form the center of this work’s contribution.


Prognostics is derived from the Greek word Prognostikos and means foreknowing or fore-seeing. ISO13381-1 defines prognostics as: ―the estimation of time to failure and risk for one or more existing and future failure modes‖.
As detailed in Vachtsevanos et al. (Vachtsevanos, George et al., 2007), prognostics promises to produce major improvements over the traditional maintenance approaches, including both reduced operational and support (O&S) costs and complete life-cycle total ownership costs (TOC). ―With the provision of a sufficient lead-time between the detection of an incipient fault condition and the occurrence of equipment failure, maintenance actions can become proactive instead of reactive, allowing necessary remedial maintenance work to be planned in advance‖ (Vachtsevanos, George et al., 2007). This is on contrary to more traditional maintenance approaches, in which equipment failure typically occurs without prior notice, leading to delays in organizing the necessary personnel, spares, and tools, necessary to return the equipment to good health.
In last one decade, with on-growing rapid research in the area of prognostics, a lot of definitions have been proposed as tabulated in Table 1-I. They essentially imply that (Sikorska et al., 2011):
1. Prognostics involves predicting the time progression of a specific failure mode from its incipience to the time of component failure (Sikorska et al., 2011).
2. Prognostics is related to, but not same as, diagnostics.
3. Prognostics requires the consideration of :
i. existing failure modes and deterioration rates.
ii. initiation criteria for future failure modes.
iii. Inter-relationship between failure modes and their deterioration rates.
iv. the effect of maintenance on failure degradations
v. the conditions and assumptions underlying the prognostic approach
To realize the benefits of prognostic capabilities, a reliable estimate of how long a system can continue to be operated safely, i.e. the remaining useful life (RUL) of the system, until a detected fault condition progresses to a failure condition, is sought. Since prognostics is associated with predicting the future, it inherently involves a large degree of uncertainty (Vachtsevanos, George et al., 2007). Indeed, the task of prognostics is considered to be significantly more difficult task than diagnostics, since the evolution of equipment fault conditions is subject to stochastic processes which have not yet happened (Engel et al., 2000).
In essence, the degradation process undergone by the component from a healthy state to the failure state must be studied to predict at any time the RUL. Consider Fig. 1.3 that shows degradation curves for three different failure modes that may correspond to different component degradation in system (e.g. bearing wear, frictional wear, electrical resistance drift etc.) or same component degradation but of dissimilar kind (e.g. inner race spall, outer race spall, cage crack in a rolling element bearing). Each degradation pattern may vary depending upon the factors that trigger the damage process and may follow a variable degradation pattern (even under the same environmental conditions and operational routines). Anomalous events may modify the deterioration rate and thus, can accelerate or slow down the degradation process.
In face of all such conditions, the prognostic procedures must be able to answer the one important question: How much time remains before the component achieves the state of failure. In other words, determining accurate and reliable RUL estimate forms the core objective of any prognostic procedure.

Table of contents :

1. Background, Tools and Techniques 
1.1 Condition Based Maintenance
1.1.1 Diagnostics
1.1.2 Prognostics
1.2 Prognostics and Health Management
1.3 The Diagnostics-Prognostics Process
1.4 Diagnostics Approaches
1.5 Approaches of Prognostics
1.6 Conclusions
2. Robust Fault Detection with Interval Valued Uncertainties 
2.1 Assumptions
2.2 Interval Arithmetic: A Brief Discussion
2.3 Modelling Uncertainties as Intervals
2.3.1 Measurement Uncertainty
2.4 Interval Valued Analytical Redundancy Relations
2.5 Interval Valued Robust Thresholds
2.6 Application: Robust Fault Detection of Steam Generator System
2.7 Conclusions and Contribution
3. A Methodology of Hybrid Prognostics 
3.1 Assumptions and Objectives
3.2 Degradation Model
3.3 Methodology for Hybrid Prognostics in BG Framework
3.4 Health monitoring of Prognostic Candidate
3.5 Evaluation Metrics
3.6 Case Study on Mechatronic System through Simulations
3.7 Application: Health Monitoring of Mechanical Torsion Bar System
3.8 Conclusions and Contributions
4. Hybrid Prognostics of Proton Exchange Membrane Fuel Cell 
4.1 Description of a PEMFC
4.2 Bond Graph Model of PEMFC
4.3 Generation of Deterministic ARRs and Robust Thresholds
4.5 Prognostics of the Electrical-Electrochemical Part
4.6 Conclusions and Contributions
4.7 Acknowledgements
5. General Conclusions and Perspectives 


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