Fault isolation

In online FDI, the coherence vector is computed at every sampling step. If it is not a null vector, a fault is detected and an alarm is raised. Clearly, detectability is a necessary condition for a fault to be isolated. In order to simplify the task of isolating the fault, often a single fault hypothesis is adopted. It is assumed that more than one fault have not occurred simultaneously, that only one single fault may occur at a time. 

4 Bond Graph Model-based Quantitative FDI in Hybrid Systems 

This also means that faults do not cancel each other in their effect on an ARR residual. Given a single fault hypothesis, the faulty component is identified by comparing the coherence vector against the rows of the FSM, i.e. the component fault signatures. If this comparison results in a match, the faulty component is isolated. However, there may be no match, or more than one match may be obtained. That is, the faulty component cannot be isolated. In the case of multiple simultaneous faults, FDI can be performed e.g. by means of parameter estimation as is discussed in Chap. 6. 

If the number of fault candidates exceeds the number of sensors, structured residuals cannot be obtained. In that case, the FSM is non-square, rows, i.e. some component fault signatures are identical and not all faults can be isolated. More faults may be isolated by adding more detectors to the model if the real system permits to attach more real sensors. 

Moreover, as to hybrid system models, the previously considered examples show that fault detectability and isolability is mode dependent. As can be seen from the FSM in Table4.2, faults in some components may be detectable in all modes, e.g. a faulty capacitance in the switched network of Fig. 3.4, while other faults can only be detected in some modes, such as faulty resistances R and R2. (Wang et al. call such faults weakly detectable [9].) It may also be possible that a fault cannot be detected in none of the system modes. Similar observations can be made with regard to fault isolation bearing in mind that a necessary condition for a fault to be isolated is that it can be detected. 

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These two simple examples highlight how an uncertainty managing framework like Evidence theory can improve fault isolation performances. 

Table 3. Fault isolation performances of the Evidence theory based FDI system...

Several kinds of failures may compromise safety and productivity of industrial processes. Indeed, faults may affect the efficiency of the process (e.g., lower product quality) or, in the worst scenarios, could lead to fatal accidents (e.g., temperature runaway) with injuries to personnel, environmental pollution, and equipments damage. In the chemical process fault diagnosis area, the term fault is generally defined as a departure from an acceptable range of an observed variable or a parameter. Fault diagnosis (FD) consists of three main tasks fault detection, i.e., the detection of the occurrence of a fault, fault isolation, i.e., the determination of the type and/or the location of the fault, and fault identification, i.e., the determination of the fault profile. After a fault has been detected, controller reconfiguration for the self-correction of the fault effects (fault accommodation) can be achieved in some cases. 

Since perfect knowledge of the model is rarely a reasonable assumption, soft computing methods, integrating quantitative and qualitative modeling information, have been developed to improve the performance of observer-based schemes for uncertain systems [36], Major contributions to observer-based approaches can be found in [39, 56] as well, where fault isolation is achieved via a bank of observers, while identification is based on the adoption of online universal interpolators (e.g., ANNs whose weights are updated on line). As for the use of observers in the presence of advanced control techniques, such as MPC or FLC, in [44] an unknown input observer is adopted in conjunction with an MPC scheme. 

Approaches based on parameter estimation assume that the faults lead to detectable changes of physical system parameters. Therefore, FD can be pursued by comparing the estimates of the system parameters with the nominal values obtained in healthy conditions. The operative procedure, originally established in [23], requires an accurate model of the process (including a reliable nominal estimate of the model parameters) and the determination of the relationship between model parameters and physical parameters. Then, an online estimation of the process parameters is performed on the basis of available measures. This approach, of course, might reveal ineffective when the parameter estimation technique requires solution to a nonlinear optimization problem. In such cases, reduced-order or simplified mathematical models may be used, at the expense of accuracy and robustness. Moreover, fault isolation could be difficult to achieve, since model parameters cannot always be converted back into corresponding physical parameters, and thus the influence of each physical parameters on the residuals could not be easily determined. 

Whilst a single residual may be sufficient to detect faults, a vector of residuals is usually required for fault isolation. For isolation purposes, structured residuals [8, 17] can be generated, i.e., each residual is affected only by a specific subset of faults, and each fault only affects a specific subset of residuals. This concept can be expressed in a mathematical form by introducing a boolean fault code vector and a boolean structure matrix [8],... 

A suitable designed diagnostic system, together with a Decision Making System (DMS), declares the occurrence of a fault, isolates the possible faulty sensor, and outputs an healthy signal. 

Then, the healthy signal is used to feed a bank of /Vp + 1 nonlinear adaptive observers (where /Vp is the number of the possible process/actuator faults). The first observer is in charge of detecting the occurrence of process/actuator faults. The other /Vp observers, each corresponding to a particular type of process/actuator fault, achieve fault isolation and identification by adopting a suitable adaption mechanism. Figure 6.3 shows a block diagram representation of the overall architecture. 

Step 2. If, in case (b), fault isolation is not achieved (i.e., both rsMi II and / sm2II are below the respective thresholds), a missed isolation is declared. In this case, the weighted average of the signals provided by the physical and virtual sensors is voted. The weighted average is computed as the arithmetic mean of the measured variable and the output of the sole observer not signaling the occurrence of the fault. 

To achieve fault isolation, the following residuals are computed ... 

Figures 6.13 and 6.14 report the results obtained when a fault of type 1 has been simulated, with ry = 300 s, Sy = —0.5 kJ s-1 K-1 m-2, and /[ = 5000 s. Figure 6.13 shows that the fault is detected and identified, i.e., its magnitude is correctly estimated moreover, Fig. 6.14 shows that only the residuals output of the first observer remains always below the threshold, whereas the other two residuals exceed their corresponding thresholds a few minutes after ff, thus achieving fault isolation.

Figures 6.17 and 6.18 report the results obtained in the presence of a fault of type 3, with ru = 600 s, Su = 10 K, and = 14000 s. Figure 6.17 shows that the fault has been detected and its magnitude correctly estimated, while isolation residuals in Fig. 6.18 show that fault isolation is achieved as well.

Fig. 6.22 Sensor Sr, 2 and thermal insulation faults isolation residuals for the thermal insulation fault...

Pilots immediately aware of malfunction (either through failure flag or totally off-line ) and will cross refer to standby display for fault isolation... 

Static/Dynamic Scheduling, Timing Constraints, SAV Fault Isolation... 

The enterprise assesses the testability of design alternatives to determine built-in test (BIT) and/or fault-isolation test (FIT) requirements to support operational or maintenance considerations. BIT-FIT mechanisms should be provided for those elements that are normally maintained by the operators, customer, or field support engineers. BIT-FIT can be used for diagnostic operations to support lower-level maintenance actions. 

Diistegor D., Frisk E., Cocquempot V., Krysander M., Staroswieki M. 2006, Stmctural Analysis of Fault Isolability in the DAMADICS Benchmark, In Control Engineering Practice. Vol 14, issue 6, pp. 597-608... 

Fault detection means to decide whether a fault has happened or not and to determine the time instant at which a fault has occurred. Fault isolation aims at finding the component in which a detected fault has occurred. Once a fault has been detected and... 

Samantaray, A. K., Ghoshal, S. K. (2007). Sensitivity bond graph approach to multiple fault isolation through parameter estimation. Proceedings of the Institution ofMechanical Engineers Part I Journal of Systems and Control Engineering, 221(4), 577-587. 

On the basis of a single fault hypothesis, fault isolation is performed by comparing the periodically updated coherence vector with the rows of the FSM. However, for a hybrid system model, the entries of a FSM are mode dependent. For a model with Ks switches, < 2 physical feasible switch state combinations, i.e. n/ system modes are to be considered. The FSM holding for all modes provides a specific FSM for each mode. To make sure that the coherence vector is compared with the component fault signatures in the right FSM, the current system mode of operation must be identified from measured system or process outputs. Figure4.7 depicts a flowchart of a bond graph model-based FDI process. 

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