System mode identification

In online model-based FDI, ARRs are evaluated using measurements from the real system being subject to disturbances. The time evolution of ARR residuals serve as fault indicators. For hybrid systems, ARRs are system mode dependent. Hence, an unobserved mode change invalidates the actual set of ARRs. As a result, computed values of fault indicators may exceed current thresholds indicating faults in some system components that have not happened. ARR residuals derived from a bond graph can not only serve as fault indicators but may also be used for model-based system mode identification. 

Chapter demonstrates that ARR residuals cannot only serve as fault indicators but may also be used for system mode identification in online FDI. First, the general case of switched LTI systems is considered and it is assumed that ARRs can be expressed in explicit form relating known system inputs and inputs either obtained by measurements or by simulation of the real system behaviour. A small example illustrates bond graph based system mode identification using ARRs. 

In order to isolate the faulty component the coherence vector is matched with the rows of the FSM, i.e with the component fault signatures. Given a hybrid system model, there is a FSM for each system mode. That is, in order to use the correct FSM for comparison, it is important to know in which mode the monitored system is at the present time point. Chapter shows that ARRs derived from a diagnostic bond graph can also be used for system mode identification. 

Furthermore, an all-mode structural FSM holds for all modes. That is, from this FSM one FSM for each mode can be obtained. In online FDI, the current system mode must be identified from measured system outputs in order to use the correct FSM. Chapter presents an ARR-based approach to system mode identification. 

Bond Graph Based System Mode Identification Using ARRs... 

Alternatively, a DBG with non-ideal switches and mode invariant causalities can be developed that holds for all system modes. It is assumed that the system under consideration is healthy and that no faults occur during system mode identification. For simplicity it is assumed that mode dependent ARRs in closed symbolic form can be deduced from the DBG. Let s be the number of switches in the model and / < V the number of physically feasible switch state combinations, i.e. denotes the number of system modes. Furthermore, let u = (u U2 - un) be the vector of N known system inputs and y = (yi Jm) the vector of M inputs into a DBG either obtained by measurements from the real system or by evaluating a behavioural model of the real system. Then each ARR residual n(r), / = 1, is the weighted sum of known system inputs, known measurements and derivatives of measurements. 

For each of the technically feasible system modes, there is a set of ARRs. Some of them may be system mode independent and can be discarded with regard to system mode identification. Furthermore, for each sampled time instant t, the weighting factors and are constants. 

This system mode identification may require considerable computational costs especially if ARRs cannot be deduced in closed symbolic form so that the entire DBG model is to be evaluated to obtain numerically the time history of ARR residuals. However, as it is one and same the problem with different sets of discrete switch state variables, this computation can be easily and efficiently performed in parallel on multicore processors or multiprocessor computers. 

For these reasons, in the following, it is assumed that no parametric faults happen during system mode identification and that an initial system mode is known. System mode identification in the presence of faults is more difficult. In [4], Arogeti et al. present an advanced method for this more general case that categorises ARRs into different types and provides a refined set of fault candidates to the fault parameter estimation procedure. Multiple fault detection, isolation and identification for hybrid systems with no available information on the nature of faults (abrupt or incipient) and on system mode changes has been recently addressed in [5],... 

ARRs derived from hybrid system models are mode-dependent. For ARR-based FDI it is therefore necessary to know the current system mode so that ARRs with the correct set of discrete switch state values are evaluated. When ARR residuals are outside admissible parameter uncertainty bounds it is not clear whether a parametric fault has occurred or a mode change has happened. If a mode change has happened then an evaluation of ARRs with the discrete switch states of the last known mode yields wrong and misleading results. This chapter considers system mode identification for healthy systems only. For the more complex case of system mode changes in the presence of faults, it is suggested to see latest publications, e.g. [4],... 

The current system mode of a healthy system can be identified by evaluating all ARRs for all feasible switch state combinations. This may require considerable computational effort. The computational time, however, can be reduced by distributing the task on multiple parallel processors. Moreover, this task is only necessary if an initial system mode is not known or if the last known system mode is no longer valid because rapid system modes have taken place while system mode identification is still in progress. Once the current system mode is known, the all-mode FSM can be consulted to identify a subset of ARRs that is to be evaluated to identify the new current system. This has been illustrated by application to a simple circuit with three semiconductor switches. 

Borutzky, W. (2014). Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems. Mathematical and Computer Modelling of Dynamical Systems, 20(06), 585-616. 

The previous chapters address various aspects of quantitative bond graph-based FDI and system mode identification for systems represented by a hybrid model. This chapter illustrates applications of the presented methods by means of a number of small case studies. The examples chosen are widely used switched power electronic systems. Various kinds of electronic power converters, e.g. buck- or boost converters, or DC to AC converters are used in a variety of applications such as DC power supplies for electronic equipment, battery chargers, motor drives, or high voltage direct current transmission line systems [1]. 

System Mode Identification in the Case of a Healthy System... 

ARR-based system mode identification has been illustrated for the boost converter with only two modes and for the three-phase diode bridge inverter with six active... 

The focus of this book has been on the presentation of a bond graph model-based approach to FDI and failure prognosis for hybrid systems. It turns out that ARRs derived from a bond graph play a key role in all tasks that have been considered, in FDI, in system mode identification and in failure prognosis. Simulation results have been obtained by using the dassl solver as part of the open source software Scilab [5]. 

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