Erik Frisk

Sensor Placement for Fault Diagnosis

An algorithm is developed for computing which sensors to add to meet a diagnosis requirement specification concerning fault detectability and fault isolability. The method is based only on the structural information in a model, which means that possibly large and nonlinear differential-algebraic models can be handled in an efficient manner. The approach is exemplified on a model of an industrial valve where the benefits and properties of the method are clearly shown.

Brief A minimal polynomial basis solution to residual generation for fault diagnosis in linear systems

A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the minimal polynomial basis approach can find all possible residual generators and explicitly those of minimal order.

Residual Generation for Fault Diagnosis of Systems Described by Linear Differential-Algebraic Equations

Linear residual generation for differential-algebraic equation (DAE) systems is considered within a polynomial framework where a complete characterization and parameterization of all residual generators is presented. Further, a condition for fault detectability in DAE systems is given. Based on the characterization of all residual generators, a design strategy for residual generators for DAE systems is presented. The design strategy guarantees that the resulting residual generator is sensitive to all the detectable faults and also that the residual generator is of lowest possible order. In all results derived, no assumption about observability or controllability is needed. In particular, special care has been devoted to assure the lowest-order property also for non-controllable systems

Sensor placement for fault isolation in linear differential-algebraic systems

An algorithm is proposed for computing which sensor additions make a diagnosis requirement specification regarding fault detectability and isolability attainable for a given linear differential-algebraic model. Restrictions on possible sensor locations can be given, and if the diagnosis specification is not attainable with any available sensor addition, the algorithm provides the solutions that maximize specification fulfillment. Previous approaches with similar objectives have been based on the model structure only. Since the proposed algorithm utilizes the analytical expressions, it can handle models where structural approaches fail.

Brief paper: An observer for non-linear differential-algebraic systems

In this paper, we consider design of observers for non-linear models containing both dynamic and algebraic equations, so-called differential-algebraic equations (DAE), of index 1. The observer is formulated as a DAE that, by construction, has index 1. The main results of the paper include conditions that ensure local stability of the observer error dynamics. Design methodology is presented and illustrated using a small simulation study.

A Minimal Polynomial Basis Solution to Residual Generation for Fault Diagnosis in Linear Systems

Abstract A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the minimal polynomial basis approach can find all possible residual generators, including those of minimal McMillan degree, and the solution has a minimal parameterization. It is shown that some other well known design methods, do not have these properties.

Improving fault isolability properties by structural analysis of faulty behavior models : application to the DAMADICS benchmark problem

Structural analysis is a powerful tool for early determination of detectability/isolability possibilities. It is shown how different levels of knowledge about faults can be incorporated in a structural fault-isolability analysis and how they result in different isolability properties. The results are evaluated on the DAMADICS valve benchmark model. It is also shown how to determine which faults in the benchmark that need further modeling to get desired isolability properties of the diagnosis system.

Diagnosability Analysis Considering Causal Interpretations for Differential Constraints

This paper is focused on structural approaches to study diagnosability properties given a system model taking into account, both simultaneously or separately, integral and differential causal interpretations for differential constraints. We develop a model characterization and corresponding algorithms, for studying system diagnosability using a structural decomposition that avoids generating the full set of system analytical redundancy relations. Simultaneous application of integral and differential causal interpretations for differential constraints results in a mixed causality interpretation for the system. The added power of mixed causality is demonstrated using a Reverse Osmosis Subsystem from the Advanced Water Recovery System developed at the NASA Johnson Space Center. Finally, we summarize our work and provide a discussion of the advantages of mixed causality over just derivative or just integral causality.

Fault Diagnosis Based on Causal Computations

This paper focuses on residual generation for model-based fault diagnosis. Specifically, a methodology to derive residual generators when nonlinear equations are present in the model is developed. A main result is the characterization of computation sequences that are particularly easy to implement as residual generators and that take causal information into account. An efficient algorithm, based on the model structure only, which finds all such computation sequences, is derived. Furthermore, fault detectability and isolability performances depend on the sensor configuration. Therefore, another contribution is an algorithm, also based on the model structure, that places sensors with respect to the class of residual generators that take causal information into account. The algorithms are evaluated on a complex highly nonlinear model of a fuel cell stack system. A number of residual generators that are, by construction, easy to implement are computed and provide full diagnosability performance predicted by the model.

Lowering orders of derivatives in non-linear residual generation using realization theory

Consistency relations are often used to design residual generators based on non-linear process models. A main difficulty is that they generally include time differentiated versions of known signals which are difficult to estimate in a noisy environment. The main results of this paper show how to lower the need to estimate derivatives of known signals in order to compute a residual. Necessary and sufficient conditions for lowering the order of the derivatives in one step are presented and a main step in the approach is to obtain a state-space realization of the residual generator. An attractive feature of the approach is that general differential algebraic system descriptions can be handled in the same way as for example ordinary differential equations and also that stability of the residual generator is always guaranteed.