Syndrome-decoding algorithms for static-diagnosis models

The problem of finding fault patterns consistent with a given syndrome is discussed for graph-theoretical diagnosis models such as the fault-diagnosis and self-diagnosis models. The fault-diagnosis model consists of two types of vertices, fault units and measurements, and is expressed by a bipartite graph. Faulty states of a fault unit always imply abnormal states of all the measurements which are adjacent to the unit, otherwise a measurement remains normal. A self-diagnosis model consists of one type of unit which has the capability of testing other units and being tested itself. The testing relation is represented by a directed arc; this produces test outcomes which are invalid if the testing unit is faulty. The inverse system which yields a fault pattern from a corresponding syndrome for fault-diagnosis models is studied and a syndrome-decoding algorithm is proposed which works for some class of diagnosis models with observation noise. The algorithm uses a similar measure to the syndrome-decoding algorithm of error-correcting codes which use the Hamming distance. Another measure is presented for the self-diagnosis model expressed by a directed graph and this measure is characterized by a ranking method.     

Diagnosis model for dynamical systems Part 2. Continuous system

While most existing systems requiring diagnosis are dynamical, most models proposed for diagnosis are static. Consequently, a mathematical model of differential equations is used for a model-based diagnosis of dynamical systems. Although this model-based diagnosis has been well studied, it is not used much in practice owing to the computational difficulty and the difficulty of obtaining the mathematical model. We propose a diagnosis model for continuous dynamical systems. The model can be expressed by a signed directed-graph, which has been studied extensively in qualitative matrix theory. We interpret these qualitative results in terms of the diagnosis model, and also present new results for the model. The dynamic aspects of the qualitative stabilities of the model are mainly discussed. The distinguishability of the sign pattern is also studied with a new concept of invariant fault pattern defined in the model. Strategies for monitoring as well as for the diagnosis of the dynamical systems are derived by these qualitative results.     

A diagnosability analysis by means of fault distance

A new concept of fault distance is introduced in a failure-diagnosis model. Diagnosability measures such as t-fault diagnosability and t/s-diagnosability are expressed in terms of the fault distance. A new diagnosability measure of partial t-fault diagnosability characterized in terms of fault distance is proposed. In addition, the fault distance of various types of self-diagnosis models are expressed in graph theoretical terms. Applying the fault distance to various types of self-diagnosis models, conditions for diagnosabilities of these models, which have been studied separately, are obtained in a unified manner. Conditions for t-fault diagnosability and sufficient conditions for t/s-diagnosability are obtained with this fault distance.     

Diagnosis model for dynamical systems Part 1. Discrete system

Many static diagnosis models, which express the static relation between faults and syndrome, have been studied extensively. However, it is difficult to apply these static models to dynamical systems in which the syndrome changes dynamically. In order to construct diagnostic systems for dynamical systems, a dynamic diagnosis model that can express the dynamic relation of fault propagation should be studied. In this paper, we propose a failure propagation model which explicitly expresses some dynamic aspects of failure propagation in a system. Two concepts of dynamic diagnosabilities are defined for the model. Algorithms are presented which are designed to evaluate these diagnosabilities of the model as well as to locate a primary failure from a syndrome.     

Conditions for the delay-independent stabilization and the decay rate assignability of linear systems

In a previous paper (Amemiya 1983) two sufficient conditions were introduced for the delay-independent stabilization of linear systems by means of state-variable feedback including no delays.

In this paper the concept of delay-independently upper or lower bound of decaying rate assignability (DIUDA or DILDA) are introduced and it is proved that the two conditions previously obtained are necessary and sufficient condition for DIUDA and necessary condition for DILDA of linear systems by means of state-variable feedback including no delays. The conditions obtained are also applicable to systems including time-varying delays.     

Further condition for the delay-independent stabilization of linear systems

There are two different conditions for the delay-independent stabilization of linear systems by means of state variable feedback including no delays, one of which is also sufficient for decay rate assignability. In this paper a wider condition is presented for delay-independent stabilization. It is proved that this condition includes the conditions so far obtained