1. Technical Field
The invention relates to system monitoring apparatus employing intelligent classifiers such as neural networks responding to measured control inputs and system responses or symptoms causally related to tile control inputs for classifying the current state of the system relative to its known failure modes.
2. Background Art
References
The invention and its background will be described herein with reference to the following publications:
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Introduction
Continuous monitoring of complex dynamic systems is an increasingly important issue in diverse areas such as nuclear plant safety, production line reliability, and medical health monitoring systems. Recent, advances in both sensor technology and computational capabilities have made on-line permanent monitoring much more feasible than it was in the past.
Health monitoring of complex dynamic systems is a basic requirement in many domains where safety, reliability and longevity of the system under study are considered critical. The system of interest might be a nuclear power plant, a large antenna system, a telecommunications network or a human heart. Health monitoring can involve a variety of tasks such as detection of abnormal conditions, identification of faulty components, or prediction of impending failures. The availability at low cost of highly sensitive sensor technology, data acquisition equipment, and VLSI computational power, has made round-the-clock permanent monitoring an attractive alternative to the more traditional periodic manual inspection.
The specification will focus on the problem of accurately determining the state of the monitored system as a function of time. In particular, it is assumed that a sequence of observed sampled sensor readings .gamma. are available at uniformly-spaced discrete time intervals--without loss of generality the sampling interval is assumed to be 1. Each .gamma. is a k-dimensional measurement. Given a sequence of such sample vectors, .gamma.(t),.gamma.(t-1), . . . , .gamma.(0), the task is to infer the current state of the system at time t.
It is assumed that the system must be in one, and only one, of a finite set of m states, w.sub.i, 1.ltoreq.i.ltoreq.m, at any time. Let .OMEGA. be the discrete random variable corresponding to the (unobservable) state of the system, taking values in the set {w.sub.1, . . . , w.sub.m }. Note that the words "states" and "classes" will both be used in this specification but refer to the same thing. One of these states is deemed "normal", the other m-1 correspond to fault conditions. This assumption, that the known fault classes are mutually exclusive and exhaustive, limits the proposed method to problems where only single-faults occur at any given time and all faults can be described in advance. The first limitation, single fault detection, is a known limitation of most fault detection methods and is inherent in the underlying nature of the sensor information available and the nature of the faults themselves. For example, it is possible that in some problems, multiple faults result in predictable combinations of single fault symptoms--however, this is usually a domain specific issue and is beyond the scope of discussion in this specification. In practice, since faults are often relatively rare compared to the sampling interval at which decisions are made, the probability of two independent faults occurring within the same time interval is extremely small. It will be shown below that the second limitation, the assumption that the known faults {w.sub.2, . . . , w.sub.m } comprise the set of all faults which could potentially occur, can be relaxed in a general domain- independent manner. It is also assumed throughout that the monitoring process of the invention is entirely passive and cannot effect any changes in the system.
Background on Fault Detection for Dynamic Systems
In the typical dynamic system fault detection problem certain signals are easily and directly measurable (the "sensors") while others may be unobservable for various physical and practical reasons. For some applications, direct statistical analysis of the observed signals is sufficient to detect all faults of interest. For example, it may be sufficient to detect a change in the mean value of a time series. However, it is more typical that the observed signals must be transformed in some manner in order to infer the relevant fault information. In the ideal cause where the system dynamics and measurement process can be completely modelled in an accurate manner, a variety of optimal control-theoretic methods for fault detection can be derived using on-line state estimation and statistical analysis of the residual error signals (see Willsky [1] for an overview of such methods). FIG. 1 is a block diagram of this method where u(t) is the system input and y(t) is the observed system output.
In practice, however, particularly for large complex systems, it is common to find that the system model may not be that reliable, if indeed there is any system model available. A common technique (Isermann [2], Frank [3]) is to fit a dynamic model to the relationship between the measured input and output signals of the system. In FIG. 1, u(t) and y(t) are the measured input and output signals respectively, and v(t) represents unmeasured disturbances to the system.
The model is often a linear difference equation (in the discrete time case) relating inputs and outputs, e.g., ##EQU1## where e(t) is an additive noise term, p and q are the orders of the model, and .delta. is a delay term. In this example the observed data at time t would be .gamma.(t)={u(t),y(t)} and the model parameters would be denoted as .theta.={.alpha..sub.1, . . . , .alpha..sub.p, .beta..sub.1, . . . , .beta..sub.q }.
Typically the order or structure of the model (p and q) can be judiciously estimated based upon known system properties--however, the parameters .theta. of the model are estimated in an on-line manner using observed input/output data. The lumped parameters of the model can often be related to particular system components. Hence, fault detection occurs by observing changes in the values of the estimated parameter values of the fitted model (compared with some model of their normal condition), which in turn depend on the system components. This method has become known as the parameter method of fault detection--faults are detected by analyzing changes in the parameters of the fitted model. How much the parameter vector needs to change to be considered a real fault is the decision part of the problem and is beyond the scope of this specification, as it is a field for the application of statistical decision theory and pattern recognition (Frank [3]).
The focus of this specification is on the problem of detecting changes in the underlying system state from parameter estimates .theta.(t),.theta.(t-1), . . . using both data-derived estimates of the parameter-state dependence and prior knowledge of the temporal behavior of the system. As mentioned earlier the system is assumed to always be in one, but only one, state w.sub.i, 1.ltoreq.i.ltoreq.m, at any point in time, i.e., the states are mutually exclusive and exhaustive. It is also assumed that the distribution of parameters conditioned on a given state, p(.theta..vertline..OMEGA.=w.sub.i) (where both are measured at the same time t) is stationary, but that there may be some overlap of these state-conditional distributions. This specification will refer to the dependence p(.theta..vertline..OMEGA.=w.sub.i) as the instantaneous model between the parameters and states. In the case of complete overlap (where two or more states possess identical distributions) there is naturally no way to identify the underlying states just by observing the parameters and knowing the instantaneous model. However, as will be shown later in this specification, even when there is significant overlap in the instantaneous model, accurate state identification is still possible by taking temporal context into account using a hidden Markov model.
It will be assumed herein that the application is such that a database or fault library can be generated for both the normal class w.sub.1 and the fault classes {w.sub.2, . . . , w.sub.m }. The database consists of pairs of symptom vectors and class labels, {.theta., .OMEGA.(.theta.)}, where .theta. is the d-dimensional parameter vector estimated from the observed system data. Note that the mapping from .theta. to .OMEGA.(.theta.) need not be one-to-one, since the conditional dependence of .theta. given that .OMEGA.(.theta.)=w.sub.i is typically probabilistic in nature.
The assumption of availability of labelled training data rules out, applications where it is not possible to gather such data--perhaps no such data has been collected in tile past and it is not possible to simulate faults in a controlled manner. However, there are many applications where either a fault library already exists, or can be created under controlled conditions (perhaps by testing a particular system in a laboratory). The important point is that for fault diagnosis problems for which such symptom-fault data is readily available, standard supervised classification or discrimination methods can be used to learn a fault diagnosis model from this database.
It is important to note that the parameter estimation technique generally requires far less precise knowledge about the system than the previously-mentioned state-space approach and, hence, tends to be both more widely applicable and more robust from a practical standpoint. For example, in the case of tile antenna monitoring problem to be described later, both the presence of non-linearities and the inherent complexity of the system make it difficult to develop an accurate state-space model. In contrast, the parameter model method can be implemented with relative ease. Naturally, if there is enough knowledge of the system available such that the state-space approach is feasible, then this should give better results since it takes advantage of more information.
As an aside, mention should also be made of knowledge-based or artificial intelligence models which employ qualitative models of system behavior to detect faults. First-generation knowledge-based systems typically use experiential heuristics (described in the form of expert-supplied rules) to describe symptom-fault relationships. More sophisticated second-generation methods (under the broad heading of "model-based reasoning") use qualitative causal models of the system to represent "first-principles" knowledge (Bratko, Mozetic and Lavrac [4] and Davis [5]). In principle, this allows the system to identify faults which have never occurred before. Both approaches have limited applicability at present in terms of handling the dynamic and uncertain nature of many real-world problems. In general, the qualitative symbolic representation is not particularly robust for dealing with noisy, continuous data containing temporal dependencies. Furthermore there are many applications for which neither domain experts nor strong causal models exist, thus making the development of a knowledge-base very difficult.