From: AAAI Technical Report SS-99-04. Compilation copyright © 1999, AAAI (www.aaai.org). All rights reserved. Fault Prognosis Using Dynamic Wavelet Neural Networks P. Wang and G. Vachtsevanos School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 Email: [email protected] Abstract and, in certain cases, almost impossible to identify and localize in a timely manner. Scheduled maintenance Large manufacturing companies are practices tend to reduce machine lifetime and increase considering to deliver to their customer base down-time, resulting in loss of productivity. Recent “guaranteed uptime” instead of the conventional advances in instrumentation, telecommunications and service contracts. Modern industry is concerned computing are making available to manufacturing about extending the lifetime of its critical processes companies new sensors and sensing strategies, plant-wide and maintaining them only when required. networking and information technologies that are assisting Significant aspects of these trends include the to improve substantially the production cycle. Machine ability to diagnose impending failures, prognose diagnostics/prognostics for condition-based maintenance the remaining useful lifetime of the process and involves an integrated system architecture with a schedule maintenance operations so that uptime is diagnostic module – the diagnostician – which assesses maximized. Prognosis is probably the most through on-line sensor measurements the current state of difficult of the three issues leading to condition- critical machine components, a prognostics module – the based maintenance. This paper attempts to address prognosticator – which takes into account input from the this challenging problem with intelligence-oriented diagnostician and decides upon the need to maintain techniques, specifically dynamic wavelet neural certain machine components on the basis of historical networks. Dynamic wavelet neural networks failure rate data and appropriate fault models, and a incorporate temporal information and storage maintenance scheduler whose task is to schedule capacity into their functionality so that they can maintenance operations without affecting adversely the predict into the future, carrying out fault prognostic overall system functionalities of which the machine in tasks. An example is presented in which a trained question is only one of its constituent elements. dynamic wavelet neural network successfully This paper addresses issues relating to the prognostic prognoses a defective bearing with a crack in its module – the Achilles heel of the Condition-Based- inner race. Maintenance (CBM) architecture. Fault diagnosis is a mature field with contributions ranging from model-based Introduction techniques to data-driven configurations that capitalize The manufacturing and industrial sectors of our upon soft computing and other “intelligent” tools [1][2]. economy are increasingly called to produce at higher Condition-based maintenance scheduling is a complex task throughput and better quality while operating their that involves finding the “optimum” time to perform processes at maximum yield. As manufacturing facilities maintenance within the window prescribed by the Prognosticator while meeting a host of constraints. This become more complex and highly sophisticated, the scheduling problem may be formulated as a multi- quality of the production phase has become more crucial. objective optimization problem where the main objective The manufacture of such typical products as aircraft, automobiles, appliances, medical equipment, etc, involves is to maximize process uptime while satisfying a set of a large number of complex processes most of which are constraints that relate to resource and maintenance characterized by highly nonlinear dynamics coupling a personnel availability, production and scheduling variety of physical phenomena in the temporal and spatial requirements, redundant or relocatable machines, timing domains. It is not surprising, therefore, that these processes constraints, etc [3]-[5]. The word “prognosis” implies the are not well understood and their operation is “tuned” by foretelling of the probable course of a disease [6], a term experience rather than through the application of scientific widely used in medical practice. In the industrial and principles. Machine breakdowns are common limiting manufacturing arenas, prognosis is interpreted to answer uptime in critical situations. Failure conditions are difficult the question: what is the remaining useful lifetime of a machine or a component once an impending failure condition is detected and identified? Stochastic Auto- Figure 1 depicts the overall architecture of the Regressive Integrated Moving Average (ARIMA) models prognostic system. The diagnostician monitors [7], fuzzy pattern recognition principles [8], knowledge- continuously critical sensor data and decides upon the intensive expert systems [9], nonlinear stochastic models existence of impending or incipient failure conditions. The of fatigue crack dynamics [10], polynomial neural detection and identification of an impending failure networks [11] and other techniques have been introduced triggers the prognosticator. The latter reports to the CBM over the past years to address the diagnostic/prognostic module the remaining useful lifetime of the failing problem. This paper attempts to address this issue by machine or component. The CBM module schedules the introducing a novel combination of a “virtual” sensor as a maintenance so that uptime is maximized while certain mapping tool between known measurements and constraints are satisfied. The schematic of Figure 1 focuses “difficult-to-access” quantities and a dynamic wavelet on the functionalities of the prognosticator. The neural network as the “predictor”, i.e. the construct that diagnostician alerts the prognostic module and provides projects into the future the temporal behavior of a faulted failure and other pertinent sensor data to it. The prognostic component. architecture is based on two constructs: a static “virtual sensor” that relates known measurements to fault data and The Prognosticator a predictor which attempts to project the current state of the faulted component into the future thus revealing the The prognosticator performs the vital function of time evolution of the failure mode and allowing the linking the diagnostic information with the maintenance estimation of the component’s remaining useful lifetime. scheduler. It is probably the least understood but most Both constructs rely upon a wavelet neural network model crucial component of the diagnostic/prognostic/CBM acting as the mapping tool. It is appropriate, therefore, to hierarchical architecture. Furthermore, it entails ambiguity digress for a brief discussion of the Wavelet Neural and large-grain uncertainty since the historical evolution of Network (WNN). a failure event – the growth of a structural fault, for example – is difficult if not impossible to model The Wavelet Neural Networks accurately, historical data is not readily available and the particular growth phenomenon may be strongly dependent The Wavelet Neural Network belongs to a new class on the system structure, operating conditions, of neural networks with unique capabilities in addressing environmental effects, etc. It is viewed as a dynamic identification and classification problems. Wavelets are a predictor which receives fault data from the diagnostic class of basic elements with oscillations of effectively module and determines the allowable time window during finite-duration that makes them look like “little waves”. which machine maintenance must be performed if the The self-similar, multiple resolution nature of wavelets integrity of the process is to be kept as high as possible. offers a natural framework for the analysis of physical The term “dynamic predictor” implies also the functional signals and images. On the other hand, artificial neural requirement that the target output, i.e. remaining useful networks constitute a powerful class of nonlinear function lifetime or time-to-failure, is dynamically updated as more approximants for model-free estimation. A common information becomes available from the diagnostician. ground between these two technologies may be coherently Thus, this scheme should reduce the uncertainty and exploited by introducing a WNN. Indeed, the improve the prediction accuracy as the accumulated implementation of a neural network is closely related to a evidence grows. truncated version of the wavelet series. A MIMO WNN can be formulated as [12]: Features Virtual Sensor y = [y (x) y (x) LL y (x)]C + [x 1]C (1) A1 ,b1 A2 ,b2 AM ,bM lin (WNN) Fault where x is the 1´n input row-vector; y is the 1xK output Classes Time-To row-vector and K is the number of outputs; A is the nxn Signals -Failure j squashing matrix for the jth node; bj is the 1xn translation Feature Classifier Process Predictor CBM vector for the jth node; C is the M´K matrix of output Extraction (WNN) (DWNN) coefficients, where M is the number of wavelet nodes; Clin is the (n+1)´K matrix of output coefficients for the linear direct link; and y is the wavelet function that can take the form: y (x) = | A |1 / 4 y( (x - b)A(x - b)T ) (2) Figure 1 The overall architecture of the prognostic A,b system where x is the input row-vector; A the squashing matrix algorithm. In addition, such fundamental performance for the wavelet; b the translation vector; and T