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The classical reliability theory assumes that a component or a system can only be in one of two possible states, either working or failed. However, in many real-life situations, the systems and their components are capable of assuming a whole range of levels of performance, varying from perfect functioning (denoted by level M, say) to complete failure (denoted by level 0). In these situations, the dichotomous model is an oversimplification of the actual systems. Models treating the systems and the components as multi-state entities are needed to describe the performance of these systems in terms of the performances of the components. In a discrete multi-state system reliability model, a system and each component may experience states in the set {0, 1, 2, ..., M}. In a continuous multi-state system reliability model, a system and each component may experience states in the closed interval [0, 1]. We are analyzing different multi-state system structures and developing efficient algorithms for performance evaluation of the system given performance distributions of the components. These models should also be applied in optimal system design and maintenance decision optimization.
Manufacturers of capital equipment often state that periodic inspections and preventive maintenance activities must be conducted following their recommendations for the warranty to be valid and for the equipment to operate properly. Thus, the maintenance departments in various industries have to follow predetermined schedules for most of their maintenance activities. These periodic maintenance schedules do have the advantage of easy job scheduling. However, the information of the health conditions of the equipment in operation is not used to modify the maintenance schedule. Thus, some facilities are over-maintained while others are under-maintained. Vibration-monitoring systems have been used to indicate when replacements are required on selected components such as bearings in rotary equipment, in-core flux detectors in CANDU nuclear reactors, and gears in transmissions. They are also used in fault diagnosis at the system level in order to pinpoint the failed components. In these situations, they are for reacting to failures rather than preventing failures. They are not used to predict the statistical remaining life of the components. As a result, they do not consider planning or optimization issues for the maintenance of the whole system. How to monitor the critical components of a system, predict how much longer the components can reliably perform their functions and how much longer the system can continue to be used, and provide an optimal maintenance schedule as to when inspection, preventive maintenance, and/or replacement should be performed in order to minimize the total cost deserves further investigations. In view of these, the Reliability Research Lab is using multi-channel data collection and analysis systems to monitor the degradation of laboratory equipment conditions and use the collected data to model the degradation process and schedule maintenance activities to minimize the total operation and maintenance cost of the equipment. The machinery studied includes gearboxes (fixed shaft and planetary types), slurry pumps, wind turbines, and rotor systems.
A fault signature database includes vibration signatures of common failure modes (including misalignment, imbalance, rub, wearout, cavities or cracks, and oil whirl) of critical components (rotor and shaft, bearings, gears, seals, blades) in rotating equipment. Figures and look-up tables can be used to determine the fault sources based on observed symptoms. The probability for each fault source corresponding to observed vibration signals should be established. Wavelet analysis has been successfully applied in signal processing, pattern recognition and machinery fault diagnosis. We are testing and developing advanced algorithms with wavelet analysis, principal component analysis, and empirical mode decomposition in fault detection and diagnosis of gearboxes, roller bearings and rotary systems. Efficient feature extraction methods are being developed based on non-orthogonal wavelet transforms, which can be used in analysis of vibration signals from gearboxes, roller bearings and reciprocating machines. This method can also be generalized to speech and image de-noising. Other signal processing methods being investigated for fault diagnosis and detection include cyclostationary analysis, independent component analysis (ICA), neural networks, and kurtosis indicators.
Equipment deteriorates as it is used. Its life follows certain statistical distributions. Equipment health indicators based on vibration signals can be used in prediction of the remaining life of deteriorating equipment. Statistical methods have been used extensively in prediction of time series. Lately, a new technique called support vector machines (SVM) has been developed for pattern recognition and regression analysis. They have been shown to perform very well in predicting time series. We are exploring their use in vibration monitoring and prediction of equipment degradation. The formulation of SVM embodies the Structural Risk Minimization (SRM) principle, as opposed to the Empirical Risk Minimization (ERM) approach commonly employed within statistical learning methods. SRM minimizes an upper bound on the generalization error, while ERM minimizes the error on the training data. It is this difference, which equips SVM with a greater flexibility and thus potentially better prediction capabilities. In SVM, the basic idea is to map the data into a high dimensional feature space via a nonlinear mapping. Once in the feature space, linear regression can be performed. Another tool that is being investigated for remaining life prediction is neural networks.
The reliable performance of systems is becoming more and more important in many industrial, military and everyday life situations. Such development has resulted from the increasing need for systems and components with higher reliability and lower cost. Thus, reliability based design of systems has become an important research area. However, Most of the research results in the literature are either for system design with constant component reliabilities or for optimal maintenance planning given a fixed system design. In this project, we propose to develop guidelines for selection of parameters within various maintenance models, develop reliability based design models and methodologies considering periodic maintenance and for special systems structures such as standby systems and k-out-of-n systems, and fine tune genetic algorithms for their efficient application in solving reliability based design problems.
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