Generalized Kernel Fuzzy Modeling And Its Applications To Fault Tolerant Control

This dissertation proposes an effective fuzzy modeling method and applys it to faulttolerant control systems to improve the performance of fault tolerant control. A new fuzzymodeling method named generalized kernel fuzzy modeling is proposed. Based on thegeneralized kernel fuzzy model, a generalized fuzzy rule base reduction strategy is proposedto reduce the number of fuzzy rules, and a generalized kernel TS modeling method based ondual kernel mapping is proposed to improve the approximation ability. Then the generalizedkernel fuzzy model is applied to fault tolerant control systems.The content of this dissertation can be summarized as follows:(1) A connection between generalized kernels and fuzzy systems is established. Generalizedkernel fuzzy modeling is proposed. Generalized kernel is a generalization of Mercerkernel. Fuzzy models are built based on smooth support vector learning, where the kernelis a generalized kernel. Fuzzy rules are then extracted from the model. The advantage ofthis method is that the positive definiteness restriction on membership functions inducedby the Mercer condition can be relaxed. Any form of membership functions can be used,including adaptive membership functions. The generalization ability, robustness andinterpretability of the fuzzy model are enhanced.(2) For the problem of fuzzy rule base reduction of the generalized kernel fuzzy model, ageneralized kernel fuzzy rule base reduction strategy is proposed. This strategy can bedivided into two steps. The first step is generalized kernel reduction. Instead ofconventional Nystr m method-based kernel reduction which is specified for Mercer kernels, a kernel reduction method based on CUR decomposition is developed forgeneralized kernels. A representative subset of the entire dataset is selected according to anonuniform sampling probability based on the length of the rows/columns. This subsetprovides a low-rank approximation to the full kernel. The approximation error bound islower than conventional uniform sampling-based Nystr m method. The second step is afuzzy rule base reduction strategy. Redundant fuzzy rules are removed from the fuzzyrule base. This generalized kernel fuzzy rule base reduction strategy reduces the numberof fuzzy rules without scarifying the generalization ability(3) In order to improve the approximation ability of the generalized kernel fuzzy model, it islinked to TS models. A generalized kernel TS modeling method based on dual kernelmapping is proposed. A TS-type kernel is constructed by applying kernel mapping to theantecedent and the consequent space of the fuzzy rules. This TS-type kernel is not aMercer kernel but a generalized kernel. A generalized kernel TS model is obtained bygeneralized kernel learning. The approximation ability of the model is improved by usingTS model, and the fuzzy rule base can be reduced by the generalized kernel fuzzy rulebase reduction strategy. Based on the generalized kernel TS model, an online generalizedkernel TS model is developed for online problems. This model incrementally selectsrepresentative samples for fuzzy modeling. It has good generalization ability withreduced fuzzy rule base.(4) A fault detection and diagnosis approach based on generalized kernel fuzzy rules isproposed. By taking advantage of the generalized kernel fuzzy model that non-positivedefinite membership functions can be used, the trapezoid membership function is used ingeneralized kernel TS fuzzy modeling of the process variables. A set of Mamdani-typefuzzy rules are generated based on the extracted TS-type fuzzy rules. A fuzzy decisionfactor is proposed to detect and isolate faults using the Mamdani-type fuzzy rules. Thefault information is then sent to a fault decision system for fault dignosis. (5) A fault tolerant control system based on adaptive generalized kernel TS model isproposed. Taking advantage of the generalized kenel TS model, any form of membershipfunction can be used. By using adaptive membership functions, an adaptive generalizedkernel TS model is proposed. This model is then used as the reference model in a faulttolerant control system. When a process fault occurs, the shape of the membershipfunction is adjusted adaptively and the model is changed according to the status of theprocess. The reference model is combined with principal component analysis for faultdetection and diagnosis. After the fault is detected, fault tolerant control is realized byapplying model based predictive control.The performance of the algorithms is illustrated by extensive experiments using differentdatasets. Process data collected during the cooling process of cryogenic ground supportequipment (CGSE) in Alpha Magnetic Spectrometer-02(AMS-02) experiment is used forsimulation.