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Embedded radial basis function networks to compensate for modeling uncertainty of nonlinear dynamic systems

Chengyu Gan, University of Massachusetts Amherst


This thesis provides a bridge between analytical modeling and neural network modeling. Two different approaches have been explored. Both approaches rely on embedding radial basis function (RBF) modules in the approximate model of the plant so that they can be trained to compensate for modeling uncertainty. One approach has led to the development of a model-based recurrent neural network (MBRNN) for modeling nonlinear dynamic systems. The RBF modules take the form of activation functions in the MBRNN network, that is formu1ulated according to a linearized state-space model of the plant. This network is trained to represent the process nonlinearities through modifying the activation functions of its nodes, while keeping the original topology of the neural network intact. The performance of the MBRNN is demonstrated via several examples. The results indicate that it requires much shorter training than needed by ordinary recurrent networks. The utility of the MBRNN is tested in fault diagnosis of the IFAC Benchmark Problem and its performance is compared with ‘black box’ neural solutions. The results indicate that the MBRNN provides better results than ‘black box’ neural networks, and that with training it improves the results from other model-based residual generators. The second approach incorporates RBF modules in the nonlinear estimation model to enhance the performance of the extended Kalman filter (EKF) in coping with the uncertainty of this model. In this method, single-input single-output radial basis function (RBF) modules are embedded within the nonlinear estimation model to provide additional degrees of freedom for model adaptation. The weights of the embedded RBF modules are. adapted by the EKF concurrent with state estimation. This modeling compensation method is tested in application to an induction motor benchmark problem. Simulation results indicate that the RBF modules provide the means to model the uncertain components of the estimation model within their range of variation. The utility of the embedded RBF-based nonlinear adaptive observer was tested in fault diagnosis of a throttle sensor fault in an internal combustion engine. The test results show that this observer enhances the residuals obtained for fault diagnosis.

Subject Area

Computer science|Automotive materials|Electrical engineering|Systems design

Recommended Citation

Gan, Chengyu, "Embedded radial basis function networks to compensate for modeling uncertainty of nonlinear dynamic systems" (2000). Doctoral Dissertations Available from Proquest. AAI9960753.