The Modeling and the Sensor Fault Diagnosis of a Continuous Stirred Tank Reactor with a Takagi-Sugeno Recurrent Fuzzy Neural Network

Abstract

In this paper, a novel Takagi-Sugeno recurrent fuzzy neural network (TSRFNN) is constructed for modeling and sensor fault diagnosis of a Continuous Stirred Tank Reactor (CSTR), a nonlinear dynamic system. The TSRFNN is composed of 9 layers, including premise network and consequence network. The temporal information is embedded in the TSRFNN by adding the feedback connections between the output layer and the input layer of the fuzzy neural network (FNN). It is assumed that the inputs are Gaussian membership functions; the product operation is utilized for the premise and implication, and the weighted center-average method is adopted for defuzzification. The network is a Fuzzy Basis Function(FBF). The general approximation characteristic of the network was proven by the theory reasoning. The identification of the TSRFNN consists of two steps: structure identification and parameter identification. Unsupervised clustering is used to determine the structure of the fuzzy system, the number of fuzzy rules, and the membership functions of the premise using the input-output data of a system. Then in the parameter identification, the Dynamic Backpropagation (DBP) is adopted to determine the membership functions of the conclusion of the fuzzy system. Then the network is applied to the modeling and diagnosis of a CSTR system. The network is applied to set up the sensors models of a CSTR system, including the models of the temperature sensor faults and the models of concentration sensor faults. To set up a high performance diagnosis model, a persistent signal was chosen to sufficiently activate the plant. Finally an Adaptive Threshold Algorithm based on statistics is used to fault diagnose. If there are sensor faults in the CSTR, the bias between the actual output of the plant and the output of the network surpasses the threshold and the faults are detected on-line according to it. The effectiveness of the modeling and diagnosis approach proposed was verified by the simulation results with Matlab. Therefore, the proposed network and the fault diagnosis approach can be employed to a CSTR system successfully and be extended to the modeling and fault detection of other nonlinear systems.