Fault occurrence in systems causes loss of life and financial damage; therefore diagnosing a fault occurrence in the shortest time decreases this damage. The persistence of the fault existence for a long time in the system causes damage; so it is essential to supervise the system to diagnose faults in the shortest time. Intelligent networks can diagnose the fault faster and more accurate than huma so different kinds of intelligent networks can be used to diagnose the fault. One of the common networks for the fault diagnosis is the neural network which has appropriate adaptation; however, it is not appropriate because of constrains on the results interpretation. The fuzzy logic is one of the other methods which is used for diagnosing the fault and has appropriate interpretation; however it does not have appropriate adaptation unlike neural networks. So the combination of the neural network and the fuzzy logic can resolve the constrains. The type-1 neuro fuzzy makes by the combination of fuzzy logic and neural network. The analysis functions in the conclusion part are used in the type-1 neuro fuzzy. In this study, in the conclusion, the wavelet functions, which show the conception of the type-1 fuzzy wavelet neural network, have been used to improve the network efficiency and decrease the numbers of rules in the type-1 neuro fuzzy. Also available data for the fault diagnosis is with noise that decrease the accuracy of the fault diagnosis networks. The fuzzy function is not appropriate in the noisy situations and does not have acceptable accuracy. So, the type-2 fuzzy was used in this research. The use of the type-2 fuzzy decreases the noise effect and uncertainty in the fault diagnosis networks. According to the mentioned information, in this study, the structure of a type-2 fuzzy wavelet neural network has been proposed with an appropriate combination algorithm. In this algorithm, three algorithms were used: the k-means cluster algorithm to initialize nonlinear parameters, the least square algorithm to initialize the linear parameters, and the recursive least square method with the adaptive forgetting parameter to update linear parameters. Also to update the nonlinear algorithms, back propagation with the adaptive momentum parameter was used to accelerate convergence and the learning amount that guarantee convergence. In this study, convergence and stability of the proposed combination algorithm were proved and to show the ability of the network and algorithm, examples of the Key Words: Fault diagnosis, Three tank system, Type-2 fuzzy wavelet neural network.
