Fuzzy wavelet networks are a combination of fuzzy systems with wavelet networks used in applications, including controller design for nonlinear systems and fault detection. These systems have high convergence speeds and acceptable accuracy in approximating functions. In fuzzy wavelet networks, determining the effective parameters and also network training and learning are the most important issues. To date, various algorithms for training these networks have been studied, most of which are based on iterative methods and also have computational complexity, waste of time, learning, and training in batches. Incorporating the time-frequency localization properties of wavelets and the learning abilities of neural network approximate reasoning characteristics of fuzzy inference system approximate reasoning characteristics of fuzzy inference system and the advantages of Online Sequential Extreme Learning Machine (one-pass learning and good generalization performance at extremely fast learning speed)it can provide a suitable solution for identifying nonlinear systems with uncertainty. Therefore, in this research, a new structure called fuzzy wavelet type 2 based on the online Sequential learning Extreme Learning Machine method has been proposed. The main objectives of this algorithm are: Reduce the volume and time of calculations, Reduction of approximation error, Check the uncertainty of nonlinear systems, Reduce the effect of disturbance and disruption of input data, Presenting the algorithm online and using it as an observer in nonlinear systems. In the proposed structure, each fuzzy law is related to a wavelet neural network, which consists of expanded and shifted versions of a mother wavelet. In this model, to achieve the balance between network complexity and performance accuracy in the latter part of each fuzzy rule, only one coefficient is considered for the total wavelet transform of each of the inputs. In this research, first, the equivalence of a type two fuzzy wavelet model and a leading latent single-layer network is proved. The maximum online learning machine algorithm is then applied directly to the model, so that all parameters of type 2 fuzzy membership functions as well as wavelet coefficients are randomly selected and only the network output weights are obtained analytically using a one-step learning method. Also, the convergence of this algorithm is proved by the least-squares method, and then the self-optimization proof of the algorithm is described. For eva‎luation, the proposed structure is used to approximate the functions, identify the nonlinear systems, and identify the Narendra nonlinear system and compare it with the previous methods. Also in the next step, the proposed structure is proposed to design the observer for nonlinear systems. In the simulation section, an example of a four-tank system is presented. The four-tank system is a non-linear system that has two inlet valves and four tanks in which the output of the two inlet valves enters tanks one and two, and tanks three and four are commanded by tanks one and two. Four height sensors have been considered for each tank. In this study, the sensors have noise and also the inlet valves have uncertainty. Hence, the role of the observer is very effective in resolving internal and external turmoil. In the simulation section, the observer designed based on the proposed algorithm is compared with a well-known observer called Extended State observer. The simulation results of the effective performance of the proposed method.

مريم ذكري، فريد شيخ الاسلام

ايمان ايزدي

مرضيه كمالي، جواد عسگري