Online sequential type-2 fuzzy wavelet extreme learning machine: A nonlinear observer application

Abstract

The aim of this paper is to combine the time-frequency attributes of wavelets and neural network learning ability besides approximate reasoning features of type 2- fuzzy systems, and the advantages of online sequential extreme learning machine (one-pass learning and valid generalization achievement with extremely fast learning) in order to present a new effective algorithm in many applications. The novel structure is named Online Sequential Type-2 Fuzzy Wavelet Extreme Learning Machine (OS-T2-FW-ELM) and has been developed for function approximation and nonlinear systems identification. In addition, OS-T2-FW-ELM is designed in an online manner and applied as a nonlinear observer for nonlinear systems. In this model, it is considered that balance among the complexity of structure, computation time, and approximation error will be accomplished. To elaborate, in the proposed method, the THEN-part of each fuzzy rule corresponds to a sub-Wavelet Neural Network (sub-WNN) generated with different dilation and translation parameters of a mother wavelet and thus, only one coefficient is considered for the wavelet transform of the whole inputs. As far as the excellence is concerned, the performance of OS-T2-FW-ELM compares with other existing algorithms. As a result of this comparison, the number of linear learning parameters and sensitivity of the random initialization procedure is decreased while the performance accuracy of OS-T2-FW-ELM is preserved. In the method of nonlinear observer design, both OS-T2-FW-ELM observer and nonlinear Extended State Observer (ESO) are applied for the quadruple tank in the presence of noise and uncertainty. In the simulation results, the comparison of the performance of both mentioned algorithms indicates the remarkable capabilities of the OS-T2-FW-ELM observer.