A novel nonlinear optimization method for fitting a noisy Gaussian activation function

Abstract

Summary It is significant to fit a Gaussian function with the observation data for artificial intelligence or other engineering fields. Considering the influence of noises, this article proposes a nonlinear optimization method for fitting the Gaussian activation functions. By means of the gradient search and the Newton search, a direct gradient‐based iterative algorithm and a direct Newton iterative algorithm are presented for identifying the Gaussian functions. Considering the computational cost, the authors develop a multi‐innovation stochastic gradient algorithm for the noisy Gaussian functions. After introducing a forgetting factor, the parameter estimation accuracy can be further improved. The simulation results indicate that the proposed nonlinear optimization method and gradient‐based algorithms can fit the noisy Gaussian functions very well.

Filtered multi‐innovation‐based iterative identification methods for multivariate equation‐error ARMA systems

“…The simulation results demonstrate that the F-D-GI algorithm can effectively reduce the influence of noises on parameter estimation. In addition, the basic idea of the proposed method in this paper can be extended to study identification problems of other linear systems and nonlinear systems with colored [97][98][99][100][101][102][103][104][105][106] and can be applied to other literatures such as information and practical…”

Identification of dual‐rate sampled nonlinear systems based on the cycle reservoir with regular jumps network

“…Finally, the effectiveness of the proposed method have been well confirmed from the identification results for both the numerical simulation and the CSTR process. The proposed parameter identification algorithm in this paper can be combined with other identification algorithms to investigate new parameter estimation methods of other linear and nonlinear stochastic systems with colored noises, [82][83][84][85][86][87][88][89] and can be applied to other control and schedule areas such as the information processing systems and transportation communication systems and so on.…”

Filtered auxiliary model recursive generalized extended parameter estimation methods for Box–Jenkins systems by means of the filtering identification idea

“…$$ The proposed parameter identification methods in this paper are based on the identification model in (12). In fact, many estimation methods are derived based on the identification models of the systems 54‐59 and these estimation methods can be used to identify the parameters of other linear systems and nonlinear systems 60‐64 and can be applied to other fields 65‐71 such as chemical process control systems. In the identification model in (12), the parameter vector $$$ \boldsymbol{\theta} $$$ contains all the parameters $$$ {a}_i $$$, $$$ {b}_i $$$, $$$ {c}_i $$$, and $$$ {d}_i $$$ of the systems.…”