Kernel approximation-based mathematical modeling for nonlinear parameter estimation in intelligent monitoring systems

Abstract

cNonlinear parameter estimation with accuracy is crucial in intelligent monitoring systems where the relationship between the variables and the system's state is complicated, and thus cannot be sufficiently modeled by conventional fixed-model approaches. In this study, a kernel approximation-based mathematical model framework is developed for nonlinear parameter estimation that incorporates flexibility in function approximation and regularization in constrained optimization. The suggested formulation involves an approximation of the unknown nonlinear function using a finite expansion of positive definite kernels and estimating the parameters using a regularized error function approximation. A Gaussian kernel is utilized for modeling nonlinearities, whereas the regularization ensures that the complexity of the model and estimation stability are controlled in the presence of noise. Experiments are performed on the controlled nonlinear functions where varying size samples and noisy data are considered. Proposed model performance analysis is done by using the measures like root mean square error, mean absolute error, mean absolute percentage error, coefficient of determination, normalized root means square error, parameter estimation error, and computation time. Comparison with polynomial nonlinear regression, radial basis function regression, Gaussian process regression, support vector regression, kernel ridge regression, and nonlinear least squares is done for the