Open Access

ARTICLE

Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

by Cheng Han^1,*, Zhengguang Xu^1,2

1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China
2 Key Laboratory of Knowledge Automation for Industrial Processes, University of Science and Technology Beijing, Beijing, 100083, China

* Corresponding Author: Cheng Han. Email:

Computer Modeling in Engineering & Sciences 2024, 139(1), 515-536. https://doi.org/10.32604/cmes.2023.043464

Received 03 July 2023; Accepted 27 October 2023; Issue published 30 December 2023

Abstract

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems, assuming that the system satisfies the generalized Lipschitz condition. As a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics, the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables, which poses difficulties in predicting and estimating the system’s output. In this article, the temporal variation of the system is described by constructing pattern category variables, which are non-deterministic variables. Since pattern category variables have statistical attributes but not operational attributes, operational attributes are assigned to them by posterior probability density, and a method for analyzing their motion laws using probability density evolution is proposed. Furthermore, a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative (PPD), achieving prediction of the probability density satisfying the system’s output uncertainty. Based on this, the final prediction estimation of the system’s output value is realized by minimum variance unbiased estimation. Finally, a corresponding PPD estimation algorithm is designed using an extended state observer (ESO) to estimate the parameters to be estimated in the proposed prediction method. The effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis, and the accuracy of the algorithm is verified by two numerical simulation examples.

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Keywords

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