Parameter estimation method, system and device of nonlinear diffusion model and storage medium

By introducing the Levy stochastic process to improve the particle swarm optimization algorithm, and combining a low-order model and a projective approximation nonlinear term, the local optimum problem in parameter estimation of nonlinear diffusion systems is solved, achieving more efficient parameter identification and accurate modeling.

CN115422815BActive Publication Date: 2026-05-05CHINA UNIV OF GEOSCIENCES (WUHAN)
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Patent Information

Application Number
CN202210994521.8
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-08-18
Publication Date
2026-05-05
Estimated Expiration
2042-08-18

AI Technical Summary

Technical Problem

In the parameter estimation of nonlinear diffusion systems, the classical particle swarm optimization algorithm is prone to getting trapped in local optima, which increases the complexity of system modeling and computation, making it difficult to accurately characterize the reaction diffusion process.

Method used

The Levy stochastic process is used to improve the particle swarm optimization algorithm (Levy-PSO). By combining low-order model construction and projection approximation of nonlinear terms, the search and learning capabilities of particles are enhanced, and the Levy process can help them escape local optima.

Benefits of technology

It simplifies the complexity of system modeling, improves the accuracy and computational efficiency of parameter estimation, enhances the global search capability of the particle swarm optimization algorithm, avoids getting trapped in local optima, and improves prediction accuracy.

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Abstract

This invention discloses a parameter estimation method, system, device, and storage medium for a nonlinear diffusion model. The parameter estimation method includes: constructing a spatial basis function based on system data snapshots for a nonlinear Fisher-type diffusion system applied to the heating and cooling process of an iron rod, and separating spatiotemporal variables using an orthogonal decomposition method; sparsely sampling the nonlinear terms using a discrete empirical interpolation method to obtain the optimal low-order approximation of the high-order system; initializing a particle swarm to obtain n particles corresponding to the m-dimensional solution vector of the low-order time series model, and calculating the fitness of each particle according to the calculation formula of the parameters to be identified and the objective function; iterating and optimizing each particle, and outputting the position of the particle with the global optimum value; adding a non-Gaussian Levy process to the traditional particle swarm algorithm, and avoiding premature concentration of the particle swarm in the same direction through the random jump of the Levy process, thereby increasing the mutual learning ability between particles.
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