Parameter Determination of the 2S2P1D Model and Havriliak–Negami Model Based on the Genetic Algorithm and Levenberg–Marquardt Optimization Algorithm

Abstract

This study utilizes the genetic algorithm (GA) and Levenberg–Marquardt (L–M) algorithm to optimize the parameter acquisition process for two commonly used viscoelastic models: 2S2P1D and Havriliak–Negami (H–N). The effects of the various combinations of the optimization algorithms on the accuracy of the parameter acquisition in these two constitutive equations are investigated. Furthermore, the applicability of the GA among different viscoelastic constitutive models is analyzed and summarized. The results indicate that the GA can ensure a correlation coefficient of 0.99 between the fitting result and the experimental data of the 2S2P1D model parameters, and it is further proved that the fitting accuracy can be achieved through the secondary optimization via the L–M algorithm. Since the H–N model involves fractional power functions, high-precision fitting by directly fitting the parameters to experimental data is challenging. This study proposes an improved semi-analytical method that first fits the Cole–Cole curve of the H–N model, followed by optimizing the parameters of the H–N model using the GA. The correlation coefficient of the fitting result can be improved to over 0.98. This study also reveals a close relationship between the optimization of the H–N model and the discreteness and overlap of experimental data, which may be attributed to the inclusion of fractional power functions in the H–N model.

Study on the Flow Behavior of 5052 Aluminum Alloy over a Wide Strain-Rate Range with a Constitutive Model Based on the Arrhenius Model Extension

“…The genetic algorithms model the process of natural selection as an optimization protocol and are a well-established class of evolutionary methods suitable for solving minimization or maximization problems, even when the search space is large and the topology is complex, which means it is suitable for multi-parameter optimization in our study. However, the maintenance of a large population pool and the staged modeling of fitness-dependent selection, reproduction, and mutation processes require a large number of merit function (fitness) assessments per iteration, and are therefore computationally costly [47]. Thus, the gradient-based Levenberg-Marquardt algorithm, which costs less computation per iteration and is more efficient, was coupled into the iteration to accelerate convergence.…”

“…means it is suitable for multi-parameter optimization in our study. However, the maintenance of a large population pool and the staged modeling of fitness-dependent selection, reproduction, and mutation processes require a large number of merit function (fitness) assessments per iteration, and are therefore computationally costly [47]. Thus, the gradient-based Levenberg-Marquardt algorithm, which costs less computation per iteration and is more efficient, was coupled into the iteration to accelerate convergence.…”

Dynamic Fractional-Order Model of Proton Exchange Membrane Fuel Cell System for Sustainability Improvement

“…The LM method, renowned for its precision in nonlinear optimization, complements this by refining the globally optimized solution, although it risks converging to local minima if initial values are suboptimal[41]. The combination of these two methods aims to harness GA's global search capabilities alongside LM's precise local optimizations, providing both comprehensive exploration and meticulous refinement[42][43][44][45]. This dual approach is particularly beneficial for complex models, as demonstrated in our experiments where frequencies range from 0.1 Hz to 10,000 Hz across 51 data points.In the practical application of this abovementioned method, as illustrated in Figure2, the GA initially explores a broad spectrum of solutions, sifting through and eliminating the less effective ones.…”