Qiu Mingzhu, Cao Peng, Cao Liang, Tan Zhifei, Hou Chuantao, Wang Long, Wang Jianru
Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100084, China.
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong SAR, China.
Polymers (Basel). 2023 May 31;15(11):2540. doi: 10.3390/polym15112540.
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.
本研究利用遗传算法（GA）和列文伯格-马夸尔特（L-M）算法，对两种常用的粘弹性模型（2S2P1D和哈弗里利亚克-内加米（H-N）模型）的参数获取过程进行优化。研究了优化算法的不同组合对这两个本构方程中参数获取精度的影响。此外，还对GA在不同粘弹性本构模型中的适用性进行了分析和总结。结果表明，GA能确保2S2P1D模型参数的拟合结果与实验数据之间的相关系数达到0.99，并且进一步证明通过L-M算法进行二次优化可实现拟合精度。由于H-N模型涉及分数幂函数，直接将参数拟合到实验数据以实现高精度拟合具有挑战性。本研究提出了一种改进的半解析方法，该方法首先拟合H-N模型的科尔-科尔曲线，然后使用GA对H-N模型的参数进行优化。拟合结果的相关系数可提高到0.98以上。本研究还揭示了H-N模型的优化与实验数据的离散性和重叠性之间的密切关系，这可能归因于H-N模型中包含分数幂函数。
