高聚物离散松弛时间谱计算的CMPSO方法

CMPSO Method for Computing Polymer's Discrete Relaxation Time Spectra

在广义Maxwell模型基础上,基于聚合物熔体储能模量和耗能模量数据,建立了计算离散松弛时间谱的优化模型.为了改善标准粒子群(Particle SwarmOptimizer,PSO)算法的缺点以用于计算离散松弛时间谱,提出了基于混沌映射和非线性惯性权重改进的粒子群方法(Chaos Modified PSO,CMPSO).首先通过算例检验了CMPSO算法的有效性.通过和文献结果比较,表明其精度均比文献结果高一个数量级.其次对Maxwell模态数的分析表明其取值在大于4以后,对计算结果影响不大.最后,通过结果分析确定出最优Maxwell模态数.在最优模态数情况下,储能模量和耗能模量的拟合数据与实验数据吻合较好,并采用最小二乘线性回归法验证了离散松弛时间谱的正确性.

An optimizing model is established for computing discrete relaxation time spectra based on the generalized Maxwell model and polymer＇s storage and loss modulus data.The Chaos Modified PSO（CMPSO）algorithm is proposed on the basis of the nonlinear inertial weights and chaos maps to enable the standard Particle Swarm Optimizer（PSO）to compute discrete relaxation time spectra.Firstly,an example was given to testify the validity of CMPSO algorithm.Comparison between the results of CMPSO and those of literatures showed that the accuracy of CMPSO was an order of magnitude higher than that of the methods adopted in other literatures.Meanwhile,the effect of the number of Maxwell mode on the simulation results of relaxation spectra was discussed,which showed that the number of Maxwell mode had little influence on the simulation results when greater than 4.At last,the optimal number of Maxwell mode was determined by CMPSO.The storage and loss modulus data exhibit good agreement with experimental data and correctness of the discrete relaxation time spectrum can also be proved by least-squares linear regression method under the condition of optimal number of Maxwell mode.