基于改进MH算法的结构损伤识别

Damage identification based on improved MH algorithm

将粒子群算法(PSO)中的粒子位置更新方式与自适应方法融入到标准梅特罗波利斯-黑斯廷斯算法(MH)中,得到了一种自适应PSO-MH算法,用以求解贝叶斯损伤识别中的后验概率密度函数.首先,以粒子位置更新公式代替建议分布更新马尔科夫链的候选样本值,构建出自适应PSO-MH算法的采样流程;然后,采用一个横梁数值算例来对比该算法与标准MH算法之间的采样效果差异;最后,通过洛斯阿拉莫斯国家实验室(LANL)的一个八自由度结构试验验证了该算法的有效性.通过分析数值算例与试验实例的结果得出:自适应PSO-MH算法的损伤识别精度高于标准MH算法,且生成的马尔科夫链的统计效果优于标准MH算法,同时该算法生成的马尔科夫链的自相关函数(ACF)值呈现出截尾,表明马尔科夫链的连续样本间相关性低,计算时间更少,收敛速度更快.

The particle position update mechanism in PSO and adaptive method were integrated into the standard MH algorithm to establish an adaptive PSO-MH algorithm, which was used to solve the posterior probability density function in Bayesian damage identification.Firstly,the particle optimal value in the particle position update formula was obtained by random sampling from the adaptive uniform distribution, and then the formula was used to replace the proposed distribution to update the candidate sample value of the Markov chain, so as to construct the sampling process of the adaptive PSO-MH algorithm. Then, a numerical example of a beam was used to compare the sampling effect difference between the proposed algorithm and the standard MH algorithm. Finally, the effectiveness of the algorithm was verified by an eight degree-of-freedom system of LANL. Through analyzing the results of numerical and experimental examples, it is concluded that the damage identification accuracy of the adaptive PSO-MH algorithm is slightly higher than that of the standard MH algorithm,and the statistical effect of the Markov chain is better than that of the standard MH algorithm. Moreover, the ACF value of the Markov chain generated by the adaptive PSOMH algorithm is censoring,indicating that the correlation between the samples of the Markov chain is low,the calculation time is less,and the convergence rate is faster.