基于多链差分进化的贝叶斯有限元模型修正方法

BAYESIAN FINITE ELEMENT MODEL UPDATING METHOD BASED ON MULTI-CHAIN DIFFERENTIAL EVOLUTION

针对传统贝叶斯算法在高维参数下采样效率低且收敛难的问题,建立了基于多链差分进化算法的贝叶斯有限元模型修正方法。在标准马尔可夫链蒙特卡罗(MCMC)方法的基础上,引入差分进化算法,通过多条马氏链间的随机差分运算来自适应选择条件分布的大小和方向以快速逼近目标分布;引入子空间采样算法,通过自适应选择优良的参数维度进行采样以提高采样效率;引入异常链检测算法,通过在采样的非平稳期对马氏链进行异常检测与剔除以提高在平稳期的采样效率。简支梁理论模型和实验室4层框架结构的模型修正结果表明:该方法修正精度较高,且具有良好的抗噪性,在高阶频率以及振型下的修正效果均优于DRAM 算法,为解决不确定性模型修正中的计算精度提供了一种新手段。

To cope with the shortages of low sampling efficiency and difficult convergence of traditional Bayesian method under high-dimension parameters, a Bayesian based finite element model is proposed by the base of a multi-chain differential evolution algorithm. Based on the standard Markov chain Monte Carlo (MCMC) method, a differential evolution algorithm is introduced, and a random difference operation among multiple Markov chains is derived from the size and direction of an adaptive selection condition distribution to quickly approximate the target distribution. A subspace sampling algorithm which uses adaptive selection to select good parameter dimensions for sampling is introduced to improve sampling efficiency. Also, an anomaly Markov chain detection algorithm which detects and eliminates abnormities in Markov chains in the non-stationary period is introduced to improve the sampling efficiency in the stationary phase. The correction results of a simply-supported-beam model and a four-floor-frame-structure model show that the proposed method has a higher correction accuracy, better noise resistance, and better correction effects than that of DRAM algorithm under high order frequency and mode shapes, which provides a new way to improve the computational accuracy in uncertainty model correction.