Inverse analysis of vibratory system is an important subject in fault identification, model updating, and robust design and control. It is challenging subject because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield results that are similar with respect to actual response measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic framework using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimization, whereas Bayesian inference is employed to account for the effect of uncertainties. To overcome the computational cost barrier, we adopt Markov chain Monte Carlo (MCMC) to characterize the target function/distribution. Instead of using single Markov chain in conventional Bayesian approach, we develop a new sampling theory with multiple parallel, interactive and adaptive Markov chains and incorporate it into Bayesian inference. This can harness the collective power of these Markov chains to realize the concurrent search of multiple local optima. The number of required Markov chains and their respective initial model parameters are automatically determined via Monte Carlo simulation-based sample pre-screening followed by K-means clustering analysis. These enhancements can effectively address the aforementioned challenges in finite element inverse analysis. The validity of this framework is systematically demonstrated through case studies.

振动系统的逆分析是故障识别、模型更新、鲁棒设计和控制的重要课题。这是一个具有挑战性的主题，因为 1) 在测量有限和/或不完整的情况下，问题通常是不确定的；2) 许多参数组合可能会产生与实际响应测量相似的结果；3) 不确定性不可避免地存在。这项研究的目的是通过统计推断利用计算智能来促进使用不完整模态响应测量的增强的概率框架。这个新框架建立在通过优化的有效逆识别之上，而贝叶斯推理则用于解释不确定性的影响。为了克服计算成本障碍，我们采用马尔可夫链蒙特卡罗（MCMC）来表征目标函数/分布。我们没有在传统的贝叶斯方法中使用单个马尔可夫链，而是开发了一种具有多个并行、交互和自适应马尔可夫链的新采样理论，并将其纳入贝叶斯推理。这可以利用这些马尔可夫链的集体力量来实现多个局部最优的并发搜索。所需马尔可夫链的数量及其各自的初始模型参数通过基于蒙特卡罗模拟的样本预筛选自动确定，然后 交互式和自适应马尔可夫链并将其合并到贝叶斯推理中。这可以利用这些马尔可夫链的集体力量来实现多个局部最优的并发搜索。所需马尔可夫链的数量及其各自的初始模型参数通过基于蒙特卡罗模拟的样本预筛选自动确定，然后 交互式和自适应马尔可夫链并将其合并到贝叶斯推理中。这可以利用这些马尔可夫链的集体力量来实现多个局部最优的并发搜索。所需马尔可夫链的数量及其各自的初始模型参数通过基于蒙特卡罗模拟的样本预筛选自动确定，然后K-均值聚类分析。这些增强功能可以有效地解决有限元逆分析中的上述挑战。通过案例研究系统地证明了该框架的有效性。