关于结构劣化不确定性量化的离线与在线贝叶斯滤波
On off-line and on-line Bayesian filtering for uncertainty quantification of structural deterioration
AI总结：
研究离线与在线贝叶斯滤波在结构劣化参数估计中的性能，对比粒子滤波和MCMC滤波等三种方法，发现定制的在线粒子滤波器在精度与计算成本上具竞争力。
摘要：
数据驱动的预测性维修规划在很大程度上依赖于随机劣化模型。监测信息可用于在离线（批处理）或在线（递归）贝叶斯框架内，顺序更新关于时不变劣化模型参数的知识。为了量化完整的参数不确定性，我们回顾、调整并研究了选定的用于参数估计的贝叶斯滤波器：一种在线粒子滤波器，一种执行马尔可夫链蒙特卡洛（MCMC）移动步骤的在线迭代批处理重要性采样滤波器，以及一种基于MCMC的离线顺序蒙特卡洛滤波器。在这三种滤波器中，均使用高斯混合模型在重采样过程中近似后验分布。两个数值算例作为对比评估离线和在线贝叶斯估计时不变劣化模型参数的基础。第一个案例研究考虑一个低维、非线性、非高斯概率疲劳裂纹扩展模型，该模型通过顺序裂纹监测测量进行更新。第二个高维、线性、高斯案例研究采用随机场对梁的腐蚀劣化进行建模，并通过来自传感器的顺序测量进行更新。数值研究提供了关于离线和在线滤波器在应用于不同性质、增加维度和变化的传感器信息量问题时，在后验估计精度和计算成本方面的性能见解。重要的是，它们表明在线粒子滤波器的定制实现被证明与计算要求高的基于MCMC的滤波器具有竞争力。提供了根据问题特征选择合适方法的建议。
英文摘要：
Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an off-line (batch) or an on-line (recursive) Bayesian framework. With a focus on the quantification of the full parameter uncertainty, we review, adapt and investigate selected Bayesian filters for parameter estimation: an on-line particle filter, an on-line iterated batch importance sampling filter, which performs Markov chain Monte Carlo (MCMC) move steps, and an off-line MCMC-based sequential Monte Carlo filter. A Gaussian mixture model is used to approximate the posterior distribution within the resampling process in all three filters. Two numerical examples serve as the basis for a comparative assessment of off-line and on-line Bayesian estimation of time-invariant deterioration model parameters. The first case study considers a low-dimensional, nonlinear, non-Gaussian probabilistic fatigue crack growth model that is updated with sequential crack monitoring measurements. The second high-dimensional, linear, Gaussian case study employs a random field to model corrosion deterioration across a beam, which is updated with sequential measurements from sensors. The numerical investigations provide insights into the performance of off-line and on-line filters in terms of the accuracy of posterior estimates and the computational cost, when applied to problems of different nature, increasing dimensionality and varying sensor information amount. Importantly, they show that a tailored implementation of the on-line particle filter proves competitive with the computationally demanding MCMC-based filters. Suggestions on the choice of the appropriate method in function of problem characteristics are provided.
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