Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the calibration of noise covariance matrices is cumbersome. For instance, calibration of input noise covariance matrix in augmented or dual Kalman filters is a critical task since a slight variation in its value can adversely affect estimations. The present study develops a Bayesian Expectation-Maximization (BEM) methodology for the uncertainty quantification and propagation in coupled input-state-parameter-noise identification problems. It also proposes the incorporation of input dummy observations for stabilizing low-frequency components of the latent states and mitigating potential drifts. In this respect, the covariance matrix of the dummy observations is also calibrated based on the measured data. Additionally, an explicit formulation is provided to study the theoretical observability of the Bayesian estimators, which helps characterize the minimum sensor requirements. Ultimately, the BEM is tested and verified through numerical and experimental examples, wherein sensor configurations, multiple input forces, and abrupt stiffness changes are investigated. It is confirmed that the BEM provides accurate estimations of states, input, and parameters while characterizing the degree of belief in these estimations based on the posterior uncertainties driven by applying a Bayesian perspective.
翻译:通过同时估计输入力、物理参数和动态状态,可以普遍地确定和探测结构和损害。虽然Kalman型过滤器是解决这一问题的有效工具,但校准噪声共变矩阵十分繁琐。例如,在加固或双加固的卡尔曼过滤器中校准输入噪声共变矩阵是一项关键任务,因为其价值的微小差异可能会对估计产生不利影响。本项研究开发了一种巴耶西亚期望-最大化(BEM)方法,用于在输入状态和参数的混合识别问题中进行不确定性的量化和传播。它还提议纳入输入的模拟观测,以稳定潜在状态的低频率组成部分和减少潜在漂移。在这方面,根据测量的数据对虚构观测的共变矩阵进行校准。此外,为研究巴耶斯估计器的理论易懂性提供了明确的表述,有助于确定最低传感器要求。最终,BEM通过数字和实验实例进行测试和核实,其中含有传感器配置、多重输入力和突然的僵硬性变化。在这方面,根据测测测测度的参数,通过测测测测测测测测了BEM状态,同时测量了BEM的精确度的参数。