Bayesian inference has been demonstrated as a rigorous tool for updating models and predicting responses in structural dynamics. Most often, the likelihood function within the Bayesian framework is formulated based on a point-to-point probabilistic description of the discrepancy between the measurements and model predictions. This description results in an underestimation of uncertainties due to the inherent reduction of the parameter uncertainty as the number of data points increases. In this paper, the problem of estimating the uncertainty of parameters is re-visited using time-domain responses. Specifically, spatially and temporally uncorrelated/correlated prediction models are developed to re-formulate the likelihood function based on data features between the measurements and model predictions. The relation between the proposed probabilistic technique and the likelihood-free approximate Bayesian computation (ABC) strategy is investigated, analytically demonstrating that the proposed data features-based models can offer consistent uncertainties for the model parameters. Linear and nonlinear models with time histories data of building systems are utilized to demonstrate the effectiveness of the proposed framework. Results show that the proposed models yield consistent parameter uncertainties and realistic uncertainty bounds for quantities of interest (QoI). These uncertainty bounds are independent of the sampling rate used for the time history response. In contrast, the classical Bayesian formulation tends to underestimate parameter uncertainties and produces overly narrow, unrealistic bounds for response predictions.

中文翻译：

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基于数据特征的贝叶斯学习，用于结构动力学中的时域模型更新和稳健预测


贝叶斯推理已被证明是更新模型和预测结构动力学响应的严格工具。大多数情况下，贝叶斯框架中的似然函数是根据测量值和模型预测之间差异的点对点概率描述来制定的。这种描述导致对不确定性的低估，因为随着数据点数量的增加，参数不确定性的固有减少。在本文中，使用时域响应重新审视了估计参数不确定性的问题。具体来说，开发了空间和时间上不相关/相关的预测模型，以根据测量和模型预测之间的数据特征重新构建似然函数。研究了所提出的概率技术与无似然近似贝叶斯计算 （ABC） 策略之间的关系，分析证明所提出的基于数据特征的模型可以为模型参数提供一致的不确定性。利用线性和非线性模型以及建筑系统的时间历史数据来证明所提出的框架的有效性。结果表明，所提出的模型为感兴趣量 （QoI） 产生了一致的参数不确定性和实际不确定性边界。这些不确定性边界与用于时间历史记录响应的采样率无关。相比之下，经典的贝叶斯公式往往低估了参数的不确定性，并为响应预测产生了过于狭窄、不切实际的边界。