Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown physics-based model's parameters. Bayesian Inference techniques for model updating require the assumption of a prior distribution. This choice of prior may affect posterior predictions and subsequent decisions on maintenance requirements, specially under the typical case in engineering applications of little informative data. Therefore, understanding how the choice of prior may affect the posterior prediction is of great interest. In this paper, a Robust Bayesian Inference technique evaluates the optimal and worst-case prior in the vicinity of a chosen nominal prior, and their corresponding posteriors. This technique employs an interacting Wasserstein gradient flow formulation. Two numerical case studies are used to showcase the proposed algorithm: a double-banana-posterior and a double beam structure. Optimal and worst-case prior are modelled by specifying an ambiguity set containing any distribution at a statistical distance to the nominal prior, less or equal to the radius. Examples show how particles flow from an initial assumed Gaussian distribution to the optimal worst-case prior distribution that lies inside the defined ambiguity set, and the resulting particles from the approximation to the posterior. The resulting posteriors may be used to yield the lower and upper bounds on subsequent calculations used for decision-making. If the metric used for decision-making is not sensitive to the resulting posteriors, it may be assumed that decisions taken are robust to prior uncertainty.

翻译：模型更新在结构健康监测中常用于确定结构的运行状态及是否需要维护。通过传感器采集的数据，可更新某些初始未知的基于物理模型参数的值。用于模型更新的贝叶斯推断方法需假设先验分布。该先验选择可能影响后验预测及后续维护需求的决策，尤其在工程应用中常出现信息量不足的数据情形下。因此，理解先验选择如何影响后验预测具有重要价值。本文提出一种稳健贝叶斯推断技术，评估所选名义先验邻近范围内的最优和最劣先验及其对应后验。该技术采用一种相互作用Wasserstein梯度流公式。通过两个数值案例（双香蕉形后验分布与双梁结构）展示所提算法。最优和最劣先验通过指定模糊集建模，该模糊集包含与名义先验统计距离小于或等于给定半径的所有分布。示例展示了粒子如何从初始假设的高斯分布流向定义模糊集内的最优最劣先验分布，以及通过近似后验得到的粒子结果。所得后验可用于为决策所需的后续计算提供上下界。若用于决策的度量对所得后验不敏感，则可认为所做出的决策对先验不确定性具有稳健性。