Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even after model calibration due to the model discrepancy, which may result from deliberate modeling decisions, ignorance, or lack of knowledge. If the mismatch between simulation and measurements are deemed unacceptable, the model has to be improved. Targeted model improvement is challenging due to a non-local impact of model discrepancies on measurements and the dependence on sensor configurations. Many approaches to model improvement, such as Bayesian calibration with additive mismatch terms, gray-box models, symbolic regression, or stochastic model updating, often lack interpretability, generalizability, physical consistency, or practical applicability. This paper introduces a non-intrusive approach to model discrepancy analysis using mixture models. Instead of directly modifying the model structure, the method maps sensor readings to clusters of physically meaningful parameters, automatically assigning sensor readings to parameter vector clusters. This mapping can reveal systematic discrepancies and model biases, guiding targeted, physics-based refinements by the modeler. The approach is formulated within a Bayesian framework, enabling the identification of parameter clusters and their assignments via the Expectation-Maximization (EM) algorithm. The methodology is demonstrated through numerical experiments, including an illustrative example and a real-world case study of heat transfer in a concrete bridge.

翻译：在土木工程应用中，对复杂物理系统进行建模时，需要在物理保真度与实用性之间寻求平衡。因此，即使经过模型校准，由于模型差异（可能源于有意的建模决策、认知局限或知识缺乏），仿真结果与实测数据之间的偏差仍然普遍存在。若仿真与实测之间的失配被认为不可接受，则必须对模型进行改进。由于模型差异对测量结果具有非局部影响且依赖于传感器配置，针对性的模型改进具有挑战性。现有许多模型改进方法（如添加失配项的贝叶斯校准、灰箱模型、符号回归或随机模型更新）往往在可解释性、泛化能力、物理一致性或实际适用性方面存在不足。本文提出一种基于混合模型的非侵入式模型差异分析方法。该方法不直接修改模型结构，而是将传感器读数映射至具有物理意义的参数簇，自动将传感器读数分配至参数向量簇。这种映射能够揭示系统性差异和模型偏差，从而指导建模者进行有针对性的、基于物理原理的模型精修。该方法在贝叶斯框架内构建，可通过期望最大化（EM）算法识别参数簇及其分配关系。通过数值实验（包括一个示意性案例和一个混凝土桥梁热传递的实际案例研究）验证了所提方法的有效性。