Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

翻译：贝叶斯模型标定是数字孪生与计算机实验的核心，它通过估计标定参数并修正系统模型偏差，使模型输出与实地观测对齐。经典贝叶斯标定引入潜在参数和差异函数来建模偏差，但存在参数与差异的混杂问题，且通常基于平稳数据假设被构建为离线流程。这些局限性在现代数字孪生应用中构成制约——系统随时间演变，可能呈现渐变漂移与突变状态切换。尽管数据同化方法支持序贯更新，但它们通常不显式建模系统偏差，且在突变场景下效果欠佳。本文提出贝叶斯递归投影标定（BRPC），一种面向模拟器失配与非平稳流式数据的在线贝叶斯标定框架。BRPC将投影标定扩展至在线设置，通过为标定参数分离无差异粒子更新、为差异函数分离条件高斯过程更新，在系统渐变演化下保持可辨识性并实现偏差感知自适应。为应对突变变化，BRPC集成重启机制以检测状态切换并重置标定过程。我们为这两个组件建立理论保障，包括渐变演化下的跟踪性能，以及重启机制的虚警与检测行为。合成数据与工厂仿真基准实验表明，BRPC在渐变变化下提升了标定精度；而相较于滑动窗口贝叶斯标定与数据同化基线方法，带重启增强的BRPC进一步提升了突变状态切换下的鲁棒性与预测性能。