Leveraging Adapted Polynomial Chaos Metamodels for Real-Time Bayesian Updating

Abstract

As engineered systems face an ever-increasing array of threats, the ability to perform real-time predictions and decision-making is central for coping with potential menaces. For thorough real-time predictions, uncertainty measures need to be incorporated, albeit conventional uncertainty quantification (UQ) efforts are often time-consuming and thus go against the essence of real-time decision-making. A fast, metamodel-based Bayesian updating scheme within a decision-making framework under uncertainty framework is proposed. The latter combines data harnessing, assimilation, and parameter updating in an online setting. For fast parameter updating in the online phase, the adaptation property of polynomial chaos (PC) metamodels is exploited. In the offline phase, a global Gaussian approximation of the response surface is obtained through a first-order PC surrogate, from which, a rotated basis of the underlying Gaussian Hilbert space is identified. In the subsequent online phase, a cheap, locally adapted solution embedded in a lower dimensional subspace is leveraged within a Bayesian updating setting to perform fast data assimilation. Incorporating uncertainty into real-time decision-making paves the way for higher confidence in online predictions, increased system resilience, and adaptivity to surroundings. The aforementioned fast parameter updating scheme based on adapted PC metamodels is evaluated on a set of problems with varying complexity.