Bayesian Surrogate Learning for Uncertainty Analysis of Coupled Multidisciplinary Systems

Engineering systems are often composed of many subsystems that interact with each other. These subsystems, referred to as disciplines, contain many types of uncertainty and in many cases are feedback-coupled with each other. In designing these complex systems, one needs to assess the stationary behavior of these systems for the sake of stability and reliability. This requires the system level uncertainty analysis of the multidisciplinary systems, which is often computationally intractable. To overcome this issue, techniques have been developed for capturing the stationary behavior of the coupled multidisciplinary systems through available data of individual disciplines. The accuracy and convergence of the existing techniques depend on a large amount of data from all disciplines, which are not available in many practical problems. Toward this, we have developed an adaptive methodology that adds the minimum possible number of samples from individual disciplines to achieve an accurate and reliable uncertainty propagation in coupled multidisciplinary systems. The proposed method models each discipline function via Gaussian process (GP) regression to derive a closed-form policy. This policy sequentially selects a new sample point that results in the highest uncertainty reduction over the distribution of the coupling design variables. The effectiveness of the proposed method is demonstrated in the uncertainty analysis of an aerostructural system and a coupled numerical example.