A New Approach to Solve Uncertain Multidisciplinary Design Optimization Based on Conditional Value at Risk

Abstract

Design optimization of complex engineering problems often involves multiple disciplines or subsystems that usually exist couplings or data interactions with each other. Multidisciplinary design optimization (MDO) is an advanced methodology to deal with such problems. Besides, uncertainty is a crucial factor affecting the performance of complex systems. Therefore, uncertain MDO (UMDO) is the focus of current engineering design research. This article proposes a novel (UMDO) method based on the conditional value at risk (CVaR) as a supplement and alternative scheme to traditional (UMDO) approaches. First, the number of multidisciplinary analyses of complex systems was reduced using collaboration models. Second, metamodels were constructed to simulate data interaction between multidisciplinary systems. Then, an approximate method for CVaR under uncertainty risk analysis was derived. A UMDO framework based on CVaR was constructed. The optimization process was driven by the gradient-based Monte Carlo simulation method. Finally, three different complexity examples verified the accuracy and efficiency of the proposed approach. Note to Practitioners —This article is motivated by the problem of optimization under uncertainty for complex multidisciplinary systems, but it is also applicable to other single-disciplinary uncertain optimizations. Existing uncertain multidisciplinary design optimization (UMDO) methods usually require complex multidisciplinary decoupling and uncertainty propagation analysis, which limits the application of complex system optimization methods. This article suggests a new method that uses the conditional value at risk (CVaR) analysis to quantify uncertain parameters and uses a collaboration model to decouple multidisciplinary systems. This method provides an effective new scheme for the optimization of complex systems under uncertainties. In this article, we describe mathematically the expression and approximation methods of CVaR analysis. We then show how to effectively decouple multidisciplinary systems through a collaboration model. Finally, a framework for UMDO is constructed. By applying this method to three examples, the results suggest that this method is feasible and effective. In future research, the problem of complex system optimization under mixed uncertainties of parameters and models will be investigated.