Dedicated enrichment strategy for gradient-based MDO using disciplinary surrogates

Abstract Gradient-based optimization is commonly used to solve nonlinear, constrained optimization problems, and it is widely used in multidisciplinary design analysis and optimization (MDAO). The success of gradient-based MDAO relies on accurate evaluation of the gradient and Jacobian matrix of the objective function and constraints of the problem. High fidelity multidisciplinary design analyses (MDAs) are often built and solved by coupling blackbox disciplinary solvers that do not necessarily provide derivative information. The gradient and Jacobian matrices must then be approximated. This article builds on the concept of disciplinary surrogate models to create these approximations. We study the important characteristics that surrogate models should respect and propose an adaptive construction of these approximations in an MDAO context. The corresponding enrichment strategy is shown to improve disciplinary solver derivative approximation, without significantly compromising the accuracy of the MDA solution at the queried point. Moreover, the proposed approach can be used in a blackbox disciplinary solver context, while incurring a significantly lower computational cost when compared to the use of finite-difference approximations. Numerical results on an analytical and an engineering test case (structural wing sizing) illustrate and validate the proposed methodology.