Active Manifold and Model Reduction for Multidisciplinary Analysis and Optimization

Abstract

View Video Presentation: https://doi.org/10.2514/6.2021-1694.vid A computational framework is proposed for efficiently solving multidisciplinary analysis and optimization (MDAO) problems in a relatively high-dimensional design space. It relies on the appropriate blend of linear and nonlinear projection-based model order reduction to accelerate analysis and optimization; and on a new concept of nonlinear active manifold (AM) to mitigate the curse of dimensionality during the training of projection-based reduced-order models (PROMs). The method of AM relies on the nonlinear concept of a deep convolutional autoencoder for dimensionality reduction: it is proposed as a superior alternative to the concept of an active subspace whose capabilities are limited by the capabilities of an affine approximation. The proposed computational framework also blends the concept of a global PROM as a surrogate model of a discretized nonlinear partial differential equation (PDE)- based behavior function with that of a database of local, linear PROMs for approximating, wherever appropriate, a linear PDE-based behavior function. Adaptive parameter sampling is performed for training the global, nonlinear PROM as well as for populating the database of local, linear PROMs. The proposed computational framework is demonstrated for the solution of an MDAO problem formulated for a flexible instance of NASA’s Common Research Model, where the objective function pertains to aerodynamics in the transonic regime, the constraint relates to flutter, and the design space contains 58 structural and aerodynamic shape design variables. The obtained numerical results illustrate the potential of the AM method for addressing the curse of dimensionality. They also demonstrate the feasibility of the computational framework for realistic MDAO problems and highlight its potential for reducing solution time.