Model Reduction Framework with a New Take on Active Subspaces for Optimization Problems with Linearized Fluid‐Structure Interaction Constraints

Abstract

In this paper, a new take on the concept of an active subspace for reducing the dimension of the design parameter space in a multidisciplinary analysis and optimization (MDAO) problem is proposed. The new approach is intertwined with the concepts of adaptive parameter sampling, projection-based model order reduction, and a database of linear, projection-based reduced-order models equipped with interpolation on matrix manifolds, in order to construct an efficient computational framework for MDAO. The framework is fully developed for MDAO problems with linearized fluidstructure interaction constraints. It is applied to the aeroelastic tailoring, under flutter constraints, of two different flight systems: a flexible configuration of NASA's Common Research Model; and NASA's Aeroelastic Research Wing #2 (ARW-2). The obtained results illustrate the feasibility of the computational framework for realistic MDAO problems and highlight the benefits of the new approach for constructing an active subspace in both terms of solution optimality and wall-clock time reduction.

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

“…Recently a component‐based data‐driven approach has been proposed to assess the structural integrity of aircraft components 7 , 8 in the context of modern digital twins incorporating not only data but also physical models, also referred to as hybrid twins. 9 For multidisciplinary analysis and optimization involving reduction in both input and output spaces we cite References 10 and 11 , while for a specific naval engineering application we suggest. 12 …”

Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction

“…As highlighted in (13) and the first bullet below that equation, it is important to perform the ECSW training for the PROM predictions and not those of its underlying HDM. In the case of the traditional affine approximation, this is achieved by projecting the solution snapshots collected in the matrix S on the right ROB V; and constructing the matrix C and vector d defining the least squares problem (16) and its early termination criterion (17) using the projected snapshots.…”

“…Using this approximation and a projection that may or may not be orthogonal, PMOR transforms the HDM of interest into a lower dimensional computational model of dimension n N known as a projection-based reduced-order model (PROM). The technique is becoming increasingly invaluable for many different forms of parametric applications arising in computational structural dynamics (CSD) [1,2], multiscale modeling [3,4,5,6], computational fluid dynamics (CFD) [7,8,9], uncertainty quantification (UQ) [10], model predictive control (MPC) [11], optimization [12], and multidisciplinary design analysis and optimization (MDAO) [13]. It allows for the parsimonious representation of a large-scale, dynamically complex, and computationally intensive HDM.…”

A non‐linear non‐intrusive reduced order model of fluid flow by auto‐encoder and self‐attention deep learning methods

“…In this case, the reduced‐order models (ROMs) technology plays an important role as they are able to simulate physical systems accurately with several orders of magnitude CPU speed‐up. The ROMs have been applied successfully to a number of research fields such as data assimilation, 3 ocean modeling, 4 shallow water equations, 5,6 air pollution prediction, 7 polynomial systems, 8 viscous and inviscid flows, 9 fluid‐structure interaction, 10 aerodynamic shape optimization, 11 large‐scale time‐dependent systems, 12 optimal control, 13 circuit systems, 14,15 inverse problems, 16 fluids, 17 reservoir history matching, 18 and turbulent flows 19,20 …”