Active Manifold and Model-Order Reduction to Accelerate Multidisciplinary Analysis and Optimization

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

“…However, such a linear subspace based approach will often not be able to approximate the solutions of hyperbolic systems, which involve discontinuity and non-linearity, with small number of modes. One has to make use of the local reducedorder models interpolation [31] or nonlinear manifold based [32] approaches. Another interesting aspect of our future work within this research project will be to address these issues in the context pertinent to the guided ultrasonic wave propagation in damaged fiber metal laminates.…”

“…The accuracy of such reduced models depends on the parameters that are sampled from the domain. In POD-based PMOR, the parameter sampling is accomplished in a greedy fashion-an approach that takes a locally best solution hoping that it would lead to the global optimal solution [25][26][27][28][29][30][31][32][33][34][35][36][37]. It seeks to determine the configuration at which the reduced-order model yields the largest error, solves to obtain the Hi-Fi response for that configuration and subsequently updates the reduced-order model.…”

“…Based on the type of underlying PDE several a posteriori error estimators [38][39][40][41][42], which are relevant to MOR, were developed in the past. Most of the estimators used in [26][27][28][29][30][31][32][33][36][37][38][39][40][41]43,44] focused on the affine parameter dependency of the Hi-Fi model, which resulted in an offline/online decomposition approach: expensive computations of lower-order matrices are done offline while the norm of the residual for any given parameter configuration was computed online with a minimal effort.…”

“…Therefore, a strong investigation is going on in the MOR research community to reduce the Kolmogorov n-width of the solution manifold [45,46]. Projection-based MOR along with an active manifold was carried out by Boncoraglio et al [32] to efficiently solve multidisci-plinary design optimization problem, which blends both linear and nonlinear constraints in aerodynamics. The authors used a deep convolutional autoencoder to discover the pertinent active manifold for dimensionality reduction of a high-dimensional design parameter space (58 structural and shape parameters).…”

“…The accuracy of POD-based global reduced-order model, which produces the response for any point in the parametric space, depends on the size of the extracted global reducedorder basis. In some cases, due to the extensively large parametric space obtaining an efficient global reduced-order model is quixotic (as in the case of [32]). To overcome this limitation of global reduced-order model approach, Y. Choi et al [31] presented a novel methodology that accelerates the solution of design optimization problem.…”