On-the-fly model reduction for large-scale structural topology optimization using principal components analysis

Xiao, Manyu; Lu, Dongcheng; Breitkopf, Piotr; Raghavan, Balaji; Dutta, Subhrajit; Zhang, Weihong

doi:10.1007/s00158-019-02485-3

Cited by 42 publications

(19 citation statements)

References 49 publications

(63 reference statements)

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“…Gogu 39 used reduced models constructed on‐the‐fly for minimum compliance problems. Dimension reduction of the state and adjoint problems using principal component analysis, singular value decomposition and proper orthogonal decomposition (POD) have been suggested recently 24,40,41 . Another related contribution uses POD on the density distribution map in order to roughly predict the optimized layout 42 .…”

Section: Introductionmentioning

confidence: 99%

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

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An efficient computational approach to stress‐constrained topology optimization is presented. Using a multigrid‐preconditioned Krylov solver for the state and adjoint problems, the number of Krylov iterations is reduced significantly by enforcing early termination of the iterative solves. The criterion for early termination is based on the convergence of the design sensitivities with respect to Krylov iterations. Consequently, the progress of optimization is not affected by the inexact resolution of the state and adjoint problems. The proposed approach is demonstrated on several design problems that possess different characteristics of the maximum stress. Optimization results obtained with early termination show very good agreement with those obtained with an accurate direct solver—in terms of objective value, constrained maximum stress and overall number of design cycles. Savings of 80% in the number of Krylov iterations are achieved, compared to the number of iterations required to satisfy the force residual convergence criterion to a common tolerance. The approach is directly applicable to high‐resolution problems that are solved on parallel computational environments. A MATLAB code for reproducing the results is freely available at https://github.com/odedamir/topopt-stress-inexact-sensitivities

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Section: Introductionmentioning

confidence: 99%

Efficient stress‐constrained topology optimization using inexact design sensitivities

Amir

2021

Numerical Meth Engineering

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“…Ferro et al (Ferro et al 2019) applied the principal component analysis (PCA) to the density map, obtaining an efficient numerical scheme for STO. Xiao et al (Xiao et al 2020) proposed a proper orthogonal decomposition (POD) scheme, related to PCA, to construct a reduced basis for the displacement field solution of FEA, to be used during the optimization; subsequently, the reduced basis is adaptively updated on-the-fly according to an error metric. Less recently, Wang et al (Wang et al 2007) proposed a method based on the Krylov subspaces, while Amir et al (Amir et al 2009) proposed the construction of a reduced order model using the combined approximations method.…”

Section: Introductionmentioning

confidence: 99%

A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Montanino

Alaimo

Lanzarone

2021

Struct Multidisc Optim

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Structural topology optimization (STO) is usually treated as a constrained minimization problem, which is iteratively addressed by solving the equilibrium equations for the problem under consideration. To reduce the computational effort, several reduced basis approaches that solve the equilibrium equations in a reduced space have been proposed. In this work, we apply functional principal component analysis (FPCA) to generate the reduced basis, and we couple FPCA with a gradient-based optimization method for the first time in the literature. The proposed algorithm has been tested on a large STO problem with 4.8 million degrees of freedom. Results show that the proposed algorithm achieves significant computational time savings with negligible loss of accuracy. Indeed, the density maps obtained with the proposed algorithm capture the larger features of maps obtained without reduced basis, but in significantly lower computational times, and are associated with similar values of the minimized compliance.

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“…the size of the model adopted for state estimation. The use of reduced model is widely proposed in the literature for simplifying both the model-based design (Palomba et al 2015;Xiao et al 2020;Delissen et al 2020) and the control synthesis (Caracciolo et al 2008). The model in (19) is therefore recast in the modal canonical form by using the linear transformation…”

Section: Introduction Of a State-observermentioning

confidence: 99%

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

Belotti

Richiedei

Trevisani

2020

Struct Multidisc Optim

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The paper proposes a multi-domain approach to the optimization of the dynamic response of an underactuated vibrating linear system through eigenstructure assignment, by exploiting the concurrent design of the mechanical properties, the regulator and state observers. The approach relies on handling simultaneously mechanical design and controller synthesis in order to enlarge the set of the achievable performances. The underlying novel idea is that structural properties of controlled mechanical systems should be designed considering the presence of the controller through a concurrent approach: this can considerably improve the optimization possibilities. The method is, first, developed theoretically. Starting from the definition of the set of feasible system responses, defined through the feasible mode shapes, an original formulation of the optimality criterion is proposed to properly shape the allowable subspace through the optimal modification of the design variables. A proper choice of the modifications of the elastic and inertial parameters, indeed, changes the space of the allowable eigenvectors that can be achieved through active control and allows obtaining the desired performances. The problem is then solved through a rank-minimization with constraints on the design variables: a convex optimization problem is formulated through the “semidefinite embedding lemma” and the “trace heuristics”. Finally, experimental validation is provided through the assignment of a mode shape and of the related eigenfrequency to a cantilever beam controlled by a piezoelectric actuator, in order to obtain a region of the beam with negligible oscillations and the other one with large oscillations. The results prove the effectiveness of the proposed approach that outperforms active control and mechanical design when used alone.

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On-the-fly model reduction for large-scale structural topology optimization using principal components analysis

Cited by 42 publications

References 49 publications

Efficient stress‐constrained topology optimization using inexact design sensitivities

Efficient stress‐constrained topology optimization using inexact design sensitivities

A gradient-based optimization method with functional principal component analysis for efficient structural topology optimization

Multi-domain optimization of the eigenstructure of controlled underactuated vibrating systems

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