Topology Optimization via Machine Learning and Deep Learning: A Review

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (1) TO and (2) ML perspectives. The TO perspective addresses "why" to use ML for TO, while the ML perspective addresses "how" to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined

Modular-topology optimization of structures and mechanisms with free material design and clustering

Topology optimization of modular structures and mechanisms enables balancing the performance of automatically-generated individualized designs, as required by Industry 4.0, with enhanced sustainability by means of component reuse. For optimal modular design, two key questions must be answered: (i) what should the topology of individual modules be like and (ii) how should modules be arranged at the product scale? We address these challenges by proposing a bi-level sequential strategy that combines free material design, clustering techniques, and topology optimization. First, using free material optimization enhanced with post-processing for checkerboard suppression, we determine the distribution of elasticity tensors at the product scale. To extract the sought-after modular arrangement, we partition the obtained elasticity tensors with a novel deterministic clustering algorithm and interpret its outputs within Wang tiling formalism. Finally, we design interiors of individual modules by solving a single-scale topology optimization problem with the design space reduced by modular mapping, conveniently starting from an initial guess provided by free material optimization. We illustrate these developments with three benchmarks first, covering compliance minimization of modular structures, and, for the first time, the design of non-periodic compliant modular mechanisms. Furthermore, we design a set of modules reusable in an inverter and in gripper mechanisms, which ultimately pave the way towards the rational design of modular architectured (meta)materials.Comment: 30 page

Evolutionary topology optimization of continuum structures under uncertainty using sensitivity analysis and smooth boundary representation

This paper presents an evolutionary approach for the Robust Topology Optimization (RTO) of continuum structures under loading and material uncertainties. The method is based on an optimality criterion obtained from the stochastic linear elasticity problem in its weak form. The smooth structural topology is determined implicitly by an iso-value of the optimality criterion field. This iso-value is updated using an iterative approach to reach the solution of the RTO problem. The proposal permits to model the uncertainty using random variables with different probability distributions as well as random fields. The computational burden, due to the high dimension of the random field approximation, is efficiently addressed using anisotropic sparse grid stochastic collocation methods. The numerical results show the ability of the proposal to provide smooth and clearly defined structural boundaries. Such results also show that the method provides structural designs satisfying a trade-off between conflicting objectives in the RTO problem.The authors would like to thank Dr. Francisco Periago for constructive suggestions and discussions. This work has been partially supported by the AEI/FEDER and UE under the contract DPI2016-77538-R and by the “Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia” under the contract 19274/PI/14

Multi-objective topology optimization to reduce vibration of micro-satellite primary supporting structure

We applied multi-objective topology optimization to reduce vibration of the primary supporting structure of video satellites in the frequency domain. The optimal structure is obtained by the multi-objective topology optimization with stiffness and random vibration response as the targets. This is compared with the optimal structure obtained by single-objective topology optimization with stiffness as the target. The dynamic analysis results show that the root mean square values in all three spatial directions of the optimal structure by the multi-objective optimization are smaller than that of the single-objective optimization. The maximal declining value reaches 2.94 g, and the maximal declining degree is 30.6 %. The maximal declining response value on the top of the cylinder reaches 3.87 g with a degree of 33.0 %. The results demonstrate that the multi-objective optimization method significantly improves the vibration response of the base plate, which therefore suppressed the vibration of the satellite. An acceptance condition experiment is performed for the satellite with the optimal base plate from the multi-objective optimization. The dynamic analysis results match well with the experimental data, and verify the applicability of the multi-objective optimization

On the use of Artificial Neural Networks in Topology Optimisation

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation have been proposed with varying success. Other works focused on speed-up through replacing expensive optimisers and state solvers, or reducing the design-space have been attempted, but have not yet received the same attention. The portfolio of articles presenting different applications has as such become extensive, but few real breakthroughs have yet been celebrated. An overall trend in the literature is the strong faith in the "magic" of artificial intelligence and thus misunderstandings about the capabilities of such methods. The aim of this article is therefore to present a critical review of the current state of research in this field. To this end, an overview of the different model-applications is presented, and efforts are made to identify reasons for the overall lack of convincing success. A thorough analysis identifies and differentiates between problematic and promising aspects of existing models. The resulting findings are used to detail recommendations believed to encourage avenues of potential scientific progress for further research within the field.Comment: 36 pages, 7 figures (13 figures counting sub-figures), accepted for publication in Structural and Multidisciplinary Optimizatio