Enhanced Data-driven Topology Design Methodology with Multi-level Mesh and Correlation-based Mutation for Stress-related Multi-objective Optimization

Topology optimization (TO) serves as a widely applied structural design approach to tackle various engineering problems. Nevertheless, sensitivity-based TO methods usually struggle with solving strongly nonlinear optimization problems. By leveraging high capacity of deep generative model, which is an influential machine learning technique, the sensitivity-free data-driven topology design (DDTD) methodology is regarded as an effective means of overcoming these issues. The DDTD methodology depends on initial dataset with a certain regularity, making its results highly sensitive to initial dataset quality. This limits its effectiveness and generalizability, especially for optimization problems without priori information. In this research, we proposed a multi-level mesh DDTD-based method with correlation-based mutation module to escape from the limitation of the quality of the initial dataset on the results and enhance computational efficiency. The core is to employ a correlation-based mutation module to assign new geometric features with physical meaning to the generated data, while utilizing a multi-level mesh strategy to progressively enhance the refinement of the structural representation, thus avoiding the maintenance of a high degree-of-freedom (DOF) representation throughout the iterative process. The proposed multi-level mesh DDTD-based method can be driven by a low quality initial dataset without the need for time-consuming construction of a specific dataset, thus significantly increasing generality and reducing application difficulty, while further lowering computational cost of DDTD methodology. Various comparison experiments with the traditional sensitivity-based TO methods on stress-related strongly nonlinear problems demonstrate the generality and effectiveness of the proposed method.

Data-driven topology design based on principal component analysis for 3D structural design problems

Topology optimization is a structural design methodology widely utilized to address engineering challenges. However, sensitivity-based topology optimization methods struggle to solve optimization problems characterized by strong non-linearity. Leveraging the sensitivity-free nature and high capacity of deep generative models, data-driven topology design (DDTD) methodology is considered an effective solution to this problem. Despite this, the training effectiveness of deep generative models diminishes when input size exceeds a threshold while maintaining high degrees of freedom is crucial for accurately characterizing complex structures. To resolve the conflict between the both, we propose DDTD based on principal component analysis (PCA). Its core idea is to replace the direct training of deep generative models with material distributions by using a principal component score matrix obtained from PCA computation and to obtain the generated material distributions with new features through the restoration process. We apply the proposed PCA-based DDTD to the problem of minimizing the maximum stress in 3D structural mechanics and demonstrate it can effectively address the current challenges faced by DDTD that fail to handle 3D structural design problems. Various experiments are conducted to demonstrate the effectiveness and practicability of the proposed PCA-based DDTD.

Data-driven topology design using a deep generative model

In this paper, we propose a structural design methodology called \textit{data-driven topology design}, which aims to obtain high-performance material distributions for a multi-objective optimization problem from the initially given material distributions in a given design domain. Its basic idea is iterating the following processes: (i) selecting the material distributions from a dataset according to Pareto optimality, (ii) generating new material distributions using a deep generative model with the selected material distributions as the training data, and (iii) integrating the generated material distributions into the dataset. Because of the nature of a deep generative model, the generated material distributions are diverse and inheriting features of the training data, which are material distributions on the Pareto front at that specific point. Therefore, it is expected that some of the generated material distributions are superior to the training data, whereas some are inferior, and the Pareto front is improved by integrating the generated material distributions into the dataset. The Pareto front is further improved by iterating the above processes. Data-driven topology design is used to enhance a support system for determining appropriate formulations of topology optimization problems, and its usefulness is demonstrated through numerical examples.