Machine-specified ground structures for topology optimization of binary trusses using graph embedding policy network

摘要

This paper proposes the concept of machine-specified ground structures for topology optimization of trusses. Unlike general ground structures with dense and regular connectivity, machine-specified ground structures are sparse stable ground structures with a specified number of members designed by machines. Firstly, the generation process of machine-specified ground structures from a given node-set is formulated as a reinforcement learning task. Graph embedding is used to integrate the structural information into a comprehensive feature matrix to describe the state. By establishing the policy network, the probability of each action, i.e., selecting each node in the node-set, is obtained based on the comprehensive feature matrix. The task is solved using a gradient-based algorithm called REINFORCE. A randomized 4×4 node-set is used to train the agent. The policy converges with a high average reward, and generates different yet reasonable structures because a stochastic policy is employed. Besides, the agent can handle different-sized node-sets without re-training. Hence, the machine-specified ground structures generated by the trained agent can be utilized to assist the structural topology design. Subsequently, a method for a typical problem with singular optimal solutions, i.e., topology optimization of binary trusses with stress and displacement constraints, is proposed based on machine-specified ground structures. Finally, through different-sized numerical examples, it is demonstrated that the machine-specified ground structures lead to a variety of optimal solutions, and it is more likely to obtain the global optimum than fully-connected ground structures. It is worth noting that machine-specified ground structures can also be applied to other problems without re-training.