Momentum-based accelerated mirror descent stochastic approximation for robust topology optimization under stochastic loads

Robust topology optimization (RTO) improves the robustness of designs with respect to random sources in real-world structures, yet an accurate sensitivity analysis requires the solution of many systems of equations at each optimization step, leading to a high computational cost. To open up the full potential of RTO under a variety of random sources, this article presents a momentum-based accelerated mirror descent stochastic approximation (AC-MDSA) approach to efficiently solve RTO problems involving various types of load uncertainties. The proposed framework performs high-quality design updates with highly noisy and biased stochastic gradients. The sample size is reduced to two (minimum for unbiased variance estimation) and is shown to be sufficient for evaluating stochastic gradients to obtain robust designs, thus drastically reducing the computational cost. The AC-MDSA update formula based on entropic ℓ₁-norm is derived, which mimics the feasible space geometry. A momentum-based acceleration scheme is integrated to accelerate the convergence, stabilize the design evolution, and alleviate step size sensitivity. Several 2D and 3D examples are presented to demonstrate the effectiveness and efficiency of the proposed AC-MDSA to handle RTO involving various loading uncertainties. Comparison with other methods shows that the proposed AC-MDSA is superior in computational cost, stability, and convergence speed.