SVR-TO-APMA: Hybrid efficient modelling and topology framework for stable topology optimization with accelerated performance measure approach

Abstract

The topology design under uncertainties is an acceptable framework for providing a safe design and optimum configuration of structures. In this regard, the accuracy, efficiency, and robustness of the analytical topology optimization coupled with reliability analysis are the main efforts for reliability-based topology optimization (RBTO) of continuous structures. In the present investigation, a hybrid RBTO approach is developed for robust iterative formulation of reliability loop and an effective and simple optimization approach for topology loop. A multi-level set analytical framework is proposed based on the performance measure approach to seek the optimum results under multi uncertainties in size, mechanical properties, and loads of structures. The considered topology optimization procedure to derive the optimal layout of the structure which is called moving iso-surface threshold (MIST) is a powerful and enhanced topology optimization method in which, unlike other optimization methods, it has the capability of having no direct sensitivity analysis making it easier and simple. The accelerated first-order reliability method is introduced for searching the most probability points in the reliability loop of the RBTO model. The proposed reliability method is developed based on a stable iterative formulation. For reducing the computational burden of the topology optimization loop, the machine learning approach given from the support vector regression (SVR) is applied for estimating the probabilistic constraints in the RBTO model. Four examples of 2D, and 3D compliance, 2D complaint mechanism problem, and frequency maximization are presented for validation and highlighting the abilities in having the most accuracy and safety levels of the proposed hybrid framework named SVR-TO-APMA. The results indicate that the hyperparameters of SVR are directly affected by the accuracy of RBTO results. The stability of the RBTO model is shown by the accelerated PMA and the optimum layout is different from topology optimization in comparison with the RBTO results for 3D compliance and frequency maximization problems. The optimum design with uncertainties is increased by about 40%–90% with a reliability index of 3 compared to TO results for the studied example.