Global reliability analysis-based optimization design of steel frame structure using direct probability integral method and genetic algorithm

Traditional reliability-based optimization design faces challenges, such as difficulties in identifying failure modes and calculating correlation coefficients. To address these issues, this paper specifically investigates the optimization design problem of steel frame structures that meet normal serviceability performance requirements and develops a structural optimization design method based on the Direct Probability Integral Method and Genetic Algorithm (DPIM-GA). First, a joint probability density integral equation for the extremal mappings of multiple performance functions is derived based on the principle of probability conservation. The equation is solved with probability space partitioning and Dirac function smoothing techniques. Second, the performance function of the structural failure mode is identified, and the global reliability index of structures is calculated using DPIM with the Heaviside function. The global reliability index is used as a constraint condition and incorporated into the objective function through the penalty function method, transforming it into an unconstrained optimization problem. Additionally, to address the difficulty of obtaining performance functions of multi-layer structural systems through simple analytical formulas, a method employing response surface functions to fit the performance functions is proposed. Finally, a ten-story steel frame structural is used as a case, optimizing the cross-sectional design to meet the target reliability index. The optimized results are compared with Monte Carlo simulations (MCS) to verify the efficiency and accuracy of the proposed method.