An Efficient Optimization Procedure for Reliability-Based Robust Multi-objective Design Applied to Reinforced Concrete Structures

Abstract

Concrete structure designs use semi-probabilistic methods that apply safety factors to compensate for uncertainties, increasing loads and reducing resistances. While this ensures safety and reliability, probabilistic methods offer a more comprehensive approach by quantifying the probability of failure for a structure. We applied Reliability-Based Design Optimization (RBDO) and Reliability-Based Robust Multi-objective Design Optimization (RBRMDO) to a reinforced concrete linear plane frame. The study compared efficiency among procedures, considering accuracy, processing time, iterations, function evaluations, and Pareto point distribution quality. The main contribution lies in investigating various algorithm combinations to identify the most efficient and robust procedure for multi-objective optimization under uncertainties in concrete structure designs. The numerical methods Reliability Index Approach (RIA), Performance Measure Approach (PMA), Single-Loop Approach (SLA), and Sequential Optimization and Reliability Assessment (SORA) were coupled with Weighted Sum (WS) and Normal-Boundary Intersection (NBI) methods to build the Pareto frontier. The optimization used Sequential Quadratic Programming (SQP) through the Scipy library. The structural analysis employed the Finite Element Method (FEM) through the CasPy package. The reliability analysis employed the First-Order Reliability Method (FORM) for RIA and PMA through the Pystra package. SLA and SORA used a FORM routine implemented by us. HL-RF algorithm assessed the Most Probable Point (MPP) and finite differences calculated numerical derivatives. We tested four examples before the main design. SLA is the most efficient algorithm, and SORA presents excellent results. RIA and PMA underperformed in processing time and limit state function evaluations. NBI outperformed in the Pareto point distribution quality compared to WS.