Efficient And Robust Algorithms For Reliability-Based Design Optimization Of Structures

There are a lot of uncertainty factors in practical engineering, such as external load environment, material property, geometrical shape, initial condition, manufacturing tolerance, boundary condition, etc. Reliability method measures the structural safety level based on probabilistic theory. Reliability-based design optimization (RBDO) combines the reliability theory and optimization to minimize the structural cost or other performance under uncertainty variables. RBDO approach consists of a nested double loop structures, and it should deal with reliability analysis and outer deterministic optimization. Accuracy, efficiency and robustness are the key of the RBDO approaches, thus many new approaches were suggested to improve these three aspects for RBDO. In general, the RBDO approaches can be divided into three types:double loop approaches, decoupled approaches and single loop approaches. However, all these approaches meet non-convergence problems when RBDO models with the high nonlinear performance function, non-normal distribution variables and large variable coefficient are involved. Thus, it is of great theoretical and practical significance to propose an efficient, robust and effective RBDO approaches. In this paper, the efficient and robust reliability analysis/inverse reliability analysis methods are proposed. Furthermore, the effective RBDO approaches are established to improve the efficiency and robustness of existing RBDO approaches.1. The modified chaos control method of HL-RF algorithm is proposed to evaluate the reliability index. The non-convergence phenomenon for non-normal distribution variables and highly nonlinear problems is analyzed. The efficiency and robustness of RBDO approaches are improved remarkably by controlling the different directions of iterative points. Besides, the function type criterion is used to identify the oscillation of iterative point. By comparing with different approaches, it is found that the modified chaos control method is more efficient and robust than other HL-RF methods.2. The phenomenon of non-convergence for concave performance functions is analyzed, and the sequential optimization and reliability assessment (SORA) based on modified chaos control method is suggested. Firstly, the failure reason of non-convergence for complicated performance function is analyzed, and the iterative point of inverse reliability analysis has directivity. The modified chaos control (MCC) method is further introduced, and the efficiency of inverse reliability analysis is improved significantly. Secondly, the function type criterion is employed for MCC, and the hybrid chaos control (HCC) method is suggested to evaluate both convex and concave problems efficiently. Thirdly, the HCC method is applied for SORA to evaluate the concave problems efficiently and robustly.3. The adaptive hybrid loop approach (AHLA) is proposed to solve RBDO problems with different types of performance functions. Firstly, the adaptive chaos control (ACC) method is introduced to conquer the difficulty of selecting control factor. Secondly, the oscillate criterion of design point is proposed to combine the efficiency of single loop approach and robustness of double loop approach, and the AHLA is further established. Therefore, AHLA performs well for black-box function, and it shows more efficiency and robust than other RBDO approaches.4. In order to solve the RBDO model of stiffened shells with multiple optima and high nonlinear performance measure function, a global RBDO approach is suggested based on ACC method, surrogate model and evolutionary algorithm, and the stiffened shells with geometric imperfections are optimized. Firstly, the MPTP is calculated efficiently based on ACC method. Secondly, the global RBDO approach is established by combining the merits of surrogate model and particle swarm optimization (PSO). Thirdly, the updating strategy are adopted to enhance the local accuracy of surrogate model, thus the framework of the proposed method contains three loops:reliability analysis, global optimum search and surrogate model updating strategy. The effectiveness of the proposed method is validated by benchmark examples. Then, the proposed method is applied for lightweight design of stiffened shells with geometric imperfections. It is found that RBDO shows superiority compared to the initial design and deterministic optimization from the aspects of safety and economical cost.