Study On Probabilistic Structural Design Optimization Based On Performance Measurement Analysis

Due to the shortage of natural resources and energy, the research on optimization design of engineering structures has been highly valued. However, the fact that traditional structural optimization methods could not take full account of the uncertainties in material properties and external loads during structures'lifetime may lead to structural failure because of low reliability or resource waste because of high reliability. As a result, probabilistic structural design optimization(PSDO) has been proposed. However, the prohibitive computation cost of PSDO limits its application in engineering. Therefore, It is significant to study how to develop an efficient and robust algorithm for PSDO.The content in this paper can be summarized as follows:1. The common calculation methods for PSDO have been introduced detailedly, including reliability index approach (RIA), performance measure approach (PMA), single loop and single vector (SLSV) and sequential optimization and reliability assessment (SORA). Because PMA is more efficient, stable and less dependent on probabilistic distribution than RIA, we mainly conducted the research on PMA and SORA that is based on PMA. Therefore the general methods for calculating probabilistic performance measure(PPM) in PMA are also reviewed, which include advanced mean value(AMV), hybrid mean value(HMV), chaos control(CC) and modified chaos control(MCC).2. In this paper a step length adjustment (SLA) iterative algorithm, which introduces a "new" step length to control the convergence of the sequence, is proposed. The step length may be constant during the whole iteration process or decrease successively several times using a self-adjust strategy. It is proved that the AMV method is a special case of SLA when the step length tends to infinity. SLA is as simple as AMV and does not need the prior knowledge of convexity or concavity of the performance function as other modified algorithms do. Numerical results of several highly nonlinear performance functions indicate that SLA is more effective and robust compared with other methods like AMV, HMV and CC. Moreover, several examples also indicate that PSDO based on SLA is more efficient than other methods.3. In this paper, approximate sequential optimization and reliability assessment (ASORA) is proposed, which is based on the concept of SORA. Approximate most probable target point (MPTP) is adopted in reliability assessment. In each cycle, the approximate MPTP and the sensitivity of performance function at this point need to be reserved, which will be used to build approximate constraint and obtain new approximate MPTP in the next cycle. The adoption of approximate MPTP can dramatically reduce the number of performance function evaluations since the calculation of PPM no longer needs multiple iterations. Besides, there is no need to evaluate the performance functions in the deterministic optimization since the approximate MPTP and the sensitivity of performance function at this point are used to formulate the linear Taylor expansion of the constraint functions, which also enhance efficiency. The numerical examples indicate that the design variables and approximate MPTP can converge simultaneously. Numerical results of several examples also show that the proposed method is robust and more efficient than SORA and other common RBDO methods.