Reliability-based design and load tolerance evaluation using stochastic response surface and probabilistic sensitivities.

摘要

Uncertainty is inevitable in structural design. This research presents an efficient uncertainty analysis technique based on stochastic response surfaces (SRS). The focus is on calculating uncertainty propagation using fewer number of function evaluations. Due to sensitivity analysis, the gradient information of the performance is efficiently calculated and used in constructing SRS.; Based on SRS, reliability-based design optimization (RBDO) is studied intensively in this research. Probability sensitivity analysis using the sampling technique is also proposed. Since the computational cost of RBDO increases significantly proportional to the increasing number of random variables, global sensitivity analysis is introduced to adaptively reduce unessential random variables. It has been shown that the global sensitivity indices can be calculated analytically because the SRS employs the Hermite polynomials as bases.; Traditional structural design focuses on designing a reliable structure under well characterized random factors (dimensions, shape, material properties, etc). Variations of these parameters are relatively small and well characterized. However, everyday engineering life tends to use the existing structural part in a different applications instead of designing a completely new part. In this research, a reliability-based safety envelope concept for load tolerance is introduced. This shows the capacity of the current design as a future reference for design upgrade, maintenance and control. The safety envelope is applied to estimate the load tolerance of a structural part with respect to the reliability of fatigue life.; Stochastic response surface is also applied on robust design in this research. It is shown that the polynomial chaos expansion with appropriate bases provides an accurate and efficient tool in evaluating the performance variance. In addition, the sensitivity of the output variance, which is critical in the mathematical programming method, is calculated by consistently differentiating the polynomial chaos expansion with respect to the design variables. A reliability-based robust design method that can reduce the variance of the output performance as well as the deviation of the mean value is proposed using SRS and efficient sensitivity analysis. Numerical examples are shown to verify accuracy of the sensitivity information and the convergence of the robust design problem.