Iterative Most Probable Point Search Method for Problems With a Mixture of Random and Interval Variables

To represent input variability accurately, an input distribution model for random variables should be constructed using many data. However, for certain input variables, engineers may have only their intervals, which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. To consider both input variability and uncertainty, inverse reliability analysis should be carried out considering both random and interval variables—mixed variables—and their mathematical correlation in a performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed-variable problem. The update procedures for MPP search are developed considering the features of mixed variables in the inverse reliability analysis. MPP search for random and interval variables proceed simultaneously to consider the mathematical correlation. An interpolation method is introduced to find a better candidate MPP without additional function evaluations. Mixed-variable design optimization (MVDO) has been formulated to obtain cost-effective and reliable design in the presence of mixed variables. In addition, the design sensitivity of a probabilistic constraint has been developed for an effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds an accurate MPP more efficiently than the generic optimization method does. In addition, it is verified that the developed method enables the MVDO process with a small number of function evaluations.

Reliability-Based Design Optimization Using Step Length Adjustment Algorithm and Sequential Optimization and Reliability Assessment Method

A step length adjustment (SLA) iterative algorithm was proposed for locating the minimum performance target point (MPTP) in the inverse reliability analysis. This paper elaborates SLA and two deliberately designed numerical examples are used to compare SLA with other algorithms appearing in recent literatures for locating MPTP. The results show that SLA is much more robust and efficient. Then SLA and sequential optimization and reliability assessment (SORA) are combined to solve reliability-based design optimization (RBDO) problems. In the reliability assessment of SORA, with the design obtained from the previous cycle, SLA is used to locate MPTP. Then in the deterministic optimization, the boundaries of violated constraints are shifted to the feasible direction according to the MPTP obtained in the reliability assessment. Several examples frequently cited in similar studies are used to compare SORA-SLA with other RBDO algorithms. The results indicate the effectiveness and robustness of SORA-SLA.

Iterative Most Probable Point Search Method for Problems With Mixture of Random and Interval Variables

To represent input variability accurately, input distribution model for random variables should be constructed using many observations or data. However, for certain input variables, engineers may have only their bounds which represent input uncertainty. In practical engineering applications, both random and interval variables could exist at the same time. For the applications, to consider both input variability and uncertainty, inverse reliability analysis should be carried out considering the mixed variables and their mathematical correlation in performance measure. In this paper, an iterative most probable point (MPP) search method has been developed for the mixed variable problem. The random and interval variables update procedures are developed considering the features of mixed variable in the inverse reliability analysis. Both variable update methods proceed one iteration simultaneously to consider the mathematical correlation. An interpolation method is introduced to find better candidate MPP without additional function evaluations. Mixed variable design optimization (MVDO) has been formulated to obtain cost effective and reliable design in the presence of the mixed variables. In addition, the design sensitivity of probabilistic constraint has been developed for effective and efficient MVDO procedure. Using numerical examples, it is found that the developed MPP search method finds accurate MPP more efficiently than generic optimization method. In addition, it is verified that the developed method enables MVDO process with small number of function evaluations.