Reliability-based design optimization (RBDO) in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Kriging-model-based RBDO is an effective method to overcome this difficulty. However, the accuracy of Kriging model depends directly on how to select the sample points. In this paper, the local adaptive sampling (LAS) is proposed to enhance the efficiency of constructing Kriging models for RBDO problems. In LAS, after initialization, new samples for probabilistic constraints are mainly selected within the local region around the current design point from each optimization iteration, and in the local sampling region, sample points are first considered to be located on the limit state constraint boundaries. The size of the LAS region is adaptively defined according to the nonlinearity of the performance functions. The computation capability of the proposed method is demonstrated using three mathematical RBDO problems and a honeycomb crash-worthiness design application. The comparison results show that the proposed method is very efficient.

A local adaptive sampling method for reliability-based design optimization using Kriging model

A comparative study and stiffness analysis of angular contact ball bearings under different preload mechanisms

Reliability-based design optimization (RBDO) combined with metamodel is a powerful tool to deal with variation of system output induced by uncertainties during practical engineering design. In this paper, the importance boundary sampling (IBS) method is proposed to enhance the efficiency of Kriging-model-based RBDO. Rather than fitting all the parts of the limit state constraints precisely within the design region, the proposed IBS mainly selects sample points on the critical parts of the limit state constraints. Two importance coefficients are proposed to identify these critical boundary parts: the first importance coefficient is determined by the objective function value; and the second one is calculated using the joint probability density value of the design variables. The sampling and optimization processes are conducted alternately to select the sample points more rationally. The computation capability of the proposed method is demonstrated using several mathematical RBDO problems and a box girder design application. The comparison results show that the proposed IBS method is very efficient.

An important boundary sampling method for reliability-based design optimization using kriging model

Formulation of five degrees of freedom ball bearing model accounting for the nonlinear stiffness and damping of elastohydrodynamic point contacts

Constrained design optimization of selected mechanical system components using Rao algorithms

Design optimization of an angular contact ball bearing for the main shaft of a grinder

One of the most challenging obstacles to overcome when implementing reliability-based design optimization (RBDO) is the intensive computational demand of the reliability analysis. Among the many reliability analysis techniques, the enhanced dimension reduction (eDR) method is known to have a high efficiency. While the goal is to generate an accurate and efficient reliability analysis using the smallest possible number of sampling points, it is difficult to determine such a number a priori since it mostly depends on the nonlinearity of the constraint to be approximated and the degree of uncertainty in the design factor along which we want to integrate. In order to resolve this issue, an eDR method with variable sampling points is proposed in this work. The main idea of the suggested method is to employ a different number of axial sampling points for each random design factor. We first use three sampling points for each random variable and employ the proposed criteria to decide whether or not to increase the number of sampling points. This notion of employing variable sampling points increases the efficiency of the conventional eDR method without sacrificing accuracy. In order to evaluate the performance of RBDO using the suggested reliability analysis method, the proposed scheme is applied to mathematical and engineering RBDO problems and the results are compared with those obtained using both the conventional eDR method with fixed sampling points and the performance measure approach (PMA) method. The results of the comparison clearly demonstrate that RBDO using the suggested reliability analysis method is superior to conventional methods in terms of accuracy and efficiency.

Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points

The performances of an angular contact ball bearing (ACBB) are influenced by its geometric dimensions that can have uncertainty due to manufacturing tolerances. Uncertainty of these geometric dimensions results in uncertainty of the performances. This study performed robust design optimization considering the uncertainty of the geometric dimensions which affect the performances of an ACBB, mounted on the main shaft of a grinder. Six geometric parameters and an axial preload were selected as design variables. Among these design variables, three geometric variables were regarded as random design variables that have significant uncertainty of geometric dimensions. To ensure manufacturing precision of the grinder, simultaneously maximizing means and minimizing standard deviations of both axial and radial stiffness values were defined as objective functions. Constraints were imposed to consider uncertainty of the performance functions. A quasi-static analysis was employed to evaluate the bearing performances. The means and standard deviations of the performances were evaluated by the enhanced dimensional reduction method. Robust design optimization was performed using the progressive quadratic response surface method. The robust optimum design revealed that the performance and robustness of both stiffness values were improved than the initial design of the ACBB while satisfying all constraints.

Kibong Kang

Papers

Design optimization of an angular contact ball bearing for the main shaft of a grinder

Reliability-based design optimization using an enhanced dimension reduction method with variable sampling points

Robust design optimization of an angular contact ball bearing under manufacturing tolerance