Efficient sampling-based Rbdo by using virtual support vector machine and improving the accuracy of the Kriging method

The objective of this study is to propose an efficient sampling-based RBDO using a new classification method to reduce the computational cost. In addition, accuracy improvement strategies for the Kriging method are proposed to reduce the number of expensive computer experiments. Current research effort involves: (1) developing a new classification method that is more efficient than conventional surrogate modeling methods while maintaining required accuracy level; (2) developing a sequential adaptive sampling method that inserts samples near the limit state function; (3) improving the efficiency of the RBDO process by using a fixed hyper-spherical local window with an efficient uniform sampling method and identification of active/violated constraints; and (4) improving the accuracy of the Kriging method by introducing several strategies.

In the sampling-based RBDO, only accurate classification information is needed instead of accurate response surface. On the other hand, in general, surrogates are constructed using all available DoE samples instead of focusing on the limit state function. Therefore, the computational cost of surrogates can be relatively expensive; and the accuracy of the limit state (or decision) function can be sacrificed in return for reducing the error on unnecessary regions away from the limit state function. On the contrary, the support vector machine (SVM), which is a classification method, only uses support vectors, which are located near the limit state function, to focus on the decision function. Therefore, the SVM is very efficient and ideally applicable to sampling-based RBDO, if the accuracy of SVM is improved by inserting virtual samples near the limit state function.

The proposed sequential sampling method inserts new samples near the limit state function so that the number of DoE samples is minimized. In many engineering problems, expensive computer simulations are used and thus the total computational cost needs to be reduced by using less number of DoE samples.

Several efficiency strategies such as: (1) launching RBDO at a deterministic optimum design, (2) hyper-spherical local windows with an efficient uniform sampling method, (3) filtering of constraints, (4) sample reuse, (5) improved virtual sample generation, are used for the proposed sampling-based RBDO using virtual SVM.

The number of computer experiments is also reduced by implementing accuracy improvement strategies for the Kriging method. Since the Kriging method is used for generating virtual samples and generating response surface of the cost function, the number of computer experiments can be reduced by introducing: (1) accurate correlation parameter estimation, (2) penalized maximum likelihood estimation (PMLE) for small sample size, (3) correlation model selection by MLE, and (4) mean structure selection by cross-validation (CV) error.