A sampling-based reliability-based design optimization using kriging metamodel with constraint boundary sampling

초록

First Order reliability Method (FORM) is the most common approach to calculate probability of failure for reliability analysis. It is used in Reliability Based Design Optimization (RBDO) and provides acceptable solutions. However, for problems involving highly nonlinear performance functions, this method may not provide reliable results. Compared to FORM, Monte Carlo Simulation (MCS) is more accurate and provides a simple sampling method. The limitations of MCS are that it is very computationally intensive and may not be used in gradient-based optimization algorithms for RBDO. In order to overcome the disadvantages of both methods, we propose a new RBDO method based on a Latin Hypercube Sampling (LHS) using the Kriging metamodel with Constraint Boundary Sampling (CBS). In this new method, an MPP search is not required and it can provide more improved computational efficiency than the MCS techniques for reliability analysis. A LHS technique applied to the Kriging metamodel is used in this work to assess the uncertainty in a design, which can be incorporated with a gradient based optimizer for RBDO. Because the proposed method can make use of analytic sensitivities and smoothness of probability of failure estimate using the Cumulative Distribution Function (CDF) and Probability Density Function(PDF), which are constructed using Moving Least Square (MLS). RBDO test problems are used to demonstrate the effectiveness of the proposed method in reducing the number of function evaluations.

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