Summary and conclusions
A new sampling technique is proposed in this study. This sampling technique is based on salient features of the Latin hypercube sampling technique and the point concentration method. In this technique, the original probability density function of a random variable is replaced by к probability concentrations determined from the point estimate method. These probability concentrations are then used with the Latin hypercube sampling technique to obtain samples. It is shown that by using this technique an unbiased estimator of the expectation of a performance function that is a polynomial of degree less than 2к-1 can be obtained. For highly nonlinear functions, the proposed technique provides an approximate estimate and the error is due to terms of order higher than 2k-1.
Illustrative numerical examples indicate that the proposed technique could be more efficient than the Latin hypercube sampling technique since the former could significantly reduce the required number of evaluations of the performance function. This is particularly important when the numerical evaluation of the performance function is computationally intensive. Also the numerical results suggest that the proposed technique provides relatively stable and accurate results even for highly nonlinear performance functions.
The financial support of the Natural Science and Engineering Research Council of Canada is gratefully acknowledged.
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