Distribution-free Monte Carlo simulation: Premise and refinement

From cost estimation to reliability analysis, Monte Carlo simulation has found its niche in a wide variety of applications in civil engineering. With recognition of correlations among variables, recent efforts have been devoted to model the correlations more accurately and with no restriction on the form of marginal distributions, i.e., being distribution free. Yet, the conventional method introduced by Iman and Conover, although widely accepted, is bound to have errors: The generated correlation matrix may bear no resemblance to the desired correlation matrix. The purposes of this study are to shed light on the underlying premises of the conventional method and to refine the method by reducing the errors to an acceptable level automatically. A particle swarm optimization algorithm is proposed to repair invalid (nonpositive definite) correlation matrices and to bring the generated correlation matrix into conformity with the desired target. The effectiveness of the proposed algorithm has been verified in estimating cost of electrical services based on historical data.