A new kind of regional importance measure of the input variable and its state dependent parameter solution

Abstract To further analyze the effect of different regions within input variable on the variance and mean of the model output, two new regional importance measures (RIMs) are proposed, which are the “contribution to variance of conditional mean (CVCM)” and the “contribution to mean of conditional mean (CMCM)”. The properties of the two RIMs are analyzed and their relationships with the existing contribution to sample variance (CSV) and contribution to sample mean (CSM) are derived. Based on their characteristics, the highly efficient state dependent parameter (SDP) method is introduced to estimate them. By virtue of the advantages of the SDP-based method, the same set of sample points utilized for solving CSM and CSV is enough to estimate CVCM and CMCM. Several examples demonstrate that CVCM can provide further information on the existing CSV, which can effectively instruct the engineer on how to achieve a targeted reduction of the main effect of each input variable. CMCM can act as effectively as the CSM, but the convergence and stability for estimating CMCM by numerical simulation is better than those for estimating CSM. Besides, the efficiency and accuracy of the SDP-based method are also testified by the examples.

[1]  A. Saltelli,et al.  Non-parametric statistics in sensitivity analysis for model output: A comparison of selected techniques , 1990 .

[2]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[3]  T. Ishigami,et al.  An importance quantification technique in uncertainty analysis for computer models , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[4]  Terry Andres,et al.  Sensitivity analysis of model output: an investigation of new techniques , 1993 .

[5]  Peter C. Young,et al.  Non-parametric estimation of conditional moments for sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[6]  Peter C. Young,et al.  State Dependent Parameter metamodelling and sensitivity analysis , 2007, Comput. Phys. Commun..

[7]  Harry Millwater,et al.  Development of a localized probabilistic sensitivity method to determine random variable regional importance , 2012, Reliab. Eng. Syst. Saf..

[8]  M. Ratto,et al.  Using recursive algorithms for the efficient identification of smoothing spline ANOVA models , 2010 .

[9]  S. Hora,et al.  A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis , 1990 .

[10]  E. Nadaraya.  On Estimating Regression , 1964 .

[11]  Enrique F. Castillo,et al.  Sensitivity analysis in optimization and reliability problems , 2008, Reliab. Eng. Syst. Saf..

[12]  Stefano Tarantola,et al.  Contribution to the sample mean plot for graphical and numerical sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[13]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[14]  Eugenijus Uspuras,et al.  Sensitivity analysis using contribution to sample variance plot: Application to a water hammer model , 2012, Reliab. Eng. Syst. Saf..

[15]  Andrea Saltelli,et al.  Sensitivity Analysis for Importance Assessment , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  A. Sudjianto,et al.  First-order saddlepoint approximation for reliability analysis , 2004 .

[17]  Agus Sudjianto,et al.  Relative Entropy Based Method for Probabilistic Sensitivity Analysis in Engineering Design , 2006 .

[18]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox , 2002 .

[19]  Moon-Hyun Chun,et al.  An uncertainty importance measure using a distance metric for the change in a cumulative distribution function , 2000, Reliab. Eng. Syst. Saf..

[20]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .