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AUTHOR(S):

Zdenek Kala

 

TITLE

Benchmark of Goal Oriented Sensitivity Analysis Methods Using Ishigami Function

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ABSTRACT

The present paper deals with the Goal Oriented Sensitivity Analysis. The median-oriented sensitivity analysis (MSA) is presented which measures sensitivities by applying absolute distances between model outputs Y and median of Y. The median is used as the alternative central parameter to arithmetical mean applied by the established Sobol sensitivity analysis (SSA). General agreements and differences between MSA and SSA are studied by applying the Ishigami function. The paper shows that the sensitivity analysis need not necessarily be based on the analysis of variance known as ANOVA, but that there exist alternate approaches, too. CPU demanding character of MSA is approximately identical to that of SSA. The proposed MSA is efficient and practical for the problems in which it is necessary to quantify the importance of each input variable with respect to the median.

KEYWORDS

Sensitivity analysis, interaction, mean value, median, model, stochastic, uncertainty, Sobol

REFERENCES

[1] E. Borgonovo, E. Plischke, Sensitivity analysis: A review of recent advances, European Journal of Operational Research, Vol.248, No.3, 2016, pp. 869–887.

[2] A. Saltelli, M. Ratto, T. Andress, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Global Sensitivity Analysis Guiding the Worth of Scientific Models, New York: John Wiley and Sons, 2007.

[3] A. Saltelli, S. Tarantola, F. Campolongo, M. Ratto, Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, New York: John Wiley and Sons, 2004.

[4] I.M. Sobol', Sensitivity Estimates for Nonlinear Mathematical Models, Matematicheskoe Modelirovanie 2, pp.112–118, 1990. (in Russian, translated into English in Sobol' 1993)

[5] A. Saltelli, I.M. Sobol’, About the use of rank transformation in sensitivity analysis of model output, Reliability Engineering and System Safety 50 (1995) 225–239.

[6] S. Xiao, Z. Lu, P. Wang, Global Sensitivity Analysis Based on Distance Correlation for Structural Systems with Multivariate Output, Engineering Structures, Vol.167, 2018, pp. 74–83.

[7] Fort JC, Klein T, Rachdi N. New sensitivity analysis subordinated to a contrast. Communications in Statistics - Theory and Methods 2016;45(15):4349–4364.

[8] T. Ishigami, T. Homma, An Importance Quantification Technique in Uncertainty Analysis for Computer Models, in: Proc. of the ISUMA’90, First International Symposium on Uncertainty Modeling and Analysis, University of Maryland, 1990, pp. 398–403.

[9] K. Cheng, Z. Lu, Y. Wei, Y. Shi, Y. Zhou, Mixed Kernel Function Support Vector Regression for Global Sensitivity Analysis, Mechanical Systems and Signal Processing, Vol.96, 2017, pp. 201–214.

[10] E. Borgonovo, A New Uncertainty Importance Measure, Reliability Engineering and System Safety, Vol.92, 2007, pp. 771–784.

[11] B. Sudret, Global Sensitivity Analysis using Polynomial Chaos Expansions, Reliability Engineering and System Safety, Vol.93, 2008, pp. 964–979.

[12] P. Wei, Z. Lu, W. Ruan, J. Song, Regional Sensitivity Analysis using Revised Mean and Variance Ratio Functions, Reliability Engineering and System Safety, Vol.121, 2014, pp. 121–135.

[13] J. Cariboni, D. Gatelli, R. Liska, A. Saltelli, The Role of Sensitivity Analysis in Ecological Modelling, Ecological modelling, Vol.203, No.1-2, 2007, pp. 167–182.

[14] M. Crosetto, S. Tarantola, A. Saltelli, Sensitivity and Uncertainty Analysis in Spatial Modelling based on GIS, Agriculture, Ecosystems & Environment, Vol.81, No.1, 2000, pp. 71-79.

[15] J.P.C. Kleijnen, Design and Analysis of Simulation Experiments, Springer (2008).

[16] F. Campolongo, A. Saltelli, J. Cariboni, From Screening to Quantitative Sensitivity Analysis. A unified approach, Computer Physics Communications, Vol.182, 2011, pp. 978-988.

[17] A. Saltelli, S. Tarantola, K. Chan, Quantitative model-independent method for global sensitivity analysis of model output, Technometrics, Vol.41, No.1, 1999, pp. 39-56.

[18] V. Maume-Deschamps, I. Niang, Estimation of Quantile Oriented Sensitivity Indices, Statistics and Probability Letters, Vol.134, 2018, pp. 122-127.

[19] C. Delenne, B. Cappelaere, V. Guinot, Uncertainty Analysis of River Flooding and Dam Failure Risks using Local Sensitivity Computations, Reliability Engineering & System Safety, Vol.107, 2012, pp. 171-183.

[20] Y. Xiong, Y. Jing, T. Chen, Sensitivity Analysis and Sensitivity-based Design for Linear Alarm Filters, Control Engineering Practice, Vol.70, 2012, pp. 29-39.

[21] F. Ferretti, A. Saltelli, S. Tarantola, Trends in Sensitivity Analysis Practice in the Last Decade, Science of the Total Environment, Vol.568, 2016, pp. 666-670.

[22] G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experiment. An Introduction to Design, Data Analysis and Model Building, Wiley, New York (1978).

[23] Z. Kala, Factorial Designs as a Tool for Fuzzy Sensitivity Analysis Problems, International Journal of Mathematical and Computational Methods, Vol.1, 2016, pp. 264-267.

[24] K. Tang, P.M. Congedo, R. Abgrall, Adaptive Surrogate Modeling by ANOVA and Sparse Polynomial Dimensional Decomposition for Global Sensitivity Analysis in Fluid Simulation, Journal of Computational Physics, Vol.314, 2016, pp. 557-589.

[25] E. Borgonovo, E. Plischke, Sensitivity analysis: A review of recent advances, European Journal of Operational Research, Vol.248, No.3, 2016, pp. 869–887.

[26] W. Tian, A Review of Sensitivity Analysis Methods in Building Energy Analysis, Renewable and Sustainable Energy Reviews, Vol.20, 2013, pp. 411–419.

[27] P. Wei, Z. Lu, J. Song, Variable Importance Analysis: A Comprehensive Review, Reliability Engineering & System Safety, Vol.142, 2015, pp. 399–432.

[28] J. Antucheviciene, Z. Kala, M. Marzouk, E.R. Vaidogas, Solving Civil Engineering Problems by Means of Fuzzy and Stochastic MCDM Methods: Current State and Future Research, Mathematical Problems in Engineering, Vol.2015, 2015, Article number 362579.

[29] R. C. Iman, W. J. Conover, Small Sample Sensitivity Analysis Techniques for Computer Models with an Application to Risk Assessment, Communications in Statistics – Theory and Methods, Vol.9, No.17, 1980, pp. 1749–1842.

[30] M. D. McKey, R. J. Beckman, W. J. Conover, A Comparison of the Three Methods of Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, Vol.21, 1979, pp. 239–245.

[31] Z. Kala, J. Valeš, J. Jönsson, Random Fields of Initial out of Straightness Leading to Column Buckling, Journal of Civil Engineering and Management, Vol.23, No.7, 2017, pp. 902-913.

[32] J. Antucheviciene, Z. Kala, M. Marzouk, E.R. Vaidogas, Solving Civil Engineering Problems by Means of Fuzzy and Stochastic MCDM Methods: Current State and Future Research, Mathematical Problems in Engineering, Vol.2015, 2015, Article number 362579.

[33] Z. Kala, J. Valeš, Global Sensitivity Analysis of Lateral-torsional Buckling Resistance Based on Finite Element Simulations, Engineering Structures, Vol.134, 2017, pp. 37-47.

[34] Z. Kala, J. Valeš, Sensitivity Assessment and Lateral-torsional Buckling Design of I-beams using Solid Finite Elements, Journal of Constructional Steel Research, Vol.139, 2017, pp. 110-122.

[35] W. Liu, X. Wu, L. Zhang, Y. Wang, J. Teng, Sensitivity Analysis of Structural Health Risk in Operational Tunnels, Automation in Construction, Vol.94, 2018, pp. 135-153.

[36] Z. Kala, J. Valeš, Imperfection Sensitivity Analysis of Steel Columns at Ultimate Limit State, Archives of Civil and Mechanical Engineering, Vol.18, 2018, pp. 1207-1218.

Cite this paper

Zdenek Kala. (2018) Benchmark of Goal Oriented Sensitivity Analysis Methods Using Ishigami Function. International Journal of Mathematical and Computational Methods, 3, 43-50

 

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