Quantile-oriented global sensitivity analysis of design resistance
Abstract
The article investigates the application of a new type of global quantile-oriented sensitivity analysis (called QSA in the article) and contrasts it with established Sobol’ sensitivity analysis (SSA). Comparison of QSA of the resistance design value (0.1 percentile) with SSA is performed on an example of the analysis of the resistance of a steel IPN 200 beam, which is subjected to lateral-torsional buckling. The resistance is approximated using higher order polynomial metamodels created from advanced non-linear FE models. The main, higher order and total effects are calculated using the Latin Hypercube Sampling method. Noticeable differences between the two methods are found, with QSA apparently revealing higher sensitivity of the resistance design value to random input second and higher order interactions (compared to SSA). SSA cannot identify certain reliability aspects of structural design as comprehensively as QSA, particularly in relation to higher order interactions effects of input imperfections. In order to better understand the reasons for the differences between QSA and SSA, two simple examples are presented, where QSA (median) and SSA show a general agreement in the calculation of certain sensitivity indices.
Keyword : sensitivity analysis, quantile, resistance, lateral-torsional buckling, imperfections, steel, random sampling
How to Cite
Kala, Z. (2019). Quantile-oriented global sensitivity analysis of design resistance. Journal of Civil Engineering and Management, 25(4), 297-305. https://doi.org/10.3846/jcem.2019.9627
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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D’Angelo, L., & Nussbaumer, A. (2017). New framework for calibration of partial safety factors for fatigue design. Journal of Constructional Steel Research, 139, 466-472. https://doi.org/10.1016/j.jcsr.2017.10.006
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Galambos, T. V. (1998). Guide to stability design criteria for metal structures (5th ed.). Wiley.
Hariri-Ardebili, M. A., & Pourkamali-Anaraki, F. (2018). Simplified reliability analysis of multi hazard risk in gravity dams via machine learning techniques. Archives of Civil and Mechanical Engineering, 18(2), 592-610. https://doi.org/10.1016/j.acme.2017.09.003
Iman, R. L., & Conover, W. J. (1980). Small sample sensitivity analysis techniques for computer models. With an application to risk assessment. Communications in Statistics – Theory and Methods, 9(17), 1749-1842. https://doi.org/10.1080/03610928008827996
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Kala, Z. (2012). Geometrically non-linear finite element reliability analysis of steel plane frames with initial imperfections. Journal of Civil Engineering and Management, 18(1), 81-90. https://doi.org/10.3846/13923730.2012.655306
Kala, Z. (2015). Reliability analysis of the lateral torsional buckling resistance and the ultimate limit state of steel beams with random imperfections. Journal of Civil Engineering and Management, 21(7), 902-911. https://doi.org/10.3846/13923730.2014.971130
Kala, Z. (2016a). Global interval sensitivity analysis of hermite probability density function percentiles. International Journal of Mathematical Models and Methods in Applied Sciences, 10, 373-380.
Kala, Z. (2016b). Global sensitivity analysis in stability problems of steel frame structures. Journal of Civil Engineering and Management, 22(3), 417-424. https://doi.org/10.3846/13923730.2015.1073618
Kala, Z. (2018). Benchmark of goal oriented sensitivity analysis methods using Ishigami function. International Journal of Mathematical and Computational Methods, 3, 43-50.
Kala, Z., & Valeš, J. (2017a). Sensitivity assessment and lateral-torsional buckling design of I-beams using solid finite elements. Journal of Constructional Steel Research, 139, 110-122. https://doi.org/10.1016/j.jcsr.2017.09.014
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Kala, Z., & Valeš, J. (2018). Imperfection sensitivity analysis of steel columns at ultimate limit state. Archives of Civil and Mechanical Engineering, 18(4), 1207-1218. https://doi.org/10.1016/j.acme.2018.01.009
Kala, Z., Valeš, J., & Jönsson, J. (2017). Random fields of initial out of straightness leading to column buckling. Journal of Civil Engineering and Management, 23(7), 902-913. https://doi.org/10.3846/13923730.2017.1341957
Kucherenko, S., Song, S., & Wang, L. (2019). Quantile based global sensitivity measures. Reliability Engineering and System Safety, 185, 35-48. https://doi.org/10.1016/j.ress.2018.12.001
Li, L., Lu, Z., Zhang, K., & Gao, Q. (2017). General validation and decomposition of the variance-based measures for models with correlated inputs. Aerospace Science and Technology, 62, 75–86. https://doi.org/10.1016/j.ast.2016.12.003
Liu, C., He, L., Yhenyu, W., & Yuan, J. (2018). Experimantal study on joint stiffness with vision-based system and geometric imperfections of temporary member structure. Journal of Civil Engineering and Management, 24(1), 43-52. https://doi.org/10.3846/jcem.2018.299
Massart, P. (2003). Concentration ineQualities and model selection. New York: Springer.
Maume-Deschamps, V., & Niang, I. (2018). Estimation of quantile oriented sensitivity indices. Statistics and Probability Letters, 134, 122-127. https://doi.org/10.1016/j.spl.2017.10.019
McKey, M. D., Beckman, R. J., & Conover, W. J. (1979). A comparison of the three methods of selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.
Melcher, J., Kala, Z., Holický, M., Fajkus, M., & Rozlívka, L. (2004). Design characteristics of structural steels based on statistical analysis of metallurgical products. Journal of Constructional Steel Research, 60(3-5), 795-808. https://doi.org/10.1016/S0143-974X(03)00144-5
Melcher, J., Kala, Z., Karmazínová, M, Fajkus, M., Holický, M., Rozlívka, L., & Puklický, L. (2008). Statistical evaluation of material characteristics and their influence on design strength of structural steel of S355. In Proceedings of the 5th European Conference on Steel and Composite Structures, Research – Practice – New materials (Eurosteel 2008) (pp. 809-814). Graz, Austria.
Model Code. (2001). Joint Committee of Structural Safety (JCSS). Retrieved from http://www.jcss.ethz.ch
Rachdi, N. (2011). Apprentissage statistiQue et computer experiments – Approche Quantitative du risQue et des incertitudes en modélisation (PhD thesis, Université Toulouse). Retrieved from http://thesesups.ups-tlse.fr/1538/1/2011TOU30283.pdf
Rubinstein, R. Y. (1981). Guide to stability design criteria for metal structures. New York: John Wiley and Sons.
Sadowski, A., Rotter, J. M., Reinke, T., & Ummenhofer, T. (2015). Statistical analysis of the material properties of selected structural carbon steels. Structural Safety, 53, 26-35. https://doi.org/10.1016/j.strusafe.2014.12.002
Saltelli, A., Chan, K., & Scott, E. M. (2004). Sensitivity analysis. Wiley series in probability and statistics. New York: John Wiley and Sons.
Sedlacek, G., & Kraus, O. (2007). Use of safety factors for the design of steel structures according to the Eurocodes. Engineering Failure Analysis, 14(3), 434-441. https://doi.org/10.1016/j.engfailanal.2005.08.002
Sedlacek, G., & Müller, C. (2006). The European standard family and its basis. Journal of Constructional Steel Research, 62(11), 1047-1059. https://doi.org/10.1016/j.jcsr.2006.06.027
Sobol’, I. M. (1993). Sensitivity analysis for non–linear mathematical models. Mathematical Modelling and Computational Experiment, 1, 407-414. [Translated from Russian: I. M. Sobol’. 1990. Sensitivity estimates for nonlinear mathematical models. Matematicheskoe Modelirovanie, 2, 112-118].
Sobol’, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3), 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6
STATREL Manual. (1996). Statistical analysis of data for reliability applications. Version: 3.10.
Vales, J., & Stan, T. C. (2017). FEM modelling of lateral-torsional buckling using shell and solid elements. Procedia Engineering, 190, 464-471. https://doi.org/10.1016/j.proeng.2017.05.365
Vapnik, V. N. (1998). Statistical learning theory. New York: John Wiley and Sons.
Xiao, S., Lu, Z., & Wang, P. (2018). Global sensitivity analysis based on distance correlation for structural systems with multivariate output. Engineering Structures, 167, 74-83. https://doi.org/10.1016/j.engstruct.2018.04.027
Zhang, K., Lu, Z., Wu, D., & Zhang, Y. (2017). Analytical variance based global sensitivity analysis for models with correlated variables. Applied Mathematical Modelling, 45, 748-767. https://doi.org/10.1016/j.apm.2016.12.036
ANSYS. (2014). ANSYS theory release 15.1.
Antucheviciene, J., Kala, Z., Marzouk, M., & Vaidogas, E. R. (2015). Solving civil engineering problems by means of fuzzy and stochastic MCDM methods: Current state and future research. Mathematical Problems in Engineering, Article ID 362579. https://doi.org/10.1155/2015/362579
Borgonovo, E. (2007). A new uncertainty importance measure. Reliability Engineering and System Safety, 92(6), 771-784. https://doi.org/10.1016/j.ress.2006.04.015
Browne, T., Fort, J. C., Iooss, B., & Gratiet, L. L. (2017). Estimate of Quantile-oriented sensitivity indices. Preprint. Retrieved from https://hal.archives-ouvertes.fr/hal-01450891
Chalmovsky, J., Stefanak, J., Mica, L., Kala, Z., Skudois, S., Norkus, A., & Zilioniene, D. (2017). Statistical-numerical analysis for pullout tests of ground anchors. The Baltic Journal of Road and Bridge Engineering, 12(3), 145-153. https://doi.org/10.3846/bjrbe.2017.17
D’Angelo, L., & Nussbaumer, A. (2017). New framework for calibration of partial safety factors for fatigue design. Journal of Constructional Steel Research, 139, 466-472. https://doi.org/10.1016/j.jcsr.2017.10.006
European Committee for Standardization. (2003). Eurocode: Basis of structural design (EN 1990:2002). Brussels. Retrieved from https://www.unirc.it/documentazione/materiale_didattico/599_2010_260_7481.pdf
European Committee for Standardization. (2005). Eurocode 3: Design of steel structures – Part 1: General rules and rules for buildings (EN 1993-1:2005). Retrieved from https://eurocodes.jrc.ec.europa.eu/showpage.php?id=133
Fort, J. C., Klein, T., & Rachdi, N. (2016). New sensitivity analysis subordinated to a contrast. Communications in Statistics – Theory and Methods, 45(15), 4349-4364. https://doi.org/10.1080/03610926.2014.901369
Freudenthal, A. M. (1956). Safety and the probability of structural failure. American Society of Civil Engineers Transactions, 121, 1337-1397.
Galambos, T. V. (1998). Guide to stability design criteria for metal structures (5th ed.). Wiley.
Hariri-Ardebili, M. A., & Pourkamali-Anaraki, F. (2018). Simplified reliability analysis of multi hazard risk in gravity dams via machine learning techniques. Archives of Civil and Mechanical Engineering, 18(2), 592-610. https://doi.org/10.1016/j.acme.2017.09.003
Iman, R. L., & Conover, W. J. (1980). Small sample sensitivity analysis techniques for computer models. With an application to risk assessment. Communications in Statistics – Theory and Methods, 9(17), 1749-1842. https://doi.org/10.1080/03610928008827996
Jönsson, J., & Stand, T. C. (2017). European column buckling curves and finite element modelling including high strength steels. Journal of Constructional Steel Research, 128, 136-151. https://doi.org/10.1016/j.jcsr.2016.08.013
Kala, Z. (2012). Geometrically non-linear finite element reliability analysis of steel plane frames with initial imperfections. Journal of Civil Engineering and Management, 18(1), 81-90. https://doi.org/10.3846/13923730.2012.655306
Kala, Z. (2015). Reliability analysis of the lateral torsional buckling resistance and the ultimate limit state of steel beams with random imperfections. Journal of Civil Engineering and Management, 21(7), 902-911. https://doi.org/10.3846/13923730.2014.971130
Kala, Z. (2016a). Global interval sensitivity analysis of hermite probability density function percentiles. International Journal of Mathematical Models and Methods in Applied Sciences, 10, 373-380.
Kala, Z. (2016b). Global sensitivity analysis in stability problems of steel frame structures. Journal of Civil Engineering and Management, 22(3), 417-424. https://doi.org/10.3846/13923730.2015.1073618
Kala, Z. (2018). Benchmark of goal oriented sensitivity analysis methods using Ishigami function. International Journal of Mathematical and Computational Methods, 3, 43-50.
Kala, Z., & Valeš, J. (2017a). Sensitivity assessment and lateral-torsional buckling design of I-beams using solid finite elements. Journal of Constructional Steel Research, 139, 110-122. https://doi.org/10.1016/j.jcsr.2017.09.014
Kala, Z., & Valeš, J. (2017b). Global sensitivity analysis of lateral-torsional buckling resistance based on finite element simulations. Engineering Structures, 134, 37-47. https://doi.org/10.1016/j.engstruct.2016.12.032
Kala, Z., & Valeš, J. (2018). Imperfection sensitivity analysis of steel columns at ultimate limit state. Archives of Civil and Mechanical Engineering, 18(4), 1207-1218. https://doi.org/10.1016/j.acme.2018.01.009
Kala, Z., Valeš, J., & Jönsson, J. (2017). Random fields of initial out of straightness leading to column buckling. Journal of Civil Engineering and Management, 23(7), 902-913. https://doi.org/10.3846/13923730.2017.1341957
Kucherenko, S., Song, S., & Wang, L. (2019). Quantile based global sensitivity measures. Reliability Engineering and System Safety, 185, 35-48. https://doi.org/10.1016/j.ress.2018.12.001
Li, L., Lu, Z., Zhang, K., & Gao, Q. (2017). General validation and decomposition of the variance-based measures for models with correlated inputs. Aerospace Science and Technology, 62, 75–86. https://doi.org/10.1016/j.ast.2016.12.003
Liu, C., He, L., Yhenyu, W., & Yuan, J. (2018). Experimantal study on joint stiffness with vision-based system and geometric imperfections of temporary member structure. Journal of Civil Engineering and Management, 24(1), 43-52. https://doi.org/10.3846/jcem.2018.299
Massart, P. (2003). Concentration ineQualities and model selection. New York: Springer.
Maume-Deschamps, V., & Niang, I. (2018). Estimation of quantile oriented sensitivity indices. Statistics and Probability Letters, 134, 122-127. https://doi.org/10.1016/j.spl.2017.10.019
McKey, M. D., Beckman, R. J., & Conover, W. J. (1979). A comparison of the three methods of selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.
Melcher, J., Kala, Z., Holický, M., Fajkus, M., & Rozlívka, L. (2004). Design characteristics of structural steels based on statistical analysis of metallurgical products. Journal of Constructional Steel Research, 60(3-5), 795-808. https://doi.org/10.1016/S0143-974X(03)00144-5
Melcher, J., Kala, Z., Karmazínová, M, Fajkus, M., Holický, M., Rozlívka, L., & Puklický, L. (2008). Statistical evaluation of material characteristics and their influence on design strength of structural steel of S355. In Proceedings of the 5th European Conference on Steel and Composite Structures, Research – Practice – New materials (Eurosteel 2008) (pp. 809-814). Graz, Austria.
Model Code. (2001). Joint Committee of Structural Safety (JCSS). Retrieved from http://www.jcss.ethz.ch
Rachdi, N. (2011). Apprentissage statistiQue et computer experiments – Approche Quantitative du risQue et des incertitudes en modélisation (PhD thesis, Université Toulouse). Retrieved from http://thesesups.ups-tlse.fr/1538/1/2011TOU30283.pdf
Rubinstein, R. Y. (1981). Guide to stability design criteria for metal structures. New York: John Wiley and Sons.
Sadowski, A., Rotter, J. M., Reinke, T., & Ummenhofer, T. (2015). Statistical analysis of the material properties of selected structural carbon steels. Structural Safety, 53, 26-35. https://doi.org/10.1016/j.strusafe.2014.12.002
Saltelli, A., Chan, K., & Scott, E. M. (2004). Sensitivity analysis. Wiley series in probability and statistics. New York: John Wiley and Sons.
Sedlacek, G., & Kraus, O. (2007). Use of safety factors for the design of steel structures according to the Eurocodes. Engineering Failure Analysis, 14(3), 434-441. https://doi.org/10.1016/j.engfailanal.2005.08.002
Sedlacek, G., & Müller, C. (2006). The European standard family and its basis. Journal of Constructional Steel Research, 62(11), 1047-1059. https://doi.org/10.1016/j.jcsr.2006.06.027
Sobol’, I. M. (1993). Sensitivity analysis for non–linear mathematical models. Mathematical Modelling and Computational Experiment, 1, 407-414. [Translated from Russian: I. M. Sobol’. 1990. Sensitivity estimates for nonlinear mathematical models. Matematicheskoe Modelirovanie, 2, 112-118].
Sobol’, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3), 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6
STATREL Manual. (1996). Statistical analysis of data for reliability applications. Version: 3.10.
Vales, J., & Stan, T. C. (2017). FEM modelling of lateral-torsional buckling using shell and solid elements. Procedia Engineering, 190, 464-471. https://doi.org/10.1016/j.proeng.2017.05.365
Vapnik, V. N. (1998). Statistical learning theory. New York: John Wiley and Sons.
Xiao, S., Lu, Z., & Wang, P. (2018). Global sensitivity analysis based on distance correlation for structural systems with multivariate output. Engineering Structures, 167, 74-83. https://doi.org/10.1016/j.engstruct.2018.04.027
Zhang, K., Lu, Z., Wu, D., & Zhang, Y. (2017). Analytical variance based global sensitivity analysis for models with correlated variables. Applied Mathematical Modelling, 45, 748-767. https://doi.org/10.1016/j.apm.2016.12.036