Quantile-oriented global sensitivity analysis of design resistance

    Zdeněk Kala   Affiliation


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.
Published in Issue
Apr 2, 2019
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Ahammed, M., & Melchers, R. E. (2006). Gradient and parameter sensitivity estimation for systems. Reliability Engineering and System Safety, 91(5), 594-601.

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.

Borgonovo, E. (2007). A new uncertainty importance measure. Reliability Engineering and System Safety, 92(6), 771-784.

Browne, T., Fort, J. C., Iooss, B., & Gratiet, L. L. (2017). Estimate of Quantile-oriented sensitivity indices. Preprint. Retrieved from

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.

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.

European Committee for Standardization. (2003). Eurocode: Basis of structural design (EN 1990:2002). Brussels. Retrieved from

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

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.

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.

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.

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.

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.

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.

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.

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.

Kala, Z., & Valeš, J. (2017b). Global sensitivity analysis of lateral-torsional buckling resistance based on finite element simulations. Engineering Structures, 134, 37-47.

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.

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.

Kucherenko, S., Song, S., & Wang, L. (2019). Quantile based global sensitivity measures. Reliability Engineering and System Safety, 185, 35-48.

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.

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.

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.

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.

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

Rachdi, N. (2011). Apprentissage statistiQue et computer experiments – Approche Quantitative du risQue et des incertitudes en modélisation (PhD thesis, Université Toulouse). Retrieved from

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.

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.

Sedlacek, G., & Müller, C. (2006). The European standard family and its basis. Journal of Constructional Steel Research, 62(11), 1047-1059.

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.

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.

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.

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.