Simulation-based sensitivity analysis: Methods and software tools

  • Drahomír Novák ,
  • David Lehký,
  • Ondřej Slowik
  • a,b,c  Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Veveří 95, Brno, 60200, Czech Republic
Cite as
Novák D., Lehký D., Slowik O. (2021). Simulation-based sensitivity analysis: Methods and software tools. Proceedings of the 33rd European Modeling & Simulation Symposium (EMSS 2021), pp. 158-164. DOI:


The topic of the paper is simulation-based sensitivity analysis with emphasize on the use of the small-sample Latin Hypercube Sampling simulation method. Three approaches are described in the paper: Spearman’s rank-order correlation, covariance-based sensitivity analysis and input perturbation-based sensitivity analysis. Software tools are briefly described, especially SEAN software as an effective sensitivity analysis environment developed to simplify sensitivity analysis of a user-defined numerical model. An example application is presented.


  1. Antucheviciene, J., Kala, Z., Marzouk, M. and 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, 2015 (Article ID 362579), 1–16. 
  2. Borgonovo, E. and Plischke, E. (2016). Sensitivity analysis: A review of recent advances. European Journal of Operational Research, 248:869-887.
  3. Downing, D. J., Gardner, R. H. and Hoffman, F. O. (1985). An examination of response-surface methodologies for uncertainty analysis in assessment models. Technometrics, 27(2):151-163.
  4. Gevrey, M., Dimopoulos, I. and Lek, S. (2003). Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecological modelling, 160(3):249-264.
  5. Huntington, D.E. and Lyrintzis C.S. (1998). Improvements to and limitations of Latin Hypercube Sampling”, Probabilistic Engineering Mechanics; 13 (4):245–253.
  6. Iman, R.L. and 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. 
  7. Kala, Z. (2016). Higher-order approximations methods for global sensitivity analysis of nonlinear model outputs, International Journal of Mathematics and Computers in Simulation, 10:260-264.
  8. Kala, Z. (2021). Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles. Symmetry 13(2):263.
  9. Kala, Z., Valeš, J. (2017). Global sensitivity analysis of lateral-torsional buckling resistance based on finite element simulations, Engineering Structures, 134:37-47.
  10. Kleijnen, J.P.C (2010). Sensitivity Analysis of Simulation Models: An Overview. Procedia Social and Behavioral Sciences, 2:7585–7586.
  11. Liu, N., Hosking, J. and Grundy, J. (2007). A visual language and environment for specifying user interface event handling in design tools. Conferences in Research and Practice in Information Technology.
  12. McKay, M.D., Conover, W.J. and Beckman, R.J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code”, Technometrics; 21:239–245.
  13. Novák, L. and Novák, D. (2019). On the possibility of utilizing Wiener-Hermite polynomial chaos expansion for global sensitivity analysis based on Cramér-von Mises Distance. In 2019 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE), 1-9.
  14. Novák, D., Teplý, B. and Shiraishi, N. (1993). Sensitivity analysis of structures: A review. In Proc. Of Int. Conference CIVIL COMP´93: Edinburgh, Scotland, 201-207.
  15. Novák, D., Vořechovský, M., and Teplý, B. (2014). FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module, Advances in Engineering Software, 72:179-192.
  16. Pan, L., Novák, L., Novák, D., Lehký, D. and Cao, M. (2021). Neural network ensemble-based sensitivity analysis in structural engineering: Comparison of selected methods and the influence of statistical correlation. Computers & Structures, 242(1):1-19.
  17. Scardi, M. and Harding Jr, L. W. (1999). Developing an empirical model of phytoplankton primary production: a neural network case study. Ecological modelling, 120(2-3):213-223.
  18. Slowik, O. and Novák, D. (2019). Node based software concept for general purpose reliability-based optimization tool. In Proc. of 2019 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering.
  19. Slowik, O., Novák, D, Novák, L and Strauss, A. (2020). Stochastic modelling and assessment of long-span precast prestressed concrete elements failing in shear. Engineering Structures, 2020, 111500.
  20. Sobol, I.M. (1993). Sensitivity analysis for non–linear mathematical models. Mathematical Modelling and Computational Experiment, 1, pp. 407–414. Translated from Russian: I. M. Sobol’. 1990. Sensitivity estimates for nonlinear mathematical models, Matematicheskoe Modelirovanie 2:112–118.
  21. Sobol, I.M (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55:271–280.
  22. Stein, M. (1987). Large sample properties of simulations using Latin hypercube sampling. Technometrics, 29(2):143-151.
  23. Strauss, A., Krug, B., Slowik, O. and Novák D. (2017). Combined shear and flexure performance of prestressing concrete T-shaped beams: Experiment and deterministic modeling. Structural Concrete, 1–20.
  24. Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety, 93:964–979. 
  25. Vořechovský, M. and Novák, D. (2009). Correlation control in small sample Monte Carlo type simulations I: A Simulated Annealing approach, Probabilistic Engineering Mechanics, 24(3):452-462.
  26. Vořechovský, M. (2012). Correlation control in small sample Monte Carlo type simulations II: Analysis of estimation formulas, random correlation and perfect uncorrelatedness. Probabilistic Engineering Mechanics, 29:105–120.
  27. Wegman, E.J. (1990). Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association, 85:664–675.