Model Distance–Based Global–Local Response-Sensitivity Indexes for Randomly Inhomogeneous Structures under Stochastic Excitations
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4, Issue 3
Abstract
Linear engineering skeletal structures with spatially varying random stiffness and mass properties, acted upon by a set of random vibratory loads, are considered in this paper. The focus of the study is on characterizing the global–local response sensitivity indexes for this class of structures by taking into account dependency among system parameters and/or forcing functions. This is achieved by extending the recently developed tools for modeling the sensitivity indexes based on various definitions of probability distance measures to problems involving stochastic inhomogeneities. The study allows for the non-Gaussian nature of stochastic variations and employs Monte Carlo simulation strategies and stochastic finite-element modeling tools. The spatially varying random properties are discretized using the optimal linear expansion methods. Illustrative examples include studies on single-span beams under the combined action of a train of random moving masses and earthquake support motions, and randomly parameterized skeletal structures under biaxial earthquake support motions.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work reported in this study has been financially supported by funding from the Board of Research in Nuclear Sciences (BRNS) (Grant No. 2012/36/35-BRNS/1628), Department of Atomic Energy, Government of India. We thank the anonymous reviewers for helpful comments. The phrase global–local response sensitivity indexes was suggested by one of the reviewers.
References
Abhinav, S., and C. S. Manohar. 2015. “Global response sensitivity analysis of randomly excited dynamic structures.” J. Eng. Mech. 142 (3): 04015094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001019.
Arwade, S. R., M. Moradi, and A. Louhghalam. 2010. “Variance decomposition and global sensitivity for structural systems.” Eng. Struct. 32 (1): 1–10. https://doi.org/10.1016/j.engstruct.2009.08.011.
Blatman, G., and B. Sudret. 2010. “Efficient computation of global sensitivity indices using sparse polynomial chaos expansions.” Reliab. Eng. Syst. Saf. 95 (11): 1216–1229. https://doi.org/10.1016/j.ress.2010.06.015.
Cao, J., F. Du, and S. Ding. 2013. “Global sensitivity analysis for dynamic systems with stochastic input processes.” Reliab. Eng. Syst. Saf. 118: 106–117. https://doi.org/10.1016/j.ress.2013.04.016.
Clough, R. W., and J. Penzien. 1993. Dynamics of structures. New York: McGraw-Hill.
Ghanem, R. 1999. “The nonlinear Gaussian spectrum of lognormal stochastic processes and variables.” ASME J. Appl. Mech. 66 (4): 964–973. https://doi.org/10.1115/1.2791806.
Ghanem, R. G., and P. D. Spanos. 1991. Stochastic finite elements: A spectral approach. New York: Springer.
Greegar, G., and C. S. Manohar. 2015. “Global response sensitivity analysis using probability distance measures and generalization of Sobol’s analysis.” Probab. Eng. Mech. 41: 21–33. https://doi.org/10.1016/j.probengmech.2015.04.003.
Greegar, G., and C. S. Manohar. 2016. “Global response sensitivity analysis of uncertain structures.” Struct. Saf. 58: 94–104. https://doi.org/10.1016/j.strusafe.2015.09.006.
Gupta, S., and C. S. Manohar. 2006. “Reliability analysis of randomly vibrating structures with parameter uncertainties.” J. Sound Vib. 297 (3): 1000–1024. https://doi.org/10.1016/j.jsv.2006.05.010.
Kloeden, P. E., and E. Platen. 1992. Numerical solution of stochastic differential equations. Berlin, Germany: Springer.
Kucherenko, S., S. Tarantola, and P. Annoni. 2012. “Estimation of global sensitivity indices for models with dependent variables.” Comput. Phys. Commun. 183 (4): 937–946. https://doi.org/10.1016/j.cpc.2011.12.020.
Lehmann, E. L., and J. P. Romano. 2005. Testing statistical hypotheses. New York: Springer.
Li, C. C., and A. D. Kiureghian. 1993. “Optimal discretization of random fields.” J. Eng. Mech. 119 (6): 1136–1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
Li, G., H. Rabitz, P. E. Yelvington, O. O. Oluwole, F. Bacon, C. E. Kolb, and J. Schoendorf. 2010. “Global sensitivity analysis for systems with independent and/or correlated inputs.” J. Phys. Chem. A. 114 (19): 6022–6032. https://doi.org/10.1021/jp9096919.
Liu, H., W. Chen, and A. Sudjianto. 2006. “Relative entropy based method for probabilistic sensitivity analysis in engineering design.” J. Mech. Design 128 (2): 326–336. https://doi.org/10.1115/1.2159025.
Mukherjee, D., B. N. Rao, and A. M. Prasad. 2011. “Global sensitivity analysis of unreinforced masonry structure using high dimensional model representation.” Eng. Struct. 33 (4): 1316–1325. https://doi.org/10.1016/j.engstruct.2011.01.008.
Owen, A. B. 2013. “Variance components and generalized Sobol’ indices.” SIAM/ASA J. Uncertain. Quantif. 1 (1): 19–41. https://doi.org/10.1137/120876782.
Patelli, E., H. J. Pradlwarter, and G. I. Schuëller. 2010. “Global sensitivity of structural variability by random sampling.” Comput. Phys. Commun. 181 (12): 2072–2081. https://doi.org/10.1016/j.cpc.2010.08.007.
Rachev, S. T. 1991. Vol. 269 of Probability metrics and the stability of stochastic models. Chichester, UK: Wiley.
Rahman, S. 2016a. “A surrogate method for density-based global sensitivity analysis.” Reliab. Eng. Syst. Saf. 155: 224–235. https://doi.org/10.1016/j.ress.2016.07.002.
Rahman, S. 2016b. “The f-sensitivity index.” SIAM/ASA J. Uncertain. Quantif. 4 (1): 130–162. https://doi.org/10.1137/140997774.
Sakamoto, S., and R. Ghanem. 2002. “Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes.” J. Eng. Mech. 128 (2): 190–201. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:2(190).
Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola. 2008. Global sensitivity analysis: The primer. Chichester, UK: Wiley.
Sobol, I. M. 1993. “Sensitivity estimates for nonlinear mathematical models.” Math. Model. Comput. Exp. 1 (4): 407–414.
Sobol, I. M. 2001. “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Math. Comput. Simul. 55 (1–3): 271–280. https://doi.org/10.1016/S0378-4754(00)00270-6.
Sobol, I. M., and S. Kucherenko. 2009. “Derivative based global sensitivity measures and their link with global sensitivity indices.” Math. Comput. Simul. 79 (10): 3009–3017. https://doi.org/10.1016/j.matcom.2009.01.023.
Sobol, I. M., and S. Kucherenko. 2010. “A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices.” Comput. Phys. Commun. 181 (7): 1212–1217. https://doi.org/10.1016/j.cpc.2010.03.006.
Sobol, I. M., and Y. L. Levitan. 1999. “On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index.” Comput. Phys. Commun. 117 (1–2): 52–61. https://doi.org/10.1016/S0010-4655(98)00156-8.
Sobol, I. M., S. Tarantola, D. Gatelli, S. S. Kucherenko, and W. Mauntz. 2007. “Estimating the approximation error when fixing unessential factors in global sensitivity analysis.” Reliab. Eng. Syst. Saf. 92 (7): 957–960. https://doi.org/10.1016/j.ress.2006.07.001.
Soong, T. T. 1973. Random differential equations in science and engineering. New York: Academic Press.
Sudret, B. 2008. “Global sensitivity analysis using polynomial chaos expansions.” Reliab. Eng. Syst. Saf. 93 (7): 964–979. https://doi.org/10.1016/j.ress.2007.04.002.
Sudret, B., and A. D. Kiureghian. 2002. “Comparison of finite element reliability methods.” Prob. Eng. Mech. 17 (4): 337–348. https://doi.org/10.1016/S0266-8920(02)00031-0.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4 • Issue 3 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 11, 2017
Accepted: Dec 19, 2017
Published online: May 26, 2018
Published in print: Sep 1, 2018
Discussion open until: Oct 26, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.