Global Response Sensitivity Analysis of Randomly Excited Dynamic Structures
Publication: Journal of Engineering Mechanics
Volume 142, Issue 3
Abstract
The response of structural dynamical systems excited by multiple random excitations is considered. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger’s metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented, and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations attributable to random support motions and guide-way unevenness.
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, Department of Atomic Energy, Government of India. The support received is gratefully acknowledged. The authors also thank the reviewers for helpful comments.
References
Arwade, S. R., Moradi, M., and Louhghalam, A. (2010). “Variance decomposition and global sensitivity for structural systems.” Eng. Struct., 32(1), 1–10.
Blatman, G., and Sudret, B. (2010). “Efficient computation of global sensitivity indices using sparse polynomial chaos expansions.” Reliab. Eng. Syst. Saf., 95(11), 1216–1229.
Cao, J., Du, F., and Ding, S. (2013). “Global sensitivity analysis for dynamic systems with stochastic input processes.” Reliab. Eng. Syst. Saf., 118, 106–117.
Filho, F. V. (1978). “Finite element analysis of structures under moving loads.” Shock Vib. Inform. Center Shock Vibr. Digest, 10(8), 27–35.
Fryba, L. (1999). Vibration of solids and structures under moving loads, Thomas Telford, London.
Greegar, G., and Manohar, C. S. (2015). “Global response sensitivity analysis using probability distance measures and generalization of Sobol’s analysis.” Probab. Eng. Mech., 41, 21–33.
Grigoriu, M. (2002). Stochastic calculus: Applications in science and engineering, Springer, Berlin.
Kloeden, P. E., and Platen, E. (1992). Numerical solution of stochastic differential equations, Springer, Berlin.
Kucherenko, S., Tarantola, S., and Annoni, P. (2012). “Estimation of global sensitivity indices for models with dependent variables.” Comput. Phys. Commun., 183(4), 937–946.
Küchler, U., and Platen, E. (2000). “Strong discrete time approximation of stochastic differential equations with time delay.” Math. Comput. Simul., 54(1–3), 189–205.
Küchler, U., and Platen, E. (2002). “Weak discrete time approximation of stochastic differential equations with time delay.” Math. Comput. Simul., 59(6), 497–507.
Lehmann, E. L., and Romano, J. P. (2005). Testing statistical hypotheses, Springer, New York.
Li, G., et al. (2010). “Global sensitivity analysis for systems with independent and/or correlated inputs.” J. Phys. Chem. A, 114(19), 6022–6032.
Lin, Y. H., and Trethewey, M. W. (1990). “Finite element analysis of elastic beams subjected to moving dynamic loads.” J. Sound Vib., 136(2), 323–342.
Liu, H., Chen, W., and Sudjianto, A. (2006). “Relative entropy based method for probabilistic sensitivity analysis in engineering design.” J. Mech. Des., 128(2), 326–336.
Longtin, A. (2010). “Stochastic delay-differential equations.” Complex time-delay systems, Springer, Berlin, 177–195.
Maruyama, Y., and Yamazaki, F. (2004). “Fundamental study on the response characteristics of drivers during an earthquake based on driving simulator experiments.” Earthquake Eng. Struct. Dyn., 33(6), 775–792.
Maruyama, Y., and Yamazaki, F. (2006). “Driving simulator experiment on the moving stability of an automobile under strong crosswind.” J. Wind Eng. Ind. Aerodyn., 94(4), 191–205.
Mukherjee, D., Rao, B. N., and Prasad, A. M. (2011). “Global sensitivity analysis of unreinforced masonry structure using high dimensional model representation.” Eng. Struct., 33(4), 1316–1325.
Narayanan, S., and Raju, G. V. (1990). “Stochastic optimal control of non-stationary response of a single-degree-of-freedom vehicle model.” J. Sound Vib., 141(3), 449–463.
Owen, A. B. (2013). “Variance components and generalized Sobol’indices.” SIAM/ASA J. Uncertainty Quantif., 1(1), 19–41.
Patelli, E., Pradlwarter, H. J., and Schuëller, G. I. (2010). “Global sensitivity of structural variability by random sampling.” Comput. Phys. Commun., 181(12), 2072–2081.
Rachev, S. T. (1991). Probability metrics and the stability of stochastic models, Wiley, New York.
Saltelli, A., et al. (2008). Global sensitivity analysis: The primer, Wiley, Chichester, U.K.
Saltelli, A., Tarantola, S., Campolongo, F., and Ratto, M. (2004). Sensitivity analysis in practice: A guide to assessing scientific models, Wiley, Chichester, U.K.
Samali, B., Kim, K. B., and Yang, J. N. (1986). “Random vibration of rotating machines under earthquake excitations.” J. Eng. Mech., 550–565.
Sobol, I. M. (2001). “Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.” Math. Comput. Simul., 55(1), 271–280.
Sobol, I. M., and Kucherenko, S. (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.
Sobol, I. M., Tarantola, S., Gatelli, D., Kucherenko, S. S., and Mauntz, W. (2007). “Estimating the approximation error when fixing unessential factors in global sensitivity analysis.” Reliab. Eng. Syst. Saf., 92(7), 957–960.
Song, M. K., Noh, H. C., and Choi, C. K. (2003). “A new three-dimensional finite element analysis model of high-speed train–bridge interactions.” Eng. Struct., 25(13), 1611–1626.
Soong, T. T. (1973). Random differential equations in science and engineering, Academic Press, New York.
Sudret, B. (2008). “Global sensitivity analysis using polynomial chaos expansions.” Reliab. Eng. Syst. Saf., 93(7), 964–979.
Yamada, Y., Iemura, H., Kawano, K., and Venkataramana, K. (1989). “Seismic response of offshore structures in random seas.” Earthquake Eng. Struct. Dyn., 18(7), 965–981.
Zerva, A. (2009). Spatial variation of seismic ground motions, CRC Press, Boca Raton, FL.
Zhu, B., and Frangopol, D. M. (2013). “Risk-based approach for optimum maintenance of bridges under traffic and earthquake loads.” J. Struct. Eng., 422–434.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 3 • March 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 12, 2015
Accepted: Aug 31, 2015
Published online: Oct 16, 2015
Published in print: Mar 1, 2016
Discussion open until: Mar 16, 2016
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.