Evolutionary Spectra-Based Time-Varying Coherence Function and Application in Structural Response Analysis to Downburst Winds
Publication: Journal of Structural Engineering
Volume 144, Issue 7
Abstract
Priestley’s oscillatory process theory is widely employed to model nonstationary excitation. However, the underlying coherence function of this theory can only be time invariant. To take into account the time-varying coherence function, the Sigma-oscillatory process theory and Wold-Cramer decomposition model have been introduced in literature. Due to its straightforwardness, the Wold-Cramer decomposition model is used in this study. Based on the Wold-Cramer decomposition model of nonstationary wind excitation, the alongwind response analysis framework of tall buildings to nonstationary winds is presented. The time-varying coherence function models of two downburst events are developed using the measured downburst data. The influence of time-varying coherence of nonstationary winds on the alongwind tall building response is investigated. Numerical examples show that the time-varying coherence function may lead to larger structural response compared with the corresponding time-invariant coherence function model. Considering the large variation of nonstationary downburst winds, the observation drawn from this study should be further evaluated using more measurement wind data. It can be expected that the time-varying coherence function may play an important role in better modeling the nonstationary winds and their load effects on structures.
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Acknowledgments
The support by the National Natural Science Foundation of China (Grant Nos. 51720105005, 51578471, 51408504, and 51478401) are greatly acknowledged. Dr. Lombardo at University of Illinois at Urbana-Champaign is also greatly acknowledged for providing the measured downburst data.
References
Battaglia, F. 1979. “Some extensions in the evolutionary spectral analysis of a stochastic process.” Boll. Un. Mat. Ital. B 16 (3): 1154–1166.
Chakraborty, A., and B. Basu. 2008. “Nonstationary response analysis of long span bridges under spatially varying differential support motions using continuous wavelet transform.” J. Eng. Mech. 134 (2): 155–162. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:2(155).
Chen, L., and C. W. Letchford. 2004. “A deterministic-stochastic hybrid model of downbursts and its impact on a cantilevered structure.” Eng. Struct. 26 (5): 619–629. https://doi.org/10.1016/j.engstruct.2003.12.009.
Chen, X. 2008. “Analysis of alongwind tall building response to transient nonstationary winds.” J. Struct. Eng. 134 (5): 782–791. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:5(782).
Chen, X. 2015. “Estimation of wind load effects with various mean recurrence intervals with a closed-form formulation.” Int. J. Struct. Stab. Dyn. 16 (9): 1–14.
Chen, X., and A. Kareem. 2005. “Proper orthogonal decomposition-based modeling, analysis, and simulation of dynamic wind load effects on structures.” J. Eng. Mech. 131 (4): 325–339. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(325).
Cohen, E. A., and A. T. Walden. 2011. “Wavelet coherence for certain nonstationary bivariate processes.” IEEE Trans. Signal Process. 59 (6): 2522–2531. https://doi.org/10.1109/TSP.2011.2123893.
Conte, J. P., and B. F. Peng. 1996. “An explicit closed-form solution for linear systems subjected to nonstationary random excitation.” Prob. Eng. Mech. 11 (1): 37–50. https://doi.org/10.1016/0266-8920(95)00026-7.
Conte, J. P., and B. F. Peng. 1997. “Fully nonstationary analytical earthquake ground-motion model.” J. Eng. Mech. 123 (1): 15–24. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:1(15).
Davenport, A. G. 1961. “The spectrum of horizontal gustiness near the ground in high winds.” Q. J. R. Meteorol. Soc. 87 (372): 194–211. https://doi.org/10.1002/qj.49708737208.
Deodatis, G. 1996. “Non-stationary stochastic vector processes: Seismic ground motion applications.” Prob. Eng. Mech. 11 (3): 149–167. https://doi.org/10.1016/0266-8920(96)00007-0.
Der Kiureghian, A., and J. Crempien. 1989. “An evolutionary model for earthquake ground motion.” Struct. Saf. 6 (2): 235–246. https://doi.org/10.1016/0167-4730(89)90024-6.
Dinh, V. N., B. Basu, and R. B. Brinkgreve. 2013. “Wavelet-based evolutionary response of multispan structures including wave-passage and site-response effects.” J. Eng. Mech. 140 (8): 04014056. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000708.
Gurley, K., T. Kijewski, and A. Kareem. 2003. “First-and higher-order correlation detection using wavelet transforms.” J. Eng. Mech. 129 (2): 188–201. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:2(188).
Harichandran, R., and E. Vanmarcke. 1986. “Stochastic variation of earthquake ground motion in space and time.” J. Eng. Mech. 112 (2): 154–174. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:2(154).
Huang, G., and X. Chen. 2009. “Wavelets-based estimation of multivariate evolutionary spectra and its application to nonstationary downburst winds.” Eng. Struct. 31 (4): 976–989. https://doi.org/10.1016/j.engstruct.2008.12.010.
Huang, G., X. Chen, H. Liao, and M. Li. 2013. “Predicting tall building response to nonstationary winds using multiple wind speed samples.” Wind. Struct. 17 (2): 227–244. https://doi.org/10.12989/was.2013.17.2.227.
Huang, G., Y. Su, A. Kareem, and H. Liao. 2016. “Time-frequency analysis of nonstationary process based on multivariate empirical mode decomposition.” J. Eng. Mech. 142 (1): 04015065. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000975.
Huang, G., H. Zheng, Y. Xu, and Y. Li. 2015. “Spectrum models for nonstationary extreme winds.” J. Struct. Eng. 141 (10): 04015010. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001257.
Kwon, D. K., and A. Kareem. 2009. “Gust-front factor: New framework for wind load effects on structures.” J. Struct. Eng. 135 (6): 717–732. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:6(717).
Li, Y., J. P. Conte, and M. Barbato. 2016. “Influence of time-varying frequency content in earthquake ground motions on seismic response of linear elastic systems.” Earthquake. Eng. Struct. Dyn. 45 (8): 1271–1291. https://doi.org/10.1002/eqe.2707.
Lombardo, F. T. 2009. “Analysis and interpretation of thunderstorm wind flow and its effects on a bluff body.” Ph.D. thesis, Texas Tech Univ.
Lombardo, F. T., D. A. Smith, J. L. Schroeder, and K. C. Mehta. 2014. “Thunderstorm characteristics of importance to wind engineering.” J. Wind. Eng. Ind. Aerodyn. 125 (2): 121–132. https://doi.org/10.1016/j.jweia.2013.12.004.
Melard, G., and A. H. D. Schutter. 1989. “Contributions to evolutionary spectral theory.” J. Time. Ser. Anal. 10 (1): 41–63.
Orwig, K. D., and J. L. Schroeder. 2007. “Near-surface wind characteristics of extreme thunderstorm outflows.” J. Wind. Eng. Ind. Aerodyn. 95 (7): 565–584. https://doi.org/10.1016/j.jweia.2006.12.002.
Oseguera, R. M., and R. L. Bowles. 1988. A simple analytic 3-dimentional downburst model based on boundary layer stagnation flow. Hampton, VA: Langley Research Center.
Peng, L., G. Huang, X. Chen, and A. Kareem. 2017. “Simulation of multivariate nonstationary random process: A hybrid stochastic wave and proper orthogonal decomposition approach.” J. Eng. Mech. 143 (9): 04017064. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001273.
Priestley, M. B. 1965. “Evolutionary spectra and non-stationary processes.” J. R. Statist. Soc. Ser. B 27 (2): 204–237.
Priestley, M. B., and H. Tong. 1973. “On the analysis of bivariate non-stationary processes.” J. R. Statist. Soc. Ser. B 35 (2): 153–166.
Solari, G. 2016. “Thunderstorm response spectrum technique: Theory and applications.” Eng. Struct. 108 (Feb): 28–46. https://doi.org/10.1016/j.engstruct.2015.11.012.
Solari, G., M. Burlando, P. De Gaetano, and M. P. Repetto. 2015. “Characteristics of thunderstorms relevant to the wind loading of structures.” Wind Struct. 20 (6): 763–791. https://doi.org/10.12989/was.2015.20.6.763.
Spanos, P. D., and G. Failla. 2004. “Evolutionary spectra estimation using wavelets.” J. Eng. Mech. 130 (8): 952–960. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:8(952).
Spanos, P. D., A. Giaralis, and N. P. Politis. 2007. “Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition.” Soil. Dyn. Earthquake Eng. 27 (7): 675–689. https://doi.org/10.1016/j.soildyn.2006.11.007.
Su, Y., G. Huang, and Y. L. Xu. 2015. “Derivation of time-varying mean for non-stationary downburst winds.” J. Wind. Eng. Ind. Aerodyn. 141 (Jun): 39–48. https://doi.org/10.1016/j.jweia.2015.02.008.
Vicroy, D. D. 1992. “Assessment of microburst models for downdraft estimation.” J. Aircraft. 29 (6): 1043–1048. https://doi.org/10.2514/3.46282.
White, L. B., and B. Boashash. 1990. “Cross spectral analysis of nonstationary processes.” IEEE Trans. Inform. Theory 36 (4): 830–835. https://doi.org/10.1109/18.53742.
Wood, G. S., K. C. S. Kwok, N. A. Motteram, and D. F. Fletcher. 2001. “Physical and numerical modeling of thunderstorm downbursts.” J. Wind. Eng. Ind. Aerodyn. 89 (6): 535–552. https://doi.org/10.1016/S0167-6105(00)00090-8.
Zhan, Y., D. Halliday, P. Jiang, X. Liu, and J. Feng. 2006. “Detecting time-dependent coherence between non-stationary electrophysiological signals-a combined statistical and time-frequency approach.” J. Neurosci. Methods 156 (1): 322–332. https://doi.org/10.1016/j.jneumeth.2006.02.013.
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Published In
Journal of Structural Engineering
Volume 144 • Issue 7 • July 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 12, 2017
Accepted: Dec 28, 2017
Published online: Apr 28, 2018
Published in print: Jul 1, 2018
Discussion open until: Sep 28, 2018
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