Simulating Stationary Non-Gaussian Processes Based on Unified Hermite Polynomial Model
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
In determining structural responses under random excitation using the Monte Carlo method, simulation of non-Gaussian processes is always a challenge. Various methods have been developed to simulate non-Gaussian processes but literature suggests that the complete expression of the Gaussian correlation function matrix (CFM) and the corresponding applicable range of the target non-Gaussian CFM have not been attempted in the transformation based on the Hermite polynomial model (HPM) to date. The intention of this paper is to derive a complete transformation model of CFM from non-Gaussian to Gaussian processes with the applicable range of the target non-Gaussian CFM based on the unified Hermite polynomial model (UHPM). An efficient procedure for simulating stationary non-Gaussian processes is also presented for easy application. It is found in the paper that the complete transformation model of Gaussian CFM is necessary because HPMs are not always monotonic and that the proposed method can simulate stationary non-Gaussian processes efficiently and accurately. The proposed method can equip researchers and engineers with a more efficient and accurate tool to handle non-Gaussian processes frequently encountered in engineering practices.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The research reported in this paper is partially supported by the National Natural Science Foundation of China (Grant Nos. 51820105014, U1934217, and 51738001). The support is gratefully acknowledged.
References
Bocchini, P., and G. Deodatis. 2008. “Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields.” Probab. Eng. Mech. 23: 393–407. https://doi.org/10.1016/j.probengmech.2007.09.001.
Bracewell, R. N. 1986. The Fourier transform and its applications. New York: McGraw Hill.
Deodatis, G. 1996. “Simulation of ergodic multivariate stochastic process.” J. Eng. Mech. 122 (8): 778–787. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:8(778).
Deodatis, G., and R. Micaletti. 2001. “Simulation of highly skewed non-Gaussian stochastic processes.” J. Eng. Mech. 127 (12): 1284–1295. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:12(1284).
Grigoriu, M. 1995. Applied non-Gaussian processes. Englewood Cliffs, NJ: PTR Prentice-Hall.
Grigoriu, M. 1998. “Simulation of stationary non-Gaussian translation processes.” J. Eng. Mech. 124 (2): 121–126. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:2(121).
Gurley, K. R. 1997. “Modeling and simulation of non-Gaussian processes.” Ph.D. thesis, Dept. of Civil Engineering and Geological Sciences, Univ. of Notre Dame.
Gurley, K. R., and A. Kareem. 1997. “Analysis, interpretation, modeling and simulation of unsteady wind and pressure data.” J. Wind Eng. Ind. Aerodyn. 69–71 (Jul): 657–669. https://doi.org/10.1016/S0167-6105(97)00195-5.
Gurley, K. R., and A. Kareem. 1998a. “A conditional simulation of non-normal velocity/pressure fields.” J. Wind Eng. Ind. Aerodyn. 77–78 (Sep): 39–51. https://doi.org/10.1016/S0167-6105(98)00130-5.
Gurley, K. R., and A. Kareem. 1998b. “Simulation of correlated non-Gaussian pressure fields.” Meccanica 33 (3): 309–317. https://doi.org/10.1023/A:1004315618217.
Gurley, K. R., A. Kareem, and M. A. Tognarelli. 1996. “Simulation of a class of non-normal random processes.” Int. J. Non Linear Mech. 31 (5): 601–617. https://doi.org/10.1016/0020-7462(96)00025-X.
Gurley, K. R., M. A. Tognarelli, and A. Kareem. 1997. “Analysis and simulation tools for wind engineering.” Probab. Eng. Mech. 12 (1): 9–31. https://doi.org/10.1016/S0266-8920(96)00010-0.
Ho, T. C. E., D. Surry, D. Morrish, and G. A. Kopp. 2005. “The UWO contribution to the NIST aerodynamic database for wind loads on low buildings. 1: Archiving format and basic aerodynamic data.” J. Wind Eng. Ind. Aerodyn. 93 (1): 1–30. https://doi.org/10.1016/j.jweia.2004.07.006.
Ji, X. W., G. Q. Huang, X. X. Zhang, and G. A. Kopp. 2018. “Vulnerability analysis of steel roofing cladding: Influence of wind directionality.” Eng. Struct. 156 (Feb): 587–597. https://doi.org/10.1016/j.engstruct.2017.11.068.
Lancaster, H. O. 1957. “Some properties of the bivariate normal distribution consideration in the form of a contingency table.” Biometrika 44 (1/2): 289–292. https://doi.org/10.2307/2333274.
Masters, F., and K. R. Gurley. 2003. “Non-Gaussian simulation: Cumulative distribution function map-based spectral correction.” J. Eng. Mech. 129 (12): 1418–1428. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1418).
Pierre, L. M. S., G. A. Kopp, D. Surry, and T. C. E. Ho. 2005. “The UWO contribution to the NIST aerodynamic database for wind loads on low buildings. 2: Comparison of data with wind load provisions.” J. Wind Eng. Ind. Aerodyn. 93 (1): 31–59. https://doi.org/10.1016/j.jweia.2004.07.007.
Shields, M. D., and G. Deodatis. 2013. “A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic vector process by a translation process with applications in wind velocity simulation.” Probab. Eng. Mech. 31 (Jan): 19–29. https://doi.org/10.1016/j.probengmech.2012.10.003.
Shields, M. D., G. Deodatis, and P. Bocchini. 2011. “A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process.” Probab. Eng. Mech. 26 (4): 511–519. https://doi.org/10.1016/j.probengmech.2011.04.003.
Shinozuka, M., and G. Deodatis. 1991. “Simulation of stochastic processes by spectral representation.” Appl. Mech. Rev. 44 (4): 191–204. https://doi.org/10.1115/1.3119501.
Shinozuka, M., and C. M. Jan. 1972. “Digital simulation of random processes and its applications.” J. Sound Vib. 25 (1): 111–128. https://doi.org/10.1016/0022-460X(72)90600-1.
Winterstein, S. R. 1988. “Nonlinear vibration models for extremes and fatigue.” J. Eng. Mech. 114 (10): 1772–1790. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:10(1772).
Winterstein, S. R., and T. Kashef. 2000. “Moment-based load and response models with wind engineering applications.” J. Solar Energy Eng. 122 (3): 122–128. https://doi.org/10.1115/1.1288028.
Yamazaki, F., and M. Shinozuka. 1988. “Digital generation of non-Gaussian stochastic fields.” J. Eng. Mech. 114 (7): 1183–1197. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:7(1183).
Yang, L., and K. R. Gurley. 2015. “Efficient stationary multivariate non-Gaussian simulation based on a Hermite PDF model.” Probab. Eng. Mech. 42 (Oct): 31–41. https://doi.org/10.1016/j.probengmech.2015.09.006.
Yang, L., K. R. Gurley, and D. O. Prevatt. 2013. “Probabilistic modeling of wind pressure on low-rise buildings.” J. Wind Eng. Ind. Aerodyn. 114 (Mar): 18–26. https://doi.org/10.1016/j.jweia.2012.12.014.
Zhang, X. Y., Y. G. Zhao, and Z. H. Lu. 2019. “Unified Hermite polynomial model and its application in estimating non-Gaussian processes.” J. Eng. Mech. 145 (3): 04019001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001577.
Zwillinger, D. 2018. CRC standard mathematical tables and formulae. 32nd ed. Boca Raton, FL: CRC Press.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 7 • July 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Sep 18, 2019
Accepted: Feb 18, 2020
Published online: Apr 27, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 27, 2020
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