Author(s)

Jinyu Zhang ¹, Xiaowen Ji ¹

Affiliation(s)

¹ Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

Corresponding Author

Jinyu Zhang

ABSTRACT

Simulation of stationary non-Gaussian stochastic processes with prescribed marginal distributions and second-order dependence structures is important in wind engineering and random vibration analysis. This study proposes a new power-spectrum-based simulation method to jointly represent the marginal distribution and dependence structure. A distribution process is introduced as an intermediate representation, and the distribution correlation of the target non-Gaussian process is transformed into the Pearson correlation of the underlying Gaussian process within the Gaussian copula framework. The corresponding power spectrum is further defined to describe the frequency-domain dependence structure. Based on this formulation, a standard procedure and a simplified procedure are developed. The standard procedure retains the complete correlation transformation, whereas the simplified procedure uses a linear approximation to reduce computational complexity. Numerical examples of single-point non-Gaussian processes and a two-dimensional multi-point inflow wind field show that the proposed method can reproduce the target marginal distributions, power spectral densities, cross-power spectra, and coherence structures. The standard procedure is more stable for multi-point dependence, while the simplified procedure provides an efficient approximation for rapid simulation and large-scale parametric analysis.

KEYWORDS

Non-Gaussian Stochastic Process; Power Spectrum; Distribution Correlation; Gaussian Process; Spectral Representation

CITE THIS PAPER

Jinyu Zhang, Xiaowen Ji. Distribution Transformation-Based Method for Simulating Stationary Non-Gaussian Stochastic Processes. Journal of Civil Engineering and Urban Planning (2026). Vol. 8, No.2, 46-61. DOI: http://dx.doi.org/10.23977/jceup.2026.080206.

REFERENCES

[1] Rice SO. Mathematical analysis of random noise. Bell Syst Tech J 1944;23(3):282–332.
[2] Borgman LE. Ocean wave simulation for engineering design. J Waterw Harbors Div 1969;95(4):557–583.
[3] Shinozuka M. Monte Carlo solution of structural dynamics. Comput Struct 1972;2(5–6):855–874.
[4] Shinozuka M, Jan CM. Digital simulation of random processes and its applications. J Sound Vib 1972;25(1):111–128.
[5] Yang JN. Simulation of random envelope processes. J Sound Vib 1972;21(1):73–85.
[6] Yang JN. On the normality and accuracy of simulated random processes. J Sound Vib 1973;26(3):417–428.
[7] Shields D M, Kim H. Simulation of higher-order stochastic processes by spectral representation[J]. Probabilistic Engineering Mechanics,2017,1-15. DOI:10.1016/j.probengmech.2016.11.001.
[8] Deodatis G, Shields M. The spectral representation method: A framework for simulation of stochastic processes, fields, and waves. Reliab Eng Syst Saf 2025;254:110522.
[9] Deodatis G. Simulation of ergodic multivariate stochastic processes. J Eng Mech 1996;122(8):778–787.
[10] Li Y, Kareem A. Simulation of multivariate random processes: Hybrid DFT and digital filtering approach. J Eng Mech 1993;119(5):1078–1098.
[11] Johnson NL. Systems of frequency curves generated by methods of translation. Biometrika 1949;36(1/2):149–176.
[12] Grigoriu M. Crossings of non-Gaussian translation processes. J Eng Mech 1984;110(4):610–620.
[13] Gurley KR, Kareem A, Tognarelli MA. Simulation of a class of non-normal random processes. Int J Non-Linear Mech 1996;31(5):601–617.
[14] Puig B, Poirion F, Soize C. Non-Gaussian simulation using Hermite polynomial expansion: Convergences and algorithms. Probab Eng Mech 2002;17(3):253–264.
[15] Sakamoto S, Ghanem R. Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes. J Eng Mech 2002;128(2):190–201.
[16] Li J, Li C. Simulation of non-Gaussian stochastic process with target power spectral density and lower-order moments. J Eng Mech 2012;138(5):391–404.
[17] Ma X, Xu F. An efficient simulation algorithm for non-Gaussian stochastic processes. J Wind Eng Ind Aerodyn 2019;194:103984.
[18] Lu ZH, Zhao Z, Zhang XY, et al. Simulating stationary non-Gaussian processes based on unified Hermite polynomial model. J Eng Mech 2020;146(7):04020067.
[19] Zhao YG, Wang T, Ji X, et al. Quartic Hermite polynomial model-based translation method for extreme wind load estimation. J Wind Eng Ind Aerodyn 2024;245:105653.
[20] Wise G, Traganitis A, Thomas J. The effect of a memoryless nonlinearity on the spectrum of a random process. IEEE Trans Inf Theory 2003;23(1):84–89.
[21] Zheng R, Guoping C, Huaihai C. Stationary non-Gaussian random vibration control: A review. Chin J Aeronaut 2021;34(1):350–363.
[22] Yamazaki F, Shinozuka M. Digital generation of non-Gaussian stochastic fields. J Eng Mech 1988;114(7):1183–1197.
[23] Deodatis G, Micaletti RC. Simulation of highly skewed non-Gaussian stochastic processes. J Eng Mech 2001;127(12):1284–1295.
[24] Shields MD, Deodatis G, Bocchini P. A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process. Probab Eng Mech 2011;26(4):511–519.
[25] Shields M, Deodatis G. 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 2013;31:19–29.
[26] Bocchini P, Deodatis G. Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields. Probab Eng Mech 2008;23(4):393–407.
[27] Grigoriu M. Existence and construction of translation models for stationary non-Gaussian processes. Probab Eng Mech 2009;24(4):545–551.
[28] Seong SH, Peterka JA. Digital generation of non-Gaussian spiky excitations using spectral representation with additive phase structure. J Eng Mech 2012;138(10):1236–1248.
[29] Steinwolf A. Random vibration testing with kurtosis control by IFFT phase manipulation. Mech Syst Signal Process 2012;28:561–573.
[30] Shields MD, Kim H. Simulation of higher-order stochastic processes by spectral representation. Probab Eng Mech 2017;47:1–15.
[31] Vandanapu L, Shields MD. 3rd-order spectral representation method: Simulation of multi-dimensional random fields and ergodic multi-variate random processes with fast Fourier transform implementation. Probab Eng Mech 2021;64:103128.
[32] Sklar A .Fonctions de Repartition a n Dimensions et Leurs Marges[J].Publ.inst.statist.univ.paris, 1959.
[33] Liu PL, Der Kiureghian A. Multivariate distribution models with prescribed marginals and covariances. Probab Eng Mech 1986;1(2):105–112.
[34] Rosenblatt M. Remarks on a multivariate transformation. Ann Math Stat 1952;23(3):470–472.
[35] Genest C, Favre AC. Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 2007;12(4):347–368.
[36] Lebrun R, Dutfoy A. An innovating analysis of the Nataf transformation from the copula viewpoint. Probab Eng Mech 2009;24(3):312–320.
[37] Nelsen RB. An Introduction to Copulas. Springer; 2006.
[38] Joe H. Dependence Modeling with Copulas. CRC Press; 2014.
[39] C S. The proof and measurement of association between two things [J]. International journal of epidemiology, 2010,39(5):1137-50. DOI:10.1093/ije/dyq191.
[40] Kendall MG. A new measure of rank correlation. Biometrika 1938;30(1–2):81–93.
[41] Iman RL, Conover WJ. A distribution-free approach to inducing rank correlation among input variables. Commun Stat Simul Comput 1982;11(3):311–334.

Sponsors, Associates, and Links

---

• Journal of Sustainable Development and Green Buildings
  
  
• Landscape and Urban Horticulture
  
  
• Bridge and Structural Engineering
  
  
• Soil Mechanics and Geotechnical Engineering
  
  
• Journal of Municipal Engineering
  
  
• Heating, Ventilation and Air Conditioning
  
  
• Indoor Air Quality and Climate
  
  
• Computer Aided Architecture Design