Digital simulation of multi-variate stochastic processes

Digital simulation of multi-variate stochastic processes

Salvatore Russotto, Mario Di Paola, Antonina Pirrotta

download PDF

Abstract. Stochastic dynamic analysis of linear or nonlinear multi-degree-of-freedom systems excited by multi-variated processes is usually conducted by using digital Monte Carlo (MC) simulation. Since in structural systems few modal shapes contribute to the response in the nodal space, the computational burden of MC simulation is mainly related to the digital simulation of the input process. Usually, the generation of multi-variated samples of Gaussian input process is performed with the aid of the Shinozuka formula. However, since in this procedure the stochastic process is given as a summation of waves with random amplitude amplified by the square root of the power spectral density, the randomness is due to a random phase angle of each wave, therefore a very large number of waves is required to reach the Gaussianity, i.e. the process is only asymptotically stable. Moreover, the computational burden increases in case of multi-variated processes. The paper aims to drastically reduce the generation time of the input process through the use of a two-step procedure. In the first step, by using the Priestley formula, each wave is normally distributed. This first aspect allows to drastically reduce the computational effort for the mono-variate process since few waves are sufficient to reach the Gaussianity. In the second step, the multi-variate process is reduced as a summation of independent fully coherent vectors if the quadrature spectrum (q-spectrum) can be neglected. An application of digital simulation of the wind velocity field is discussed to prove the efficiency of the proposed approach.

Stochastic Processes, Wind Field Velocity, Monte Carlo Simulation, Reduction of the Computational Burden

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Salvatore Russotto, Mario Di Paola, Antonina Pirrotta, Digital simulation of multi-variate stochastic processes, Materials Research Proceedings, Vol. 26, pp 561-566, 2023


The article was published as article 91 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] M. Di Paola, I. Gullo, Digital generation of multivariate wind field processes, Probabilistic Eng. Mech. 16 (2001) 1-10.
[2] N.T. Thomopoulos, Essentials of Monte Carlo Simulation, first ed., Springer, New York, 2013.
[3] M. Di Paola, S. Russotto, A. Pirrotta, Self-similarity and response of fractional differential equations under white noise input, Prob. Eng. Mech. 70 (2022) 103327.
[4] S. Russotto, A. Di Matteo, A. Pirrotta, An Innovative Structural Dynamic Identification Procedure Combining Time Domain OMA Technique and GA, Buildings 12(7) (2022) 963.
[5] S. Russotto, A. Di Matteo, C. Masnata, A. Pirrotta, OMA: From research to engineering applications, Lect. Notes Civ. Eng. 156 (2021) 903-920.
[6] A. Di Matteo, C. Masnata, S. Russotto, C. Bilello, A. Pirrotta, A novel identification procedure from ambient vibration data, Meccanica 56 (2021) 797-812.
[7] M. Di Paola, A. Pirrotta, Non-linear systems under impulsive parametric input, Int. J. Non Linear Mech. 34(5) (1999) 843-851.
[8] M. Di Paola, Digital simulation of wind field velocity, J. Wind. Eng. Ind. Aerodyn. 74-76 (1998) 91-109.
[9] M. Shinozuka, Simulation of multivariate and multidimensional random processes, J. Acoust. Soc. Amer. 49(1) (1971) 357-367.
[10] E. Simiu, R.H. Scanlan, Wind effects on structures, Wiley, New York, 1978.
[11] G. Solari, Gust Buffeting. I: Peak Wind Velocity and Equivalent Pressure, J. Struct. Eng. 119(2) (1993) 365-382.