Spectral Representation for a Class of Non-Gaussian Processes
Publication: Journal of Engineering Mechanics
Volume 130, Issue 5
Abstract
A new model is developed for non-Gaussian processes. The model is based on the spectral representation theorem for weakly stationary processes, can match the second moment properties and several higher order moments of any non-Gaussian process, and consists of a superposition of harmonics with uncorrelated but dependent random amplitudes. The calibration of the model to a target non-Gaussian process may require iterations. The Ito⁁ formula is used to calculate higher-order moments of the proposed model. These moments can be used to tune the model such that it matches some of the higher-order moments of a target non-Gaussian process in addition to its second-moment properties. The proposed model is useful for both Monte Carlo simulation and analytical studies on the response of linear and nonlinear systems to non-Gaussian noise. Examples are presented to illustrate the use of the proposed model.
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References
Ariaratnam, S. T. (1994). “Some illustrative examples of stochastic bifurcation.” Nonlinearity and chaos in engineering dynamics, J. M. T. Thomson and S. R. Bishop, eds., Wiley, New York, 267–274.
Arwade, S., Grigoriu, M., Ingraffea, A. R., and Miller, M. P. (1998). “Crack growth in stochastic microstructures.” Proc., 4th Int. Conf. on Stochastic Structural Dynamics.
Cai, G. Q., and Lin, Y. K.(1995). “Generation of non-Gaussian stationary stochastic processes.” Phys. Rev. E, 54(1), 299–303.
Grigoriu, M. (1995). Applied non-Gaussian processes: Examples, theory, simulation, linear random vibration, and MATLAB solutions, Prentice-Hall, Englewoods Cliffs, N.J.
Grigoriu, M.(1997). “Estimation of effective conductivity of random heterogeneous media by diffusion processes.” J. Appl. Phys., 82, 4346–4349.
Grigoriu, M.(2000a). “Non-Gaussian models in stochastic mechanics.” Probab. Eng. Mech., 15(1), 15–23.
Grigoriu, M.(2000b). “A spectral representation based model for Monte Carlo simulation.” Probab. Eng. Mech., 15(4), 365–370.
Horsthemke, W., and Lefever, R.(1977). “Phase transitions induced by external noise.” Phys. Lett., 64A(1), 19–21.
Soong, T. T., and Grigoriu, M. (1993). Random vibration of mechanical and structural systems, Prentice-Hall, Englewood Cliffs, N.J.
Waisman, F., Gurley, K., Grigoriu, M., and Kareem, A.(2002). “Non-Gaussian model for ringing phenomena in offshore structures.” J. Eng. Mech., 128(7), 730–741.
Wong, E., and Hajek, B. (1985). Stochastic processes in engineering systems, Springer, New York.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 130 • Issue 5 • May 2004
Pages: 541 - 546
Copyright
Copyright © 2004 American Society of Civil Engineers.
History
Received: Apr 15, 2002
Accepted: Oct 14, 2002
Published online: Apr 15, 2004
Published in print: May 2004
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