Abstract
This paper presents a probability density function representing a non-Gaussian random process in closed form. The probability density is based on the Kac-Siegert solution of Volterra's stochastic series expansion of a nonlinear system. A method is developed, however, to obtain the Kac-Siegert solution from knowledge of the time history only of the random process, and the result is expressed as a function of a normal distribution. Then, by applying the change of random variable technique, the asymptotic probability density function applicable to the response of a nonlinear system (which is a non-Gaussian random process) is developed in closed form. A comparison of the presently developed probability density function and the histogram constructed from a record indicating strong non-Gaussian characteristics shows excellent agreement.
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