Crossing rate statistics of quadratic transformations of Gaussian processes |
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Authors: | A Naess |
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Affiliation: | Department of Structural Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway |
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Abstract: | The main focus of this paper is the development of a numerical procedure for calculating the average crossing rates of a stochastic process that can be expressed as a sum of a linear and a nonlinear, quadratic transformation of a Gaussian process. Such a representation applies for instance to the motion response of a linear structure subjected to wind loading, when the loading model is proportional to the square of a Gaussian wind velocity process. It is also the standard model for expressing the total wave forces or horizontal excursion responses of a moored floating offshore platform in a random sea way. Knowledge of the crossing rate is a key to many important quantities related to response statistics and reliability applications. It is demonstrated how the proposed numerical procedure can be used for calculating the average crossing rate of the type of response processes considered. |
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Keywords: | Average crossing rate Quadratic transformations Volterra series Characteristic function Quadratic filter Response statistics |
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