Nonstationary Narrow-Band Response and First-Passage Probability

1979 ◽  
Vol 46 (4) ◽  
pp. 919-924 ◽  
Author(s):  
S. Krenk
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Joint Distribution ◽  
Stationary Process ◽  
Narrow Band ◽  
Algebraic Relation ◽  
Joint Distribution Function ◽  
First Passage ◽  
First Passage Probability ◽  
First Passage Problem

The notion of a non-stationary narrow-band stochastic process is introduced without reference to a frequency spectrum, and the joint distribution function of two consecutive maxima is approximated by use of an envelope. Based on these definitions the first passage problem is treated as a Markov point process. The theory is applied to the response of a linear oscillator excited by a stationary process from t = 0, and a simple algebraic relation between the non-stationary and stationary correlation functions of the response is derived.

scholarly journals Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 64 ◽  
Author(s):  
Guilin Liu ◽  
Baiyu Chen ◽  
Song Jiang ◽  
Hanliang Fu ◽  
Liping Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Maximum Entropy ◽  
Wave Height ◽  
Joint Distribution ◽  
Height Function ◽  
Copula Function ◽  
Wave Period ◽  
Ocean Engineering ◽  
Joint Distribution Function ◽  
Design Wave Height

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

On the First-Passage Distribution for the Envelope of a Nonstationary Narrow-Band Stochastic Process

1974 ◽  
Vol 41 (3) ◽  
pp. 793-797 ◽  
Author(s):  
W. C. Lennox ◽  
D. A. Fraser
Keyword(s):  
Stochastic Process ◽  
Hypergeometric Functions ◽  
Narrow Band ◽  
First Passage Time ◽  
Wide Band ◽  
Passage Time ◽  
First Passage ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Backward Equation

A narrow-band stochastic process is obtained by exciting a lightly damped linear oscillator by wide-band stationary noise. The equation describing the envelope of the process is replaced, in an asymptotic sense, by a one-dimensional Markov process and the modified Kolmogorov (backward) equation describing the first-passage distribution function is solved exactly using classical methods by reducing the problem to that of finding the related eigenvalues and eigenfunctions; in this case degenerate hypergeometric functions. If the exciting process is white noise, the analysis is exact. The method also yields reasonable approximations for the first-passage time of the actual narrow-band process for either a one-sided or a symmetric two-sided barrier.

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