On the peak factor of stationary Gaussian processes

Abstract New simple approximate formulae are introduced for the average and the standard deviation of the peak factor of stationary Gaussian processes. The formulae take into account the bandwidth of the process and are based on the assumption that the extreme point process is Markovian. Also presented are simulation results for various spectral shapes (response of the linear oscillator to a white noise, bimodal spectrum, and ideal bandpass process). These suggest that none of the currently available bandwidth parameters can represent accurately the overall effect of the spectral shape on the peak factor. The approximate formulae, however, give reasonable estimates, if one excludes bimodal spectra with very light modal damping. The various definitions of the envelope process (essential in the Markov approximation) are reviewed and unified.

[1]  A. Kiureghian.  Structural Response to Stationary Excitation , 1980 .

[2]  Alan R. Jones,et al.  Fast Fourier Transform , 1970, SIGP.

[3]  Ieee Acoustics.  Programs for digital signal processing , 1979 .

[4]  J. Roberts,et al.  First passage time for the envelope of a randomly excited linear oscillator , 1976 .

[5]  P. Mazur.  On the theory of brownian motion , 1959 .

[6]  F. Massey.  The Kolmogorov-Smirnov Test for Goodness of Fit , 1951 .

[7]  E. Vanmarcke.  On the Distribution of the First-Passage Time for Normal Stationary Random Processes , 1975 .

[8]  K. L. Chandiramani,et al.  Some First-Passage Problems in Random Vibration , 1966 .

[9]  Masanobu Shinozuka,et al.  On the First-Excursion Probability in Stationary Narrow-Band Random Vibration, II , 1971 .

[10]  J.-N. Yang,et al.  Simulation of random envelope processes. , 1972 .

[11]  Richard H. Lyon,et al.  On the Vibration Statistics of a Randomly Excited Hard‐Spring Oscillator , 1960 .

[12]  W. D. Mark,et al.  Random Vibration in Mechanical Systems , 1963 .

[13]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[14]  Y. K. Lin,et al.  First-excursion failure of randomly excited structures , 1970 .

[15]  Lawrence L. Kupper,et al.  Probability, statistics, and decision for civil engineers , 1970 .

[16]  E. Gumbel,et al.  Extreme Values in Aeronautics , 1954 .

[17]  S. Rice.  Mathematical analysis of random noise , 1944 .

[18]  A G Davenport,et al.  NOTE ON THE DISTRIBUTION OF THE LARGEST VALUE OF A RANDOM FUNCTION WITH APPLICATION TO GUST LOADING. , 1964 .

[19]  E. Vanmarcke.  Properties of Spectral Moments with Applications to Random Vibration , 1972 .

[20]  G. D. Bergland,et al.  A guided tour of the fast Fourier transform , 1969, IEEE Spectrum.

[21]  S. H. Crandall.  First-crossing probabilities of the linear oscillator , 1970 .

[22]  M. Longuet-Higgins,et al.  The statistical distribution of the maxima of a random function , 1956, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  S. Krenk.  Nonstationary Narrow-Band Response and First-Passage Probability , 1979 .

[24]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[25]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .