Frequency-domain fatigue analysis of wide-band stationary Gaussian processes using a trimodal spectral formulation

Abstract In this paper, a procedure for fatigue analysis of a general wide-band stationary Gaussian process is developed in the frequency domain using a trimodal spectral formulation, based on a generalization of the principle proposed by Jiao and Moan for predicting bimodal fatigue damage. The novel method approximates the rainflow cycles with large amplitudes as the sum of the envelopes of the process components. First, the method is derived and the corresponding accuracy is demonstrated for ideal trimodal Gaussian processes whose spectra exhibit peaks at three well separated modes, each assumed to be narrow-banded. Hermite numerical integration method is applied to evaluate the fatigue damage due to a Rayleigh sum distribution since there is no closed-form solution for a random variable which is the sum of more than two Rayleigh random variables. Then, the method is further developed and applied to general wide-band Gaussian processes by dividing the spectrum into three segments with the same variances and calculating the fatigue damage in the same way as for the ideal trimodal processes. Based on extensive time series simulated with spectra of wave- and wind-induced structural responses and with generally defined wide-band spectra, the rainflow cycle counting method has been applied to estimate the fatigue damage in the time domain in order to check the accuracy of the proposed method and other frequency-domain methods. It is found that the narrow-band assumption can be very well made for a process with a Vanmarcke’s bandwidth parameter which is less than 0.5. For most of the simulated processes with bandwidth parameters between 0.5 and 0.85, the proposed method slightly overestimates the fatigue damage on average. If the bandwidth is greater than 0.85, the fatigue damage obtained by the trimodal formulation may be significantly overestimated in some cases, however spectra with very high bandwidth parameters might be unrealistic. Anyway, it has been shown that the overestimation can be alleviated by using a formulation with more modes for these cases. Moreover, two empirical formulae for wide-band fatigue damage estimation, one derived by Dirlik and the other proposed by Benasciutti and Tovo, have also been verified to be very accurate but slightly underestimate the fatigue damage for a wide range of the bandwidth parameters considered in this paper.

[1]  D. Benasciutti,et al.  Spectral methods for lifetime prediction under wide-band stationary random processes , 2005 .

[2]  Ivar Holand.  Safety of structures under dynamic loading , 1978 .

[3]  M. Schwartz,et al.  Communication Systems and Techniques , 1996, IEEE Communications Magazine.

[4]  Shinsuke Sakai,et al.  On the Distribution of Rainflow Range for Gaussian Random Processes with Bimodal PSD , 1995 .

[5]  Torgeir Moan,et al.  Fatigue Under Combined High and Low Frequency Loads , 2006 .

[6]  David Cebon,et al.  Predicting fatigue lives for bi-modal stress spectral densities , 2000 .

[7]  R. Rackwitz,et al.  Comparison of analytical counting methods for Gaussian processes , 1993 .

[8]  Paul H. Wirsching,et al.  Fatigue under Wide Band Random Stresses , 1980 .

[9]  Ne Dowling,et al.  Fatigue Failure Predictions for Complicated Stress-Strain Histories , 1971 .

[10]  Curtis E. Larsen,et al.  Predicting the fatigue life of offshore structures by the single-moment spectral method , 1991 .

[11]  Torgeir Moan,et al.  Uncertainty of wave-induced response of marine structures due to long-term variation of extratropical wave conditions , 2005 .

[12]  I. Rychlik.  A new definition of the rainflow cycle counting method , 1987 .

[13]  George K. Karagiannidis,et al.  On the distribution of the weighted sum of L independent Rician and Nakagami envelopes in the presence of AWGN , 2001, Journal of Communications and Networks.

[14]  J. van der Tempel,et al.  Design of support structures for offshore wind turbines , 2006 .

[15]  Torgeir Moan,et al.  Probabilistic analysis of fatigue due to Gaussian load processes , 1990 .

[16]  Norman C. Beaulieu,et al.  Accurate simple closed-form approximations to Rayleigh sum distributions and densities , 2005, IEEE Communications Letters.

[17]  Inge Lotsberg,et al.  Background for Revision of DNV-RP-C203 Fatigue Analysis of Offshore Steel Structure , 2005 .

[18]  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.

[19]  E. W. C. Wilkins,et al.  Cumulative damage in fatigue , 1956 .

[20]  Roberto Tovo,et al.  On fatigue damage assessment in bimodal random processes , 2007 .

[21]  Igor Rychlik,et al.  WAFO - A Matlab Toolbox For Analysis of Random Waves And Loads , 2000 .