POD-based dimension reduction simulation of stochastic wave force field

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (12) : 98-104.

LIU Zhangjun1,2,LIU Lei2,WANG Feng2

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Abstract

Due to the theory of multivariate stationary stochastic process, the proper orthogonal decomposition (POD) formula based on the orthogonal random variables was derived.On the basis of this, by defining the random function form of the orthogonal random variable set in the POD formula, a POD-random function approach was suggested for simulating the multivariate stationary stochastic process.Note that the proposed approach and the conventional approach based on the random phase angles are both the special cases of the POD approach based on the orthogonal random variables.However, the proposed approach can accurately represent the multivariate stationary stochastic process with just two elementary random variables.The power spectrum density matrix involved in the multivariate stationary stochastic process of wave force was derived according to the linearized Morison formula.Then by means of the proposed approach, effective dimension reduction simulation for the multivariate stationary stochastic process of wave force could thus be realized.Finally, combined with the P-M wave spectrum, the power spectrum density matrix involved in the multivariate stochastic process of the horizontal wave force was derived.And the numerical simulation analysis of the horizontal stochastic wave force field was carried out.The example shows that the proposed approach requires the least number of the elementary random variables and a small number of representative samples which constitute a complete set of probabilities.It has significant advantages in terms of simulation accuracy.

Key words

stochastic wave force field / POD / power spectrum density matrix / random function / dimension reduction simulation

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LIU Zhangjun1,2,LIU Lei2,WANG Feng2. POD-based dimension reduction simulation of stochastic wave force field[J]. Journal of Vibration and Shock, 2019, 38(12): 98-104

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