Abstract
A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.
Highlights
The generation of realizations of a vector of random processes, which are partially coherent in a prescribed manner, is of interest in testing and dynamic analysis of structures exposed to a variety of natural environments described as stochastic processes
In order to use the decomposition of the spectral density into the form of Eq (3) with the model provided by Fig. 1 and Eq (2), frames or blocks of independent random sources need to be generated in the frequency domain with a specified spectral density
Possible peaks of 4 times the rms will give a distribution that is very nearly Gaussian. This results in the recommendation that if the Random Phase (RP) method is used to generate blocks of independent noise, at least four lines in the frequency domain should be of the same order of magnitude
Summary
The generation of realizations of a vector of random processes, which are partially coherent in a prescribed manner, is of interest in testing and dynamic analysis of structures exposed to a variety of natural environments described as stochastic processes. The matrix [H(f)] describes the frequency response functions between all pairs of inputs and outputs. After the decomposition is accomplished, the factor [U(f)] of the decomposition is associated with the frequency-response functions, [H(f)] of Eq (2) and the diagonal factor, [S(f)] is associated with the auto-spectral density of the independent inputs, [Gzz(f)], in Eq (2). Independent noise sources are generated in the frequency domain, coupled with the established frequency-response functions, transformed to the time domain to generate the partially coherent realizations.
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