Search

The frequency-wavenumber spectrum-based spectral representation method (FWS-based SRM) serves as an effective and broadly utilized technique for simulating multivariate fluctuating wind fields. Despite its usefulness, it struggles with accuracy in low frequency range during simulations involving structures of considerable length when employing conventional uniform discretization in both frequency and wavenumber domains. To overcome this challenge, this study introduces a frequency-dependent uniform discretization scheme. This strategy first applies uniform discretization to the frequency domain, and then ascertains the cut-off wavenumbers based on the truncation error, and finally implements uniformly discretization in the wavenumber domain. Subsequently, the uniformly discrete wavenumbers and frequencies are integrated into the FWS-based SRM to generate wind speed time histories, in combination with the FFT technique. The numerical example serves to validate the exceptional accuracy exhibited by the frequency-dependent uniform discretization scheme in low frequency range. • A frequency-dependent uniform discretization scheme is proposed for FWS-based SRM. • The proposed scheme can be combined with the FFT technique to improve the simulation efficiency. • A FWS-based SRM with high accuracy in low frequency range was provided to simulate fluctuating wind field. [ABSTRACT FROM AUTHOR]

• An efficient method to simulate stationary strongly non-Gaussian process is proposed. • The proposed method performs well in some cases in terms of the convergence speed and accuracy. • The importance of upgrading both amplitude and phase contents is demonstrated. Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions. [ABSTRACT FROM AUTHOR]

The simulation of fluctuating wind speed fields holds paramount importance in the wind-resistant design of significant structures such as high-rise buildings, long-span bridges, and wind turbines. To address the computational challenges posed by the original spectral representation method (SRM), a novel approach has emerged. This approach, rooted in the frequency-wavenumber spectrum (FWS), offers a solution to the complexities associated with the original SRM. An enhanced non-uniform discrete technique based on the acceptance-rejection (A-R) criterion was introduced to improve the efficiency of the FWS-based SRM. Nonetheless, this technique currently faces certain constrains, including its demand for a substantial allocation of random access memory (RAM) and its inability to be seamlessly integrated with the fast Fourier transform (FFT) algorithm. Given this scenario, a notably more effective strategy for selecting representative points emerges -the frequency-dependent acceptance-rejection (A-R) scheme. This innovative scheme holds the advantage of diminishing RAM utilization, transforming wind field modeling from a supercomputers-exclusive task to one feasible on personal computers. Moreover, its seamless integration with FFT technology bolsters simulation efficiency. The provided numerical simulation instances of two-spatial dimensional fluctuating wind speed fields underscore the proficiency of this proposed frequency-dependent A-R scheme. The outcomes demonstrated the combined A-R and FFT technique's efficiency and precision, in simulating two-spatial dimensions fluctuating wind speed fields. [ABSTRACT FROM AUTHOR]

Simulation of sample realizations of stochastic processes is the bedrock of the Monte Carlo method, and the accurate modeling of stochastic processes is crucial to determine realistic structural responses. For seismic ground motion, its nonstationary property and spatially variability are well known. Furthermore, its non-Gaussian feature has been observed in some works. It is then necessary to simulate spatially varying ground motions accounting for its nonstationary and non-Gaussian characteristics. For this purpose, a computational procedure is developed for the simulation of non-Gaussian nonstationary spatially varying ground motions based on the spectral representation method (SRM). Translation process theory for the nonstationary non-Gaussian vector process is first proposed. By applying the proposed translation process theory, an iterative scheme is developed to estimate the underlying Gaussian evolutionary power spectral density (EPSD) matrix. The resulting underlying Gaussian EPSD matrix is used to simulate the underlying Gaussian ground motion by the SRM, which is finally mapped to the desired non-Gaussian nonstationary spatially varying ground motions. The capabilities of the proposed procedure are demonstrated by a numerical example. The statistical properties of the simulated non-Gaussian ground motions are compared with those of the simulated Gaussian ground motions. [ABSTRACT FROM AUTHOR]

A simple and efficient simulation method is proposed to generate multidimensional non-Gaussian vector fields based on the spectral representation method, according to the target cross spectral density matrix and the prescribed non-Gaussian marginal probability density functions. The proposed method starts by estimating the underlying Gaussian cross spectral density matrix through sample-function–free iterative scheme. Then, the resulting underlying Gaussian cross spectral density matrix can be applied to simulate a multidimensional Gaussian vector field, which is then mapped to the desired multidimensional non-Gaussian vector field through nonlinear memoryless translation. Finally, a numerical example involving a trivariate, two-dimensional, non-Gaussian vector field is presented to demonstrate the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]

The dimension reduction spectral representation method (SRM) is generally employed with the generalized probability density evolution method (GPDEM) to implement the seismic reliability assessment, where a noticeable non-zero value in the mean value of ground motion would be obtained. This study proposed an updated spectral representation method (U-SRM) to improve the simulated mean values, which coupled with GPDEM to investigate the nonlinear responses and seismic reliability assessment of a tunnel. Results obtained from the numerical study were compared between SRM and U-SRM. The horizontal displacement at the tunnel crown is more conservative using U-SRM than SRM in the reliability assessment of tunnels. Results indicated that U-SRM coupled with GPDEM is an efficient method to analyze the nonlinear responses and the seismic reliability of tunnels, and could serve as a reference for tunnel design in seismically active zones. • An updated dimensional reduction spectral representation method is proposed. • U-SRM coupled with GPDEM is an efficient method to do the seismic reliability of tunnels. • The horizontal displacement at the tunnel crown is more conservative using U-SRM than SRM. [ABSTRACT FROM AUTHOR]

The spectral representation method (SRM) is widely used when simulating spatially variable ground motions. It has mainly two formulas, i.e., the random amplitudes and the random phases formulas. There exist three methods for decomposing the cross spectral density matrix: Cholesky decomposition, eigen decomposition, and root decomposition. Therefore, there are six forms with respect to the different combinations of the simulation formulas and the decomposition methods. To provide researchers and engineers with the guidance on choosing simulation method, the six forms are systematically investigated from five aspects: the power intensity, response spectra, and stochastic error of auto/cross spectral density, Fourier spectra, and difference indexes for Fourier amplitudes and phases. Finally, we give the following advice: the characteristics of the ground motions simulated by the random amplitudes formula are independent of the decomposition method, while the characteristics of the ground motions simulated by random phases formula are dependent of the decomposition method. Furthermore, the root decomposition is strongly recommended when utilizing the random phases formula. [ABSTRACT FROM PUBLISHER]

Multivariate random processes are usually simulated by the spectral representation method (SRM). According to the matrix for decomposition, the SRM has two main types, that is, the SRM based on the decomposition of the power spectral density (PSD) matrix denoting the PSD matrix-based SRM, and the SRM based on the decomposition of the coherency matrix denoting the coherency matrix based-SRM. The stochastic errors of the PSD for the PSD matrix-based SRM have been given. This paper presents the stochastic errors of the PSD for the coherency matrix-based SRM, and makes a comparison of these errors for the PSD matrix-based SRM. For the random amplitudes formulas and random phase formula and Cholesky decomposition method, the stochastic errors of the PSDs for the PSD matrix-based SRM are the same as or the coherency matrix-based SRM, whereas for the random phases formula and eigendecomposition method and random phases formula and root decomposition method, they are different. However, the differences are slight when taking into account the sum of the PSD functions' stochastic errors. [ABSTRACT FROM AUTHOR]

Abstract: The spectral representation method (SRM), based on the Cholesky decomposition of either cross spectral density matrix or lagged coherency matrix, is widely used in the simulation of spatially varying ground motions. In this study, the SRM, based on the decomposition of lagged coherency matrix, is modified to apply to the common case which the auto spectral densities of simulation points are not the same. When using interpolation approximation approach to improve the efficiency, the SRM based on the decomposition of lagged coherency matrix exhibits much higher accuracy than the SRM based on the decomposition of cross spectral density matrix, because the elements of lower triangular matrix obtained by the Cholesky decomposition of lagged coherency matrix vary slowly with the frequency. Therefore, the SRM, based on the decomposition of lagged coherency matrix, is generally suitable for the combination with the interpolation approximation approach. [Copyright &y& Elsevier]

• A modified SRM is proposed to consider wave-passage effect in vector process. • Wave-passage effect is presented in the simulation of non-Gaussian vector process. • It is proved the wave-passage part is not changed in the nonlinear translation. Wave-passage effect is always of great importance when performing the dynamic analysis of lager scale structures. This effect can be easily considered in the simulation of Gaussian vector process, but there is not an efficient way to consider it in simulating non-Gaussian vector process. In this paper, a method is proposed to generate stationary non-Gaussian vector process considering wave-passage effect. In the simulation of vector process, wave-passage effect leads to a complex-defined cross spectral density matrix (CSDM). To separate the phase part from the CSDM, an improved form of spectral representation method (SRM) is proposed, in which the phase part representing the wave-passage effect can be directly expressed in an explicit form in the simulation formula. Then the characteristic of phase part representing the wave-passage effect during the nonlinear translation (translating underlying Gaussian vector process to the prescribed non-Gaussian vector process) is investigated. Interestingly, it is found that, the phase part is not changed. Based on this good feature, the modified SRM and the iterative scheme can be combined to simulate non-Gaussian vector process considering wave-passage effect. Two examples, involving the simulation of seismic ground motions and wind velocity time histories, are presented to show the characteristics of the simulated vector process and to verify the capabilities of the proposed method. [ABSTRACT FROM AUTHOR]