A Spectrum Correction Method Based on Optimizing Turbulence Intensity

Based on the classical spectral representation method of simulating turbulent wind speed fluctuation, a harmonic superposition algorithm was introduced in detail to calculate the homogeneous turbulence wind field simulation in space. From the view of the validity of the numerical simulation results in MATLAB and the simulation efficiency, this paper discussed the reason for the bias existing between three types of turbulence intensity involved in the whole simulation process: simulated turbulence intensity, setting reference turbulence intensity, and theoretical turbulence intensity. Therefore, a novel spectral correction method of a standard deviation compensation coefficient was proposed. The simulation verification of the correction method was carried out based on the Kaimal spectrum recommended by IEC61400-1 by simulating the uniform turbulent wind field in one-dimensional space at the height of the hub of a 15 MW wind turbine and in two-dimensional space in the rotor swept area. The results showed that the spectral correction method proposed in this paper can effectively optimize the turbulence intensity of the simulated wind field, generate more effective simulation points, and significantly improve the simulation efficiency.

Generating fractal rough surfaces with the spectral representation method

The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. The characteristics of fractal rough surfaces simulated by the spectral representation method and the conventional Fast Fourier transform filtering method are compared. Furthermore, the fractal rough surfaces simulated by these two methods are compared in the simulation of contact and lubrication problems. Next, the influence of low and high cutoff frequencies on the normality of the simulated Gaussian fractal rough surfaces is investigated with roll-off power spectral density and single power-law power spectral density. Finally, a simple approximation method to generate non-Gaussian fractal rough surfaces is proposed by combining the spectral representation method and the Johnson translator system. Based on the simulation results, the current work gives recommendations on using the spectral representation method and the Fast Fourier transform filtering method to generate fractal surfaces and suggestions on selecting the low cutoff frequency of the power-law power spectral density. Furthermore, the results show that the proposed approximation method can be a choice to generate non-Gaussian fractal surfaces when the accuracy requirements are not high. The MATLAB codes for generating Gaussian and non-Gaussian fractal rough surfaces are provided.

Simulation of Spatially Correlated Multipoint Ground Motions in a Saturated Alluvial Valley

Based on Biot’s theory, the boundary element method, and spectral representation method, an effective simulation method for multiple-station spatially correlated ground motions on both bedrock and surface is developed, incorporating the spectral density function, coherence function, and site transfer function that consider both the wave scattering effect and the medium saturation. The accuracy and feasibility of the present method are validated by a typical numerical example. Our results indicate that the local site conditions and the saturation property of the medium significantly affect the multipoint spatially correlated earthquake ground motions, especially in the long-period range. It is necessary to use spatially varying ground motions with the rational consideration of local site effects and medium saturation as input during the seismic analysis of large-span structures.

Simulation of Nonstationary and Nonhomogeneous Wind Velocity Field by Using Frequency–Wavenumber Spectrum

The time history analysis is used to estimate the peak responses of structures subjected to stationary and nonstationary winds. The time histories of the fluctuating wind processes at multiple points can be simulated based on the spectral representation method for given target auto and cross power spectral density (PSD) functions. As the number of the processes of interest increases, the computation time for the simulation increases drastically. For the stationary homogeneous or nonhomogeneous wind fields, this problem can be overcome by using the frequency-wavenumber PSD function to simulate the stochastic propagating waves or fields. In the present study, a technique to simulate the amplitude modulated and frequency modulated nonstationary and nonhomogeneous stochastic propagating wind fields is presented. The technique relies on representing the nonstationary wind velocity by amplitude modulating a process that is time transformed from a stationary process. It is based on the established relations between the PSD functions of the nonstationary and of the stationary wind velocity. Simple to use and implement equations to carry out the simulation for one-dimensional line wind velocity field and two-dimensional nonstationary and nonhomogeneous wind velocity field are presented. The use of the developed technique and its adequacy is illustrated through numerical examples.

Importance of Distribution Type on Bearing Capacity of an Embedded Foundation in Spatially Varying Soils

The objective of this paper is to investigate the effect of soil variability on bearing capacity of an embedded foundation in the presence of nonstationary undrained shear strength. The nonstationary undrained shear strength is simulated by a nonstationary random field generator based on the spectral representation method. An embedded foundation buried into the soil to two times of width is presented to investigate the influence of spatially variable undrained shear strength on bearing capacity. Firstly, Monte Carlo simulations are carried out to discuss the effect of distribution type, nonstationary gradient parameter, and horizontal autocorrelation length on the bearing capacity from the standpoint of mean value and standard deviation. Then, the influence of the distribution type on the failure probability of nonstationary random soil is also investigated, with the failure probability for the Beta distribution being demonstrated to be always larger than that for the Lognormal and Gamma distribution.