Simulation of Non-Gaussian Stochastic Process: Fluctuating Wind Pressure

In this paper, a direct simulation algorithm is presented for the generation of a class of non-Gaussian stochastic processes according to target lower-order moments and prescribed power spectral density (PSD) function. The proposed algorithm is to expand the autoregressive (AR) model and the autoregressive moving average (ARMA) model, which are available to generate Gaussian random process, to simulate directly non-Gaussian stochastic process. The coefficients of the AR or ARMA model are determined based on the prescribed PSD function. It is well known that outputting stochastic process is also non-Gaussian if inputting white noise is non-Gaussian. But the skewness and kurtosis of the outputting non-Gaussian random process are not identical to these of inputting non-Gaussian white noise. In this paper, the relationships of lower-order moments such as skewness and kurtosis between output and input are analyzed and close to linear transformations. To corroborate the feasibility and correctness of the present methodology, numerical examples involving simulation of fluctuating wind pressures are taken into consideration. Numerical results indicate that the skewness and kurtosis of generated wind pressures based on the AR or ARMA model closely match their targets. In addition, the PSD and correlation functions of simulated samples also show considerably good agreement with prescribed functions. Therefore, the proposed algorithm is effective to simulate directly the class of non-Gaussian stochastic process.

In seismic engineering, the earthquake-induced ground motion is generally represented in the form of pseudo-acceleration or displacement response spectra. There are, however, situations in which the response spectrum is not considered appropriate, and a fully dynamic analysis is required. In this case, the most effective approach is to define artificial spectrum-compatible stationary accelerograms, which are generated to match the target elastic response spectrum. So a Power Spectral Density (PSD) function is derived from the response spectrum. However, the above approach possesses the drawback that the artificial accelerograms do not manifest the variability in time and in frequency observed from the analysis of real earthquakes. Indeed, the recorded accelerograms can be considered sample of a fully non-stationary process. In this study a procedure based on the analysis of a set of accelerograms recorded in a chosen site to take into account their time and frequency variability is described. In particular the generation of artificial fully non-stationary accelerograms is performed in three steps. In the first step the spectrum-compatible PSD function, in the hypothesis of stationary excitations, is derived. In the second step the spectrum-compatible Evolutionary Power Spectral Density (EPSD) function is obtained by an iterative procedure to improve the match with the target response spectrum starting from the PSD function, once a time-frequency modulating function is chosen. In the third step the artificial accelerograms are generated by the well-known Shinozuka and Jan (J Sound Vib 25:111–128, 1972) formula and deterministic analyses can be performed to evaluate the structural response. Once the EPSD spectrum-compatible function is derived, a method recently proposed by the authors (Muscolino and Alderucci in Probab Eng Mech 40:75–89, 2015), is adopted to evaluate the EPSD response function of linear structural systems subjected to fully non-stationary excitations by very handy explicit closed-form.

Comparative analysis of BPNN, SVR, LSTM, Random Forest, and LSTM-SVR for conditional simulation of non-Gaussian measured fluctuating wind pressures

In the ABL wind tunnel, three inverted umbrella-shaped membrane structure groups were subjected to simultaneous pressure measurement model test. Time series of the fluctuating wind pressure were collected from 24 different wind angles. Upon examining the correlation coefficient of the fluctuating wind pressure between the upper and lower surfaces at the same pressure tap, it was discovered that the fluctuating wind pressure of the upwind roof exhibited asynchronous changes, which is a characteristic of a negative correlation area and has detrimental effects on the structure’s wind resistance. The local areas with non-Gaussian properties were evaluated by analyzing the probability density function of representative pressure taps. The mechanism behind non-Gaussian wind pressure was elucidated through considerations of the central limit theorem and spatial correlation of fluctuating wind pressure. This study introduces a quantitative classification criterion for identifying the non-Gaussian distribution area of fluctuating wind pressure, setting the threshold at an 80% cumulative probability for both skewness and kurtosis. The analysis showed that the steady airflow of the structure corresponds to the Gaussian distribution area, while the non-Gaussian distribution area is primarily concentrated at the front edge of the upwind roof and the rear edge of the downwind roof. To ascertain the peak factor for the non-Gaussian distribution, the improved peak factor method was utilized, providing insights into the range of peak factor in the non-Gaussian distribution area of this particular roof configuration. This information serves as a foundation for the wind resistance design of this structure.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

Reduction of leakage and increase of resolution in power spectral density and coherence functions

The problem of conditional simulation of non-Gaussian stochastic processes and fields has gained a significant interest recently because of its applications in many fields, such as wind engineering, ocean engineering, and soil engineering. In this paper, the support vector machines (SVM) approach is developed for the conditional simulation of non-Gaussian stochastic processes and fields. To show the advantages of the presented method, the conditional simulation of non-Gaussian fluctuating wind pressures is carried out by using SVM and artificial neural networks (ANN). SVM considers three kinds of kernel function, such as linear function, Gaussian radial basis function, and exponential radial basis function, whereas ANN employs back-propagation and generalized regression. In machine learning of these artificial intelligences, two ways (interpolation and extrapolation) are employed to train finite non-Gaussian samples. The feasibility and validity of these algorithms are evaluated through the correlation coefficients, root mean square errors, skewness errors, and kurtosis errors between simulated samples and target samples and probability density functions (PDF), power spectral density (PSD) functions, and autocorrelation functions (ACF) of the simulated non-Gaussian fluctuating wind pressures versus their corresponding targets. The results show that the accuracy and effectiveness of SVM with an appropriate kernel function are superior to the back-propagation neural network (BPNN) and generalized regression neural network (GRNN). Furthermore, the advantage of the presented SVM approach is very obvious when the trained non-Gaussian samples are few.

It is today generally accepted that to carry‐out realistic transport simulation trials, field data must be acquired from vehicles travelling on the actual route(s) to be used for a particular distribution environment. This approach requires time, effort, access to data recording equipment as well as the necessary expertise to analyse the collected data. Often, this is out of reach of smaller operators who want a reasonable approximation without the time and expense. Currently, the only available option is the adoption of generic test spectra and levels that have been shown to be approximate representations of distribution environments. This paper discusses an alternative and practical method that uses some knowledge of the dynamic characteristics of various vehicle types along with an assessment of the types of roads (road roughness) to be encountered along a particular route. The method exploits the fact that the spectral characteristics (power spectral density) of road profiles are well known. The paper shows how this road surface elevation spectral function is combined with a numerical model of a particular vehicle type and speed to produce a target vibration power spectral density suitable for vibration test systems. One added benefit is that the method is capable of calculating the variations in root mean square levels of the response vibrations. This is presented as the root mean square distribution which, when coupled with the target power spectral density, can be used to synthesize realistic random vibrations that bear statistical similitude with real, field vibrations. Copyright © 2012 John Wiley & Sons, Ltd.

Digital simulation of stochastic wind velocity field is prerequisite to flutter or buffeting analysis of long-span bridges in time-domain. Wavelet method was applied to the simulation of the stochastic wind field, performing the effective simulation of spatial stochastic wind field. According to the idea of multi-resolution analysis and orthonormal wavelets, relationship between wavelet coefficients and PSD(power spectral density)function is deduced , then the wavelet coefficients on each and every scale are obtained from the given PSD function, the intermittency was introduced into wavelet coefficients while at the same time preserves the target spectral characters. As a result, the inverse wavelet transform is applied to generate stationary wind velocity history through the given wavelet coefficients. A numerical example to illustrate the application of the proposed method for the simulation of a bridge wind velocity field is provided.

In this work, wind tunnel tests of pressure measurements are carried out to assess the global aerodynamic interference factors, the local wind pressure interference factors, and the local lift spectra of an square high-rise building interfered by an identical cross-sections but lower height building arranged in various relative positions. The results show that, when the interfering building is located in an area of oblique upstream, the RMS of the along-wind, across-wind, and torsional aerodynamic forces on the test building increase significantly, and when it is located to a side, the mean across-wind and torsional aerodynamic forces increase; In addition, when the interfering building is located upstream or staggered upstream, the mean wind pressures on the sheltered windward side turn form positive to negative and with a maximum absolute value of up to 1.75 times, and the fluctuating wind pressures on the sheltered windward side and leading edge of the side increase significantly with decreasing spacing ratio (up to a maximum of 3.5 times). When it is located to a side, the mean and fluctuating wind pressures on the leading edge of inner side are significantly increased. The three-dimensional flow around a slightly-shorter disturbing building has a great effect on the average and fluctuating wind pressures on the windward or cross-wind faces. When the disturbing building is near to the test building, the vortex shedding peak in the lift spectra decreases and there are no obvious signs of periodicity, however, the energies of the high frequency components undergo an obvious increase.

The present paper focuses on reliability analysis of structural systems under ground motion acceleration taking into account the inherent random nature of the excitation as well as epistemic uncertainties affecting the definition of its spectrum. Specifically, seismic excitation is modelled as a zero-mean stationary Gaussian random process fully characterized by an imprecise power spectral density (PSD) function i.e. with interval parameters. The ranges of such interval parameters are determined by analysing a large set of accelerograms recorded on rigid soil deposits. To discard outliers, the Chauvenet’s Criterion is applied iteratively. The proposed imprecise PSD function may be viewed as representative of the actual accelerograms recorded on rigid soil deposits. Reliability assessment is carried out by incorporating the imprecise PSD function of ground motion acceleration into the formulation of the classical first-passage problem using Vanmarcke’s failure criterion. Due to imprecision of the excitation, the reliability function and the fractile of order p of the selected extreme value response process turn out to have an interval nature. Thus, the aim of reliability analysis is the evaluation of the bounds of such functions which define the range of structural performance. Numerical results show that neglecting imprecision of the PSD may lead to significant overestimation of the safety level.

Simulation of non-Gaussian surfaces with FFT

Stochastic modeling of the seismic excitation for structural dynamics purposes

A modified straightforward spectral representation method for accurate and efficient simulation of the stationary non-Gaussian stochastic wave

Chapter 12 presents a detailed analysis of continuous-time signals and systems in the frequency domain, including the theory of Fourier series and Fourier transforms, and key examples relevant for the analysis and synthesis of signals processed in the digital transceiver blocks of a communication system. The amplitude, magnitude, phase, and power spectra are defined and calculated for typical signals. In particular, the Fourier transform of periodic signals is presented, due to its importance in communication systems theory and practice. Using a unique notation that distinguishes energy and power signals, the correlation, power, and energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of a linear-time-invariant system, using the concepts of impulse response, system correlation function, and power spectral density, both for power signals and energy signals, is presented. In addition, Parseval’s theorem and the Rayleigh theorem are proven.