Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

Generation of endurance time excitation functions using spectral representation method

In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.

Study of the approximate approaches to the POD based spectral representation method

The spectral representation method (SRM) is most widely used in simulating the stochastic field.The proper orthogonal decomposition (POD) based SRM is an important form.This paper investigates the approximate approaches to the POD-based SRM in simulating two typical problems,i.e.,the seismic ground motion and wind velocity fields simulations.Then,the accuracy resulting from the power spectral density matrix-based POD method (PSRM) is compared to that of the coherency matrix-based POD method (CPSRM).It is concluded that the CPSRM maintains a much higher accuracy than the PSRM.In the CPSRM,the linear interpolation of eigenvectors and third-order polynomial interpolation of eigenvalues can be accepted to attain high accuracy;the linearly distributed interpolation nodes are effective in the ground motions simulation;however,the exponentially distributed interpolation nodes are effective in the wind velocity simulation.

Spectral representation of correspondence of multi-valued logical functions

In cryptology, it is an important topic to study the best affine approach of functions. The best affine approach of Boolean functions has been discussed in ref. [1] by using the Walsh spectrum, of which the key problem is how to represent the correspondence of Boolean functions by using Walsh spectrum. For the multi-valued logical functions so far, the spectral representation of their correspondence has not been presented yet. This let-

THE STATIONALRITY ANDSPECTRAL REPRESENTATION OFONE CLASS OF NON-NEGATIVEINTEGER-VALUED TIME SERIES

This paper proposes a general integer-valued time series (IVTS) model based on the oneproposed by Al-Osh and Alzaid[1]. The model is represented by a construction from differingfrom Al-Osh's INAR(1) model in which the INAR(1) model is given only formally. Many basicproblems about the model such as stationarity, spectral representation, the strong law of largenumbers, parameter estimation have been discussed. In this paper, we only study the stationarityand spectral representation. The others will be dealt with in another paper.

Approximation approach to the SRM based on root decomposition in the simulation of spatially varying ground motions

The spectral representation method （SRM） is widely used to simulate spatially varying ground motions. This study focuses on the approximation approach to the SRM based on root decomposition, which can improve the efficiency of the simulation. The accuracy of the approximation approach may be affected by three factors： matrix for decomposition, distribution of frequency interpolation nodes and elements for interpolation. The influence of these factors on the accuracy of this approach is examined and the following conclusions are drawn. The SRM based on the root decomposition of the lagged coherency matrix exhibits greater accuracy than the SRM based on the root decomposition of the cross spectral matrix. The equal energy distribution of frequency interpolation nodes proposed in this study is more effective than the counter pith with an equal spacing. Elements for interpolation do not have much of an effect on the accuracy, so interpolation of the elements of the decomposed matrix is recommended because it is less complicated from a computational efficiency perspective.

Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.

Simulation of non-stationary ground motion processes(I)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statistical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simulation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the target power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is verified by simulation of one acceleration record in Landers earthquake.

Large eddy simulation study of 3D wind field in a complex mountainous area under different boundary conditions

Large eddy simulations generally are used to predict 3D wind field characteristics in complex mountainous areas.Certain simulation boundary conditions,such as the height and length of the computational domain or the characteristics of inflow turbulence,can significantly impact the quality of predictions.In this study,we examined these boundary conditions within the context of the mountainous terrain around a long-span cable-stayed bridge using a wind tunnel experiment.Various sizes of computational domains and turbulent incoming wind velocities were used in large eddy simulations.The results show that when the height of the computational domain is five times greater than the height of the terrain model,there is minimal influence from the top wall on the wind field characteristics in this complex mountainous area.Expanding the length of the wake region of the computational domain has negligible effects on the wind fields.Turbulence in the inlet boundary reduces the length of the wake region on a leeward hill with a low slope,but has less impact on the mean wind velocity of steep hills.

Digital simulation of 3D turbulence wind field of Sutong Bridge based on measured wind spectra

Time domain analysis is an essential implement to study the buffeting behavior of long-span bridges for it can consider the non-linear effect which is significant in long-span bridges. The prerequisite of time domain analysis is the accurate description of 3D turbulence winds. In this paper, some hypotheses for simplifying the 3D turbulence simulation of long-span cable-stayed bridges are conducted, considering the structural characteristics. The turbulence wind which is a 3D multivariate stochastic vector process is converted into four independent 1D univariate stochastic processes. Based on recorded wind data from structural health monitoring system (SHMS) of the Sutong Bridge, China, the measured spectra expressions are then presented using the nonlinear least-squares fitting method. Turbulence winds at the Sutong Bridge site are simulated based on the spectral representation method and the Fast Fourier transform (FFT) technique, and the relevant results derived from target spectra including measured spectra and recommended spectra are compared. The reliability and accuracy of the presented turbulence simulation method are validated through comparisons between simulated and target spectra (measured and recommended spectra). The obtained turbulence si-mulations can not only serve further analysis of the buffeting behavior of the Sutong Bridge, but references for structural anti-wind design in adjacent regions.

Ghost Symmetries and Multi-fold Darboux Transformations of Extended Toda Hierarchy

In this paper,the author constructs ghost symmetries of the extended Toda hierarchy with their spectral representations.After this,two kinds of Darboux transforma-tions in different directions and their mixed Darboux transformations of this hierarchy are constructed.These symmetries and Darboux transformations might be useful in Gromov-Witten theory of CP1.