Target Power Spectrum Research Articles

Enhancing the variability of simulated random processes using the spectral representation method

In this paper, the traditional spectral representation method for simulating stochastic processes is revisited. The main goal is to introduce various approaches to enhance the variability of the generated sample functions to better reflect variabilities observed in field measurements and experimental data, while keeping the ensemble-averaged power spectra unchanged. The general idea, gradually developed over the last decade, is to randomize the power spectral density function of the uncertain physical quantities by modeling certain parameters as random variables calibrated from experimental data. The potential of such approaches has not been fully explored yet. This work explores the pros and cons of using power spectral density functions with random parameters in the simulation of highly variable, stationary and nonstationary, Gaussian stochastic processes. The main characteristics of a stochastic process, such as distribution of maxima and variability in time and frequency, are examined. The use of a pass-band Butterworth filter to control the variability of the Fourier spectrum of the simulated samples is studied. The Butterworth filter is selected so that the ensemble-averaged power spectral density matches the target power spectrum, but each individual generated sample function possesses different amplitude and frequency distributions. Comparisons between samples generated using the traditional spectral representation method and those generated with enhanced variability are made through a series of illustrative examples. Results show that with the proposed enhanced-variability spectral representation method, certain characteristics of the stochastic process, such as the distribution of maxima, will be significantly different (while the ensemble-averaged power spectra will remain the same). The implications in reliability studies are obvious.

Seismic response analysis of submerged floating tunnel considering non-uniform excitation and flexible-support boundary effect

In order to ensure the safety of submerged floating tunnel(SFT) during operation, it is necessary to carry out SFT response analysis under environmental loads. Given that SFTs are often constructed in valley areas situated in seismic zones, the aseismic performance of SFT needs to be investigated. However, there are important factors of non-uniform excitation and flexible-support boundary which have not been explored thoroughly. Non-uniform excitation affects the load input characteristics while flexible-support boundary affects the dynamic characteristics of structure itself. In this paper, we built a multi-point seismic wave synthesis model which fits well with the target power spectrum and a numerical response analysis model which reflects the dynamic characteristics of SFT structure well. The results based on the proposed model show that vertical non-uniform excitation can significantly increase the peak value of SFT tether tension and tube displacement with flexible-support boundary under whether artificial or natural seismic wave series input. While flexible-support boundary can availably produce vibration control effect on peak value of tether tension and tube response of whether displacement or stress indices under non-uniform wave series input. This work can provide reference for dynamic safety assessment and vibration control design of SFT to improve the development of ocean space.

Fitting the power spectrum of stationary random sequence

Based on the spectral representation of zero-mean stationary process, another method of fitting the target power spectrum is obtained. The fitted random sequence is uniformly convergent with respect to the target sequence. Compared to the commonly used wave superposition method in simulating wind velocity fluctuations, its merits and deficiencies are shown.

Adaptive vibration control on electrohydraulic shaking table system with an expanded frequency range: Theory analysis and experimental study

Abstract Active vibration control using electrohydraulic shaking table (EHST) system is widely applied in civil engineering, automotive industry, environmental vibration testing and other situations where large actuating forces are needed. However, the electrohydraulic actuators (actuating systems) often suffer from drawbacks of limited frequency bandwidth, varying system parameters and so forth. In view of the limits mentioned above, this study hopes to seek out proper solutions to minimize the influence from those drawbacks. We first design a full state feedback-feedforward servo controller, which is able to extend the frequency bandwidth of EHST system, by constructing the analytical models of the servo valve and hydraulic cylinder. Numerical simulations show that the proposed servo controller is able to compensate for the attenuation-band of hydraulic cylinder and thus improve the upper frequency limit of the whole system to a degree that is higher than the natural frequency of servo valve. Afterwards, we propose a frequency domain adaptive power level control (APLC) algorithm for solving the problem of parametric variations of EHST system in application of power level control (i.e., simulate vibration based on certain power spectrum). Numerical simulations show that although APLC algorithm is not able to get exactly same spectrum and waveform at every independent trial, the power level of every trail will finally converge to the target power spectrum. Finally, an experimental validation was conducted based on an EHST system with 3 ton maximum force and 1.2 m × 1.2 m horizontal table. The results show that the proposed algorithms have greatly improved the effective bandwidth and the power level of the controlled system response can finally match the target power spectrum within an accuracy of ±3 dB.

Numerical simulation of non-Gaussian wind load

Compared with Gaussian wind loads, there is a higher probability of strong suction fluctuations occurrence for non-Gaussian wind pressures. These instantaneous and intermittent fluctuations are the initial cause of local damage to roof structures, particularly at the edges and corners of long-span roofs. Thus, comparative errors would occur if a Gaussian model is used to describe a non-Gaussian wind load, and structural security would not be guaranteed. This paper presents a simplified method based on the inverse fast Fourier transform (IFFT), in which the amplitude spectrum is established via a target power spectrum. Also, the phase spectrum is constructed by introducing the exponential peak generation (EPG) model. Finally, a random process can be generated via IFFT that meets the specified power spectral density (PSD), skewness and kurtosis. In contrast to a wind tunnel experiment, this method can avoid the coupled relation between the non-Gaussian and the power spectrum characteristics, and lead to the desired computational efficiency. Its fitting accuracy is not affected by phase spectrum. Moreover, the fitting precision of the kurtosis and PSD parameters can be guaranteed. In a few cases, the fitting precision of the skewness parameter is fairly poor, but kurtosis is more important than skewness in the description of the non-Gaussian characteristics. Above all, this algorithm is simple and stable and would be an effective method to simulate a non-Gaussian signal.

Power spectrum sensitivity of raster-scanned CMB experiments in the presence of1/fnoise

We investigate the effects of $1/f$ noise on the ability of a particular class of cosmic microwave background experiments to measure the angular power spectrum of temperature anisotropy. We concentrate on experiments that operate primarily in raster-scan mode and develop formalism that allows us to calculate analytically the effect of $1/f$ noise on power-spectrum sensitivity for this class of experiments and determine the benefits of raster-scanning at different angles relative to the sky field versus scanning at only a single angle (cross-linking versus not cross-linking). We find that the sensitivity of such experiments in the presence of $1/f$ noise is not significantly degraded at moderate spatial scales ($\ensuremath{\ell}\ensuremath{\sim}100$) for reasonable values of scan speed and $1/f$ knee. We further find that the difference between cross-linked and non-cross-linked experiments is small in all cases and that the non-cross-linked experiments are preferred from a raw sensitivity standpoint in the noise-dominated regime---i.e., in experiments in which the instrument noise is greater than the sample variance of the target power spectrum at the scales of interest. This analysis does not take into account systematic effects.

A wavelet-based method to generate artificial wind fluctuation data

A method using the inverse wavelet transform is proposed to generate artificial wind velocity fluctuations. At first, in order to investigate the time-scale structure of natural wind, the wavelet transform is applied to the time history of a measured wind velocity data. Taking the results into account, the wavelet-based method is constructed such that the created time history possesses the characteristics similar to those of the natural wind data. The time histories are in particular synthesized to have a target power spectrum and intermittency similar to measured time histories. The characteristics of the time histories produced with the proposed method are discussed.

Flow simulation by wind tunnel with computer-controlled multiple fans

This paper presents the simulation of turbulent flow by controlling multiple fans in a two-dimensional wind tunnel. The main purposes of this study are to generate a large turbulence scale and simulate a turbulent flow fitted to specified power spectrum and co-coherence in a low frequency range, both of which are not easily accomplished only by the means of roughness blocks, spires and grids. It was relatively easy to obtain a large turbulence scale by controlling multiple fans numerically. According to the proposed procedure, turbulent characteristics of wind flow were successfully simulated to satisfy a specified condition for the target power spectrum and co-coherence.

Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results

Abstract The hybrid optoelectronic processor, presented in this paper, realizes the dual nonlinear correlation (DNC) in a set-up based on a two-step nonlinear joint transform correlator architecture. In the first step three power spectrum distributions (input scene power spectrum, reference target power spectrum, and the joint power spectrum) necessary for the nonlinear processing are captured with a CCD camera. Nonlinear modification of the joint power spectrum, which does not have to be symmetrical in the input and reference channels, is introduced digitally. In the second step, the modified joint power spectrum is Fourier transformed optically. Numerical analysis of this processor shows a crucial influence of the dynamic range and the limited number of grey levels of the CCD camera during image acquisition in the first step, on the output signal parameters and the discrimination capability of the set-up. Optical results of recognition obtained for noise-free segmented input scenes show that the set-up enables the realization of various correlation operations as CMF, POF, IF, PPC, etc. without any filters and that the discrimination capability is easy to control by a proper selection of the type of nonlinear processing.

Dual nonlinear correlator based on computer controlled joint transform processor: Digital analysis and optical results

The hybrid optoelectronic processor, presented in this paper, realizes the dual nonlinear correlation (DNC) in a set-up based on a two-step nonlinear joint transform correlator architecture. In the first step three power spectrum distributions (input scene power spectrum, reference target power spectrum, and the joint power spectrum) necessary for the nonlinear processing are captured with a CCD camera. Nonlinear modification of the joint power spectrum, which does not have to be symmetrical in the input and reference channels, is introduced digitally. In the second step, the modified joint power spectrum is Fourier transformed optically. Numerical analysis of this processor shows a crucial influence of the dynamic range and the limited number of grey levels of the CCD camera during image acquisition in the first step, on the output signal parameters and the discrimination capability of the set-up. Optical results of recognition obtained for noise-free segmented input scenes show that the set-up enables the realization of various correlation operations as CMF, POF, IF, PPC, etc. without any filters and that the discrimination capability is easy to control by a proper selection of the type of nonlinear processing.

Simulating Quadratically Nonlinear Random Processes

A technique to generate realizations of quadratically nonlinear non-Gaussian time series with a desired ("target") power spectrum and bispectrum is presented. Specifically, by generating a Gaussian time series (using amplitude information from the target power spectrum and random phases) and passing it through a quadratic filter (that uses phase information from the target bispectrum), a realization of a quadratically nonlinear random process with a specified power spectrum and bispectrum can be produced. Second- and third-order statistics from many realizations of simulated nonlinear time series compare well to those from the original time series providing the target power spectrum and bispectrum, with deviations consistent with theory. The simulation technique is shown to simulate accurately ocean waves in shallow water, which are well known to be quadratically nonlinear.

Simulation of Homogeneous Two-Dimensional Random Fields: Part I—AR and ARMA Models

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Simulation of Homogeneous Two-Dimensional Random Fields: Part II—MA and ARMA Models

Alternatively to the autoregressive (AR) models examined in Part I, the determination of moving average (MA) algorithms for simulating realizations of twodimensional random fields with a specified (target) power spectrum is presented. First, the mathematical form of these models is addressed by considering infinitevariate vector processes of an appropriate spectral matrix. Next, the MA parameters are determined by relying on the maximization of an energy-like quantity. Then, a technique is formulated to derive an autoregressive moving average (ARMA) simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Image synthesis from nonimaged laser-speckle patterns: comparison of theory, computer simulation, and laboratory results

The performance of an imaging technique relying on the spatial correlation of laser-speckle intensity measurements is evaluated on the basis of theoretical analysis, computer simulation, and laboratory results. A theoretical expression for the signal-to-noise ratio of the recovered imaging target's power spectrum is used to estimate the imaging performance expected in the computer simulation and laboratory experiment. Power-spectrum estimates for an imaging target, obtained both in the laboratory and through simulation, are compared with the theoretical results and with the true spectrum of the target. Images recovered from the simulation data and the laboratory data are also compared. Our results suggest that the signal-to-noise ratio expression provides an accurate means for estimating the recoverable frequency content of a simple target.

Wave group statistics from numerical simulations of a random sea

Two commonly used methods of simulating random time series, given a target power spectrum, are discussed. Wave group statistics, such as the mean length of runs of high waves, produced by the different simulation schemes are compared. The target spectra used are obtained from ocean measurements, and cover a wide range of ocean conditions. For a sufficiently large number of spectral components, no significant differences are found in the wave group statistics produced by the two simulation techniques.

PREDICTION OF WAVE GROUP STATISTICS

Two methods of numerically simulating random seas, given a target power spectrum, are discussed. Wave group statistics, such as the mean length of runs of high waves, produced by the different simulation schemes are compared. For a large number of spectral components, no significant differences are found in the wave group statistics produced by the two simulation techniques. Using the simulation techniques, it is shown that ocean gravity wave group statistics are not inconsistent with an underlying wave field composed of linearly superposed random waves. The majority of the field data examined were collected in 9-10 m depth, significant wave heights ranged from about 20 to 200 cm, and the spectral shapes ranged from fairly narrow to broad. For the 9-10 m depth data, observed mean run length, variance of run length, and the probabilities of runs of a given number of high waves were statistically consistent with the linear simulations. In contrast to the apparent linear behavior in 9-3 0 m depth, waves in 2-3 m depth showed substantial departures from the linear simulations.