Target Power Spectral Density Research Articles

Generation Method of Target Power Spectral Density for Seismic Design of Nuclear Power Plant Equipment

The input ground motion for the seismic design of nuclear power plant (NPP) equipment is required to envelop both the required response spectrum (RRS) and target power spectral density (PSD). However, no unified algorithm exists to generate the target PSD, whether at home or abroad. Based on the generation methodology for target PSD suggested in Section 3.7.1 of the Standard Review Plan (SRP) of U.S. Nuclear Regulatory Commission, this paper proposes an improved method for target PSD synthesis with the original iteration process optimized. The proposed method is applied successfully to the two RRS cases for nuclear equipment. The result shows that the improved method for target PSD generation is highly compatible with RRS and provides simple and rapid calculation, while its convergence accuracy is similar to the calculations by random vibration theory (RVT). This method is considered as the target PSD test basis for the input artificial ground motion (AGM) for the seismic design of NPP equipment.

Impact of Local Site Conditions on Simulation of Non-stationary Spatial Variable Seismic Motions

It is commonly accepted that multi-scale structures are subject to spatially variable seismic motions. This spatial variability of seismic motions is described by different intensities at different locations due to the coherency loss effect, wave passage effect and local site conditions. For multi-scale structures, the estimation of seismic excitations must consider these factors. Often, the influence of the spatial variability of seismic motion on the dynamic response of structures is performed by neglecting the site effect. In several cases, it has been observed that the high intensities of seismic motion are caused by the site amplification besides coherency loss and wave passage effects. This study aims to analyze the impact of local site conditions on seismic motions. For this purpose, a method of simulation of spatially variable seismic motions is performed. The seismic signals on the bedrock are defined by considering a target power spectral density and a coherency loss model. According to the seismic wave propagation theory, the projection of these seismic motions on the surface is realized. The results of this study show that neglecting the local site conditions induces an undervaluation of spatially variable seismic excitations.

Adaptive Radar Waveform Design Based on Weighted MI and the Difference of Two Mutual Information Metrics

This study deals with the problem of radar waveform design based on the weighted mutual information (MI) and the difference of two mutual information metrics (DMI) in signal-dependent interference. Since the target and clutter information are included in the received signal at the beginning of the design, DMI-based waveform is designed according to the following criterion: maximizing the MI between the received signal and target impulse response while minimizing the MI between the received signal and the clutter impulse response. This criterion is equivalent to maximizing the difference between the first MI and the second MI. Then maximizing the difference of two types of MI is used as the objective function, and the optimization model with the transmitted waveform energy constraint is established. In order to solve it, we resort to maximum marginal allocation (MMA) method to find the DMI-based waveform. Since DMI-based waveform does not allocate energy to the frequency band where the clutter power spectral density (PSD) is greater than the target PSD, we propose to weight the MI-based waveform and DMI-based waveform to synthesize the final optimal waveform. It could provide different trade-offs between two types of MI. Simulation results show the proposed algorithm is valid.

Generation of non-Gaussian stationary random excitations with specified cross-power spectral densities using zero memory non-linear transformation for fatigue test purposes

Zero-memory non-linear (ZMNL) methods have long been a type of very useful tools in creating super-Gaussian random excitations for fatigue test. The major drawback of this method is that the magnitude distortion can be seen in both auto-power spectral density (ASD) and cross power-spectral density (CSD) of the excitation if the dynamic range of the target power spectral density (PSD) is large. To study the problem, we introduced Fourier series of a Gaussian signal into a cubic system, which is a common mathematical model shared by most of the ZMNL functions. We found that the cubic system produces a component leading to the distortion of both ASD and CSD. Meanwhile, if the shape of the reference ASD is flat in a frequency band, the distortion will not happen in the band. Based on this findings, a novel method is proposed in this article. It employs a pseudo reference PSD with flat ASDs to generate non-Gaussian signals in order to avoid the PSD distortions. Designed FIR filters are then applied to rescale the ASDs of the generated signals. After, iterative processes are introduced to recover the kurtoses of these filtered signals. The method is applied on a two-input and two-output numerical model, the feasibility and the availability of the method is verified. Finally, two control schemes based on the proposed pseudo reference PSD method are provided for a shaker table test. Test results show that both control schemes can eliminate the mismatch between the target PSD and the measured PSD of a shaker table.

An efficient simulation algorithm for non-Gaussian stochastic processes

Using linear filter method and Johnson transformation, an efficient algorithm for simulating non-Gaussian wind load is developed in this study. Simulations with target first four-order marginal moments and power spectral density are produced by filtering the underlying non-Gaussian white noise that generated by Johnson transformation into non-Gaussian process using linear filter, such as autoregressive (AR) or autoregressive moving average (ARMA) model. For AR and ARMA models, the explicit relationships between the first four-order marginal moments of the input and those of the output are ascertained, thereby the moments of the underlying non-Gaussian white noise input can be calculated. Different from the traditional probability-dependent incompatibility for existing algorithms, a distinctive type of incompatibility which is characterized by spectrum-dependent for the new simulation algorithm is discovered and discussed. In addition, the incompatible ranges of the two types of incompatibilities are compared. We investigated several numerical examples and they demonstrated that the first four-order moments, PSD, and correlation functions of the generations closely matched the targets.

Method of Developing Target Power Spectral Density Compatible with Design Response Spectra

U.S. NRC SRP 3.7.1 requires that the time history for the SCCs seismic design of nuclear power plants should envelop both the design response spectra and the target power spectral density (PSD) function compatible with the design response spectra. According to SRP 3.7.1(2014), the method of developing the target PSD compatible with the design response spectra and the corresponding computer program was presented in this paper. The results of the computer program were verified by some examples. The results show that the calculated target PSD compatible with RG1.60, CEUS and WUS rock sites response spectra were consistent with the corresponding results provided in SRP 3.7.1, and the spectrum from the artificial time history which developed by the target PSD and the superposition method of trigonometric series adequately matched the design response spectra. The generation of target PSD in this paper can provide technical basis for the PSD check on the time history for the SSCs seismic design of nuclear power plants, and when the target PSD were developed using the method described in this paper, the PSD check should be set at 70 percent of the target PSD.

Cognitive radar waveform optimization based on Kalman filtering for target estimation

As the target-radar feature is time-variant in the cognitive radar (CR) system, the target information should be continuously updated by the receiver and considered to provide the prior knowledge for the optimization of the next waveform. To solve this problem, a two-step CR waveform optimization approach for target estimation is proposed. During the first echo pulse, waveform optimization for target-radar signature estimation is done by minimizing the mean square error of target power spectral density estimation. Then, to take advantage of the temporal correlation of target scattering coefficients (TSC) during the pulses interval, a Kalman filtering-based method is used to processing successive radar echoes for TSC estimation. A convex cost function is established and the optimal solution can be obtained by the existing convex programming algorithm with multiple iterations. Finally, subject to the transmitted power, peak-to-average power ratio, and detection performance constraints, the simulation results show that the proposed waveform optimization algorithm is able to improve the performance of target estimation for extended target.

An approach for predicting multi-support seismic underground motions in layered saturated soil under surface water

Simulation of multi-support (i.e. spatially variable) seismic underground motions in sea areas plays a significant role in the seismic analysis of cross-sea structures such as cross-sea bridges or subsea tunnels. However, existing approaches for predicting multi-support seismic motions mainly focus on the dry site soils without overlying surface water. This paper proposes an approach for predicting multi-support seismic underground motions in layered saturated half space under surface water, subjected to oblique incident P waves. The transfer function in saturated soil under surface water, as the theoretical basis of the subsequent numerical simulation, is first derived based on wave propagation theory and the calculated reflection coefficients of P wave–induced P1, P2, SV waves in saturated soils. The derived transfer function is further employed to deduce and obtain the underground (sub-seabed) power spectral density function and response spectrum function. The two obtained functions, combined with the additional cross-coherence function, are subsequently employed to construct the cross power spectral density matrix and thus to simulate multi-support seismic underground motions. The solutions are validated against the target power spectral density, target response spectrum and target cross-coherence functions. A parametric analysis is presented where the effects of the soil thickness, the incident angle and the overlying water depth are investigated. Results show that the soil thickness, incident angle and overlying water depth have significant influences on the amplitude of transfer functions, which further affect the ratios between seismic ground and underground motions.

Jamming power allocation strategy for MIMO radar based on MMSE and mutual information

Jamming in defence applications is increasingly difficult because of advanced signal processing countermeasures. The jamming power allocation techniques for MIMO radar are investigated based on two criteria, namely the minimum mean square error (MMSE) for target estimation and the mutual information (MI) between the radar echo and the target impulse response. Different jamming power allocation strategies are obtained using the two criteria, respectively. Furthermore, the robust jamming power allocation strategies are studied when the target, environment or waveform information are not perfectly known. The worst case performance is optimised considering two cases of uncertainty. The analysis indicates that the least favourable sets (LFSs) of the MMSE- and MI-based robust jamming are different if the radar waveform power and the target power spectral density (PSD) lie in the uncertainty sets which are confined by known upper and lower bounds. The LFSs of the MMSE- and MI-based robust jamming are the same if the target PSD and the noise PSD lie in the uncertainty sets. Results are useful for the implementation of cognitive jammer.

Seismic Responses of the Supporting Structure of FAST under Multiple-Support Excitations

Seismic ground motions are spatial incoherent partly due to uncertainty in fault mechanism and wave propagation. The spatial coherency and its effect can be important and need to be investigated for multiple-support structures. In this study, an investigation of seismic responses of a five-hundred-meter aperture spherical telescope (FAST) is investigated. The structure is a cable net structure with multiple supports. For the structural analysis, parameters of an existing coherency model for excitations along the same orientation but considering the multi-component excitations and spatially separated locations are developed using the records from Taiwan. This coherency model together with adopted target power spectral density function and phase difference spectrum model are used to simulate multi-component seismic ground motions at 338 grid points covering the FAST. The simulated records are used as the basis to interpolate the time history of the ground motions at 2395 supports for the considered structure. The time-history responses of the structure under incoherent multiple-support excitations are evaluated and compared to that under uniform excitations. The results show that the influence of coherency on the supporting structure of the FAST in three excitation directions differs. The analysis results show that as compared to uniform excitations, the consideration of the seismic coherency in seismic excitations leads to, on average, 87% of increase in stress for 94% of the main cables, and 22% of increase in stress for 44% of the tie-down cables. It was also noted that the maximum tensile stress of the cable by considering the coherency is 835 MPa while that under uniform excitations is 671 MPa. In both cases, they are smaller than the characteristic tensile strength of the cables used for design and construction of the FAST.

Fatigue Life of Curved Panels Under Combined Loading

The nonlinear response of shallow shells subjected to combined acoustic and thermal loads is analyzed using an efficient nonlinear modal finite element (FE) formulation. The acoustic loads have non-Gaussian probabilistic characteristics and are simulated by an algorithm capable of reliably converging to a target power spectral density (PSD) function and marginal probability density function (PDF). Factors contributing to the panel structural stiffness, softening and hardening effects, and modal contribution are also investigated along with their impact on the root-mean-square responses. The Palmgren–Miner cumulative damage theory in combination with the rainflow counting (RFC) cycles methods was used to estimate the panel fatigue life. Parametric studies for cylindrical and spherical curved panels considering stacking laminations, radii of curvatures, acoustic and thermal loads are studied in detail.

Error Assessment of Multivariate Random Processes Simulated by a Conditional-Simulation Method

AbstractRandom processes, such as the wind velocity field and spatially varying ground motions, are usually simulated as N-variate stochastic processes by the conditional-simulation method. However, the temporal power spectral density (PSD) function of a single, simulated sample process may be different from the target PSD. Such differences can usually be assessed by the statistical errors (i.e., the bias and stochastic errors). Therefore, this paper investigates the bias errors and the stochastic errors of the PSD functions produced by the conditional-simulation method. For the bias errors, it was found that the conditional-simulation method might produce the nonzero bias error of the PSD functions in some cases. However, this usually does not occur in the unconditional simulation, and it should be avoided. To avoid the nonzero bias error of the PSD functions, a modified conditional-simulation method was proposed. It was verified using both the theoretical derivation and the numerical example. For the st...

Random vibration Monte Carlo simulation using multiple harmonic function schemes

The reliability study of structures under random vibration involves the performance of Monte Carlo simulation in time domain. One important part of such analyses is the generation of load time histories that must accurately represent the characteristics of the stochastic loads. There are several methods to generate time histories from a power spectral density (PSD) function. One common approach is based on the linear combination of harmonic functions with random amplitudes and fixed frequencies. This method requires considering numerous harmonic terms to simulate the target PSD function. In this paper, a new approach is presented to improve the performance of Monte Carlo simulation under random vibration when the excitation is represented by a PSD function. This goal is accomplished by refreshing the frequencies for every new time history of excitation. This can considerably reduce the number of replications that are required to perform a Monte Carlo simulation. The method is demonstrated through an example which involves a linear quarter car model.

Simulation of non-Gaussian wind pressure fields on domed structures

Wind pressure fluctuations acting on structures are important for the prediction of peak pressure values and for design against fatigue. Collection of time histories of pressure fluctuations by traditional wind tunnel measurements is time consuming and expensive. To overcome this problem, a study on developing a new wind pressure simulation technique for domed structures is carried out. A simulation algorithm to generate non-Gaussian wind pressure fields using wavelet bases is proposed. It presents an efficient, flexible, and easily applied stochastic non-Gaussian simulation using a cumulative distribution function mapping technique that converges to a desired target power spectral density. This method first generates Gaussian sample fields using wavelet bases and then maps them into non-Gaussian sample fields with the aid of an iterative procedure. Results from this technique are presented and compared for domes of different rise–span ratios to demonstrate its efficacy. The advantages and limitations of this method are also discussed.

Stochastic Harmonic Function Representation of Stochastic Processes

An approach to represent a stochastic process by the combination of finite stochastic harmonic functions is proposed. The conditions that should be satisfied to make sure that the power spectral density function of the stochastic harmonic function process is identical to the target power spectral density are firstly studied. Then, two kinds of stochastic harmonic functions, of which the distribution of the amplitudes and the random frequencies are different, are discussed. The probabilistic characteristics of the two kinds of stochastic harmonic functions, including the asymptotic distribution, the one-dimensional probability density function, and the rate of approaching the asymptotic distribution, etc., are studied in detail by theoretical treatment and numerical examples. Responses of a nonlinear structure subjected to strong earthquake excitation are investigated. The studies show that the proposed approach can capture the target power spectral density exactly with any number of components. The reduction of the components provides flexibility and reduces the computational cost. Finally, problems that need further investigations are discussed.

Creating Transport Vibration Simulation Profiles from Vehicle and Road Characteristics

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.

Simulation of Non-Gaussian Stochastic Process with Target Power Spectral Density and Lower-Order Moments

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.

Instantaneous Binaural Target PSD Estimation for Hearing Aid Noise Reduction in Complex Acoustic Environments

Some hearing aid models such as the in-the-ear or in-the-canal model are small, and due to size constraints, only a single microphone per hearing aid can be fitted. As a result, only the single-channel noise reduction schemes can be integrated in them. However, in the near future, binaural hearing aids will be available. These hearing aids will allow hearing devices on each side of the head to receive information from the microphones located on both devices via a wireless link. This additional information allows the use of joint statistics and/or spatial information, which allows the use of better denoising methods. The main contribution of this paper is to introduce a binaural target power spectral density (PSD) estimator for binaural hearing aids under the presence of a background interfering talker (or a lateral transient noise). This paper then presents an example of how the proposed target PSD estimator and another recently developed binaural diffuse noise PSD estimator can be integrated to produce a binaural noise reduction scheme that can operate in real-life complex acoustic environments that are composed of time-varying diffuse noise, multiple directional nonstationary talkers (or noises), and reverberant conditions. Such a binaural noise reduction system allows the substantial reduction of different combinations of diverse background noises and the increase in speech intelligibility while guaranteeing the preservation of the interaural cues of both the target speech and the directional background noises. A comparison with several advanced denoising algorithms is made in this paper by using several objective measures and real-life hearing aid signals, showing the good performance of the example binaural noise reduction scheme that uses the proposed PSD estimator.

On the Generation of Correlated Gaussian Random Variates by Inverse DTF

In this paper the problem of generating a stationary band-limited Gaussian random vector with arbitrary complex autocorrelation by the inverse discrete Fourier transform (IDTF) algorithm is considered. Instead of using the classical frequency mask (FM), determined from samples of the (band-limited) target power spectral density (PSD) of the process, a new FM is obtained by matching the autocorrelation obtained with the IDFT algorithm to a desired arbitrary autocorrelation. Example results presented show that the new FM is able to significantly increase the autocorrelation accuracy of the generated process at no additional online computational cost.

Simulation of Non-Gaussian Wind Pressure Fields on Domed Structures

Wind pressure fluctuations acting on space structures are important for prediction of peak pressure values and for fatigue design purpose. Collection of several time histories of pressure fluctuations by traditional wind tunnel measurements is time consuming and expensive. Thus, a study on developing new wind pressure simulation technique on domed structures is carried out. An efficient, flexible and easily applied stochastic non-Gaussian simulation algorithm is presented using a cumulative distribution function (CDF) mapping technique that converges to a desired target power spectral density. This method first generates Gaussian sample fields using wavelet bases and then maps them into non-Gaussian sample fields with the aid of an iterative procedure. Results from this technique are presented and compared with those from the wind tunnel experiments. The advantages and limitations of this method are also discussed.