Model parameter estimations of the multi-channel turbulence response from flutter flight tests based on autoregressive spectra

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

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.

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation

In order to simulate the non-Gaussian fluctuating wind pressure with prescribed lower-order moments and its target power spectral density (PSD) function, the following framework is proposed in the present paper: Firstly, the PSD function of fluctuating wind pressure is deduced rigorously according to the relationship between the wind pressure and velocity; Then, an efficient yet practical method by which the fluctuating wind pressure may be reproduced with the designated skewness and kurtosis is presented based on the derived PSD function, Johnson translator system, and digital filter; Finally, in order to corroborate the feasibility and correctness of the present methodology, a numerical example of simulating one-dimensional univariate non-Gaussian fluctuating wind pressure is taken into consideration. Numerical results indicate that the statistical parameters, such as the skewness and kurtosis, of the simulated fluctuating wind pressure are in remarkably agreement with their targets. Likewise, the PSDs of the simulated records and target show considerably good agreement with each other.

In the paper, two algorithms that allow identification of a parametric models of random time-series from binary-valued observations of their realizations, as well as from quantized measurements of their values, are proposed. The proposed algorithms are based on the idea of time-series decomposition either on a direct power spectral density or autocorrelation function approximation. They use the concepts of randomized search algorithms to recover the corresponding parametric models from calculated estimates of power spectral density or autocorrelation function. The considerations presented in the paper are illustrated with simulated identification examples in which linear and nonlinear block-oriented dynamic models of timeseries are identified from the binary-valued observations and quantized measurements.

SUMMARY The problem of testing for periodicities in multiple time series is considered. The test statistic proposed is based on the Euclidean norm of the matrix of periodograms. We first obtain the exact distribution of our test statistic under the hypothesis that observations are taken from an n-vector time series consisting of independent series of independent normal variables. We extend the theory to normal linear series with a specified spectral density matrix and then show that a suitable estimate can be used to replace this matrix in our test statistic. These results are asymptotic in nature. Extreme value theorems are stated for the case of normal variates and it is shown that the distributions for nonnormal series can be approximated adequately by those for normal series. An exact test for periodic components in an univariate time series was first proposed by Fisher (1929) who considered the null hypothesis of normal white noise. The test was based upon the maximum of a set of periodogram ordinates each divided by their sum, the division making it unnecessary to know in advance the variance of the components of the series. The use of the rth largest of these ordinates, r > 1, in testing for periodicities was also discussed by Fisher (1940). Whittle (1951, p. 101) showed how one could apply the Fisher tests to normal linear series provided the number of observations was large and one could specify the spectral density for the series. Hannan (1961) proposed a modification to this test that removed the necessity of knowing beforehand the spectral density function. Nicholls (1967) proposed a variation on Hannan's test statistic that improves its power under certain alternatives. Some extreme value results for periodogram ordinates were given by Walker (1965), who also demonstrated that dropping the normality condition has little effect on the large sample distributions, at least in the upper tails. In the sequel we consider the problem of testing for periodicities in multiple time series and pursue a course that parallels the historical development for univariate series as outlined in the paragraph above. Our tests are based on the Euclidean norm of the matrix of periodo- grams. In this connection Nicholls (1969) has discussed a test for discrete mass in a cross- spectrum. We consider real, discrete time parameter, n-vector, time series, Z(t) (t = 0, + 1, + 2, ...), where Z(t) = It+m(t) +X(t), with ,u+m(t) being a mean value function and X( ) being a weakly stationary, zero mean, time series possessing a spectral density matrix fxx(A) with tr{fxx(A)} <1 M < oo (JAI < 7r). We also assume the existence of a moving average representation 00 wo,t) , CO v - )

The radar return from a group of distributed scatterers exhibits a fluctuating nature whose intensity and rate of change appear to be a function of the frequency of the radiation and the motion of the scatterers. Because of their appearance on radar displays, the fluctuating echo signals are referred to as clutter. A digital computer synthesis of a simulated ground clutter signal is presented in which the clutter is characterized by its power spectral density and probability density functions. The output of a random number generator producing uniformly distributed white noise is shaped to yield a sequence of numbers having a Gaussian probability density function. The Gaussian, white noise is then filtered to yield the desired power spectral density. Equations are derived which relate the noise statistics to the shaping and filtering operators. Experimental results are presented to illustrate the clutter characteristics that have been obtained utilizing an available noise generator.

The use of light scatter to determine flat surface statistical information, such as a bandwidth limited section of the surface power spectral density (PSD) function and the associated rms roughness and slope numbers, is well documented in the literature. Systems which mea-sure scatter as a function of angular position often make use of the fact that the surface power spectral density function is essentially produced in the scatter pattern. Low spatial frequencies scatter close to the direc-tion of specular reflection and higher frequencies scatter further out. The technique relies on the one-to-one relationship between spatial frequen-cy and scatter position in the far field. This relationship is exact to within dimensions corresponding to the diffraction limit (i.e., dimensions much smaller than the usual detector aperture). For a curved surface, this one-to-one relationship is destroyed as scatter from a single spatial frequency can spread out to dimensions far exceeding those of a diffraction limited spot. As the spread approaches detector aperture dimensions, the ability to extract useful surface information is impaired. The amount of spread is determined by the illuminated spot radius r, the radius of curvature of the surface R, and the angle of incidence 01(r) and is plotted, for constant 01, as a function of r/R. Analytical data show that by reducing r to 0.5 mm, reasonable results are obtainable with workable scatter system geometries for curved surfaces with R _> 5 cm.

In this paper we present several results for three different canonical forms of linear prediction on a plane. These filters have causal, semicausal, and noncausal prediction geometries. Starting from their properties we consider the problem of realization of these filters from a given power spectral density function (SDF). Since it is not possible in general to obtain rational spectral factors of a two-dimensional SDF, we propose algorithms for obtaining rational approximations which are stable and converge to their limit (irrational) factors as the order of approximation is increased. It is also shown that the normal equations associated with the minimum variance two-dimensional prediction filters give a useful algorithm for obtaining rational approximations which are stable and converge to their unique limit filters. This result allows design of finite-order stable filters by solving a finite number of equations while realizing the given SDF arbitrarily closely.

A volume integral method for the calculation of Doppler ultrasound spectral power density (spd) functions is described. Axisymmetric flow in a circular tube with a power law velocity profile is assumed. The spd function is regarded as a probability density function for scatterer velocity, and the assumptions under which this is justified are considered. It is shown that the spd function is independent of Doppler angle except in the presence of wall reflection effects. A coordinate system centered on the beam is used and this enables the integrals to be easily formulated for arbitrary beams. Irregularly shaped and nonuniform beams can be treated. For the common flow and beam patterns, which exhibit symmetry, the volume integrals can often be reduced to a single integral and evaluated directly. The method is applied and the spectra are calculated for various different cases. Results are obtained for uniform rectangular and circular insonating beams, and for nonuniform beams with Gaussian, jinc, and sinc profiles. The effects of narrow beams and wall reflection are shown. The method may be readily applied to other beam and flow patterns, and extension to more complicated situations is also discussed.

The paper presents how to identify natural frequencies and mode shapes of structures by Operational Modal Analysis (OMA) technique, in which the Frequency Domain Decomposition (FDD) method is used. This method is an experimental method only base on the data of measuring the dynamic response of the structures under the excitation due to ambient forces and operational loads to determine the vibration characteristics. Measure vibration (acceleration) and determine spectral density matrix, using the singular values decomposition method of spectral density matrix to determine the natural frequencies and mode shapes of structures. The calculation results show that the natural frequencies, the mode shapes form determined by the OMA technique is consistent with the calculation results according to the theory and show the reliability of the method.KeywordsNatural frequencyMode shapeIdentifyEMAOMAFDD

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.

Fitts' law as a low-pass filter effect of muscle stiffness

A method is presented for the determination of the transverse response of the idealized suspended span of an offshore pipeline to random seismic input. The method is based on spatial discretization of the pipe with nodal lumped masses. The earthquake is assumed to be a stationary random process characterized by a power spectral density function. The cross spectral density function between two random seismic excitations along the pipe length is defined with the help of a local earthquake power special density function, which is assumed to be the same for the two end supports of the pipeline, and a frequency dependent weighted function which decays exponentially with distance from the pipe supports. The solution is obtained in the frequency domain using the spectral approach and is presented in terms of r.m.s. displacements and stresses. The formulation adequately includes the pressure drag effect which tends to dampen the pipe motions. Utilizing this method of analysis, several idealized pipe sea bed configurations, in which the pipe is anchored between two end blocks and subjected to horizontal ground excitations normal to the pipe axis, have been analysed to predict the influence of certain important parameters on the response.

Let {X n } and {Y n } be two stationary and ergodic processes with power spectral density functions P x (f) and Px (f) respectively. The problem considered is that of deriving nonparametric tests for the null-hypothesis for all Three test statistics are used, viz. a Kolmogorov-Smirnov type statistic, a X 2-statistic and a Kullback-Leibler type statistic. The bootstrap method is applied to obtain critical values and to compare the power functions of these test procedures. The results of some Monte Carlo studies, which illustrate the performance of the various procedures, are also given.