Evolutionary Spectral Density Research Articles

Analysis of Oral Carcinogenesis Factors Based on Non Negative Matrix Evolutionary Spectrum Clustering Decomposition

To explore the risk factors of Oral Submucosal fibrous carcinogenesis and provide theoretical basis for selfprevention and clinical treatment. First of all, an evolutionary non negative matrix factorization framework based on clustering quality is proposed for dynamic oral carcinogenesis detection. Then, the equivalence among evolutionary spectral clustering, ENMF and density optimization of evolutionary modules is proved theoretically. At the same time, based on this equivalence, a new semi-supervised ENMF algorithm is proposed by adding a priori information to ENMF without increasing the time complexity. Using this algorithm, 42 patients with Oral Submucosal Fibrosis and 40 non-cancerous patients with oral submucosal fibrosis were analyzed by single factor and multi-factor analysis to study the quantitative relationship between Oral Submucosal Fibrosis and 14 related factors. The results suggested that age, betel nut chewing duration, smoking duration and leukoplakia or lichen planus were the four factors which were introduced into the cluster quality analysis. Age, betel nut chewing duration, smoking duration and complications of leukoplakia or lichen planus are risk factors for Oral Submucosal fibrous carcinogenesis.

Spectral Inference under Complex Temporal Dynamics

We develop a unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with asymptotically correct coverage rates are constructed for the evolutionary spectral densities on a nearly optimally dense grid of the joint time-frequency domain. A simulation based bootstrap method is proposed to implement the SCR. The SCR enables researchers and practitioners to visually evaluate the magnitude and pattern of the evolutionary power spectra with asymptotically accurate statistical guarantee. The SCR also serves as a unified tool for a wide range of statistical inference problems in time-frequency analysis ranging from tests for white noise, stationarity and time-frequency separability to the validation for non-stationary linear models.

Detection, simulation, modelling and loading of thunderstorm outflows to design wind-safer and cost-efficient structures

Wind actions are crucial for the safety and sustainability of structures. The wind climate of Europe and many other parts of the world is dominated by synoptic extra-tropical cyclones and mesoscale thunderstorms. Thunderstorms are frequent events that cause wind speeds and damage often greater than those of cyclones. This paper describes a wide research activity including an extensive monitoring network, an unprecedented database of transient wind speed recordings, a broad spectrum of numerical tools for elaborating data and extracting their statistical properties relevant to the wind loading of structures, the development of wind tunnel tests and CFD simulations, investigations on weather scenarios and damage surveys aiming to complete the information provided by field measurements. Based on these resources, a new generation of wind loading models is being developed – response spectrum technique, time-domain integration, evolutionary spectral density - robustly coherent with measured data and intrinsically coherent with each other. These studies are being carried out in the framework of the project THUNDERR, funded by the European Research Council (ERC) with an Advanced Grant 2016 in order to produce outcomes physically correct, transferable to design and standards, suitable to modify the current wind loading format and make constructions wind-safer and cost-efficient.

Estimation of the Evolutionary Spectra With Application to Stationarity Test

In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the distinguishing feature of the evolutionary spectra is its focus on the physical meaning of frequency. The classical estimate of the evolutionary spectral density is based on a double-window technique consisting of a short-time Fourier transform and a smoothing. However, smoothing is known to suffer from the so-called bias leakage problem. By incorporating Thomson's multitaper method that was originally designed for stationary processes, we propose an improved estimate of the evolutionary spectral density, and analyze its bias/variance/resolution tradeoff. As an application of the new estimate, we further propose a non-parametric rank-based stationarity test, and provide various experimental studies.

Частотно-временной анализ акселерограмм природных землетрясений

An example of a frequency-time analysis of a long-period accelerogram of Tohoku earthquake is considered (Tohoku earthquake, Japan, March 11, 2011) including seismic intensity definition as a function of time; evolutionary spectral power density; prevailing frequencies of seismic ground motion for different earthquake phases . The function of seismic intensity is obtained as pseudo-envelope of nonstationary seismic accelerations. The time dependent pseudo-envelope is calculated as standard deviation at small time intervals. The analysis of the time dependent prevailing frequencies is performed using the Welch’s power spectral density estimation smoothed with the Hamming windows. For the considered accelerogram, a decrease in prevailing frequencies from 0.77 Hz at the beginning to 0.38 Hz at the end of seismic motion was determined. All calculations were realized using Matlab. The results of the research may be useful for performing seismic analysis based on accelerograms using response spectrum method, when it is necessary to estimate seismic intensity. Spectral analysis of different earthquake phases is necessary to prevent resonance phenomena in the situation, for example, when during a long-term earthquake both the natural frequencies of the structure and the prevailing frequency of the impact are reduced. In general, the understanding of the changes in the time-dependent parameters of accelerograms is relevant in the seismic analysis taking duration of the earthquake into account. Such calculation should include a preliminary time-frequency analysis of seismic impact.

Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment

ABSTRACTWe develop a new time series model to investigate the dynamic interactions between the nucleus accumbens and the hippocampus during an associative learning experiment. Preliminary analyses indicated that the spectral properties of the local field potentials at these two regions changed over the trials of the experiment. While many models already take into account nonstationarity within a single trial, the evolution of the dynamics across trials is often ignored. Our proposed model, the slowly evolving locally stationary process (SEv-LSP), is designed to capture nonstationarity both within a trial and across trials. We rigorously define the evolving evolutionary spectral density matrix, which we estimate using a two-stage procedure. In the first stage, we compute the within-trial time-localized periodogram matrix. In the second stage, we develop a data-driven approach that combines information from trial-specific local periodogram matrices. Through simulation studies, we show the utility of our proposed method for analyzing time series data with different evolutionary structures. Finally, we use the SEv-LSP model to demonstrate the evolving dynamics between the hippocampus and the nucleus accumbens during an associative learning experiment. Supplementary materials for this article are available online.

Aliasing free for evolutionary spectrum of non stationary processes

This paper proposes a non parametric discrete estimate of evolutionary spectral density of non-stationary process with continuous time. To solve a problem related to aliasing effects, we assume that the evolutionary spectral density has a compact support and we use a specific uniform sampling depending on the width of the compact support. An asymptotically unbiased and consistent estimate is given.

Fuzzy stochastic elements method. Spectral approach

We study a complex dynamic problem, which concerns a structure with uncertain parameters subjected to a stochastic excitation. Formulation of such a problem introduces fuzzy random variables for parameters of the structure and fuzzy stochastic processes for the load process. The uncertainty has two sources, namely the randomness of structural parameters such as geometry characteristics, material and damping properties, load process and imprecision of the theoretical model and incomplete information or uncertain data. All of these have a great influence on the response of the structure. By analyzing such problems we describe the random variability using the probability theory and the imprecision by use of fuzzy sets. Due to the fact that it is difficult to find an analytic expression for the inversion of the stochastic operator in the stochastic differential equation, a number of approximate methods have been proposed in the literature which can be connected to the finite element method. To evaluate the effects of excitation in the frequency domain we use the spectral density function. The spectral analysis is widely used in stochastic dynamics field of linear systems for stationary random excitation. The concept of the evolutionary spectral density is used in the case of non-stationary random excitation.We solve the considered problem using fuzzy stochastic finite element method. The solution is based on the idea of a fuzzy random frequency response vector for stationary input excitation and a transient fuzzy random frequency response vector for the fuzzy non-stationary one. We use the fuzzy random frequency response vector and the transient fuzzy random frequency response vector in the context of spectral analysis in order to determine the influence of structural uncertainty on the fuzzy random response of the structure.We study a linear system with random parameters subjected to two particular cases of stochastic excitation in a frequency domain. The first one when the excitation is a weakly stationary stochastic process with a given spectral density function and the second one which is constituted by a non stationary process with evolutionary spectral density function. We derive the formulas for both cases. The presented computational algorithm has a quite general scope and may be used in the vibration analysis of different kinds of structures.

Simulation of non-stationary conditional ground motion fields in the time domain

This paper addresses the topic of simulating spatially variable ground motion fields conditioned on a known accelerogram. The conditional ground motion fields can be used in design or verification studies where seismic analysis has to be performed for a couple of natural accelerograms that have been preselected by seismologists or other experts. The methodology is based on conditional densities. In contrast to most authors, the conditional densities method is not applied to the Fourier coefficients, but it is used for the construction of a conditional Gaussian process model in the time domain. This has the advantage that fully non-stationary conditional time histories can be simulated directly in the time domain. The cross-correlation functions needed for this approach are evaluated from commonly used ground motion models expressed as evolutionary power spectral densities. An application to the El Centro earthquake record is presented. The properties of the simulated ground motion fields are analysed and compared to the data and the theoretical model.

The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes

The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space–frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed.

Statistical Properties for Coherence Estimators From Evolutionary Spectra

Evolutionary spectra were developed by Priestley to extend spectral analysis to some nonstationary time series, in particular semistationary processes, of which the ubiquitous uniformly modulated processes are a subclass. Coherence is well defined for bivariate semistationary processes and can be estimated from such processes. We consider Priestley's estimator for the evolutionary spectral density matrix, and show that its elements can be written as weighted multitaper estimators with calculable weights and tapers. Under Gaussianity an approximating Wishart-distribution model follows for the spectral matrix, valid for all frequencies except small computable intervals near zero and Nyquist. Moreover, the critically important degrees of freedom are known. Consequently, the statistical distribution of the coherence is given by Goodman's distribution and the raw coherence estimate can be accurately debiased. Theoretical results are verified using a model for wind fluctuations: Simulations give excellent agreement between the mean debiased coherence estimates and true coherence, and between the proposed and empirical distributions of coherence.

Singularity detection of the rabbit electrocardiogram: An evolutionary spectral method

The time–frequency characteristics of the spectral density of non-stationary signals (NSS) in the neighborhood of an instant time point can be determined using the evolutionary spectral analysis. An experimental rabbit model involving ligation of the left anterior descending coronary artery to simulate the physiology of early phase myocardial ischemia (EPMI) has been previously described. Clinically, EPMI derived from left coronary artery stenosis is the main symptom of coronary heart diseases including acute myocardial infarction. Here, we propose a new algorithm for estimating the evolutionary spectral density functions, which is an effective approach to determine the instantaneous frequency spectra (IFS) of NSS under the uncertainty principle in the time–frequency domain. The localization singularity information in the data recorded from a living system could be detected by means of the IFS. Electrocardiogram (ECG) data recorded from experimental rabbits were analyzed with the new algorithm. Results showed that the Q’s value of the evolutionary spectral quality number of the QRS-complex data was the characteristic parameter of ECG, and there was a matched connection between the time–frequency characteristics of QRS-complex data and the myocardial ischemia symptoms of the rabbits. These results provide valuable information regarding features of the EPMI for use in clinical diagnoses.

Analysis of structural break models based on the evolutionary spectrum: Monte Carlo study and application

We investigate the instability problem of the covariance structure of time series by combining the non-parametric approach based on the evolutionary spectral density theory of Priestley [Evolutionary spectra and non-stationary processes, J. R. Statist. Soc., 27 (1965), pp. 204–237; Wavelets and time-dependent spectral analysis, J. Time Ser. Anal., 17 (1996), pp. 85–103] and the parametric approach based on linear regression models of Bai and Perron [Estimating and testing linear models with multiple structural changes, Econometrica 66 (1998), pp. 47–78]. A Monte Carlo study is presented to evaluate the performance of some parametric testing and estimation procedures for models characterized by breaks in variance. We attempt to see whether these procedures perform in the same way as models characterized by mean-shifts as investigated by Bai and Perron [Multiple structural change models: a simulation analysis, in: Econometric Theory and Practice: Frontiers of Analysis and Applied Research, D. Corbea, S. Durlauf, and B.E. Hansen, eds., Cambridge University Press, 2006, pp. 212–237]. We also provide an analysis of financial data series, of which the stability of the covariance function is doubtful.

Wide-Sense Stationarity of Mobile MIMO Radio Channels

Tests for the wide-sense stationarity (WSS) of multivariate random processes are developed and applied to measured multiple-input-multiple-output (MIMO) radio channel responses. Evolutionary spectral density functions are used to estimate the time-dependent power spectral density, and analysis of variance procedures are applied to determine whether the first and second moments of the data series exhibit statistically significant changes over short intervals. It is found that while the assumption of WSS is met in 40%-70% of half-second intervals for a single element at the transmitter and receiver, only 2%-12% of intervals with two elements at the transmitter and receiver are jointly WSS; furthermore, the occurrence of non-WSS intervals is not dependent on the antenna separation. The analyses also show that WSS intervals are interspersed with long non-WSS intervals.

Propagation of partially coherent non-stationary random waves in a viscoelastic layered half-space

This paper presents a highly accurate method based on the precise integration method (PIM) and on the pseudo excitation method (PEM). The method computes the propagation behaviour of partially coherent non-stationary random waves in a viscoelastic, transversely isotropic solid, which consists of a multi-layered soil resting on a homogeneous semi-infinite space. The excitation source is a local rupture between two layers, which causes a partially coherent non-stationary random field. The analysis of non-stationary random wave propagation is transformed into that for deterministic waves by using PEM. The resulting governing equations in the frequency-wavenumber domain are linear ordinary differential equations, which are solved very precisely by using PIM. The evolutionary power spectral densities of the ground level responses are investigated and some typical earthquake phenomena are explained.

Non-stationary random vibrations of a shear beam under high frequency seismic effects

Band-limited, non-stationary random vibrations of a shear beam are studied in order to investigate high frequency seismic effects on building structures. A solution for the evolutionary spectral density of the shear beam response to a time segment of band-limited white noise is given in a closed form. The root mean square (rms) and peak response of the shear beam are studied for two characteristic frequency bands: the conventional 1–4 Hz and higher frequency 4–16 Hz, characteristic for rockburst ground motion. Applying the criterion of equal excitation intensity with constant rms velocity, both responses are analyzed in detail and compared. The “switching off” fundamental mode for high frequency excitations results in characteristic overshoot of the stationary response level by the non-stationary rms response and an amplification of the response in the upper part of the shear beam.

Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density

This article estimates the number of breaks and their locations in the covariance structure of a series based on the evolutionary spectral density and uses some standard information criteria. The adopted approach is non-parametric and does not privilege a priori any modelling of the series. One carries out a Monte Carlo analysis and an empirical illustration using the daily return series of exchange rate euro/US dollar to support the relevance of the theory and to produce additional insights. The simulation results are globally adequate and show that the criteria having heavy penalty are more accurate in the selection of the number of breaks. The empirical results indicate that the covariance structure of the return series considerably varies between 30 March 2000 and 6 April 2001. The unconditional volatility appears non-constant over this interval.

Tests for covariance stationarity and white noise, with an application to Euro/US dollar exchange rate: An approach based on the evolutionary spectral density

This paper proposes two non parametric tests for stationarity and white noise against the alternative of time-varying covariance structure with an application to euro/US dollar exchange rate. These tests are based on stability of evolutionary spectral density of the process. Graphical methods using the size and power, confirm the efficiency of our approach when compared with other stationarity tests, especially when data are non stationary with an approximately constant variance.

Conditional Simulation of a Class of Nonstationary Space-Time Random Fields

This paper first addresses the problem of conditionally simulating stationary, space-time, Gaussian random fields. A method developed for quadrant-symmetric, stationary, space-time fields is extended to account for the imaginary part of the complex cross-spectrum. The case of amplitude- and frequency-modulated (AFM) nonstationary space-time fields is studied next. The evolutionary spectral density and cross-correlation structure of such a class of nonstationary random fields are analyzed in terms of the envelope and frequency modulation functions. A method for the conditional simulation of AFM space-time fields is advanced. The AFM nonstationary fields are mapped to a domain where the conditional simulation is performed as for stationary, space-time fields. Examples are given to illustrate the use and capabilities of the method including applications to the simulation of earthquake ground motions.

Earthquake Ground Motion Modeling. II: Stochastic Line Source

The pulse shape function obtained in a companion paper is incorporated in the development of a stochastic earthquake model. It is assumed that seismic ground motion is caused by shear dislocation that propagates along a line. This line source is further discretized into point sources at equal intervals. The times at which seismic signals are activated are assumed to be Poisson events with a time‐varying average occurrence rate λ(t) per unit time. This is equivalent to assuming an average speed λ(t) for the propagation of shear dislocation. The strengths of seismic signals emitted from discretized point sources are assumed to be independent and identically distributed random variables. A generalized version of the random‐pulse‐train theory is used to compute the mean and auto‐correlation functions of the ground motion at one site, and the cross‐correlation function at two sites. The auto‐correlation and cross‐correlation functions can then be converted to the evolutionary spectral density and evolutionary ...