Spectral analysis nonstationary

The nonstationary quantum-mechanical spectral analysis uses the time-dependent Schrodinger equation [2] ... 

PRIESTLEY, M.B. Power spectral analysis of nonstationary random processes. Journal of Sound and Vibration 6, (1967), 86-97. 

Adak S (1998) Time-dependent spectral analysis of nonstationary time saies. J. Amer. Statist. Assoc. 93 1488-1501. 

In postulating the stationarity of the stochastic process, very strong assumptions regarding the structure of the process are made. Once these assumptions are dropped, the process can become nonstationary in many different ways. In the framework of the spectral analysis of nonstationary processes, Priestley (see, e.g., Priestley 1999) introduced the evolutionary power spectral density (EPDS) function. The EPSD function has essentially the same type of physical interpretation of the PSD function of stationary processes. The main difference is that whereas the PSD function describes the power-frequency distribution for the whole stationary process, the EPSD function is time dependent and describes the local power-frequency distribution at each instant time. The theory of EPSD function is the only one which preserves this physical interpretation for the nonstationary processes. Moreover, since the spectrum may be estimated by fairly simple numerical techniques, which do not require any specific assumption of the structure of the process, this model, based on the EPSD function, is nowadays the most adopted model for the analysis of structures subjected to nonstationary processes as the seismic motion due to earthquakes. 

Flicker-noise spectroscopy — The spectral density of - flicker noise (also known as 1// noise, excess noise, semiconductor noise, low-frequency noise, contact noise, and pink noise) increases with frequency. Flicker noise spectroscopy (FNS) is a relatively new method based on the representation of a nonstationary chaotic signal as a sequence of irregularities (such as spikes, jumps, and discontinuities of derivatives of various orders) that conveys information about the time dynamics of the signal [i—iii]. This is accomplished by analysis of the power spectra and the moments of different orders of the signal. The FNS approach is based on the ideas of deterministic chaos and maybe used to identify any chaotic nonstationary signal. Thus, FNS has application to electrochemical systems (-> noise analysis). 

Transformation — Several approaches are available for transformation of time domain data into the - frequency domain, including - Fourier transformation, the maximum entropy method (MEM) [i], and wavelet analysis [ii]. The latter two methods are particularly useful for nonstationary signals whose spectral composition vary over long periods of time or that exhibit transient or intermittent behavior or for time records with unevenly sampled data. In contrast to Fourier transformation which looks for perfect sine... 

In the late fifties, Eringen and his co-workers [1-3] have analyzed the responses of beams and plates to random loads. Since these pioneering works, response analysis of structures subjected to random excitations has attracted considerable attention in the past thirty years. An extensive review of the recent developments have been provided by Crandall and Zhu [4]. Most of the earlier studies on nonstationary random vibrations were concerned with the analysis of mean-square response statistics [5,6]. Recently, evaluation of the time-dependent power spectra of structural response has attracted considerable interest. Priestley [7] introduced the orthogonal representation of a random function. Hammond [5], Corotis and Vanmarcke [8] and To [9] have studied the time-dependent spectral content of responses of single- and multi-degree-of-freedom structures. 

It has to be emphasized that in the framework of nonstationary analysis of structures, other time-dependent parameters, very useful in describing the time-variant spectral properties of the stochastic process, are (i) the mean frequency, vj(f), which evaluate the variation in time of the mean up-crossing rate of the time axis, and (ii) the central frequency, coc,x(t), which scrutinizes the variation of the frequency content of the stochastic process with respect to time. The two functions introduced before can be evaluated as a function of NGSMs and have been defined, respectively, as (Michaelov et al. 1999a, b)... 

The d3mamic behavior of structural systems subjected to uncertain dynamic excitations can be performed through the stochastic analysis, which requires the probabilistic characterization of both input and output processes. The characterization of output processes can be extremely complex, when nonstationary and/or non-Gaussian input processes are involved. However, in several cases the approximate description of the dynamic structural response based on its spectral characteristics may be sufficient. 

Lutes LD, Sarkani S (2004) Random vibrations - analysis of structural and mechanical vibrations. Elsevier, Boston Michaelov G, Sarkani S, Lutes LD (1999a) Spectral characteristics of nonstationary random processes - a critical review. Struct Saf 21 223-244 Michaelov G, Sarkani S, Lutes LD (1999b) Spectral characteristics of nonstationary random processes -response of a simple oscillator. Struct Saf 21 245-267 Muscolino G (1991) Nonstationary pre-envelope covariances of nonclassically damped systems. J Sound Vib 149 107-123... 

A common technique for measuring noise is frequency domain analysis, such as plotting the acceleration power spectral density (PSD) of the seismic data over some time period. While tmies are readily distinguishable from broadband noise, nonstationary events such as pops have a broadband spectral characteristic (typically proportional to j) that can nuslead the troubleshooter. However, small pops may not be readily identified by examining the time-domain time-series data as they may have amplitudes too small to be distinguished from the background seismic activity. 

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