http://swrc.ontoware.org/ontology#Thesis
Nonstationary spectral analysis based on peakfrequencies of power spectrum
en
生駒 哲一
イコマ ノリカズ
IKOMA Norikazu
総研大甲第111号
A new statistical model and an extension of the original model are proposed in this paper. The proposed model provides a new approach for nonstitationary spectral analysis by directly obtaining the peaks estimation of power spectrum. The decomposition of power spectrum into time variant and time invarlant factors is also possible by the modified model proposed in this research. <br /> A new statistical model which has peaks of power spectrurn as time varying factor is proposed. This new model is motivated by the natural modeling of nonstationary spectral analysls. <br /> In the convensional models of nonstationary spectral analysis, linearity and Gaussian assumption take important role in the implementation of the model. By these assumptions, there are many advantages since Kalman filter and smoothing algorithms can be applied. On the other hand, for the analysis of irregular vibration, the peak of power spectrum is essential and estimation of the peak information is an important problem. <br /> However, the conventional modeling cannot estimate the information of peak directly, because of the linearlity and Gaussian assumption. By the recent development of computational approaches, it becomes possible to estimate the model without the linearity and Gaussian assumption. The direct formulation of peak information to the model construction is now possible. There have been no attempt to such theme up to this time. <br /> The newly proposed model has a formulation of Bayesian context with smoothness prior of changing frequencies of peak for power spectrum, and it consists of autoregressive (AR) model with time varying coefficients parametrized by peak frequencies and damping factors of power spectrum. The proposed model contains nonlinear factors with respect to the state vector due to the parametrization of the time varying factors. Because of the nonlinear formulation, linear filtering and smoothing method such as Kalman filter cannot be applied directly. Extended Kalman filter is one solution to obtain the state estimation of filtering and smoothing. Another solution, which is found to be better than the former, is the application of nonlinear non-Gaussian filtering and smoothing methood proposed by Kitagawa (1987) . <br /> A modification of the model for the analysis of real time series data is also proposed in this paper. By the modification, it becomes possible to decompose the spectrum of time series into the time invariant spectrum and time varying peaks of power spectrum. The modification of the original model is motivated by the following problem. In case of nonlinear non-Gaussian filtering is applied to obtain the state estiamtion, the proposed model has a problem that the dimension of the state vector cannot be taken higher. The dimension should be at most 3 or 4 because of the computational cost. The originally proposed model has a relationship that the AR lag is twice of the dimension of the state vector. Then this restriction limits the AR lag of the original model. However, the real applications often require high order of AR lag to obtain the enough solution of analysis. So the limit of AR lag becomes a serious problem to the application of real data. hence the modification is required to the original model that the modified model cam treat the high order AR lag without increasing the dimension of the state vector. <br /> Since the modification has been done by adding the time invariant factors to the original model, the modified model can treat both time variant and tme invariantfactors with respect to the spectrum. <br /> For the verification of the proposed model and modified model, simulations experiments are performed. The comparison between extended Kalman filter and non-Gaussian filter has been done. Comparison with the conventional models, such as time-varying cients AR model is also considred. As the criteria of the comparison, AlC, expected log-likelihood , and mean spueare error of estinated peaks are emproyed. Through the siumilation experlments, the proposed method scores better than the conventional ones for any criteria when the simulation data have been generated from the pocess which have time varying peak frequencies of power spectrum. <br /> Applications by using real time series data sets are also reported. As the real data, seismic wave data and viblation of delta wing in wind tunnel are considered. <br /> The structure of the paper is as follows. Chapter 1 is an introducition of this research containing the background and motivations of the research. Chapter 2 gives a survey of nonstationary spectral analysis and it, contains definitions required in the following chapters. Chapter 3 conains the first half of main results of this research. In this chapter, the proposed model is defined after mentioning the problems of orinary analysis of non-stationary spectrum. Chapter 4 shows the non-Gaussian filter and the implementation of the proposed model. Kalman filter and smoother, extended Kalman filter are summarized and the detail of the nonlineal non- Gaussian filtering is described. An extension of the model is discussed in Chapter 5. This chapter presents the latter half of the main content of this research. A model which can decompose a power spectrum into time variant and time invariant peaks of power spectrum is propopsed. In chapter 6, experiments with simulation data are reported for the verification of the proposed model. The comparisons with time-varying coefficients AR model are also reported. In Chapter 7, applications for the real time series data sets are given comparing with time-varying coefficents AR model. Conslusion is given in Chapter 8 with some discussion and future problems related to this research.