Kuniharu Kishida

Equivalent random force and time‐series model in systems far from equilibrium

Under the condition that observed time‐series data is given, a stochastic Markovian equation for a physical system can be transformed into an observable non‐Markovian equation used in the time‐series analysis. The physical random force satisfying the fluctuation dissipation theorem is also transformed into a stochastically equivalent random force in the derivation of the time‐series model of observable variables. Statistical quantities, i.e., correlation and power spectral density functions for observable variables, can be expressed not only by the physical random force, but also by the equivalent random force. A relation between the variance of physical random force and that of equivalent random force is also found.

Application of ar model to reactor noise analysis

Abstract Though an autoregressive model is one of linear statistical equations, a problem of pole location is not made clear. We examine pole locations of autoregressive models in a simple example of reactor noise process. Poles of autoregressive model are classified as four types; 1) multiple ring poles, 2) identified system poles, 3) non-robust singular pole, and 4) robust singular pole. The ring poles are explained as equivalent representations of zeros of autoregressive moving average model which is derived from a physical state equation with the contraction of system information due to the observation. The zero of autoregressive moving average model closest to the unit circle in the complex plane plays an important role in the convergence of power spectral density of autoregressive models.

Notes on poles and convergence rate of autoregressive model

The convergence rate of the power spectral density function and the properties of the poles of the AR model as an approximate representation of an ARMA(2,1) process are studied with full use of numerical analysis of specific examples. Attention is focused on the case where the ARMA(2,1) model transfer function in z -1 (time shift operator) has two real system poles 1/r1, 1/r2 and the system zero 1/b in the z -1-plane (complex-plane) with the relationship . When the AR model fitting is applied for the theoretical covariance sequence of the process based on the Levinson-Durbin Algorithm, (1) the convergence rate of power spectrum of the AR model is asymptotically proportional to b, (2) the pole 1/r1 is transferred into the AR model as a real pole, however, the information about 1/r2 merges into all poles of the AR model, and (3) the zero 1/b is equivalently represented in the AR model by a set of poles almost equally spaced on a circle centered at the origin in the complex plane. For the qualitative analysi...

A Theory of Reactor Diagnosis in Feedback Systems

A unified theory is presented for diagnosis of power reactors with feedback mechanism. In terms of correlation functions calculated from stationary time series data, a feedback system can be expressed by an equivalent innovation model. From the formalism the identifiability of open loop transfer functions in the feedback system is discussed under conditions; (1) the minimum phase system, (2) the independence of noise sources. From the feedback structure, the property of the nonminimum phase is related to that the reactivity is positive or zero-power reactor transfer function is supercritical. In the case of the nonminimum phase and correlated noise sources, there is a possibility of new additional loops in an innovation model equivalent to the feedback system.

Contraction of information in systems far from equilibrium

The relationship between a physical model and a time series model (or an innovation model) is discussed from the viewpoint of contraction of information due to the way of observation. In this framework, measurable correlation functions are expressed in terms of both models. By using the Riccati type equation and the singular value decomposition of the Hankel matrix, a data‐oriented model is derived from measurable correlation functions. There occurs the contraction in a noise source space (or random forces). From the mechanism of contraction, random forces of systems can be identified by using two innovation models in different states.

Notes on poles of autoregressive type model part II: Robust singular pole

Abstract The non-robust singular pole of a scalar T.AR model which is defined by truncating the Taylor expansion of physical AR.MA model has been introduced in the previous paper [this journal]. A two dimensional T.AR model is obtained when two state variables are observed from a linear Gauss-Markovian system described with three degrees of freedom. The vector T.AR model has a robust singular pole, which has no direct correspondence to poles and/or zeros of the original vector AR.MA model. The comparison of pole locations between T.AR model and AR model is studied in a simple example.

Systematic approach for stochastic model in reactor noise analysis

Abstract A systematic approach to construct a time-series model for reactor noise analysis is discussed starting from stochastic Markovian equations for a system without measurement noise. Properties of the zeros of the model are also discussed using the system-matrix representation, and conditions are presented to calculate the number of zeros of the model.

Poles and their weights of AR type model

Abstract A separation rule of AR poles is proposed in system identification of reactor noise with AR model. Weights of AR poles corresponding to some of system poles are constant for model order change. On the other hand, weights of AR poles corresponding to ring (or circular) poles decrease in inverse proportion to AR model order. These properties of weights can be utilized for distinguishing between system poles and ring poles equivalent to zeros.

Notes on poles of autoregressive type model. Part III. General case

Abstract Pole locations of a multivariate autoregressive (AR) type model for a Gaussian Markovian process are examined by using the Rouches theorem. The formalism of the previous papers by the authors (J. Math. Anal. Appl. 124, 1987, 98–116; 123, 1987, 480–493) is generalized. It is shown that when the order of the AR type model becomes large, poles of the AR type model can be classified into three types: (1) poles distributing almost equally spaced on circles which are centered at the origin with radiuses equal to the absolute value of zeros, (2) system poles inside the smallest circle, and (3) robust and non-robust singular poles which were introduced in the papers referenced above.

Reactor noise analysis. Recent research activities in Japan.

A review is presented on the recent research activities in Japan in the field of reactor noise analysis. It covers six selected areas : nonlinear stochastic theory and identification of nonlinearit...