T. Soeda

Linear fixed-point smoothing by using functional analysis

A new approach to the fixed-point smoothing problem for linear stochastic distributed parameter systems is proposed by using functional analysis. The number of sensor locations is assumed to be finite and the error criterion is based on the unbiased and least-squares estimations. The algorithm for an optimal fixed-point smoothing estimate is derived by using Itos stochastic calculus in Hilbert spaces. By applying the kernel theorem to these results, a family of partial differential equations for the optimal fixed-point smoothing estimate is derived. The existence and uniqueness theorems concerning the solutions for both the smoothing gain and the smoothing estimator equations are proved. Finally, usefulness of the algorithm is illustrated with a numerical example.

An application of the stochastic automaton to the investment game

Abstract An application of the stochastic automaton to the investment game is considered. It is shown that the use of the stochastic automaton with learning properties is an efficient method for the investment game.

The optimal filtering problem for a discrete-time distributed parameter system

In this paper, the optimal filtering problem for a discrete-time linear distributed parameter system is considered. Using the least squares estimation error criterion, the Wiener-Hopf equation for the discrete-time distributed parameter system is derived. Based on the Wiener-Hopf equation, the equations satisfied by the optimal filtering estimate and the minimum error covariance matrix function are derived by using the matrix inversion lemma for a distributed parameter system. Finally, we show that the approximation of the results obtained for a distributed parameter system by using the Fourier expansion method produces those of the Kalman filtering problem for the lumped parameter system.

Identification of unknown parameters in linear discrete-time systems by a modified extended Kalman filter

Abstract This paper treats an identification technique for discrete-time linear systems whim noisy measurements are taken. The technique is based on the extended Kalman filter and the model reference adaptive approach. Firstly, the extended Kalman filter derived by augmenting unknown parameters as the state variables is modified by neglecting the information between the states and unknown parameters ; and secondly the stability of the modified filter is compensated by the idea of the model reference adaptive approach. Lastly, the convergence of the obtained estimates for unknovm parameters to the exact values is proved. A numerical example shows the effectiveness of the proposed method.

Failure Detection and Prediction System by using Adaptive Digital Filter

Abstract This paper deals with the detection of the catastrophic failure and the detection and prediction of the deteriorative failure by using adaptive digital filter. Assuming that the change of states of system can be measured as the change of statistical characteristics of observed randam signals, the autoregressive(AR) model is fitted to the signals, and the deteriorative performance index is calculated to detect and predict the deteriorative failure continuously in time. The index is computed to measure the statistical difference between normal and other states quantitatively. The three kinds of indices, that is, quadratic distance of AR parameter differencies, variance of the residuals for prediction scheme, and distance of the time series by the Kullback information, are introduced. Furthermore, the present method is able to eliminate the inferior signals contained in the observed signals and to improve the detection and prediction accuracies by an on-line algorithm. Finally, the effectiveness of the present algorithm is shown by numerical simulations.

Prediction of the peak flood using revised GMDH alogrithms

This paper is concerned with the prediction problem of the peak flood for designing bridges in small and medium catchments in India. Revised GMDH (Group Method of Data Handling) algorithms are proposed for constructing prediction models using collected data for fixed parameters of catchments and variable parameters of flood events. The numerical experiment indicates that the proposed methods are useful to the prediction of peak flood.

Optimal estimation problems for a linear distributed parameter system

A new approach by using functional analysis to the estimation problems for a linear distributed parameter system is proposed. It is assumed that the number of the sensor locations is finite and the error criterion is based on the unbiased and minimum variance estimations. Using the comparison theorem for the operator-valued differential equations and Itos stochastic calculus in Hilbert spaces, we solve the abstract filtering, smoothing, and prediction problems. By applying the kernel theorem, due to Schwartz, to these results, a class of partial differential equations for the optimal estimators is derived. Furthermore, the existence and uniqueness theorem concerning the solutions for the optimal estimation problems is considered.

Optimal Sensor Location in a Linear Distributed Parameter System

Abstract In this paper, we treat the optimal sensor location problem by using functional analysis. Thus, the partial differential equations are embedded into the ordinary differential equations in Hilbert spaces. It is assumed that a criterion for the sensor location is to minimize the trace of the estimation error covariance operator described by the operator-valued differential equations of Riccati type plus the measurement cost. We prove the existence and uniqueness theorem concerning the solution of the estimation error covariance operator by using the theory of the evolution operator and Picards method. Furthermore, we prove the comparison theorem for the operator-valued differential equations. Based on the theorems, we derive the sufficient condition for the optimal sensor location and then derive the necessary condition. Finally, some numerical examples for the optimal sensor locations are shown.

Design of a discrete adaptive observer based on Lyapunov's direct method

A new scheme for designing the stable discrete adaptive observer for single-input single-output linear systems is proposed. Using Lyapunovs direct method, the asymptotic stability of the observer is established when the input is sufficiently general. Furthermore, the interrelation between complete controllability and complete observability conditions and the sufficiently general condition is made clear. Computer simulation is carried out for a second-order plant to illustrate the feasibility of the scheme.

Applications of Revised GMDH Algorithms to the Prediction of Air Pollutant Concentrations

Abstract This paper is concerned with the prediction problem of air pollutant concentration in the industrial area of Tokushima prefecture, Japan, using revised GMDH algorithms. Two kinds of methods are presented, in which prediction models are constructed using data of sulphur dioxide concentration, wind speed and wind direction at two monitoring stations. The prediction accuracy is often more improved when data of pollutant concentration are transformed into the logarithm expressions for the model construction if the resultant frequency distribution more approaches a normal distribution. The effect with wind data in the model construction contributes to more improvement of the prediction accuracy than the effect without wind data when locations to be predicted are close to main emissions.