Stable identification scheme for linear discrete-time systems

This paper is concerned with the problem of identifying parameters in stochastic systems described by single-input single-output linear discrete-time equations. A stable estimation error system is developed by using the extended Kalman filter technique and the concept of strictly positive real transfer function. The identifier corresponding to the estimation error system is constructed, and the convergence of parameter estimates to the exact values is proved under some bounded conditions. It is shown that the recursive maximum likelihood identifier and the recursive extended least squares identifier are obtained by neglecting the correction terms in the proposed identifier. Numerical examples for a fourth-order system are presented to illustrate the effectiveness of the proposed method.     

A method of predicting failure or life for stochastic systems by using autoregressive models

This paper discusses on-line detection and prediction problems of the failure or life of stochastic systems by using autoregression (AR) models. We regard the change of the equipment from an ordinary state to failure as a variation of the characteristics of a time aeries signal. An AR model is fitted to the time aeries signal and the change is detected by variations of the model. Using four types of performance index of the variations, we detect the failure of a cutting tool of a lathe and predict the width of flank wear.     

The optimal smoothing estimators based on the Wiener-Hopf theory

It is well known that the Wiener-Hopf theory plays a fundamental role in estimation problems. In this paper, we derive the basic equations for the optimal smoothing estimators by using the Wiener-Hopf theory. The interrelation between the Wiener-Hopf theory and the innovation theory is also considered. Finally based on the basic equations three kinds of the smoothing estimators, that is, the fixed-point, fixed-interval, and fixed-lag smoothing estimators are derived.     

On the stability of control systems with randomly time-varying characteristics†

The purpose of this paper is to study the stability conditions of randomly time-varying control systems.

First we define the stability, in the stoehastic sense, of the control system with randomly time-varying characteristics and secondly we obtain the conditions for global stability in the mean for a control system which is governed in each time interval by two different differential equations with probability p and 1-q respectively.

Finally we examine the stability condition for the concrete control systems by experiments of the Monte Carlo method.     

Sodium Caseinate and Skim Milk Gels Formed by Incubation with Microbial Transglutaminase

Several suspensions and emulsions containing commercial sodium caseinate or skim milk were gelatinized by Ca²⁺-independent microbial transglutaminase treatment. The characteristics of the gels were largely affected by the enzyme concentrations employed. For caseinate gels generally the higher enzyme concentration gave steep decreases in breaking strength, strain and cohesiveness of the gels. The creep tests on emulsified gels prepared to two different enzyme concentrations showed that the gel made with a higher enzyme concentration was the more viscoelastic. For skim milk gels, the enzyme treatment in higher concentration caused substantial increase of the breaking and hardness while the strain and cohesiveness had little or no changes.     

Production of Restructured Meat using Microbial Transglutaminase without Salt or Cooking

To produce restructured meat, microbial transglutaminase (MTGase) was evaluated for its ability to introduce covalent crosslinks between protein molecules. Pork muscle cubes were mixed with MTGase and held at 5°C for 2 hr for the enzyme reaction. Restructured products were analyzed for binding strength without cooking. MTGase treatment resulted in effective binding of meat pieces provided there was addition of salt (NaCl). To ensure proper binding without NaCl, some food proteins with MTGase were also investigated. Meat cubes in combination with MTGase and sodium caseinate showed acceptable bind, and sodium caseinate appeared to be a superior substrate for the crosslinking to meat proteins than soy protein, whey protein, or gelatin. These results suggest a useful method for producing restructured meat which can be distributed in the raw, chilled state.     

Gel Strength Enhancement by Addition of Microbial Transglutaminase during Onshore Surimi Manufacture

Surimi from Alaska pollock flesh was manufactured onshore with Microbial transglutaminase (MTGase). Effect of MTGase was investigated by evaluating breaking strength and deformation of gels from MTGase-treated surimi with and without setting at 30°C. Quantitative analysis of ε-(γ-glutamyl)lysine (GL) crosslink was also carried out to monitor the MTGase reaction. In set gels, breaking strength and GL crosslink increased, and myosin heavy chain decreased correspondingly with MTGase concentration. These changes were smaller in gels prepared without setting. Results suggest that surimi gel could be improved through the formation of GL crosslinks by added MTGase in surimi.     

Fixed-interval smoothing for a linear distributed parameter system

The fixed-interval smoothing estimator for a linear distributed parameter system with a noisy observation at discrete points on the spatial domain or its boundary is derived from the Wiener-Hopf theoretical viewpoint. The present derivation of the smoothing estimator is based on the Wiener-Hopf theory. Thus, using the Wiener-Hopf equations both for the optimal smoothing problem and for the optimal filtering problem, the optimal fixed-interval smoothing estimator which corresponds to the results obtained by using Kalman's limiting procedure is derived. Finally, for the convenience of the numerical computation, we rewrite the results for the optimal fixed-interval smoothing estimator and the error covariance function by using the Fourier expansion method.     

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.     

On the estimation of noise covariances in linear discrete-time systems

This paper is concerned with an approach for estimating or tracking the time-varying input and measurement noise covariances in time-varying discrete-time linear systems. The approach is firstly to introduce the estimators for the case where the noise co-variances are unknown constants. (The estimators are defined as the mean squares of the estimators of noises based on all the available measurement data.) They arc then transformed in sequential form, and are subsequently modified by incorporating a fading memory to yield estimates for time-varying noise covariances. The time-varying noise covariance estimates are evaluated as the fading mean squares of the estimates of noises based on all the measurement data up to present time. A numerical example for a simple system indicates acceptable performance of the proposed method.