Research on reactor diagnosis based on a new system identification method

在反应器噪声中多变量时间序列数据的系统辨识中，有必要系统地考察创新模型的性质。利用以关联函数为元素的Hankel矩阵的奇异值分解确定了面向数据的创新模型的系数矩阵，并考察了其极点和零点等守恒量的性质。此外，还考察了观测噪声对创新模型零点的影响，并将其归纳为规则。由于核反应堆是一个具有热动力和流体动力反馈力学的系统，因此有必要研究描述反馈回路的闭环传递函数和开环传递函数之间的关系。由于两个传递函数之间的关系是一种非线性变换，因此拟合模型的极点和零点一般不守恒。据报道，在拟合的时间序列模型中，存在极零抵消的可能性。通过以上研究，我们认识到Riccati方程存在一个稳定的特解，这个特解出现在创新模型的表述中。研究了稳定特解的存在性，得到了反馈系统零点可逆时满足表解的条件。当电抗器为最小相时（零可逆），Riccati方程在此条件下有稳定解，理论上可以识别出开环传递函数。否则，反馈系统中会出现一个附加的等效环，这个附加环给系统的开环传递函数辨识带来困难。虽然公式中的关键模型是等效创新模型，但其表现形式并不独特。研究了从一种表示到另一种表示的转换。研究了相应的里卡第方程，明确了里卡第方程的性质和相互关系。少

On sysytem identification with multivariate time series data in the reactor noise, it is necessary to examine properties of innovation models systematically. Coefficient matrices of a data-oriented innovation model have been determined by using the singular value decomposition of Hankel matrix of which the elements are correlation functions, and properties of its conservation quantities such as poles and zeros have been examined. Furthermore, effects of observation noise to zeros of innovation model have been examined, and summarized as rules.Since the nuclear reactor is a system with thermal and hydro-dynamical feedback mechanics, it is necessary to examine relations between closed loop transfer functions and open loop transfer functions describing feedback loops. Since the relationship between both transfer functions is a nonlinear transformation, poles and zeros of the fitted model are not conserved in general. It has been reported that there is a possibility of pole-zero cancellati … More on in a fitted time series model.Along the line of above studies it has been recognized that there exists a stable particular solution of Riccati equation, which appears in the formulation of the innovation model. The investigation of existence of the stable particular solution brings us to know that the condition of atable solution is satisfied if zeros of feedback system are invertible. If a reactor is of minimun phase (of which zeros are invertible), the Riccati equation has a stable solution under the condition, and open loop transfer functions can be identified theoretically. Otherwise, there appears an additional equivalent loop in the feedback system, and then the additional loop makes difficulty in system identification of open loop transfer functions.Although the key model in the formulation is an equivalent innovation model, its representation is not unique. The transformation from one representation to the other has been studied. Corresponding Riccati equations are also examined, and properties and relationship between Riccati equations have been made clear. Less