Properties of Autoregressive Model in Reactor Noise Analysis, (I)

Abstract

Under appropriate conditions, stochastic processes are described by the ARMA model, however, the AR model is popularly used in reactor noise analysis. Hence, the properties of AR model as an approximate representation of the ARMA model should be made clear. Here, convergence of AR-parameters and PSD of AR model were studied through numerical analysis on specific examples such as the neutron noise in subcritical reactors, and it was found that:

1.	The convergence of AR-parameters and AR model PSD is governed by the “zero nearest to the unit circle in the complex plane” (μ−1,|μ|<1) of the ARMA model transfer function.
2.	The AR-parameters of AR(M) model have biases from those for the infinite model order, and these biases decrease approximately in proportion to |μ|M.
3.	The AR model of the neutron noise of subcritical reactors needs a large model order because of an ARMA-zero very close to unity corresponding to the decay constant of the 6-th group of delayed neutron precursors.
4.	In applying AR model for system identification, much attention has to be paid to a priori unknown error as an approximate representation of the ARMA model in addition to the statistical errors.

KEYWORDS:

• ARMA model
• ARMA zero
• AR model
• AR model PSD convergence
• AR parameter bias
• AR parameter convergence
• neutron noise
• stochastic process
• subcritical reactor