JP2838002B2 - Monitoring method for reactor power instability - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for determining the degree of instability of a reactor based on time series data including a noise signal of a reactor output signal, including nonlinear instability caused by excessive feedback or the like. Evaluate and monitor.

[0002]

2. Description of the Related Art Conventionally, in order to evaluate stability based on time-series data of output signals of a nuclear reactor, an attenuation ratio and a power spectral density have been used. The damping ratio is obtained by identifying a linear autoregressive model from the time series data and evolving it. The power spectrum density can be easily obtained by the Blackman, Turkey method or the fast Fourier transform method. However, since these methods are based on linear theory in principle, the stability in the presence of a nonlinear effect cannot be correctly evaluated.

[0003]

Consider a process in which certain parameters of the reactor gradually change, instability occurs, and the vibration eventually reaches a limit cycle. At the first stage of instability, the vibration is intermittent, and the frequency of the vibration, the frequency of the vibration, and the like are important information. Monitoring by power spectral density is effective for this.

In the second stage of generation of instability, the vibration gradually becomes continuous, and the stability against the fundamental wave becomes useful information. At this stage, the time-series data can be approximated by a linear model, and a method using an attenuation ratio is effective.

[0005] In the third stage, the vibration becomes a continuous vibration having a large amplitude and a non-linear effect appears, and the vibration becomes non-sinusoidal, and reaches the limit cycle in the fourth stage. It is difficult to accurately measure the damping ratio in the third-stage continuous vibration and the fourth-stage limit cycle vibration. This is because the autoregressive model is linear. In general, as nonlinearity increases, harmonics to the fundamental wave increase in the power spectral density, but this is relative information, and absolute information on whether the limit cycle has been reached cannot be obtained. . Thus, in the conventional method, there is no way to clearly know the characteristics of these vibrations.

[0006]

In the present invention, oscillation is considered from the viewpoint of chaos theory in order to deal with instability including nonlinear effects.

When a solution is obtained for an n-dimensional nonlinear system over a long period of time, the trajectory of the behavior is drawn into a figure peculiar to the nonlinear system in an n-dimensional space, and this figure is called an attractor. . That is, the set of solutions of the nonlinear system forms an attractor in n-dimensional space. According to chaos theory, nonlinear systems can be classified according to the dimensions of attractors. The dimension in this case does not indicate a normal Euclidean dimension, but is an amount of information necessary to accurately represent a point belonging to a set. For example, if the system is asymptotically stable, the attractor is a point and its dimension is zero. If the behavior of the system is like a limit cycle, the attractor is a periodic trajectory. At this time, since one point can represent all points on the periodic trajectory, the dimension is 1. Similarly, the behavior of the system is quasi-periodic,
That is, if it can be decomposed into a superposition of two different fundamental frequency vibrations, the attractor becomes a torus and its dimension is two. Being chaotic, the dimension becomes a non-integer greater than two.

In the above example, the attractor for the first to third stages of instability occurrence is an asymptotically stable point and has a dimension of 0, the attractor for the fourth stage is a periodic orbit, and its dimension is 1 It is. This change from the third stage to the fourth stage is called hop branching. Therefore, if the dimensions can be measured from the neutron flux time-series data obtained from the reactor, it is possible to evaluate whether the vibration has reached the limit cycle.

The evaluation method according to the present invention is performed as follows.

<Step 1> Time-series data u _i (i = 1, 2, 3, ---, M: M
It is assumed that a sufficiently large value, for example, 5000) is read into the memory in the computer. In principle, it is not possible to obtain an attractor from finite time-series data. I do. That is,

X _i = {u _i , u _i−1 , −−−, u _ik , −−−−, u _{i− (d−1)} } (1) where x _i is reconstructed Orbit. The parameter d in the equation (1) is set so that the maximum time delay is at least larger than (１ ／) of the period of the vibration.

<Step 2> Next, integration of the distance correlation function of points on the attractor (reconstructed trajectory) (correlation integration)
C (r) is calculated by the following equation.

[0012]

C (r) = {the number of (i, j) pairs where distance | x _j −x _i | is smaller than r} / N (2) where x _i represents the position of a point on the attractor , R is the length of the correlation and N is the number of pairs of points on the attractor. The correlation integral obtained in this manner becomes a monotonically increasing function.

<Step 3> The correlation integral is expressed on a logarithmic scale and its slope is expressed.

## EQU3 ## d (logC (r)) (3) d (logr) is calculated and expressed as a graph on the horizontal axis logr. Figures 1 and 2
The example of the graph calculated | required was shown. Since C (r) is a monotonically increasing function, the values in these graphs are non-negative. The r values in the graph does not change C (r) will always be zero at the maximum larger diameter r ₁ of the attractor.

In principle, a region where the value of the graph does not depend on r, that is, a region where the graph is flat and where r is the largest is selected, and the value of the graph at that time is set as a dimensional value.
In FIG. 1, a flat portion does not appear in a region smaller than r ₁ , and therefore has a zero dimension. In FIG. 2, the dimension is about 1.3. This is because dimension 1 is slightly larger due to noise, and the correct dimension is 1.
In addition, a peak appears slightly below r _{1 in} the graph of FIG. This is distributed to x _i is periodic orbits after when namely hop branch vibration limit cycle specific, due to the presence of r which is always a distance correlation is stronger.
When the noise level is high, the flat part in FIG. 2 may become narrow. In such a case, the dimension is determined to be 0 or 1 depending on the presence or absence of a peak.

[0015] Since no quasi-periodic or chaotic oscillations of the reactor power have been found to date, data that is not applicable to the above cases are considered to be too short or too transient.

[0016]

According to the method of the present invention, the nature of the instability is classified by evaluating the slope of the correlation integral.

[0017]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 3 shows a simple conceptual diagram for implementing the present invention. In the analysis of the mathematical expression model, all processes can be performed in the computer.

FIG. 4 shows a neutron flux n (t) obtained by adding noise to the reactor model. Here, when no noise is added, (a) is stable (that is, before hop branching),
In (b), the parameters are adjusted to be periodic (that is, after hop branching). Also, the levels of noise added to the models in the two cases are equal. At first glance, the two time series data seem to differ from each other only in the amplitude. The results of calculating the damping ratio of these vibrations using the autoregressive model are 0.98 in (a) and 0.2 in (b).
It is almost equal to 99. The power spectrum densities are shown in FIG. 5, but no significant and characteristic differences are obtained. That is, in the conventional evaluation method, these two data are qualitatively identified.

FIG. 6 shows the slope of the correlation integral C (r) measured from the two data. In this figure, the values in the graph coincide with each other where r is relatively small. This is due to the added noise levels being equal. In the ideal case, that is, when the influence of noise is very small, there are regions of r where the slopes of the correlation integrals are 0 and 1 in (a) and (b), respectively, where r is relatively large. Corresponds to the dimension of the time series data. In this example, such a region of r does not exist because the noise level is large.
However, there is a range of r where a significant difference appears in the slope of the correlation integral. From the values of the graph in that range, and since there are no non-integer dimensions less than or equal to 2, the dimensions are 0 to 1
It can be seen that it has changed. The graph before the hop branch is a simple decreasing function, whereas the graph after the hop branch has a peak at the right end. This peak confirms that the oscillation has reached the limit cycle.

[0020]

As described above, the dimension measurement method according to the present invention makes it possible to obtain more detailed information on the development stage of the power instability of the reactor, and it is possible to more appropriately monitor the power instability.

[Brief description of the drawings]

FIG. 1 is a diagram showing a slope (in the case of dimension 0) of a correlation integral in a first stage to a third stage of occurrence of instability of a reactor output.

FIG. 2 is a diagram illustrating a gradient (in the case of dimension 1) of a correlation integral in a fourth stage of occurrence of instability of a reactor output.

FIG. 3 is a simple conceptual diagram when implementing the present invention.

FIG. 4 is a diagram showing a neutron flux signal obtained from a reactor model.

FIG. 5 is a diagram showing a comparison of power spectral densities for two cases (before and after hop branching).

FIG. 6 is a diagram showing a comparison of the slope of the correlation between two cases (before (a) and after (b) hop branching).

────────────────────────────────────────────────── ─── Continued on the front page (58) Field surveyed (Int.Cl. ⁶ , DB name) G21C 17/00 JICST file (JOIS)

Claims (1)

(57) [Claims] 1. Time-series data u _i (i
= 1,2,3, --- M: M is a sufficiently large value of about 5,000) and the time of the same signal such as _uik (k = 1, ---, d-1) D-dimensional vector x obtained by combining the delay data with the following equation (1)
The integral (correlation integral) of the distance correlation function of the trajectory of _i [where d is selected to satisfy the following equation (2)] is expressed by the following equation (3).
And the slope of the correlation integral is calculated as in the following equation (4), and is represented as a graph of the horizontal axis logr, and the reactor power becomes unstable depending on whether a peak appears or monotonically decreases in the graph. A method for evaluating and monitoring the instability of the reactor power, characterized in that it is determined whether the limit cycle is oscillating or stable. _{x i = {u i, u} i-1, ----, u ik, ----, u i- (d-1)} (1) d> ( cycle ÷ 4 reactor power oscillation) ÷ (Data sampling period) +1 (2) C (r) = {the number of (i, j) pairs where distance | x _j −x _i | is smaller than r} / N (3) (r is the length of the correlation, N Is the number of pairs of points on the d-dimensional orbit. D (logC (r)) (4) d (logr)