Patent Number: 049903020
Section: description

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A preferred embodiment of the present invention will be described below in detail referring to the accompanying drawings. First, principle and function of the present invention will be described with reference to FIG. 4. Integrated values P.sub.j on each interval of the reactor power distribution P(Z) and detector outputs D.sub.k are normalized so that their summation may each become unity (step ST1, ST2) and thereby these values are represented as NP.sub.j, ND.sub.k, respectively. Then, NP.sub.j and ND.sub.k are each applied with Fourier coefficient calculation matrix [Q].sup.-1 as in the expression (4)' by using a Fourier coefficient calculation means (step ST3, ST4), and the results are represented respectively as Fourier coefficients CP.sub.i of the integrated values of the reactor power on each interval and Fourier coefficients CD.sub.i of the neutron detector outputs. Hence EQU [CP.sub.i ]=[Q.sub.ji ].sup.-1 [NP.sub.j ] (6) EQU [CD.sub.i ]=[Q.sub.ki ].sup.-1 [ND.sub.k ] (7) Fourier coefficients CP.sub.i of integrated values of the reactor power on each interval is then obtained from the Fourier coefficients CD.sub.i of the neutron detector outputs using a transformation means. Prior to that, however, characteristics of the Fourier coefficients CD.sub.i will be described. First, the detector outputs D.sub.k is a representative of the neutron flux distribution that has reached the position of the detector deriving itself from the reactor power distribution P(Z) and undergoing diffusion and scattering of neutrons, and hence CD.sub.i have the high frequency component (those terms whose i are larger) attenuated more than CP.sub.i. This means that the diffusion and scattering of neutrons has an action of a low-pass filter. From this point of view, the law of mutual transformation between CD.sub.i and CP.sub.i is considered to be expressed, using a diagonal matrix [A.sub.ii ] to be determined at step ST5, as EQU [CP.sub.i ]=[A.sub.ii ] [CD.sub.i ] (8) That the diagonal matrix [A.sub.ii ] needs not have other elements than the diagonal elements is assured of by the fact that the diffusion or scattering of the neutrons is a linear physical process. In view of the geometrically larger scale, however the diffusion of the neutrons will be such that spreads in the form of spherical wave with the nuclear reactor taken as the center. Hence the pattern of power distribution may have expanded to a certain degree at the position of the neutron detector 20 located on the outside of the reactor. This phenomenon, however, merely means a difference in scale factor and does not mean any interference between different frequency components. Therefore, there is no problem in the use of the expression (8). A second characteristic of the Fourier coefficients CD.sub.i originates from the fact that the detector outputs D.sub.k is flatter than the integrated values P.sub.j of the reactor power on each interval because the former has derived itself from the latter undergoing diffusion and scattering of neutrons and that the domain of variable of Z in the expression (1) is a half period of the lowest frequency component (i=1). That is, the detector outputs D.sub.k, as compared with the integrated values P.sub.j of the reactor power on each interval, is smaller at the central portion (k=2, 3) and larger at both end portions (k=1, 4), and hence, in the Fourier coefficients obtained from the detector outputs D.sub.k, there is produced additionally a component of the third order which was not present originally in the integrated values P.sub.j of the reactor power on each interval. Because of this fact, the transformation rule between CD.sub.i and CP.sub.i cannot be treated simply as a frequency filter. Even if there is such an additional frequency component, it can be expected that the relationship between CD.sub.i and CP.sub.i is expressed by a transformation rule of a linear expression. Namely, it is considered possible to avoid the difficulty resulting from the addition of the third order component nonexistent in the integrated values P.sub.i by using, instead of the expression (8), the following expression with a compensation vector [Bi] introduced into the expression (8) EQU [CP.sub.i ]=[A.sub.ii ] [CD.sub.i ]+[B.sub.i ] (9) When the detector outputs D.sub.k have been normalized in advance, a constant vector will serve as the compensation vector [B.sub.i ] (step ST5). When the detector outputs D.sub.k have not been normalized, the following expression may be used instead of the expression (9). EQU [CP.sub.i ]=[A.sub.ii ] [CD.sub.i ]+(.SIGMA..sub.k CD.sub.k) [B.sub.i ](9) As the other characteristic of the Fourier coefficient CD.sub.i, there is considered possibility of addition or subtraction of an apparent high-frequency component, which is not included in the original data, besides the aforementioned third order component, because of nonuniformity in sensitivities of the small size detectors 21-24, or nonuniformity of shielding effects of the structures between the nuclear reactor 10 and the neutron detector 20. The transformation rule of the expression (9) is considered to hold good even where there is such a phenomenon (step ST6). To prove validity of the above consideration, investigations were made using actually measured data on a nuclear reactor. As the result, the validity was proved in the following way. From many sets of data of integrated values P.sub.j of the reactor power on each interval and detector outputs D.sub.k obtained through actual measurement performed on the nuclear reactor, many sets of CP.sub.i and CD.sub.i were obtained, and these were plotted with CD.sub.i taken along the axis of abscissa and CP.sub.i along the axis of ordinate. As the result, the plotted points were arranged in separate straight lines for each frequency component, whereby the linear transformation rule according to the linear expression (9) was proved to hold good. The actually measured reactor power distribution P(Z) was inclusive of a variety of power distribution at the stage of test operations, and hence, the transformation rule according to the expression (9) indicates that the same transformation rule is applicable to a wide variety of power distribution. Further it was found out that the plotting is effective for checking abnormal data before determining the transformation rule. Any data being abnormal or with error are plotted apart from the above mentioned straight lines and therefore are easily detected and deleted. This was unattainable by the prior art as shown in FIG. 3. [A.sub.ii ] and [B.sub.i ] in the expression (9) can be obtained from a large number of sets of the integrated values P.sub.j of the reactor power and detector outputs D.sub.k that are measured simultaneously by the method of least squares or the like (step ST5). This is the initial calibration on S/W in the present method. The calculation is much easier than that performed for obtaining the transformation matrix [A.sub.kj ].sup.-1 in the expression (5)' in the prior art. In the case where the coefficients in the constant matrix [A.sub.kj ] of the expression (5) gently vary and the diagonal elements are slightly dominant, the calculation to obtain the inverse matrix is sensitive and susceptible to errors in the data, which is a well-known general mathematical character in such cases. What should be noted here is that just two is the required number in the minimum of sets of the data of the integrated values P.sub.j of the reactor power and detector outputs D.sub.k necessary for determining [A.sub.ii ], [B.sub.i ] in the expression (9). This is due to the fact that the expression (9) is a linear expression. By virtue of this feature, the conditions required of the data used for initial calibration can be greatly relaxed as against those in the prior art. After the expression (9) has been determined in the initial calibration, the reactor power distribution P(Z) will be obtained by use of the expression (4)' and the expression (1) the same as in the prior art. However, for the reason that the detector outputs D.sub.k in the present embodiment have been normalized according to expressions (6), (7), the reactor power distribution P(Z) obtained here is a relative power distribution Prel(Z) (step ST7). Hence, in order to obtain absolute power distribution Pabs(z), the relative power distribution Prel(Z) may be multiplied by a total power signal Ptotal (%) or by a coefficient obtained from the sum of the detector outputs D.sub.k divided by the sem of the detector outputs D.sub.k at the time of 100% output power (step ST8). Another embodiment shown in FIG. 5 is what is formed of the function of FIG. 4 and in abnormal data deleting means added thereto. This additional function is performed prior to the initial calibration (step ST5: determination of [A.sub.ii ], [B.sub.i ]) in the embodiment of FIG. 4. That is, after executing calculation of the expressions (6), (7) at steps ST3, ST4 as described above, [CP.sub.i ], [CD.sub.i ] are plotted on a plane at step ST9 and thereafter abnormal data are detected at step ST10. The abnormal data are deleted at step ST11 prior to determination of [A.sub.ii ], [B.sub.i ] in the expression (9), whereby initial calibration can be performed smoothly and accurately. The abnormal data may be deleted by human visual inspection of a display of the planar plotting or may be automatically deleted by an algorithm set up, for example, as shown in FIG. 6. That is, step ST12 is that for counting number of data, step ST13 is that for deciding whether or not the number of data is larger than 5 i.e. data is sufficient for partial deletion or not, step ST14 is that for processing K=[.sqroot.N]-1 i.e. determining degree of deletion, step ST15 is that for preliminary determining [A.sub.ii ], [B.sub.i ], step ST16 is that for deleting K pieces of errornious data from one of the largest error, and step ST17 is that for determining [A.sub.ii ], [B.sub.i ] again from the remaining data. As described so far, according to the first invention, an apparatus for measuring nuclear reactor power distribution is structured of a Fourier coefficient calculation means and a transformation means so that data for initial calibration are obtained. Hence, it is made possible to greatly relax the conditions required of the data for initial calibration such as necessary number of the data and variety of the data. Thus, the initial calibration is made very easily, and therefore, such an effect is obtained that the apparatus can be applied not only to a plant at the stage before commencement of commercial operation but also to an existing nuclear reactor. And, according to the second invention, abnormal data can be easily detected and deleted prior to initial calibration, and therefore, such an effect is obtained that stable operation of the apparatus with high accuracy can be attained.