CN113032732B - Dose rate fitting method and system based on relative error segmentation - Google Patents
Dose rate fitting method and system based on relative error segmentation Download PDFInfo
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Abstract
The invention discloses a dose rate fitting method and a dose rate fitting system based on relative error segmentation, wherein the method comprises the following steps of: acquiring detector count values under different dose rate values, and performing data fitting according to the detector count values and the dose rate values to obtain a first fitting curve; acquiring a first fitting interval according to the first fitting curve, and performing secondary fitting on data in the first fitting interval; wherein, the relative error value of the fitting point in the first fitting interval is greater than the relative error threshold value; and repeating the steps until the relative error of each fitting point on the obtained fitting curve is less than or equal to the relative error threshold. The invention aims to provide a dose rate fitting method and system based on relative error segmentation, which can automatically judge the reasonability of each interval of a fitting curve by taking relative errors as judgment bases, and re-fit unreasonable intervals, wherein the relative error between the dose rate value after the segmentation fitting and a true value in the whole dose rate interval is very small.
Description
Technical Field
The invention relates to the technical field of dose rate measurement, in particular to a dose rate fitting method and system based on relative error segmentation.
Background
For dose rate measurement, detectors such as a GM counting tube, a semiconductor and an ionization chamber are mostly adopted, the detectors mostly adopt a pulse counting mode, and in the conversion process of a counting value and dose rate, a least square method is mostly adopted for curve fitting. Because the least square method carries out data fitting with minimum variance, the fitting result is in a high dose rate area, and the relative error is very small; in the low dose rate region, the relative error between the partial regions can be very large.
In order to make the count-to-dose converted values closer to the true values at low dose rates, it is desirable to reduce the relative error of the fit curve in the fractional region, especially the low dose rate region. To reduce the relative error, it is common to employ:
1. performing data fitting in a pre-segmentation mode, segmenting a fitting area, performing metering rate fitting after segmentation, wherein the relative error of a fitting result is related to the segmentation size and experience of the fitting area;
2. the least square method fitting based on relative errors is very complex for function fitting of more than 2 orders, and causes large relative errors in high dose rate areas.
Disclosure of Invention
The invention aims to provide a dose rate fitting method and system based on relative error segmentation, which can automatically judge the reasonability of each interval of a fitting curve by taking relative errors as judgment bases, and re-fit unreasonable intervals, wherein the relative error between the dose rate value after the segmentation fitting and a true value in the whole dose rate interval is very small.
The invention is realized by the following technical scheme:
a dose rate fitting method based on relative error segmentation comprises the following steps:
s1: acquiring detector count values under different dose rate values, and performing data fitting according to the detector count values and the dose rate values to obtain a first fitting curve;
s2: acquiring a first fitting interval according to the first fitting curve, and performing secondary fitting on data in the first fitting interval;
wherein the relative error value of the fitting points in the first fitting interval is greater than a relative error threshold value;
s3: and repeating the step S2 until the relative error of each fitting point on the obtained fitting curve is less than or equal to the relative error threshold.
Preferably, the data fitting is performed using a least squares method.
Preferably, said S1 comprises the following sub-steps:
s11: collecting detector count values under different dose rate values; wherein a plurality of detector count values are collected at any one dose rate value;
s12: acquiring the average counting value of detectors under different dose rate values;
s13: and performing data fitting on the detector counting average value and the dose rate value by using a least square method to obtain the first fitting curve.
Preferably, said S2 comprises the following sub-steps:
s21: obtaining relative error values of all fitting points on the first fitting curve;
s22: comparing the relative error value of each fitting point with the relative error threshold value, and acquiring a first fitting interval according to the comparison result;
s23: and performing data fitting on the detector counting average value and the dose rate value of the first fitting interval by adopting a least square method to obtain a second fitting curve.
A dose rate fitting system based on relative error segmentation comprises a fitting module, a correction module and a judgment module;
the fitting module is used for obtaining detector counting values under different dose rate values and performing data fitting according to the detector counting values and the dose rate values to obtain a first fitting curve;
the correction module is used for acquiring a first fitting interval according to the first fitting curve and performing quadratic fitting on data in the first fitting interval;
wherein the relative error value of the fitting points in the first fitting interval is greater than a relative error threshold value;
the judging module is used for judging whether the relative error of each fitting point on the fitting curve transmitted by the correcting module is larger than a relative error threshold value, if so, the fitting curve is transmitted to the correcting module, and the correcting module corrects the fitting curve again.
Preferably, the fitting module comprises the following processes:
collecting detector count values under different dose rate values; wherein a plurality of detector count values are collected at any one dose rate value;
acquiring the average counting value of detectors under different dose rate values;
and performing data fitting on the detector counting average value and the dose rate value by adopting a least square method to obtain the first fitting curve.
Preferably, the correction module comprises the following processing procedures:
obtaining relative error values of all fitting points on the first fitting curve;
comparing the relative error value of each fitting point with the relative error threshold value, and acquiring a first fitting interval according to the comparison result;
and performing data fitting on the average detector count value and the dose rate value in the first fitting interval by using a least square method to obtain a second fitting curve.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the relative error is used as the judgment basis for the fitting rationality of the dose rate conversion data, so that the fitting data result is more appropriate to the actual application requirement;
2. the rationality judgment basis of the dose rate fitting data is a relative error, a relative error threshold value can be preset, dose rate data fitting is carried out according to the set relative error judgment threshold value, and the relative error of a dose rate fitting result is controllable;
3. compared with the traditional pre-segmentation method, the method eliminates the influence of human factors, can realize automatic segmentation of the dose rate value through programming, and has more rationality than the pre-segmentation method;
4. carrying out dose rate numerical fitting from a high dose rate region to a low dose rate region in sequence, and fully utilizing the premise that a least square method has small relative error of a relatively high dose rate point in the fitting region, so that the relative error of a high dose rate section in the fitting dose rate value is very close to a true value;
5. by presetting a relative error judgment threshold value, the final dosage rate relative to the inherent error is mainly determined by the statistical fluctuation of the count after smoothing.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a first fit graph of the present invention;
FIG. 3 is a plot of the residuals of a first fitted curve according to the present invention;
FIG. 4 is a second fit graph of the present invention;
FIG. 5 is a plot of the residuals of a second fitted curve according to the present invention;
FIG. 6 is a third fit graph of the present invention;
FIG. 7 is a plot of the residuals of a third fitted curve according to the present invention;
FIG. 8 is a prior art fitting graph
FIG. 9 is a residual plot of a prior art fitted curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and the accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limiting the present invention.
Example 1
A dose rate fitting method based on relative error segmentation, as shown in fig. 1, comprising the steps of:
s1: acquiring detector count values under different dose rate values, and performing data fitting according to the detector count values and the dose rate values to obtain a first fitting curve;
specifically, collecting detector count values at different dose rate values; in order to enable the acquired data to be more accurate, the counting value of the detector is acquired for multiple times under any dosage rate value, the average value is obtained, and the average value is used as the technical value of the detector under the dosage rate value, so that the influence caused by inaccurate acquisition of single data is avoided; at the same time, in order to make the fitted curve closer to the true value, the number of samples should be large enough, preferably larger than 1000 sample values.
S2: acquiring a first fitting interval according to the first fitting curve, and performing quadratic fitting on data in the first fitting interval;
wherein, the relative error value of the fitting point in the first fitting interval is greater than the relative error threshold value; the relative error threshold is set in advance.
Since the fitting curve is fit according to a large amount of data, most data can only be located on or relatively to the fitting curve, and therefore, the error of the data located outside or relatively to the fitting curve is large, so that the fitting correction needs to be performed again. Therefore, in the present application, by obtaining the relative error value of each fitting point on the first fitting curve; and comparing the relative error value of each fitting point with a relative error threshold value, selecting the fitting point with the relative error larger than the relative error threshold value so as to form a first fitting interval, and then performing data refitting on the detector counting average value and the dose rate value of the first fitting interval by adopting a least square method so as to obtain a second fitting curve.
Preferably, in the process of quadratic fitting, dose rate numerical fitting can be carried out from a high dose rate region to a low dose rate region in sequence, and in the quadratic fitting process, the premise that relative errors of relatively high dose rate points in the fitting region are small by a least square method is fully utilized, so that relative errors of high dose rate sections in the fitted dose rate value are very close to a true value.
It should be noted that there may be more than one first fitting interval on one fitting interval, and the first fitting interval may be reasonably set according to the actual distribution of the fitting points.
S3: and S2, repeating the step until the relative error of each fitting point on the obtained fitting curve is less than or equal to the relative error threshold.
In the prior art, when the counting and the dose rate curve are fitted, the least square method is mostly adopted for curve fitting. Since the least square method performs data fitting with the minimum variance (residual variance), the relative error is very large in a partial interval in a low dose rate region, as shown in fig. 8 and 9; if the least square method fitting based on the relative error is adopted, the weight of the least square method fitting becomes the relative error, so the weight of the least square method fitting in the high dosage rate interval is the same as that of the least square method fitting in the low dosage rate interval, and the relative error of the high dosage rate interval is larger.
Based on this, in order to solve the problem that the relative error of the sub-regions is large after data fitting, in this embodiment, a method for fitting the dose rate by using a least square method is constructed, and the relative error is used as a judgment basis, so that reasonability of each region of a fitting curve can be automatically judged, and refitting is performed on an unreasonable region again, and the relative error between the dose rate value after the piecewise fitting and a true value in the whole dose rate region is very small. The invention is implemented with the relative error between the fitted dose rate value and the true value. On one hand, the fitted dose rate value is closer to the true value than the dose rate value fitted by the traditional method, and the relative error is obviously improved; on the other hand, the fitting relative error judgment threshold value can be adjusted to obtain a controllable relative error.
Example 2
The embodiment provides a relative error segmentation-based dose rate fitting system which comprises a fitting module, a correcting module and a judging module;
the fitting module is used for obtaining detector count values under different dose rate values and performing data fitting according to the detector count values and the dose rate values to obtain a first fitting curve;
the correction module is used for acquiring a first fitting interval according to the first fitting curve and performing quadratic fitting on data in the first fitting interval;
wherein, the relative error value of the fitting point in the first fitting interval is greater than the relative error threshold value;
and the judging module is used for judging whether the relative error of each fitting point on the fitting curve transmitted by the correcting module is greater than the relative error threshold value or not, and if so, transmitting the fitting curve to the correcting module.
Further, the fitting module includes the following processes:
collecting detector count values under different dose rate values; wherein, a plurality of detector count values are collected under any one dose rate value;
acquiring the average counting value of detectors under different dose rate values;
and performing data fitting on the detector counting average value and the dose rate value by adopting a least square method to obtain the first fitting curve.
Further, the correction module comprises the following processing procedures:
obtaining relative error values of all fitting points on the first fitting curve;
comparing the relative error value of each fitting point with a relative error threshold value, and acquiring a first fitting interval according to the comparison result;
and performing data fitting on the average value of the counting number of the detector and the dose rate value in the first fitting interval by adopting a least square method to obtain a second fitting curve.
Example 3
The technical scheme of the application is further explained by taking a GM tube ZP1202 as an example as follows:
the detector count values for different dose rate values are shown in table 1:
TABLE 1 Detector count values at different dose rate values
According to the data, a first fitting curve fitted by a least square method is as follows:
f(x)＝p1*x^4+p2*x^3+p3*x^2+p4*x+p5；
wherein p1=6.978e-12; p2= -2.816e-08; p3= -3.421e-05; p4=0.9428; p5= -3.529;
the first fitted graph is shown in fig. 2, and a fitted residual graph can be obtained according to the first fitted graph or the first fitted graph, which is shown in fig. 3; from FIG. 3, it can be determined that the first fit interval is [0.38, 326.789]; fitting again based on the data in this interval to obtain a second fitted curve:
f(x)＝p1*x^4+p2*x^3+p3*x^2+p4*x+p5；
wherein p1=3.951e-08; p2= -1.408e-05; p3=0.001631; p4=0.5095; p5= -0.01991;
the second fitted graph is shown in fig. 4, and a fitted residual error map of the second fitted graph can be obtained according to the second fitted graph or the second fitted graph, which is shown in fig. 5; from FIG. 5, it can be determined that the quadratic fit interval is [0.38, 87.47]; fitting again based on the data in this interval to obtain a third fitted curve:
f(x)＝p1*x^4+p2*x^3+p3*x^2+p4*x+p5；
wherein, p1=2.899e-06, p2= -0.000431, p3=0.01705, p4=0.439, p5= -0.06927;
as can be seen from fig. 7, the residual error after the third fitting is negligible, and the relative error is obtained from the residual error, so the relative error is also very small and negligible.
Finally, the transformation consists of three segments of data fitting, respectively: [0.38, 87.47],[87.47, 326.789],[326.789, 4604.68].
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A dose rate fitting method based on relative error segmentation is characterized by comprising the following steps:
s1: acquiring detector count values under different dose rate values, and performing data fitting according to the detector count values and the dose rate values to obtain a first fitting curve;
wherein, the step S1 includes the following substeps:
s11: collecting detector count values under different dose rate values; wherein, a plurality of detector count values are collected under any one dose rate value;
s12: acquiring the average counting value of detectors under different dose rate values;
s13: performing data fitting on the detector count average value and the dose rate value by using a least square method to obtain a first fitting curve;
s2: acquiring a first fitting interval according to the first fitting curve, and performing secondary fitting on data in the first fitting interval; the relative error value of the fitting points in the first fitting interval is greater than a relative error threshold value;
wherein, the step S2 includes the following substeps:
s21: obtaining relative error values of all fitting points on the first fitting curve;
s22: comparing the relative error value of each fitting point with the relative error threshold value, and acquiring the first fitting interval according to the comparison result;
s23: performing data fitting on the average detector count value and the dose rate value in the first fitting interval by using a least square method to obtain a second fitting curve;
s3: and S2, repeating the step until the relative error of each fitting point on the obtained fitting curve is less than or equal to the relative error threshold.
2. A relative error segmentation based dose rate fitting method as claimed in claim 1 wherein the data fitting is performed using a least squares method.
3. A dose rate fitting system based on relative error segmentation is characterized by comprising a fitting module, a correcting module and a judging module;
the fitting module is used for obtaining detector counting values under different dose rate values and performing data fitting according to the detector counting values and the dose rate values to obtain a first fitting curve;
the correction module is used for acquiring a first fitting interval according to the first fitting curve and performing quadratic fitting on data in the first fitting interval;
wherein the relative error value of the fitting points in the first fitting interval is greater than a relative error threshold value;
the judging module is used for judging whether the relative error of each fitting point on the fitting curve transmitted by the correcting module is larger than a relative error threshold value, if so, the fitting curve is transmitted to the correcting module, and the correcting module corrects the fitting curve again.
4. A relative error segment based dose rate fitting system as defined in claim 3, wherein the fitting module comprises the processes of:
collecting detector count values under different dose rate values; wherein, a plurality of detector count values are collected under any one dose rate value;
acquiring the average counting value of detectors under different dose rate values;
and performing data fitting on the detector counting average value and the dose rate value by adopting a least square method to obtain the first fitting curve.
5. The relative error segment based dose rate fitting system of claim 4 wherein the correction module comprises the processes of:
obtaining relative error values of all fitting points on the first fitting curve;
comparing the relative error value of each fitting point with the relative error threshold value, and acquiring a first fitting interval according to a comparison result;
and performing data fitting on the average detector count value and the dose rate value in the first fitting interval by using a least square method to obtain a second fitting curve.
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