CN105989410B - A kind of overlap kernel impulse decomposition method - Google Patents

A kind of overlap kernel impulse decomposition method Download PDF

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CN105989410B
CN105989410B CN201510097583.9A CN201510097583A CN105989410B CN 105989410 B CN105989410 B CN 105989410B CN 201510097583 A CN201510097583 A CN 201510097583A CN 105989410 B CN105989410 B CN 105989410B
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pulse
nuclear
pulses
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exponential
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CN105989410A (en
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黄洪全
闫萍
方方
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Chengdu Univeristy of Technology
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Abstract

The invention discloses a kind of overlap kernel impulse decomposition method.First, by the original overlapping core pulse for being intended to be decomposed obtained in radioactivity survey be expressed as the linear of N number of core pulse and;Then, the parameter combination of N number of core pulse is regarded as a chromosome;Finally, optimum individual, using the selection of genetic algorithm, intersection, mutation operator, is obtained after excessive generation operation as object function with the error of original overlapping core pulse using the overlapping core pulse represented by individual, and then obtain the parameter value of each pulse, that is, realize the decomposition of overlapping core pulse.When N takes different value, same decompose is carried out to overlapping core pulse and obtains new optimum individual, then selection target function value is reckling as last solution from these optimum individuals.The result shows that the method that the present invention carries out overlap kernel impulse decomposition based on population search technique, is the optimum combination that core pulse is searched for from global sense, to realize the decomposition of overlapping core pulse, and then obtains the parameter of wherein each core pulse.

Description

Overlapped nuclear pulse decomposition method
Technical Field
The invention relates to an overlapped nuclear pulse decomposition method.
Background
In performing a radioactivity measurement, acquisition and processing of nuclear pulse signals are important links. With the development of high-speed integrated circuits, digital forming technology has become an important method for processing nuclear pulse signals, and the performance of nuclear instruments is greatly improved. In practice, overlapping of adjacent nuclear pulses is unavoidable, especially at high-speed counting, which is still a difficult problem to identify and resolve for current wave shaping techniques. In recent years, intensive research has been carried out in the aspects of acquisition, identification and decomposition of nuclear pulses at home and abroad, and methods of discarding overlapping pulses are often adopted in these methods. In addition, the consistency and stability of signal parameters are influenced by the fluctuation of response characteristics of the detector and subsequent circuits thereof, and the situation also exists in a high-speed and high-precision circuit system. For example, the response characteristics of the detector and subsequent circuits thereof can be known by acquiring fast and slow time constants of exponential or double-exponential pulse signals, which is of great significance for research on waveform shaping, energy spectrum drift and the like of nuclear instruments. For the decomposition and identification of the signal after Gaussian shaping, the decomposition and identification problem thereof is always a technical problem worthy of research. The invention provides a decomposition method of overlapped nuclear pulse aiming at a typical nuclear pulse signal. The method has important significance for the verification of a forming algorithm, the analysis of the response characteristic of a measuring circuit, the analysis of the change relation of parameters along with time and external conditions, the acquisition of subsequent nuclear pulse parameters and other processes.
Disclosure of Invention
The invention aims to disclose an overlapped nuclear pulse decomposition method. The method solves the technical problem that the adjacent nuclear pulses are difficult to accurately extract related information due to overlapping to a certain extent, and has great significance for improving the accuracy of the radioactivity measurement.
The decomposition of the overlapping nuclear pulses is realized by the following specific steps (1) to (4).
The original overlapped nuclear pulse to be decomposed obtained in the radioactivity measurement is expressed as the linear sum of N nuclear pulses in the step (1), and the number N of the nuclear pulses is determined according to the specific situation of the overlapped nuclear pulse to be decomposed.
Step (2) regarding the parameter combination of N nuclear pulses as a chromosome, wherein each chromosome gene is composed according to one of the following methods (a), (b) and (c):
(a) For an overlapped kernel pulse consisting of N exponential kernel pulses, the amplitude A of each exponential kernel pulse i And time of occurrence T i Respectively corresponding to one gene, the decay time constant tau of exponential nuclear pulse corresponds to one gene, and each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N τT 1 T 2 …T N ]The gene order may vary;
(b) For an overlapped nuclear pulse consisting of N bi-exponential nuclear pulses, the amplitude A of each bi-exponential nuclear pulse i And time of occurrence T i Time constant tau of double-exponential nuclear pulse corresponding to one gene respectively 1 And τ 2 Each corresponding to a groupThus, each chromosome has a total of 2N +2 genes, namely [ A ] 1 A 2 …A N τ 1 τ 2 T 1 T 2 …T N ]The gene order may vary;
(c) For the overlapped nuclear pulse composed of N Gaussian nuclear pulses, the amplitude A of each Gaussian nuclear pulse i And time of occurrence T i Respectively corresponding to one gene, the standard deviation sigma of Gaussian nuclear pulse corresponds to one gene, each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N σ T 1 T 2 …T N ]The order of the genes may vary.
Step (3) carrying out population initialization on the chromosomes combined in the step (2), taking the error between the overlapped nuclear pulse represented by the individuals and the original overlapped nuclear pulse as a target function, constructing a fitness function, and obtaining the optimal individuals through multi-generation operation by adopting selection, intersection and mutation operators of a genetic algorithm; the genetic algorithm of the step (3) is realized according to the following links A, B, C, D and E.
A. Population initialization
And creating an initial population with uniform distribution, wherein the number PopSize of the initial population can be determined by the waveform of the overlapped nuclear pulse, and the value range of each gene is determined according to the characteristics of the overlapped nuclear pulse.
B. Calculating the individual fitness value according to the following steps:
(a) The error of the overlapped kernel pulse represented by an individual from the original overlapped kernel pulse is taken as an objective function,
(b) And solving a fitness value according to the sequence number of the individual objective function values, and recording the optimal and worst individuals in the current group.
C. And (4) carrying out genetic operation by adopting selection, crossing and mutation operators of a genetic algorithm to generate a progeny population.
D. And D, calculating the fitness value of each individual chromosome for the filial generation population generated in the step C, recording the optimal and worst individuals in the current population, and replacing the total optimal with the current optimal individuals if the optimal individuals in the current population are better than the total optimal individuals, otherwise, replacing the current worst with the total optimal individuals.
E. If the stopping condition of the genetic algorithm is not met, the genetic algorithm operation is carried out again from the step C; if the stop condition of the genetic algorithm is reached, the found optimal individual is the solution when the pulse number is N.
The stop condition of the genetic algorithm may be the maximum number of repeated executions, the maximum time before the algorithm stops, or the optimum objective function value less than or equal to a certain value set in advance; the stopping condition may also be provided if the objective function value does not improve at a set number of generations, or within a set time interval.
Step (4) if the pulse number N is larger than 1, taking N = N-1, and performing the operations of the steps (1) to (3) again to search for the optimal individual; if N =1, the number of comparison pulses N is 1,2,3 \8230, and the optimal individual with the minimum objective function value is the optimal decomposition form of the original overlapped nuclear pulse, and the chromosome of the optimal individual is decoded to obtain the parameters of each nuclear pulse.
The decomposition of the overlapped nuclear pulse is completed through the steps (1) to (4).
The invention has the beneficial effects that:
in the radioactivity measurement, the overlapping of adjacent nuclear pulses is inevitable, and particularly, the overlapping phenomenon is more rare and serious at the high-speed counting, which brings difficulties to the wave shaping and the acquisition of nuclear signal parameters. In recent years, intensive research has been carried out in the aspects of acquisition, identification and decomposition of nuclear pulses at home and abroad, and methods of discarding overlapping pulses are often adopted in these methods. The invention provides a group technology-based overlapped nuclear pulse decomposition method aiming at typical nuclear pulse signals, which searches the optimal combination of nuclear pulses in the global sense to realize the decomposition of the overlapped nuclear pulses and further acquire the parameters of each nuclear pulse. The rejection rate of overlapped nuclear pulses is greatly reduced, and the accuracy and the reliability of radioactivity measurement are improved; the method is beneficial to analyzing the fluctuation of signal parameters caused by the change of response characteristics of the detector and subsequent circuits thereof, such as the fluctuation of time constants of exponential or double-exponential pulse signals; the method has important significance for the verification of a nuclear instrument waveform forming algorithm and an energy spectrum drift correction algorithm, the analysis of the response characteristic of a measuring circuit, the analysis of the change relation of parameters along with time and external conditions, the acquisition of subsequent nuclear pulse parameters and other processes.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings, which are implemented on the premise of the technical solution of the present invention, and provide detailed embodiments and procedures, but the scope of the present invention is not limited to the following embodiments.
Let V (t) be the overlapped nuclear pulse to be decomposed obtained in the radioactivity measurement, and the decomposition of the overlapped nuclear pulse by the method is carried out according to the following specific steps (1) to (4).
Step (1) discretizes the original overlapped nuclear pulse V (t) to be decomposed obtained in the radioactivity measurement and represents the linear sum of N nuclear pulses:
for exponentially overlapping kernel pulses
For dual exponential type overlapping kernel pulses
For overlapping kernel pulses of Gaussian type
In formulas (1) to (3), u (.) represents a step function; k =0,1,2,3, \8230; tau is 1 And τ 2 Respectively a slow time constant and a fast time constant of the double-exponential signal; v (.) is noise; t is S Is a sampling period; a. The i And T i Respectively representing the amplitude and the occurrence time of the ith nuclear pulse; σ represents the standard deviation of the Gaussian kernel pulse; n is the number of kernel pulses, and is determined according to the specific situation of the overlapped kernel pulses to be decomposed.
Step (2) regarding the parameter combination of N nuclear pulses as a chromosome, wherein each chromosome gene is composed according to one of the following methods (a), (b) and (c):
(a) For an overlapped kernel pulse consisting of N exponential kernel pulses, the amplitude A of each exponential kernel pulse i And time of occurrence T i Respectively corresponding to one gene, the decay time constant tau of exponential nuclear pulse corresponds to one gene, each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N τT 1 T 2 …T N ]The gene order may vary;
(b) For an overlapped nuclear pulse consisting of N bi-exponential nuclear pulses, the amplitude A of each bi-exponential nuclear pulse i And time of occurrence T i Time constant tau of double-exponential nuclear pulse corresponding to one gene respectively 1 And τ 2 Each corresponds to a gene, each chromosome has 2N +2 genes, namely [ A ] 1 A 2 …A N τ 1 τ 2 T 1 T 2 …T N ]The gene order may vary;
(c) For the overlapped nuclear pulse composed of N Gaussian nuclear pulses, the amplitude A of each Gaussian nuclear pulse i And time of occurrence T i Respectively corresponding to one gene, the standard deviation sigma of the Gaussian nuclear pulse corresponds to one gene, and each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N σ T 1 T 2 …T N ]The gene order may vary.
Performing population initialization on the chromosomes combined in the step (2), taking the error of the overlapped nuclear pulse represented by the individual and the original overlapped nuclear pulse as a target function, constructing a fitness function, and performing multi-generation operation by adopting selection, intersection and mutation operators of a genetic algorithm to obtain an optimal individual; the genetic algorithm of the step (3) is realized according to the following links A, B, C, D and E.
A. Population initialization
And creating an initial population with uniform distribution, wherein the number PopSize of the initial population can be determined by the waveform of the overlapped nuclear pulse, and the value range of each gene is determined according to the characteristics of the overlapped nuclear pulse.
B. Calculation of individual fitness values
The fitness value reflects the strength of the individual to the environmental adaptability, and the survival opportunity of the individual can be well controlled by adopting the fitness value so as to embody the natural law of survival of the suitable person; the calculation of the fitness value is as follows:
(a) Establishing an objective function f (theta)
Exponential overlapping kernel pulse:
dual-exponential overlapping kernel pulses:
gaussian-shaped overlapped kernel pulse:
in the formulae (4) to (6), V l () overlapping kernel pulses represented by individual # l, f (θ) l ) The objective function value represented by the unit I, and u (.) represents a step function; k =0,1,2,3, \ 8230; tau is 1 And τ 2 Respectively a slow time constant and a fast time constant of the double-exponential signal; v (.) is noise; t is S Is a sampling period; a. The i And T i Individual watchShowing the amplitude and the occurrence time of the ith nuclear pulse; σ represents the standard deviation of the Gaussian kernel pulse; and N is the number of the nuclear pulses.
(b) Calculating a fitness value
Sorting the objective function values f (theta) of all individuals in the initial population from small to large, and numbering the objective function values f (theta) as 1,2, \ 8230;
the fitness value of each individual is calculated as the fitness function:
FitValue(j)=ε(1-ε) j-1 ,j=1,2,…,PopSize (7)
the value range of epsilon is (0, 1), and the best and worst individuals in the current population are recorded.
C. Adopting selection, crossover and mutation operators of a genetic algorithm to carry out genetic operation, and carrying out the following steps (a) to (c):
(a) Selection operation
Firstly, establishing a selection array cFit:
wherein
Then, circularly generating a random number p, and when p < cFit (i), copying the corresponding ith individual into the next generation until an intermediate population is generated;
the selection operation has the function of determining whether the individual is eliminated or copied in the next generation according to the quality degree of the individual;
(b) Crossing the middle population
Randomly creating a binary vector, if a certain bit of the vector is 1, the gene comes from a first parent, if the bit of the vector is 0, the gene comes from a second parent, and the genes are combined to form an individual;
(c) Mutation operation
The variation function adopted is a Gaussian function (Gaussian), and a Gaussian distribution random number with the average value of 0 is added to each item of the parent vector; mutation is primarily to prevent precocity and accelerate convergence.
D. Calculating the objective function value f (theta) of each individual chromosome for the filial generation population generated in the step C according to formulas (4) to (6); and recording the optimal and worst individuals in the current population, if the optimal individuals in the current population are superior to the total optimal individuals, replacing the total optimal with the current optimal individuals, and otherwise, replacing the current worst with the total optimal individuals.
E. If the stopping condition of the genetic algorithm is not met, the genetic algorithm operation is carried out again from the step C; if the stopping condition of the genetic algorithm is reached, the searched optimal individual is the solution when the pulse number is N; the stop condition of the genetic algorithm may be the maximum number of repeated executions, the maximum time before the algorithm stops, or the optimum objective function value f (θ) is less than or equal to a certain value set in advance; the stopping condition may also be provided if the value of the objective function does not improve at a set number of generations, or within a set time interval.
If the number of pulses N in step (4)&1, taking N = N-1, and performing the operations of the steps (1) to (3) again to search for the optimal individual; if N =1, the number of comparison pulses N is 1,2,3 \8230, and the optimum individual V having the smallest value of objective function f (theta), f (theta) is obtained opt (t) is the optimal decomposition form of the original overlapped kernel pulse, and the chromosome of the original overlapped kernel pulse is decoded to obtain the parameters of each kernel pulse.
The decomposition of the energy spectrum overlapping peak is completed through the steps (1) to (4).
The method for performing overlapped nuclear pulse decomposition based on the population search technology searches the optimal combination of the nuclear pulses in the global sense to realize the decomposition of the overlapped nuclear pulses and further acquire the parameters of each nuclear pulse. The processing reduces the probability of forced counting or discarding processing due to the problem of overlapping interference, namely, the situation of counting more or less pulses is reduced; meanwhile, the effectiveness judgment and the parameter identification of the pulse are not obtained by single acquisition, but are realized by the 'useful' degree and the waveform parameter matching degree of the pulse, so that the 'minimum loss' of the original pulse is ensured. The accuracy and the reliability of the radioactivity measurement are improved; the method is beneficial to analyzing the fluctuation of signal parameters caused by the change of response characteristics of the detector and subsequent circuits thereof, such as the fluctuation of time constants of exponential or double-exponential pulse signals; the method has important significance for the verification of a nuclear instrument waveform forming algorithm and an energy spectrum drift correction algorithm, the analysis of the response characteristic of a measuring circuit, the analysis of the change relation of parameters along with time and external conditions, the acquisition of subsequent nuclear pulse parameters and other processes.
Although the above-mentioned embodiments of the present invention have been described in detail for the decomposition of overlapped nuclear pulses, it should be understood that the above description is only an embodiment of the present invention, and the present invention can be used for decomposing other types of overlapped nuclear pulses, and any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
The invention is funded by a scientific and technological support plan 2014GZ0020 of Sichuan province and a key project 13ZA0066 of a teaching hall of Sichuan province.

Claims (1)

1. A method for decomposing overlapped nuclear pulses is characterized by comprising the following specific steps:
(1) the original overlapping nuclear pulses to be decomposed obtained in the radioactivity measurement are represented as a linear sum of the N nuclear pulses as follows:
for an exponentially overlapping kernel pulse,
for a bi-exponential overlapping kernel pulse,
for a gaussian-shaped overlapping kernel pulse,
in formulas (1) to (3), u (.) represents a step function; k =0,1,2,3, \ 8230; tau is 1 And τ 2 Respectively a slow time constant and a fast time constant of the double-exponential signal; v (.) is noise; t is a unit of S Is a sampling period; a. The i And T i Respectively representing the amplitude and the occurrence time of the ith nuclear pulse; σ represents the standard deviation of the Gaussian kernel pulse; n is the number of nuclear pulses;
(2) considering the parameter combination of N nuclear pulses as a chromosome, the composition of each chromosome gene is one of the following methods (a), (b) and (c):
(a) For an overlapped kernel pulse consisting of N exponential kernel pulses, the amplitude A of each exponential kernel pulse i And time of occurrence T i Respectively corresponding to one gene, the decay time constant tau of exponential nuclear pulse corresponds to one gene, and each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N τT 1 T 2 …T N ];
(b) For an overlapped nuclear pulse consisting of N bi-exponential nuclear pulses, the amplitude A of each bi-exponential nuclear pulse i And time of occurrence T i Time constant tau of double-exponential nuclear pulse corresponding to one gene respectively 1 And τ 2 Each corresponds to a gene, each chromosome has total 2N +2 genes, namely [ A ] 1 A 2 …A N τ 1 τ 2 T 1 T 2 …T N ];
(c) For an overlapped kernel pulse consisting of N Gaussian kernel pulses, the amplitude A of each Gaussian kernel pulse i And time of occurrence T i Respectively corresponding to one gene, the standard deviation sigma of the Gaussian nuclear pulse corresponds to one gene, and each chromosome has 2N +1 genes, namely [ A ] 1 A 2 …A N σT 1 T 2 …T N ];
(3) Performing population initialization on the chromosomes combined in the step (2), taking the error between the overlapped nuclear pulse represented by the individual and the original overlapped nuclear pulse as a target function, constructing a fitness function, and obtaining an optimal individual by adopting selection, intersection and mutation operators of a genetic algorithm through multi-generation operation; the objective function is realized by the following method:
for exponentially overlapping kernel pulses
For dual exponential type overlapping kernel pulses
For overlapping kernel pulses of Gaussian type
In the formulae (4) to (6), V l () overlapping kernel pulses represented by individual # l, f (θ) l ) The objective function value expressed by the ith individual is represented by u (. -) which represents a step function; k =0,1,2,3, \8230; tau is 1 And τ 2 Respectively a slow time constant and a fast time constant of the double-exponential signal; v (.) is noise; t is S Is a sampling period; a. The i And T i Respectively representing the amplitude and the occurrence time of the ith nuclear pulse; σ represents the standard deviation of the Gaussian kernel pulse; n is the number of nuclear pulses;
the fitness function is realized according to the following method:
the objective function values f (theta) of all individuals in the initial population are sorted from small to large, and are numbered as 1,2, \ 8230, popSize, and the fitness value of each individual is as follows:
FitValue(j)=ε(1-ε) j-1 ,j=1,2,…,PopSize (7)
the value range of epsilon is (0, 1), and the optimal individuals and the worst individuals in the current population are recorded;
(4) if the pulse number N is larger than 1, taking N = N-1, and performing the operations of the steps (1) to (3) again to search for the optimal individual; if N =1, the number of comparison pulses N is 1,2,3 \8230, and the optimal individual with the minimum objective function value is the optimal decomposition form of the original overlapped nuclear pulse, and the chromosome of the optimal individual is decoded to obtain the parameters of each nuclear pulse.
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