CN105989410A - Overlap kernel pulse separation method - Google Patents

Abstract

The invention discloses an overlap kernel pulse separation method, which comprises the following steps: firstly, expressing an original overlap kernel pulse to be separated, which is obtained in radiometry, as the linear sum of N nuclear pulses; then, taking the parameter composition of the N nuclear pulses as a chromosome; and finally, taking the error of the overlap kernel pulse represented by an individual and the original overlap kernel pulse as a target function, adopting the selection, cross and mutation operators of a genetic algorithm, and obtaining an optimal individual after a multi-generation operation so as to obtain the parameter value of each pulse, i.e. realizing the separation of the overlap kernel pulse. When N takes different values, the overlap kernel pulse is subjected to the same separation to obtain new optimal individuals, and the optimal individual with a minimum target function value is selected from the optimal individuals to serve as a final solution. A result indicates that the overlap kernel pulse separation method based on a population searching technology is an optimal combination for searching the kernel pulse from the global meaning to realize the separation of the overlap kernel pulse so as to obtain the parameter of each kernel pulse.

Description

A kind of overlap kernel impulse decomposition method

Technical field

The present invention relates to a kind of overlap kernel impulse decomposition method.

Background technology

In carrying out radiometry, the acquisition of core pulse signal and process are important steps.Along with the development of high speed integrated circuit, digital forming technology has become the important method that core pulse signal processes, substantially increases the performance of nuclear instrument.And it practice, the overlap of adjacent core pulse is inevitable, particularly when high-speed counting, from the point of view of this is for present waveshaping technique, remain the difficult problem being difficult to Yu decomposing.In recent years, both at home and abroad core pulse collection, identify, carried out more in-depth study in terms of decomposition, these methods often use the method giving up overlapping pulses.Further, since detector and the fluctuation of subsequent conditioning circuit response characteristic thereof, will certainly affect concordance and the stability of signal parameter, at a high speed, high-precision circuit system also can be such.Such as, the acquisition of slow time constant fast to index or Double exponential pulse signal, it will be appreciated that detector and subsequent conditioning circuit response characteristic thereof, this is significant for carrying out the research such as nuclear instrument waveform shaping, energy Frequency bias.After shaping for Gauss, decomposition and identification, its decomposition and the identification problem of signal are always a technical barrier being worth research.Patent of the present invention is for typical case's core pulse signal, it is proposed that the decomposition method of overlap kernel pulse.This checking to shaping Algorithm, the analysis of the response characteristic of measuring circuit, in time and the variation relation analysis of external condition, and the process such as the acquisition of follow-up core pulse parameter is significant for parameter.

Summary of the invention

It is an object of the invention to open a kind of overlap kernel impulse decomposition method.The method to some extent solves adjacent core pulse and is difficult to accurately extract the technical barrier of relevant information because of overlapping, and this has greater significance for improving radiometric precision.

Overlap kernel pulse is decomposed and 1.～is 4. realized by step in detail below by the present invention.

The original overlap kernel pulse that 1. being intended to obtained in radiometry decomposed by step be expressed as the linear of N number of core pulse and, depending on number N of core pulse should be according to the concrete condition of the overlap kernel pulse to be decomposed.

2. the parameter of N number of core pulse is combined by step regards a chromosome as, the composition of each chromogene one of (a), (b), (c) as follows:

A () is for the overlap kernel pulse being made up of N number of index core pulse, amplitude A of each index core pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of damping time constant τ of index core pulse, each chromosome has 2N+1 gene, i.e. [A₁ A₂…A_N τT₁ T₂…T_N], gene order alterable；

B () is for the overlap kernel pulse being made up of N number of pair of index core pulse, amplitude A of each pair of index core pulse_iWith time of origin T_iThe most corresponding gene, the timeconstantτ of double index core pulses₁And τ₂Each corresponding gene, each chromosome has 2N+2 gene, i.e. [A₁ A₂…A_N τ₁ τ₂T₁ T₂…T_N], gene order alterable；

C () is for the overlap kernel pulse being made up of N number of gaussian kernel pulse, amplitude A of each gaussian kernel pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of the standard deviation sigma of gaussian kernel pulse, each chromosome has 2N+1 gene, i.e. [A₁ A₂…A_Nσ T₁ T₂…T_N], gene order alterable.

The chromosome that 2. 3. step combined by step carries out initialization of population, as object function and fitness function is constructed using the error by the overlap kernel pulse represented by individuality Yu original overlap kernel pulse, use the selection of genetic algorithm, intersection, mutation operator, after too much generation operation, obtain optimum individual；This step i.e. step genetic algorithm 3. is specifically realized by following A, B, C, D, E link.

A, initialization of population

Establishment has equally distributed initial population, depending on the individual amount PopSize of initial population can be by the waveform of overlap kernel pulse, depending on the span of each gene is according to overlap kernel pulse characteristic.

B, the calculating of ideal adaptation angle value, as follows:

(a) by the error of the overlap kernel pulse represented by individuality and original overlap kernel pulse as object function,

B () seeks fitness value by the arrangement sequence number of individual goal functional value, and record optimum and worst individuality in current group.

C, the employing selection of genetic algorithm, intersection, mutation operator carry out genetic manipulation, generate progeny population.

D, the progeny population generating C step calculate the fitness value of each individual chromosome, optimum and worst individuality in record current group, if optimum individual is better than total optimum individual in current group, then replace total optimum with current optimum individual, otherwise the most worst with total optimum replacement.

If E does not reaches the stop condition of genetic algorithm, start to re-start genetic algorithm computing from C step；If reaching the stop condition of genetic algorithm, then the optimum individual searched be exactly umber of pulse be solution during N.

The stop condition of genetic algorithm can be maximum repeat number of times, algorithm stop before maximum time or optimization objective function value less than or equal to certain value being previously set；If target function value does not improve at the algebraically set, or improvement can be as stop condition yet in the time interval set.

If step 4. umber of pulse N > 1, then take N=N-1, re-start step computing 1.～3. to search optimum individual；If N=1, then compare umber of pulse N and be respectively 1,2,3 ... time these optimum individuals target function value, the optimum individual that target function value is minimum is exactly the optimal Decomposition form of original overlap kernel pulse, obtains the parameter of each core pulse after the decoding of its chromosome.

1. the decomposition of overlap kernel pulse～is the most i.e. completed by above step.

The invention has the beneficial effects as follows:

In carrying out radiometry, the overlap of adjacent core pulse is inevitable, and particularly when high-speed counting, overlapping phenomenon is the most of common occurrence and even more serious, and this brings difficulty to the acquisition of waveform shaping and nuclear signal parameter.In recent years, both at home and abroad core pulse collection, identify, carried out more in-depth study in terms of decomposition, these methods often use the method giving up overlapping pulses.Patent of the present invention is for typical case's core pulse signal, it is proposed that the decomposition method of overlap kernel pulse based on population technology, searches for the optimum combination of core pulse from global sense, to realize the decomposition of overlap kernel pulse, and then obtains the parameter of wherein each core pulse.Greatly reduce the rejection rate of overlap kernel pulse, improve radiometric accuracy and credibility；Beneficially analyze the undulatory property of the signal parameter caused by the change of detector and subsequent conditioning circuit response characteristic thereof, such as, index or the undulatory property of Double exponential pulse signal time constant；This for nuclear instrument waveform shaping algorithm and can the checking of Frequency bias correct algorithm, the analysis of the response characteristic of measuring circuit, in time and the variation relation analysis of external condition, and the process such as the acquisition of follow-up core pulse parameter is significant for parameter.

Accompanying drawing explanation

Fig. 1 is the flow chart of the inventive method.

Detailed description of the invention

Elaborating embodiments of the invention below in conjunction with the accompanying drawings, the present embodiment is implemented under premised on technical solution of the present invention, gives detailed embodiment and process, but protection scope of the present invention is not limited to following embodiment.

If the overlap kernel pulse that being intended to obtained in radiometry carries out decomposing is V (t), uses this method that overlap kernel pulse is decomposed and 1.～4. carry out by following concrete steps.

Original overlap kernel pulse V (t) that 1. being intended to obtained in radiometry decomposed by step carry out discretization and be expressed as the linear of N number of core pulse and:

For exponential type overlap kernel pulse

$V\left({\mathrm{kT}}_s\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left[u({\mathrm{kT}}_s-T_i)A_i{e}^{-({\mathrm{kT}}_s-T_i)/\mathrm{\τ}}\right]+v\left({\mathrm{kT}}_s\right)---\left(1\right)$

For double exponential type overlap kernel pulses

$V\left({\mathrm{kT}}_s\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left[u({\mathrm{kT}}_s-T_i)A_i(e^{-({\mathrm{kT}}_s-T_i)/{\mathrm{\τ}}_1}-e^{-({\mathrm{kT}}_s-T_i)/{\mathrm{\τ}}_2})\right]+v\left({\mathrm{kT}}_s\right)---\left(2\right)$

For Gaussian overlap kernel pulse

$V\left({\mathrm{kT}}_s\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left[\frac{A_i}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{\frac{-{({\mathrm{kT}}_s-T_i)}^2}{{2\mathrm{\σ}}^2}}\right]+v\left({\mathrm{kT}}_s\right)---\left(3\right)$

In formula (1)～(3), u (.) represents jump function；K=0,1,2,3 ...；τ₁And τ₂It is respectively double slow time constant of exponential signal and fast time constant；V (.) is noise；T_SFor the sampling period；A_iAnd T_iRepresent amplitude and the time of origin of i-th core pulse respectively；σ represents the standard deviation of gaussian kernel pulse；N is the number of core pulse, should be according to the concrete condition of the overlap kernel pulse to be decomposed depending on.

2. the parameter of N number of core pulse is combined by step regards a chromosome as, the composition of each chromogene one of (a), (b), (c) as follows:

A () is for the overlap kernel pulse being made up of N number of index core pulse, amplitude A of each index core pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of damping time constant τ of index core pulse, each chromosome has 2N+1 gene, i.e. [A₁ A₂…A_N τT₁ T₂…T_N], gene order alterable；

B () is for the overlap kernel pulse being made up of N number of pair of index core pulse, amplitude A of each pair of index core pulse_iWith time of origin T_iThe most corresponding gene, the timeconstantτ of double index core pulses₁And τ₂Each corresponding gene, each chromosome has 2N+2 gene, i.e. [A₁ A₂…A_N τ₁ τ₂T₁ T₂…T_N], gene order alterable；

C () is for the overlap kernel pulse being made up of N number of gaussian kernel pulse, amplitude A of each gaussian kernel pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of the standard deviation sigma of gaussian kernel pulse, each chromosome has 2N+1 gene, i.e. [A₁ A₂…A_N σ T₁ T₂…T_N], gene order alterable.

The chromosome that 2. 3. step combined by step carries out initialization of population, as object function and fitness function is constructed using the error by the overlap kernel pulse represented by individuality Yu original overlap kernel pulse, use the selection of genetic algorithm, intersection, mutation operator, after too much generation operation, obtain optimum individual；This step i.e. step genetic algorithm 3. is specifically realized by following A, B, C, D, E link.

A, initialization of population

Establishment has equally distributed initial population, depending on the individual amount PopSize of initial population can be by the waveform of overlap kernel pulse, depending on the span of each gene is according to overlap kernel pulse characteristic.

B, the calculating of ideal adaptation angle value

Fitness value reflects the individual power to adaptive capacity to environment, uses fitness value can control individual survival chance well, to embody the natural law of survival of the fittest；The calculating of fitness value is as follows:

A () sets up object function f (θ)

Exponential type overlap kernel pulse:

$\begin{array}{c}f\left({\mathrm{\θ}}_l\right)=\underset{k}{\mathrm{\Σ}}{[V\left({\mathrm{kT}}_s\right)-V_l\left({\mathrm{kT}}_s\right)]}^2\\ =\underset{k}{\mathrm{\Σ}}\left\{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\right[u({\mathrm{kT}}_s-T_j)A_j{e}^{-({\mathrm{kT}}_s-T_j)/\mathrm{\τ}}]+v\left({\mathrm{kT}}_s\right)\\ -\underset{l=1}{\overset{M}{\mathrm{\Σ}}}\left[u({\mathrm{kT}}_s-T_l)A_l{e}^{-({\mathrm{kT}}_s-T_l)/\mathrm{\τ}}\right]{\}}^2\end{array}---\left(4\right)$

Double exponential type overlap kernel pulses:

$\begin{array}{c}f\left({\mathrm{\θ}}_l\right)=\underset{k}{\mathrm{\Σ}}{[V\left({\mathrm{kT}}_s\right)-V_l\left({\mathrm{kT}}_s\right)]}^2\\ =\underset{k}{\mathrm{\Σ}}\left\{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\right[u({\mathrm{kT}}_s-T_j)A_j(e^{-({\mathrm{kT}}_s-T_j)/{\mathrm{\τ}}_1}-e^{-({\mathrm{kT}}_s-T_j)/{\mathrm{\τ}}_2})]+v\left({\mathrm{kT}}_s\right)\\ -\underset{l=1}{\overset{M}{\mathrm{\Σ}}}\left[u({\mathrm{kT}}_s-T_l)A_l(e^{-({\mathrm{kT}}_s-T_l)/{\mathrm{\τ}}_1}-e^{-({\mathrm{kT}}_s-T_l)/{\mathrm{\τ}}_2})\right]{\}}^2\end{array}---\left(5\right)$

Gaussian overlap kernel pulse:

$\begin{array}{c}f\left({\mathrm{\θ}}_l\right)=\underset{k}{\mathrm{\Σ}}{[V\left({\mathrm{kT}}_s\right)-V_l\left({\mathrm{kT}}_s\right)]}^2\\ =\underset{k}{\mathrm{\Σ}}\left\{\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\right[\frac{A_j}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{\frac{-{({\mathrm{kT}}_s-T_j)}^2}{2{\mathrm{\σ}}^2}}]+v\left({\mathrm{kT}}_s\right)\\ -\underset{l=1}{\overset{N}{\mathrm{\Σ}}}\left[\frac{A_l}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{\frac{-{({\mathrm{kT}}_s-T_l)}^2}{{2\mathrm{\σ}}^2}}\right]{\}}^2\end{array}---\left(6\right)$

In formula (4)～(6), V_l(.) is the overlap kernel pulse represented by l individuality, f (θ_l) it is the target function value represented by l individuality, u (.) represents jump function；K=0,1,2,3 ...；τ₁And τ₂It is respectively double slow time constant of exponential signal and fast time constant；V (.) is noise；T_SFor the sampling period；A_iAnd T_iRepresent amplitude and the time of origin of i-th core pulse respectively；σ represents the standard deviation of gaussian kernel pulse；N is the number of core pulse.

B () seeks fitness value

The target function value f (θ) of individualities all to initial population carries out ascending sequence, and number consecutively is 1,2 ..., PopSize；

Fitness value by the following fitness function each individuality of calculating:

FitValue (j)=ε (1-ε)^j-1, j=1,2 ..., PopSize (7)

The span of ε is (0,1), optimum and worst individuality in record current group.

C, the employing selection of genetic algorithm, intersection, mutation operator carry out genetic manipulation, carry out by following (a)～(c) step:

(a) Selecting operation

First set up and select array cFit:

$\mathrm{cFit}\left(i\right)=\frac{\underset{k=1}{\overset{i}{\mathrm{\Σ}}}\mathrm{FitValue}\left(k\right)}{S}---\left(8\right)$

Wherein

$S=\underset{j=1}{\overset{\mathrm{popsize}}{\mathrm{\Σ}}}\mathrm{FitValue}\left(j\right)---\left(9\right)$

Then, circulation produces random number p, when p is < during cFit (i), in corresponding i-th individual replicate to the next generation, until generating transitional population；

The effect of Selecting operation is to determine that it can be eliminated or be replicated the next generation according to individual good and bad degree；

B transitional population is intersected by ()

Creating binary vector at random, if this certain position of vector is 1, then this gene is from first former generation, if 0, then this gene is from second former generation, combines these genes and forms body one by one；

(c) mutation operation

The variation function used is Gaussian function (Gaussian), the random number that a Gauss distribution, average are 0 is added to each item of former generation's vector；Mutation operation is primarily to prevent precocious and accelerate convergence.

D, the progeny population generating C step are calculated the target function value f (θ) of each individual chromosome by formula (4)～(6)；Optimum and worst individuality in record current group, if optimum individual is better than total optimum individual in current group, then replaces total optimum with current optimum individual, otherwise the most worst with total optimum replacement.

If E does not reaches the stop condition of genetic algorithm, start to re-start genetic algorithm computing from C step；If reaching the stop condition of genetic algorithm, then the optimum individual searched be exactly umber of pulse be solution during N；The stop condition of genetic algorithm can be maximum repeat number of times, algorithm stop before maximum time or optimization objective function value f (θ) less than or equal to certain value being previously set；If target function value does not improve at the algebraically set, or improvement can be as stop condition yet in the time interval set.

If step 4. umber of pulse N > 1, then take N=N-1, re-start step computing 1.～3. to search optimum individual；If N=1, then compare umber of pulse N and be respectively 1,2,3 ... time these optimum individuals target function value f (θ), f (θ) be minimum optimum individual V_optT () is exactly the optimal Decomposition form of original overlap kernel pulse, obtain the parameter of each core pulse after the decoding of its chromosome.

1. the decomposition of power spectrum fused peaks～is the most i.e. completed by above step.

The method carrying out overlap kernel impulse decomposition based on population search technique as mentioned above, is the optimum combination searching for core pulse from global sense, to realize the decomposition of overlap kernel pulse, and then obtains the parameter of wherein each core pulse.So process and decrease because of overlapping interference problem forced counting or the probability of giving up process, even if many meters of also pulse or less meter situation reduce；Meanwhile, the validity judge of pulse and parameter identification thereof are not to be collected by single, but are realized by its " useful " degree and waveform parameter matching degree thereof, it is ensured that " the minimum loss " of former pulse.Improve radiometric accuracy and credibility；Beneficially analyze the undulatory property of the signal parameter caused by the change of detector and subsequent conditioning circuit response characteristic thereof, such as, index or the undulatory property of Double exponential pulse signal time constant；This for nuclear instrument waveform shaping algorithm and can the checking of Frequency bias correct algorithm, the analysis of the response characteristic of measuring circuit, in time and the variation relation analysis of external condition, and the process such as the acquisition of follow-up core pulse parameter is significant for parameter.

In embodiments of the invention described above; the decomposition method of overlap kernel pulse has been described in detail; but it should be noted that; the foregoing is only one embodiment of the present of invention; other type of overlapping pulses can be decomposed by the present invention; all within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

The present invention is by Sichuan Province science and technology supporting project 2014GZ0020 and education department of Sichuan Province key project 13ZA0066 fund assistance.

Claims (2)

1. an overlap kernel impulse decomposition method, it is characterised in that specifically comprise the following steps that

1. the original overlap kernel pulse that being intended to obtained in radiometry being carried out decomposes be expressed as the linear of N number of core pulse and: for exponential type overlap kernel pulse,

For double exponential type overlap kernel pulses,

For Gaussian overlap kernel pulse,

In formula (1)～(3), u (.) represents jump function；K=0,1,2,3 ...；τ₁And τ₂It is respectively double slow time constant of exponential signal and fast time constant；V (.) is noise；T_SFor the sampling period；A_iAnd T_iRepresent amplitude and the time of origin of i-th core pulse respectively；σ represents the standard deviation of gaussian kernel pulse；N is the number of core pulse；

2. the parameter of N number of core pulse is combined and regard a chromosome as, the composition of each chromogene one of (a), (b), (c) as follows:

A () is for the overlap kernel pulse being made up of N number of index core pulse, amplitude A of each index core pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of damping time constant τ of index core pulse, each chromosome has 2N+1 gene, i.e. [A₁A₂…A_NτT₁T₂…T_N], gene order alterable；

B () is for the overlap kernel pulse being made up of N number of pair of index core pulse, amplitude A of each pair of index core pulse_iWith time of origin T_iThe most corresponding gene, the timeconstantτ of double index core pulses₁And τ₂Each corresponding gene, each chromosome has 2N+2 gene, i.e. [A₁A₂…A_Nτ₁τ₂T₁T₂…T_N], gene order alterable；

C () is for the overlap kernel pulse being made up of N number of gaussian kernel pulse, amplitude A of each gaussian kernel pulse_iWith time of origin T_iThe most corresponding gene, the corresponding gene of the standard deviation sigma of gaussian kernel pulse, each chromosome has 2N+1 gene, i.e. [A₁A₂…A_NσT₁T₂…T_N], gene order alterable；

3. chromosome step 2. combined carries out initialization of population, as object function and fitness function is constructed using the error by the overlap kernel pulse represented by individuality Yu original overlap kernel pulse, use the selection of genetic algorithm, intersection, mutation operator, after too much generation operation, obtain optimum individual；

If 4. umber of pulse N > 1, then take N=N-1, re-start step computing 1.～3. to search optimum individual；If N=1, then compare umber of pulse N and be respectively 1,2,3 ... time these optimum individuals target function value, the optimum individual that target function value is minimum is exactly the optimal Decomposition form of original overlap kernel pulse, obtains the parameter of each core pulse after the decoding of its chromosome.

Overlap kernel impulse decomposition method the most according to claim 1, is characterized in that, described step 3. in using by the error of the overlap kernel pulse represented by individuality and original overlap kernel pulse as object function, realize as follows:

For exponential type overlap kernel pulse

For double exponential type overlap kernel pulses

For Gaussian overlap kernel pulse

In formula (4)～(6), V_l(.) is the overlap kernel pulse represented by l individuality, f (θ_l) it is the target function value represented by l individuality, u (.) represents jump function；K=0,1,2,3 ...；τ₁And τ₂It is respectively double slow time constant of exponential signal and fast time constant；V (.) is noise；T_SFor the sampling period；A_iAnd T_iRepresent amplitude and the time of origin of i-th core pulse respectively；σ represents the standard deviation of gaussian kernel pulse；N is the number of core pulse.