CN102298153B - Method for decomposing multiple spectral peaks during radioactive measurement - Google Patents

Abstract

The invention discloses a method for decomposing multiple spectral peaks during radioactive measurement, and the method comprises the following steps: firstly, performing background rejection on an energy spectrum acquired from radioactive measurement, thereby acquiring a net count of overlapped peaks of a to-be-decomposed spectrum section; secondly, normalizing the acquired net count of the overlapped peaks, taking normalized data as a probability density function and generating a random number which complies with the distribution of the probability density function; thirdly, establishing an initial Gaussian mixture model of the probability density function; and finally, performing iterative operation on the generated random number by adopting an expectation maximizing method till achieving convergence, updating parameters of the Gaussian mixture model and acquiring a final value, thereby finishing decomposing the overlapped peaks. The method is high in decomposing precision and is an effective method used for quantitative and qualitative analysis on radionuclide.

Description

The decomposition method at multiple spectral peak in radioactivity survey

Technical field

The present invention relates to the decomposition method at multiple spectral peak in a kind of radioactivity survey.

Background technology

In carrying out radiative gamma spectrometry, tend to occur the overlapping phenomenon of full energy peak, at the overlapping especially severe of some low-yield section full energy peak.In order to extract relevant information, the decomposition of carrying out overlap peak is very necessary, and the precision of its decomposition directly has influence on the quantitatively even qualitative analysis to radioactive nuclide.As, NaI (Tl) airborne Gamma-ray spectrometry instrument is not high to gamma-ray energy resolution, ²³⁸In U series ²¹⁴The 0.609MeV of Bi, ²³²In Th series ²⁰⁸The 0.583MeV feature gamma-rays of Tl with ¹³⁷The 0.662MeV of Cs, ¹³⁴The gamma ray spectrum summit of the 0.605MeV of Cs overlaps, thereby causes ¹³⁷Cs and ¹³⁴The Cs activity concentration calculates inaccurate, and sometimes too much because of spectrum stripping, local location can occur ¹³⁷The negative value of Cs.

Once there was the nuclear technology worker to adopt the methods such as full spectral filter technology, Gauss's least square fitting to carry out unimodal or bimodal match to the experiment spectral line; Adopt the reliable and effective filtering interference signals of wavelet analysis, extract feeble signal.But these methods are for lap for the more overlap peak of more and overlapping peak number, the shortcoming such as existence can not be decomposed or Decomposition Accuracy is relatively poor.

Summary of the invention

The object of the invention is to disclose the decomposition method at multiple spectral peak in a kind of radioactivity survey.The method has overcome the deficiency of present overlap peak decomposition method.

The present invention is achieved by the following technical solutions, and concrete steps of the present invention are as follows:

1. can carry out background rejection by spectral coverage to what wanting of obtaining in radioactivity survey carried out that overlap peak decomposes, and net peak area and each location, road corresponding to overlap peak net peak area of trying to achieve overlap peak are counted only.Each location, road is here only counted sum and is equaled the overlap peak net peak area;

2. the 1. clean counting of the overlap peak that obtains of step is carried out normalization, that is, the clean counting of overlap peak each location, road respectively divided by 1. going on foot required overlap peak net peak area, is obtained the power spectrum that area equals 1;

Required area is equaled 1 normalization power spectrum as probability density function, and adopt discrete direct sampling method to produce the random number of obeying this probability density function profiles;

The probability density function that 3. will 2. go on foot be expressed as roughly a plurality of gauss of distribution function linearity and, namely be expressed as gauss hybrid models, in the overlap peak spectral coverage that the number M of these gauss of distribution function should decompose according to wish, the concrete distribution situation of full energy peak be decided; The weights of each gauss of distribution function are initialized as 1/M usually, and the weights here refer to each gauss of distribution function shared proportion in probability density function, that is the coefficient of each gauss of distribution function in the linearity of probability density function and expression formula; The variance of each gauss of distribution function can be carried out initialization according to the guestimate of peak shape or detector energy resolution; The average of each gauss of distribution function is carried out initialization according to the roughly peak position of full energy peak in the overlap peak spectral coverage of wish decomposition; Each peak position also can be fixed up each peak position in the situation that know for sure, that is does not upgrade 4. going on foot the interative computation hourly value;

4. adopt the expectation maximization method, be Expectation Maximization (being abbreviated as EM), 2. the random number that step is produced carries out interative computation until convergence, realize gauss hybrid models weights, variance and average renewal and obtain end value, namely complete the decomposition of overlap peak; Each peak position if know for sure, the interative computation hourly value does not upgrade; The convergence here, refer to when carrying out interative computation and the difference of the parameter of computing last time (weights, variance and average) minimum.

The invention has the beneficial effects as follows:

regard overlap peak as the distinguished random signal probability density distribution of---the Special complex random signal with radioactive nature---, use GMM (the Gaussian mixture model) Function approximation capabilities that model is good, and the statistical property in the binding radioactivity measurement, adopt expectation maximization (EM, ExpectationMaximization) iterative algorithm, all measurement data are added up and classified, obtain belonging to the probability of each gauss of distribution function, this just matches with radiometric statistical property, the overlap peak decomposition of carrying out has like this guaranteed the optimum under the statistical significance, guaranteed less statistical error.The method can be decomposed the overlap peak by spectrum peak stack more than three.In a word, as long as the number of initial value and the gauss of distribution function of GMM rationally is set according to actual conditions, the accuracy that restrains in the time of just can guaranteeing iterative algorithm just can be effectively applied to the method the quantitative and qualitative analysis of radioactive nuclide.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are elaborated: the present embodiment is implemented under take technical solution of the present invention as prerequisite, has provided detailed embodiment and process, but protection scope of the present invention is not limited to following embodiment.

The present embodiment with the NaI detector surveyed by ²⁰⁶Tl spectrum peak (583keV), ²¹⁴Bi spectrum peak (609keV), ¹³⁷The overlap peak that three peaks, Cs spectrum peak (0.662MeV) consist of is example, it is decomposed, and carried out corresponding experiment to verify validity of the present invention.Concrete steps are as follows:

1. to obtain in radioactivity survey by ²⁰⁶Tl spectrum peak (583keV), ²¹⁴Bi spectrum peak (609keV), ¹³⁷The energy spectral coverage (ch195-ch260) of the overlap peak that three peaks, Cs spectrum peak (0.662MeV) consist of carry out background rejection, and the net peak area of trying to achieve overlap peak is 29262, and the clean counting in each location, road (ch195-ch260) corresponding to overlap peak net peak area.Each location, road (ch195-ch260) is here only counted sum and is equaled overlap peak net peak area 29262;

2. be that 29262 the clean counting of overlap peak carries out normalization to the 1. net peak area that obtains of step, that is, the clean counting of overlap peak each location, road (ch195-ch260) respectively divided by 1. going on foot required overlap peak net peak area 29262, is obtained the power spectrum that area equals 1;

Required area is equaled 1 normalization power spectrum as probability density function, and sampling produces the random number of obeying this probability density function profiles and amounts to 4877, and in order to guarantee 4. to go on foot the precision of computing, the number of random number can be more; The methods of sampling that adopts is following discrete direct sampling method:

At first, the discrete distribution functional form that probability density function is expressed as:

$F\left(x\right)=\underset{x_i<x}{\mathrm{\&Sigma;}}{P}_i---\left(1\right)$

Wherein: x _iBe the discrete point of discrete distribution function, i.e. location, the road sequence number (ch195-ch260) of power spectrum; P _iBe corresponding probability,

Produce random number x by formula (2) sampling and amount to 4877, namely try to achieve and obey the random number that F (x) distributes, wherein ε is for obeying [0-1] equally distributed random number:

X _F=X _I, when $\underset{i=1}{\overset{I-1}{\mathrm{\&Sigma;}}}{P}_i\&le;\mathrm{\&epsiv;}<\underset{i=1}{\overset{I}{\mathrm{\&Sigma;}}}{P}_i---\left(2\right)$

The probability density function that 3. will 2. go on foot be expressed as roughly a plurality of gauss of distribution function linearity and, namely be expressed as gauss hybrid models, as follows:

Probability density is expressed as:

$P(x,\mathrm{\&theta;})=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_i{p}_i(x;{\mathrm{\&theta;}}_i)---\left(3\right)$

In formula (3), M is the number of Gaussian distribution density function; a ₁..., a _MThe weight of each Gaussian distribution density function, and

a _i〉=0, (i=1 ..., M); p _i(x) be i Gaussian distribution density function, its average is μ _i, variance is

θ _iUnknown parameter μ _iWith

Vector representation, namely

Density function p _i(x, θ _i) form as follows:

$p_i(x,{\mathrm{\&theta;}}_i)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^{1/2}{\mathrm{\&sigma;}}_i}\exp [-\frac{1}{2}{(x-{\mathrm{\&mu;}}_i)}^2{\left({\mathrm{\&sigma;}}_i^2\right)}^{-1}]---\left(4\right)$

The parameter of whole hybrid density is θ=(a ₁..., a _Mθ ₁..., θ _M).

In the present embodiment, overlap peak spectral coverage (ch195-ch260) full energy peak that wish is decomposed is ²⁰⁶Tl spectrum peak (583keV), ²¹⁴Bi spectrum peak (609keV), ¹³⁷Cs composes three peaks, peak (0.662MeV), therefore M=3.

The weights of each gauss of distribution function are initialized as 1/M, i.e. weight a ₁=a ₂=a ₃=1/3, the weights here refer to each gauss of distribution function shared proportion in probability density function, that is the coefficient of each gauss of distribution function in the linearity of probability density function and expression formula (3);

In the present embodiment, the average---peak position of each full energy peak---of each gauss of distribution function of overlap peak spectral coverage (ch195-ch260) that wish is decomposed is known, peak position u ₁, u ₂, u ₃Be respectively 210,218,239 locations, road, therefore EM interative computation hourly value does not upgrade in the back; Otherwise, provide u ₁, u ₂, u ₃Initialization value, and EM interative computation hourly value (peak position) must upgrade in the back;

The variance of each gauss of distribution function can be carried out initialization according to the guestimate of peak shape or detector energy resolution; In the present embodiment, according to the peak shape guestimate, ²⁰⁶The initial variance at Tl spectrum peak (583keV) Be set to 50; ²¹⁴Bi spectrum peak (609keV) and ¹³⁷The initial variance at Cs spectrum peak (0.662MeV)

Revise according to the relational expression (5) of detector energy resolution and peak position:

$R_D=\frac{\mathrm{FWHM}}{\stackrel{\&OverBar;}{V}}100\%=\frac{{2.355\mathrm{\&sigma;}}_D}{\stackrel{\&OverBar;}{V}}100\%---\left(5\right)$

In formula (5): R _DExpression energy resolution (%), FWHM represents halfwidth (keV),

Expression peak position (keV), σ _DExpression mean square deviation (keV).

Try to achieve initial variance

Be 54.56,

Be 64.47.

4. adopt the expectation maximization method, be Expectation Maximization (being abbreviated as EM), to carry out interative computation until convergence realizes the renewal of each gauss hybrid models weights and obtains end value in 4877 random number substitution formulas (6) that 2. step produces;

To carry out interative computation until convergence realizes the renewal of each gauss hybrid models variance and obtains end value in 4877 random number substitution formulas (8) that 2. step produces; In order to shorten computing time or to avoid converging to local minimum, can first try to achieve when each interative computation

So back-pushed-type (5) correction obtains

With

In the present embodiment, with the difference of last iteration computing parameters obtained less than 10 ^-4The time be called convergence, difference can be chosen as the case may be;

In the present embodiment, the average of each gauss of distribution function---peak position of each full energy peak---is known, so EM interative computation hourly value does not upgrade; Otherwise, average u ₁, u ₂, u ₃Should carry out interative computation until restrain and obtain end value by formula (7);

$a_l^{\mathrm{new}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}p\left(l\right|x_i,{\mathrm{\&theta;}}^g)---\left(6\right)$

${\mathrm{\&mu;}}_l^{\mathrm{new}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_{i}p\left(l\right|x_i,{\mathrm{\&theta;}}^g)}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}p\left(l\right|x_i,{\mathrm{\&theta;}}^g)}---\left(7\right)$

${\mathrm{\&sigma;}}_l^{2\left(\mathrm{new}\right)}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}p\left(l\right|x_i,{\mathrm{\&theta;}}^g){(x_i-{\mathrm{\&mu;}}_l^{\mathrm{new}})}^2}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}p\left(l\right|x_i,{\mathrm{\&theta;}}^g)}---\left(8\right)$

In formula (6)～(8), 2. N goes on foot the number of the random number that produces, x _iBe random number, a _l, μ _lAnd

Respectively weight, average and the variance of each gauss of distribution function;

By 1. above～4. the step is namely completed the decomposition of overlap peak.

The probability density distribution that this method is regarded overlap peak as the distinguished random signal---the Special complex random signal with radioactive nature---, use the good Function approximation capabilities of GMM model, and the statistical property in the binding radioactivity measurement, adopt expectation maximization (EM) iterative algorithm, all measurement data are added up and classified, obtain belonging to the probability of each gauss of distribution function, this just matches with radiometric statistical property.A large amount of emulation and experimental results show, as long as the initial value of GMM rationally is set according to actual conditions, the overlap peak decomposition of carrying out has like this guaranteed the optimum under the statistical significance, (error is usually less than 5% to have guaranteed less statistical error, statistical property better, the slightly large time error of peak separation is close to zero), therefore, the method can be effectively applied to the quantitative and qualitative analysis of radioactive nuclide.

In the embodiment of the invention described above; decomposition to overlap peak has been described in detail; but it should be noted that; the above is only one embodiment of the present of invention; the present invention can decompose the different spectral coverage of other various rays, the overlapping spectrum peak of different peak numbers equally; within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (7)

1. the decomposition method at multiple spectral peak in radioactivity survey, is characterized in that, concrete steps are as follows:

1. the power spectrum that obtains in radioactivity survey is carried out background rejection, obtain the clean counting that wish is decomposed the spectral coverage overlap peak;

2. the clean counting of the overlap peak that obtains is carried out normalization, the data after normalization as probability density function, and are produced the random number of obeying this probability density function profiles;

3. set up the initial Gaussian mixture model of this probability density function, method is as follows:

With probability density function be expressed as roughly a plurality of gauss of distribution function linearity and, namely be expressed as gauss hybrid models, in the overlap peak spectral coverage that the number M of these gauss of distribution function should decompose according to wish, the concrete distribution situation of full energy peak be decided; The weights of each gauss of distribution function are initialized as 1/M, and the weights here refer to each gauss of distribution function shared proportion in probability density function, that is the coefficient of each gauss of distribution function in the linearity of probability density function and expression formula; The variance of each gauss of distribution function is carried out initialization according to the guestimate of peak shape or detector energy resolution; The average of each gauss of distribution function is carried out initialization according to the roughly peak position of full energy peak in the overlap peak spectral coverage of wish decomposition;

4. adopt the expectation maximization method that the random number that produces is carried out interative computation until convergence realizes the renewal of each parameter of gauss hybrid models and obtains end value, namely complete the decomposition of overlap peak.

2. the decomposition method at multiple spectral peak in radioactivity survey according to claim 1, is characterized in that, described 1. middle background rejection refers to ask for the net area that wish is decomposed the spectral coverage overlap peak.

3. the decomposition method at multiple spectral peak in radioactivity survey according to claim 2, is characterized in that, described 1. in the clean counting of overlap peak, refer to the counting of each location, road of overlap peak after background rejection.

4. the decomposition method at multiple spectral peak in radioactivity survey according to claim 3, it is characterized in that, describedly the clean counting of the overlap peak that obtains is carried out normalization in 2., the clean counting of overlap peak each location, road that refers to try to achieve obtains respectively divided by the net area after background rejection the power spectrum that area equals 1.

5. the decomposition method at multiple spectral peak in radioactivity survey according to claim 4, it is characterized in that, the described 2. middle random number of obeying this probability density function profiles that produces, refer to that required area is equaled 1 power spectrum is used as probability density function, and adopt discrete direct sampling method to produce the random number of obeying this probability density function profiles.

6. the decomposition method at multiple spectral peak in radioactivity survey according to claim 5, it is characterized in that, described 4. in interative computation, refer to adopt the expectation maximization method to calculate the described random number that produces in 2., weights, variance and the average of each gauss of distribution function in are 3. upgraded.

7. the decomposition method at multiple spectral peak in radioactivity survey according to claim 6, is characterized in that, described 4. in the convergence, refer to when carrying out interative computation and the difference of the weights of computing last time, variance and average minimum.

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