CN110376638A - Peak searching method based on deconvolution iterative ray energy spectrum resolution enhancement - Google Patents
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Abstract
The invention discloses a peak searching method based on deconvolution iteration ray energy spectrum resolution enhancement, which can ensure the accuracy of peak searching and improve the effectiveness of peak searching. The peak searching method based on deconvolution iterative ray energy spectrum resolution enhancement firstly obtains response energy spectrums of rays with different energy through response of a Monte Carlo simulation detector to ray energy spectrums, and establishes a response matrix H; measuring by a detector to obtain an energy spectrum vector y; and then calculating by using Gold deconvolution iteration, and searching peaks of the energy spectrum obtained after Gold deconvolution iteration by using a first derivative peak searching method. The peak searching method based on the resolution enhancement of the deconvolution iteration ray energy spectrum can improve the energy resolution of the ray energy spectrum, weaken the asymmetric severity of the ray energy spectrum and ensure the accuracy of peak searching.
Description
Technical field
The present invention relates to nuclear radiation spectral measurement and analyses, especially a kind of to be based on deconvolution iteration ray energy spectrum resolution ratio
The Peak Search Method of enhancing.
Background technique
It is well-known: usually radioactivity to be carried out using ray energy spectrum measurement method in nuclear radiation detection qualitative and quantitative
Analysis, processing and analysis to ray energy spectrum data are the foundations of qualitative and quantitative analysis.The analysis of ray energy spectrum data includes:
Gamma-spectrometric data is smooth, peak-seeking, peak shape fitting etc., wherein peak-seeking is the basis of peak shape fitting, while be also power spectrum automatically parse and
The basis of nuclide identification.Common Peak Search Method has: derivative method, Symmetric Zero area-method, covariance method etc..The basic think of of derivative method
Think it is that peak position is maximum, then the single order at this, second order, three order derivatives have corresponding feature, pass through the spy of derivative
Sign can identify peak position；The basic thought of Symmetric Zero area-method is the window function and modal data progress convolution for being zero by an area
Transformation, there are peaks in the place that transformation results are not zero；The basic thought of covariance method be with a peak-shaped function and modal data by
Section is fitted, and fitting result illustrates it is peak if peak value is relatively high, and the peak value of fitting the big more can determine that it is peak.
The peak-seeking of these methods power spectrum high for energy resolution (such as HPGe- gamma spectrum) has preferable effect,
But it is sought if the power spectrum (such as NaI- gamma spectrum, LaBr3- gamma spectrum, PIPS- alpha energy spectrum etc.) low for energy resolution, repeatability is big
Peak effect is poor.
Summary of the invention
Technical problem to be solved by the invention is to provide one kind can ensure the accuracy of peak-seeking, improves the effective of peak-seeking
Property based on deconvolution iteration ray energy spectrum resolution ratio enhancing Peak Search Method.
The technical solution adopted by the present invention to solve the technical problems is: being increased based on deconvolution iteration ray energy spectrum resolution ratio
Strong Peak Search Method, comprising the following steps:
S1, detector measurement radioactive substance obtain power spectrum；Establish response matrix；
Assuming that input ray signal function is f (x), detector response function is h (x), and output spectrum signal function is y
(x), then output spectrum be input signal and detector response function convolution, due to power spectrum be discrete system, then:
Above formula is transformed to matrix form again:
Y=Hf, (2)
Wherein H is response matrix, 2N-1 × N size, and the length of y is 2N-1, i.e., ray energy spectrum data obtained, f's
Length is N；Matrix form is shown below after expansion:
(3) formula is done such as down conversion:
HTY=HTHf. (4)
Therefore:
It enables: A=HTH, then A is Teoplitz (Toeplitz) matrix；Using Gold iterative algorithm, iteration form is such as
Under:
Wherein:
A=HTH, y '=HTy；
S2, A=H is calculatedTH, y '=HTy；
Initial vector f (0)=[1,1,1 ..., 1] is arranged at the n-th=0 in S3, basis (6) formulaT；
Maximum number of iterations L required for S4, setting；
S5, basis (6) formula iteratively solve f(L)；
If S6, n=L, stop iteration, exports as a result, otherwise: n=n+1；Return to S3；
The first derivative of S7, node-by-node algorithm deconvolution power spectrum；
Wherein, KbFor normaliztion constant, AjFor smooth coefficients, yi+jFor the raw spectral data in the i-th road+j,Become for i-th
Modal data after changing；
S8, increase direction along i, retrieve first derivative, numerical value is by just becoming negative, the corresponding road location of zero crossing, as peak position, such as
Fruit thinks that the road location nearest from zero is peak position without the road location of just zero passage at this time；
S9, the differentiation that peak position obtained in S8 is carried out to effective peak position；
S91, the width for examining peak: the distance between positive and negative maximum of first derivative D meets:
0.8FWHM≤D≤3FWHM；
S92, statistic discriminance；
On the both sides at peak, first derivative is just equal to 0 by negative become, and obtains left margin Chleft and right margin Chright, counts
Peak width W=Chright-Chleft+1 is calculated, is then differentiated by following formula:
Wherein, W is peak width, NpFor cumulative tale, ApFor " net " peak area；Think if the peak position for meeting above formula
It is effective peak position；
The calculating of S10, accurate peak position；
It is respectively taken together on effective peak position both sides, forms three points with peak position road, seek the secondary multinomial of these three point compositions
Formula is the corresponding accurate peak position of effective peak position according to the corresponding road location of the quadratic polynomial maximum value；
S11, output peak position.
The beneficial effects of the present invention are: the peak-seeking of the present invention based on the enhancing of deconvolution iteration ray energy spectrum resolution ratio
Method can be improved the energy resolution of ray energy spectrum, weaken its asymmetric severity, it can be ensured that peak-seeking it is accurate
Property, improve peak-seeking validity.
Detailed description of the invention
Fig. 1 is the process of the Peak Search Method based on the enhancing of deconvolution iteration ray energy spectrum resolution ratio in the embodiment of the present invention
Figure；
Fig. 2 is LaBr3Detector detection152First derivative peak-seeking Comparative result after the gamma spectrum original spectrum of Eu and deconvolution
Figure；
Fig. 3 is239First derivative peak-seeking comparative result figure after Pu- alpha energy spectrum original spectrum and deconvolution.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
As shown in Figure 1, the Peak Search Method of the present invention based on the enhancing of deconvolution iteration ray energy spectrum resolution ratio, including
Following steps:
S1, detector measurement radioactive substance obtain power spectrum；Establish response matrix；
Assuming that input ray signal function is f (x), detector response function is h (x), and output spectrum signal function is y
(x), then output spectrum be input signal and detector response function convolution, due to power spectrum be discrete system, then:
Above formula is transformed to matrix form again:
Y=Hf, (2)
Wherein H is response matrix, 2N-1 × N size, and the length of y is 2N-1, i.e., ray energy spectrum data obtained, f's
Length is N；Matrix form is shown below after expansion:
(3) formula is done such as down conversion:
HTY=HTHf. (4)
Therefore:
It enables: A=HTH, then A is Teoplitz (Toeplitz) matrix；Using Gold iterative algorithm, iteration form is such as
Under:
Wherein:
A=HTH, y '=HTy；
S2, A=H is calculatedTH, y '=HTy；
Initial vector f (0)=[1,1,1 ..., 1] is arranged at the n-th=0 in S3, basis (6) formulaT；
Maximum number of iterations L required for S4, setting；
S5, basis (6) formula iteratively solve f(L)；
If S6, n=L, stop iteration, exports as a result, otherwise: n=n+1；Return to S3；
The first derivative of S7, node-by-node algorithm deconvolution power spectrum；
Wherein, KbFor normaliztion constant, AjFor smooth coefficients, yi+jFor the raw spectral data in the i-th road+j,Become for i-th
Modal data after changing；
S8, increase direction along i, retrieve first derivative, numerical value is by just becoming negative, the corresponding road location of zero crossing, as peak position, such as
Fruit thinks that the road location nearest from zero is peak position without the road location of just zero passage at this time；
S9, the differentiation that peak position obtained in S8 is carried out to effective peak position；
S91, the width for examining peak: the distance between positive and negative maximum of first derivative D meets:
0.8FWHM≤D≤3FWHM；
S92, statistic discriminance；
On the both sides at peak, first derivative is just equal to 0 by negative become, and obtains left margin Chleft and right margin Chright, counts
Peak width W=Chright-Chleft+1 is calculated, is then differentiated by following formula:
Wherein, W is peak width, NpFor cumulative tale, ApFor " net " peak area；Think if the peak position for meeting above formula
It is effective peak position；
The calculating of S10, accurate peak position；
It is respectively taken together on effective peak position both sides, forms three points with peak position road, seek the secondary multinomial of these three point compositions
Formula is the corresponding accurate peak position of effective peak position according to the corresponding road location of the quadratic polynomial maximum value；
S11, output peak position.
For the ray energy spectrum detector of low energy resolution ratio, since the registration at peak is larger or low energy hangover is serious
Etc. reasons, weak peak be often submerged in strong peak in the following, peak position can not be recognized correctly, therefore effectively improving energy resolution is to mention
The important channel of high peak position identification accuracy.For detector signal system, ray energy spectrum be by detector response with
The input signal convolution of ray is formed.Theoretically, if detector does not have statistic fluctuation, after singly energy ray enters detector,
The power spectrum of output will be only upper in the presence of counting at one, i.e., power spectrum is not in broadening, therefore in order to improve detector energy resolution
Rate can be based on power spectrum obtained, by the receptance function of detector, deconvolution is inputted by the method for deconvolution
Power spectrum realizes the reconstruction of incident power spectrum.
Specific: detector measurement radioactive substance obtains power spectrum in step sl；Establish response matrix；
Assuming that input ray signal function is f (x), detector response function is h (x), and output spectrum signal function is y
(x), then output spectrum be input signal and detector response function convolution, due to power spectrum be discrete system, then:
Above formula is transformed to matrix form again:
Y=Hf, (2)
Wherein H is response matrix, 2N-1 × N size, and the length of y is 2N-1, i.e., ray energy spectrum data obtained, f's
Length is N；Matrix form is shown below after expansion:
If obtaining detector response function and its matrix in advance, f can be solved by above formula equation group
(k), here it is deconvolution, the i.e. inverse process of convolution.
Need to know the inverse matrix of response matrix H due to solving f (k), it is obvious that this is an ill-condition matrix, is usually needed
To be solved by the method for regularization, guarantee solution can confidence level and stability；(3) formula is done such as down conversion:
HTY=HTHf. (4)
Therefore:
It enables: A=HTH, then A is Teoplitz (Toeplitz) matrix；If directly calculated using (5) formula, often
Lesser error or noise will lead to serious oscillation, and result credibility is very poor.Alternative manner can be by continuously attempting to give birth to
A suitable solution is finally converged at a series of approximations, avoids seeking the requirement that Toeplitz matrix accurately solves, this is big
It is fairly effective method in the case of part response matrix is morbid state.Due to ray energy spectrum data be it is non-negative, it is conventional repeatedly
Negative value can be all generated for algorithm, such as Gauss-Newton method, Gauss-Seidel method, therefore is not suitable for the anti-of ray energy spectrum
Convolution.2011, MiroslavEt al. on the basis of Gold algorithm, extend Gold iterative algorithm, and answered
It has used in gamma spectrum deconvolution parsing, while having had studied the property of this method.
Using Gold iterative algorithm, iteration form is as follows:
Wherein:
A=HTH, y '=HTy；
The iteration will converge on the least-squares estimation of constraint subspace, it is found that as long as hi>=0, yi>=0, then it is solved
fiAlso inevitable is all positive number, this conforms exactly to the needs that ray energy spectrum is positive number, this is the sharpest edges of Gold iterative algorithm.
Based on the response power spectrum for obtaining different-energy ray in step S1, response matrix H is established according to (3) formula；Detector
Measurement obtains power spectrum vector y；The Gold iterative algorithm of power spectrum is realized into step S6 in step S2；It is specific:
S2, A=H is calculatedTH, y '=HTy；
Initial vector f (0)=[1,1,1 ..., 1] is arranged at the n-th=0 in S3, basis (6) formulaT；
Maximum number of iterations L required for S4, setting；
S5: according to (6) formula, f is iteratively solved(L)；
S6: if n=L, stop iteration, export as a result, otherwise: n=n+1；Return to S3；
The f of power spectrum is obtained by step S2 to step S6(L)；Then pass through first derivative again into step S9 in step S7
Carry out peak-seeking；It is specific:
The first derivative of S7, node-by-node algorithm deconvolution power spectrum；
Wherein, KbFor normaliztion constant, AjFor smooth coefficients, yi+jFor the raw spectral data in the i-th road+j,Become for i-th
Modal data after changing；Specifically, cubic polynomial least square method parameter see the table below 1:
1 First derivative spectrograply parameter list of table
S8, increase direction along i, retrieve first derivative, numerical value is by just becoming negative, the corresponding road location of zero crossing, as peak position, such as
Fruit thinks that the road location nearest from zero is peak position without the road location of just zero passage at this time；
S9, the differentiation that peak position obtained in S8 is carried out to effective peak position；
S91, the width for examining peak: the distance between positive and negative maximum of first derivative D meets:
0.8FWHM≤D≤3FWHM；
S92, statistic discriminance；
On the both sides at peak, first derivative is just equal to 0 by negative become, and obtains left margin Chleft and right margin Chright, counts
Peak width W=Chright-Chleft+1 is calculated, is then differentiated by following formula:
Wherein, W is peak width, NpFor cumulative tale, ApFor " net " peak area；Think if the peak position for meeting above formula
It is effective peak position；
Finally calculated to accurate peak position, so that effective peak position is obtained, it is specific:
The calculating of S10, accurate peak position；
It is respectively taken together on effective peak position both sides, forms three points with peak position road, seek the secondary multinomial of these three point compositions
Formula is the corresponding accurate peak position of effective peak position according to the corresponding road location of the quadratic polynomial maximum value；
S11, output peak position.
Embodiment 1
Using conventional method to LaBr3Detector detection152Eu original spectrum carries out peak-seeking and of the present invention is based on
The Peak Search Method pair of deconvolution iteration ray energy spectrum resolution ratio enhancing152Eu carries out peak-seeking, obtained Comparative result such as table 2 and Fig. 2
It is shown:
Table 2152First derivative peak-seeking Comparative result after Eu original spectrum and deconvolution
It can be observed from fig. 2 that152After deconvolution iteration, energy resolution is significantly improved Eu original spectrum, and
And two peaks of overlapping are all significantly parsed.Table 2 is the result of first derivative peak-seeking after original spectrum and deconvolution
Comparison, it can be seen that peak-seeking can incite somebody to action after deconvolution152Whole characteristic peaks of Eu all recognize, and seeking based on original power spectrum
The energy peak at peak, overlapping fails to seek.
Embodiment 2
Using conventional method pair239Pu- α original spectrum carry out peak-seeking and it is of the present invention be based on deconvolution iteration ray
The Peak Search Method pair of energy spectral resolution enhancing239Pu- alpha energy spectrum carry out peak-seeking, obtained Comparative result as shown in table 3 and figure 3:
Table 1239First derivative peak-seeking Comparative result after Pu- alpha energy spectrum original spectrum and deconvolution
| Energy | Branching ratio (%) | Original spectrum peak-seeking | Peak-seeking after deconvolution |
| 5105.5 | 11.94 | √ | √ |
| 5144.3 | 17.11 | - | √ |
| 5156.59 | 70.77 | √ | √ |
As seen from Figure 3,239After deconvolution iteration, energy resolution is significantly improved Pu- α original spectrum,
And two peaks (5156.59keV and 5144.3keV) of overlapping are significantly parsed.Table 3 is239Pu- alpha energy spectrum is former
The Comparative result for the spectrum and first derivative peak-seeking after deconvolution of beginning, it can be seen that due to two peaks 5156.59keV and 5144.3keV
Resolved to come out, therefore, peak-seeking can incite somebody to action after deconvolution239Three peaks of Pu- α all recognize, and seeking based on original power spectrum
The energy peak at peak, 5144.3keV fails to seek.
Claims (1)
1. the Peak Search Method based on the enhancing of deconvolution iteration ray energy spectrum resolution ratio, which comprises the following steps:
S1, detector measurement radioactive substance obtain power spectrum；Establish response matrix；
Assuming that input ray signal function is f (x), detector response function is h (x), and output spectrum signal function is y (x), then
Output spectrum is the convolution of input signal and detector response function, since power spectrum is discrete system, then:
Above formula is transformed to matrix form again:
Y=Hf, (2)
Wherein H is response matrix, and 2N-1 × N size, the length of y is 2N-1, i.e., ray energy spectrum data obtained, the length of f
For N；Matrix form is shown below after expansion:
(3) formula is done such as down conversion:
HTY=HTHf. (4)
Therefore:
It enables: A=HTH, then A is Teoplitz (Toeplitz) matrix；Using Gold iterative algorithm, iteration form is as follows:
Wherein:
A=HTH, y '=HTy；
S2, A=H is calculatedTH, y '=HTy；
Initial vector f (0)=[1,1,1 ..., 1] is arranged at the n-th=0 in S3, basis (6) formulaT；
Maximum number of iterations L required for S4, setting；
S5: according to (6) formula, f is iteratively solved(L)；
S6: if n=L, stop iteration, export as a result, otherwise: n=n+1；Return to S3；
The first derivative of S7, node-by-node algorithm deconvolution power spectrum；
Wherein, KbFor normaliztion constant, AjFor smooth coefficients, yi+jFor the raw spectral data in the i-th road+j,After the i-th transformation
Modal data；
S8, increase direction along i, retrieve first derivative, numerical value is by just becoming negative, the corresponding road location of zero crossing, as peak position, if do not had
There is the road location of just zero passage, thinks that the road location nearest from zero is peak position at this time；
S9, the differentiation that peak position obtained in S8 is carried out to effective peak position；
S91, the width for examining peak: the distance between positive and negative maximum of first derivative D meets:
0.8FWHM≤D≤3FWHM；
S92, statistic discriminance；
On the both sides at peak, first derivative is just equal to 0 by negative become, and obtains left margin Chleft and right margin Chright, calculates peak
Wide W=Chright-Chleft+1, is then differentiated by following formula:
Wherein, W is peak width, NpFor cumulative tale, ApFor " net " peak area；It is considered have if the peak position for meeting above formula
Imitate peak position；
The calculating of S10, accurate peak position；
It is respectively taken together on effective peak position both sides, forms three points with peak position road, seek the quadratic polynomial that these three points are constituted, root
It is the corresponding accurate peak position of effective peak position according to the corresponding road location of the quadratic polynomial maximum value；
S11, output peak position.
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| CN114859397A (en) * | 2022-03-17 | 2022-08-05 | 合肥金星智控科技股份有限公司 | Neutron activation energy spectrum processing method, device, equipment and medium |
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