The Geant4 software is used to simulate the CsI detector to measure the mixed energy spectrum from three radionuclides in the nuclear waste barrel. In this paper, a variety of methods are used to perform peak-seeking analysis on the mixed energy spectrum generating from 60Co, 137Cs and 226Ra, the effects of each peak-seeking method are compared for this complex energy spectrum. In this comparative experiment, the results show that the morphological energy spectrum peak-seeking method is more suitable for the energy spectrum from a mixture of multiple radionuclides.
A large amount of nuclear waste is produced during the decommissioning of nuclear facilities. For security and effective management, these radioactive wastes need to be packaged and stored in waste barrels according to the actual situation. Plenty of nuclear wastes generated in the process of nuclear energy mining, production and application [
Peak-seeking has always been a necessary process for nuclide identification. The determination of peak position and boundary affects directly the calculation of peak area, and it affects the accuracy of nuclide characterization furtherly [
Geant4 is developed by the European Organization for Nuclear Research in the C++ language development environment, which is mainly used to simulate the interaction process of particles in matter [
The measured energy spectrum data contains not only the effective energy spectrum data representing the nuclide information, but also the electronic noise signal of the detector instrument and its own statistical fluctuations [
The simple comparison method of peak searching is a relatively simple analysis method for early energy spectrum data analysis. The peaks and the determination of peak positions are judged by simple comparison [
k is the peak-seeking threshold, which is generally between 1 and 1.5. And channel corresponding to the maximum value from d a t a i − m to d a t a i + m is peak position. The spectrum after peak-seeking is showed as
The Gaussian function is usually used to describe the shape of the peak of the spectrum, due to the peak reflects the statistical properties of the system noise and statistical fluctuation process [
G ( i ) = A 2 π σ e [ − ( i − i 0 ) 2 / 2 σ 2 ] (1)
Based on the Gaussian function, a new function is defined by adjacent data points. It is obvious that the first-order Gaussian function depends only on the width H. As shown in Equation (2):
P m = 1 = G ( i ) G ( i + m − 2 ) G ( i − 2 ) G ( i + 1 ) = exp ( 11.092 H 2 ) (2)
where, m is the step length of the peak-seeking and it is also the order of the Gaussian function, which determines the sensitivity of the peak-seeking. With m increasing, the sensitivity gradually increases, however, it is not suitable to determine the peak position after increasing to a certain value. Theoretically, the peak is determine by the P m = 1 . When P m = 1 ( i ) = 1 , it is not a peak, when C > 1, it is a peak.
Derivative method [
d a t a ′ i ¯ = 1 K b ∑ j = − m m ( A j d a t a i + j ) (3)
The peak located at i when the derivative value changes from positive to negative at zero crossing.
The basic idea of the covariant peak finding method is to gradually fit the peak line function to the actual spectrum, the fitting result is used to distinguish true and false peaks. Those with a higher degree of fit are true, and those with a lower degree of fit are judged as false. Calculate h i by gradually sliding fitting at w = 2 m + 1 .
h i = ∑ j = − m m g j ∑ j = − m m g j C j d a t a i + j − ∑ j = − m m g j C j ∑ j = − m m g j d a t a i + j ∑ j = − m m g j ∑ j = − m m g j C j 2 − ( ∑ j = − m m g j C j ) 2 (4)
where h i is the peak height, g j is the weighting factor, C j is the peak shape function (Including Gaussian function, Cauchy function, cosine function, hyperbolic secant function).
The calculation formula of fit is defined as:
R i = h i Δ h i (5)
Δ h i = [ ∑ j = − m m g j ∑ j = − m m g j ∑ j = − m m g j C j − ( ∑ j = − m m g j C j ) 2 ] 2 (6)
where Δ h i is the partial variance of the fitting process. The peak is judged according to the degree of fit R i , R i is the maximum value and when R i > R t h (where, R t h is described as a threshold, and depends on the half-width H and the number of points selected W, generally between 2 and 5) the peak lies in the corresponding channel. The detail is showed in
The symmetric zero-area method utilizes the symmetric window function and the smoothed energy spectrum for convolution transformation, and threshold processing is carried out on the transformed data to obtain the spectral peak position [
Y ^ i = ∑ j = − m m C j d a t a i + j (7)
where ∑ j = − m m C j = 0 , C j = C − j realized symmetry. Convolution transformation
is developed when W = 2 m + 1 . The transformation function of the symmetric zero areas can be a square wave function or a peak-like function, where the whole square wave function is defined as follows:
C j = { − b − m ≤ j < − ( H − 1 ) / 2 a − ( H − 1 ) / 2 ≤ j ≤ ( H − 1 ) / 2 − b ( H − 1 ) / 2 < j ≤ m (8)
where H is center width. And the peak-like function is the difference between a specific function G j and a constant d. G j could be described as Gaussian function, Cauchy function, cosine square function, hyperbolic secant function,
Gaussian second derivative function, etc. And d = 1 W ∑ j = − m m G j . In order to make
the sensitivity of peak searching independent of the statistics of the measured spectrum, the standard deviation of the transformed spectrum is generally used as the peak searching unit. The criteria are as follows:
S S i = Y ^ i Δ Y ^ i = ∑ j = − m m C j d a t a i + j ( ∑ j = − m m C j 2 d a t a i + j ) > f (9)
where ƒ is the peak-seeking threshold, when S S i > 0 ∩ S S i > f , it could conclude that it is a peak. The peak position is at the channel corresponding to the positive value and the peak boundary is determined by the adjacent negative peaks on both sides, as shown in
The morphological peak finding method is a new method based on the characteristics of image processing morphological changes. Its basic principle is to perform a morphological transformation of energy spectrum by selecting appropriate structural elements. The basic steps are: Firstly, the opening operation of the corrosion operation and the expansion treatment are performed to obtain the filtered energy spectrum. That A is corroded by structure B shows as follows:
A ⊗ B = { r | ( B ) r ⊆ A } (10)
where the arithmetic symbol ⊗ means “Corrosion calculation” to eliminate unwanted signals. Then, white hat transformation is performed to get new energy spectrum data. The formula for A to be expanded by B is as follows:
A ⊕ B = { r | ( B ^ ) r ∩ A } (11)
where the symbol ⊗ means to fill in image holes and eliminate small noise. Finally, after removing false peaks according to the peak width setting, the peak-seeking is performed, and the determined peak position is output to the original energy spectrum to complete the entire peak search. And here is a peak criterion, L i > W . where L i is peak-width to be found.
The peak-seeking algorithm based on morphology combines the advantages of image processing technology, and the low accuracy of traditional algorithms is avoided [
This paper compares five traditional peak-seeking methods and a new peak-seeking method based on morphology by using the mixed energy spectrum generated by multiple nuclides. The results have shown that simple comparison method have been difficult to reach the peak-seeking requirements of the complex energy spectrum, and the peak-seeking effect is relatively poor. And only four peaks can be found in the smoothed energy spectrum, and lost the peak of 300 or so. In the result of the debugged Gaussian function, five peaks were found, which is different from the first method in the second peak. Similar to the results of the derivative method, covariant method and the symmetric zero area method, the peak positions are also roughly the same in Gaussian product function method, but the resolution effect of reunion is poor. And the positions of the third and fourth peaks in the searched peaks cannot be determined very well, especially in the area where the third peak has two peaks. These traditional methods perform better than the first two methods, but they still have poor peak-seeking effects in the complex energy spectrum. The peak-seeking method based on morphology is better adapted to the complex energy spectrum, and its effect is also the best in this comparative study. It can be further concluded that the morphological method is more suitable for peak-searching in the mixed energy spectrum obtained by multiple nuclides.
The authors declare no conflicts of interest regarding the publication of this paper.
Luo, R., Huang, Y. and Liu, X.H. (2020) Comparative Study on Peak-Seeking Methods of the Mixed Radioactive Energy Spectrum. Open Access Library Journal, 7: e6676. https://doi.org/10.4236/oalib.1106676