CN111982949A - A method for separating overlapping peaks of EDXRF spectrum by combining the fourth derivative with three-spline wavelet transform - Google Patents

Abstract

The invention discloses a method for separating an EDXRF spectrum overlapping peak by combining a fourth derivative with three-spline wavelet transform, which comprises the following steps: step 1, carrying out four times of differential processing on the EDXRF spectrum signal to increase the separation degree of overlapped peaks; step 2, performing multi-scale decomposition on the signals subjected to the four-time differential processing by utilizing wavelet transformation to find out appropriate-scale high-frequency discrete detail signals where the overlapping peaks are located; step 3, multiplying the high-frequency signal by a coefficient more than 1 to amplify in a certain proportion; and 4, performing wavelet inverse transformation on the amplified high-frequency detail signal to reconstruct a signal to obtain a separated overlapping peak. The invention has the advantages that: the method can effectively decompose the overlapping peak with lower separation degree, and has practicability in solving the overlapping peak phenomenon of the EDXRF spectrum.

Description

A fourth derivative combined with three-spline wavelet transform to separate overlapping peaks in EDXRF spectra method

technical field

The invention relates to a detection method for X-ray fluorescence spectrum analysis, in particular to a method for separating overlapping peaks of EDXRF spectrum by combining four derivatives with three-spline wavelet transformation.

Background technique

Energy dispersive X-ray fluorescence (EDXRF) spectroscopy is an important detection method for radioactive substances, which is widely used in the fields of geology, environment and archaeology. Among them, the decomposition of overlapping peaks of X-ray fluorescence spectrum is a crucial link. In recent years, researchers at home and abroad have proposed a variety of overlapping peak decomposition methods. Mainly include: Fourier transform method, derivative method, wavelet transform method, and so on. However, the Fourier transform method is too difficult in practical operation, the derivative method has high requirements on the signal-to-noise ratio, the selection of the wavelet base plays a crucial role in the wavelet transform method, and the peak-division error is too large when the overlapping peak separation degree is low. The paper by Lin Zhaopei, Li Yu, Wu Huiwen, et al.: Chromatographic Overlapped Peak Analysis Based on Quadratic Differentiation and Wavelet Transform The quadratic differential and the approximately symmetric compactly supported orthogonal series wavelet transform are applied to the overlapping peak decomposition of chromatograms, but only Overlapping peaks with a resolution higher than 0.4 were resolved and no error analysis was performed. The quadratic derivative can effectively improve the resolution and remove the impurity peaks compared with the quadratic derivative. Combined with the three-spline wavelet transform method, the overlapping peaks can be separated more accurately. When the X-ray energy is close to the element, the X-ray fluorescence spectrum will be seriously overlapped or even completely overlapped. For this problem, this paper proposes a method of quadratic derivative combined with three-spline wavelet transform to solve the problem of serious overlapping of overlapping peaks.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a method for separating overlapping peaks of EDXRF spectrum by combining four-derivative and three-spline wavelet transform, this method can effectively decompose overlapping peaks with lower separation degree, and has practicality in solving the overlapping peak phenomenon of EDXRF spectrum .

The technical scheme adopted in the present invention is as follows: a method for separating the overlapping peaks of EDXRF spectrum by combining four derivative with three-spline wavelet transform, which is characterized in that the steps are as follows:

The first step is to perform four differential processing on the EDXRF spectral signal to make the separation degree of the overlapping peaks larger;

The second step is to use the three-spline wavelet transform to perform multi-scale decomposition on the signal processed by the quadratic differentiation, and find the appropriate scale high-frequency discrete detail signal where the overlapping peak is located;

The third step is to multiply the high-frequency discrete detail signal by a coefficient greater than 1 to amplify a certain proportion;

Step 4: Use the amplified high-frequency discrete detail signal to perform wavelet inverse transform to reconstruct the signal to obtain separated overlapping peaks.

The fourth derivative method of the present invention is defined as: assuming a discrete signal is X={x ₁ , x ₂ ,..., x _n }, then its derivative spectrum can be expressed as:

In the above formula, n is the derivative order, n≥1; h is the step size; the derivative spectrum has the following properties;

(1) The extremum point of the even-order derivative of the signal function or the zero point of the odd-order derivative is the extremum point of the original signal function;

(2) The extreme point of the even-order derivative or the extreme point of the odd-order derivative of the signal function is the deformation point of the original signal function;

(3) As the derivative order of the signal function increases, the peak width becomes smaller and the peak shape becomes sharper.

The method for decomposing overlapping peaks by the three-spline wavelet transform of the present invention is as follows: selecting a scale function and a wavelet function, then discretizing the overlapping signal by wavelet transform, and then obtaining components on different scales, wherein the high-frequency part represents energy spectrum peaks signal, the high-frequency signal is multiplied by a weighting coefficient to decompose it;

Let m be a natural number, then define the m-order B-spline N _m (x) as follows:

The B-spline can be obtained by recursion. First, take N ₁ (x) as the Haar scale function, and then define N _m (x) by convolution of N _m-1 (x) and N ₁ (x); If the formula (2) is taken as:

m>1.这时，称M_m(x)为m阶中心B样条。and define

m>1. At this time, M _m (x) is called the center B-spline of order m.

The definition of the degree of separation in the first step of the present invention is specifically: the degree of separation R is an index describing the degree of overlap between two adjacent peaks, which is defined as

The smaller the value of R, the higher the degree of overlap;

Overlapping spectral peaks usually have three peak signals for simulation: Gaussian peak signal, Lorentzian peak signal and Tsallis peak signal;

Gaussian peak signal:

Lorentzian peak signal:

f(x)=Aσ ² /[(x-μ) ² +σ ² ] (7)

Tsallis peak signal:

In the above formula, σ is the width of the peak, A represents the peak value, and μ is the apex position of the peak; while the Gaussian peak and the Lorentzian peak can be obtained by adjusting the q of the Tsallis peak; when q is close to 1, it is the Gaussian peak, and when q=2, it is the Lorentzian peak. peak; select the Tsallis peak signal for modeling.

If q=1.8, the values of A are 2, 1.5, 1.5 respectively; σ is 4, 2, 1; μ is 20, 24, 28; that is, the peak positions are 20, 24, 28; and the peak 1 The R1 for peak 2 and peak ₂ was 0.33, and the R2 for peaks ₂ and 3 was 0.67.

The advantages of the invention are as follows: the scheme proposes a new method for decomposing overlapping peaks by combining quartic derivative and three-spline wavelet transform; simulation experiments prove that overlapping peaks can be effectively decomposed. Then, the simulated energy dispersive X-fluorescence (EDXRF) spectrum and the measured X-fluorescence spectrum were processed with this method, and the decomposition of overlapping peaks was achieved with less error, and element identification could be achieved. The results show that this method can effectively decompose overlapping peaks with low resolution, and is practical in solving the overlapping peak phenomenon of EDXRF spectrum.

Description of drawings

FIG. 1 is a schematic diagram of the coefficients of a low-pass filter decomposed by a third-order spline wavelet bior3.5 according to the present invention.

FIG. 2 is a schematic diagram of the coefficients of the high-pass filter decomposed by the third-order spline wavelet bior3.5 according to the present invention.

FIG. 3 is a schematic diagram of the coefficients of the third-order spline wavelet bior3.5 reconstructed pass filter according to the present invention.

FIG. 4 is a schematic diagram of the low-pass filter coefficients reconstructed by the third-order spline wavelet bior3.5 according to the present invention.

FIG. 5 is a schematic diagram of overlapping peaks of analog signals of the present invention.

FIG. 6 is a schematic diagram of an analog signal preliminarily processed by the fourth derivative of the present invention.

FIG. 7 is a schematic diagram of the simulation result of overlapping peak decomposition according to the present invention.

FIG. 8 is a schematic diagram of a simulation result of overlapping peak decomposition in the present invention.

9 is a schematic diagram of the X-ray fluorescence spectrum of the measured T lead brass element of the present invention.

FIG. 10 is a schematic diagram of the decomposition results of the overlapping peaks of the measured T lead brass element of the present invention.

FIG. 11 is a schematic diagram of the X-fluorescence spectrum of the light element measured in the present invention.

FIG. 12 is a schematic diagram of the decomposition result of the measured light elements in the present invention.

Detailed ways

The present invention works and is carried out in such a way that the information of the analyte in the energy dispersive X-ray fluorescence (EDXRF) spectrum is contained in the characteristic peak position and the characteristic peak net peak area. Accurate detection of characteristic peaks is the key to EDXRF spectral analysis. The energy difference between the characteristic X-rays of many elements is very small, especially in the low atomic number, there are various interferences in the fluorescence spectrum generation process, resulting in the serious overlapping of the spectral peaks of the measured X-fluorescence data. The present invention uses the overlapping peaks. As the research object, a method of dealing with overlapping peaks with the combination of the fourth derivative and the three-spline wavelet transform is proposed. The feasibility of the method was tested by simulating overlapping peaks with a mathematical model, and the measured X fluorescence spectrum data was simulated to obtain good results. Finally, the CIT-3000SY X fluorescence element logging instrument was used to measure the T lead-brass data and mixed light Elemental data fluorescence spectra were used as validation.

The present invention first introduces the principle of the derivative method and the three-spline wavelet method for decomposing and overlapping in detail. The higher the derivative method is, the more deformed the signal is, but it can effectively improve the resolution of the double peaks, while the three-spline wavelet transform is weaker to deal with the low resolution double peaks, but it can effectively maintain the peak shape. Through the simulation data, it is found that the separation degree of peak 1 and peak 2 in the three overlapping peaks is R=0.33, and the separation degree of peak 2 and peak 3 is R=0.67. After the fourth-order derivative, the signals have a certain overlap, but the fourth-order After the derivative processing, not only the peak value of the signal is retained, but also the phenomenon of increasing the separation degree occurs. Combined with the characteristics of the three-spline wavelet transform, the value of the decomposition level is adjusted and the high-frequency signal is multiplied by a coefficient greater than 1. A certain percentage of amplification is then reconstructed, resulting in the decomposition of the simulated overlapping peaks. Among them, the number of decomposition layers for the three-spline wavelet is four layers, and the high-frequency amplification factor is six times. Then, the overlapping spectrum of K element was simulated, and the decomposition of the overlapping peaks was realized. The simulation experiments showed that the new method could accurately identify the peak position, and the error was within 1%. applicability. The feasibility of this method for decomposing overlapping peaks is verified. Finally, this method is used to process the measured T lead-brass element data of CIT-3000SY X fluorescence element logging instrument and the X fluorescence spectrum of mixed light element data, and realize the decomposition of overlapping peaks, and the peak position error after decomposition is controlled within 1 Within %, it has a high accuracy rate.

1. Derivative method.

Definition of derivative: Assuming a discrete signal is X={x ₁ , x ₂ ,...,x _n }, then its derivative spectrum can be expressed as:

In the above formula, n is the derivative order, n≥1; h is the step size. The derivative spectrum has the following properties;

(1) The extremum point of the even-order derivative of the signal function or the zero point of the odd-order derivative is the extremum point of the original signal function.

(2) The extremum point of the even-order derivative or the extremum point of the odd-order derivative of the signal function is the deformation point of the original signal function.

(3) As the derivative order of the signal function increases, the peak width becomes smaller and the peak shape becomes sharper.

Some literatures show that the fourth-order derivative method can effectively remove the small impurity peaks in the spectrum, and can separate the overlapping characteristic peaks. The theory of using derivative to locate characteristic peaks of X-ray fluorescence spectrum is mature and simple, and has wide applicability. According to the above properties of the derivative spectrum, after the fourth-order derivative method is performed on the energy spectrum signal, each extreme point and zero point of the signal can be clearly displayed, and the half-peak width of the signal becomes smaller and the peak shape becomes sharper. Thereby, the signals of the overlapping peaks that are seriously overlapped are initially separated, and the basis for distinguishing the overlapping peaks is provided, and the fine structure of the signal can be accurately judged. However, due to the characteristic that the higher the derivative is used, the noise will be amplified, which cannot be widely promoted in the specific application process, so a method is urgently needed to make the derivative work.

2. Three-spline wavelet transform theory.

For different spline wavelet bases, because of the different filters, the effect of decomposing overlapping peaks is also different. The peak shape decomposed by the second-order spline wavelet base is jagged, and the peak position value decomposed by the fourth-order spline wavelet base has a large error. The overlapping peak decomposition effect of the third-order spline wavelet base is better, the peak position of the signal obtained after decomposing the overlapping peak remains unchanged, and the peak area error is also small, considering the advantages of spline wavelet. Therefore, the third-order spline wavelet basis is used.

2.1. The nature and definition of spline wavelet: The basic idea of using wavelet transform to decompose overlapping peaks is: first select the appropriate scale function and wavelet function, and then perform discrete wavelet transform on the overlapping signal, and then obtain components on different scales, The high frequency part represents the peak signal of the energy spectrum, and finally the high frequency signal is multiplied by a weighting coefficient to decompose it.

Let m be a natural number, then define the m-order B-spline N _m (x) as follows:

The B-spline can be obtained by recursion. First, take N ₁ (x) as the Haar scale function, and then define N _m (x) by convolution of N _m-1 (x) and N ₁ (x). If the formula (2) is taken as:

m>1.这时，称M_m(x)为m阶中心B样条。and define

m>1. At this time, M _m (x) is called the center B-spline of order m.

The low-pass and high-pass filter coefficients of the third-order spline wavelet bior3.5 are shown in Figure 1-4.

2.2. The fourth-order derivative method combined with the third-order B-spline wavelet algorithm realizes the following steps:

Step 1: Differentiate the signal four times to make the separation of overlapping peaks larger;

Step 2: Use wavelet transform to perform multi-scale decomposition on the signal processed by the quadratic differentiation, and find out the appropriate scale high-frequency discrete detail signal where the overlapping peaks are located;

The third step is to multiply the high-frequency signal by a coefficient greater than 1 to amplify a certain proportion;

Step 4: Use the amplified high-frequency detail signal to perform wavelet inverse transform to reconstruct the signal to obtain separated overlapping peaks.

3. Quadratic derivative combined with three-spline wavelet transform to decompose overlapping peaks with low separation degree.

The degree of separation R is an index describing the degree of overlap between two adjacent peaks, which is defined as

The smaller the value of R, the higher the degree of overlap.

There are usually three kinds of peak signals for overlapping spectral peaks to simulate: Gaussian peak signal, Lorentzian peak signal and Tsallis peak signal.

Gaussian peak signal:

Lorentzian peak signal:

f(x)=Aσ ² /[(x-μ) ² +σ ² ] (7)

Tsallis peak signal:

In the above formula, σ is the width of the peak, A represents the peak value, and μ is the position of the apex of the peak. The Gaussian and Lorentzian peaks can be obtained by adjusting the q of the Tsallis peak. When q is close to 1, it is a Gaussian peak, and when q=2, it is a Lorentzian peak. Therefore, it is more representative to use the Tsallis peak signal for modeling.

Take q=1.8, and take the value of A as 2, 1.5, and 1.5 respectively. σ takes 4, 2, and 1 respectively. μ is taken as 20, 24, and 28 respectively. That is, the peak positions are 20, 24, and 28. While R1 for peaks 1 and 2 was 0.33, and R2 for peaks 2 and 3 was 0.67. In Figure 5, it can be seen that peak 1, peak 2, and peak 2 are severely overlapped.

As shown in Figure 6, the position and number of peaks are clearly displayed after preliminary processing by the fourth-order derivative, so it is feasible to use the fourth-order derivative for preliminary processing, but at the same time, it can be seen that there is a certain overlap in the signals after the fourth-order derivative. So another method is needed for further processing.

As shown in FIG. 7 , the three-spline wavelet processing is performed by performing preliminary processing of the fourth-order derivative on the analog signal, and the peak positions of the analog signal peaks are 20, 24, and 28. The errors of the processed peak positions at 19.9, 24.2 and 27.8 are 0.05%, 0.83% and 0.71%, respectively. The decomposition effect is ideal and the error is small, which can meet the requirements of quantitative and qualitative analysis. The results show that the quartic derivative combined with the three-spline wavelet transform can effectively decompose the overlapping peaks.

Table 1 Analysis of peak position results

Table 1 Peak position analysis

4. Analysis of spectral simulation experiments.

According to the X-ray energy table: K _α of K element is 3.313 keV, K _β is 3.589 keV, and the energy difference is only 279 keV; when the K element is measured by the spectrometer, the spectral peaks are seriously overlapped. Knowing a set of spectra with non-overlapping K series lines, identify its energy peak track address as the standard energy peak track address, and carry out the energy linear scale E=0.0307keV/ch. The K _α K _β energy addresses of element K are 113 and 122, respectively. The low-resolution overlapping peaks present in the EDXRF spectra were simulated using equation (8). The _{ratio of KαKβ energy} peaks is 5:1. The simulation expression is shown in (9), and the result is shown in Figure 8.

As shown in Figure 8, the overlapping peaks of the simulated EDXRF spectrum are decomposed, and the overlapping peaks in the original spectral line in Figure 8 are already difficult to observe with the naked eye. Identify the peak positions after decomposition, and the results are shown in Table 2. The error of the decomposition results of overlapping peaks is less than 1%. According to the results, the quartic derivative combined with the three-spline wavelet transform can better decompose the overlapping peaks in the EDXRF spectrum.

Table 2 Analysis of peak position results

Table 2 Peak position analysis

5. Measured X-ray fluorescence data analysis results.

In this experiment, the T lead brass element data and mixed light element data measured by the CIT-3000SY X fluorescence element logging instrument are used. In the T lead brass data, the K _α of Ni and the The K _β energies of Co are 7.477 and 7.649 kev, respectively, with a difference of only 0.172 kev, which is in a state of severe overlap. In the light element data, it can be observed that the Cr and Mn elements between the sites 230-270 have a serious overlap, and the energy difference is 0.484kev, which makes it difficult to distinguish the elements. These two groups of data have been preprocessed by spectral smoothing background subtraction, and then the fourth-order differential combined with three-spline wavelet decomposition, in which the number of wavelet decomposition layers is four, and the amplification factor is 6 times. The decomposition result is shown in Figure 9-12 below.

It is known that the standard peak position of K _α of Ni is 410, and the K _β of Co is 419. The peak positions of the decomposed spectrum are identified by the peak-finding method as 408 and 420, and the error is only 0.5%, 0.2%, Cr and Mn. The standard peak positions of 241 and 254 are respectively, and the error after decomposition is only 0.4%. And the decomposition effect of the overlapping peaks is obvious. The results show that the fourth-order derivative combined with the three-spline wavelet decomposes the overlapping peaks with low resolution in the actual X-fluorescence spectrum to obtain accurate results.

Table 3 Analysis of peak value results

Table 3 Peak position analysis

6. Research results.

The invention studies the derivative method and the spline wavelet method in detail, and proposes a new method of decomposing overlapping peaks by combining the quadratic derivative and the three-spline wavelet transform. It is proved by simulation experiments that overlapping peaks can be decomposed effectively. Then, the simulated energy dispersive X-ray fluorescence spectrum and the measured EDXRF spectrum were processed with this method, and the decomposition of overlapping peaks was achieved with less error, and the identification of elements could be realized. The results show that this method can effectively decompose overlapping peaks with low resolution, and is practical in solving the overlapping peak phenomenon of EDXRF spectrum.

Claims (5)

1. a fourth derivative is combined with three-spline wavelet transform to separate the EDXRF spectrum overlapping peak method, it is characterized in that the steps are as follows: The first step is to perform four differential processing on the EDXRF spectral signal to make the separation degree of the overlapping peaks larger; Step 2: Use wavelet transform to perform multi-scale decomposition on the signal processed by the quadratic differentiation, and find out the appropriate scale high-frequency discrete detail signal where the overlapping peaks are located; The third step is to multiply the high-frequency signal by a coefficient greater than 1 to amplify a certain proportion; Step 4: Use the amplified high-frequency detail signal to perform wavelet inverse transform to reconstruct the signal to obtain separated overlapping peaks. 2. a kind of fourth derivative according to claim 1 combines three-spline wavelet transform to separate EDXRF spectrum overlapping peak method, it is characterized in that: described fourth derivative method is defined as: suppose a discrete signal is X={x ₁ , x ₂ ,...,x _n }, then his derivative spectrum can be expressed as:

In the above formula, n is the derivative order, n≥1; h is the step size; the derivative spectrum has the following properties; (1) The extremum point of the even-order derivative of the signal function or the zero point of the odd-order derivative is the extremum point of the original signal function; (2) The extreme point of the even-order derivative or the extreme point of the odd-order derivative of the signal function is the deformation point of the original signal function; (3) As the derivative order of the signal function increases, the peak width becomes smaller and the peak shape becomes sharper. 3. a kind of fourth derivative according to claim 1 combines three-spline wavelet transform to separate EDXRF spectrum overlapping peak method, it is characterized in that: The method for decomposing overlapping peaks by the three-spline wavelet transform is as follows: selecting a scale function and a wavelet function, and then performing discrete wavelet transform on the overlapping signal to obtain components on different scales, wherein the high-frequency part represents the energy spectrum peak signal, Multiply the high frequency signal by a weighting factor to decompose it; Let m be a natural number, then define the m-order B-spline N _m (x) as follows:

The B-spline can be obtained by recursion. First, take N ₁ (x) as the Haar scale function, and then define N _m (x) by convolution of N _m-1 (x) and N ₁ (x); If the formula (2) is taken as:

and define

m>1. At this time, M _m (x) is called the center B-spline of order m. 4. a kind of fourth derivative according to claim 1 combines three-spline wavelet transform to separate EDXRF spectrum overlapping peak method, it is characterized in that: The definition of the degree of separation in the first step is specifically: the degree of separation R is an index describing the degree of overlap between two adjacent peaks, which is defined as

The smaller the value of R, the higher the degree of overlap; Overlapping spectral peaks usually have three peak signals for simulation: Gaussian peak signal, Lorentzian peak signal and Tsallis peak signal; Gaussian peak signal:

Lorentzian peak signal: f(x)=Aσ ² /[(x-μ) ² +σ ² ] (7) Tsallis peak signal:

In the above formula, σ is the width of the peak, A represents the peak value, and μ is the apex position of the peak; while the Gaussian peak and the Lorentzian peak can be obtained by adjusting the q of the Tsallis peak; when q is close to 1, it is the Gaussian peak, and when q=2, it is the Lorentzian peak. peak; select the Tsallis peak signal for modeling. 5. a kind of fourth derivative according to claim 4 combines three-spline wavelet transform to separate EDXRF spectrum overlapping peak method, it is characterized in that: If q=1.8, the values of A are 2, 1.5, 1.5 respectively; σ is 4, 2, 1; μ is 20, 24, 28; that is, the peak positions are 20, 24, 28; and the peak 1 The R1 for and peak ₂ was 0.33, and the R2 for peaks ₂ and 3 was 0.67.

Images