CN111597762B - X-ray fluorescence spectrum overlapping peak decomposition method - Google Patents
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Abstract
The invention discloses a method for calculating the characteristic peak intensity of an X-ray fluorescence spectrum, which comprises the following steps: generating a simulation spectrum by using a Monte Carlo method, calculating the ratio of the intensity of each element characteristic peak to the sum of the intensities of all element characteristic peaks, and constructing a simulation spectrum library; designing a three-layer BP neural network and a hierarchical genetic algorithm; optimizing a neural network by adopting a hierarchical genetic algorithm; training the neural network optimized by the genetic algorithm by using the training sample: and predicting the characteristic peak intensity of the specific element by utilizing the trained neural network to perform the spectral data required to be subjected to element analysis, so as to realize the quantitative analysis of the element. According to the invention, the intensity of the characteristic peak of each element in the spectrum is calculated by using the neural network optimized by the hierarchical genetic algorithm, the calculation result of the intensity of the characteristic peak is more accurate, and the spectrum analysis precision is improved.
Description
Technical Field
The invention relates to the field of X-ray fluorescence spectrum analysis, in particular to a method for improving analysis precision by utilizing a neural network to carry out overlapping peak decomposition on X-ray fluorescence spectrum signals.
Background
Energy dispersion X-ray fluorescence spectrum analysis is a multi-element analysis technology, and can accurately measure the types and contents of elements in a sample. However, the energy-dispersive X-ray fluorescence spectrum has a complex structure, a large number of frequency components, overlapping spectral peaks, and many singular points are contained in the spectrum due to the presence of the absorption edge, so that it is difficult to analyze the energy-dispersive X-ray fluorescence spectrum.
Energy dispersive X-ray fluorescence spectroscopy requires a series of steps. Firstly, denoising the signal, avoiding misjudgment of a spectrum peak caused by noise, then deducting the background, and reducing the influence of the low-frequency background on the calculation of the spectrum peak intensity. Then, carrying out overlap peak decomposition, calculating the peak position (characteristic energy value) and the net peak area (characteristic peak intensity) of the spectrum peak, looking up the element characteristic energy value table according to the peak position value to obtain element types, and carrying the spectrum peak intensity into an intensity-content correction curve to obtain element content, thereby realizing qualitative and quantitative analysis of the elements.
The energy difference between the characteristic X-rays of a plurality of elements is very small, various interferences exist in the fluorescence spectrum generation process, and when the energy resolution of the spectrometer is low, overlapping peaks appear in the spectrum. Even if the same element is adopted, the energy of characteristic X-rays generated after electrons with different layers are excited is different, and spectral lines of the characteristic X-rays are overlapped. Spectral peak overlap presents great difficulty in calculating the number of peaks, peak position and net peak area, and therefore, overlap peak decomposition is one of the key steps in spectral analysis.
Disclosure of Invention
The invention aims to solve the technical problem of providing an X-ray fluorescence spectrum overlap peak decomposition method aiming at the defects of the prior art, wherein the X-ray fluorescence spectrum overlap peak decomposition method utilizes a neural network optimized by a hierarchical genetic algorithm to calculate the intensity of each element characteristic peak in a spectrum, the characteristic peak intensity calculation result is more accurate, the spectrum analysis precision is improved, and the accurate decomposition of spectrum overlap peaks is realized.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
an X-ray fluorescence spectrum overlap peak decomposition method, comprising:
step 1: generating a simulation spectrum by using a Monte Carlo method, calculating the ratio of the intensity of each element characteristic peak to the sum of the intensities of all element characteristic peaks, and constructing a simulation spectrum library serving as a neural network training and testing database;
step 2: constructing a three-layer BP neural network;
step 3: constructing a hierarchical genetic algorithm, wherein chromosomes in the hierarchical genetic algorithm comprise control genes and parameter genes;
the control genes adopt binary codes, and each control gene corresponds to one hidden layer unit, namely the length of the control gene is the number n of the hidden layer units;
the parameter genes adopt real number codes, and each parameter gene represents the weight and bias from the input layer to the hidden layer and from the hidden layer to the output layer, which are connected with the corresponding hidden layer unit;
step 4: optimizing a neural network by adopting a hierarchical genetic algorithm;
step 5: training the neural network optimized by a genetic algorithm by using a training sample, wherein the input vector of the training sample is the count value or count rate of the spectrum in each channel, and the expected output vector is the ratio of the intensity of the element characteristic peak to the sum of the intensities of all the element characteristic peaks;
step 6: and predicting the peak intensity of a specific element by utilizing the trained neural network to perform element analysis on the spectrum data, so as to realize quantitative element analysis.
As a further improved technical scheme of the invention, the simulation spectrum in the step 1 is an EDXRF simulation spectrum.
As a further improved technical scheme of the invention, the specific steps of the step 2 comprise:
three layers of BP neural networks are designed:
the first layer is an input layer, the number of source nodes is set to be the spectrum length m, and the spectrum is set to be X= (X) 1 ,x 2 ,…,x m ) T Inputting the count value of each channel of the spectrum into the spectrum;
the second layer is a hidden layer, the node number of the layer is set as n, the hidden layer adopts a double tangent function as an activation function, and the output vector of the hidden layer is marked as Y= (Y) 1 ,y 2 ,…,y n ) T The output of the j-th node of the hidden layer is:
wherein w is i,j To connect the weight of the i-th input layer element to the j-th hidden layer element, b j Bias for the j-th cell of the hidden layer;
the third layer is an output layer, the number of nodes is set to be the number q of characteristic peaks of specific elements to be measured, an activation function adopts a softmax function, the softmax function maps the output of each unit of the output layer to (0, 1), the output of each unit represents the ratio of the intensity of the characteristic peak of each element to the sum of the intensities of the characteristic peaks of all elements, and the sum of the output of each unit of the output layer is 1; the input of the kth node of the output layer is:
wherein w' j,k To connect the weight of the jth cell of the hidden layer to the kth cell of the output layer, b' k Bias for the kth cell of the output layer; the output of the kth node, i.e. the specific gravity of a certain characteristic peak intensity to the sum of the characteristic peak intensities of all elements, is:
the neural network performs supervised learning, and samples for training the neural network are vectors formed by spectral vectors and the ratio of the intensity of each characteristic peak to the total intensity in the spectrum.
As a further improved technical scheme of the invention, the length of the parameter gene is as follows: m+n+q+n+q.
As a further improved technical scheme of the invention, the specific steps of the step 4 comprise:
(4.1) initializing a population, and randomly generating P individuals according to the chromosome structure and the coding form determined in the step 3;
(4.2) decoding to obtain weights and biases of different neural networks according to the group parameters;
respectively training the P neural networks by using training samples, and respectively evaluating the P neural networks by using test sample books to obtain output errors of the P neural networks;
the input vector in the training sample and the test sample is the count value or the count rate of the spectrum in each channel, and the expected output vector is the ratio of the intensity of the element characteristic peak to be calculated to the sum of the intensities of all the element characteristic peaks;
(4.3) calculating an fitness function, wherein the fitness function of the ith individual is defined as:
where S is the number of samples, o s,k Output of the kth output unit when the s-th sample is taken as input, o s,k ' is the corresponding expected output, q is the number of output layer nodes;
(4.4), genetic manipulation:
(4.4.1), selection:
the probability of the ith individual being selected is:
wherein Σf i Sum of individual fitness for a population; using a wagering round selection mechanism, the probability of being selected for each individual in the current population, p, is first calculated s1 ，p s2 ，…，p sP Thereafter, a [0,1 ] is generated]Random number r in, if p s1 +p s2 +...+p s(i-1) ＜r≤p s1 +p s2 +...+p si The ith individual is selected to the pairing library, otherwise not selected;
(4.4.2), crossover and mutation to give a new population:
the control gene and the parameter gene are crossed by a single point, and the crossing probability is selected between 0.5 and 0.7;
the control gene directly exchanges 0 and 1 which are changed into different positions;
the parameter genes adopt cauchy variation, namely, any real number c needing compiling in the parameter genes i The transformation is as follows:
c i ＝c i +δ i ,i＝1,2,…,n；
in delta i To obey the random variable of the cauchy distribution for the scale parameter t=1, the cauchy distribution density function is:
(4.5), judging whether the genetic algorithm is stopped or not:
the genetic algorithm stops operating when one of the following two termination conditions is met:
(4.5.1) completing a predetermined evolution algebra;
(4.5.2) the optimal individuals in the population are not improved over consecutive generations or the average fitness is not substantially improved over consecutive generations;
when the termination condition is met, acquiring the optimal individual from the last generation, jumping to the step (4.6), and when the termination condition is not met, returning to the step (4.2) for recalculation;
(4.6) extracting the optimal initial connection weight and bias of the neural network from the optimal individual.
As a further improved technical scheme of the invention, the specific steps of the step 6 comprise:
(6.1) predicting spectral data to be subjected to element analysis by using a trained neural network to obtain the ratio of the intensity of each element characteristic peak predicted by the neural network to the sum of the intensities of all element characteristic peaks;
integrating the spectrum data to obtain the sum of the intensities of all element characteristic peaks, and multiplying the sum of the intensities of all element characteristic peaks by the ratio of the intensity of each element characteristic peak predicted by the neural network to the sum of the intensities of all element characteristic peaks to obtain the intensity of each element characteristic peak;
(6.2) qualitative and quantitative analysis: according to the relation between the element content and the element characteristic peak intensity of a standard sample known in advance, obtaining an element characteristic peak intensity and element content calibration curve by using a least square method, wherein the expression is as follows:
C＝D+EI；
wherein C is the element content, D is the intercept, E is the slope, and I is the element strength; and (3) bringing the characteristic peak intensity of the element obtained in the step (6.1) into a formula to obtain the content of the element and realize quantitative analysis of the element.
The beneficial effects of the invention are as follows:
the invention aims to provide an energy dispersion X-ray fluorescence spectrum characteristic peak intensity prediction technology, which utilizes a neural network optimized by a hierarchical genetic algorithm to calculate the characteristic peak intensity, the characteristic peak intensity calculation result is more accurate, the spectrum analysis precision is improved, and the accurate decomposition of spectrum overlapping peaks is realized.
The invention adopts the Monte Carlo method to generate the simulated spectrum training neural network, thereby reducing the requirement on actual samples. The weight of the neural network is optimized by adopting a hierarchical genetic algorithm, the characteristic peak intensity of the element to be detected can be directly predicted by using the neural network, the influence of spectral peak overlapping is avoided, and the calculation of the characteristic peak position is not required.
Drawings
FIG. 1 is a roadmap of energy dispersive X-ray fluorescence spectroscopy.
FIG. 2 is a block diagram of hierarchical genetic algorithm control genes and parameter genes.
FIG. 3 is a flowchart of a hierarchical genetic algorithm optimization neural network.
Detailed Description
The following is a further description of embodiments of the invention, with reference to the accompanying drawings:
the invention provides an X-ray fluorescence spectrum overlapping peak decomposition method, which is an energy dispersion X-ray fluorescence spectrum characteristic peak intensity prediction technology, and the adopted technical scheme is shown in figure 1. Firstly, generating a simulated spectrum by using a Monte Carlo method, constructing a simulated spectrum library, then deducting background from the spectrum, then designing a neural network structure and a genetic algorithm, training a neural network optimized by the genetic algorithm, and extracting the peak intensity of a specific element from a spectrum signal to be analyzed by using the trained neural network to realize qualitative and quantitative analysis of the element.
The method comprises the following specific steps:
And 2, designing a three-layer BP neural network. The first layer is an input layer, the number of source nodes is set to be the spectrum length m, and the spectrum is set to be X= (X) 1 ,x 2 ,…,x m ) T The spectrum is input with the count value of each channel of the spectrum.
The second layer is a hidden layer with node number of n, and the hidden layer adopts double tangent functionThe number is used as an activation function. The hidden layer output vector is noted as y= (Y) 1 ,y 2 ,…,y n ) T The output of the j-th node of the hidden layer is:
wherein w is i,j To connect the weight of the i-th input layer element to the j-th hidden layer element, b j To conceal the bias of the jth cell.
The third layer is an output layer, the number of nodes is set to be the number q of characteristic peaks of specific elements to be measured, the activation function adopts a softmax function, the softmax function maps each unit output of the output layer to (0, 1), each unit output represents the ratio of the measured characteristic peak intensity of each element to the sum of all spectrum peak intensities (namely the sum of the characteristic peak intensities of all elements), and the sum of each unit output of the output layer is 1. The input of the kth node of the output layer is:
wherein w' j,k To connect the weight of the jth cell of the hidden layer to the kth cell of the output layer, b' k Is the bias of the kth cell of the output layer. The output of the kth node, i.e. the specific gravity of the total intensity occupied by a certain characteristic peak intensity, is:
the neural network performs supervised learning, and samples for training the neural network are vectors formed by spectral vectors and the ratio of the intensity of each characteristic peak to the total intensity in the spectrum.
And 3, each chromosome corresponds to a complete neural network. The chromosome in the hierarchical genetic algorithm comprises two genes of a control gene and a parameter gene, wherein the upper layer control gene controls the lower layer parameter gene, and the structure of one chromosome is shown in figure 2.
As shown in FIG. 2, the control genes are binary coded, each control gene corresponds to one hidden layer unit, namely, the length of the gene is the number n of hidden layer units, 1 indicates that the parameter gene corresponding to the bit is activated, and 0 indicates dormancy.
The parameter genes adopt real number coding, and each parameter gene represents the weight and bias from the input layer to the hidden layer and from the hidden layer to the output layer, which are connected with the corresponding hidden layer units, and the length is m+n+n+q.
And step 4, the process of optimizing the neural network by the hierarchical genetic algorithm is shown in fig. 3, and the step 4.1-step 4.6 are included.
And 4.1, initializing a population, and randomly generating P individuals according to the chromosome structure and the coding form determined in the step 3.
And 4.2, decoding to obtain weights and biases of different neural networks according to the group parameters. And respectively training the P neural networks by using the training samples, and respectively evaluating the P neural networks by using the test sample to obtain the output errors of the P neural networks.
The input vector in the training sample and the test sample is the count value or count rate of the spectrum in each channel, and the expected output vector is the ratio of the intensity of the element characteristic peak to be calculated to the sum of the intensities of all the characteristic peaks. Since the calculation is performed with a specific element, the calculation of the peak position is not necessary.
Step 4.3, calculating a fitness function, and defining the fitness function of the ith individual as:
where S is the number of samples, o s,k Output of the kth output unit when the s-th sample is taken as input, o s,k ' is the corresponding desired output and q is the number of output layer nodes.
Step 4.4, genetic manipulation:
(1) selecting:
the probability of the ith individual being selected is:
wherein Σf i Is the sum of individual fitness of the population. Using a betting round selection mechanism, the selection probability of each individual in the current population, i.e. p, is calculated s1 ，p s2 ，…，p sP Thereafter, a [0,1 ] is generated]Random number r in, if p s1 +p s2 +...+p s(i-1) ＜r≤p s1 +p s2 +...+p si The ith individual is selected to the pairing library, otherwise not selected.
(2) Crossover and mutation to give new populations:
single-point crossover is used for control genes and parameter genes. The crossover probability is typically chosen between 0.5 and 0.7.
The control gene directly exchanges the ectopic 0 and 1, and the parameter gene adopts cauchy variation, namely, any one of the parameter genes in figure 2 needs to be compiled real number c i The transformation is as follows:
c i ＝c i +δ i ,i＝1,2,…,n；
in delta i To obey the random variable of the cauchy distribution for the scale parameter t=1, the cauchy distribution density function is:
step 4.5, judging whether the genetic algorithm is stopped or not:
the genetic algorithm stops operating when one of the following two conditions is met:
(1) a predetermined evolution algebra is completed;
(2) the optimal individuals in the population are not improved over consecutive generations or the average fitness is not substantially improved over consecutive generations.
When the termination condition is satisfied, the optimal individual is acquired from the last generation, the step is skipped to step 9, and when the termination condition is not satisfied, the step is returned to step 5 for recalculation.
And 4.6, extracting the optimal initial connection weight and bias of the neural network from the optimal individual.
And step 5, training the neural network by using a training sample according to the optimized neural network parameters.
And 6, predicting the element characteristic peak intensity of the spectral data needing element analysis by using the trained neural network. Specifically, the sum of the intensities of all the element characteristic peaks is obtained after the spectrum is integrated, and then the ratio of each element characteristic peak predicted by the neural network to the sum of the intensities of all the element characteristic peaks is multiplied by the sum of the intensities of the characteristic peaks, so that the intensities of each element characteristic peak can be obtained.
Step 7, qualitative and quantitative analysis, wherein according to the relation between the element content and the characteristic peak intensity of a standard sample known in advance, a least square method is utilized to obtain a characteristic peak intensity-content calibration curve of the element, and the expression is as follows:
C＝D+EI；
wherein C is the element content, D is the intercept, E is the slope, and I is the element intensity. The intensity predicted by the neural network is brought into a formula, so that the content of the element can be obtained, and the quantitative analysis of the element is realized.
The scope of the present invention includes, but is not limited to, the above embodiments, and any alterations, modifications, and improvements made by those skilled in the art are intended to fall within the scope of the invention.
Claims (6)
1. An X-ray fluorescence spectrum overlapping peak decomposition method is characterized in that: comprising the following steps:
step 1: generating a simulation spectrum by using a Monte Carlo method, calculating the ratio of the intensity of each element characteristic peak to the sum of the intensities of all element characteristic peaks, and constructing a simulation spectrum library serving as a neural network training and testing database;
step 2: constructing a three-layer BP neural network;
step 3: constructing a hierarchical genetic algorithm, wherein chromosomes in the hierarchical genetic algorithm comprise control genes and parameter genes;
the control genes adopt binary codes, and each control gene corresponds to one hidden layer unit, namely the length of the control gene is the number n of the hidden layer units;
the parameter genes adopt real number codes, and each parameter gene represents the weight and bias from the input layer to the hidden layer and from the hidden layer to the output layer, which are connected with the corresponding hidden layer unit;
step 4: optimizing the neural network by adopting a hierarchical genetic algorithm to obtain the optimal initial connection weight and bias of the neural network;
step 5: training the neural network optimized by a genetic algorithm by using a training sample, wherein the input vector of the training sample is the count value or count rate of the spectrum in each channel, and the expected output vector is the ratio of the intensity of the element characteristic peak to the sum of the intensities of all the element characteristic peaks;
step 6: and predicting the peak intensity of a specific element by utilizing the trained neural network to perform element analysis on the spectrum data, so as to realize quantitative element analysis.
2. The method for decomposing the overlapping peaks of the X-ray fluorescence spectrum according to claim 1, wherein:
the simulation spectrum in the step 1 is an EDXRF simulation spectrum.
3. The method for decomposing the overlapping peaks of the X-ray fluorescence spectrum according to claim 2, wherein: the specific steps of the step 2 include:
three layers of BP neural networks are designed:
the first layer is an input layer, the number of source nodes is set to be the spectrum length m, and the spectrum is set to be X= (X) 1 ,x 2 ,…,x m ) T Inputting the count value of each channel of the spectrum into the spectrum;
the second layer is a hidden layer, the node number of the layer is set as n, the hidden layer adopts a double tangent function as an activation function, and the output vector of the hidden layer is marked as Y= (Y) 1 ,y 2 ,…,y n ) T The output of the j-th node of the hidden layer is:
wherein w is i,j To connect the weight of the i-th input layer element to the j-th hidden layer element, b j Bias for the j-th cell of the hidden layer;
the third layer is an output layer, the number of nodes is set to be the number q of characteristic peaks of specific elements to be measured, an activation function adopts a softmax function, the softmax function maps the output of each unit of the output layer to (0, 1), the output of each unit represents the ratio of the intensity of the characteristic peak of each element to the sum of the intensities of the characteristic peaks of all elements, and the sum of the output of each unit of the output layer is 1; the input of the kth node of the output layer is:
wherein w' j,k To connect the weight of the jth cell of the hidden layer to the kth cell of the output layer, b' k Bias for the kth cell of the output layer; the output of the kth node, i.e. the specific gravity of a certain characteristic peak intensity to the sum of the characteristic peak intensities of all elements, is:
the neural network performs supervised learning, and samples for training the neural network are vectors formed by spectral vectors and the ratio of the intensity of each characteristic peak to the total intensity in the spectrum.
4. The method for decomposing an overlapping peak of an X-ray fluorescence spectrum according to claim 3, wherein: the length of the parameter gene is as follows: m+n+q+n+q.
5. The method for decomposing an overlapping peak of an X-ray fluorescence spectrum according to claim 3, wherein: the specific steps of the step 4 include:
(4.1) initializing a population, and randomly generating P individuals according to the chromosome structure and the coding form determined in the step 3;
(4.2) decoding to obtain weights and biases of different neural networks according to the group parameters;
respectively training the P neural networks by using training samples, and respectively evaluating the P neural networks by using test sample books to obtain output errors of the P neural networks;
(4.3) calculating an fitness function, wherein the fitness function of the ith individual is defined as:
where S is the number of samples, o s,k Output of the kth output unit when the s-th sample is taken as input, o s,k ' is the corresponding expected output, q is the number of output layer nodes;
(4.4), genetic manipulation:
(4.4.1), selection:
the probability of the ith individual being selected is:
wherein Σf i Sum of individual fitness for a population; using a wagering round selection mechanism, the probability of being selected for each individual in the current population, p, is first calculated s1 ，p s2 ，…，p sP Thereafter, a [0,1 ] is generated]Random number r in, if p s1 +p s2 +...+p s(i-1) ＜r≤p s1 +p s2 +...+p si The ith individual is selected to the pairing library, otherwise not selected;
(4.4.2), crossover and mutation to give a new population:
the control gene and the parameter gene are crossed by a single point, and the crossing probability is selected between 0.5 and 0.7;
the control gene directly exchanges 0 and 1 which are changed into different positions;
the parameter gene adopts cauchy variation, namely, the parameterReal number c of any one gene to be compiled i The transformation is as follows:
c i ＝c i +δ i ,i＝1,2,…,n；
in delta i To obey the random variable of the cauchy distribution for the scale parameter t=1, the cauchy distribution density function is:
(4.5), judging whether the genetic algorithm is stopped or not:
the genetic algorithm stops operating when one of the following two termination conditions is met:
(4.5.1) completing a predetermined evolution algebra;
(4.5.2) the optimal individuals in the population are not improved over consecutive generations or the average fitness is not substantially improved over consecutive generations;
when the termination condition is met, acquiring the optimal individual from the last generation, jumping to the step (4.6), and when the termination condition is not met, returning to the step (4.2) for recalculation;
(4.6) extracting the optimal initial connection weight and bias of the neural network from the optimal individual.
6. The method for decomposing an overlapping peak of an X-ray fluorescence spectrum according to claim 5, wherein: the specific steps of the step 6 include:
(6.1) predicting spectral data to be subjected to element analysis by using a trained neural network to obtain the ratio of the intensity of each element characteristic peak predicted by the neural network to the sum of the intensities of all element characteristic peaks;
integrating the spectrum data to obtain the sum of the intensities of all element characteristic peaks, and multiplying the sum of the intensities of all element characteristic peaks by the ratio of the intensity of each element characteristic peak predicted by the neural network to the sum of the intensities of all element characteristic peaks to obtain the intensity of each element characteristic peak;
(6.2) qualitative and quantitative analysis: according to the relation between the element content and the element characteristic peak intensity of a standard sample known in advance, obtaining an element characteristic peak intensity and element content calibration curve by using a least square method, wherein the expression is as follows:
C＝D+EI；
wherein C is the element content, D is the intercept, E is the slope, and I is the element strength; and (3) bringing the characteristic peak intensity of the element obtained in the step (6.1) into a formula to obtain the content of the element and realize quantitative analysis of the element.
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