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- Nachgewiesen in: USPTO Patent Applications
- Sprachen: English
- Document Number: 20240035991
- Publication Date: February 1, 2024
- Appl. No: 18/186035
- Application Filed: March 17, 2023
- Claim: 1. A method of XRF quantitative analysis of heavy metal elements based on LLE-SVR, wherein the method comprises: establishing the relationship between peak information and element content by using Local Linear Embedding For Dimensionality Reduction and Support Vector Regression Predictive Algorithms based on machine learning, to quantitatively analyze of the content information of elements contained in substances.
- Claim: 2. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 1, wherein the method comprises the following steps of: a first step of obtaining a soil sample set and constructing an element set based on the soil sample set, and using ED-XRF Fluorescence Spectrometer to identify peak information and content information of the elements in the sample to be measured of the soil sample set corresponding to the element set, to obtain the measured component value and the content value of each element; a second step of constructing an LLE-SVR model, and determining an input matrix and an output matrix of the LLE-SVR model, and normalizing the input matrix and the output matrix of the LLE-SVR model to obtain the normalized matrixes of the input matrix and the output matrix; a third step of searching for neighbor points and calculating a weight value of the neighbor points based on the normalized matrixes of the input matrix and the output matrix, and performing LLE for dimensionality reduction and calculating a component matrix after LLE for dimensionality reduction; a fourth step of performing nonlinear function mapping and constructing a classification hyperplane, and introducing a penalty factor and a slack variable for constraint, and training the LLE-SVR model via parameter optimization to quantitatively predict the element content; and a fifth step of denormalizing the normalized output matrix of the target element content to obtain the denormalized output matrix, and calculating the coefficient of determination to evaluate the predicting effect of the LLE-SVR model.
- Claim: 3. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 2, wherein the first step of obtaining the soil sample set and constructing the element set based on the soil sample set comprises: obtaining a standard sample set, and identifying all elements of all samples to be measured in the standard sample set by using ED-XRF Fluorescence Spectrometer, to obtain an element set A containing all elements of all samples to be measured in the standard sample set; where said all elements are element Nos. 12-92 in periodic table; the input matrix of the LLE-SVR model in the second step is a matrix composed of the measured component values of all target elements of the element set A and their corresponding interfering elements; the output matrix of the LLE-SVR model is a matrix composed of the measured content values of the target elements; the target elements are the elements to be quantitatively analyzed; the interfering elements are the elements that interfere with the target elements; the matrix of the measured component values is a matrix composed of the component values of m element(s) contained in each of n sample(s) to be measured; the first column of the matrix of the measured component values is the measured component values of a single target element, and the remaining m-1 column(s) of the matrix of the measure component values is composed of the measured component values of other target elements and the interfering elements corresponding to all target elements; and the matrix of the measured content values is a matrix composed of the concentration values of the single target element contained in each of n samples to be measured.
- Claim: 4. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 2, wherein the second step of normalizing the input matrix and the output matrix of the LLE-SVR model comprises: normalizing the input matrix and the output matrix to obtain the normalized matrixes: [mathematical expression included] [mathematical expression included] [mathematical expression included] [mathematical expression included] wherein x′ij represents the component value of the element in the jth column of the ith sample of the normalized input matrix Xnm in the LLE-SVR model, and xij represents the component value of the element in the jth column of the ith sample of the input matrix Xnm, and xmin represents the minimum of the input matrix Xnm, and xmax represents the maximum of the input matrix Xnm; Xnm represents the normalized matrix of the input matrix Xnm in the LLE-SVR model; the row vector x′iT(x′i1, x′i2, . . . , x′im) of the ith row of the matrix Xnm represents the normalized vector of the component values of m element(s) contained in the ith sample to be measured; n represents the number of the samples to be measured contained in the standard sample set; m represents the number of the elements in each sample to be measured; y′i1represents the content values of the target elements of the ith sample of the normalized output matrix Yn1in the LLE-SVR model; yi1represents the content values of the target elements of the ith sample of the output matrix Yn1; ymin represents the minimum of the output matrix Yn1; ymax represents the maximum of the output matrix Yn1; Ŷn1 represents the normalized matrix of output matrix in the LLE-SVR model; i=1, 2, . . . , n, j=1, 2, . . . , m
- Claim: 5. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 2, wherein the step of searching for neighbor points and calculating a weight value of the neighbor points based on the normalized matrixes of the input matrix and the output matrix, and performing LLE for dimensionality reduction and calculating a component matrix after LLE for dimensionality reduction comprises: (1) searching for the neighbor points: in local neighborhood, calculating Euclidean Distance between each normalized sample point x′ij and the points of other n-1 samples, and selecting I neighbor points of x′ij; (2) calculating the weight value W of the neighbor points: calculating the weight value W of each sample point x′ij and I neighbor points of each sample point; [mathematical expression included] wherein, x′ij represents the normalized component value of the element in the jth column of the ith sample, and x′pq represents the normalized component value of the element in the qth column of the pth sample, and wip represents the weight value between the sample point x′ij and the sample point x′pq, and when the sample point x′pq does not belong to the neighbor of the sample point x′ij, wip=0; and (3) mapping the m-dimensional data of each row in the matrix Xnm to the k-dimensional data by nonlinear function mapping: obtaining k principal components by using the local linear embedding method (LLE) for dimensionality reduction, and using the k-dimensional data to reflect the information expressed in the original m-dimensional data, and obtaining the dimensionality-reduced feature Z: [mathematical expression included] wherein the dimensionality-reduced feature Z satisfies the following two conditions: [mathematical expression included] [mathematical expression included] [mathematical expression included] wherein Z represents the dimensionality-reduced feature matrix, and the dimension k of the dimensionality-reduced feature matrix Z is lower than the dimension n of the original sample (k≤n), and zij represents the component value of the jth column of the ith sample after LLE for dimensionality reduction, and the row vector ZiT=(zi1, zi2, . . . , zik) of the ith row of the matrix Z represents the component value vector of k elements contained in the ith samples to be measured i=1, 2, . . . , n, j=1, 2, . . . , k.
- Claim: 6. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 2, wherein the forth step of performing nonlinear function mapping and constructing a classification hyperplane, and introducing a penalty factor and a slack variable for constraint, and training the LLE-SVR model via parameter optimization to quantitatively predict the element content comprises: 1) mapping the k-dimensional element component value data from the low-dimensional nonlinear separable space to a high-dimensional linear separable feature space, and constructing a classification hyperplane in this high-dimensional linear separable feature space: hp[(w·φ(xp))+b]−1≥0; wherein p represent the class marker under p dimension, and when located above the hyperplane w·φ(xp)+b it is defined hp=1; when located below the hyperplane w·φ(xp)+b, it is defined hp=−1; p=1, 2, . . . , k, k≤m; w represents the weight value vector of the feature, and b represents the bias; xp represents the element component value vector after the dimensionality reduction of the sample to be measured into p dimensions via PCA, and φ(xp)represents a nonlinear mapping function mapping the data xp to the high-dimensional linear separable feature space; 2) introducing the penalty factor ξp and the slack variable for constraint and converting the classification hyperplane problem into a quadratic programming model: [mathematical expression included] 3) training the LLE-SVR model by parameter optimization using the cross-validation method based on grid search: obtaining the optimal parameter penalty factor and the optimal slack variable by iteratively searching for the optimal parameters; and 4) introducing a Lagrangian multiplier αp and a kernel function K to calculate the the minimum classification hyperplane satisfying the quadratic programming model, which is prediction result ŷ′i of the target element content, and the calculation formula for predicting the target element content of any ith sample to be measured being: [mathematical expression included] [mathematical expression included]
- Claim: 7. The method of XRF quantitative analysis of heavy metal elements based on LLE-SVR according to claim 2, the fifth step of denormalizing the normalized output matrix of the target element content to obtain the denormalized output matrix, and calculating the coefficient of determination to evaluate the predicting effect of the LLE-SVR model comprises: (1) denormalizing the normalized output matrix Ŷ′n1 in of the target element content to obtain the denormalized output matrix in Ŷ′n1: [mathematical expression included] [mathematical expression included] wherein ŷi1 represents the prediction value of the target element content of the ith sample of the denormalized output matrix and Ŷn1, and y′min represent the minimum of the output matrix Ŷ′n1 , and y′max represents the maximum of the output matrix Ŷ′n1; i=1, 2, . . . , n; and (2) comparing the predicted target element content ŷi1 with the true target element content yi1, and calculating the coefficient of determination R2: [mathematical expression included] [mathematical expression included] wherein yi1represents the true value of the target element content of the ith sample, and ŷi1 represents the prediction value of the target element content of the ith sample, and yi1 represents the average of the true value of the target element content of the ith sample to be measured; i=1, 2, . . . , n.
- Claim: 8. A computer device, comprising a storage storing a computer program, and a processor configured to perform the steps of the method of XRF quantitative analysis of heavy metal elements based on LLE-SVR as claimed in claim 1 when executing the computer program.
- Claim: 9. A computer-readable storage medium storing a computer program, wherein a processor is configured to perform the steps of the method of XRF quantitative analysis of heavy metal elements based on LLE-SVR as claimed in claim 1 when executing the computer program.
- Claim: 10. An information data processing terminal, configured to implement the method of XRF quantitative analysis of heavy metal elements based on LLE-SVR as claimed claim 1.
- Current International Class: 01; 06; 01
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