XRF quantitative analysis method for multi-material system based on density clustering and sherman physical model

Abstract

The application discloses a multi-material system XRF quantitative analysis method based on density clustering and Sherman physical model, relates to the technical field of fluorescence spectrum analysis, and comprises the following steps: obtaining a material type parameter of a sample to be measured and calling a corresponding parameter library; performing multi-point X-ray fluorescence spectrum acquisition, performing total intensity threshold preliminary screening on an original spectrum, performing characteristic dimension reduction representation, and performing density-based clustering processing to extract a main cluster average spectrum; performing background deduction and spectral line interference correction on the average spectrum, combining a Sherman physical model to iteratively solve a concentration, and outputting element content or oxide content according to a material mode; performing result quality evaluation based on a main cluster proportion, a main cluster dispersion degree and a model fitting residual error, and performing abnormal rollback when preset conditions are not met. Through weakening of abnormal sampling interference, reduction of continuous background and peak overlap influence, unification of metal and oxidized slag analysis processes, detection stability, accuracy, result reliability and application efficiency are improved.

Description

Technical Field

[0001] This invention relates to the field of fluorescence spectroscopy analysis technology, specifically to a quantitative XRF analysis method for multi-material systems based on density clustering and the Sherman physical model. Background Technology

[0002] X-ray fluorescence analysis is a commonly used elemental analysis technique. It excites samples to generate fluorescence signals with characteristic energies, and identifies and determines the content of elements based on the energy, location, and intensity of the fluorescence signals. This technique has advantages such as fast analysis speed, minimal sample damage, and suitability for on-site testing, and has been widely applied in scenarios such as metallic material composition analysis, metallurgical process control, mineral detection, and solid waste analysis.

[0003] In existing applications, X-ray fluorescence quantitative analysis of different material systems, such as metallic materials and oxide slag materials, is often affected by factors such as uneven sample surface, non-uniform particle size, local segregation, and insufficient sample preparation consistency. This leads to significant spectral differences between different sampling points of the same sample, easily resulting in abnormal spectra. If abnormal spectra are directly used for quantitative calculations, it often causes distortion of characteristic peak intensities, thereby affecting the stability and accuracy of elemental content determination results.

[0004] Meanwhile, quantitative X-ray fluorescence analysis is also commonly affected by matrix effects. On the one hand, different elements can have absorption and response coupling effects on fluorescence signals; on the other hand, the matrix composition varies greatly between different material systems, and even the same target element may exhibit significantly different response patterns in metallic and oxide slag materials. In existing technologies, a common approach is to establish empirical calibration curves or configure independent analytical models for different materials. This approach typically relies on numerous standard samples, has poor model transferability, and is cumbersome in scenarios involving multiple material switching.

[0005] Furthermore, in actual detection, there may be spectral overlap between characteristic peaks of different elements. If the detection resolution is limited or the peak positions are close, the response signal of one element is easily superimposed on the measurement result of another element, resulting in inaccurate extraction of net peak intensity. In addition, the presence of continuous background makes low-content elements and weak peak elements more susceptible to interference, thereby further reducing the reliability of quantitative results.

[0006] Therefore, current technologies lack a method for X-ray fluorescence quantitative analysis that can address multiple material systems while simultaneously performing anomalous spectral removal, net spectral intensity extraction, matrix effect correction, and unified quantitative processing of metallic and oxide slag materials within the same analytical framework. To this end, it is necessary to propose a new technical solution to improve the accuracy, stability, and applicability of X-ray fluorescence quantitative analysis in multiple material systems. Summary of the Invention

[0007] Based on the shortcomings of the prior art described above, the purpose of this invention is to provide a quantitative XRF analysis method for multi-material systems based on density clustering and Sherman physical models, so as to solve the above-mentioned technical problems.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a quantitative XRF analysis method for multi-material systems based on density clustering and Sherman physics models, comprising:

[0009] Obtain the material type parameters of the sample to be tested, and call the corresponding parameter library according to the material type parameters. The parameter library shall include at least the set of elements to be tested, the set of matrix elements, mass absorption parameters, spectral information, interference coefficient matrix, pre-calibrated instrument constants, oxide conversion coefficients and normalization rules.

[0010] Multi-point X-ray fluorescence spectroscopy acquisition was performed on the sample to be tested to construct the original spectral set;

[0011] The total intensity threshold is used to initially screen each spectrum in the original spectral set to obtain a candidate spectral set.

[0012] The candidate spectral set is characterized by feature dimensionality reduction and density-based clustering to remove noisy spectra, determine the main cluster with the largest number of samples, and average the spectra within the main cluster channel by channel to obtain the representative input spectrum.

[0013] Background subtraction is performed on the representative input spectrum to extract the measured net intensity of each target element. Spectral interference correction is performed based on the interference coefficient matrix to obtain the true net intensity of each target element.

[0014] Based on material type parameters and the Sherman physics model, the correspondence between the theoretical fluorescence intensity and element concentration of the target element is established. The concentration is then iteratively solved by combining the instrument constant, mass absorption parameters and the actual net intensity to obtain the element concentration result.

[0015] When the material type parameter indicates the slag oxidation mode, the element concentration results are converted to oxides and normalized to obtain the oxide content results; when the material type parameter indicates the metal mode, the element concentration results are processed according to the metal mode normalization rules.

[0016] The quality of the results is evaluated based on the main cluster ratio, main cluster dispersion, and model fitting residual. The main cluster ratio is obtained by the ratio of the number of spectra in the main cluster to the number of spectra in the candidate spectrum set. The main cluster dispersion is obtained by the degree of deviation of each spectrum in the main cluster from the main cluster feature center. The model fitting residual is obtained by the difference between the actual net intensity and the theoretical fluorescence intensity.

[0017] When the result quality evaluation meets the preset output conditions, the quantitative analysis results are output; when the result quality evaluation does not meet the preset output conditions, an abnormal rollback is triggered.

[0018] The present invention is further configured to perform a preliminary screening of each spectrum in the original spectral set using a total intensity threshold, specifically including:

[0019] Count the total intensity of each original spectrum across all channels;

[0020] Calculate the average value of the total intensity of all original spectra;

[0021] Set the lower limit threshold of total intensity to three times the average value, and set the upper limit threshold of total intensity to twice the average value;

[0022] The original spectra with total intensity between the lower and upper thresholds are retained as the candidate spectrum set.

[0023] The present invention is further configured to perform feature dimensionality reduction characterization and density-based clustering on the candidate spectral set, specifically including:

[0024] Principal component analysis is performed on the candidate spectrum set to obtain the low-dimensional eigenvectors corresponding to each candidate spectrum;

[0025] The core samples are determined based on the characteristic distance between candidate spectra, combined with the neighborhood radius and the minimum number of neighborhood points.

[0026] Starting from any core sample, all density-reachable samples are grouped into the same cluster, and samples that do not belong to any cluster are removed as noise samples;

[0027] Compare the number of samples in all the obtained clusters, and determine the cluster with the largest number of samples as the master cluster;

[0028] The minimum number of neighborhood points is determined based on the feature dimension after dimensionality reduction, and is a value that is not less than twice the feature dimension.

[0029] The present invention is further configured to perform channel-by-channel averaging of the spectrum within the main cluster to obtain a representative input spectrum, specifically including:

[0030] The average of all spectra within the main cluster is calculated according to the channel position to form a representative input spectrum;

[0031] The dispersion of the main cluster is determined by the degree of deviation of each low-dimensional feature vector within the main cluster from the feature center of the main cluster.

[0032] The dispersion of the main cluster is used as an input for evaluating the quality of the results, and is used to characterize the spectral consistency within the main cluster.

[0033] The present invention is further configured to perform background subtraction on a representative input spectrum and extract the measured net intensity of each target element, specifically including:

[0034] For each target element's characteristic peak, select non-interfering background points on both the left and right sides of the characteristic peak;

[0035] Linear estimation of background intensity at the location of characteristic peaks is performed based on undisturbed background points.

[0036] Subtract the background intensity from the total intensity of the characteristic peak to obtain the measured net intensity of the corresponding target element;

[0037] The measured net intensities of all target elements are combined into a set of measured net intensities.

[0038] The present invention is further configured to perform spectral interference correction based on the interference coefficient matrix, specifically including:

[0039] Establish a matrix of spectral interference coefficients between target elements, where the diagonal positions represent the response of the target element itself, and the off-diagonal positions represent the proportion of spectral interference between different elements.

[0040] Based on the interference coefficient matrix, the measured net intensity set is decoupled to obtain the true net intensity of each target element;

[0041] The interference coefficient matrix is ​​obtained by calibration using single-element standard samples or mixed standard samples of known components, and is stored and retrieved separately according to different material types.

[0042] The present invention is further configured such that the instrument constants in the parameter library are instrument constants obtained in advance through calibration using similar matrix standard samples, and the calibration specifically includes:

[0043] For each target element, select one or more standard samples that are similar to the matrix of the sample to be tested;

[0044] Obtain the known concentration of the target element in the standard sample and the net intensity after background subtraction and spectral interference correction;

[0045] The instrument constants are determined by combining the absorption parameters and physical response parameters corresponding to the standard samples.

[0046] When multiple standard samples exist, the instrument constants corresponding to the multiple standard samples are processed in a comprehensive manner to obtain the final instrument constant corresponding to the target element, and the final instrument constant is stored in the parameter library.

[0047] The present invention is further configured to establish a correspondence between the theoretical fluorescence intensity of the target element and the elemental concentration based on the Sherman physics model, specifically as follows:

[0048] Based on the target element concentration, instrument constant, excitation efficiency, fluorescence yield, transition probability, geometric parameters, and the absorption and matrix response of the current material system to the target element's fluorescence signal, a calculation relationship for the theoretical fluorescence intensity of the target element is established. Among them, the absorption and matrix response of the current material system to the target element's fluorescence signal are jointly determined by the combined influence of each element in the current material system on the target element's fluorescence signal.

[0049] The present invention further specifies that the concentration iterative solution specifically includes:

[0050] Establish the initial concentration distribution of the target elements, wherein the initial concentration of non-matrix elements is determined based on the true net intensity and the preset initial value rule, and the concentration of matrix elements is determined based on the remaining mass fraction.

[0051] Calculate the theoretical fluorescence intensity of each target element based on the concentration distribution of the current round;

[0052] A concentration correction factor is constructed based on the difference between the actual net intensity and the theoretical fluorescence intensity, and the concentration of the target element is updated accordingly.

[0053] Set the updated concentration values ​​that are less than zero to zero;

[0054] When the material type parameter indicates metal mode, the concentration results are normalized according to the metal mode normalization rule after each iteration.

[0055] When the concentration change in two consecutive iterations is less than the preset convergence threshold, the iteration stops and the element concentration result is output.

[0056] The present invention is further configured such that oxide conversion and result quality evaluation specifically include:

[0057] When the material type parameter indicates the slag oxidation mode, the element concentration is converted into oxide content according to the preset oxide conversion factor, and the total oxide content is normalized.

[0058] The quality of the results is evaluated based on the proportion of main clusters, the dispersion of main clusters, and the model fitting residuals.

[0059] When the proportion of the main cluster is higher than the preset threshold, the dispersion of the main cluster is lower than the preset threshold, and the model fitting residual is less than the preset threshold, the element content or oxide content, standard deviation, and confidence level are output.

[0060] If any condition is not met, an abnormal rollback is executed. An abnormal rollback includes at least one of resampling, re-sample preparation, or reselection of the detection mode.

[0061] This invention provides a quantitative XRF analysis method for multi-material systems based on density clustering and the Sherman physical model. The method involves acquiring material type parameters of the sample, calling a corresponding parameter library based on these parameters. The parameter library includes at least the set of elements to be tested, the set of matrix elements, mass absorption parameters, spectral line information, interference coefficient matrix, pre-calibrated instrument constants, oxide conversion coefficients, and normalization rules. Multi-site X-ray fluorescence spectral acquisition is performed on the sample to construct an initial spectral set. Each spectrum in the initial spectral set is initially screened using a total intensity threshold to obtain a candidate spectral set. The candidate spectral set undergoes feature reduction and density-based clustering to remove noisy spectra, identifying the main cluster with the largest number of samples. Channel-by-channel averaging is performed on the spectra within the main cluster to obtain representative input spectra. Background subtraction is performed on the representative input spectra to extract the measured net intensity of each target element. Spectral line interference correction is performed based on the interference coefficient matrix to obtain the true net intensity of each target element. Based on material type parameters and... The Sherman physics model is used to establish the correspondence between the theoretical fluorescence intensity and elemental concentration of the target element. The concentration is then iteratively solved using instrument constants, mass absorption parameters, and the actual net intensity to obtain the elemental concentration result. When the material type parameter indicates oxide slag mode, the elemental concentration result is converted to oxides and normalized to obtain the oxide content result. When the material type parameter indicates metal mode, the elemental concentration result is processed according to the metal mode normalization rules. Result quality is evaluated based on the main cluster ratio, main cluster dispersion, and model fitting residual. The main cluster ratio is obtained by the ratio of the number of spectra within the main cluster to the number of spectra in the candidate spectral set. The main cluster dispersion is obtained by the degree of deviation of each spectrum within the main cluster from the main cluster's characteristic center. The model fitting residual is obtained by the difference between the actual net intensity and the theoretical fluorescence intensity. Quantitative analysis results are output when the result quality evaluation meets the preset output conditions. An abnormal rollback is triggered when the result quality evaluation does not meet the preset output conditions. The beneficial effects include:

[0062] 1. After performing multi-site X-ray fluorescence spectroscopy acquisition on the sample to be tested, the original spectra are first screened by total intensity thresholding. Then, the candidate spectra are characterized by feature reduction and density-based clustering to remove noisy spectra and extract the main cluster with the most samples. Subsequently, the spectra within the main cluster are averaged channel by channel to obtain representative input spectra. This method can effectively reduce the interference of sample surface unevenness, particle size inhomogeneity, local segregation, and occasional sampling anomalies on the input spectra, reduce the probability of abnormal spectra entering the subsequent quantitative calculation stage, and thus improve the consistency of input data and the stability of analysis results.

[0063] 2. By further performing background subtraction and spectral interference correction on representative input spectra, the true net intensity of each target element is obtained. Concentration is then iteratively solved based on the Sherman physics model, combined with instrument constants, mass absorption parameters, and the true net intensity. This method more effectively reduces the impact of continuous background, peak overlap, and differences in the absorption response of the material system on the quantitative results, providing a clearer physical constraint basis for the concentration calculation of target elements. Furthermore, the method introduces the proportion of the main cluster, the dispersion of the main cluster, and the model fitting residuals to evaluate the quality of the results. Anomaly backoff is triggered when preset conditions are not met, thus not only improving the accuracy of element content calculation but also enhancing the credibility and usability of the final output results.

[0064] 3. By acquiring material type parameters and calling the corresponding parameter library, unified processing of metallic and oxide slag material modes is achieved within the same analytical framework. Specifically, elemental concentration results are output in metallic mode, while oxide conversion and total amount normalization are further performed in oxide slag mode. This approach adapts to the quantitative needs of different material systems while maintaining consistent analytical logic, reducing processing complexity when switching between multiple materials, and minimizing reliance on large numbers of standard samples and repetitive modeling processes. This improves detection efficiency, expands the method's applicability, and enhances its engineering application value in metallurgical analysis, material composition detection, and rapid on-site detection scenarios.

[0065] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0067] Figure 1 The flowchart illustrates an exemplary embodiment of the present invention, showing a quantitative XRF analysis method for multi-material systems based on density clustering and the Sherman physical model. Detailed Implementation

[0068] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0069] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0070] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0071] XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model, such as Figure 1 As shown, it includes:

[0072] Obtain the material type parameters of the sample to be tested, and call the corresponding parameter library according to the material type parameters. The parameter library shall include at least the set of elements to be tested, the set of matrix elements, mass absorption parameters, spectral information, interference coefficient matrix, pre-calibrated instrument constants, oxide conversion coefficients and normalization rules.

[0073] Multi-point X-ray fluorescence spectroscopy acquisition was performed on the sample to be tested to construct the original spectral set;

[0074] The total intensity threshold is used to initially screen each spectrum in the original spectral set to obtain a candidate spectral set.

[0075] The candidate spectral set is characterized by feature dimensionality reduction and density-based clustering to remove noisy spectra, determine the main cluster with the largest number of samples, and average the spectra within the main cluster channel by channel to obtain the representative input spectrum.

[0076] Background subtraction is performed on the representative input spectrum to extract the measured net intensity of each target element. Spectral interference correction is performed based on the interference coefficient matrix to obtain the true net intensity of each target element.

[0077] Based on material type parameters and the Sherman physics model, the correspondence between the theoretical fluorescence intensity and element concentration of the target element is established. The concentration is then iteratively solved by combining the instrument constant, mass absorption parameters and the actual net intensity to obtain the element concentration result.

[0078] When the material type parameter indicates the slag oxidation mode, the element concentration results are converted to oxides and normalized to obtain the oxide content results; when the material type parameter indicates the metal mode, the element concentration results are processed according to the metal mode normalization rules.

[0079] The quality of the results is evaluated based on the main cluster ratio, main cluster dispersion, and model fitting residual. The main cluster ratio is obtained by the ratio of the number of spectra in the main cluster to the number of spectra in the candidate spectrum set. The main cluster dispersion is obtained by the degree of deviation of each spectrum in the main cluster from the main cluster feature center. The model fitting residual is obtained by the difference between the actual net intensity and the theoretical fluorescence intensity.

[0080] When the result quality evaluation meets the preset output conditions, the quantitative analysis results are output; when the result quality evaluation does not meet the preset output conditions, an abnormal rollback is triggered.

[0081] Specifically, the XRF quantitative analysis method for multi-material systems based on density clustering and the Sherman physics model is applied to a multi-material system XRF quantitative analysis system based on density clustering and the Sherman physics model. The system includes an X-ray excitation module, a spectrometer module, a detection module, a control module, and a display module. The X-ray excitation module generates high-energy X-rays to excite the sample. The X-ray tube can use a rhodium or tungsten target structure, and the high-voltage power supply outputs an accelerating voltage of 10 kV to 60 kV. The spectrometer module adopts a wavelength dispersive structure and decomposes the composite X-rays through a spectroscopic crystal to improve spectral resolution. The detection module uses a silicon drift detector or a multichannel analyzer to convert the received X-ray photons into electrical signals and form spectral data. The control module includes a processor and a memory. The processor executes the following procedures: anomaly spectrum identification, net intensity extraction, quantitative calculation based on the Sherman physics model, and result quality evaluation. The display module displays the elemental content results, oxide content results, standard deviation, confidence level, and the original spectrum and the processed spectral curves.

[0082] To enable the same system to be applied to both metallic and oxide slag materials, this embodiment pre-establishes a material model parameter library in the control module. The material model parameter library is divided according to material type parameters; when the material type parameter is zero, it corresponds to the metallic material model; when the material type parameter is one, it corresponds to the oxide slag material model. The parameter library for the metallic material model stores the set of analytes, the set of matrix elements, mass absorption parameters, spectral information, the overlap peak interference coefficient matrix, pre-calibrated instrument constants, and metallic model normalization rules. The parameter library for the oxide slag material model further stores oxide conversion coefficients and total oxide normalization rules based on the above parameters. For iron-based metallic materials, manganese, chromium, and nickel can be used as the main analytes, with iron as the matrix element; for oxide slag materials, calcium, silicon, magnesium, aluminum, iron, manganese, and chromium can be used as analytes, and corresponding conversion coefficients for calcium oxide, silicon dioxide, magnesium oxide, aluminum oxide, and iron oxide are stored. This parameter library structure allows for quantitative solutions to be achieved through parameter switching within a unified analytical framework, rather than establishing completely independent empirical calibration curves for different material systems.

[0083] The methods specifically include:

[0084] Step one involves instrument preparation and parameter loading. The control module first receives the material type parameters based on the detection object selected by the user on the interface and then calls the corresponding parameter library. For the detection of iron-based metal materials, the metal mode parameter library is called; for the detection of oxide slag, the oxide slag mode parameter library is called. Simultaneously, the corresponding characteristic peak positions, background ranges, mass absorption parameters, interference coefficient matrices, and instrument constants are loaded. The instrument constants are obtained through pre-calibration and storage. Specifically, one or two standard samples with a matrix similar to the sample to be tested are selected for the target element. Background subtraction and spectral interference correction are performed on the standard samples to obtain the corrected net intensity of the target element. Then, the instrument constant of the element is determined by combining the known concentration of the standard sample, the corresponding total absorption term, and the comprehensive physical response parameters. If multiple standard samples exist, the instrument constants are averaged or determined comprehensively based on the principle of smaller fitting residuals, and the final result is written into the parameter library. This method allows the system to directly call the calibrated instrument constants in subsequent detection processes, improving on-site analysis efficiency.

[0085] Step two: Perform multi-point spectral acquisition. Considering the potential for unevenness, non-uniform particle size, and localized segregation on the sample surface, a single-point acquisition method is not used. Instead, multiple sampling points are set on the sample surface. The control module directs the X-ray excitation module to irradiate the sample surface point by point according to a preset scanning path, while the detection module simultaneously acquires the X-ray fluorescence spectra at each sampling point. Assume a total of [number missing] X-ray fluorescence spectra are acquired. The original spectrum, number The original spectra are denoted as: ,in, Indicates the first The original spectrum in the first Count intensity on each channel This represents the total number of channels. For engineering applications, the number of sampling points can be selected based on the sample size and surface uniformity. For example, twenty to thirty sampling points can be set on iron-based alloy samples, and fifteen to twenty-five sampling points can be set on oxide slag samples to obtain sufficient statistical representativeness.

[0086] Step 3: Perform initial screening using the total intensity threshold of the original spectra. Calculate the total intensity of all channels for each original spectrum: Then calculate the average value of the total intensity of all original spectra: The lower limit threshold for total intensity is set to three times the average value, and the upper limit threshold for total intensity is set to twice the average value, i.e.: , , retain satisfaction The original spectra are used as a candidate spectrum set. Spectra below the lower threshold are classified as insufficient excitation, abnormal coupling, or locally obstructed spectra, while spectra above the upper threshold are classified as locally contaminated, abnormally enhanced, or distorted in counting. This step allows for the initial elimination of spectra that significantly deviate from the overall distribution, providing a more stable database foundation for subsequent density clustering.

[0087] Step four involves dimensionality reduction of the candidate spectral set. Since the original spectra have a large number of channels and strong correlations exist between adjacent channels, direct density clustering in high-dimensional space can easily lead to instability in the distance scale. Therefore, principal component analysis is performed on the candidate spectra first. Let the dimensionality reduction result in the... The eigenvectors corresponding to the candidate spectra are ,in, This refers to the feature dimensions retained when the cumulative variance contribution rate reaches a preset threshold. For general metallic material samples, the cumulative variance contribution rate threshold can be set to around 95%; for oxide slag samples with large background fluctuations, it can be appropriately increased to around 97% to ensure that the main feature information is fully preserved.

[0088] Step 5: Perform density-based clustering on the candidate spectra. The Euclidean distance between the feature vectors of any two candidate spectra is defined as: For any eigenvector ,That The neighborhood sample number is defined as: ;

[0089] when When the corresponding sample is marked as a core point, the neighborhood radius is... pass The inflection point of the distance curve is determined, and the minimum number of neighborhood points is determined. The feature dimension is determined based on the reduced dimension and is set to a value no less than twice the feature dimension. Starting from any core point, all density-reachable samples are grouped into the same cluster, resulting in multiple cluster sets. Samples not belonging to any cluster are designated as noise points. The number of samples in each cluster is compared, and the cluster with the largest number of samples is determined as the master cluster. This master cluster reflects the most concentrated spectral distribution of the same sample under normal sampling conditions and can effectively eliminate outliers caused by particle anomalies, localized oxide scale, surface deposits, or occasional sampling jitter.

[0090] Step six: Average the main cluster spectrum channel by channel to form a representative input spectrum. Let the main cluster be... Then the average spectrum of the main cluster is: ,in, ;

[0091] Simultaneously, to evaluate the internal consistency of the primary cluster, the primary cluster dispersion is calculated: ,in, The main cluster feature centers are used. The average spectrum of the main cluster serves as the input spectrum for subsequent background subtraction and net intensity extraction, while the dispersion of the main cluster is used as an input for subsequent result quality evaluation. The main process is not interrupted immediately at this step, but rather comprehensively judged together with other evaluation indicators in the final output stage. This process reduces random noise and avoids the impact of single-point distortion on the subsequent Sherman model solution.

[0092] Step 7: Perform background subtraction on the representative input spectrum. For the target element... The characteristic peak, let the peak energy be... Select interference-free background points on both sides of the peak. and The corresponding background intensities are respectively and The background intensity at the peak position was determined using a two-point linear interpolation method. Let the total peak intensity at the peak position be... Then the measured net intensity of the target element is: After performing the above processing on all target elements, the measured net intensity vector can be constructed: ,in, The number of target elements.

[0093] Step 8: Perform spectral interference correction. For element pairs with close energy positions and overlapping spectral lines, pre-establish an interference coefficient matrix: Where the diagonal elements represent the response of the target element itself, and the off-diagonal elements represent the proportion of spectral interference between different elements. The measured intensity vector and the true intensity vector satisfy the following: ;

[0094] Therefore, we can conclude that: The interference coefficients in the matrix are obtained through calibration using single-element standards or mixed standards with known compositions, and are stored separately in metallic and oxide spectral modes. Taking the adjacent peaks of chromium and manganese in iron-based alloys as an example, the response ratio of each element to adjacent peaks can be measured using standard samples containing a single element or elements in known proportions, thereby constructing an interference coefficient matrix suitable for this material system. For cases with high matrix condition numbers, a constrained robust solution method can be used to obtain the true net intensity, thereby enhancing numerical stability. This step can mitigate the overestimation and underestimation problems caused by overlapping spectral lines.

[0095] Step nine: Establish the theoretical fluorescence intensity relationship based on the Sherman physics model and perform iterative concentration calculation. For any target element... Its theoretical fluorescence intensity is expressed as: ,in, For target element The instrument constant, For the concentration to be determined, It is a comprehensive physical response term determined by excitation efficiency, fluorescence yield, transition probability, and geometric parameters. Let be the total absorption term of the fluorescence signal of the target element in the current material system, which satisfies: ,in, Represents element For elements The absorption contribution parameter.

[0096] In numerical solutions, an initial concentration vector is first established: ;

[0097] The initial concentration of non-matrix elements is determined based on the true net strength and a preset initial value rule, while the concentration of matrix elements is determined based on the remaining mass fraction. During each iteration, the total absorption term of each target element is first calculated based on the current concentration distribution, and then the theoretical fluorescence intensity is calculated: ;

[0098] Concentration correction is constructed based on the difference between the actual net intensity and the theoretical fluorescence intensity: ,in, To correct the step size, For stable terms. Update the concentration using the following formula: ;

[0099] If the updated concentration is less than zero, it is set to zero. When the material type parameter indicates metallic mode, the concentration of each element is normalized according to the metallic mode normalization rule after each iteration to meet the total elemental constraint of the metallic sample. When the iteration converges, the elemental concentration results are output, where, This is a preset convergence threshold. For general metallic material samples, convergence is usually achieved within five to ten iterations; for oxide slag samples with more complex matrices, the allowed number of iterations can be appropriately increased.

[0100] Step 10: Perform oxide conversion in oxidized slag mode. When the material type parameter is one, the elemental state concentration output by the Sherman model is further converted into oxide content. Let the element... The corresponding oxide conversion factor is The oxide content is: ;

[0101] Then normalize the total amount using the following formula: ;

[0102] For example, calcium can be converted to calcium oxide, brick can be converted to silicon dioxide, magnesium can be converted to magnesium oxide, aluminum can be converted to aluminum oxide, and iron can be converted to iron oxide.

[0103] Step 11: Execution Result Quality Evaluation and Anomaly Rollback. To ensure the reliability of the final output, the concentration calculation result is not used directly as the final output. Instead, a comprehensive quality evaluation is performed based on the main cluster proportion, main cluster dispersion, and model fitting residuals. The main cluster proportion is defined as: ;

[0104] The main cluster dispersion is adopted as described above. The model fitting residual is defined as: ;

[0105] When the proportion of the main cluster is higher than a preset threshold, the dispersion of the main cluster is lower than a preset threshold, and the model fitting residual is less than a preset threshold, the detection result is deemed reliable, and the elemental or oxide content, standard deviation, and confidence level are output. If any condition is not met, an anomaly rollback is triggered. An anomaly rollback may include at least one of the following: resampling, re-sample preparation, or reselection of the detection mode. The standard deviation can be calculated based on the concentration results obtained from each sampling point within the main cluster. ,in, For target element The average concentration at each sampling point in the main cluster. Confidence level can be displayed in a graded manner based on a combination of main cluster proportion, dispersion, and fitting residuals, for example, divided into three levels: high, medium, and low. Through quality evaluation and anomaly backoff, results affected by outlier sampling, peak overlap distortion, or model non-convergence can be avoided from being directly provided to the user.

[0106] In a specific testing scenario, taking the testing of iron-based alloy samples as an example, the material type parameter is set to zero, the metal mode parameter library is called, the target elements are manganese, chromium, and nickel, and the matrix element is iron. A rhodium target X-ray tube is used, with the tube voltage set to 50 kV and the tube current set to 40 mA. Twenty-four sampling points are arranged on the sample surface, and the original spectrum is collected point by point. After initial screening by the total intensity threshold, twenty-one candidate spectra are retained. Principal component analysis is performed on the candidate spectra, and six-dimensional eigenvectors are retained. The distance curve determines the neighborhood radius, with a minimum neighborhood of twelve points. Density clustering identifies three clusters and two noise points, with the main cluster containing eighteen spectra. Channel-by-channel averaging of the main cluster spectra is performed, followed by background subtraction and spectral interference correction at the characteristic peak positions of manganese, chromium, and nickel to obtain the true net intensity. Then, combined with stored instrument constants and mass absorption parameters, a Sherman model is iteratively solved. After seven iterations, the solution converges, outputting the manganese, chromium, and nickel content results. The final main cluster proportion exceeds a preset threshold, and the main cluster dispersion and model fitting residuals both meet preset conditions. Therefore, the system marks the result as high confidence and displays it. This example demonstrates that for iron-based alloy samples with minute surface inhomogeneities, relatively stable quantitative results can be obtained through main cluster identification and physical model constraints.

[0107] Secondly, taking the detection of oxide slag samples as an example. The material type parameter is set to one, and the oxide slag model parameter library is called, with the target elements being calcium, silicon, magnesium, aluminum, iron, manganese, and chromium. Using a tungsten target X-ray tube, twenty sampling points are arranged on the sample surface. After completing the initial spectral acquisition, two abnormal spectra are first screened out using a total intensity threshold, and then the main clusters are determined through feature reduction and density clustering. After background subtraction and spectral interference correction are performed on the average spectrum of the main clusters, the elemental state concentration is obtained using the Sherman model, and then converted to the content of oxides such as calcium oxide, silicon dioxide, magnesium oxide, aluminum oxide, and iron oxide according to the oxide conversion coefficients stored in the parameter library, and the total amount is normalized and output. If, during the detection process, the dispersion of the main clusters is too high due to excessively coarse sample particles, or if there is still a large fitting residual after correction of some overlapping peaks, the system will not directly output the final result, but will prompt for re-grinding or re-sampling. Therefore, this embodiment is not only suitable for metal composition analysis, but also maintains a unified technical approach and high engineering applicability in the scenario of oxide slag material analysis.

[0108] In summary, a complete processing chain was established, including multi-point spectral sampling, initial screening using the total intensity threshold, feature dimensionality reduction, density-based main cluster extraction, background subtraction, spectral interference correction, iterative solution based on the Sherman physical model, oxide conversion, quality evaluation, and anomaly backoff, enabling unified X-ray fluorescence quantitative analysis of metallic and oxide slag materials.

[0109] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A quantitative XRF analysis method for multi-material systems based on density clustering and Sherman physics model, characterized in that, include: Obtain the material type parameters of the sample to be tested, and call the corresponding parameter library according to the material type parameters. The parameter library shall include at least the set of elements to be tested, the set of matrix elements, mass absorption parameters, spectral information, interference coefficient matrix, pre-calibrated instrument constants, oxide conversion coefficients and normalization rules. Multi-point X-ray fluorescence spectroscopy acquisition was performed on the sample to be tested to construct the original spectral set; The total intensity threshold is used to initially screen each spectrum in the original spectral set to obtain a candidate spectral set. The candidate spectral set is characterized by feature dimensionality reduction and density-based clustering to remove noisy spectra, determine the main cluster with the largest number of samples, and average the spectra within the main cluster channel by channel to obtain the representative input spectrum. Background subtraction is performed on the representative input spectrum to extract the measured net intensity of each target element. Spectral interference correction is performed based on the interference coefficient matrix to obtain the true net intensity of each target element. Based on material type parameters and the Sherman physics model, the correspondence between the theoretical fluorescence intensity and element concentration of the target element is established. The concentration is then iteratively solved by combining the instrument constant, mass absorption parameters and the actual net intensity to obtain the element concentration result. When the material type parameter indicates the slag oxidation mode, the element concentration results are converted to oxides and normalized to obtain the oxide content results; when the material type parameter indicates the metal mode, the element concentration results are processed according to the metal mode normalization rules. The quality of the results is evaluated based on the main cluster ratio, main cluster dispersion, and model fitting residual. The main cluster ratio is obtained by the ratio of the number of spectra in the main cluster to the number of spectra in the candidate spectrum set. The main cluster dispersion is obtained by the degree of deviation of each spectrum in the main cluster from the main cluster feature center. The model fitting residual is obtained by the difference between the actual net intensity and the theoretical fluorescence intensity. When the result quality evaluation meets the preset output conditions, the quantitative analysis results are output; when the result quality evaluation does not meet the preset output conditions, an abnormal rollback is triggered.

2. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 1, characterized in that, The initial screening of each spectrum in the original spectral set is performed using the total intensity threshold, specifically including: Count the total intensity of each original spectrum across all channels; Calculate the average value of the total intensity of all original spectra; Set the lower limit threshold of total intensity to three times the average value, and set the upper limit threshold of total intensity to twice the average value; The original spectra with total intensity between the lower and upper thresholds are retained as the candidate spectrum set.

3. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 2, characterized in that, The candidate spectral set is characterized by feature dimensionality reduction and density-based clustering, specifically including: Principal component analysis is performed on the candidate spectrum set to obtain the low-dimensional eigenvectors corresponding to each candidate spectrum; The core samples are determined based on the characteristic distance between candidate spectra, combined with the neighborhood radius and the minimum number of neighborhood points. Starting from any core sample, all density-reachable samples are grouped into the same cluster, and samples that do not belong to any cluster are removed as noise samples; Compare the number of samples in all the obtained clusters, and determine the cluster with the largest number of samples as the master cluster; The minimum number of neighborhood points is determined based on the feature dimension after dimensionality reduction, and is a value that is not less than twice the feature dimension.

4. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 3, characterized in that, Channel-by-channel averaging of the spectra within the main cluster yields representative input spectra, specifically including: The average of all spectra within the main cluster is calculated according to the channel position to form a representative input spectrum; The dispersion of the main cluster is determined by the degree of deviation of each low-dimensional feature vector within the main cluster from the feature center of the main cluster. The dispersion of the main cluster is used as an input for evaluating the quality of the results, and is used to characterize the spectral consistency within the main cluster.

5. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 4, characterized in that, Background subtraction is performed on the representative input spectrum to extract the measured net intensity of each target element, specifically including: For each target element's characteristic peak, select non-interfering background points on both the left and right sides of the characteristic peak; Linear estimation of background intensity at the location of characteristic peaks is performed based on undisturbed background points. Subtract the background intensity from the total intensity of the characteristic peak to obtain the measured net intensity of the corresponding target element; The measured net intensities of all target elements are combined into a set of measured net intensities.

6. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 5, characterized in that, Spectral interference correction based on the interference coefficient matrix specifically includes: Establish a matrix of spectral interference coefficients between target elements, where the diagonal positions represent the response of the target element itself, and the off-diagonal positions represent the proportion of spectral interference between different elements. Based on the interference coefficient matrix, the measured net intensity set is decoupled to obtain the true net intensity of each target element; The interference coefficient matrix is ​​obtained by calibration using single-element standard samples or mixed standard samples of known components, and is stored and retrieved separately according to different material types.

7. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 1, characterized in that, The instrument constants in the parameter library are instrument constants that have been pre-calibrated using similar matrix standard samples. The calibration specifically includes: For each target element, select one or more standard samples that are similar to the matrix of the sample to be tested; Obtain the known concentration of the target element in the standard sample and the net intensity after background subtraction and spectral interference correction; The instrument constants are determined by combining the absorption parameters and physical response parameters corresponding to the standard samples. When multiple standard samples exist, the instrument constants corresponding to the multiple standard samples are processed in a comprehensive manner to obtain the final instrument constant corresponding to the target element, and the final instrument constant is stored in the parameter library.

8. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 7, characterized in that, The relationship between the theoretical fluorescence intensity and elemental concentration of the target element is established based on the Sherman physics model, specifically as follows: Based on the target element concentration, instrument constant, excitation efficiency, fluorescence yield, transition probability, geometric parameters, and the absorption and matrix response of the current material system to the target element's fluorescence signal, a calculation relationship for the theoretical fluorescence intensity of the target element is established. Among them, the absorption and matrix response of the current material system to the target element's fluorescence signal are jointly determined by the combined influence of each element in the current material system on the target element's fluorescence signal.

9. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 8, characterized in that, The concentration iterative solution specifically includes: Establish the initial concentration distribution of the target elements, wherein the initial concentration of non-matrix elements is determined based on the true net intensity and the preset initial value rule, and the concentration of matrix elements is determined based on the remaining mass fraction. Calculate the theoretical fluorescence intensity of each target element based on the concentration distribution of the current round; A concentration correction factor is constructed based on the difference between the actual net intensity and the theoretical fluorescence intensity, and the concentration of the target element is updated accordingly. Set the updated concentration values ​​that are less than zero to zero; When the material type parameter indicates metal mode, the concentration results are normalized according to the metal mode normalization rule after each iteration. When the concentration change in two consecutive iterations is less than the preset convergence threshold, the iteration stops and the element concentration result is output.

10. The XRF quantitative analysis method for multi-material systems based on density clustering and Sherman physical model according to claim 1, characterized in that, Oxide conversion and result quality evaluation specifically include: When the material type parameter indicates the slag oxidation mode, the element concentration is converted into oxide content according to the preset oxide conversion factor, and the total oxide content is normalized. The quality of the results is evaluated based on the proportion of main clusters, the dispersion of main clusters, and the model fitting residuals. When the proportion of the main cluster is higher than the preset threshold, the dispersion of the main cluster is lower than the preset threshold, and the model fitting residual is less than the preset threshold, the element content or oxide content, standard deviation, and confidence level are output. If any condition is not met, an abnormal rollback is executed. An abnormal rollback includes at least one of resampling, re-sample preparation, or reselection of the detection mode.

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