A raman quantitative method for cresol isomers based on binary non-additive response migration

Abstract

The application discloses a cresol isomer Raman quantitative method based on binary non-additive response migration, comprising the following steps: acquiring Raman spectra of pure o-cresol, m-cresol and p-cresol and measured Raman spectra of three binary systems under multiple known volume ratios, and dividing multiple Raman peak cluster windows; establishing a binary non-additive response model according to the difference between the binary measured peak cluster spectrum and the corresponding pure linear superposition peak cluster spectrum; migrating the binary non-additive response to a ternary system, constructing ternary forward peak cluster spectra corresponding to different candidate compositions, and respectively obtaining local ternary composition vectors of each peak cluster; determining dynamic weights according to peak cluster distinguishability, reconstruction residual error and binary model fitting residual error; and obtaining the final volume ratio of o-cresol, m-cresol and p-cresol through multi-peak cluster robust consistency constraint. The application utilizes measured response information of a binary system to quantitatively analyze a ternary cresol isomer, and the quantitative analysis is fast, stable and reliable without separation and detection.

Description

Technical Field

[0001] This invention relates to Raman testing technology, and more specifically to a Raman quantitative method for cresol isomers based on binary nonadditive response migration. Background Technology

[0002] o-cresol, m-cresol, and p-cresol are common and important phenolic compounds in coal chemical, petrochemical, fine chemical, and environmental monitoring fields. These three are positional isomers with highly similar molecular structures, making accurate quantitative analysis crucial for quality control of cresol mixtures and monitoring of chemical production processes. Raman spectroscopy offers advantages such as simple sample pretreatment, fast detection speed, strong structure recognition capability, and suitability for in-situ analysis, showing great potential for application in the identification and quantitative analysis of aromatic compounds and phenolic positional isomers. However, for positional isomers like o-cresol, m-cresol, and p-cresol, which have highly similar structures, their Raman spectra still suffer from problems such as similar overall profiles, overlapping characteristic peaks, small peak position differences, and mutual interference in local responses. Especially in three-component mixtures, some characteristic peaks are contributed by multiple components, and the Raman response coefficients, peak shape changes, peak overlap, and baseline perturbations of different components are not entirely consistent.

[0003] In existing quantitative analyses, representative Raman peaks with certain differences among the components can be selected, and the content of each component in the mixture can be estimated by peak height, peak area, or their ratio. For example, characteristic response relationships between o-cresol and m-cresol, o-cresol and p-cresol, and m-cresol and p-cresol can be established separately, and then the component ratio in the ternary mixture can be deduced based on the response ratios of each pair of components. However, the responses of each Raman peak in a ternary mixture are usually not completely independent of each other; there may be spectral overlap, local peak shape changes, and differences in response coefficients between different components. Directly using a single characteristic peak or averaging the area ratios of each pair of peaks is difficult to fully reflect the coupling relationship between the components in the ternary system. This can easily lead to contradictions between local ratios obtained from different component combinations, or cause the calculation results of a certain component to be excessively affected by local abnormal peaks and baseline fluctuations, thereby reducing the quantitative accuracy, stability, and applicability of the o-cresol, m-cresol, and p-cresol ternary mixture. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a binary non-additive response migration-based Raman quantitative method for cresol isomers that can improve the accuracy of identification and the reliability of quantification, and to solve the problems in the prior art where the accuracy of direct modeling is low due to severe overlap of cresol Raman spectra, and the inconsistency of results when the binary ratio method is simply extended to ternary systems.

[0005] Technical solution: The Raman quantification method for cresol isomers based on binary non-additive response migration described in this invention includes the following steps: (1) Obtain the pure Raman spectra of o-cresol, m-cresol and p-cresol, respectively, and the measured Raman spectra of the three binary systems composed of o-cresol, m-cresol and p-cresol in multiple known volume ratios; perform the same spectral preprocessing on the above spectra, and obtain the pure peak cluster spectra and the measured peak cluster spectra of the three binary systems according to the predetermined K fixed Raman peak cluster windows; (2) For each component pair and each Raman peak cluster window, construct an ideal linear superimposed peak cluster spectrum based on the pure peak cluster spectrum of the two components, and define the binary non-additive response by the difference between the measured peak cluster spectrum and the ideal linear superimposed peak cluster spectrum; use the binary non-additive responses obtained by the three binary systems under multiple known volume ratios to fit the boundary constraint model and obtain the model parameters used to characterize the symmetric response part and the asymmetric response part in the binary non-additive response; (3) For the candidate ternary composition vector, within each Raman peak cluster window, a linear combination term is constructed based on the three pure peak cluster spectra, and a binary non-additive response migration term is constructed based on the model parameters to obtain the ternary forward peak cluster spectrum of the corresponding candidate ternary composition vector; (4) Obtain the Raman spectrum of the ternary sample to be tested containing o-cresol, m-cresol and p-cresol, and perform the same spectral preprocessing; for each Raman peak cluster window, according to the normalized reconstruction error between the spectrum of the peak cluster to be tested and the spectrum of the ternary forward peak cluster, solve the problem under the composition constraint condition to obtain the local ternary composition vector of the peak cluster corresponding to each Raman peak cluster window; the composition constraint condition is that the composition ratio of o-cresol, m-cresol and p-cresol is not less than 0 and the sum of the composition ratios of the three is 1; (5) At the local ternary composition vector of each peak cluster, calculate the singular value index of the local Jacobian matrix of the ternary forward peak cluster spectrum, and combine it with the mean square of the reconstruction residual of the peak cluster spectrum to be measured and the mean square of the binary non-additive response fitting residual of the corresponding Raman peak cluster window to determine the dynamic weight of each Raman peak cluster window. (6) Based on the local ternary composition vectors of each peak cluster and their corresponding dynamic weights, construct a dynamic weighted robust consistency objective function under the composition constraints and solve it. Output the volume ratio of o-cresol, m-cresol and p-cresol in the ternary sample to be tested based on the solution results.

[0006] Furthermore, the Raman quantification method for cresol isomers based on binary non-additive response migration includes the following steps: Raman spectra of pure o-cresol, m-cresol, and p-cresol were obtained, as well as the measured Raman spectra of three binary systems composed of o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol at multiple known volume ratios. The pure spectra and the measured binary spectra were subjected to the same preprocessing, and the corresponding peak cluster spectra were obtained according to K fixed Raman peak cluster windows, where K is the total number of peak cluster windows and is a positive integer. Let o-cresol, m-cresol, and p-cresol be denoted as o, m, and p, respectively; i, j ∈ {o, m, p} and i ≠ j, k = 1, ..., K; This represents the volume proportion of component i in the corresponding binary system, where 0 ≤ r ≤ 1; This represents the Raman shift within the window of the k-th Raman peak cluster; and Let represent the pure peak cluster spectral response vectors of components i and j within the k-th window after undergoing the same pretreatment. An ideal linearly superimposed peak cluster spectrum is constructed based on the pure peak cluster spectra of the two components: ; in, This represents the ideal linear superposition peak cluster spectrum of component pairs i and j at volume ratio r and Raman shift ν. This represents the measured peak cluster spectrum of a binary system under the same conditions and pretreatment. The superscript lin indicates ideal linear superposition, and the superscript obs indicates measured values. ; Obtained using three binary systems at multiple known volume ratios For each group pair and each window, a boundary constraint model is fitted separately: ; in, For symmetric non-additive response parameters, For the asymmetric non-additive response parameter, the subscript ij indicates the component pair, the subscript k indicates the window number, and r(1-r) is the boundary factor that makes the non-additive response zero when r=0 or 1; For candidate triplet vectors , where c o c m and c p The candidate volume ratios for o-cresol, m-cresol, and p-cresol are respectively. Constructing pure linear combination terms ,in c represents the summation over i∈{o,m,p}. i Let i be the candidate volume proportion of component i. Let i be the pure peak cluster spectral response vector of component i within the k-th window: ; Constructing a binary non-additive response transition term The superscript na indicates a non-additive response. This represents the summation over three disordered component pairs: (o, m), (o, p), and (m, p). This indicates a default positive number to prevent the denominator from being zero. ; The ternary forward peak cluster spectrum was obtained. It represents the candidate composition. At the k-th window and Raman displacement Forward spectral response at: ; Among them, c o c m and c p All three elements are not less than 0 and their sum is 1. The candidate triplets form a vector that satisfies the following conditions: ; Perform the same pretreatment on the ternary samples to be tested; Let be the spectral response vector of the sample under test within the k-th window. To normalize the reconstruction error, This represents a preset positive number to prevent the denominator from being zero. The normalized reconstruction error is calculated according to the following formula: ; Solve under the ternary composition constraints, where arg min represents the expression that makes e k (c) The value of the variable that reaches its minimum value: ; Obtain the local ternary vector of the peak cluster corresponding to the k-th Raman peak cluster window. , where the superscript loc indicates a local result within a single window; Local ternary vectors in the peak cluster At this point, calculate the local Jacobian matrix of the ternary forward peak cluster spectrum with respect to the two independent component coordinates, and use... The minimum singular value of the local Jacobian matrix is ​​represented; the unnormalized peak cluster confidence of the k-th window is calculated according to the following formula. The superscript "raw" indicates that the element has not been truncated or normalized. ; in, For the spectrum of the peak cluster to be measured in Mean square of the reconstructed residuals at the location, Let the mean square of the non-additive response fitting residuals for the k-th window across all binary modeling samples be denoted as . To prevent the default positive number with a denominator of zero, The unnormalized confidence level of the k-th window; for The upper limit is truncated, and the confidence scores of each truncated window are divided by their sum to obtain the dynamic weights. ; Based on the local ternary composition vector of each peak cluster and dynamic weights A dynamically weighted Huber consistency loss term is constructed under ternary composition constraints. ;in Indicates the threshold is Huber loss function A positive threshold The Euclidean distance between the candidate component and the k-th local component is: ; Constructing a dynamically weighted reconstruction loss term ,in The normalized reconstruction error for the k-th window: ; Construct the overall objective function ,in Non-negative balancing coefficients for reconstructing the loss term: ; Solve under ternary composition constraints, where The final ternary volume ratio vector: ; This is the Huber loss threshold. These are non-negative balance coefficients; based on the obtained... Output the volume ratio of o-cresol, m-cresol, and p-cresol in the ternary sample to be tested.

[0007] Note: o-cresol, m-cresol, and p-cresol have the same molecular composition but different substitution positions, resulting in high similarity in their Raman spectra. In binary and ternary mixtures, the measured Raman response is not necessarily equal to a simple linear superposition of the Raman responses of the pure components according to their volume ratios. This invention first establishes a binary non-additive response model by utilizing the difference between the measured Raman spectra of the three binary systems at different known volume ratios and the ideal linear superposition spectra, and then transfers the obtained binary non-additive response information to the forward spectrum construction of the ternary system. Based on this, the local ternary composition vectors of the peak clusters are obtained using multiple Raman peak cluster windows. Then, dynamic weights are determined according to the local identifiability of each peak cluster, the reconstruction residual of the sample under test, and the fitting residual of the binary non-additive response. Finally, the results of multiple peak clusters are fused through robust consistency constraints to obtain the final volume ratios of o-cresol, m-cresol, and p-cresol.

[0008] Furthermore, binary mixed samples with component volume ratios of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% were respectively set up for the three binary systems of o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol, and the measured Raman spectra corresponding to each volume ratio were obtained respectively.

[0009] Note: By constructing three binary systems at 10% intervals within a composition range of 10% to 90%, the measured spectra of each binary system cover different compositional states from one component dominance to another component dominance, providing basic data for obtaining the non-additive response that varies with the binary volume ratio.

[0010] Furthermore, the K fixed Raman peak cluster windows are predetermined based on the pure Raman spectra of o-cresol, m-cresol, and p-cresol, where K is the total number of peak cluster windows and is a positive integer; non-overlapping continuous windows are divided according to the peak position, peak shape, peak shoulder, and overlapping region of the pure spectrum, so that each window covers at least one identifiable peak cluster and its complete peak shape, and the window boundary is located in the low response region between adjacent peak clusters without cutting off the main peak top or obvious peak shoulder; the same window position and range are used in the modeling stage and the prediction stage.

[0011] Note: A pre-determined Raman peak cluster window is used and remains consistent in both the modeling and prediction stages. This ensures that the pure Raman response, the measured response of the binary system, and the response of the ternary system under test within the same peak cluster have the same wavenumber correspondence, thereby guaranteeing data consistency in the binary non-additive response modeling and ternary forward spectral reconstruction processes.

[0012] Furthermore, for the three binary systems of o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol, the volume ratio of one cresol isomer in the total amount of the corresponding binary system is taken as r, and the ideal linear superimposed peak cluster spectrum is established based on the pure peak cluster spectrum of the corresponding two cresol isomers, so that the three binary systems form independent binary non-additive response data.

[0013] Furthermore, the three component pairs—o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol—and the windows of each Raman peak cluster were determined independently. and ;in For a specific component pair and a specific window, the symmetric non-additive response parameters are given. These are the corresponding asymmetric non-additive response parameters, and the parameters are not shared between different component pairs or between different windows.

[0014] Note: The non-additive Raman responses produced by different combinations of components in the three binary systems, as well as the non-additive responses exhibited by the same component combination in different windows, may differ. Therefore, and Each corresponds to a specific component pair and a specific window.

[0015] Furthermore, the ternary forward peak cluster spectrum consists only of linear combination terms of the peak cluster spectra of pure o-cresol, m-cresol, and p-cresol, as well as binary non-additive response migration terms corresponding to the three binary systems o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol, without using ternary mixed samples to fit the ternary non-additive response terms of the combined effect of the three components.

[0016] Explanation: This invention utilizes the Raman spectra of pure samples and the Raman spectra of three binary systems at known volume ratios to establish ternary forward peak cluster spectra. It does not require additional fitting of the ternary non-additive response parameters of the three components through the ternary mixed sample, thus allowing the volume ratio solution of the ternary sample to be based on the migration of the pure sample response and the binary non-additive response.

[0017] Furthermore, in the binary non-additive response transition term, for any pair of components i and j, and These represent the volume ratios of component i and component j in the candidate ternary composition, respectively; using The corresponding binary non-additive response is ternary compositionally scaled, and the asymmetric response portion is corrected for relative composition using the following formula: ; The compositional modification allows the non-additive response parameters obtained from binary mixed samples to be directly transferred to the construction of ternary forward peak cluster spectra.

[0018] illustrate: The migration terms of components i and j change together with the volume ratio of the two components in the ternary system. For relative composition correction terms, where To prevent the use of pre-defined positive numbers with a denominator of zero; and These are the symmetric and asymmetric non-additive response parameters for the corresponding component pairs and windows, respectively.

[0019] Furthermore, the ternary composition constraints are solved independently for each of the K fixed Raman peak cluster windows. Each Raman peak cluster window yields a local ternary composition vector, and each local ternary composition vector satisfies the following: ; Note: Different Raman peak cluster windows respond differently to changes in the composition of o-cresol, m-cresol, and p-cresol. This invention does not directly merge all peak clusters into a single solution. Instead, it first obtains the local ternary composition vectors of each peak cluster under the same ternary composition constraints, providing a basis for subsequent weighted fusion based on the credibility of different peak clusters.

[0020] Furthermore, the dynamic weights are simultaneously determined by the minimum singular value of the local Jacobian matrix, the variance of the reconstructed residual of the spectrum of the peak cluster to be measured, and the variance of the binary non-additive response fitting residual. Specifically, increasing the minimum singular value improves the confidence level of the corresponding Raman peak cluster window, while increasing the variance of the reconstructed residual or the variance of the binary non-additive response fitting residual decreases the confidence level of the corresponding Raman peak cluster window. The confidence levels of each peak cluster after upper limit truncation are normalized to: ; Explanation: The minimum singular value of the local Jacobian matrix characterizes the identifiability of the corresponding peak cluster in the vicinity of different compositional variations in its local composition; the variance of the reconstructed residual of the spectrum of the peak cluster to be tested reflects the reconstruction of the spectrum of the peak cluster to be tested by the current forward model; the variance of the binary non-additive response fitting residual reflects the fitting of the binary non-additive response model of the corresponding peak cluster. By combining the above three types of information, dynamic weights are determined so that the contribution of each Raman peak cluster to the final compositional result is adjusted according to the actual response of the sample to be tested and the corresponding peak cluster.

[0021] Furthermore, the ternary mixed sample of o-cresol, m-cresol, and p-cresol does not participate in the fitting of the parameters of the binary non-additive response model; and The composition ratios of the three binary systems (o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol) are determined only by samples with known composition ratios. The ternary sample to be tested is only used to solve the ternary composition ratio.

[0022] Explanation: Thus, the parameter determination process of the binary non-additive response model is separated from the composition solution process of the ternary sample to be tested. When establishing the binary non-additive response model, only the pure sample and the known composition ratio Raman spectral data of the three binary systems are used. In the test stage, the ternary forward peak cluster spectrum is constructed through the predetermined binary non-additive response model and the composition ratio of the ternary sample to be tested is solved.

[0023] Furthermore, the spectral preprocessing includes, but is not limited to, one or more of baseline correction and smoothing; wherein the baseline correction includes asymmetric least squares baseline correction, and the smoothing includes Savitzky-Golay smoothing.

[0024] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. This invention utilizes the Raman spectra of pure o-cresol, m-cresol, and p-cresol, as well as the measured Raman spectra of the three binary systems at multiple known volume ratios, to construct a binary non-additive response model. The obtained binary non-additive response is then transferred to the construction of the forward peak cluster spectrum of the ternary mixed system, which can characterize the deviation of the measured Raman response of the mixed system from the simple linear superposition of the pure components. Compared with the traditional linear superposition assumption, this invention, through the non-additive response, reduces the average absolute error of the ternary mixed sample prediction from above 0.134 and 0.113 to within 0.013.

[0025] 2. This invention further performs ternary composition constraint solutions for multiple predetermined Raman peak cluster windows, and determines dynamic weights by combining the minimum singular value of the local Jacobian matrix, the mean square of the spectral reconstruction residuals of the peak clusters to be measured, and the mean square of the binary non-additive response fitting residuals. Then, it performs joint constraint solutions through dynamic weighted Huber consistency loss terms and dynamic weighted reconstruction loss terms, thereby reducing the impact of local peak overlap, abnormal peak clusters, and fitting bias on the final results, and improving the stability, reliability, and accuracy of quantitative analysis of the ternary mixed system of o-cresol, m-cresol, and p-cresol.

[0026] 3. In the process of establishing a binary non-additive response model, this invention only uses pure samples and samples with known volume ratios of three binary systems. Ternary mixed samples do not participate in the model parameter fitting, thus realizing the transfer from binary system response information to ternary system volume ratio solution. Attached Figure Description

[0027] Figure 1 These are the molecular structural formulas of o-cresol, m-cresol, and p-cresol in the embodiments of the present invention.

[0028] Figure 2 These are the standard Raman spectra of o-cresol, m-cresol, and p-cresol in the embodiments of the present invention.

[0029] Figure 3 This is the Raman spectrum of the o-cresol-m-cresol mixture in an embodiment of the present invention.

[0030] Figure 4 This is the Raman spectrum of the o-cresol-p-cresol mixture in an embodiment of the present invention.

[0031] Figure 5 This is the Raman spectrum of the p-cresol-m-cresol mixture in an embodiment of the present invention.

[0032] Figure 6 This is the Raman spectrum of a mixture with an unknown volume fraction in an embodiment of the present invention.

[0033] Figure 7 This is a flowchart of the cresol volume ratio prediction process in Example 1 of the present invention. Detailed Implementation

[0034] To further illustrate the methods and effects of this invention, the technical solution of this invention will be clearly and completely described below in conjunction with experiments.

[0035] This invention obtains the Raman spectra of pure o-cresol, m-cresol, and p-cresol, as well as a binary mixture of each of the three cresols in pairs. Based on the difference between the linear superposition spectra of the pure cresols and the measured spectra of the binary mixture, a binary non-additive response is established, and this response is then transferred to a ternary system. Furthermore, local ternary composition vectors of multiple Raman peak clusters are obtained, and a dynamic weighted consistency solution is performed based on the confidence level of each peak cluster, thereby obtaining the volume ratio of the o-cresol, m-cresol, and p-cresol ternary mixture. The following embodiments use the o-cresol, m-cresol, and p-cresol ternary mixture as an example for detailed explanation. Example 1: A Raman quantification method for cresol isomers based on binary non-additive response migration, comprising the following steps: S1. Raman spectra of pure o-cresol, m-cresol, and p-cresol were obtained separately. Samples of three binary systems—o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol—were prepared in nine known volume ratios, resulting in 27 measured Raman spectra of binary mixed samples. The structural formulas of o-cresol, m-cresol, and p-cresol are shown below. Figure 1 As shown; Methods for obtaining Raman spectra of pure and binary mixed samples and forming fixed peak cluster window spectral data include: S1-1. Obtain the Raman spectra of pure o-cresol, m-cresol, and p-cresol, specifically including: o-cresol, m-cresol, and p-cresol standards were taken and their standard Raman spectra were acquired under the same instrument conditions and the same Raman shift grid. The spectra of the three pure products were used to determine the fixed peak cluster window and to form the complete spectral response vector of the corresponding pure product within each window. S1-2. Determine a fixed Raman peak cluster window based on the peak position, peak shape, and overlapping regions of the pure spectra of o-cresol, m-cresol, and p-cresol, and extract the complete spectral response vector within the same window during the pure product, binary modeling, and ternary prediction stages. For example, in combination Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, the specific implementation process of S1-1~S1-2 includes (1)~(3): (1) Establish standard Raman spectra of o-cresol, m-cresol, and p-cresol: Take pure samples of the three cresol isomers respectively, and use a pipette to draw 5 μL of sample each time and drop it onto the clean Si wafer surface; focus a 638 nm laser on the sample area, with a laser power of 30 mW and a spectral acquisition range of 150~1800 cm⁻¹. -1 The integration time is 10 seconds, and 3 scans are performed to obtain... Figure 2 The standard Raman spectrum shown is shown. (2) Place the Raman spectra of the three pure samples on the same Raman shift grid. Based on the position, shape, shoulder, and overlap of the main response peaks, divide the spectrum into non-overlapping continuous windows along the Raman shift axis. Each window should cover at least one identifiable peak cluster and its complete peak shape. The window boundaries should be set in the low-response region between adjacent peak clusters where none of the three pure samples have a main peak, without crossing the main peak or obvious shoulder, and each window should contain at least 5 Raman shift sampling points. Thus, 7 windows are pre-determined: 180~380 cm⁻¹. -1 430~680 cm -1 700~900 cm -1 940~1080 cm -1 1120~1320 cm -1 1340~1430 cm -1 and 1560~1660 cm -1 Once the window is determined, its position and range remain unchanged during the binary modeling and ternary prediction stages, and are not adjusted based on the prediction results of the ternary sample to be tested; (3) Obtain the measured Raman spectra of the three binary systems at different known volume ratios, and form the binary peak cluster spectral response vector according to the above fixed window; Prepare binary standards of o-cresol / m-cresol, o-cresol / p-cresol and m-cresol / p-cresol with volume ratios of 10% to 90%, and collect Raman spectra in the same manner as in step (1). For example, mixed liquid samples with o-cresol accounting for 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, and 90% of the total volume of o-cresol and m-cresol were prepared; mixed liquid samples with o-cresol accounting for the total volume of o-cresol and p-cresol at the above nine ratios were prepared; and mixed liquid samples with m-cresol accounting for the total volume of m-cresol and p-cresol at the above nine ratios were prepared. Complete Raman spectra were acquired according to the conditions in step (1). Each complete spectrum was first smoothed using a third-order, 11-point Savitzky-Golay method, followed by first-order derivative processing; the mean was calculated and centered using all sampling points within the union of seven fixed windows; then, the L2 norm of the spectral vectors within the union of these windows was used for overall normalization; finally, the complete spectral response vectors within each window were extracted. Pure samples, binary modeled samples, and ternary test samples used the exact same window, sampling grid, and preprocessing order.

[0036] S2. Based on the measured peak cluster spectra of three binary systems under different known volume ratios, construct ideal linear superimposed peak cluster spectra respectively, calculate the binary non-additive response of the measured peak cluster spectra relative to the ideal linear superimposed peak cluster spectra, and independently fit the binary non-additive response model for each component pair and each fixed Raman peak cluster window. Let o-cresol, m-cresol, and p-cresol be denoted as o, m, and p, respectively. For any binary component pair i, j, i, j ∈ {o, m, p} and i ≠ j; r represents the volume proportion of component i in the binary system, and k = 1, ..., 7 represents the window number. Indicates the Raman shift within the window. and This represents the window spectral response vector of two pure products after undergoing the same pretreatment. Representing the spectrum of an ideal linearly superimposed peak cluster: ; The measured peak cluster spectra of binary samples with the same volume ratio and pretreatment were compared. Subtracting the spectrum from the ideal linear superposition of peak clusters yields a binary non-additive response. The superscript "obs" indicates actual measurement, and the superscript "lin" indicates ideal linear superposition. ; The binary non-additive responses of three binary systems—o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol—at volume ratios of 10%–90% were used to independently fit the component pairs and the windows of each Raman peak cluster. The boundary constraint model used was as follows: ; in, This represents the component pair i and j in the k-th window and the Raman shift. Symmetric non-additive response parameters at the location, Let r(1-r) represent the corresponding asymmetric non-additive response parameter, and r(1-r) be the boundary factor that makes the non-additive response zero when r=0 or 1.

[0037] In this embodiment, the windows for the three binary systems and the seven fixed Raman peak clusters are determined independently. and The parameters for different component pairs and different windows are not shared.

[0038] S3. Construct a ternary forward peak cluster spectrum based on the binary non-additive response, and solve for the local composition of the multi-peak cluster and perform consistency fusion. Let the volume ratios of o-cresol, m-cresol, and p-cresol in the ternary system to be tested be c. o c m and c p The vectors formed are denoted as: ; Among them, c o c m and c p All three are not less than 0 and their sum is 1: ; For any candidate ternary combination c, first construct a pure linear combination term within each window. Then, the binary non-additive response parameters obtained from S2 are used to construct... The two are added together to obtain the ternary forward peak cluster spectrum. The superscript 'na' indicates a non-additive response. This represents the summation of three disordered component pairs: (o, m), (o, p), and (m, p). ; in, To prevent the use of a pre-defined positive number with a denominator of zero, this embodiment... Take 10 -12 .

[0039] For the ternary sample to be tested, the measured peak cluster spectra within the 7 Raman peak cluster windows are compared with the ternary forward peak cluster spectra corresponding to different candidate compositions. Under the condition that the volume ratios of o-cresol, m-cresol, and p-cresol are non-negative and their sum is 1, the constraint solution is performed with the goal of minimizing the normalization reconstruction error of the peak cluster spectra, so as to obtain the local ternary composition vectors of the peak clusters corresponding to the 7 Raman peak clusters.

[0040] Since different Raman peak clusters respond differently to changes in the composition of o-cresol, m-cresol, and p-cresol, this embodiment further calculates the local Jacobian matrix of the ternary forward peak cluster spectrum relative to two independent composition coordinates at the local composition of each peak cluster, and extracts its minimum singular value; simultaneously, it calculates the reconstruction residual of the spectrum of the peak cluster to be measured and the fitting residual of the corresponding binary non-additive response of the peak cluster. The confidence level of each Raman peak cluster is calculated based on the above three parameters: ; in, For the k-th window in local composition The minimum singular value of the local Jacobian matrix at a given location. For the spectrum of the peak cluster to be measured in Mean square of the reconstructed residuals at the location, The mean square of the fitting residuals for the corresponding window's bivariate non-additive response. The confidence level of the window before truncation and normalization.

[0041] Unnormalized confidence level of the 7 windows Perform robust upper limit truncation and normalization: first filter for values ​​greater than 100%. The positive confidence level is calculated and its median M is determined; the upper limit of the cutoff is set to 20 times the positive confidence median M, i.e., C = 20M. For each Take values ​​that are not greater than C and not less than C in sequence. The value is then divided by the sum of the confidence scores of the seven truncated values ​​to obtain the dynamic weight. If there is no greater than The positive credibility of each =1 / 7. Where M is the median of positive confidence, C is the upper limit of confidence cutoff, and 20 is a pre-set robustness coefficient, which is based on providing a confidence scale that is not significantly affected by extreme values ​​using the median, and limiting the dominance of a single abnormally high confidence window on the fusion result while preserving the relative confidence differences between windows. This coefficient is fixed before ternary sample prediction and does not participate in ternary sample fitting or adjustment.

[0042] Furthermore, using the consistency between the local ternary component vectors of each peak cluster and the reconstruction effect of the spectrum of the peak cluster to be measured as common constraints, a dynamic weighted Huber consistency loss and a dynamic weighted reconstruction loss are constructed. These are then solved under the condition that the ternary volume ratios are non-negative and their sum is 1, yielding the final volume ratios of o-cresol, m-cresol, and p-cresol. In this embodiment, the Huber loss threshold is... Set to 0.10, balance coefficient In the model building phase, the values ​​are determined by binary samples, with candidate values ​​of 0, 0.01, 0.03, 0.10, 0.30, 1, and 3. The parameter corresponding to the smallest prediction error of the binary sample is selected as the final value.

[0043] During the model building process, only pure o-cresol, m-cresol, and p-cresol, as well as samples with known volume ratios of the three binary systems, were used to determine the binary non-additive response model and related parameters. After the above model and parameters were determined, a ternary mixed sample was loaded for prediction. The ternary mixed sample did not participate in the refitting of model parameters and hyperparameters. S4. Based on the above prediction model, predict the volume ratio of the ternary mixed system of o-cresol, m-cresol and p-cresol; Take the ternary mixed liquid sample of o-cresol, m-cresol and p-cresol to be tested, and collect Raman spectra according to the test conditions in step S1 to obtain the Raman spectrum of the sample to be tested. The Raman spectra of the samples to be tested were pretreated using the same method as those used for the pure sample and the binary mixture sample in step S1, and the spectra were extracted from 180 to 380 cm⁻¹. -1 430~680 cm -1 700~900 cm -1 940~1080 cm -1 1120~1320cm -1 1340~1430 cm -1 and 1560~1660 cm -1 Spectral data within a total of 7 fixed Raman peak cluster windows; Based on the non-additive response parameters obtained from the three binary systems of o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol in step S2, ternary forward peak cluster spectra corresponding to different candidate ternary compositions are constructed in seven Raman peak cluster windows. The local ternary composition vector of each Raman peak cluster is obtained by constraining the solution through the reconstruction error between the spectrum of the peak cluster to be measured and the ternary forward peak cluster spectrum. Based on the minimum singular value of the local Jacobian matrix of each window Mean square of the reconstructed residual of the spectrum of the peak cluster to be measured and the mean square of the binary non-additive response fitting residuals Determine dynamic weights And combined with dynamically weighted Huber consistency loss and dynamic weighted reconstruction loss For the 7 local ternary components A robust and consistent fusion was performed to obtain the final volume ratio of the three cresol isomers in the test sample. For example, in this embodiment, a ternary mixed sample of o-cresol, m-cresol, and p-cresol was prepared with a volume ratio of 2:5:3, i.e., the actual volume fractions of o-cresol, m-cresol, and p-cresol were 0.2, 0.5, and 0.3, respectively. Raman spectroscopy was performed on this ternary mixed sample according to the above method to obtain the local ternary composition and dynamic weights of seven fixed Raman peak clusters. After dynamic weighted Huber consistency fusion, the final predicted proportions of o-cresol, m-cresol, and p-cresol were 0.2065, 0.4820, and 0.3115, respectively. Table 1 lists the actual proportions, predicted proportions, and corresponding errors of this sample. In Tables 1-3, True_o, True_m, and True_p represent the true volume ratios of o-cresol, m-cresol, and p-cresol, respectively; Pred_o, Pred_m, and Pred_p represent the corresponding predicted volume ratios; AbsErr_o, AbsErr_m, and AbsErr_p represent the corresponding absolute errors; L1Error represents the sum of the absolute errors of the three components; and L2Error represents the Euclidean norm of the errors of the three components.

[0044] Table 1. Actual proportions, predicted proportions, and errors of the ternary mixture sample in Example 1

[0045] Comparative Example 1: Linear Superposition Peak Fitting Method Based on Peak Area of ​​Pure Substances To further illustrate the technical effects of the method described in this invention, a conventional peak fitting method based on the linear superposition of pure peak templates was used to quantitatively analyze a ternary mixed sample of o-cresol, m-cresol, and p-cresol, and this sample was used as a comparative example.

[0046] The conventional peak fitting method described above uses only the Raman spectra of pure o-cresol, m-cresol, and p-cresol to establish a ternary quantitative model, without using binary mixed samples of o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol to participate in the establishment of the ternary prediction model. The Raman spectral acquisition conditions for pure o-cresol, m-cresol, and p-cresol, as well as the ternary mixed sample to be tested, are the same as in Example 1.

[0047] First, the Raman spectra of pure o-cresol, m-cresol, and p-cresol were subjected to AsLS baseline correction and Savitzky-Golay smoothing. Automatic peak finding was performed within the preset Raman peak regions, and pseudo-Voigt peak shaping was used to fit the peaks of each pure sample, establishing pure peak templates for o-cresol, m-cresol, and p-cresol respectively. For the ternary mixed sample to be tested, after the same spectral preprocessing, the Raman spectra of the three pure sample templates were non-negatively decomposed, assuming that the mixed spectrum could be obtained by linear superposition of the three pure sample templates, i.e.: ; in, Indicates the spectrum of the mixture to be measured. Indicates Raman shift; , and These represent the pure peak templates for o-cresol, m-cresol, and p-cresol, respectively. , and , respectively, represent the non-negative fitting coefficients of the three pure peak templates in the mixed spectrum to be tested.

[0048] The response factors for o-cresol, m-cresol, and p-cresol were determined based on the total response of the three pure peak templates. The non-negative fitting coefficients were corrected for the response factors, and the corrected responses of the three components were closed-loop normalized to obtain the apparent volume ratios of o-cresol, m-cresol, and p-cresol in the ternary mixed sample to be tested.

[0049] The basic assumption of the conventional peak fitting method is that the Raman peak response of each component changes approximately linearly with its content, and that the Raman peak shapes of the pure product and the mixed product are basically consistent. Therefore, the linear combination of the three pure product peak templates is directly used to characterize the ternary mixed sample. This method does not utilize the spectral response changes that occur during the actual binary mixing process, nor does it model the deviation of the mixed spectrum from the linear superposition spectrum of the pure products.

[0050] Unlike Comparative Example 1, Example 1, in addition to using the spectra of three pure products—o-cresol, m-cresol, and p-cresol—also utilized the measured Raman spectra of 27 samples with known volume ratios from three binary systems to obtain the non-additive response of the actual mixed spectra within each peak cluster relative to the linear superposition spectra of the pure products. The ternary forward spectrum was then corrected using the binary non-additive response. Simultaneously, Example 1 independently inverted the ternary composition within multiple Raman peak clusters and performed dynamic weighting and robust consistency fusion based on the identifiability, reconstruction error, and binary model fitting error of each peak cluster to obtain the final ternary volume ratios of o-cresol, m-cresol, and p-cresol.

[0051] The conventional peak fitting method described above was used to predict the ternary mixed sample, which was the same as in Example 1. The prediction results are shown in Table 2. By comparing the prediction results of Comparative Example 1 with those of Example 1, the difference between the linear superposition method using only pure peak templates and the ternary composition inversion method using binary non-additive responses in the quantitative analysis of cresol isomers can be evaluated.

[0052] Table 2. Prediction results and errors of the ternary composition based on conventional peak fitting in Comparative Example 1.

[0053] In Comparative Example 1, the predicted proportions of o-cresol, m-cresol, and p-cresol were 0.4011, 0.4933, and 0.1056, respectively, which deviated significantly from the actual proportions of 0.2, 0.5, and 0.3. Although the spectral fitting coefficient of determination for this sample was 0.9738, relying solely on linear superposition of pure peak templates, response factor correction, and closure normalization was insufficient to fully characterize the non-additive response produced by the mixing of cresol isomers. Therefore, the composition inversion error of the sample in this example was relatively large.

[0054] Comparative Example 2: A quantitative method based on binary feature decoupling, partial least squares dimensionality reduction, and global constraint solution. To further illustrate the technical effects of the method described in this invention, a three-component Raman quantification method based on binary feature decoupling, partial least squares dimensionality reduction, and global constraint solution was used to quantitatively analyze a ternary mixed sample of o-cresol, m-cresol, and p-cresol, and this sample was used as a comparative example.

[0055] The comparative method utilizes Raman spectra of three binary systems—o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol—at multiple known volume ratios to establish binary local proportion prediction models. Each binary system comprises nine samples with known normalized volume ratios, and a total of 27 binary mixture samples were used for model training. The Raman spectral acquisition conditions for the o-cresol, m-cresol, and p-cresol binary mixture samples and the ternary mixture sample to be tested were the same as in Example 1.

[0056] First, the Raman spectra of each binary mixture sample were processed for anomalous pulse points, AsLS baseline correction, and Savitzky-Golay smoothing. The 1043 cm⁻¹ spectrum was pre-selected. -1 998 cm -1 and 842 cm -1 The characteristic peak centers for o-cresol, m-cresol, and p-cresol were determined, and pseudo-Voigt peak shapes were used for fitting within a fixed fitting window to extract the peak area, peak height, and peak position shift of each characteristic peak. The fitted peak center was allowed to be within ±3 cm of the preset peak center. -1 An offset occurred within the range.

[0057] For three binary systems—o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol—characteristic peak parameters of only the two corresponding components were selected, and proportional variables including peak area closure ratio, peak height closure ratio, normalized difference, logarithmic area ratio, logarithmic peak height ratio, and peak position shift combination were constructed. After standardizing these variables by mean-standard deviation, partial least squares single-output regression models with no more than two latent variables were used to predict the local proportions of the two components in the corresponding binary systems. Therefore, two local output models were established for each binary system, resulting in a total of six local output models for the three binary systems.

[0058] For the ternary mixture samples to be tested, the same spectral preprocessing, fixed characteristic peak fitting, and variable construction methods as for the binary training samples were used to form feature vectors for the three binary systems: o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol, respectively. These feature vectors were then input into the corresponding six partial least squares local output models. The original outputs of each local model were truncated to the range of 0 to 1 and normalized within each binary system to obtain three local proportions: ; ; ; in, , and Let represent the volume proportions of o-cresol in the o-cresol-m-cresol local system, the o-cresol in the o-cresol-p-cresol local system, and the m-cresol in the m-cresol-p-cresol local system, respectively; the six local model outputs after being truncated to 0~1 are denoted as . , , , , and The superscript indicates the corresponding binary system, and the subscript indicates the component being predicted; To prevent the default positive number with a denominator of zero.

[0059] Let the normalized volume ratios of o-cresol, m-cresol, and p-cresol in the ternary mixed sample to be tested be c o c m and c p ; , and These are the fixed weights of the three binary local systems, calculated from the reciprocal of the variance of the leave-one cross-validation error of the corresponding local model and normalized to a mean of 1; J represents the global constraint optimization objective function. To prevent the default positive number with a denominator of zero, the following function is established: ; The constraints are: ; By solving the above optimization problem, the final normalized volume ratios of o-cresol, m-cresol, and p-cresol in the ternary mixed sample to be tested are obtained.

[0060] Unlike Comparative Example 2, Example 1 is based on 27 measured Raman spectra of three binary systems. Binary non-additive response models are established in 7 fixed Raman peak clusters, and the obtained non-additive responses are transferred to the construction of ternary forward peak cluster spectra. Subsequently, under the constraint that the proportions of each component are non-negative and the sum is 1, the local ternary composition of each peak cluster is inverted according to the reconstruction error between the measured spectrum and the candidate ternary forward spectrum. Dynamic weighting and robust consistency fusion are performed based on the minimum singular value of the local Jacobian matrix, the reconstruction residual of the measured peak cluster, and the fitting residual of the binary model.

[0061] The same ternary mixed sample as in Example 1 was predicted using the method described in Comparative Example 2, and the results are shown in Table 3.

[0062] Table 3. Prediction results and errors of ternary composition in Comparative Example 2

[0063] In Comparative Example 2, the predicted proportions of o-cresol, m-cresol, and p-cresol were 0.3456, 0.3306, and 0.3236, respectively, which deviated significantly from the actual proportions of 0.2, 0.5, and 0.3. Although this method uses the characteristic peak parameters of the three binary systems to establish partial least squares local prediction models and obtains the ternary proportions through internal normalization and global composition constraints, it essentially transfers the regression relationship between fixed characteristic peaks and volume proportions in the binary system directly to the ternary system. It does not explicitly characterize the non-additive spectral response produced after mixing cresol isomers, nor does it dynamically adjust the composition prediction based on the identifiability and reconstruction error of different peak clusters in the sample. Therefore, the composition prediction of the sample in this embodiment still has a large deviation.

[0064] In summary, this invention, based on the spectra of three pure products (o-cresol, m-cresol, and p-cresol) and the measured spectra of 27 samples with known volume ratios from three binary systems, establishes a binary non-additive response model within seven fixed Raman peak clusters and transfers this response to ternary forward spectra. Subsequently, under the constraint that each component is non-negative and the composition sum is 1, the local ternary composition of each peak cluster is inverted. Dynamic weighting is performed based on the minimum singular value of the local Jacobian matrix, the mean square of the reconstruction residuals of the tested peak clusters, and the mean square of the binary model fitting residuals. The final normalized volume ratios of o-cresol, m-cresol, and p-cresol are obtained through robust and consistent fusion. Compared with conventional peak fitting that relies solely on the linear superposition of pure peak templates, this invention utilizes measured binary mixed spectra to explicitly characterize the non-additive response under mixed conditions and reduces the influence of peak clusters with insufficient discernibility or large residuals on the final results, thereby reducing composition inversion bias in the ternary samples tested in this embodiment.

Claims

1. A Raman quantification method for cresol isomers based on binary non-additive response migration, characterized in that, Includes the following steps: (1) Obtain the pure Raman spectra of o-cresol, m-cresol and p-cresol respectively, and the measured Raman spectra of the three binary systems composed of o-cresol, m-cresol and p-cresol in multiple known volume ratios. The same spectral preprocessing was performed on the above spectra, and the pure sample peak cluster spectrum and the measured peak cluster spectrum of the three binary systems were obtained according to the predetermined K fixed Raman peak cluster windows. (2) For each component pair and each Raman peak cluster window, construct an ideal linear superimposed peak cluster spectrum based on the pure peak cluster spectrum of the two components, and define the binary non-additive response by the difference between the measured peak cluster spectrum and the ideal linear superimposed peak cluster spectrum; use the binary non-additive responses obtained by the three binary systems under multiple known volume ratios to fit the boundary constraint model and obtain the model parameters used to characterize the symmetric response part and the asymmetric response part in the binary non-additive response; (3) For the candidate ternary composition vector, within each Raman peak cluster window, a linear combination term is constructed based on the three pure peak cluster spectra, and a binary non-additive response migration term is constructed based on the model parameters to obtain the ternary forward peak cluster spectrum of the corresponding candidate ternary composition vector; (4) Obtain the Raman spectrum of the ternary sample to be tested containing o-cresol, m-cresol and p-cresol, and perform the same spectral preprocessing; for each Raman peak cluster window, according to the normalized reconstruction error between the spectrum of the peak cluster to be tested and the spectrum of the ternary forward peak cluster, solve the problem under the composition constraint condition to obtain the local ternary composition vector of the peak cluster corresponding to each Raman peak cluster window; the composition constraint condition is that the composition ratio of o-cresol, m-cresol and p-cresol is not less than 0 and the sum of the composition ratios of the three is 1; (5) At the local ternary composition vector of each peak cluster, calculate the singular value index of the local Jacobian matrix of the ternary forward peak cluster spectrum, and combine it with the mean square of the reconstruction residual of the peak cluster spectrum to be measured and the mean square of the binary non-additive response fitting residual of the corresponding Raman peak cluster window to determine the dynamic weight of each Raman peak cluster window. (6) Based on the local ternary composition vectors of each peak cluster and their corresponding dynamic weights, construct a dynamic weighted robust consistency objective function under the composition constraints and solve it. Output the volume ratio of o-cresol, m-cresol and p-cresol in the ternary sample to be tested based on the solution results.

2. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 1, characterized in that, In step (1), binary mixed samples with component volume ratios of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90% were set up for the three binary systems respectively, and the measured Raman spectra corresponding to each volume ratio were obtained respectively.

3. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 1, characterized in that, The K fixed Raman peak cluster windows mentioned in step (1) are predetermined based on the pure Raman spectra of o-cresol, m-cresol, and p-cresol, where K is the total number of Raman peak cluster windows and is a positive integer. The three pure Raman spectra are placed on the same Raman shift grid. Based on the peak position, peak shape, peak shoulder, and mutual overlap of the main response peak, non-overlapping continuous windows are divided along the Raman shift axis so that each window covers at least one identifiable peak cluster and its complete peak shape. The window boundary is located in the low response region between adjacent peak clusters where none of the three pure samples have a main peak, and does not cross the main peak or obvious peak shoulder. The same Raman peak cluster window position and window range are used in the binary non-additive response modeling stage of the three binary systems and the volume ratio prediction stage of the ternary sample to be tested.

4. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 1, characterized in that, The specific method for step (2) is as follows: Let o-cresol, m-cresol, and p-cresol be denoted as o, m, and p, respectively; i, j ∈ {o, m, p} and i ≠ j, i and j represent two cresol isomers in a binary component pair; k = 1, ..., K, k represents the Raman peak cluster window number; This represents the volume proportion of component i in the corresponding binary system, where 0 ≤ r ≤ 1; This represents the Raman shift within the window of the k-th Raman peak cluster; and Let i and j represent the pure peak cluster spectral response vectors of components i and j within the k-th window after undergoing the same pretreatment, respectively; construct an ideal linearly superimposed peak cluster spectrum based on the pure peak cluster spectra of the two components: ； in, This represents the ideal linear superposition peak cluster spectrum of component pairs i and j at volume ratio r and Raman shift ν. This represents the measured peak cluster spectrum of a binary system under the same conditions and pretreatment. The superscript lin indicates ideal linear superposition, and the superscript obs indicates measured values; the difference between the two is used to define the spectrum. , Represents the binary non-additive response within the k-th window: ； Using the binary non-additive responses of the three binary systems at multiple known volume ratios, the boundary constraint model shown in the following equation is fitted for each component pair and each Raman peak cluster window: ； in, This represents the symmetric non-additive response parameters of components i and j at the k-th window and Raman shift ν. The parameters represent the corresponding asymmetric non-additive response parameters, with subscripts ij indicating component pairs and k indicating window indices; r(1-r) is the boundary factor, making... It is zero when r is 0 or 1.

5. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 4, characterized in that, The specific method for step (3) is as follows: For candidate triplet vectors Where c represents the candidate triplet composition vector, c o c m and c p These represent the candidate volume ratios of o-cresol, m-cresol, and p-cresol, respectively. Within the k-th Raman peak cluster window, construct linear combination terms for pure products based on the pure peak cluster spectra of o-cresol, m-cresol, and p-cresol. In the formula c represents the summation over i∈{o,m,p}. i This represents the candidate volume proportion of component i. This represents the spectral response vector of the pure peak cluster of component i within the k-th window: ； And based on the three binary systems obtained and Constructing a binary non-additive response transition term The superscript na indicates a non-additive response. This represents the summation over three disordered component pairs: (o, m), (o, p), and (m, p). This indicates a default positive number to prevent the denominator from being zero. ； Adding the linear combination term of the pure product to the binary non-additive response migration term yields the ternary forward peak cluster spectrum. , Indicates candidate composition At the k-th window and Raman displacement Forward spectral response at: ； Among them, c o c m and c p All three elements are not less than 0 and their sum is 1. The candidate triplets form a vector that satisfies the following conditions: 。 6. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 5, characterized in that, The specific method for step (4) is as follows: Acquire the Raman spectra of the ternary sample containing o-cresol, m-cresol, and p-cresol, and perform the same spectral preprocessing; for the k-th Raman peak cluster window, This represents the preprocessed spectral response vector of the sample under test within this window, with the superscript "test" indicating the sample under test. This represents the normalized reconstruction error corresponding to candidate component c. This represents a preset positive number to prevent the denominator from being zero. The normalized reconstruction error is calculated according to the following formula: ； And under the aforementioned ternary composition constraints, the solution is obtained for each Raman peak cluster window, where arg min represents the variable value that minimizes the objective function: ； This yields the local ternary vector of the peak cluster corresponding to the k-th Raman peak cluster window. The superscript loc indicates a local result obtained independently by a single window.

7. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 6, characterized in that, The specific method for step (5) is as follows: Local ternary vectors in the peak cluster At this point, calculate the local Jacobian matrix of the ternary forward peak cluster spectrum with respect to the two independent component coordinates, and use... The minimum singular value of the local Jacobian matrix is ​​represented; the unnormalized peak cluster confidence of the k-th window is calculated according to the following formula. The superscript "raw" indicates that the element has not been truncated or normalized. ； in, For the spectrum of the peak cluster to be measured in Mean square of the reconstructed residuals at the location, Let the mean square of the non-additive response fitting residuals for the k-th window across all binary modeling samples be denoted as . To prevent the default positive number with a denominator of zero, The unnormalized confidence level of the k-th window; for The upper limit is truncated, and the confidence scores of each truncated window are divided by their sum to obtain the dynamic weights. .

8. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 7, characterized in that, The specific method for step (6) is as follows: based on the local ternary vector composition of each peak cluster... and dynamic weights A dynamically weighted Huber consistency loss term is constructed under ternary composition constraints. ;in Indicates the threshold is Huber loss function A positive threshold The Euclidean distance between the candidate component and the k-th local component is: ； Simultaneously construct a dynamically weighted reconstruction loss term ,in The normalized reconstruction error for the k-th window is given by the superscript R, which denotes the reconstruction term. ； The two are combined into a dynamically weighted robust consistency objective function. ,in Let be the overall objective function. Non-negative balancing coefficients for reconstructing the loss term: ； Under the constraints of the ternary composition, the solution is obtained according to the following formula, where Let J(c) represent the final ternary volume ratio vector, and arg min represent the candidate vectors that minimize J(c). composition: ； in, This is the Huber loss threshold. These are non-negative balance coefficients; based on the obtained... Output the volume ratio of o-cresol, m-cresol, and p-cresol in the ternary sample to be tested.

9. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 1, characterized in that, The model parameters are determined only by samples of known volume ratios of the three binary systems: o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol. The ternary forward peak cluster spectrum consists only of the linear combination term and the binary non-additive response migration term. Ternary mixed samples of o-cresol, m-cresol, and p-cresol do not participate in the fitting of the model parameters.

10. The Raman quantification method for cresol isomers based on binary non-additive response migration according to claim 4, characterized in that, The three component pairs, o-cresol-m-cresol, o-cresol-p-cresol, and m-cresol-p-cresol, as well as the windows of each Raman peak cluster, were determined independently. and ;in For a specific component pair and a specific window, the symmetric non-additive response parameters are given. These are the corresponding asymmetric non-additive response parameters, and the parameters are not shared between different component pairs or between different windows.

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