MCR-ALS-based method for removing matrix spectrum of mixture system

Abstract

Disclosed in the present invention is an MCR-ALS-based method for removing a matrix spectrum of a mixture system, comprising: S1) acquiring an original mixed spectrum containing a target substance and a matrix and an original matrix spectrum only comprising a matrix; S2) performing baseline correction and normalization processing to obtain a preprocessed mixed spectrum D and a preprocessed matrix spectrum B; S3) using an MCR-ALS algorithm to iteratively calculate a pure substance-based spectral matrix S and a weight matrix C; S4) reducing a target substance spectrum and a matrix spectrum on the basis of the matrix S and the matrix C; S5) matching the decomposed matrix spectrum with a known standard matrix spectrum and performing qualitative identification; and S6) calculating explained variance between the generated spectrum and the original spectrum. According to the present invention, a matrix substance spectrum in a mixture spectrum can be relatively completely removed, and the impact on a characteristic peak of a target substance spectrum is small, so that the impact of the matrix spectrum on the characteristic peak of the target substance spectrum is reduced, thereby facilitating subsequent quantitative and qualitative analysis.

Description

A method for removing matrix spectrum from mixture system based on MCR-ALS Technical Field

[0001] The present invention relates to a spectrum processing method, in particular to a mixture system matrix spectrum removal method based on MCR-ALS. Background Art

[0002] The matrix refers to the packaging materials of the substance and solvents such as water in the mixture. At present, there are mainly the following methods to eliminate matrix interference.

[0003] 1. Spectral subtraction method

[0004] Patent document CN104749155B proposes a Raman spectroscopy detection method. First, a matrix spectrum and a matrix and sample mixed spectrum are obtained. The two spectra are divided, and the minimum value is taken as the coefficient. The coefficient is multiplied by the matrix spectrum and subtracted from the mixed spectrum.

[0005] In patent document CN108169201B, a Raman spectroscopy detection method for subtracting packaging interference is described. The Raman spectroscopy signal of the packaged sample is gradually subtracted from the Raman spectroscopy signal of the packaged sample to obtain a series of Raman spectroscopy signals subtracting the packaging interference. The information entropy of each of the series of Raman spectroscopy signals subtracting the packaging interference is calculated. The information entropy of the Raman spectroscopy signal greater than the packaging is used as a candidate information entropy sequence, from which the minimum information entropy is selected. The Raman spectroscopy signal subtracting the packaging interference corresponding to the minimum information entropy is used as the optimized Raman spectroscopy signal subtracting the packaging interference.

[0006] In patent document CN103063648B, a method for detecting liquid preparations using Raman spectroscopy is disclosed, which includes the following steps: measuring the Raman spectrum of a solution containing a solvent and a sample to obtain a Raman spectrum signal of the solution; measuring the Raman spectrum of the solvent to obtain a Raman spectrum signal of the solvent; gradually subtracting the Raman spectrum signal of the solvent from the Raman spectrum signal of the solution to obtain a series of Raman spectrum signals from which solvent interference has been removed; calculating the information entropy of each of the series of Raman spectrum signals from which solvent interference has been removed; selecting the maximum information entropy from the calculated series of information entropies; and using the Raman spectrum signal from which solvent interference has been removed corresponding to the maximum information entropy as the optimized Raman spectrum signal from which solvent interference has been removed.

[0007] 2. Spectral Analysis

[0008] Patent document CN113984736A proposes a method for separating packaged food signals based on spatially offset Raman spectroscopy. Based on the information entropy of the Raman spectra at different offset distances, the method extracts Raman spectra from a certain area of ​​the initial spectral data as observation data. Independent component analysis is then performed on the observation data to separate and obtain several independent signal components. The method then combines characteristic spectral peak clustering to identify the attribution of the independent signal components separated by independent component analysis, ultimately determining the Raman signal of the food being tested.

[0009] The existing methods for eliminating matrix interference mainly have the following problems:

[0010] 1. In many cases, the presence of the matrix will affect the spectrum of the target substance, making the characteristic peak of the target substance unclear, which will affect some subsequent quantitative or qualitative analysis; even when the characteristic peak of the matrix Raman spectrum coincides with the target substance, it will seriously affect the analysis of the target substance.

[0011] 2. Subtract the background spectrum from the original mixed spectrum. In this method, the background spectrum needs to be multiplied by a coefficient. The size of the coefficient is related to the effect of removing the background signal. The appropriate coefficient value is difficult to determine. If the coefficient is too large, it may destroy the Raman signal of some target substances. If the coefficient is too small, the background subtraction will not be clean.

[0012] 3. Some spectrum decomposition algorithms require multiple spectrum measurements, and the measurement and calculation processes are complex.

[0013] Therefore, it is necessary to improve the existing methods for eliminating matrix interference. Technical issues

[0014] The technical problem to be solved by the present invention is to provide a method for removing the matrix spectrum of a mixture system based on MCR-ALS, which can completely remove the matrix material spectrum in the mixture spectrum without affecting the characteristic peaks of the target material spectrum; thereby reducing the influence of the matrix spectrum on the characteristic peaks of the target material spectrum, facilitating subsequent quantitative and qualitative analysis. Technical Solutions

[0015] The technical solution adopted by the present invention to solve the above-mentioned technical problems is to provide a method for removing matrix spectra of a mixture system based on MCR-ALS, comprising the following steps: S1) obtaining an original mixed spectrum containing a target substance and a matrix and an original matrix spectrum containing only the matrix; S2) performing baseline correction and normalization on the original mixed spectrum and the original matrix spectrum to obtain a pre-processed mixed spectrum D and a pre-processed matrix spectrum B; S3) using the MCR-ALS algorithm to iteratively calculate the pure substance spectrum matrix and weight matrix of the matrix and the target substance; S4) restoring the target substance spectrum based on the pure substance spectrum matrix and the weight matrix; S5) matching the decomposed matrix spectrum with the standard matrix spectrum for qualitative identification to ensure the accuracy of the separated matrix spectrum; S6) calculating the explained variance between the spectrum generated by MCR-ALS and the original spectrum to evaluate the decomposition result.

[0016] Furthermore, the step S3) uses the MCR-ALS algorithm to perform conditional constraints during the iteration process, controlling the values ​​of the weight matrix C and the pure substance base spectrum matrix S to be non-negative, and the base spectrum matrix S to have no inverted peak.

[0017] Furthermore, the step S3) includes: S31) establishing a hybrid system: ; is the error matrix; S32) initialize the weight matrix C and the pure substance base spectrum matrix S: the weight matrix C is randomly initialized, and in the base spectrum matrix S, the initial value of the first component is the preprocessed matrix spectrum B, and the initial value of the second component is randomly initialized; the initial values ​​of the weight matrix C and the base spectrum matrix S are all positive numbers; S33) use the alternating least squares method to control the iterative process.

[0018] Furthermore, the step S33) detects the residuals between two adjacent iterations, and terminates the iteration when the residuals between two adjacent iterations are less than 0.0001, or terminates the iteration when the number of iterations exceeds 150.

[0019] Furthermore, the step S5) evaluates the similarity between the decomposed matrix spectrum and the standard matrix spectrum by calculating the spectral angular distance.

[0020] Furthermore, the spectral angular distance is calculated as follows:

[0021] ;

[0022] S0 is the first substance in the base spectrum matrix S after the iterative decomposition is completed, that is, the substance base spectrum.

[0023] Furthermore, the step S6) evaluates the decomposition result by calculating the data explained variance:

[0024]

[0025] Data explained variance R 2 The closer it is to 1, the better the effect. , D is the preprocessed mixed spectrum, and e is the error between the spectrum calculated by MCR-ALS and the original mixed spectrum. Beneficial effects

[0026] Compared with the prior art, the present invention has the following beneficial effects: the MCR-ALS-based mixture system matrix spectrum removal method provided by the present invention can completely remove the matrix material spectrum in the mixture spectrum without affecting the characteristic peaks of the target material spectrum; thereby reducing the influence of the matrix spectrum on the characteristic peaks of the target material spectrum, facilitating subsequent quantitative and qualitative analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG1 is a schematic diagram of the process of removing matrix spectrum of a mixture system based on MCR-ALS of the present invention;

[0028] FIG2 is an original spectrum diagram of the matrix spectrum and the mixture spectrum in an embodiment of the present invention;

[0029] FIG3 is a spectrum diagram of the matrix spectrum and the mixture spectrum after pretreatment in an embodiment of the present invention;

[0030] FIG4 is a basic spectrum diagram of the matrix S obtained by decomposition of the present invention;

[0031] FIG5 is a spectrum of the substance reduced by the present invention and a spectrum of the matrix. Modes for Carrying Out the Invention

[0032] The present invention will be further described below with reference to the accompanying drawings and examples.

[0033] This paper proposes a method for removing Raman matrix spectra based on the MCR-ALS algorithm, which effectively solves the problems of existing technologies. MCR-ALS (Multivariate Curve Resolution Alternating Least Squares) is a multivariate curve resolution method primarily used to resolve mixing issues in multispectral and multichromatographic data.

[0034] Referring to FIG1 , the present invention provides a method for removing matrix Raman signals based on the MCR-ALS algorithm, comprising the following steps: S1: obtaining original mixed spectral data and matrix spectra, namely, a mixed original spectrum containing a target substance and a matrix and a spectrum containing only the matrix; S2: performing baseline correction and normalization on the mixed original spectrum and the matrix-only spectrum to obtain a pre-processed mixed spectrum D and a pre-processed matrix spectrum B; S3: performing the MCR-ALS algorithm, subjecting the algorithm to conditional constraints during the iteration process, such as matrix values ​​cannot be negative and base spectrum matrix S cannot have inverted peaks; obtaining a pure substance base spectrum matrix S and a weight matrix C for the matrix and target substance; S4: restoring the target substance spectrum and matrix spectrum based on the pure substance base spectrum matrix S and weight matrix C. S5: matching the decomposed matrix spectrum with the standard matrix spectrum for qualitative identification to ensure the accuracy of the separated matrix spectrum; S6: calculating the explained variance of the spectrum generated by MCR-ALS and the original spectrum to evaluate the results of the model decomposition.

[0035] The present invention ensures that the matrix spectrum used in the MCR-ALS algorithm is correct, preventing erroneous signals from being subtracted in subsequent algorithms. It also ensures that the error between the synthesized spectrum after decomposition and the original spectrum is within a reasonable range. This data is used to determine whether the spectrum of the pure substance obtained by decomposition is correct. The main steps of the present invention are described in detail below.

[0036] 1. First, obtain the data set required by the algorithm

[0037] The present invention uses the MCR-ALS algorithm to remove the background spectrum, which requires obtaining pure matrix spectra and matrix and substance mixed spectra. In the experiment of the present invention, 5 NH4 + Aqueous solution spectrum, NH4 + is the target substance, and water is the matrix to be removed; Figure 2 shows the original spectrum of the matrix spectrum and the mixture spectrum.

[0038] 2. Spectral Preprocessing

[0039] For these spectral data, baseline correction and normalization operations need to be performed respectively, as shown in Figure 3.

[0040] 3. MCR-ALS Iteration

[0041] The matrix spectrum was removed from the original spectrum using the MCR-ALS algorithm.

[0042] MCR-ALS (Multivariate Curve Resolution Alternating Least Squares) is a multivariate curve resolution method used to resolve mixing issues in multispectral and multichromatographic data. The core idea behind this algorithm is to decompose the raw data into multiple components, each corresponding to the spectrum or chromatogram of a substance and its relative concentration in each measurement. The algorithm's main steps are as follows:

[0043] 1. Establish a hybrid system:

[0044]

[0045] D is the mixed spectrum of matrix and substance, C is the weight matrix related to concentration, S is the spectrum of pure substance basis matrix, T is the matrix transpose sign, and E is the error matrix.

[0046] 2. Weight and pure component matrix initialization

[0047] Initialize the parameters of the two matrices of the algorithm, usually use some initial guesses, or generate random numbers as the initial values ​​of the matrices. The number of target components of the MCR-ALS decomposition of the present invention is 2, that is, decomposed into matrix spectrum and material spectrum. When initializing the matrix, the weight matrix C is randomly initialized. In the material-based spectrum matrix S, the initial value of the first component is the matrix spectrum, and the second component is the material spectrum.

[0048] Since there will be no negative values ​​in the two matrices according to known information, non-negativity constraints are required during the iteration process.

[0049] In this experiment, D is a 5×1024 matrix of mixed material spectra, C is a randomly initialized 5×2 matrix, and S is a 2×1024 matrix, where the first row is initialized to the matrix spectra data and the second row is randomly initialized. The values ​​of matrices C and S are all positive.

[0050] 3. Alternating Least Squares

[0051] Alternating Least Squares (ALS) is an iterative optimization algorithm commonly used to solve least squares problems. Its basic idea is to decompose the least squares problem of multiple variables into a single least squares problem, solving it through alternating iterations. The ALS algorithm is commonly used for problems such as matrix factorization, regression, and least squares support vector machines.

[0052] For example: About To optimize the problem, we alternately iterate and optimize X and Y, optimizing only one of the matrices each time while keeping the other fixed. This is equivalent to converting it into an ordinary least squares problem.

[0053] The least squares method was discovered by Legendre in the 19th century. Its matrix form is as follows:

[0054] For n independent variables X=[x1,x2,...,x n ], dependent variables [y1,y2,...,y n ],have:

[0055]

[0056] That is, AX = Y

[0057] To minimize the residual, The observed values ​​Y are the multiple samples of the present invention, and the theoretical values ​​AX are the hypothetical fitting functions of the present invention. The objective function is also the loss function. The goal of the present invention is to obtain a model of the fitting function that minimizes the objective function.

[0058] Finally, convert to solve , and get the fitting coefficients.

[0059] The ALS algorithm is simple and easy to implement. Compared to other matrix decomposition algorithms, it is relatively simple to implement. It also has good stability and is generally less sensitive to the choice of initial values, making it easier to converge in practice. Therefore, the ALS algorithm is selected for matrix update.

[0060] When performing alternating least squares in the present invention, it is important to ensure that the values ​​of the two decomposed matrices C and S are both positive numbers. Therefore, after each least squares calculation, it is necessary to judge the matrix data, and modify the data less than or equal to 0 to an extremely small number, which is preferably set to 0.0001 in the present invention. This also prevents the matrix value from being 0, causing the iteration to stop.

[0061] After each iterative matrix calculation is completed, the peak of the spectrum needs to be constrained to prevent the occurrence of inverted peaks.

[0062] 4. Convergence determination

[0063] Check whether the algorithm has converged by detecting the residuals of two adjacent iterations; preferably, the iteration is terminated when the residuals of two adjacent iterations are less than 0.0001, or when the number of iterations exceeds 150.

[0064] 5. Analysis results

[0065] The final model pure component spectral matrix and weighted spectrum are analyzed to restore the matrix spectrum and target substance spectrum, respectively. The calculated matrix spectrum is compared with the standard matrix spectrum, and their similarity is evaluated by calculating the spectral angular distance to determine whether the decomposition result is incorrect.

[0066] The two components of the base spectrum of the matrix S obtained by decomposition are shown in Figure 4.

[0067] The resulting weight matrix C is shown below:

[0068]

[0069] The material spectrum and matrix spectrum are restored according to the matrices S and C. The experimental results are shown in Figure 5.

[0070] Decomposition effect analysis

[0071]

[0072] R2 is the explained variance. The closer the value is to 1, the better the decomposition effect. , D is the preprocessed mixed spectrum, and e is the error between the spectrum calculated by MCR-ALS and the original mixed spectrum.

[0073]

[0074] S0 is the first substance in the base spectrum matrix S after iterative decomposition, i.e., the base spectrum. B is the preprocessed matrix spectrum. The angular distance θ between the standard matrix spectrum and the matrix spectrum decomposed by MCR-ALS is calculated to assess the similarity between the two spectra. The angular distance ranges from 0 to 90, with smaller values ​​indicating better results.

[0075] In this experiment, the explained variance R 2 is 0.9868, and the angular distance θ=1.14218.

[0076] 1. Use the MCR-ALS algorithm to deconvolve the mixed spectrum, separate the matrix spectrum from the substance spectrum, and reduce the influence of the matrix spectrum on the target substance spectrum.

[0077] 2. Compared with taking out the substance for measurement, it is more convenient and will not cause pollution or damage to the substance. Compared with other spectral subtraction methods, the matrix spectrum separation is cleaner.

[0078] 3. The spectrum measurement and data calculation process during the spectrum interpretation process is also relatively simple.

[0079] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make some modifications and improvements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the definition of the claims.

Claims

1. A method for removing matrix spectra of a mixture system based on MCR-ALS, characterized in that, It includes the following steps: S1) Obtain the original mixed spectrum containing the target substance and the matrix, and the original matrix spectrum of only the matrix; S2) Perform baseline correction and normalization on the original mixed spectrum and the original matrix spectrum to obtain the preprocessed mixed spectrum D and the preprocessed matrix spectrum B; S3) Use the MCR-ALS algorithm to iteratively calculate the pure substance basis spectrum matrix S and the weight matrix C of the matrix and the target substance; S4) Restore the target substance spectrum according to the pure substance basis spectrum matrix S and the weight matrix C; S5) Match and qualitatively identify the decomposed matrix spectrum with the standard matrix spectrum; S6) Calculate the explained variance of the spectrum generated by MCR-ALS and the original spectrum to evaluate the decomposition result; In step S3), the MCR-ALS algorithm performs conditional constraints during the iteration process to control the values of the weight matrix C and the pure substance basis spectrum matrix S to be non-negative, and no inverted peaks appear in the basis spectrum matrix S; Step S3) includes: S31) Establish a hybrid system: ； D is the mixed spectrum of the matrix and the substance, C is the weight matrix related to the concentration, S is the pure substance basis spectrum matrix spectrum, T is the matrix transpose symbol, and E is the error matrix; S32) Initialize the weight matrix C and the pure substance basis spectrum matrix S The weight matrix C is randomly initialized. In the basis spectrum matrix S, the initial value of the first component is the preprocessed matrix spectrum B, and the initial value of the second component is randomly initialized; the initial values of the weight matrix C and the basis spectrum matrix S are all positive numbers; S33) Use the alternating least squares method to control the iteration process; In step S5), the similarity between the decomposed matrix spectrum and the standard matrix spectrum is evaluated by calculating the spectral angle distance; The calculation of the spectral angle distance is as follows: ； S0 is the first substance in the basis spectrum matrix S after the iterative decomposition is completed, that is, the substance basis spectrum, and B is the preprocessed matrix spectrum.

2. The method for removing matrix spectra of a mixture system based on MCR-ALS according to claim 1, wherein, In step S33), the residuals of two adjacent iterations are detected, and the iteration ends when the residuals of two adjacent iterations are less than 0.0001, or the iteration ends when the number of iterations exceeds 150 times.

3. The method for removing matrix spectrum of a mixture system based on MCR-ALS according to claim 1, characterized in that, In step S6), the decomposition result is evaluated by calculating the data explained variance: ； Data interpretation variance R 2 The closer it is to 1, the better the effect is. , D is the preprocessed mixed spectrum, and e is the error between the spectrum calculated by MCR-ALS and the original mixed spectrum.

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