CN109738413B - Mixture Raman spectrum qualitative analysis method based on sparse nonnegative least square - Google Patents
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Abstract
The invention discloses a mixture Raman spectrum qualitative detection method based on sparse nonnegative least square, relating to the Raman spectrum field, the method processes the Raman spectrum to be measured into column vectors with the same dimension as the Raman spectrum of each purified object in the Raman spectrum standard library, then, the suspected substance in the mixture to be tested is preliminarily screened out from the Raman spectrum standard library by solving a target function constructed by the Raman spectrum to be tested and the Raman spectrum standard library, and then calculating residual errors of the mixture to be detected and the suspected substance by a sparse non-negative least square method, sequentially calculating the significance difference of adjacent residual errors by adopting double-tail T test, and secondarily screening out pure substances contained in the mixture to be detected from the suspected substance based on the significance difference, so that the qualitative detection of the unknown mixture to be detected is realized, the accuracy is high, the operation is simple, and the method is quick and effective.
Description
Technical Field
The invention relates to the field of Raman spectroscopy, in particular to a mixture Raman spectrum qualitative analysis method based on sparse nonnegative least square.
Background
Over thirty years of development raman spectroscopy has become a powerful tool for qualitative and quantitative analysis, and raman spectroscopic analysis of mixtures is becoming increasingly popular due to the simplicity of its sampling method, which can be obtained directly from powders, liquids and even transparent containers.
In mixture analysis, the amount of information hidden in the spectral data consists of hundreds of points. To obtain basic information about the mixture, various chemometric, statistical and numerical methods have been developed to process the spectral data. The conventional method is to determine the composition of the mixture by matching the spectrum of the mixture with the spectrum of each pure substance sample in a standard library in turn by peak position and peak intensity. However, as the complexity of the mixture spectrum increases, overlapping peaks may occur, resulting in a substantial decrease in the spectral similarity of the mixture spectrum to its components, and the accuracy of detection of this method is greatly reduced as the number of pure species in the standard library increases.
Disclosure of Invention
The invention provides a mixture Raman spectrum qualitative analysis method based on sparse nonnegative least square aiming at the problems and the technical requirements, and the method is high in detection precision, rapid and effective.
The technical scheme of the invention is as follows:
a mixture Raman spectrum qualitative detection method based on sparse nonnegative least squares comprises the following steps:
establishing a Raman spectrum standard library of the purified substances, wherein the Raman spectrum standard library comprises Raman spectra of N purified substances, the Raman spectrum of each purified substance is a column vector with M dimensions, and M and N are positive integers;
acquiring a Raman spectrum of a mixture to be detected, and preprocessing the Raman spectrum to be detected to obtain the Raman spectrum to be detected, wherein the Raman spectrum to be detected is a column vector with M dimensions;
establishing a target function of f (X) | | AX-y | | + lambda | | | X | | ventilation according to the Raman spectrum standard library and the Raman spectrum to be detected1Wherein A represents a Raman spectrum standard library with M rows and N columns, y represents a Raman spectrum to be detected, lambda is a penalty factor in a target function, X is a coefficient vector and comprises N coefficients, the N coefficients form an N-dimensional column vector, and a coefficient X in XiCorresponding to the i pure substance, i is a form parameter, i is more than or equal to 1 and less than or equal to N, xiNot less than 0; minimizing the objective function to obtain a coefficient vector X;
screening suspected coefficients from N coefficients in the coefficient vector X obtained by solving based on a 2 delta criterion, and determining the purities corresponding to the suspected coefficients as suspected substances;
and performing least square matching on the Raman spectrum of each suspected substance and the Raman spectrum to be detected, and detecting the result of the least square matching through a double-tail T test, thereby screening out the pure substances contained in the mixture to be detected from each suspected substance.
The further technical scheme is that the method comprises the following steps of performing least square matching on the Raman spectrum of each suspected substance and the Raman spectrum to be detected, and detecting the result of the least square matching through a double-tail T test, so that purified substances contained in a mixture to be detected are screened out from the various suspected substances, and the method comprises the following steps:
arranging various suspected substances according to the sequence of the corresponding suspected coefficients from large to small to obtain a suspected substance sequence, wherein the suspected substance sequence comprises L pure substances in total, and L is a positive integer;
performing least square matching on the Raman spectrum of the 1 st pure object in the suspected substance sequence and the Raman spectrum to be detected, and calculating to obtain a 1 st residual error;
performing least square matching on the Raman spectrum of the first pure object in the suspected substance sequence and the Raman spectrum to be detected, and calculating to obtain the first residual error, wherein L is a parameter, L is less than or equal to L, and the initial value of L is 1;
detecting whether the l residual error and the l-1 residual error have significant difference through double-tail T test, wherein the 0 th residual error is defined as the Raman spectrum to be detected;
if the difference is significant, making l ═ l +1, and performing least square matching between the Raman spectrum of the first l purified substances in the suspected substance sequence and the Raman spectrum to be detected again, and calculating to obtain the first residual error;
and if the difference is not significant, determining that the mixture to be tested comprises the first l-1 purified substances in the suspected substance sequence.
The further technical scheme is that minimizing the objective function to obtain the coefficient vector X comprises processing the objective function into a corresponding augmented objective function as follows:
wherein t is a penalty factor in the augmented objective function, and the augmented objective function is solved iterativelyTo the coefficient vector X, the iterative solution process includes:
initializing the solution of a coefficient vector X as e, and obtaining a dual equation of the target function by a Lagrange multiplier method as L (X) ═ Ax-y2-2(Ax-y)Ty, determining the expression of the dual error as L (x) -f (x) according to the target function and the dual equation of the target function;
substituting the solution of the coefficient vector X into an expression of the dual error to calculate the dual error;
judging whether the calculated dual error is within a preset range or not, and outputting a solution of the coefficient vector X if the dual error is within the preset range;
and if the dual error exceeds the preset range, determining the iteration direction of the coefficient vector by a Newton method, determining the iteration step length by backtracking search, updating the solution of the coefficient vector X by using the iteration direction and the iteration step length, and performing the step of substituting the solution of the coefficient vector X into the expression of the dual error again by using the updated solution of the coefficient vector X to obtain the dual error.
The further technical scheme is that the method for screening out the suspected coefficients from N coefficients in the coefficient vector X obtained by solving based on the 2 delta criterion comprises the following steps:
calculating the mean and standard deviation of N coefficients in the coefficient vector X;
judging whether the N coefficients are in the range of (u-2 delta, u +2 delta), wherein u is a calculated mean value, and delta is a calculated standard deviation;
and determining each coefficient which is not in the range of (u-2 delta, u +2 delta) as a suspected coefficient.
The further technical scheme is that the establishment of a Raman spectrum standard library of the purified substance comprises the following steps:
collecting original Raman spectra of N purified substances by using a Raman spectrometer;
preprocessing the acquired original Raman spectrum, and interpolating and taking points by a linear interpolation method to obtain a processed original Raman spectrum, wherein the processed original Raman spectrum is an M-dimensional column vector;
and normalizing the processed original Raman spectrum by adopting a linear function to obtain the Raman spectrum of N purified substances, thereby establishing and obtaining a Raman spectrum standard library.
The method further adopts the technical scheme that the method for obtaining the Raman spectrum of the mixture to be detected and preprocessing the Raman spectrum to be detected comprises the following steps:
collecting a Raman spectrum of the mixture to be detected by using a Raman spectrometer;
preprocessing the collected Raman spectrum of the mixture to be detected, and interpolating and taking points by a linear interpolation method to obtain a processed Raman spectrum of the mixture to be detected, wherein the processed Raman spectrum of the mixture to be detected is an M-dimensional column vector;
and normalizing the processed Raman spectrum of the mixture to be detected by adopting a linear function to obtain the Raman spectrum to be detected.
The beneficial technical effects of the invention are as follows:
the application discloses a mixture Raman spectrum qualitative detection method based on sparse nonnegative least square, wherein a Raman spectrum to be detected is processed into column vectors with the same dimension as Raman spectra of various pure objects in a Raman spectrum standard library, suspected substances in the mixture to be detected are preliminarily screened out from the Raman spectrum standard library by solving a target function constructed by the Raman spectrum to be detected and the Raman spectrum standard library, residual errors of the mixture to be detected and the suspected substances are calculated by a sparse nonnegative least square method, the significance difference of adjacent residual errors is calculated sequentially by adopting double-tail T inspection, the pure objects in the mixture to be detected are screened out secondarily from the suspected substances based on the significance difference, the qualitative detection of an unknown mixture to be detected is realized, the accuracy is high, the operation is simple, and the method is quick and effective.
Drawings
Fig. 1 is a flowchart of a method for a mixture raman spectrum qualitative detection method based on sparse non-negative least squares disclosed in the present disclosure.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The application discloses a mixture Raman spectrum qualitative detection method based on sparse nonnegative least squares, which comprises the following steps, please refer to the flow chart of FIG. 1:
step S01, establishing a Raman spectrum standard library A of the purities, wherein the Raman spectrum standard library A comprises Raman spectra of N purities, N is a positive integer, and the value of N should be as large as possible to enrich the Raman spectrum standard library A so as to improve the detection coverage. The Raman spectrum of each pure substance is a column vector with M dimension, M is also a positive integer, and the value of M is determined according to the actual situation. The established Raman spectrum standard library A is in a matrix form of M rows and N columns, the Raman spectrum of the i-th purified substance is in the i-th column of the Raman spectrum standard library A, the sequence of various purified substances in the Raman spectrum standard library A is determined according to actual needs, the method is not limited in the application, i is a form parameter, i is more than or equal to 1 and less than or equal to N, and M row elements in the i-th column are the M-dimensional Raman spectrum of the i-th purified substance. The specific steps for establishing the Raman spectrum standard library A are as follows:
1. and collecting original Raman spectrums of the N pure substances by using a Raman spectrometer.
2. The acquired original raman spectrum is preprocessed, and the preprocessing process includes but is not limited to denoising and background removing, mainly for removing interference signals in the original raman spectrum, and the adopted method is the conventional method, and is not described in this application. And then interpolating and taking points by a linear interpolation method to obtain an M-dimensional column vector, namely the processed original Raman spectrum.
3. And normalizing the processed original Raman spectrum by adopting a linear function to obtain the Raman spectrum of N purified substances, thereby establishing and obtaining a Raman spectrum standard library A.
Step S02, obtaining the Raman spectrum of the mixture to be detected and preprocessing the Raman spectrum to be detected to obtain a Raman spectrum y to be detected, wherein the Raman spectrum y to be detected is a column vector with M dimension, and the specific steps of obtaining the Raman spectrum to be detected are similar to the steps S01 and specifically comprise the following steps:
1. and collecting the Raman spectrum of the mixture to be detected by using a Raman spectrometer.
2. And preprocessing the acquired Raman spectrum of the mixture to be detected, wherein the preprocessing process comprises but is not limited to denoising and background removing. And then interpolating and taking points by a linear interpolation method to obtain an M-dimensional column vector, namely the processed Raman spectrum of the mixture to be detected.
3. And normalizing the processed Raman spectrum of the mixture to be detected by adopting a linear function to obtain the Raman spectrum y to be detected.
Step S03, establishing a target function according to the Raman spectrum standard library and the Raman spectrum to be measured as follows: (X) | | AX-y | + lambda | | | X | | | non-woven hair1Wherein, X is a coefficient vector which is an N-dimensional column vector, the coefficient vector X comprises N coefficients, and the ith row in the coefficient vector is the ith coefficient XiCoefficient xiCorresponding to the i pure substance, and xiAnd more than or equal to 0, and the synchronization step S01, i is a form parameter, and i is more than or equal to 1 and less than or equal to N. Lambda is a punishment factor in the target function, the sparsity of the coefficient vector X is ensured, | | | | represents a two-norm, | | | | | | luminance1Representing a norm.
Minimizing the objective function to solve for the coefficient vector X, since directly solving for the objective function f (X) does not guarantee XiNot less than 0, so the augmented objective function obtained by adding a barrier logarithm function to the objective function f (x) is:
wherein t is a penalty factor in the augmented objective function. Then, iterative solution of the augmented objective function F (X) is carried out to obtain a coefficient vector X, and then X can be ensurediAnd the iterative solution process is greater than or equal to 0 and comprises the following steps:
1. initializing the solution of a coefficient vector X as e, and obtaining a dual equation of an objective function f (X) by a Lagrange multiplier method as L (X) ═ Ax-y2-2(Ax-y)Ty, the dual error is expressed as Δ L (x) -f (x) according to the target function f (x) and the dual equation L (x) of the target function.
2. And substituting the solution of the coefficient vector X into an expression of the dual error to calculate the dual error.
3. And judging whether the dual error obtained by calculation is within a preset range, wherein the preset range is configured according to actual needs, for example, in the application, the step is realized by judging whether the delta is less than or equal to 0.001. And if the dual error is within the preset range, the solution of the coefficient vector X is the optimal solution at the moment, and the solution of the coefficient vector X is output.
3. if the dual error exceeds the preset range, determining an iteration direction dX of the coefficient vector X by a Newton method, determining an iteration step α by backtracking search, updating the solution of the coefficient vector X to be X + alpha dX by using the iteration direction dX and the iteration step length alpha, and executing the step 2 again by using the updated solution of the coefficient vector X for repeated iteration until an optimal solution is found.
Step S04, based on the 2 δ criterion, screening out suspected coefficients from N coefficients in the solved coefficient vector X, specifically:
1. the mean u and standard deviation δ of the N coefficients in the coefficient vector X are calculated.
2. It is determined whether the N coefficients are within the range of (u-2 δ, u +2 δ).
3. If the coefficients are distributed in the range of (u-2 delta, u +2 delta), determining the coefficients as incoherent coefficients; if the coefficient is not in the range of (u-2 δ, u +2 δ), the coefficient is a pseudo coefficient.
And determining that the purified matter corresponding to the incoherent coefficient is an incoherent substance, determining that the purified matter corresponding to the suspected coefficient is a suspected substance, and preliminarily screening out the purified matter contained in the mixture to be tested from the Raman spectrum standard library A.
And step S05, performing least square matching on the Raman spectra of the various suspected substances and the Raman spectrum to be detected, and detecting the result of the least square matching through a two-tail T test, thereby secondarily screening the purified substances contained in the mixture to be detected from the various suspected substances. Specifically, the method comprises the following steps:
1. arranging various suspected substances according to the sequence of the corresponding suspected coefficients from large to small to obtain a suspected substance sequence, wherein the suspected substance sequence comprises L pure substances in total, L is a positive integer, and the suspected substance sequence can be expressed as phi1，φ2，……φL。
2. Performing least square matching by using the Raman spectrum of the first pure object in the suspected substance sequence and the Raman spectrum to be detected, and calculating the first residual error as epsilonl＝y-φ1kl1-φ2kl2-…-φlkllL is a parameter, L is less than or equal to LAnd l has an initial value of 1, where kl1The Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum phi of the 1 st pure object when the Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum to be detected1Corresponding matching coefficient, kl2The Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum phi of the second pure object when the Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum to be detected2Corresponding matching coefficient, kllThe Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum phi of the first pure object when the Raman spectrum of the first pure object is subjected to least square matching with the Raman spectrum to be detectedlCorresponding matching coefficients, and the rest not shown are analogized in turn, and the calculated residual is a column vector of M dimensions.
3. Detection of the l-th residual ε by two-tailed T testlAnd the l-1 th residual error epsilonl-1Whether there is a significant difference between them. The detection of significant differences is an existing method, and the principle is not described in the present application, where the step is implemented to detect two sets of residuals epsilonlAnd εl-1Whether or not the P value of (c) satisfies P (ε)l,εl-1)>0.1。
4. If P (ε)l,εl-1) Less than or equal to 0.1, the first residual error epsilon is representedlAnd the l-1 th residual error epsilonl-1If there is a significant difference, let l ═ l +1 and perform step 2 again for iterative computation.
5. If P (ε)l,εl-1)>0.1, then the l-th residual εlAnd the l-1 th residual error epsilonl-1The mixture to be detected does not have significant difference, at the moment, the calculation is stopped, and the first l-1 pure substances in the suspected substance sequence are determined to be contained in the mixture to be detected, so that the qualitative detection of the mixture to be detected is realized.
In the above iteration, if the initial value of l is 1, the Raman spectrum phi of the 1 st pure object in the suspected substance sequence is used1Performing least square matching with the Raman spectrum y to be measured, and calculating to obtain the 1 st residual error as epsilon1＝y-φ1k11Wherein k is11Raman spectrum phi of the 1 st pure substance1And matching coefficient when performing least square matching with the Raman spectrum y to be detected. Define the 0 th residual ε0To be measured in RamanSpectrum y, then whether P (epsilon) is satisfied or not is detected1,ε0)>0.1. If not, let l be 2, and use the Raman spectrum phi of the first 2 purified substances in the suspected substance sequence1And phi2Performing least square matching with the Raman spectrum y to be measured, and calculating to obtain the 2 nd residual error as epsilon2＝y-φ1k21-φ2k22Again, whether P (epsilon) is satisfied is detected2,ε1)>0.1, and so on, and continuously iterating and circulating.
The qualitative detection method disclosed in the present application is presented more intuitively in the following example, in which the mixture to be detected is a mixed solution of ethanol and diethyl malonate. Collecting original Raman spectra of 520 purified substances, preprocessing the original Raman spectra, unifying the preprocessed Raman spectra into 1760-dimensional column vectors, and establishing and obtaining a Raman spectrum standard library A1760×520. Collecting the Raman spectrum of the mixture to be measured, adjusting the Raman spectrum to be 1760-dimensional column vector after pretreatment, and obtaining the Raman spectrum y to be measured1760×1. The suspected substance in the mixture to be tested screened out in the above steps S01-S04 and the corresponding coefficient are shown in the following table, in which the coefficient xiThe subscript i of (a) indicates the corresponding pure substance in the Raman spectroscopy standard library A1760×520Column i of (1), each pure in Raman spectroscopy standard library A1760×520The number of columns in (1) is merely an arbitrary example and has no special meaning:
| pure substance | Coefficient xi | Pure substance | Coefficient xi |
| Ethylene glycol Ether | x20＝0.099348 | N-butyric acid | x170＝0.072523 |
| Ethanol | x58＝0.298552 | Ethylene glycol | x400＝0.070585 |
| Dioxane (dioxane) | x62＝0.045283 | Malonic acid diethyl ester | x500＝0.220215 |
The suspected substance is arranged according to the sequence of the coefficients from big to small to obtain the suspected substance sequence as follows:
| pure substance | Coefficient xi | |
| φ1 | Ethanol | x58＝0.298552 |
| φ2 | Malonic acid diethyl ester | x500＝0.220215 |
| φ3 | Ethylene glycol Ether | x20＝0.099348 |
| φ4 | N-butyric acid | x170＝0.072523 |
| φ5 | Ethylene glycol | x400＝0.070585 |
| φ6 | Dioxane (dioxane) | x62＝0.045283 |
Sequentially obtaining residual errors epsilon according to the sequence of the suspected substance1～ε6The result of performing a two-tailed T-test to obtain a P value is as follows, due to the residual ε1～ε6Only the median value of the calculated P value, and therefore the application does not show the result of the residual error in detail:
due to P (epsilon)1,ε0)≤0.1，P(ε2,ε1)≤0.1，P(ε3,ε2)>0.1, it was thus determined that the mixture to be tested contained the first 2 purities of the sequence of suspected substances, i.e., ethanol and diethyl malonateAnd the detection result is correct, and the accuracy of the method disclosed by the application can reach 95.83% after the actual measurement test, which indicates that the method disclosed by the application is very effective.
What has been described above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiment. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.
Claims (4)
1. A mixture Raman spectrum qualitative detection method based on sparse nonnegative least squares is characterized by comprising the following steps:
establishing a Raman spectrum standard library of the purified substances, wherein the Raman spectrum standard library comprises Raman spectrums of N purified substances, the Raman spectrum of each purified substance is a column vector with M dimension, and M and N are positive integers;
acquiring a Raman spectrum of a mixture to be detected, and preprocessing the Raman spectrum to be detected to obtain the Raman spectrum to be detected, wherein the Raman spectrum to be detected is a column vector with M dimensions;
establishing a target function of f (X) | | AX-y | | + lambda | | | X | | as the non-woven hair according to the Raman spectrum standard library and the Raman spectrum to be detected1Wherein A represents a Raman spectrum standard library with M rows and N columns, y represents the Raman spectrum to be detected, lambda is a penalty factor in the objective function, X is a coefficient vector and comprises N coefficients, the N coefficients form an N-dimensional column vector, and a coefficient X in XiCorresponding to the i pure substance, i is a form parameter, i is more than or equal to 1 and less than or equal to N, xiNot less than 0; minimizing the objective function to obtain the coefficient vector X, including: processing the objective function into a corresponding augmented objective function as:
wherein t is a penalty factor in the augmented objective function, the augmented objective function is iteratively solved to obtain the coefficient vector X, and the iterative solving process comprises the following steps: initializing the solution of the coefficient vector X as e, and obtaining the target function by a Lagrange multiplier methodThe dual equation of (a) is L (x) ═ Ax-y2-2(Ax-y)Ty, determining the expression of a dual error as L (x) -f (x) according to the target function and a dual equation of the target function; substituting the solution of the coefficient vector X into the expression of the dual error to calculate the dual error; judging whether the dual error obtained by calculation is within a preset range, and if the dual error is within the preset range, outputting a solution of the coefficient vector X; if the dual error exceeds the preset range, determining the iteration direction of a coefficient vector through a Newton method, determining the iteration step length through backtracking search, updating the solution of the coefficient vector X by using the iteration direction and the iteration step length, and performing the step of substituting the solution of the coefficient vector X into the expression of the dual error again by using the updated solution of the coefficient vector X to obtain the dual error;
screening suspected coefficients from N coefficients in the coefficient vector X obtained by solving based on a 2 delta criterion, and determining the purified substances corresponding to the suspected coefficients as suspected substances;
performing least square matching on the Raman spectrum of each suspected substance and the Raman spectrum to be tested, and testing the result of the least square matching through a two-tail T test, so as to screen out a purified substance included in the mixture to be tested from each suspected substance, wherein the method comprises the following steps: arranging various suspected substances according to the sequence of the corresponding suspected coefficients from large to small to obtain a suspected substance sequence, wherein the suspected substance sequence comprises L pure substances in total, and L is a positive integer; performing least square matching on the Raman spectrum of the first L purified substances in the suspected substance sequence and the Raman spectrum to be detected, and calculating to obtain the first residual error, wherein L is a parameter, L is less than or equal to L, and the initial value of L is 1; detecting whether the l residual error and the l-1 residual error have significant difference through double-tail T test, wherein the 0 th residual error is defined as the Raman spectrum to be detected; if the difference is significant, making l +1 and performing the step of performing least square matching on the Raman spectrum of the first l purified substances in the suspected substance sequence and the Raman spectrum to be detected again and calculating to obtain the first residual error; and if the difference is not significant, determining that the mixture to be tested comprises the first l-1 purified substances in the suspected substance sequence.
2. The method of claim 1, wherein the step of screening the suspected coefficients from the N coefficients in the solved coefficient vector X based on a 2 δ criterion comprises:
calculating the mean and standard deviation of the N coefficients in the coefficient vector X;
judging whether the N coefficients are in a (u-2 delta, u +2 delta) range or not, wherein u is the calculated mean value, and delta is the calculated standard deviation;
and determining each coefficient which is not in the range of (u-2 delta, u +2 delta) as a suspected coefficient.
3. The method of claim 1 or 2, wherein the establishing of the standard library of raman spectra of the purities comprises:
collecting original Raman spectra of the N purified substances by using a Raman spectrometer;
preprocessing the acquired original Raman spectrum, and interpolating and taking points by a linear interpolation method to obtain a processed original Raman spectrum, wherein the processed original Raman spectrum is an M-dimensional column vector;
and normalizing the processed original Raman spectrum by adopting a linear function to obtain the Raman spectrum of the N purified substances, thereby establishing and obtaining the Raman spectrum standard library.
4. The method according to claim 1 or 2, wherein the obtaining and preprocessing the raman spectrum of the mixture to be measured to obtain the raman spectrum to be measured comprises:
collecting a Raman spectrum of the mixture to be detected by using a Raman spectrometer;
preprocessing the collected Raman spectrum of the mixture to be detected, and interpolating and taking points by a linear interpolation method to obtain a processed Raman spectrum of the mixture to be detected, wherein the processed Raman spectrum of the mixture to be detected is an M-dimensional column vector;
and normalizing the processed Raman spectrum of the mixture to be detected by adopting a linear function to obtain the Raman spectrum to be detected.
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