CN109738413A - Mixture Raman spectra qualitative analysis method based on sparse non-negative least square - Google Patents
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Abstract
The invention discloses a kind of mixture Raman spectra qualitative checking methods based on sparse non-negative least square, it is related to Raman spectrum field, Raman spectrum to be measured processing is the Raman spectrum with each pure substance in Raman spectrum java standard library with the column vector of dimension by this method, then go out the doubtful substance for including in testing mixture by solving the objective function constructed using Raman spectrum to be measured and Raman spectrum java standard library preliminary screening from Raman spectrum java standard library, then the residual error of testing mixture and doubtful substance is calculated by sparse nonnegative least, the significant difference for successively calculating adjacent residual error is examined using double tail T again, based on significant difference, postsearch screening goes out the pure substance for including in testing mixture from doubtful substance, realize the qualitative detection to unknown testing mixture, accuracy rate is high, it is easy to operate, quickly and effectively.
Description
Technical field
The present invention relates to Raman spectrum field, especially a kind of mixture Raman spectrum based on sparse non-negative least square
Method for qualitative analysis.
Background technique
By development in more than 30 years, Raman spectrum had become the powerful of qualitative and quantitative analysis, the drawing of mixture
Graceful spectrum analysis is becoming increasingly popular due to the simple of its sampling method, this method can directly from powder, liquid even
It is obtained in transparent vessel.
In mixture analysis, the information content hidden in spectroscopic data is made of hundreds of points.Mixture in order to obtain
Essential information develops various stoichiometries, statistics and numerical method and handles spectroscopic data.Traditional method is to pass through
The spectrum of every kind of pure material sample in the spectrum and java standard library of mixture is carried out to the matching of peak position and peak intensity according to this, so that it is determined that
The ingredients of a mixture.But with the increase of spectral mixture complexity, in fact it could happen that overlap peak, cause the spectrum of mixture with
The spectrum similarity of its component substantially reduces, also, with the increase of pure material sample in java standard library, the detection essence of this method
Degree will be greatly reduced.
Summary of the invention
The present inventor regarding to the issue above and technical need, proposes a kind of mixture based on sparse non-negative least square
Raman spectra qualitative analysis method, this method detection accuracy are high, fast and effective.
Technical scheme is as follows:
A kind of mixture Raman spectra qualitative checking method based on sparse non-negative least square, this method comprises:
The Raman spectrum java standard library of pure substance is established, includes the Raman spectrum of N kind pure substance in Raman spectrum java standard library, often
A kind of Raman spectrum of pure substance is the column vector with M dimension, and M and N are positive integer；
It obtains the Raman spectrum of testing mixture and is pre-processed to obtain Raman spectrum to be measured, Raman spectrum to be measured is tool
The column vector for thering is M to tie up；
According to Raman spectrum java standard library and Raman spectrum to be measured establish objective function be f (x)=| | AX-y | |+λ | | X | |1,
Wherein A indicates that the Raman spectrum java standard library of M row N column, y indicate that Raman spectrum to be measured, λ are penalty factor, and X is coefficient vector and packet
N number of coefficient is included, N number of coefficient constitutes the column vector of N-dimensional, the coefficient x in XiCorresponding i-th kind of pure substance, i are parameter and 1≤i≤N,
xi≥0；It minimizes objective function and obtains coefficient vector X；
Doubtful coefficient is filtered out from the N number of coefficient solved in obtained coefficient vector X based on 2 δ criterion, determines each doubt
It is doubtful substance like the corresponding pure substance of coefficient；
The Raman spectrum of various doubtful substances and Raman spectrum to be measured are subjected to Least squares matching, and pass through double tail T inspections
It tests and tests to the result of Least squares matching, to filter out include in testing mixture pure from various doubtful substances
Net object.
Its further technical solution is that the Raman spectrum of various doubtful substances and Raman spectrum to be measured are carried out minimum two
Multiply matching, and tested by double tail T inspections to the result of Least squares matching, to be filtered out from various doubtful substances
The pure substance for including in testing mixture, comprising:
Various doubtful substances are arranged to obtain doubtful substance sequence according to the descending sequence of corresponding doubtful coefficient
It arranges, includes altogether L pure substance in doubtful substance sequence, L is positive integer；
Least square is carried out using the Raman spectrum of the 1st pure substance in doubtful substance sequence and Raman spectrum to be measured
Match and the 1st residual error is calculated；
Least square is carried out using the Raman spectrum of the preceding l pure substance in doubtful substance sequence and Raman spectrum to be measured
Match and be calculated first of residual error, l is parameter, and the initial value of l≤L and l are 1；
Examine between first of residual error of detection and the l-1 residual error whether there is significant difference by double tail T, wherein fixed
The 0th residual error of justice is the Raman spectrum to be measured；
If having significant difference, enables l=l+1 and execute the preceding l pure substance utilized in doubtful substance sequence again
Raman spectrum and Raman spectrum to be measured carry out Least squares matching and the step of first of residual error is calculated；
If not having significant difference, it is determined that pure including preceding l-1 in doubtful substance sequence in testing mixture
Object.
Its further technical solution is to minimize objective function to obtain coefficient vector X, including be by objective function processing
Corresponding augmented objective function are as follows:Wherein, t is penalty factor, iteration
It solves augmented objective function and obtains coefficient vector X, iterative solution process includes:
The solution for initializing coefficient vector X is e, is L (x) by the dual equation that method of Lagrange multipliers obtains objective function
=-(Ax-y)2-2(Ax-y)TY, the expression formula for determining antithesis error according to the dual equation of objective function and objective function are
Δ=L (x)-f (x)；
Antithesis error is calculated in the expression formula that the solution of coefficient vector X substitutes into antithesis error；
Whether within a preset range to judge the antithesis error being calculated, if antithesis error is within a preset range, exports
The solution of coefficient vector X；
If antithesis error exceeds preset range, the iteration direction of coefficient vector is determined, by backtracking line by Newton method
Search for and determine iteration step length, and update the solution of coefficient vector X using iteration direction and iteration step length, using updated coefficient to
The solution of amount X executes the step of antithesis error is calculated in the expression formula that the solution of coefficient vector X substitutes into antithesis error again.
Its further technical solution is to be screened from the N number of coefficient solved in obtained coefficient vector X based on 2 δ criterion
Doubtful coefficient out, comprising:
The mean value and standard deviation of N number of coefficient in design factor vector X；
N number of coefficient is judged whether in (u-2 δ, u+2 δ) range, and u is the mean value being calculated, and δ is the mark being calculated
It is quasi- poor；
Determine that each coefficient in (u-2 δ, u+2 δ) range is not doubtful coefficient.
Its further technical solution is to establish the Raman spectrum java standard library of pure substance, comprising:
Utilize the original Raman spectrum of Raman spectrometer acquisition N kind pure substance；
Collected original Raman spectrum is pre-processed, and is taken by linear interpolation method interpolation and a little to obtain that treated
Original Raman spectrum, treated original Raman spectrum are the column vector of M dimension；
To treated, original Raman spectrum normalizes to obtain the Raman spectrum of N kind pure substance using linear function, thus
Foundation obtains Raman spectrum java standard library.
Its further technical solution is to obtain the Raman spectrum of testing mixture and pre-processed to obtain Raman to be measured
Spectrum, comprising:
Utilize the Raman spectrum of Raman spectrometer acquisition testing mixture；
The Raman spectrum of collected testing mixture is pre-processed, and is taken by linear interpolation method interpolation and is a little obtained
Testing mixture treated Raman spectrum, the column vector of testing mixture treated Raman spectrum is M dimension；
Testing mixture treated Raman spectrum is normalized to obtain Raman spectrum to be measured using linear function.
The method have the benefit that:
It, will be to this application discloses a kind of mixture Raman spectra qualitative checking method based on sparse non-negative least square
Surveying Raman spectrum processing is the Raman spectrum with various pure substances in Raman spectrum java standard library with the column vector of dimension, is then led to
It crosses to solve and tentatively be sieved from Raman spectrum java standard library using the objective function that Raman spectrum to be measured and Raman spectrum java standard library construct
The doubtful substance for including in testing mixture is selected, testing mixture and doubtful is then calculated by sparse nonnegative least
The residual error of substance, then the significant difference for successively calculating adjacent residual error is examined using double tail T, significant difference is based on from doubtful object
Postsearch screening goes out the pure substance for including in testing mixture in matter, realizes the qualitative detection to unknown testing mixture, quasi-
True rate is high, easy to operate, fast and effective.
Detailed description of the invention
Fig. 1 is that the application discloses the disclosed mixture Raman spectra qualitative checking method based on sparse non-negative least square
Method flow diagram.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
This application discloses a kind of mixture Raman spectra qualitative checking method based on sparse non-negative least square, the party
Method includes the following steps, please refers to the flow chart of Fig. 1:
Step S01 establishes the Raman spectrum java standard library A of pure substance, includes N kind pure substance in Raman spectrum java standard library A
Raman spectrum, N are the covering that the value of positive integer and N should enrich Raman spectrum java standard library A greatly as far as possible to improve detection
Range.The Raman spectrum of each pure substance is the column vector with M dimension, and M is also the value of positive integer and M according to practical feelings
Condition determines.The matrix form that obtained Raman spectrum java standard library A is M row N column is established, the Raman spectrum of i-th kind of pure substance is being drawn
Graceful spectrum java standard library A i-th column, sequence of the various pure substances in Raman spectrum java standard library A be determine according to actual needs,
Without limitation, i is parameter and 1≤i≤N to the application, and the M row element in the i-th column is the M dimension Raman spectrum of i-th kind of pure substance.
Establish the specific steps of Raman spectrum java standard library A are as follows:
1, the original Raman spectrum of Raman spectrometer acquisition N kind pure substance is utilized.
2, collected original Raman spectrum is pre-processed, pretreated process includes but is not limited to denoise and go to carry on the back
Scape processing, primarily to removing the interference signal in original Raman spectrum, the method for use is existing conventional method, this Shen
It is not unfolded please to describe.Then the column vector for a little obtaining M dimension is taken by linear interpolation method interpolation to get original drawing of having arrived that treated
Graceful spectrum.
3, to treated, original Raman spectrum normalizes to obtain the Raman spectrum of N kind pure substance using linear function, from
And it establishes and obtains Raman spectrum java standard library A.
Step S02 obtains the Raman spectrum of testing mixture and is pre-processed to obtain Raman spectrum y to be measured, drawing to be measured
Graceful spectrum y is the column vector tieed up with M, and the specific steps for obtaining Raman spectrum to be measured are similar with step S01, specifically:
1, the Raman spectrum of Raman spectrometer acquisition testing mixture is utilized.
2, the Raman spectrum of collected testing mixture is pre-processed, likewise, pretreated process include but
It is not limited to denoise and go background process.Then take the column vector for a little obtaining M dimension to be measured to get having arrived by linear interpolation method interpolation
Mixture treated Raman spectrum.
3, testing mixture treated Raman spectrum is normalized to obtain Raman spectrum y to be measured using linear function.
Step S03 establishes objective function according to Raman spectrum java standard library and Raman spectrum to be measured are as follows: and f (x)=| | AX-y | |
+λ||X||1, wherein X is coefficient vector, is the column vector of N-dimensional, includes N number of coefficient in coefficient vector X, in coefficient vector
I-th row is i-th of coefficient xi, coefficient xiCorresponding i-th kind of pure substance, and xi>=0, it is parameter and 1≤i≤N with step S01, i.
λ is penalty factor, the degree of rarefication of assurance coefficient vector X, | | | | indicate two norms, | | | |1Indicate a norm.
It minimizes objective function and obtains coefficient vector X to solve, since direct solution objective function f (x) cannot be guaranteed
xi>=0, so first obtaining augmented objective function plus an obstacle logarithmic function to objective function f (x) are as follows:Wherein, t is penalty factor.Then augmented objective function F is iteratively solved
(X) x can be guaranteed by obtaining coefficient vector Xi>=0, iterative solution process includes:
1, the solution for initializing coefficient vector X is e, obtains the dual equation of objective function f (x) by method of Lagrange multipliers
For L (x)=- (Ax-y)2-2(Ax-y)TY determines antithesis according to the dual equation L (x) of objective function f (x) and objective function
The expression formula of error is Δ=L (x)-f (x).
2, antithesis error is calculated in the expression formula that the solution of coefficient vector X substitutes into antithesis error.
3, within a preset range whether, preset range configures the antithesis error that judgement is calculated according to actual needs, than
As in this application, this step is embodied as judging whether to meet Δ≤0.001.If antithesis error is within a preset range, at this time
The solution of coefficient vector X is optimal solution, the solution of output factor vector X.
If 3, antithesis error exceeds preset range, the iteration direction dX of coefficient vector X is determined by Newton method, is passed through back
Line search of tracing back determines iteration step length α, and is X=X+ α dX using the solution that iteration direction dX and iteration step length α updates coefficient vector X,
Step 2 is executed again using the solution of updated coefficient vector X and carries out iteration, until finding optimal solution.
Step S04 filters out doubtful coefficient from the N number of coefficient solved in obtained coefficient vector X based on 2 δ criterion, has
Body:
1, the mean value u and standard deviation δ of N number of coefficient in design factor vector X.
2, judge N number of coefficient whether in (u-2 δ, u+2 δ) range.
In range that 3, if coefficient is distributed in (u-2 δ, u+2 δ), it is determined that coefficient is incoherence；If coefficient is not in (u-2
δ, u+2 δ) in range, then coefficient is doubtful coefficient.
It determines that the corresponding pure substance of incoherence is incoherent substance, determines that the corresponding pure substance of doubtful coefficient is doubtful
Substance, this step preliminary screening from Raman spectrum java standard library A have gone out pure substance included in testing mixture.
The Raman spectrum of various doubtful substances and Raman spectrum to be measured are carried out Least squares matching, and passed through by step S05
Double tail T inspections test to the result of Least squares matching, so that postsearch screening goes out mixing to be measured from various doubtful substances
The pure substance for including in object.It is specific:
1, various doubtful substances are arranged to obtain doubtful substance according to the descending sequence of corresponding doubtful coefficient
Sequence includes altogether L pure substance in doubtful substance sequence, and L is positive integer, and doubtful substance sequence can be expressed as φ1,
φ2... ... φL。
2, least square is carried out using the Raman spectrum of the preceding l pure substance in doubtful substance sequence and Raman spectrum to be measured
Matching, and calculating first of residual error is εl=y- φ1kl1-φ2kl2-…-φlkll, l is parameter, and the initial value of l≤L and l are 1,
Wherein, kl1When carrying out Least squares matching for the Raman spectrum of preceding l pure substance and Raman spectrum to be measured with the 1st pure substance
Raman spectrum φ1Corresponding matching factor, kl2Least square is carried out for the Raman spectrum of preceding l pure substance and Raman spectrum to be measured
When matching with the Raman spectrum φ of the 2nd pure substance2Corresponding matching factor, kllFor preceding l pure substance Raman spectrum with to
Raman spectrum φ when surveying Raman spectrum progress Least squares matching with first of pure substancelCorresponding matching factor, other do not show
Out and so on, the residual error being calculated is the column vector of M dimension.
3, first of residual epsilon of detection is examined by double tail TlWith the l-1 residual epsilonl-1Between whether have significant difference.
The detection of significant difference is existing method, and the application is not unfolded to describe principle, and the step is embodied as detection two in this application
Group residual epsilonlAnd εl-1P value whether meet P (εl,εl-1) > 0.1.
If 4, P (εl,εl-1)≤0.1, then it represents that first of residual epsilonlWith the l-1 residual epsilonl-1Between have conspicuousness it is poor
It is different, then it enables l=l+1 and execution step 2 is iterated calculating again.
If 5, P (εl,εl-1) > 0.1, then it represents that first of residual epsilonlWith the l-1 residual epsilonl-1Between do not have conspicuousness it is poor
It is different, stop calculating at this time, determines to include preceding l-1 pure substance in doubtful substance sequence in testing mixture, that is, realize pair
The qualitative detection of testing mixture.
In above-mentioned iterative process, the initial value of l is 1, then utilizes the Raman of the 1st pure substance in doubtful substance sequence
Spectrum φ1Least squares matching is carried out with Raman spectrum y to be measured, and it is ε that the 1st residual error, which is calculated,1=y- φ1k11, wherein
k11For the Raman spectrum φ of the 1st pure substance1Matching factor when Least squares matching is carried out with Raman spectrum y to be measured.Definition
0th residual epsilon0For Raman spectrum y to be measured, then detect whether to meet P (ε1,ε0) > 0.1.If not satisfied, then enabling l=2, utilize
The Raman spectrum φ of preceding 2 pure substances in doubtful substance sequence1And φ2Least squares matching is carried out with Raman spectrum y to be measured,
And it is ε that the 2nd residual error, which is calculated,2=y- φ1k21-φ2k22, detect whether to meet P (ε again2,ε1) > 0.1, and so on,
Continuous iterative cycles.
Next the application more intuitively shows qualitative checking method disclosed in the present application with an example, in the example
In, testing mixture is ethyl alcohol+diethyl malonate mixed solution.The original Raman spectrum of 520 kinds of pure substances is acquired, it is pre- to locate
It is unified for the column vector of 1760 dimensions after reason, thus establishes and obtains Raman spectrum java standard library A1760×520.Acquire the drawing of testing mixture
Graceful spectrum, is adjusted to the column vector of 1760 dimensions after pretreatment, thus obtain Raman spectrum y to be measured1760×1.Utilize above-mentioned steps
Doubtful substance and corresponding coefficient are as shown in the table in the testing mixture that S01-S04 is filtered out, in the following table, coefficient xiUnder
Marking i indicates corresponding pure substance in Raman spectrum java standard library A1760×520In i-th column, each pure substance is in Raman spectrum mark
Quasi- library A1760×520In columns only arbitrarily illustrate, without particular meaning:
| Pure substance | Coefficient xi | Pure substance | Coefficient xi |
| Ethylene glycol ethyl ether | x20=0.099348 | N-butyric acie | x170=0.072523 |
| Ethyl alcohol | x58=0.298552 | Glycol | x400=0.070585 |
| Dioxane | x62=0.045283 | Diethyl malonate | x500=0.220215 |
Doubtful substance according to the descending sequence of coefficient is arranged to obtain doubtful substance sequence as follows:
| Pure substance | Coefficient xi | |
| φ1 | Ethyl alcohol | x58=0.298552 |
| φ2 | Diethyl malonate | x500=0.220215 |
| φ3 | Ethylene glycol ethyl ether | x20=0.099348 |
| φ4 | N-butyric acie | x170=0.072523 |
| φ5 | Glycol | x400=0.070585 |
| φ6 | Dioxane | x62=0.045283 |
Residual epsilon is successively sought according to doubtful substance sequence1~ε6And the result that the double tail T of progress examine to obtain P value is as follows, by
In residual epsilon1~ε6Only with the median that calculates P value, therefore the result of residual error is not shown in detail in the application:
Due to P (ε1,ε0)≤0.1, P (ε2,ε1)≤0.1, P (ε3,ε2) > 0.1, it is thus determined that testing mixture includes doubting
Like preceding 2 pure substances in substance sequence, namely including ethyl alcohol and diethyl malonate, testing result is correct, after measured test
The accuracy rate of disclosed method can achieve 95.83%, show that disclosed method is very effective.
Above-described is only the preferred embodiment of the application, and present invention is not limited to the above embodiments.It is appreciated that this
The other improvements and change that field technical staff directly exports or associates without departing from the spirit and concept in the present invention
Change, is considered as being included within protection scope of the present invention.
Claims (6)
1. a kind of mixture Raman spectra qualitative checking method based on sparse non-negative least square, which is characterized in that the side
Method includes:
The Raman spectrum java standard library of pure substance is established, includes the Raman spectrum of N kind pure substance in the Raman spectrum java standard library, often
A kind of Raman spectrum of pure substance is the column vector with M dimension, and M and N are positive integer；
It obtains the Raman spectrum of testing mixture and is pre-processed to obtain Raman spectrum to be measured, the Raman spectrum to be measured is tool
The column vector for thering is M to tie up；
According to the Raman spectrum java standard library and the Raman spectrum to be measured establish objective function be f (x)=| | AX-y | |+λ | | X
||1, wherein A indicates that the Raman spectrum java standard library of M row N column, y indicate the Raman spectrum to be measured, and λ is penalty factor, and X is coefficient
Vector and including N number of coefficient, N number of coefficient constitutes the column vector of N-dimensional, the coefficient x in XiCorresponding i-th kind of pure substance, i are ginseng
Number and 1≤i≤N, xi≥0；It minimizes the objective function and obtains the coefficient vector X；
Doubtful coefficient is filtered out from the N number of coefficient solved in the obtained coefficient vector X based on 2 δ criterion, determines each institute
Stating the corresponding pure substance of doubtful coefficient is doubtful substance；
The Raman spectrum of the various doubtful substances and the Raman spectrum to be measured are subjected to Least squares matching, and pass through double tails
T inspection tests to the result of Least squares matching, to filter out the mixing to be measured from the various doubtful substances
The pure substance for including in object.
2. the method according to claim 1, wherein described by the Raman spectrum of the various doubtful substances and institute
It states Raman spectrum to be measured and carries out Least squares matching, and tested by double tail T inspections to the result of Least squares matching, from
And the pure substance for including in the testing mixture is filtered out from the various doubtful substances, comprising:
The various doubtful substances are arranged to obtain doubtful substance sequence according to the descending sequence of corresponding doubtful coefficient
It arranges, includes altogether L pure substance in the doubtful substance sequence, L is positive integer；
Minimum two is carried out using the Raman spectrum and the Raman spectrum to be measured of the preceding l pure substance in the doubtful substance sequence
Multiply and match and be calculated first of residual error, l is parameter, and the initial value of l≤L and l are 1；
Examine between first of residual error of detection and the l-1 residual error whether there is significant difference by double tail T, wherein define the
0 residual error is the Raman spectrum to be measured；
If having significant difference, enables l=l+1 and execute again described pure using preceding l in the doubtful substance sequence
The step of Raman spectrum of net object and the Raman spectrum to be measured carry out Least squares matching and first of residual error are calculated；
If not having significant difference, it is determined that include preceding l-1 in the doubtful substance sequence in the testing mixture
Pure substance.
3. the method according to claim 1, wherein it is described minimize the objective function obtain the coefficient to
X is measured, including the objective function is handled as corresponding augmented objective function are as follows:
Wherein, t is penalty factor, iteratively solves the augmented objective function and obtains the coefficient vector X, iterative solution process includes:
The solution for initializing the coefficient vector X is e, is by the dual equation that method of Lagrange multipliers obtains the objective function
L (x)=- (Ax-y)2-2(Ax-y)TY determines that antithesis misses according to the dual equation of the objective function and the objective function
The expression formula of difference is Δ=L (x)-f (x)；
Antithesis error is calculated in the expression formula that the solution of the coefficient vector X substitutes into the antithesis error；
Whether within a preset range the antithesis error being calculated is judged, if the antithesis error is in the preset range
It is interior, then export the solution of the coefficient vector X；
If the antithesis error exceeds the preset range, the iteration direction of coefficient vector is determined by Newton method, is passed through back
Line search of tracing back determines iteration step length, and the solution of the coefficient vector X is updated using the iteration direction and iteration step length, using more
The solution of the coefficient vector X after new executes the expression that the solution of the coefficient vector X is substituted into the antithesis error again
The step of antithesis error is calculated in formula.
4. the method according to claim 1, wherein it is described based on 2 δ criterion from solve the obtained coefficient to
Doubtful coefficient is filtered out in N number of coefficient in amount X, comprising:
Calculate the mean value and standard deviation of N number of coefficient in the coefficient vector X；
N number of coefficient is judged whether in (u-2 δ, u+2 δ) range, and u is the mean value being calculated, and δ is to be calculated
The standard deviation；
Determine that each coefficient in (u-2 δ, u+2 δ) range is not doubtful coefficient.
5. method according to any one of claims 1 to 4, which is characterized in that the Raman spectrum standard for establishing pure substance
Library, comprising:
The original Raman spectrum of the N kind pure substance is acquired using Raman spectrometer；
The collected original Raman spectrum is pre-processed, and is taken by linear interpolation method interpolation and a little to obtain that treated
Original Raman spectrum, treated the original Raman spectrum are the column vector of M dimension；
Treated the original Raman spectrum is normalized to obtain the Raman spectrum of the N kind pure substance using linear function,
The Raman spectrum java standard library is obtained to establish.
6. method according to any one of claims 1 to 4, which is characterized in that the Raman spectrum for obtaining testing mixture
And it is pre-processed to obtain Raman spectrum to be measured, comprising:
The Raman spectrum of the testing mixture is acquired using Raman spectrometer；
The Raman spectrum of the collected testing mixture is pre-processed, and is taken by linear interpolation method interpolation and is a little obtained
The testing mixture treated Raman spectrum, the column of the testing mixture treated Raman spectrum is M dimension to
Amount；
The testing mixture treated Raman spectrum is normalized to obtain the Raman spectrum to be measured using linear function.
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| WO2021232757A1 (en) * | 2020-05-19 | 2021-11-25 | 江南大学 | Method for improving mixture component identification precision by using raman spectra of known mixtures |
| US11614408B2 (en) | 2020-05-19 | 2023-03-28 | Jiangnan University | Method for improving identification accuracy of mixture components by using known mixture Raman spectrum |
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| CN110243806A (en) * | 2019-07-30 | 2019-09-17 | 江南大学 | Component of mixture recognition methods under Raman spectrum based on similarity |
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| CN113252641A (en) * | 2021-06-11 | 2021-08-13 | 北京卓立汉光分析仪器有限公司 | Substance identification method based on residual analysis under Raman spectrum |
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