CN110501294A - A kind of multivariate calibration methods based on information fusion - Google Patents
A kind of multivariate calibration methods based on information fusion Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 34
- 230000004927 fusion Effects 0.000 title claims abstract description 21
- 239000011159 matrix material Substances 0.000 claims description 46
- 230000001419 dependent effect Effects 0.000 claims description 29
- 238000012937 correction Methods 0.000 claims description 10
- 238000005259 measurement Methods 0.000 claims description 8
- 238000007500 overflow downdraw method Methods 0.000 abstract description 3
- 238000001228 spectrum Methods 0.000 description 8
- 230000003595 spectral effect Effects 0.000 description 4
- 238000013178 mathematical model Methods 0.000 description 2
- RTHCYVBBDHJXIQ-UHFFFAOYSA-N N-methyl-3-phenyl-3-[4-(trifluoromethyl)phenoxy]propan-1-amine Chemical compound C=1C=CC=CC=1C(CCNC)OC1=CC=C(C(F)(F)F)C=C1 RTHCYVBBDHJXIQ-UHFFFAOYSA-N 0.000 description 1
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- 238000002474 experimental method Methods 0.000 description 1
- 238000002329 infrared spectrum Methods 0.000 description 1
- 238000002156 mixing Methods 0.000 description 1
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/25—Colour; Spectral properties, i.e. comparison of effect of material on the light at two or more different wavelengths or wavelength bands
- G01N21/31—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry
- G01N21/35—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light
- G01N21/359—Investigating relative effect of material at wavelengths characteristic of specific elements or molecules, e.g. atomic absorption spectrometry using infrared light using near infrared light
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- G—PHYSICS
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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Abstract
The present invention relates to chemometric techniques fields, and in particular to a kind of multivariate calibration methods based on information fusion.A kind of multivariate calibration methods based on information fusion, including first part: model is established；Second part: predicted portions.The present invention proposes a kind of multivariate calibration methods based on information fusion, and after being merged by the method that this method provides to information, predicted root mean square error, which is significantly less than, to be fusedKThe predicted root mean square error of a method；Fusion method of the present invention can offset the prediction error of each algorithm, to reduce total prediction error.
Description
Technical field
The present invention relates to chemometric techniques fields, and in particular to a kind of multivariate calibration methods based on information fusion.
Background technique
Multivariate Correction is widely used in Chemical Measurement, and main function is that founding mathematical models describe dependent variable
(such as group score value) with independent variable (such as spectrum) between relationship, then utilize established mathematical model to unknown sample dependent variable into
Row prediction.By taking near-infrared spectrum analysis as an example, the process of Multivariate Correction is generally as follows: first being carried out experiment by certain rule and is set
Meter is selected or is prepared corresponding multicomponent sample by experimental design；Sample is put near infrared spectrometer again to measure, is obtained
The independent variable (spectrum) of each sample；Then using multivariate calibration methods (such as offset minimum binary) to independent variable (spectrum) and dependent variable
(group score value) is modeled；The independent variable of unknown sample (spectrum) is finally substituted into established model, obtains unknown sample
Dependent variable (group score value).
Currently used multivariate calibration methods mainly have classical least square (CLS), main composition to return (PCR), partially minimum
Two multiply (PLS) etc..Every kind of multivariate calibration methods have the advantage and disadvantage of its own, are difficult to determine which kind of algorithm can obtain optimum prediction
As a result.In practical applications, all there is error in every kind of multivariate calibration methods prediction result.If by multiple Multivariate Correction algorithms
Prediction result is merged, and the prediction error of component is made to cancel out each other, then more accurate prediction result can be obtained.
Summary of the invention
The present invention is directed in view of the above-mentioned problems, proposing a kind of Multivariate Correction algorithm based on information fusion, fusion treatment is each
The prediction result of algorithm makes it predict that error is cancelled out each other, to improve prediction accuracy.
Technical program of the present invention lies in:
A kind of multivariate calibration methods based on information fusion,
(1) model is established:
Dependent variable matrix Yc is pcRow m column；It indicates: total pcA sample, each sample have m dependent variable；
Independent variable matrix Xc is pcRow q column；It indicates: total pcA sample, each sample have q channel measurements；
Dependent variable matrix Yv is pvRow m column；Independent variable matrix Xv is pvRow q column；
Unknown sample independent variable xuFor q member row vector；
Detailed process is as follows:
1) the K Multivariate Correction algorithm used is determined；
2) independent variable matrix Xc, dependent variable matrix Yc are modeled using each Multivariate Correction algorithm, obtains K prediction model；
3) it is utilized respectively each prediction model and acts on independent variable matrix Xv, obtain i-th (i=1,2,3 ..., m) a dependent variable
Predict column vector ypvk, and calculate the prediction error vector of a i-th of dependent variable of prediction model of kth (k=1,2 ..., K)
ek=ypvk-yvi (1)
Wherein, ypvkPrediction result for kth (k=1,2 ..., K) a prediction model to i-th of dependent variable, yviFor matrix Yv's
I-th column vector, i.e. the i-th column of dependent variable matrix Yv；ekFor the prediction error vector of k-th of prediction model.
4) the prediction error vector is formed into pvRow K column matrix e
E=[e1 e2 … eK] (2)
5) the autocorrelation matrix R of matrix e is calculated
6) column vector w is calculatedi
In formula, a is the row vector of K member, and each element is [1,1 ..., 1] 1, a=；
(2) predicted portions:
7) unknown sample independent variable x is acted on K prediction model respectivelyu, obtain the prediction result y of component iuk(k=1,2 ...,
K), and vector y=[y is formedu1,yu2,…,yuK]T；
Calculate fusion forecasting result
The technical effects of the invention are that:
The present invention proposes a kind of multivariate calibration methods based on information fusion, is melted by the method that this method provides to information
After conjunction, predicted root mean square error is significantly less than the predicted root mean square error for K method being fused；Fusion method of the present invention
The prediction error of each algorithm can be offset, to reduce total prediction error.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the multivariate calibration methods based on information fusion of the present invention.
Specific embodiment
Present embodiment is tested with analogue data, and sample is mixed by 4 kinds of pure components in test, measure spectrum wave
Number range is 10000~12500cm-1, sampling interval 10cm-1(i.e. each sample has q=251 channel measurements), it is single
The spectrum of position pure component is respectively as follows:
In formula, n (n=1,2,3 ..., N) is wave number serial number, λnFor n-th of wave number value, it can use 10000,10010 respectively,
10020 ..., 12500；
The spectrum of pure component is denoted as 4 row q column matrix Xs
If modeling group sub-matrix used is random quantity matrix Yc (the i.e. p of 100 rows 4 columnc=100, m=4), it establishes
Independent variable column matrix Xc used in model is
Xc=YcXs+Ec
Wherein, the line number p of Xcc=100, each element of columns q=251, Yc are obeyed (0,1) and are uniformly distributed；
Ec is spectral measurement error matrix, each of which element all obeys zero-mean normal distribution, and variance is 0.0001.
For determining that the group score matrix of fusion parameters is pv=100 rows, the random matrix Yv of m=4 column；
For determining that the independent variable matrix Xv of fusion parameters is
Xv=YvXs+Ev
Wherein, the line number p of Xvc=100, each element of columns q=251, Yv are obeyed (0,1) and are uniformly distributed；
Ev is spectral measurement error matrix, each of which element all obeys zero-mean normal distribution, and variance is 0.0001.
The group score value of unknown sample is m (=4) column random vector yu, the independent variable of the unknown sample for prediction is vector
xuFor
xu=yuXs+eu
Wherein, xuFor q (=251) column vector, yuEach element obey (0,1) be uniformly distributed；
euFor spectral measurement error vector, each of which element all obeys zero-mean normal distribution, and variance is 0.0001.
In the present embodiment, the method that is fused is PLS, PCR, CLS tri-, i.e. K=3；Repeat to generate 100 in prediction in advance
Survey spectral vector xu, each prediction spectrum is predicted using pre- flow gauge, obtains the prediction result of each component, and calculate
The predicted root mean square error of each group score value.
A kind of process of the multivariate calibration methods based on information fusion is as follows:
(1) model is established:
Dependent variable matrix Yc is pcRow m column；It indicates: total pcA sample, each sample have m dependent variable；
Independent variable matrix Xc is pcRow q column；It indicates: total pcA sample, each sample have q channel measurements；
Dependent variable matrix Yv is pvRow m column；Independent variable matrix Xv is pvRow q column；
Unknown sample independent variable xuFor q member row vector.
1) tri- Multivariate Correction algorithms of PLS, PCR, CLS, i.e. K=3 are determined；
2) above-mentioned 3 Multivariate Correction algorithms are utilized respectively to model independent variable matrix Xc and dependent variable matrix Yc, obtain 3 predictions
Model；
3) above-mentioned 3 prediction models act on independent variable matrix Xv, obtain the prediction column of i-th (i=1,2 ..., m) a dependent variable
Vector ypvk, and calculate the prediction error vector of a i-th of dependent variable of prediction model of kth (k=1,2 ..., K)
ek=ypvk-yvi (1)
Wherein, ypvkPrediction result for kth (k=1,2 ..., K) a prediction model to i-th of dependent variable, yviFor matrix Yv's
I-th column vector, i.e. the i-th column of dependent variable matrix Yv；ekFor the prediction error vector of k-th of prediction model.
4) the prediction error vector is formed into pvRow K column matrix e
E=[e1 e2 … eK] (2)
5) the autocorrelation matrix R of matrix e is calculated
In formula, subscript T representing matrix transposition；
6) column vector w is calculatedi
In formula, a is the row vector of K member, and each element is [1,1 ..., 1] 1, a=.
(2) pre- flow gauge:
7) unknown sample independent variable x is acted on 3 prediction models respectivelyu, obtain the prediction result y of component iuk(k=1,
2 ..., K), and form vector y=[yu1,yu2,…,yuK]T；
Calculate fusion forecasting result
It is evaluated with performance of the predicted root mean square error to each method.The calculation formula of predicted root mean square error is as follows:
In formula, riFor the true value of dependent variable, correspond to each y in embodimentuIn element (i.e. each time prediction true component
Value), rpiFor the prediction result of multivariate calibration methods, I is the sample size of forecast set, the present embodiment 100.
After the completion of modeling, the calculated fusion vector of step 6) is as shown in table 1.
Table 1 merges vector value
| Method | Component 1 | Component 2 | Component 3 | Component 4 |
| PLS | 0.0126 | -0.0741 | -0.0090 | 0.1920 |
| PCR | -0.9084 | -0.7617 | -0.8648 | -0.9943 |
| CLS | 1.8958 | 1.8358 | 1.8738 | 1.8024 |
In table, each column indicate that a fusion vector, i.e., the i-th column (i=1,2,3,4) indicate wiValue.
The predicted root mean square error of each method is as shown in table 2.
2 each method predicted root mean square error of table
As can be seen from Table 2, after fusion treatment through the invention, predicted root mean square error be significantly less than PLS, PCR with
The predicted root mean square error of CLS, the fusion method can be missed with the prediction error of each algorithm of partial offset to reduce total prediction
Difference, this blending algorithm are very effective.
Claims (1)
1. a kind of multivariate calibration methods based on information fusion, this method are as follows:
(1) model is established:
Dependent variable matrix Yc is pcRow m column；It indicates: total pcA sample, each sample have m dependent variable；
Independent variable matrix Xc is pcRow q column；It indicates: total pcA sample, each sample have q channel measurements；
Dependent variable matrix Yv is pvRow m column；Independent variable matrix Xv is pvRow q column；
Unknown sample independent variable xuFor q member row vector；
It is characterized by:
1) the K Multivariate Correction algorithm used is determined；
2) independent variable matrix Xc, dependent variable matrix Yc are modeled using each Multivariate Correction algorithm, obtains K prediction model；
3) it is utilized respectively each prediction model and acts on independent variable matrix Xv, obtain i-th (i=1,2,3 ..., m) a dependent variable
Predict column vector ypvk, and calculate the prediction error vector of a i-th of dependent variable of prediction model of kth (k=1,2 ..., K)
ek=ypvk-yvi (1)
Wherein, ypvkPrediction result for kth (k=1,2 ..., K) a prediction model to i-th of dependent variable, yviFor matrix Yv's
I-th column vector, i.e. the i-th column of dependent variable matrix Yv；ekFor the prediction error vector of k-th of prediction model；
4) the prediction error vector is formed into pvRow K column matrix e
E=[e1 e2 … eK] (2)
5) the autocorrelation matrix R of matrix e is calculated
6) column vector w is calculatedi
In formula, a is the row vector of K member, and each element is [1,1 ..., 1] 1, a=；
(2) it predicts:
7) unknown sample independent variable x is acted on K prediction model respectivelyu, obtain the prediction result y of component iuk(k=1,2 ...,
K), and vector y=[y is formedu1,yu2,…,yuK]T；
Calculate fusion forecasting result
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| CN111024229A (en) * | 2019-11-28 | 2020-04-17 | 天津津航技术物理研究所 | Single-chip integrated spectral imaging micro-system spectral data correction method |
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