CN104123424B - Method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde - Google Patents
Method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde Download PDFInfo
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- CN104123424B CN104123424B CN201410385490.1A CN201410385490A CN104123424B CN 104123424 B CN104123424 B CN 104123424B CN 201410385490 A CN201410385490 A CN 201410385490A CN 104123424 B CN104123424 B CN 104123424B
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Abstract
The present invention provides a kind of method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde, the model from physical and chemical index to flue gas crotonaldehyde is set up by existing roasting foliated data and flue gas crotonaldehyde data, for unknown baking sheet smoke crotonaldehyde sample, it is possible to use its physical and chemical composition data directly predicts baking sheet smoke crotons aldehyde value.Present invention eliminates being rolled by traditional chemical mode, burn, catch the steps such as flue gas, detection；Meanwhile, using robust regression model, it can be effectively prevented from because the drawbacks of singular value sample causes in physicochemical data or flue gas data, largely ensureing the robustness of model, this point exactly advantage of the robust regression modeling better than normal linear regression modeling.It was verified that the model can effectively predict the flue gas crotons aldehyde value of roasting piece, detection efficiency is greatly enhanced, testing cost is reduced.
Description
Technical field
The present invention relates to a kind of method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde, belong to specific calculation mould
Type technical field.
Background technology
Smoke of tobacco is a kind of extremely complex mixture, it be during cigarette smoking by result of combustion of tobacco, cracking and
Distill and produce.Cigarette products are produced for the harmfulness of human body by burning and sucking process.Harmful components in flue gas
Mainly formed in combustion, and the chemical characteristic of flue gas is changed with the change of raw tobacco material intrinsic chemical composition
's.Therefore, the chemical characteristic of tobacco leaf raw material determines the chemical characteristic and security of cigarette smoke.Crotonaldehyde is respiratory tract
Cilium toxin, can suppress the removing of lung excreta, so as to cause PUD D.The acquisition of traditional baking sheet smoke crotonaldehyde data
Mode is the chemical composition index in the flue gas after the roasting piece burning of detection.The flue gas data obtained in this way will be, it is necessary to will
Roasting piece rolls into the flue gas after cigarette burning and carries out chemical detection, and detection process wastes time and energy and testing cost is high.
In linear regression modeling, model is built upon on the basis of certain assumed condition, for example, be observed sample error
For standardized normal distribution.If the distribution of error is asymmetric or tends to outlier, then carry out linear regression modeling
Assuming that being invalid, estimation, confidential interval and other statistics calculated of parameter are all insecure.Such case
Under, the foundation for carrying out model with robust regression is very effective.Robust regression modeling contains a kind of healthy and strong approximating method,
Compared with least square method, the variation for data small portion is no so sensitive, improves the confidence level of model.
Robust regression is modeled by assigning a weights for each data point.Weighting is automatic and is to repeat
, this process is called automatic weight weighted least-squares method.In the first stage, each sample point is endowed identical weight, so
Calculated afterwards using common least square method and obtain model coefficient.In subsequent iterations, the point of each sample will be counted again
Calculate, those sample points away from model predication value will be endowed relatively low weight.The least square method being weighted is utilized afterwards
Computation model coefficient.Iterative process will go on always, until scope fluctuation of the model coefficient in a setting.
Therefore a kind of forecast model is set up with robust regression and directly obtains flue gas crotonaldehyde data by roasting foliated data
Method is imperative.
The content of the invention
The problems such as process of baking sheet smoke crotonaldehyde data is time-consuming, laborious, cost is high is detected to solve prior art, this
Invention proposes a kind of method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde.
The present invention is set up from physical and chemical index to flue gas bar by existing roasting foliated data and flue gas crotonaldehyde data
The robust regression forecast model of beans aldehyde, for unknown baking sheet smoke crotonaldehyde sample, utilizes its physical and chemical composition nest model
Directly predict baking sheet smoke crotons aldehyde value.Specifically pass through following each step：
（1）List the physicochemical data of known roasting piece is corresponding with flue gas crotonaldehyde data, set up set of data samples；
（2）Difference calculation procedure（1）The column vector x of each physicochemical data in the data obtained sample set1~xnWith flue gas crotonaldehyde
The column vector y of data, the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde is calculated by following equation, linearly respectively
This physicochemical data that the absolute value of correlation coefficient r is more than corresponding to 0.3 is the feature being had a major impact to flue gas crotonaldehyde
Index item, is used as the input variable of modeling：
（1）
In formula：xFor the column vector of a certain physicochemical data,yFor the column vector of flue gas crotonaldehyde data；
（3）According to different sources, kind, class, 245 roasting pieces are uniformly selected as training sample, with robust regression
Linear modelling algorithm, sets up flue gas crotonaldehyde forecast model, and its expression formula is following formula：
（2）
In formula：Y is the model predication value of flue gas crotonaldehyde, and X is physicochemical data vector, and b is constant term, and A is regression coefficient
Vector；
（4）According to step（2）The characteristic index of selection, regard the corresponding physicochemical data of roasting piece to be measured as input variable set
With to step（3）Forecast model in, the model predication value Y for the flue gas crotonaldehyde for obtaining roasting piece to be measured can be calculated.
The step（1）Physicochemical data include total reducing sugar, reduced sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, albumen
Matter, schmuck value, nitrogen base ratio, chlorine, potassium, sugared alkali ratio and ammonia state alkali.
The step（3）The step of with robust regression linear modelling algorithm, is as follows：
（a）Carry out local weight regression fitting：Fit procedure only considers a part for all fitting points each time, each
The individual value being fitted a little is all determined by the stroll point of adjacent local fit scope, is given at each match point
Give different weight coefficients, its weight coefficient is the power of the both sides each point of match point in the range of 1, local fit at match point
Weight coefficient is decremented to zero with certain rule successively, and the weight at the data point of fit range is 0, its algebraic expression
For：
In formula：For the weight coefficient of each match point,For measured value,For calculated value；
（b）Adjustment residual error is calculated as follows：
In formula：For the residual error of common least square method,For residual error adjust lever value, for reduce influence match value compared with
The weight located a little louder, T is transposition；
Standard adjustment residual error is given by：
In formula：K is adjusting parameter, takes 4.685；S is robust sexual deviation；MAD is the median absolute deviation of residual error；
（c）The robustness weight of the every bit in the range of local fit is calculated as follows：
（d）For formula（2）, constant term b is brought into regression coefficient vector, then formula（2）It is reduced to：
The regression coefficient vector A for causing following formula to take minimum value is solved according to weight least square method, and is calculated in x0PlaceValue：
In formula：J is the object function that weight least square method is solved.
The step（d）If robustness weight its error of fitting when being not up to following error of fitting requirement, from step（b）
Start iterative calculation, untill error reaches requirement or reaches restriction iterations：
。
The step（3）Forecast model by following each step to fitting performance and promote performance evaluate：
According to different sources, kind, class, 45 and step are uniformly selected（3）Different roasting foliated data are used as survey
Sample sheet, is applied to step（3）Forecast model in carry out performance test, predict the outcome need to while meet following two conditions,
I.e. decision model performance reaches that prediction is required：
A, test sample are suitable with the prediction mean error of training sample, as shown in following formula：
In formula：errtrainFor mean error of the forecast model to training sample, errtestIt is forecast model to test sample
Mean error；
B, the predicted value of test sample and actual value are in significant linear relationship, as shown in following formula：
In formula：For the predicted value of test sample, y is the measured value of test sample（The measured value is by conventional method
Measure）.
The present invention compared with prior art, possesses advantages below and effect：Pass through existing roasting foliated data and flue gas
Crotonaldehyde data set up the model from physical and chemical index to flue gas crotonaldehyde, for unknown baking sheet smoke crotonaldehyde sample, can be with
Baking sheet smoke crotons aldehyde value is directly predicted using its physical and chemical composition data.With robust regression linear modelling algorithm, modeling process
It is middle to find suitable vector A and constant term b in final forecast model so as to be calculated in the expression formula of flue gas crotonaldehyde forecast model
Value is fitted measured value as far as possible.Present invention eliminates being rolled by traditional chemical mode, burn, catch the step such as flue gas, detection
Suddenly；Meanwhile, using robust regression model, it can be effectively prevented from caused by singular value sample in physicochemical data or flue gas data
Drawback, largely ensures the robustness of model, and this point exactly robust regression modeling is excellent better than normal linear regression modeling
Point.It was verified that the model can effectively predict the flue gas crotons aldehyde value of roasting piece, detection efficiency, reduction inspection are greatly enhanced
Survey cost.
Brief description of the drawings
Fig. 1 is modeling procedure schematic diagram of the invention.
Embodiment
Below by embodiment, the present invention will be further described.
Embodiment 1
（1）List the physicochemical data of known roasting piece is corresponding with flue gas crotonaldehyde data, set of data samples is set up, wherein managing
Change data include total reducing sugar, reduced sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, protein, schmuck value, nitrogen base ratio, chlorine, potassium,
Sugared alkali ratio and ammonia state alkali, it is as shown in the table：
（2）Difference calculation procedure（1）The column vector x of each physicochemical data in the data obtained sample set1~xnWith flue gas crotonaldehyde
The column vector y of data, the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde is calculated by following equation respectively：
（1）
In formula：xFor the column vector of a certain physicochemical data,yFor the column vector of flue gas crotonaldehyde data；Obtain all roasting pieces
The linearly dependent coefficient r of physicochemical data and flue gas crotonaldehyde, it is as shown in the table：
The corresponding selections in physicochemical data of the linearly dependent coefficient r with absolute value more than 0.3 have weight to flue gas crotonaldehyde again
A characteristic index to be influenceed, as the input variable of modeling, that is, selects total reducing sugar, reduced sugar, total volatile alkaline, total nitrogen, albumen
Matter, schmuck value, potassium, sugared alkali ratio, ammonia state alkali：
（3）According to different sources, kind, class, 245 roasting pieces are uniformly selected as training sample, with robust regression
Linear modelling algorithm, sets up flue gas crotonaldehyde forecast model, and its expression formula is following formula：
（2）
In formula：Y is the model predication value of flue gas crotonaldehyde, and X is physicochemical data vector, and b is constant term, and A is regression coefficient
Vector；
The step of wherein using robust regression linear modelling algorithm is as follows：
（a）Carry out local weight regression fitting：Fit procedure only considers a part for all fitting points each time, each
The individual value being fitted a little is all determined by the stroll point of adjacent local fit scope, is given at each match point
Give different weight coefficients, its weight coefficient is the both sides each point of match point in the range of 1, local fit at match point
Weight coefficient is decremented to zero with certain rule successively, and the weight at the data point of fit range is 0, the expression of its algebraically
Formula is：
In formula：For the weight coefficient of each match point,For measured value,For calculated value；
（b）Adjustment residual error is calculated as follows：
In formula：For the residual error of common least square method,For residual error adjust lever value, for reduce influence match value compared with
The weight located a little louder, T is transposition；
Standard adjustment residual error is given by：
In formula：K is adjusting parameter, takes 4.685；S is robust sexual deviation；MAD is the median absolute deviation of residual error；
（c）The robustness weight of the every bit in the range of local fit is calculated as follows：
（d）For formula（2）, constant term b is brought into regression coefficient vector, then formula（2）It is reduced to：
The regression coefficient vector A for causing following formula to take minimum value is solved according to weight least square method, and is calculated in x0PlaceValue：
In formula：J is the object function that weight least square method is solved；
If its error of fitting is not up to following error of fitting requirement, from step（b）Start iterative calculation, until error reaches
Untill requiring or reaching restriction iterations：
；
A is obtained by above-mentioned computing1=-0.09537、a2=0.60850、a3=11.76652、a4=-17.37009、a5=
3.24879、a6=-0.93766、a7=-1.29710、a8=-0.17601、a9=-13.33443, b=12.47663；
Therefore, the expression formula of the flue gas crotonaldehyde forecast model is：Y=12.47663-0.09537* total reducing sugars+0.60850*
Reduced sugar+11.76652* total volatile alkaline -17.37009* total nitrogen+3.24879* protein -0.93766* schmuck values -
1.29710* potassium -0.17601* sugar alkali ratio -13.33443* ammonia state alkali；
It is evaluated by following each step to above-mentioned forecast model and is fitted performance and popularization performance：
Training sample is predicted with above-mentioned forecast model, its result see the table below：
According to different sources, kind, class, 45 and step are uniformly selected（3）Different roasting foliated data are used as survey
Sample sheet, is applied to step（3）Performance test is carried out in the forecast model of gained, test sample is carried out with above-mentioned forecast model
Prediction, as a result see the table below：
Above-mentioned predict the outcome need to be while meeting following two conditions, i.e. decision model performance reaches that prediction is required：
A, test sample are suitable with the prediction mean error of training sample, are 0.058, as shown in following formula：
In formula：errtrainFor mean error=1.28, err of the forecast model to training sampletestBe forecast model to test
Mean error=1.354 of sample；
B, the predicted value of test sample and actual value are in significant linear relationship, r=0.8737, as shown in following formula：
In formula：For the predicted value of test sample, y is the measured value of test sample（The measured value is by conventional method
Measure）；
According to the evaluation result of forecast model, the linear relationship of test sample is 0.8737, characterizes the prediction mould
Type can be good at being fitted test sample；The mean error of test sample is suitable with the mean error of training sample, characterizes this
Forecast model, which has, preferably promotes performance；
（4）According to step（2）The characteristic index of selection, by the corresponding physicochemical data of roasting piece to be measured, i.e. total reducing sugar=24.06,
Reduced sugar=21.61, total volatile alkaline=0.41, total nitrogen=2.16, protein=9.69, schmuck value=2.48, potassium=1.86, sugared alkali ratio
=6.84, ammonia state alkali=0.04 is applied to step as input variable（3）Forecast model in, can calculate and obtain roasting piece to be measured
The model predication value Y of flue gas crotonaldehyde=12.47663-0.09537* total reducing sugar+0.60850* reduced sugars+11.76652* always volatilizees
Alkali -17.37009* total nitrogen+3.24879* protein -0.93766* schmuck value -1.29710* potassium -0.17601* sugar alkali ratio -
13.33443* ammonia state alkali=15.642.To verify the reliability of model prediction result, using traditional detection method, the roasting piece is determined
Flue gas crotons aldehyde value be 14.89.
Embodiment 2
The step of with embodiment 1（1）~（3）It is identical, only replace other roasting pieces to be measured, step（4）Following operation：
According to step（2）The characteristic index of selection, by the corresponding physicochemical data of roasting piece to be measured, i.e. total reducing sugar=25.94, also
Raw sugar=22.43, total volatile alkaline=0.28, total nitrogen=1.9, protein=9.43, schmuck value=2.75, potassium=1.91, sugared alkali ratio=
11.48th, ammonia state alkali=0.04 is applied to step as input variable（3）Forecast model in, can calculate and obtain roasting piece to be measured
The model predication value Y of flue gas crotonaldehyde=12.47663-0.09537* total reducing sugar+0.60850* reduced sugars+11.76652* always volatilizees
Alkali -17.37009* total nitrogen+3.24879* protein -0.93766* schmuck value -1.29710* potassium -0.17601* sugar alkali ratio -
13.33443* ammonia state alkali=16.969.To verify the reliability of model prediction result, using traditional detection method, the roasting piece is determined
Flue gas crotons aldehyde value be 16.67.
Embodiment 3
The step of with embodiment 1（1）~（3）It is identical, only replace other roasting pieces to be measured, step（4）Following operation：
According to step（2）The characteristic index of selection, by the corresponding physicochemical data of roasting piece to be measured, i.e. total reducing sugar=28.01, also
Raw sugar=24.86, total volatile alkaline=0.29, total nitrogen=1.8, protein=8.66, schmuck value=3.24, potassium=2.03, sugared alkali ratio=
11.67th, ammonia state alkali=0.04 is applied to step as input variable（3）Forecast model in, can calculate and obtain roasting piece to be measured
The model predication value Y of flue gas crotonaldehyde=12.47663-0.09537* total reducing sugar+0.60850* reduced sugars+11.76652* always volatilizees
Alkali -17.37009* total nitrogen+3.24879* protein -0.93766* schmuck value -1.29710* potassium -0.17601* sugar alkali ratio -
13.33443* ammonia state alkali=16.955.To verify the reliability of model prediction result, using traditional detection method, the roasting piece is determined
Flue gas crotons aldehyde value be 16.35.
Claims (1)
1. a kind of method based on robust regression modeling and forecasting baking sheet smoke crotonaldehyde, it is characterised in that pass through following each step：
(1) list the physicochemical data of known roasting piece is corresponding with flue gas crotonaldehyde data, set up set of data samples；The physics and chemistry number
According to including total reducing sugar, reduced sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, protein, schmuck value, nitrogen base ratio, chlorine, potassium, sugared alkali
Than with ammonia state alkali；
(2) the column vector x of each physicochemical data in calculation procedure (1) the data obtained sample set is distinguished1~xnWith flue gas crotonaldehyde data
Column vector y, calculate the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde, linear correlation respectively by following equation
This physicochemical data that coefficient r absolute value is more than corresponding to 0.3 is the characteristic index being had a major impact to flue gas crotonaldehyde
, it is used as the input variable of modeling：
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In formula：X is the column vector of a certain physicochemical data, and y is the column vector of flue gas crotonaldehyde data；
(3) according to different sources, kind and class, 245 roasting pieces are uniformly selected as training sample, it is linear with robust regression
Modeling algorithm, sets up flue gas crotonaldehyde forecast model, and its expression formula is following formula：
Y=AX+b=a1x1+a2x2+…+anxn+b (2)
In formula：Y is the model predication value of flue gas crotonaldehyde, and X is physicochemical data vector, and b is constant term, and A is regression coefficient vector；
The step of step (3) is with robust regression linear modelling algorithm is specific as follows：
(a) local weight regression fitting is carried out：Fit procedure only considers a part for all fitting points, each quilt each time
The value of match point is all determined by the stroll point of adjacent local fit scope, is given not at each match point
Same weight coefficient Wi, its weight coefficient is the weight system of the both sides each point of match point in the range of 1, local fit at match point
Number is decremented to zero with certain rule successively, and the weight at the data point of fit range is 0, and its algebraic expression is：
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In formula：WiFor the weight coefficient of each match point, yiFor measured value,For calculated value；
(b) adjustment residual error is calculated as follows：
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In formula：riFor the residual error of common least square method, hiLever value is adjusted for residual error, it is more a little bigger for reducing influence match value
The weight at place, T is transposition；
Standard adjustment residual error is given by：
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In formula：Ks is adjusting parameter, takes 4.685；S is robust sexual deviation；MAD is the median absolute deviation of residual error；
(c) the robustness weight of the every bit in the range of local fit is calculated as follows：
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(d) for formula (2), constant term b is brought into regression coefficient vector, then formula (2) is reduced to：
Y=a1x1+a2x2+…+anxn+b
=(a1, a2..., an, b) × (x1, x2..., xn, 1)T
=AX
The regression coefficient vector A for causing following formula to take minimum value is solved according to weight least square method, and is calculated in x0PlaceValue：
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In formula：J is the object function that weight least square method is solved；
The forecast model of the step (3) is evaluated fitting performance and popularization performance by following each step：
According to different sources, kind and class, 45 roasting foliated data different from step (3) are uniformly selected as test specimens
This, is applied in the forecast model of step (3) and carries out performance test, predicts the outcome and need to sentence while meet following two conditions
Determine model performance and reach that prediction is required：
A, test sample are suitable with the prediction mean error of training sample, as shown in following formula：
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In formula：errtrainFor mean error of the forecast model to training sample, errtestTest sample is put down for forecast model
Equal error；
B, the predicted value of test sample and actual value are in significant linear relationship, as shown in following formula：
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<mi>r</mi>
<mrow>
<mo>(</mo>
<mover>
<mi>y</mi>
<mo>^</mo>
</mover>
<mo>)</mo>
</mrow>
<mi>V</mi>
<mi>a</mi>
<mi>r</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>&GreaterEqual;</mo>
<mn>0.8</mn>
</mrow>
In formula：For the predicted value of test sample, y is the measured value of test sample；
(4) characteristic index according to step (2) selection, the corresponding physicochemical data of roasting piece to be measured is applied to as input variable
In the forecast model of step (3), the model predication value Y for the flue gas crotonaldehyde for obtaining roasting piece to be measured can be calculated；
If its error of fitting of the robustness weight of the step (d) is not up to following error of fitting requirement, since step (b)
Iterative calculation, untill error reaches requirement or reaches restriction iterations：
<mrow>
<mi>R</mi>
<mi>M</mi>
<mi>S</mi>
<mi>E</mi>
<mo>=</mo>
<msqrt>
<mrow>
<mo>&Sigma;</mo>
<mfrac>
<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
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<mi>y</mi>
<mo>^</mo>
</mover>
<mi>i</mi>
</msub>
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</mrow>
<mn>2</mn>
</msup>
<mi>n</mi>
</mfrac>
</mrow>
</msqrt>
<mo><</mo>
<mn>1.</mn>
</mrow>
2
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5146541A (en) * | 1989-06-19 | 1992-09-08 | The United States Of America As Represented By The Secretary Of The Navy | Signal phase pattern sensitive neural network system and method |
| CN101419207A (en) * | 2008-10-27 | 2009-04-29 | 川渝中烟工业公司 | The Forecasting Methodology of main index of flue-cured tobacco flume |
| CN102879531A (en) * | 2012-10-11 | 2013-01-16 | 云南烟草科学研究院 | Prediction method of ammonia release amount in main stream smoke of flue-cured tobacco leaves |
| CN103020737A (en) * | 2012-12-12 | 2013-04-03 | 红塔烟草(集团)有限责任公司 | Forecasting method of baking sheet smoke |
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2014
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5146541A (en) * | 1989-06-19 | 1992-09-08 | The United States Of America As Represented By The Secretary Of The Navy | Signal phase pattern sensitive neural network system and method |
| CN101419207A (en) * | 2008-10-27 | 2009-04-29 | 川渝中烟工业公司 | The Forecasting Methodology of main index of flue-cured tobacco flume |
| CN102879531A (en) * | 2012-10-11 | 2013-01-16 | 云南烟草科学研究院 | Prediction method of ammonia release amount in main stream smoke of flue-cured tobacco leaves |
| CN103020737A (en) * | 2012-12-12 | 2013-04-03 | 红塔烟草(集团)有限责任公司 | Forecasting method of baking sheet smoke |
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