CN104123424A - Method for predicting flue gas crotonaldehyde of baked pieces on basis of robust regression modeling - Google Patents
Method for predicting flue gas crotonaldehyde of baked pieces on basis of robust regression modeling Download PDFInfo
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- CN104123424A CN104123424A CN201410385490.1A CN201410385490A CN104123424A CN 104123424 A CN104123424 A CN 104123424A CN 201410385490 A CN201410385490 A CN 201410385490A CN 104123424 A CN104123424 A CN 104123424A
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Abstract
The invention provides a method for predicting flue gas crotonaldehyde of baked pieces on the basis of robust regression modeling. A model from physical and chemical indexes to flue gas crotonaldehyde is built through existing physical and chemical data of the baked pieces and existing flue gas crotonaldehyde data, and the flue gas crotonaldehyde of baked pieces can be directly predicted through physical and chemical component data of unknown baked piece flue gas crotonaldehyde samples. The steps of rolling, burning, flue gas capturing, detection and the like in a traditional chemical mode are omitted; meanwhile, a robust regression model is adopted, the defects caused by singular value samples in physical and chemical data or flue gas data can be overcome effectively, and compared with ordinary linear regression modeling, the robust regression modeling has the advantage that the robustness of the model is ensured to the great extent. The practice proves that the model can effectively predict the flue gas crotonaldehyde of the baked pieces, the detection efficiency is improved greatly, and the detection cost is lowered.
Description
Technical field
The present invention relates to a kind of method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting, belong to specific calculation modelling technique field.
Background technology
Smoke of tobacco is a kind of very complicated potpourri, and it is produced by result of combustion of tobacco, cracking and distillation in cigarette smoking process.Cigarette products produces by burning and sucking process for the harmfulness of human body.Objectionable constituent in flue gas are mainly to form in combustion process, and the chemical characteristic of flue gas is variation with raw tobacco material intrinsic chemical composition, change.Therefore, the chemical characteristic of tobacco leaf raw material has determined chemical characteristic and the security of cigarette smoke.Crotonaldehyde is respiratory tract cilium toxin, can suppress the excremental removing of lung, thereby cause pulmonary disease.The acquisition pattern of traditional roasting sheet flue gas crotonaldehyde data is the chemical composition indexs in the flue gas detecting after roasting sheet burning.The flue gas data that obtain in this way, the flue gas that roasting sheet need to be rolled into after cigarette burning carries out chemical detection, testing process waste time and energy and testing cost high.
In linear regression modeling, model is based upon on certain assumed condition basis, and being for example observed sample error is standardized normal distribution.If the distribution of error is asymmetric or tends to outlier, the hypothesis of carrying out so linear regression modeling is invalid, and the statistic of the estimation of parameter, fiducial interval and other calculating is all insecure.In this case, with the foundation that model is carried out in robust regression, be very effective.The approximating method that robust regression modeling has comprised a kind of stalwartness, compares with least square method, so inresponsive for the variation of fraction in data, has improved the confidence level of model.
Robust regression is carried out modeling by give weights for each data point.Weighting is automatically and is repetition, and this process is called automatic heavy weighted least-squares method.In the first stage, each sample point is endowed identical weight, then utilizes common least square method to calculate model coefficient.In iteration subsequently, the point of each sample will recalculate, and those sample points away from model predication value will be endowed lower weight.Utilize afterwards the least square method computation model coefficient through weighting.Iterative process will go on always, until model coefficient is in the scope fluctuation of a setting.
Therefore directly to obtain the method for flue gas crotonaldehyde data imperative by baking foliated data with robust regression, to set up a kind of forecast model.
Summary of the invention
The problem such as detect for solving prior art that the process of roasting sheet flue gas crotonaldehyde data is time-consuming, effort, cost are high, the present invention proposes a kind of method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting.
The present invention sets up the robust regression forecast model from physical and chemical index item to flue gas crotonaldehyde by existing roasting foliated data and flue gas crotonaldehyde data, for the roasting sheet flue gas crotonaldehyde sample of the unknown, utilize its physical and chemical composition nest directly to predict roasting sheet flue gas crotons aldehyde value with model.Concrete through following each step:
(1) by the physicochemical data of known roasting sheet and corresponding the listing of flue gas crotonaldehyde data, set up set of data samples;
(2) the column vector x of each physicochemical data in difference calculation procedure (1) the data obtained sample set
1～x
ncolumn vector y with flue gas crotonaldehyde data, by following formula, calculate respectively the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde, the absolute value of linearly dependent coefficient r is greater than 0.3 corresponding this physicochemical data and is the characteristic index item that flue gas crotonaldehyde is had to material impact, the input variable of using as modeling:
（1）
In formula:
xfor the column vector of a certain physicochemical data,
ycolumn vector for flue gas crotonaldehyde data;
(3) according to the different places of production, kind, class, evenly select 245 roasting sheets as training sample, use robust regression linear modelling algorithm, set up flue gas crotonaldehyde forecast model, its expression formula is following formula:
（2）
In formula: Y is the model predication value of flue gas crotonaldehyde, X is physicochemical data vector, and b is constant term, and A is regression coefficient vector;
(4) the characteristic index item of selecting according to step (2), applies mechanically to the forecast model of step (3) the corresponding physicochemical data of roasting sheet to be measured as input variable, can calculate the model predication value Y of the flue gas crotonaldehyde that obtains roasting sheet to be measured.
The physicochemical data of described step (1) comprises total reducing sugar, reducing sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, protein, schmuck value, nitrogen base ratio, chlorine, potassium, sugared alkali ratio and ammonia state alkali.
Described step (3) uses the step of robust regression linear modelling algorithm as follows:
(a) carry out local weight regression matching: fit procedure is only considered the part that all matchings are counted each time, by the value of match point, the stroll point by the local fit scope of being close to is with it determined for each, at each match point place, gives different weight coefficients
, its weight coefficient is 1 at match point place, and within the scope of local fit, the weight coefficient of the both sides each point of match point is decremented to zero with certain rule successively, and the weight that exceeds the data point place of fit range is 0, and its algebraic expression is:
In formula:
for the weight coefficient of each match point,
for measured value,
for calculated value;
(b) be calculated as follows adjustment residual error:
In formula:
for the residual error of common least square method,
for residual error is adjusted lever value, for reducing the weight that affects match value and locate more a little louder, T is transposition;
Standard is adjusted residual error and is provided by following formula:
In formula: K, for adjusting parameter, gets 4.685; S is robustness deviation; MAD is the intermediate value absolute deviation of residual error;
(c) be calculated as follows the robustness weight of every bit within the scope of local fit:
(d) for formula (2), constant term b is brought in regression coefficient vector, formula (2) is reduced to:
According to weight least square method, solve and make following formula get the regression coefficient vector A of minimum value, and calculate at x
0place
value:
In formula: J is the objective function that weight least square method solves.
Described step (d) if its error of fitting of robustness weight when not reaching following error of fitting and requiring, from step (b), start iterative computation, until error reaches requirement or reaches, limit iterations:
。
The forecast model of described step (3) is evaluated matching performance and popularization performance by following each step:
According to the different places of production, kind, class, evenly select 45 roasting foliated data different from step (3) as test sample book, apply mechanically to the forecast model of step (3) and carry out performance test, predict the outcome and need meet following two conditions simultaneously, decision model performance reaches prediction requirement:
The prediction average error of A, test sample book and training sample is suitable, is shown in following formula:
In formula: err
trainfor the average error of forecast model to training sample, err
testfor the average error of forecast model to test sample book;
The predicted value of B, test sample book and actual value are significant linear dependence relation, are shown in following formula:
In formula:
for the predicted value of test sample book, the measured value that y is test sample book (this measured value is to record by classic method).
The present invention compared with prior art, possess following advantage and effect: by existing roasting foliated data and flue gas crotonaldehyde data, set up the model from physical and chemical index item to flue gas crotonaldehyde, for the roasting sheet flue gas crotonaldehyde sample of the unknown, can utilize the directly roasting sheet flue gas crotons aldehyde value of prediction of its physical and chemical composition data.Use robust regression linear modelling algorithm, in modeling process, find vectorial A suitable in final forecast model and constant term b, make in the expression formula of flue gas crotonaldehyde forecast model calculated value matching measured value as far as possible.The present invention has saved and by traditional chemical mode, has been rolled, burns, caught the steps such as flue gas, detection; Meanwhile, adopt robust regression model, can effectively avoid, because of the drawback that in physicochemical data or flue gas data, singular value sample causes, guaranteeing to a great extent the robustness of model, this puts the advantage that robust regression modeling is just better than common linear regression modeling.Facts have proved, this model can be predicted the flue gas crotons aldehyde value of roasting sheet effectively, greatly improves detection efficiency, reduces testing cost.
Accompanying drawing explanation
Fig. 1 is modeling schematic flow sheet of the present invention.
Embodiment
Below by embodiment, the present invention will be further described.
Embodiment 1
(1) by the physicochemical data of known roasting sheet and corresponding the listing of flue gas crotonaldehyde data, set up set of data samples, wherein physicochemical data comprises total reducing sugar, reducing sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, protein, schmuck value, nitrogen base ratio, chlorine, potassium, sugared alkali ratio and ammonia state alkali, as shown in the table:
(2) the column vector x of each physicochemical data in difference calculation procedure (1) the data obtained sample set
1～x
nwith the column vector y of flue gas crotonaldehyde data, by following formula, calculate respectively the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde:
（1）
In formula:
xfor the column vector of a certain physicochemical data,
ycolumn vector for flue gas crotonaldehyde data; Obtain the physicochemical data of all roasting sheets and the linearly dependent coefficient r of flue gas crotonaldehyde, as shown in the table:
With absolute value, be greater than linearly dependent coefficient r corresponding selection in physicochemical data of 0.3 again and flue gas crotonaldehyde had to the characteristic index item of material impact, the input variable of using as modeling, select total reducing sugar, reducing sugar, total volatile alkaline, total nitrogen, protein, schmuck value, potassium, sugared alkali ratio, ammonia state alkali:
(3) according to the different places of production, kind, class, evenly select 245 roasting sheets as training sample, use robust regression linear modelling algorithm, set up flue gas crotonaldehyde forecast model, its expression formula is following formula:
（2）
In formula: Y is the model predication value of flue gas crotonaldehyde, X is physicochemical data vector, and b is constant term, and A is regression coefficient vector;
Wherein use the step of robust regression linear modelling algorithm as follows:
(a) carry out local weight regression matching: fit procedure is only considered the part that all matchings are counted each time, by the value of match point, the stroll point by the local fit scope of being close to is with it determined for each, at each match point place, gives different weight coefficients
, its weight coefficient is 1 at match point place, and within the scope of local fit, the weight coefficient of the both sides each point of match point is decremented to zero with certain rule successively, and the weight that exceeds the data point place of fit range is 0, and its algebraic expression is:
In formula:
for the weight coefficient of each match point,
for measured value,
for calculated value;
(b) be calculated as follows adjustment residual error:
In formula:
for the residual error of common least square method,
for residual error is adjusted lever value, for reducing the weight that affects match value and locate more a little louder, T is transposition;
Standard is adjusted residual error and is provided by following formula:
In formula: K, for adjusting parameter, gets 4.685; S is robustness deviation; MAD is the intermediate value absolute deviation of residual error;
(c) be calculated as follows the robustness weight of every bit within the scope of local fit:
(d) for formula (2), constant term b is brought in regression coefficient vector, formula (2) is reduced to:
According to weight least square method, solve and make following formula get the regression coefficient vector A of minimum value, and calculate at x
0place
value:
In formula: J is the objective function that weight least square method solves;
If when its error of fitting does not reach following error of fitting requirement, start iterative computation from step (b), until reaching requirement or reach, error limits iterations:
；
By above-mentioned computing, obtain a
1=-0.09537, a
2=0.60850, a
3=11.76652, a
4=-17.37009, a
5=3.24879, a
6=-0.93766, a
7=-1.29710, a
8=-0.17601, a
9=-13.33443, b=12.47663;
Therefore, the expression formula of this flue gas crotonaldehyde forecast model is: Y=12.47663-0.09537* total reducing sugar+0.60850* reducing sugar+11.76652* total volatile alkaline-17.37009* total nitrogen+3.24879* protein-0.93766* schmuck value-1.29710* potassium-0.17601* sugar alkali ratio-13.33443* ammonia state alkali;
Above-mentioned forecast model is evaluated its matching performance and is promoted performance by following each step:
With above-mentioned forecast model, training sample is predicted, it the results are shown in following table:
According to the different places of production, kind, class, evenly select 45 roasting foliated data different from step (3) as test sample book, apply mechanically to the forecast model of step (3) gained and carry out performance test, with above-mentioned forecast model, test sample book is predicted, the results are shown in following table:
Above-mentioned predicting the outcome need meet following two conditions simultaneously, and decision model performance reaches prediction requirement:
The prediction average error of A, test sample book and training sample is suitable, is 0.058, is shown in following formula:
In formula: err
trainfor average error=1.28 of forecast model to training sample, err
testfor average error=1.354 of forecast model to test sample book;
The predicted value of B, test sample book and actual value are significant linear dependence relation, and r=0.8737 is shown in following formula:
In formula:
for the predicted value of test sample book, the measured value that y is test sample book (this measured value is to record by classic method);
According to the evaluation result of forecast model, it is 0.8737 that the linear dependence of test sample book is closed, and has characterized this forecast model and can be good at matching test sample book; The average error of test sample book is suitable with the average error of training sample, has characterized this forecast model and has had good popularization performance;
(4) the characteristic index item of selecting according to step (2), by the corresponding physicochemical data of roasting sheet to be measured, be total reducing sugar=24.06, reducing sugar=21.61, total volatile alkaline=0.41, total nitrogen=2.16, protein=9.69, schmuck value=2.48, potassium=1.86, sugar alkali ratio=6.84, apply mechanically to the forecast model of step (3) as input variable ammonia state alkali=0.04, can calculate model predication value Y=12.47663-0.09537* total reducing sugar+0.60850* reducing sugar+11.76652* total volatile alkaline-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 of the flue gas crotonaldehyde that obtains roasting sheet to be measured.Reliability for verification model predicts the outcome, adopts traditional detection method, and the flue gas crotons aldehyde value of measuring this roasting sheet is 14.89.
Embodiment 2
Identical with step (1)～(3) of embodiment 1, only replace other roasting sheet to be measured, step (4) operates as follows:
The characteristic index item of selecting according to step (2), by the corresponding physicochemical data of roasting sheet to be measured, be total reducing sugar=25.94, reducing sugar=22.43, total volatile alkaline=0.28, total nitrogen=1.9, protein=9.43, schmuck value=2.75, potassium=1.91, sugar alkali ratio=11.48, apply mechanically to the forecast model of step (3) as input variable ammonia state alkali=0.04, can calculate model predication value Y=12.47663-0.09537* total reducing sugar+0.60850* reducing sugar+11.76652* total volatile alkaline-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 of the flue gas crotonaldehyde that obtains roasting sheet to be measured.Reliability for verification model predicts the outcome, adopts traditional detection method, and the flue gas crotons aldehyde value of measuring this roasting sheet is 16.67.
Embodiment 3
Identical with step (1)～(3) of embodiment 1, only replace other roasting sheet to be measured, step (4) operates as follows:
The characteristic index item of selecting according to step (2), by the corresponding physicochemical data of roasting sheet to be measured, be total reducing sugar=28.01, reducing sugar=24.86, total volatile alkaline=0.29, total nitrogen=1.8, protein=8.66, schmuck value=3.24, potassium=2.03, sugar alkali ratio=11.67, apply mechanically to the forecast model of step (3) as input variable ammonia state alkali=0.04, can calculate model predication value Y=12.47663-0.09537* total reducing sugar+0.60850* reducing sugar+11.76652* total volatile alkaline-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 of the flue gas crotonaldehyde that obtains roasting sheet to be measured.Reliability for verification model predicts the outcome, adopts traditional detection method, and the flue gas crotons aldehyde value of measuring this roasting sheet is 16.35.
Claims (5)
1. based on robust regression modeling and forecasting, bake a method for sheet flue gas crotonaldehyde, it is characterized in that through following each step:
(1) by the physicochemical data of known roasting sheet and corresponding the listing of flue gas crotonaldehyde data, set up set of data samples;
(2) the column vector x of each physicochemical data in difference calculation procedure (1) the data obtained sample set
1～x
ncolumn vector y with flue gas crotonaldehyde data, by following formula, calculate respectively the linearly dependent coefficient r of each physicochemical data and flue gas crotonaldehyde, the absolute value of linearly dependent coefficient r is greater than 0.3 corresponding this physicochemical data and is the characteristic index item that flue gas crotonaldehyde is had to material impact, the input variable of using as modeling:
（1）
In formula:
xfor the column vector of a certain physicochemical data,
ycolumn vector for flue gas crotonaldehyde data;
(3) according to the different places of production, kind, class, evenly select 245 roasting sheets as training sample, use robust regression linear modelling algorithm, set up flue gas crotonaldehyde forecast model, its expression formula is following formula:
（2）
In formula: Y is the model predication value of flue gas crotonaldehyde, X is physicochemical data vector, and b is constant term, and A is regression coefficient vector;
(4) the characteristic index item of selecting according to step (2), applies mechanically to the forecast model of step (3) the corresponding physicochemical data of roasting sheet to be measured as input variable, can calculate the model predication value Y of the flue gas crotonaldehyde that obtains roasting sheet to be measured.
2. the method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting according to claim 1, is characterized in that: the physicochemical data of described step (1) comprises total reducing sugar, reducing sugar, nicotine, total volatile alkaline, total nitrogen, nicotine nitrogen, protein, schmuck value, nitrogen base ratio, chlorine, potassium, sugared alkali ratio and ammonia state alkali.
3. the method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting according to claim 1, is characterized in that: described step (3) uses the step of robust regression linear modelling algorithm as follows:
(a) carry out local weight regression matching: fit procedure is only considered the part that all matchings are counted each time, by the value of match point, the stroll point by the local fit scope of being close to is with it determined for each, at each match point place, gives different weight coefficients
, its weight coefficient is 1 at match point place, and within the scope of local fit, the weight coefficient of the both sides each point of match point is decremented to zero with certain rule successively, and the weight that exceeds the data point place of fit range is 0, and its algebraic expression is:
In formula:
for the weight coefficient of each match point,
for measured value,
for calculated value;
(b) be calculated as follows adjustment residual error:
In formula:
for the residual error of common least square method,
for residual error is adjusted lever value, for reducing the weight that affects match value and locate more a little louder, T is transposition;
Standard is adjusted residual error and is provided by following formula:
In formula: K, for adjusting parameter, gets 4.685; S is robustness deviation; MAD is the intermediate value absolute deviation of residual error;
(c) be calculated as follows the robustness weight of every bit within the scope of local fit:
(d) for formula (2), constant term b is brought in regression coefficient vector, formula (2) is reduced to:
According to weight least square method, solve and make following formula get the regression coefficient vector A of minimum value, and calculate at x
0place
value:
In formula: J is the objective function that weight least square method solves.
4. the method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting according to claim 1, is characterized in that: the forecast model of described step (3) by following each step to matching performance with promote performance and evaluate:
According to the different places of production, kind, class, evenly select 45 roasting foliated data different from step (3) as test sample book, apply mechanically to the forecast model of step (3) and carry out performance test, predict the outcome and need meet following two conditions simultaneously, decision model performance reaches prediction requirement:
The prediction average error of A, test sample book and training sample is suitable, is shown in following formula:
In formula: err
trainfor the average error of forecast model to training sample, err
testfor the average error of forecast model to test sample book;
The predicted value of B, test sample book and actual value are significant linear dependence relation, are shown in following formula:
In formula:
for the predicted value of test sample book, the measured value that y is test sample book.
5. the method based on the roasting sheet flue gas crotonaldehyde of robust regression modeling and forecasting according to claim 1, it is characterized in that: described step (d) if its error of fitting of robustness weight when not reaching following error of fitting and requiring, from step (b), start iterative computation, until error reaches requirement or reaches, limit iterations:
。
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| 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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| 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 |
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