Establishment and Verification of Multivariate Linear Regression Model for Prediction of Ethanol Concentration
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摘要: 设计了由光源、气室、探测器和控制器等组成的非分散红外吸收系统,往气室内通入不同浓度的多组分气体(含有乙醇、二氧化碳和水蒸气),采用红外光谱仪进行光谱数据采集,得到多组分气体混合光谱图。根据数据集样本求解回归系数,建立了多元线性回归模型,并进行干扰修正以降低二氧化碳和水蒸气对乙醇浓度预测的影响。对建立的多元线性回归模型进行评价,结果表明:模型真实有效且具有良好的线性回归效果,可以用于预测气体浓度,乙醇、二氧化碳和水蒸气浓度预测误差均在可接受的范围之内,其中乙醇浓度预测误差最小,不超过2.0×10-4。通过干扰修正尽可能排除二氧化碳和水蒸气的干扰,能够较准确地预测乙醇浓度。Abstract: A non-dispersive infrared absorption system comprising a light source, gas chamber, detector, and controller is designed, and multi-component gases of different concentrations (including ethanol, carbon dioxide, and water vapor) are injected into the chamber. An infrared spectrometer is used to collect the spectral data, and amulti-component gas mixture spectrum isobtained. A multiple linear regression model is established based on the regression coefficients of the dataset samples, and interference correction is performed to reduce the effect of carbon dioxide and water vapor on the concentration of ethanol. The established multiple linear regression model is evaluated, and the results indicate that the model is reliable and effective with a good linear regression effect. The model can be used to predict the gas concentration, and the prediction errors of ethanol, carbon dioxide, and water vapor concentration are within an acceptable range. The prediction error of ethanol concentration is the minimum, which is less than 2.0×10-4. The interference of carbon dioxide and water vapor can be mostly eliminated through interference correction. Importantly, the ethanol concentration can be predicted more accurately.
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表 1 各个通道的响应系数估值及置信区间
Table 1. The response coefficient estimation and confidence interval of each channel
Channel Single component gas Response coefficient estimation Confidence interval 0 Ethanol 0.9864 0.9254-1.0473 Carbon dioxide 0.0994 0.0321-0.1668 Water vapor 0.0325 -0.0367-0.1017 1 Ethanol 0.0617 -0.0268-0.1502 Carbon dioxide 0.972 0.9056-1.0383 Water vapor 0.2102 0.1300-0.2905 2 Ethanol 0.0695 0.0107-0.1283 Carbon dioxide 0.2298 0.1683-0.2913 Water vapor 0.762 0.6873-0.8366 表 2 回归模型评价参数
Table 2. Evaluation parameters of regression model
Channel Evaluation parameter Value 0 R2 0.9932 F 503.9468 p 0.0000 S2 0.0010 1 R2 0.9846 F 235.2015 p 0.0002 S2 0.0012 2 R2 0.9901 F 388.4631 p 0.0001 S2 0.0005 表 3 误差评价参数
Table 3. Evaluation parameters of error
Evaluation parameter Value MSE 2.7700 MAE 1.1767 MAPE 0.0336 MSPE 0.1077 RMSE 3.9174 SSE 30.6926 -
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