Multi-target Robust Prediction Model for Furnace Temperature and Flue Gas Oxygen Content in Municipal Solid Waste Incineration Process
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摘要: 为实现城市固废焚烧(Municipal solid waste incineration, MSWI)过程炉温与烟气含氧量的准确预测, 提出一种基于改进随机配置网络的多目标鲁棒建模方法(Multi-target robust modeling method based on improved stochastic configuration network, MRI-SCN). 首先, 设计了一种并行方式增量构建 SCN 隐含层, 通过信息叠加与跨越连接来增强隐含层映射多样性, 并利用参数自适应变化的监督不等式分配隐含层参数; 其次, 使用$ \text{F} $范数与$ L_{2,1} $范数正则项建立矩阵弹性网对模型参数进行稀疏约束, 以建模炉温与烟气含氧量间的相关性; 接着, 采用混合拉普拉斯分布作为每个目标建模误差的先验分布, 通过最大后验估计重新评估 SCN 模型的输出权值, 以增强其鲁棒性; 最后, 利用城市固废焚烧过程的历史数据对所提建模方法的性能进行测试. 实验结果表明, 所提建模方法在预测精度与鲁棒性方面具有优势.Abstract: To achieve accurate prediction of furnace temperature and flue gas oxygen content in municipal solid waste incineration (MSWI) process, a multi-target robust modeling method based on improved stochastic configuration network (MRI-SCN) is proposed. First, a parallel method is designed to incrementally build SCN hidden layers, which enhances the diversity of hidden layer mapping through information superposition and spanning connection, and assign hidden layer parameters using the supervised inequality with adaptive parameter changes. Second, a matrix elastic net is established by using F-norm and $ L_{2,1} $-norm regularization terms to sparsely constrain the model parameters to model the correlation between furnace temperature and flue gas oxygen content. Then, the mixture Laplace distribution is used as the prior distribution of each target modeling error, and the output weights of the SCN model are re-evaluated by maximum a posteriori estimation to enhance its robustness. Finally, the performance of the proposed modeling method is tested on the historical data of municipal solid waste incineration process. The experimental results show that the proposed modeling method has advantages in prediction accuracy and robustness.
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图 2 前馈神经网络隐含层构造方式
Fig. 2 The hidden layer construction methods of feedforward neural network
图 3 不同范数约束在原始数据集上的实验结果
Fig. 3 Results of experiments with different paradigm constraints on the original dataset
图 5 炉温与烟气含氧量散点图及预测误差概率分布曲线$(\zeta$ = 20%)
Fig. 5 Scatterplot of furnace temperature, flue gas oxygen content and probability distribution curves of prediction error $(\zeta$ = 20%)
图 6 炉温与烟气含氧量预测误差曲线及模型输出权值$(\zeta$ = 30%)
Fig. 6 Furnace temperature, flue gas oxygen content prediction error curves and model output weights $(\zeta$ = 30%)
表 1 MRI-SCN与不同类型建模方法在原始数据集上的对比实验结果
Table 1 Results of experiments comparing MRI-SCN with the different type of modeling methods on the original dataset
数据集 BP RBF RVFL MLS-SVR MRI-SCN 春季 5.80; 4.57; 86.57 5.40; 3.74; 89.14 4.55; 3.59; 92.36 3.41; 2.38; 95.70 3.12; 2.34; 96.38 夏季 5.63; 4.33; 87.48 4.85; 3.75; 91.49 4.60; 3.63; 92.14 3.37; 2.52; 95.90 3.16; 2.26; 96.25 秋季 5.39; 4.27; 89.03 4.92; 3.73; 91.25 4.52; 3.55; 92.44 3.44; 2.69; 95.41 3.08; 2.31; 96.48 冬季 5.30; 4.19; 89.93 5.72; 4.42; 89.14 4.96; 3.91; 91.46 3.52; 2.53; 95.61 3.10; 2.33; 96.68 
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表 2 MRI-SCN 与同类型建模方法在原始数据集上的对比实验结果
Table 2 Results of experiments comparing MRI-SCN with the same type of modeling methods on the original dataset
数据集 SCN MI-SCN MT-SCN MoGL-SCN MRI-SCN 春季 3.67; 2.86; 95.07 3.45; 2.64; 95.62 3.46; 2.67; 95.59 3.61; 2.68; 94.50 3.12; 2.34; 96.38 夏季 3.70; 2.80; 95.40 3.43; 2.55; 95.65 3.32; 2.57; 95.84 3.40; 2.67; 95.63 3.16; 2.26; 96.25 秋季 3.63; 2.73; 95.17 3.31; 2.56; 95.91 3.34; 2.61; 95.92 3.52; 2.76; 95.42 3.08; 2.31; 96.48 冬季 3.74; 2.94; 95.23 3.56; 2.73; 95.33 3.49; 2.81; 95.84 3.55; 2.31; 95.82 3.10; 2.33; 96.68
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表 3 四组噪声数据集上的实验结果
Table 3 Results of experiments on the four noisy datasets
数据集 $ \zeta $ SCN MI-SCN MT-SCN MoGL-SCN MRI-SCN 10% 6.62; 5.15; 83.95 5.80; 4.57; 87.67 5.59; 4.40; 88.55 3.86; 2.87; 94.43 3.65; 2.74; 95.07 15% 7.59; 5.97; 78.84 6.39; 5.07; 84.97 6.35; 5.05; 85.16 4.00; 2.95; 94.02 3.87; 2.89; 94.45 春季 20% 8.96; 7.11; 70.38 7.33; 5.80; 80.14 7.36; 5.88; 79.99 4.26; 3.11; 93.21 4.03; 3.02; 93.95 25% 10.38; 8.05; 60.18 8.26; 6.46; 74.83 8.58; 6.74; 72.80 4.48; 3.26; 92.53 4.34; 3.24; 92.95 30% 11.17; 8.71; 53.98 8.70; 6.86; 72.21 9.40; 7.41; 67.46 4.82; 3.50; 91.25 4.56; 3.38; 92.28 10% 6.31; 4.90; 85.43 5.77; 4.56; 87.74 5.50; 4.30; 88.88 4.00; 2.93; 93.81 3.76; 2.78; 94.66 15% 7.38; 5.71; 79.98 6.48; 5.13; 84.56 6.24; 4.89, 85.75 4.38; 3.14; 92.66 3.96; 2.92; 94.07 夏季 20% 8.91; 7.00; 70.13 7.45; 5.94; 79.13 7.49; 5.96; 78.73 4.38; 3.17; 92.55 4.22; 3.13; 93.10 25% 9.40; 7.48; 66.62 7.89; 6.34; 76.58 7.93; 6.35; 76.22 4.68; 3.33; 91.83 4.45; 3.27; 92.43 30% 10.39; 8.21; 59.58 8.61; 6.90; 72.39 8.85; 7.09; 70.72 5.08; 3.65; 89.94 4.65; 3.41; 91.83 10% 6.40; 5.04; 85.18 5.98; 4.79; 86.83 5.57; 4.43; 88.69 3.73; 2.75; 94.76 3.46; 2.60; 95.53 15% 7.33; 5.72; 80.40 6.33; 5.01; 85.27 6.10; 4.78; 86.37 3.80; 2.80; 94.63 3.61; 2.72; 95.11 秋季 20% 8.90; 6.85; 71.15 7.19; 5.66; 80.85 7.40; 5.74; 79.96 4.03; 2.95; 94.02 3.86; 2.88; 94.45 25% 9.82; 7.52; 65.08 7.62; 6.00; 78.77 8.00; 6.20; 76.81 4.11; 2.98; 93.71 3.96; 2.96; 94.16 30% 10.79; 8.25; 57.89 8.28; 6.44; 74.97 8.75; 6.73; 72.24 4.50; 3.22; 92.52 4.26; 3.18; 93.28 10% 6.86; 5.34; 83.29 6.55; 5.16; 84.72 6.22; 4.86; 86.29 4.10; 3.04; 94.20 3.93; 2.98; 94.56 15% 7.94; 6.20; 78.14 7.27; 5.76; 81.77 6.97; 5.50; 83.25 4.40; 3.21; 93.30 4.27; 3.18; 93.73 冬季 20% 9.40; 7.36; 69.16 8.05; 6.32; 77.44 7.91; 6.20; 78.23 4.55; 3.33; 92.83 4.37; 3.28; 93.32 25% 10.56; 8.18; 60.47 8.81; 6.94; 72.48 8.90; 6.97; 71.96 4.88; 3.56; 91.40 4.62; 3.45; 92.41 30% 11.26; 8.74; 55.94 9.50; 7.48; 68.70 9.65; 7.57; 67.57 5.02; 3.64; 91.25 4.83; 3.60; 91.72
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表 4 不同建模方法运行 30 次的时间对比
Table 4 Comparison of time for 30 runs of different modeling methods
方法 BP RBF SCN MI-SCN MT-SCN MoGL-SCN MRI-SCN 时间(s) 21.43 31.70 5.23 16.29 36.22 37.78 28.17
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A1 多目标鲁棒预测模型输入变量明细
A1 Input variable details of multi-target robust prediction model
序号 变量名称 单位 1 进料器左内侧速度 % 2 进料器左外侧速度 % 3 进料器右内侧速度 % 4 进料器右外侧速度 % 5 干燥炉排左内侧速度 % 6 干燥炉排左外侧速度 % 7 干燥炉排右内侧速度 % 8 干燥炉排右外侧速度 % 9 干燥炉排左1空气流量 $ {\rm {km^3N/h}} $ 10 干燥炉排右1空气流量 $ {\rm {km^3N/h}} $ 11 干燥炉排左2空气流量 $ {\rm {km^3N/h}} $ 12 干燥炉排右2空气流量 $ {\rm {km^3N/h}} $ 13 燃烧炉排左1-1段空气流量 $ {\rm {km^3N/h}} $ 14 燃烧炉排右1-1段空气流量 $ {\rm {km^3N/h}} $ 15 燃烧炉排左1-2段空气流量 $ {\rm {km^3N/h}} $ 16 燃烧炉排右1-2段空气流量 $ {\rm {km^3N/h}} $ 17 燃烧炉排左2-1段空气流量 $ {\rm {km^3N/h}} $ 18 燃烧炉排右2-1段空气流量 $ {\rm {km^3N/h}} $ 19 燃烧炉排左2-2段空气流量 $ {\rm {km^3N/h}} $ 20 燃烧炉排右2-2段空气流量 $ {\rm {km^3N/h}} $ 21 燃烬炉排左空气流量 $ {\rm {km^3N/h}} $ 22 燃烬炉排右空气流量 $ {\rm {km^3N/h}} $ 23 二次风量 $ {\rm {km^3N/h}} $ 24 一次风机出口空气压力 kPa 25 一次空气加热器出口空气温度 ℃ 26 干燥炉排左内侧温度 ℃ 27 干燥炉排左外侧温度 ℃ 28 干燥炉排右内侧温度 ℃ 29 干燥炉排右外侧温度 ℃ 30 燃烧炉排1-1段左内侧温度 ℃ 31 燃烧炉排1-1段左外侧温度 ℃ 32 燃烧炉排1-1段右内侧温度 ℃ 33 燃烧炉排1-1段右外侧温度 ℃ 34 燃烧炉排1-2段左内侧温度 ℃ 35 燃烧炉排1-2段左外侧温度 ℃ 36 燃烧炉排1-2段右内侧温度 ℃ 37 燃烧炉排1-2段右外侧温度 ℃ 38 燃烧炉排2-1段左内侧温度 ℃ 39 燃烧炉排2-1段左外侧温度 ℃ 40 燃烧炉排2-1段右内侧温度 ℃ 41 燃烧炉排2-1段右外侧温度 ℃ 42 燃烧炉排2-2段左内侧温度 ℃ 43 燃烧炉排2-2段左外侧温度 ℃ 44 燃烧炉排2-2段右内侧温度 ℃ 45 燃烧炉排2-2段右外侧温度 ℃ 46 当前时刻的炉温 ℃ 47 当前时刻的烟气含氧量 %
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