Dioxin Emission Concentration Soft Measurement Based on Multi-source Latent Feature Selective Ensemble Modeling for Municipal Solid Waste Incineration Process
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摘要: 二噁英(Dioxin，DXN)是导致城市固废焚烧(Municipal solid waste incineration, MSWI)建厂存在“邻避现象”的主要原因之一. 工业现场多采用离线化验手段检测DXN浓度, 难以满足污染物减排控制的需求. 针对上述问题, 本文提出了基于潜在特征选择性集成(Selective ensemble, SEN)建模的DXN排放浓度软测量方法. 首先, 采用主元分析(Principal component analysis, PCA)分别提取依据工艺阶段子系统及全流程系统过程变量的潜在特征, 并依据预设贡献率阈值进行特征初选; 接着, 采用互信息(Mutual information, MI)度量初选特征与DXN间的相关性, 并自适应确定再选的上下限及阈值; 最后, 采用具有超参数自适应选择机制的最小二乘−支持向量机(Least squares — support vector machine, LS-SVM)算法建立多源特征的候选子模型, 基于分支定界(Branch and bound, BB)优化和预测误差信息熵加权算法进行集成子模型的优化选择和加权组合, 进而得到软测量模型. 基于某MSWI焚烧厂DXN检测数据仿真验证了所提方法的有效性.
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关键词:
- 城市固废焚烧 /
- 二噁英 /
- 多源潜在特征 /
- 最小二乘−支持向量机 /
- 选择性集成建模
Abstract: One of the main reasons leading to “not in my backyard (NIMBY)” of municipal solid waste incineration (MSWI) plant construction is dioxin (DXN) emission from such process, which is a highly toxic substance to the ecological environment. In practical industrial process, the DXN emission concentration is detected by off-line. It is difficult to meet the requirements of optimal control. Aim at the above problem, a new DXN emission concentration soft measurement approach based on multi-source latent feature selective ensemble (SEN) modeling is proposed. Firstly, MSWI process is divided into different subsystems according to industrial processes. Principal component analysis (PCA) was used to extract their latent features. Primary selection of these features is made based on empirical pre-set threshold of contribution rate. Then, mutual information (MI) is used to measure the correlation between these primary selected features and DXN. The upper and lower limits and thresholds for re-selected feature are adaptively determined. Finally, based on the re-selected feature, the least squares-support vector machine (LS-SVM) algorithm with hyper-parameter adaptive selection mechanism is used to construct sub-models. A strategy based on branch and bound (BB) and prediction error information entropy weighting algorithm is used to select sub-model and calculate the weight coefficient. Thus, an SEN soft sensing model is obtained. The proposed method is verified by using DXN detection data of MSWI process in Beijing.1) 收稿日期 2019-03-27 录用日期 2019-06-27 Manuscript received March 27, 2019; accepted June 27, 2019 国家自然科学基金 (62073006, 62021003), 北京市自然科学基金 (4212032, 4192009), 科学技术部国家重点研发计划(2018YFC1900800-5), 矿冶过程自动控制技术国家(北京市)重点实验室(BGRIMM-KZSKL-2020-02)资助 Supported by National Natural Science Foundation of China (62073006, 62021003), Beijing Natural Science Foundation (4212032, 4192009), National Key Research and Development Program of the Ministry of Science and Technology (2018YFC1900800-5),2) and Beijing Key Laboratory of Process Automation in Mining and Metallurgy (BGRIMM-KZSKL-2020-02) 本文责任编委 刘艳军 Recommended by Associate Editor LIU Yan-Jun 1. 北京工业大学信息学部 北京 100124 2. 计算智能与智能系统北京市重点实验室 北京 100124 1. Faculty of Information Technology, Beijing University of Technology, Beijing 100124 2. Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing 100124 -
图 2 基于潜在特征SEN建模的DXN排放浓度软测量策略
Fig. 2 Soft sensing strategy of DXN emission concentration based on latent feature SEN modeling
图 3 不同功能子系统的前6个PC的累积贡献率
Fig. 3 Cumulative contribution rate of the first six PCs of different functional subsystems
图 4 全部子系统及MSWI全流程系统的初选潜在特征与DXN间的MI值
Fig. 4 MI value between DXN and primary potential characteristics of all subsystems and MSWI whole process systems
图 5 子模型超参数自适应寻优的第1次和第2次的曲线
Fig. 5 Curves of the 1st and 2nd curves for adaptive hyperparametric optimization of submodels
表 1 本文中的公式符号及其说明汇总表
Table 1 Summary of formula symbols and their explanations in this paper
符号 含义 符号 含义 ${ {{\boldsymbol{y}}} }$ DXN 排放浓度软测量模型的真值 ${\boldsymbol{\hat y} }$ DXN排放浓度软测量模型的预测输出 $N$ 建模样本数量 $M$ 输入过程变量数量 ${ {{\boldsymbol{X}}} }$ MSWI 全流程系统的输入数据 ${\boldsymbol{X} }_{}^i$ 第$i$个子系统的输入数据 ${ {{\boldsymbol{I}} - 1} }$ MSWI 全流程系统划分子系统个数 $M_{}^i$ 第$i$个子系统包含的过程变量个数 ${ {{\boldsymbol{Z}}} }_{ {\rm{FeAll} } }^i$ 第$i$个子系统的过程变量采用PCA提取的全部潜在特征 $M_{{\rm{FeAll}}}^i$ 第$i$个子系统的过程变量采用PCA提取的全部潜在特征的数量 ${ {{\boldsymbol{Z}}} }_{ {\rm{FeSe1st} } }^i$ 第$i$个子系统的初选潜在特征 ${\theta _{{\rm{Contri}}}}$ 对全部潜在特征进行初选的设定阈值 $M_{{\rm{FeSe1st}}}^i$ 第$i$个子系统初选潜在特征的数量 $M_{{\rm{FeSe2nd}}}^i$ 第$i$个子系统再选潜在特征的数量 ${ {{\boldsymbol{Z}}} }_{ {\rm{FeSe2nd} } }^i$ 第$i$个子系统的再选潜在特征 ${\theta _{{\rm{MI}}}}$ 再选潜在特征的选择阈值${\theta _{{\rm{MI}}}}$ ($K_{{\rm{er}}}^i$, $R_{{\rm{eg}}}^i$) 第$i$个子模型的核参数和正则化参数 , 即超参数对 $i$ 第$i$个子模型的预测输出 ${ {{\boldsymbol{t}}} }_{m_{ {\rm{FeAll} } }^i}^i$ 第$i$个子系统的第$m_{ {\rm{FeAll} } }^i$个主元的得分向量 ${ {{\boldsymbol{p}}} }_{m_{ {\rm{FeAll} } }^i}^ii$ 第$i$个子系统的第$m_{ {\rm{FeAll} } }^i$个主元的载荷向量 ${ {{\boldsymbol{T}}} }_{}^i$ 第$i$个子系统的得分矩阵 ${\boldsymbol{P}}^i $ 第$i$个子系统的载荷矩阵 $\lambda _{m_{{\rm{FeAll}}}^i}^i$ 第$i$个子系统的第$m_{ {\rm{FeAll} } }^i$个载荷向量${\boldsymbol{p} }_{m_{ {\rm{FeAll} } }^i}^i$相对应的特征值 $\theta _{m_{{\rm{FeAll}}}^i}^i$ 第$i$个子系统的第$m_{ {\rm{FeAll} } }^i$个潜在特征的贡献率 $\xi _{m_{{\rm{FeAll}}}^i}^i$ 第$i$个子系统的第$m_{ {\rm{FeAll} } }^i$个潜在特征是否被选中的标记值 $\xi _{{\rm{MI}}}^{m_{{\rm{FeSelst}}}^i}$ 第$i$个子系统的初选潜在特征${\boldsymbol{z} }_{m_{ {\rm{FeSelst} } }^i}^i$与DXN排放浓度间的MI值 $\theta _{{\rm{Contri}}}^{{\rm{Uplimit}}}$ 潜在特征再选阈值的上限值 $\theta _{{\rm{Contri}}}^{{\rm{Downlimit}}}$ 潜在特征再选阈值的下限值 $\theta _{{\rm{Contri}}}^{{\rm{Step}}}$ 潜在特征再选阈值的固定步长 $\beta _{m_{{\rm{FeSe1st}}}^i}^i$ 第$i$个子系统的第$m_{ {\rm{FeSe1st} } }^i$个初选潜在特征是否被选中的标记值 ${ { {{\boldsymbol{w}}} }^i}$ 第$i$个子模型的权重系数 ${b^i}$ 第$i$个子模型的偏置系数 ${{\bf{\beta }}^i}$ 第$i$个子模型的拉格朗日算子向量 ${{\bf{\zeta }}^i}$ 第$i$个子模型的预测误差向量 $M_{{\rm{para}}}^{}$ 候选超参数矩阵 $\{ K_{{\rm{er}}}^i,R_{{\rm{eg}}}^i\} $ 第$i$个子模型在$M_{{\rm{para}}}^{}$中自适应选择的超参数对 $K$ 候选核参数数量 $R$ 候选惩罚参数数量 $J = K \times R$ 超参数矩阵中的超参数对的数量 $\begin{array}{l}\{ {(K_{{\rm{er}}}^{{\rm{initial}}})^i}, {(R_{{\rm{eg}}}^{{\rm{initial}}})^i}\}\end{array}$ 第$i$个子模型在采用网格搜索策略在矩阵$M_{{\rm{para}}}^{}$中初选的超参数对 ${({ {{\boldsymbol{K}}} }_{ {\rm{er} } }^{ {\rm{vector} } })^i}$ 依据初选超参数对计算的新候选核参数向量 ${({ {{\boldsymbol{R}}} }_{ {\rm{eg} } }^{ {\rm{vector} } })^i}$ 依据初选超参数对计算的新候选惩罚参数向量 ${N_{{\rm{ker}}}}$ 新候选核参数的数量 ${N_{{\rm{reg}}}}$ 新候选惩罚参数的数量 $k_{{\rm{supara}}}^{{\rm{down}}}$,$k_{{\rm{supara}}}^{{\rm{up}}}$ 确定超参数向量的收缩和扩放因子 ${f^i}( \cdot )$ 第$i$个子模型 ${f^{{i_{{\rm{sel}}}}}}( \cdot )$ 第${i_{ {\rm{sel} } } }$个集成子模型 $w_{{i_{{\rm{sel}}}}}^{}$ 第${i_{ {\rm{sel} } } }$个集成子模型的加权系数 ${\hat y_{{i_{{\rm{sel}}}}}}$ 第${i_{ {\rm{sel} } } }$个集成子模型的预测值 $K_{{\rm{er}}}^{{i_{{\rm{sel}}}}}$,$R_{{\rm{eg}}}^{{i_{{\rm{sel}}}}}$ 第${i_{ {\rm{sel} } } }$个集成子模型的超参数 ${(\hat y_{{i_{{\rm{sel}}}}}^{})_n}$ 第$n$个样本基于第${i_{ {\rm{sel} } } }$个集成子模型的预测值 ${(e_{{i_{{\rm{sel}}}}}^{})_n}$ 第$n$个样本基于第${i_{ {\rm{sel} } } }$个集成子模型的相对预测误差 $E_{{i_{{\rm{sel}}}}}^{}$ 第${i_{ {\rm{sel} } } }$个集成子模型的预测误差信息熵 
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表 2 初选潜在特征的数量及其贡献率
Table 2 Number of the primary selected latent feature and their contribution ratio
子系统代号 Incinerator Boiler Flue gas Steam Stack Common MSWI 特征编号 1 29.90 70.99 54.57 63.34 42.91 46.33 43.58 2 21.75 12.66 10.42 16.56 18.06 14.10 13.40 3 11.14 6.058 8.901 7.691 17.30 8.653 8.761 4 6.952 5.014 7.146 3.906 12.65 6.798 5.921 5 6.635 3.036 5.041 2.030 7.211 4.483 4.822 6 5.075 1.356 4.269 1.533 1.854 4.221 3.246 7 3.792 — 3.237 1.184 — 3.501 3.071 8 3.208 — 2.584 1.007 — 2.842 2.919 9 2.784 — 1.190 — — 2.116 2.444 10 1.846 — — — — 1.494 2.138 11 1.514 — — — — 1.256 1.911 12 1.283 — — — — 1.164 1.731 13 1.129 — — — — — 1.481 14 — — — — — — 1.344 15 — — — — — — 1.068 初选潜在特征数量 13 6 9 5 6 12 15 原始过程变量数量 79 14 19 53 6 115 286
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表 3 全部子系统及MSWI全流程系统初选潜在特征MI值的极值统计表
Table 3 Extremum statistical table of potential characteristic MI values for primary selection latent feature of all Subsystems and MSWI whole process system
子系统 最大值集合 最小值集合 MI 值 贡献率 (%) PC 编号 MI 值 贡献率 (%) PC 编号 Incinerator 0.8559 1.514 11 0.6814 29.90 1 Boiler 0.8019 3.036 5 0.5527 70.99 1 Flue gas 0.8316 10.42 2 0.6084 54.57 1 Steam 0.8249 7.691 3 0.6059 63.34 1 Stack 0.8067 17.30 3 0.7182 42.91 1 Common 0.8613 4.221 6 0.5400 46.33 1 MSWI 0.7882 4.822 5 0.4429 43.58 1
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表 4 再选潜在特征数量和MI值统计表
Table 4 Statistical table of re-selected latent feature＇s number and MI value
子系统 数量 MI值 Incinerator 5 0.7952 0.8267 0.8258 0.8559 0.8088 — Boiler 2 0.8019 0.7952 — — — — Flue gas 1 0.8316 — — — — — Steam 3 0.8249 0.8022 0.8019 — — — Stack 2 0.7952 0.8067 — — — — Common 6 0.8019 0.8613 0.8088 0.7904 0.8383 0.8316 MSWI 1 0.7882 — — — — —
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表 5 不同建模方法统计结果
Table 5 Statistical results of different modeling methods
方法 过程变量数量 加权方法 RMSE 参数 (LV/PC) $( K_{ {\rm{er} } }^{},R_{ {\rm{eg} } }^{})$ 备注 文献 [22] 12 — 0.08869 ± 0.3000 (—) (—) 单模型, RWNN 文献 [24] 8 — 0.02695 (—) (21, 21) 单模型, SVM 文献 [37] 6 AWF 0.02306 (—) (0.1, 1; 400, 6400; 12800,
25600; 51200, 102400)SEN, 基于多核参数 PLS 286 — 0.01790 (13) (—) 单模型, MSWI系统 PCA-LS-SVM 286 — 0.01563 (18) (36240, 83904) 单模型, MSWI系统 集成建模 (EN) 286 PLS 0.01420 (5, 2, 1, 3, 2, 6, 1) (109, 109; 10000,
25.75; 5.950, 0.0595; 30.70, 2.080;
5.950, 0.5950; 1520800, 22816;
1362400, 158.5)
PCA-MI-LSSVM子模型, EN,
全部子模型AWF 0.01851 Entropy 0.01625 选择性集成建模(SEN) (本文方法) 286 (104) BB-AWF 0.01348 (5, 1, 2) (109, 109; 5.950, 0.0595; 5.950, 0.5950) PCA-MI-LSSVM子模型, SEN, Incinerator, Flue gas,
Stack共3个子模型BB-Entropy 0.01332
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