WO2021159585A1 - 一种二噁英排放浓度预测方法 - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 78
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Definitions
- the invention belongs to the technical field of urban solid waste incineration, and in particular relates to a method for predicting the concentration of dioxin emission based on the hybrid integration of random forest and gradient boosting tree.
- MSWI Municipal solid waste incineration
- the soft-sensing method has the ability to predict difficult-to-measure parameters faster and more economically than direct offline analysis and related object detection, and it has been widely used in the industrial field [13].
- Random forest (RF) algorithm has strong noise processing and nonlinear data modeling capabilities [17,18], but it is less used for nonlinear regression [19].
- Literature [20] is oriented towards electrostatic sensor arrays, and uses an RF-based integrated model to predict the moisture content of biomass in the fluidized bed.
- Literature [21] proposed a soft-sensing model based on principal component analysis and RF for online prediction of the tensile properties of polylactide during twin-screw extrusion.
- Literature [22] proposed an RF model with self-monitoring to estimate the P 80 particle size in the mill online.
- GBDT gradient boosting decision tree
- LR logistic regression
- VFI voting feature interval
- Literature [26] uses GBDT to predict building energy consumption.
- Literature [27] builds a prediction model based on GBDT to automatically determine the load cycle of the power system.
- Literature [28] proposed a GBDT-based photovoltaic power prediction model. The main idea is to integrate binary trees through gradient boosting.
- Literature [29] uses an example-based transfer learning method combined with GBDT to establish a wind power quantile regression model.
- Literature [30] combined GBDT and proposed a prediction model based on the Bagging integrated learning framework. The above studies mostly use a single RF or GBDT algorithm for modeling, and it is difficult to effectively construct a DXN emission concentration prediction model with small samples and high-dimensional characteristics.
- Dioxins are highly toxic pollutants emitted from the MSWI process.
- the actual industrial process mainly measures the DXN emission concentration by first collecting the exhaust gas samples on the spot and then testing and analyzing the DXN emission concentration in the laboratory, which has problems such as long cycle and high cost.
- This application uses the process variables collected in real time by the process control system to establish a DXN emission concentration prediction model based on the hybrid integration of Random Forest (RF) and Gradient Boosting Tree (GBDT).
- RF Random Forest
- GBDT Gradient Boosting Tree
- MSW is transported by vehicles to the weighbridge and discharged into the garbage pool. After 3-7 days of biological fermentation and dehydration, the MSW is thrown into the hopper by the garbage grab, and then pushed to the incinerator grate via the feeder. There are three main stages of drying, burning and burning.
- the combustible components in the dried MSW begin to ignite and burn through the combustion-supporting air delivered by the primary fan.
- the generated ash falls from the end of the grate to the slag conveyor and then enters the slag pit, and finally is landfilled at the designated location.
- the temperature of the high-temperature flue gas generated in the combustion process should be controlled above 850°C in the first combustion chamber to ensure the decomposition and combustion of harmful gases.
- the air transported by the secondary fan When the flue gas passes through the second combustion chamber, the air transported by the secondary fan generates a high degree of turbulence and ensures that the flue gas stays for more than 2 seconds, so that the harmful gas is further decomposed.
- the high-temperature flue gas then enters the waste heat boiler system, and the high-temperature steam generated by the absorption of heat drives the turbine generator unit to generate electricity.
- the flue gas mixed with lime and activated carbon enters the deacidification reactor for neutralization reaction, adsorbing DXN and heavy metals, and then the flue gas particles, neutralization reactants and activated carbon adsorbents are removed in the bag filter.
- Part of the soot mixture is After adding water to the mixer, re-enter the deacidification reactor for repeated treatment.
- the fly ash produced by the reactor and the bag filter enters the fly ash tank and needs to be transported to relevant institutions for further processing.
- the final exhaust gas is discharged to the atmosphere through the chimney through the induced draft fan, which contains soot, CO, NOx, SO 2 , HCL, HF, Hg, Cd, DXN and other substances.
- the MSWI process mainly converts MSW into residue, fly ash, flue gas and heat, among which the three products of residue, fly ash and flue gas are related to the emission of DXN [31].
- Furnace residues are produced in a large amount, but the DXN concentration is low; the amount of fly ash produced is less than that of residues, and its DXN concentration is higher than that of residues; the DXN concentration in flue gas includes incomplete combustion formation and new synthesis reaction formation [32 ].
- companies and environmental protection departments conduct offline testing on a monthly or quarterly cycle, which is not only a long cycle but also expensive.
- DXN modeling data has problems such as few true value samples and high dimension of process variables; at the same time, there are also objective problems such as unknown DXN content in MSW, complicated and unclear mechanism of DXN generation and absorption stage. Therefore, the use of soft measurement technology to establish a DXN emission concentration prediction model meets actual needs.
- This paper proposes a hybrid integrated DXN modeling strategy of RF and GBDT (EnRFGBDT), including random sampling of training samples and input features, RF-based DXN sub-model construction, GBDT-based DXN sub-model construction and simple average DXN integrated prediction. Two modules, as shown in Figure 2.
- the internal sub-models of the EnRFGBDT model mentioned in this paper are all constructed using the CART regression tree to maximize growth.
- the training subset of the RF-based DXN sub-model and its input features are generated by random sampling, and the number of features is much smaller than the number of features in the initial modeling data, thereby reducing the correlation between the CART regression trees and improving the outlier And the robustness of noisy data.
- Multiple serial DXN sub-models based on GBDT also further improve the prediction accuracy of the CART regression tree.
- a DXN integrated prediction model with a "parallel + serial" model was established. The functions of the different sub-modules are as follows:
- Random sampling module of training samples and input features Randomly sample the training sample set ⁇ X ⁇ R N ⁇ M ,y ⁇ R N ⁇ 1 ⁇ with replacement N times and randomly select a fixed number of input features to generate Training subset
- (2) RF-based DXN sub-model building module use the training subset generated in the previous module Establish RF-based DXN sub-model The predicted value of DXN emission concentration And measured value Subtract to get the prediction error
- DXN sub-model building module based on GBDT the error output by the previous module As the true value of the output data, and the input data of the training subset Form a new training subset After one iteration for each training subset, I ⁇ J GDBT-based DXN sub-models are constructed
- DXN integrated prediction module based on simple average the DXN sub-model based on RF And GBDT-based DXN sub-model Carry out simple averaging to establish the final DXN emission concentration prediction model.
- Step 1 Random sampling with replacement and random extraction of the specified number of features on the MSWI process data to generate J training subsets; Step 2 , Construct J DXN sub-models based on RF Step 3 to Prediction error In order to output the true value of the data, I iterative learning is performed to obtain I ⁇ J GBDT-based DXN sub-models In the fourth step, the DXN sub-model based on RF and GBDT is simply averaged and weighted to obtain the final DXN emission concentration integrated prediction model.
- the specific working process of the training sample and input feature random sampling module is:
- Bootstrap and random subspace method are used to process MSWI process data.
- Bootstrap is used to extract the training subset with the same number of samples as the training sample subset, and then the RSM mechanism is introduced to randomly select some features, and finally J training subsets containing N samples and M j features are generated.
- the generation process of the training subset can be expressed as:
- the specific working process of the RF-based DXN sub-model building module is:
- C 1 and C 2 represent the average values of the measured values of the DXN emission concentration in the regions R 1 and R 2 respectively.
- the RF-based DXN sub-model constructed by CART regression tree can be expressed as:
- (e j, 0 ) n represents the prediction error of the DXN emission concentration based on the nth training sample.
- the GBDT-based DXN sub-model of this application is implemented by constructing multiple "series" weak learner models, where: the input data of the training subset of multiple weak learner models remains unchanged, except for the first sub-model
- the true value of the output data of the training subset is the error between the predicted value and the measured value of the RF-based sub-model, and the prediction error of the previous iteration of the GBDT sub-model is used as the true value of the output data of the training subset.
- e j,1 is used as the second DXN sub-model based on GBDT The true value of the output data of the training subset.
- the second DXN sub-model can be expressed as,
- (e j, 1 ) n represents the prediction error of the first DXN sub-model based on GBDT for the nth sample.
- Ith sub-model can be expressed as,
- (e j,I-1 ) n represents the prediction error of the (I-1)th DXN sub-model based on GBDT for the nth sample.
- this paper constructs 1 RF-based and 1 GBDT-based DXN sub-models. These sub-models are generated in a serial manner, and the sum of their prediction outputs is used as the overall output of the jth training subset , Can be expressed as,
- the modeling data in this paper is the inspection data of the 1# and 2# furnaces of a MSWI power plant in Beijing in the past 6 years, including process variables as input data and DXN emission concentration measurement values as output data.
- the process variables are derived from the power generation system. (53), public electrical system (115), waste heat boiler system (14), incineration system (79), flue gas treatment system (20) and terminal detection system (6); DXN as output data
- the emission concentration is obtained by online collection and offline laboratory analysis, and its unit is ng/Nm 3 . Of the total 67 samples, 2/3 (45) are used as training data, and 1/3 (22) are used as test data.
- the RF and GBDT methods both use the square error as the loss function, the number of random samples is 45, the range of the number of input features is [10,20,30,40,50,60,70,80,90,100], the iteration of GBDT
- the frequency range is [1,2,3,4,5,6,7,8,9], and the minimum number of samples contained in the leaf node of the CART regression tree is 3.
- OOB out-of-bag data
- RMSE root mean square error
- Table 1 shows the relationship between the number of input features and the OOB error when the number of fixed CART regression trees is 5 (the experimental result is the average of 50 times).
- the modeling parameters used for the method proposed in this application are: input feature dimension 10, CART regression tree number 5, GBDT sub-model number (number of iterations) 5.
- the RMSE statistical results of different methods for the training set and the test set are shown in Table 4.
- Figures 3 and 4 show the prediction curves of RF, GBDT and the method proposed in this application, respectively.
- this paper establishes a hybrid integrated DXN emission concentration prediction model based on random forest (RF) and gradient boosting tree (GBDT), which is innovative Reflected in:
- the first layer DXN sub-model constructed by RF and GBDT are used to construct multiple DXN sub-models, and at the same time, dimensionality reduction and model prediction errors are reduced.
- the simulation experiment results based on the real data of the MSWI process show that the proposed method is superior to the single RF and GBDT prediction model in terms of prediction effect.
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Abstract
本发明公开一种基于随机森林和梯度提升树混合集成的二噁英排放浓度预测方法，首先，针对具有小样本高维特性的DXN建模数据进行训练样本和输入特征的随机采样以生成训练子集；接着，基于训练子集建立J个基于RF的DXN子模型；然后，对每个基于RF的DXN子模型进行I次迭代，构建J×I个基于GBDT的DXN子模型；最后，对基于RF和GBDT的DXN子模型的预测输出采用简单平均加权方式进行合并，获得最终输出。采用集成RF和GBDT的DXN预测模型构建方法能够提高DXN在线预测精度，辅助进行MSWI过程操作参数的运行优化，提高企业经济效益。
Description
本发明属于城市固废焚烧技术领域，尤其涉及一种基于随机森林和梯度提升树混合集成的二噁英排放浓度预测方法。
经济的迅速发展和城市化建设的不断升级使得我国城市固体废物(MSW)的产生量迅速增加，特别是在经济发达和人口密集的地区，某些城市正面临着垃圾围城危机[1]。城市固体废物焚烧(MSWI)发电是实现垃圾减量化、资源化、无害化的典型处理方式[2]。目前国内MSWI发电厂数量已超过300座，炉排炉式焚烧炉占比超过了2/3[3]。由于我国垃圾组分的特殊性，导致引进的焚烧设备多处于人工手动控制运行状态，常出现“水土不服”的现象，同时造成了MSWI排放不合标等问题[4]。针对这种现象，最为紧要的问题是：如何在满足经济效益的情况下控制MSWI过程的污染排放[5]。二噁英(DXN)作为MSWI排放的一种具有极强化学性和热稳定性的剧毒持久性有机污染物，是造成焚烧建厂出现“邻避效应”的主要原因之一[6]。
在实际工业过程中，主要通过在线采样与离线实验分析相结合的方法按照一定的周期进行DXN排放浓度检测[3]，但该方式成本昂贵且周期比较长，主要问题是：难以支撑MSWI运行参数的实时优化控制以达到使DXN排放浓度最小化的目的[7]。因此，实现DXN排放浓度的在线预测非常必要。MSWI过程具有复杂的物理和化学特性，难以建立DXN排放浓度的精确机理模型[8]。DXN排放浓度的在线预测是实现MSWI过程优化控制必不可少的重要环节[9]。针对DXN的在线检测研究，目前多是先进行相关关联物的测量再通过映射关系实现DXN的在线预测[10,11,12]；但存在设备昂贵、适应性弱和预测精度有待提升等问题[3]。软测量方法具有比直接离线分析和关联物检测更快、更经济地预测难测参数的能力，其在工业领域中已得到广泛应用[13]。针对MSWI过程，已存在采用特征选择结合神经网络构建DXN预测建模的研究[14,15,16]；由于DXN建模数据具有的样本少、维数高、共线性等特性，使得这些方法存在易落入局部最小值、过拟合和模型泛化性能差等问题。
针对传统单一预测模型存在的局限性，基于集成学习的预测模型成为当前研究热点。随机森林(RF)算法具有较强的噪声处理和非线性数据建模能力[17,18]，但较少用于非线性回归[19]。文献[20]面向静电传感器阵列，采用基于RF的集成模型预测硫化床中生物质的水分含量。文献[21]提出基于主成分分析和RF的软测量模型，用于在线预测双螺杆挤出过程中聚丙交酯的拉伸性能。文献[22]提出了具有自我监测的RF模型在线估算磨机中的P
80粒径。相对于基于建模数据采样进行并行集成的RF算法，梯度提升决策树(GBDT)是另外一种比较流行的机器学习算法[23]，但在样本特征维数较高且样本数量较大时，其效率和可伸缩性仍有待提高[24]。文献[25]集逻辑回归(LR)、GBDT和投票特征间隔(VFI)等方法于一体对滑坡敏感性进行评估。文献[26]采用GBDT进行建筑能耗预测。文献[27]构建基于GBDT的自动判断电力系统负荷周期的预测模型。文献[28]提出了一种基于GBDT的光伏功率预测模型，主要思想是通过梯度提升对二叉树进行集成融合。文献[29]采用基于实例的迁移学习方法结合GBDT建立风力发电分位数回归模型。文献[30]结合GBDT提出了基于Bagging集成学习框架的预测模型。以上研究多采用单一的RF或GBDT算法建模，难以有效构建具有小样本、高维特性的DXN排放浓度预测模型。
发明内容
二噁英(DXN)是城市固废焚烧(MSWI)过程排放的剧毒污染物。目前实际工业过程主要通过先现场采集排放烟气样品再在实验室化验分析的方式对DXN排放浓度进行检测，存在周期长、费用高等问题。本申请利用过程控制系统实时采集的过程变量，建立基于随机森林(RF)和梯度提升树(GBDT)混合集成的DXN排放浓度预测模型。首先，针对具有小样本高维特性的DXN建模数据进行训练样本和输入特征的随机采样以生成训练子集；接着，基于训练子集建立J个基于RF的DXN子模型；然后，对每个基于RF的DXN子模型进行I次迭代，构建J×I个基于GBDT的DXN子模型；最后，对基于RF和GBDT的DXN子模型的预测输出采用简单平均加权方式进行合并，获得最终输出。采用集成RF和GBDT的DXN预测模型构建方法能够提高DXN在线预测精度，辅助进行MSWI过程操作参数的运行优化，提高企业经济效益。
图1城市固废焚烧工艺流程；
图2建模策略图；
图3训练数据的预测曲线；
图4测试数据的预测曲线。
面向DXN生成的MSWI过程描述
MSW通过车辆运输到地磅称重后卸入垃圾池，经3～7天的生物发酵和脱水后，由垃圾抓斗投放至加料斗，经进料器将其推送到焚烧炉排上，先后经历干燥、燃烧和燃烬三个主要阶段。干燥后的MSW中的可燃成分通过一次风机输送的助燃空气开始着火燃烧，产生的灰渣从炉排末端落至输渣机上后再进入到渣坑，最后在指定地点进行填埋处理。燃烧过程产生的高温烟气在一燃室的温度应控制在850℃以上，以保证有害气体的分解和燃烧。烟气经过二燃室时，通过二次风机输送的空气产生高度湍流并保证烟气停留超过2s，使有害气体进一步分解。高温烟气随后进入余热锅炉系统，通过吸热产生的高温蒸汽推动汽轮发电机组进行发电。随后烟气混合石灰和活性炭进入脱酸反应器发生中和反应，吸附其中的DXN和重金属，接着在袋式除尘器中被除去烟气颗粒物、中和反应物和活性炭吸附物，部分烟灰混合物在混合器中加水后重新进入脱酸反应器进行重复处理。反应器和袋式除尘器产生的飞灰进入到飞灰罐后需运输至相关机构以进一步处理。最终的尾气通过引风机经烟囱排放到大气，其包含烟尘、CO、NOx、SO
2、HCL、HF、Hg、Cd和DXN等物质。
由图1可知，MSWI过程主要是将MSW转化为残渣、飞灰、烟气与热量，其中残渣、飞灰与烟气三种产物与DXN的排放相关[31]。炉膛残渣产生量多，但DXN浓度含量较低；飞灰产生量比残渣少，其DXN浓度比残渣高；烟气中的DXN浓度包括不完全燃烧生成和新规合成反应生成两种方式[32]。目前，针对DXN检测主要是企业和环保部门以月或者季度为周期进行离线化验，不仅周期长而且费用昂贵。由此可知，DXN建模数据存在真值样本少、过程变量维数高等问题；同时，也存在MSW中的DXN含量未知、DXN生成和吸收阶段的机理复杂不清等客观问题。因此，采用软测量技术建立DXN排放浓度预测模型符合实际需求。
本文提出RF和GBDT(EnRFGBDT)混合集成的DXN建模策略，包含训练样本与输入特征随机采样、基于RF的DXN子模型构建、基于GBDT的DXN子模型构建和基于简单平均的DXN集成预测共4个模块，如图2所示。
在图2中，
表示与采集DXN化验样品同时段的MSWI过程的炉膛温度、活性炭喷射量、烟囱排放气体浓度、炉排速度、一次风\二次风流量由过程控制系统所采集的过程变量(输入特征)所组成的输入数据，其中N为训练样本数量，M为过程变量数量；
表示在MSWI过程末端，即在烟囱排放处进行在线采集离线化验的DXN排放浓度组成的输出数据；{X,y}表示由输入数据和输出数据所组成的训练样本集；{X
j,y
j}表示第jth个从{X,y}中随机采样得到的训练子集，
表示全部训练子集；J为训练子集的数量，同时也为基于RF的DXN子模型数量；
表示第jth个基于RF的DXN子模型
的DXN排放浓度预测值，
表示全部基于RF的DXN子模型的预测输出；e
j,0表示第jth个基于RF的DXN子模型的DXN排放浓度预测值
与测量值y
j的误差；e
j,1表示基于第jth个训练子集的基于GBDT的第1个DXN子模型的误差预测值
与作为其输出数据真值e
j,0的误差；e
j,i表示针对第jth个训练子集的基于GBDT的第ith个DXN子模型
的误差预测值
与作为其输入数据真值e
j,i-1的误差；
表示针对第jth个训练子集的基于GBDT的全部DXN子模型的误差预测输出，I为针对单个训练子集基于GBDT的DXN子模型数量，也是针对单个训练子集的迭代次数；
表示混合集成模型的DXN排放浓度预测输出。
本文所提EnRFGBDT模型内部的子模型均采用最大化生长的CART回归树构建。基于RF的DXN子模型的训练子集及其输入特征采用随机采样方式产生，其特征数量远小于初始建模数据中的特征数量，进而降低了CART回归树间的相关性，提高了对异常值和噪声数据的鲁棒性。基于GBDT的多个串行DXN子模型也进一步提高了CART回归树的预测精度。最终建立了具有“并行+串行”模式的DXN集成预测模型。不同子模块的功能如下所示：
(1)训练样本与输入特征随机采样模块：对训练样本集{X∈R
N×M,y∈R
N×1}进行有放回的N次随机采样并随机选择固定数量的输入特征，生成训练子集
(2)基于RF的DXN子模型构建模块：利用前一模块中生成的训练子集
建立基于RF的DXN子模型
将DXN排放浓度预测值
与测量值
进行相减，得到预测误差
(3)基于GBDT的DXN子模型构建模块：以上一模块输出的误差
作为输出数据真值，和训练子集输入数据
组成新的训练子集
针对每个训练子集进行I次迭代后，构建I×J个基于GDBT的DXN子模型
(4)基于简单平均的DXN集成预测模块：将基于RF的DXN子模型
和基于GBDT的DXN子模型
进行简单平均，建立最终的DXN排放浓度预测模型。
综合上述模块的功能可知，本文所提方法的建模步骤为：第1步，对MSWI过程数据进行有放回的随机采样和指定特征数量的随机抽取，生成J个训练子集；第2步，构建J个基于RF的DXN子模型
第3步，以
的预测误差
为输出数据真值，进行I次迭代学习，得到I×J个基于GBDT的DXN子模型
第四步，将基于RF和GBDT的DXN子模型进行简单平均加权，得到最终的DXN排放浓度集成预测模型。
训练样本与输入特征随机采样模块的具体工作过程为：
采用自助采样法(Bootstrap)与随机子空间法(RSM)对MSWI过程数据进行处理。利用Bootstrap抽取与训练样本子集的样本数量相同的训练子集，随后引入RSM机制随机选择部分特征，最终生成包含N个样本和M
j个特征的J个训练子集。
训练子集的产生过程可表示为：
其中，{X
j,y
j}表示第jth个训练子集；
表示第jth个训练子集的第nth个输入和输出样本对；m＝1,L,M
j，M
j表示第jth个训练子集所包含的输入特征数量，通常存在M
j<<M。
基于RF的DXN子模型构建模块的具体工作过程为：
以第jth个训练子集
为例描述构建过程。
首先去除因随机采样造成的训练子集
中所存在的重复样本，并将其标记为
以第mth个输入特征x
j,m作为切分变量，以第n
selth个样本所对应的值
作为切分点，将输入特征空间切分为两个区域R
1和R
2，
基于以下准则遍历寻找最佳切分变量(输入特征)编号和切分点取值，
其中，
和
分别表示第jth个训练子集在R
1和R
2区域的DXN排放浓度的测量值；C
1和C
2分别表示在R
1和R
2两个区域的DXN排放浓度测量值的均值。
基于上述准则，首先通过遍历所有输入特征找到最优切分变量编号和切分点的取值，并将输入特征空间划分为两个区域；然后对每个区域重复上述过程，直到叶子点所包含的训练样本数量少于预先设定的阈值θ
RF；最终将输入特征空间划分为K个区域(其中K也表示CART回归树的叶子节点数)，将这些区域分别标记为R
1,L,R
k,L,R
K。
采用CART回归树构建的基于RF的DXN子模型可表示为：
其中，
其中，
表示区域R
k所包含的训练样本数量；
表示第jth个训练子集在R
k区域的第
th个DXN排放浓度测量值；I(·)为指示函数，在
时存在I(·)＝1，否则存在I(·)＝0.
第jth个训练子集
构建的基于RF的DXN子模型的预测误差为，
其中，(e
j,0)
n表示基于第nth个训练样本的DXN排放浓度预测误差。
重复上述过程，得到采用CART回归树构建的J个基于RF的DXN子模型
通过将这些子模型的预测输出
与DXN测量值{y
j}
j＝1相减，获得输出误差
基于GBDT的DXN子模型构建模块的具体工作过程为：
本申请基于GBDT的DXN子模型是通过构建多个“串联”的弱学习器模型的方式实现，其中：多个弱学习器模型的训练子集的输入数据保持不变，除第1个子模型的训练子集的输出数据真值为基于RF的子模型的预测值与测量值的误差外，其它子模型均以前一次迭代的GBDT子模型的预测误差作为训练子集的输出数据真值。
此处，以第jth个基于GBDT的DXN子模型的构建为例。假定共有I个基于GBDT的DXN子模型需要构建，并且均采用CART回归树构建。
首先，构建第1个子模型
其可表示为，
其中，
表示第1个基于GBDT的DXN子模型的预测输出。
上述子模型的损失函数的定义如下，
其中，
表示第jth个训练子集中的第nth个样本的预测值。
然后，计算子模型
的输出残差e
j,1，如下所示，
接着，e
j,1作为基于GBDT的第2个DXN子模型
的训练子集的输出数据真值。类似的，第2个DXN子模型可表示为，
其中，(e
j,1)
n表示针对第nth个样本的基于GBDT的第1个DXN子模型的预测误差。
重复上述过程，可知基于GBDT的第ith(i≤I)个DXN子模型可标记为
其残差计算如下所示，
在迭代I-1次之后，第Ith个子模型的训练子集的输出数据真值为，
其中，
为第(I-1)th个子模型
的预测输出。
进而，第Ith个子模型可表示为，
其中，(e
j,I-1)
n表示针对第nth个样本的基于GBDT的第(I-1)th个DXN子模型的预测误差。
因此，基于第jth个训练子集构建的全部I个基于GBDT的DXN子模型可表示为
其相应的输出可表示为
基于简单平均的DXN集成预测模块的具体工作流程为：
由上述过程可知，数量为J的基于RF的DXN子模型可表示为
这些模型以并行方式构建；数量为J×I的基于GBDT的DXN子模型可表示为
这些模型同时以串行和并行方式构建。
针对第jth个训练子集，本文构建了1个基于RF的和I个基于GBDT的DXN子模型，这些子模型以串行方式产生，其预测输出之和作为第jth个训练子集的总体输出，可表示为，
由于J个训练子集间是并行的，通过简单平均加权方式对上述DXN子模型进行合并，最后DXN排放浓度集成预测模型f
DXN(·)可表示如下：
实验验证
建模数据
本文建模数据为北京某MSWI发电厂1#和2#炉近6年的检验数据，包含作为输入数据的过程变量和作为输出数据的DXN排放浓度测量值，其中：过程变量分别源于发电系统(53个)、公共电气系统(115个)、余热锅炉系统(14个)、焚烧系统(79个)、烟气处理系统(20个)和末端检测系统(6个)；作为输出数据的DXN排放浓度采用在线采集离线化验分析的方式获得，其单位为ng/Nm
3。全部67个样本中的2/3(45个)用作训练数据，1/3(22个)用作测试数据。
建模实验
实验中，RF和GBDT方法均采用平方误差作为损失函数，随机样本数量为45，输入特征数量的范围为[10,20,30,40,50,60,70,80,90,100]，GBDT的迭代次数范围为[1,2,3,4,5,6,7,8,9]，CART回归树叶子节点包含的最小样本数量为3。采用Bootstrap算法抽样的袋外数据(OOB)进行模型测试，以均方根误差(RMSE)作为评估指标。
针对基于RF的DXN预测模型，表1给出了固定CART回归树的数量为5时，输入特征数量与OOB误差间的关系(实验结果为50次的均值)。
表1不同特征数量时的OOB误差
由表1可知，当特征数量为15时，OOB误差最低。固定输入特征数量后，RF模型中CAR回归树的数量与OOB误差间的关系如表2所示(实验结果为50次的均值)。
表2不同CART树数量时的OOB误差
由表2可知知，当CART回归树达到40棵时，基于RF的DXN模型具有最小的OOB误差，但其略小表1中的最小值。可见，需要在RF中同时对回归树和输入特征数量进行优化才能够获得更佳的预测性能。
针对基于GBDT的DXN预测模型，平方误差损失函数与迭代次数间的关系如表3所示。
表3 GBDT预测模型中迭代次数与损失函数间的关系
由图3可知，损失函数值随迭代次数的增加而逐渐降低，在迭代次数达到5次后，误差的下降趋势变弱。因此，确定合适的迭代次数对降低计算消耗非常必要。
综合考虑上述RF和GBDT模型的建模结果，此处针对本申请所提方法采用的建模参数为：输入特征维数10、CART回归树数量5、GBDT子模型数量(迭代次数)5。不同方法针对训练集和测试集的RMSE统计结果如表4所示。图3和4分别给出了RF、GBDT和本申请所提方法的预测曲线。
表4基于RF、GBDT和所提方法构建DXN模型的统计结果
由表4、图3和图4可知：(1)基于GBDT的DXN模型在测试集上具有最大的预测误差(0.03529)，主要原因在于GBDT采用了全部过程变量作为DXN模型的输入特征，而另外两种方法均对输入特征进行了基于随机选择的约简。可见，对高维过程变量进行特征选择非常有必要；(2)基于RF的DXN模型，在CART回归树数量设为5和输入特征设为15时，其在训练集上的RMSE值最大(0.34060)，在测试集中的RMSE(0.030199)小于GBDT(0.035291)方法，说明RF的泛化能力强于GBDT；(3)本文所提EnRFGBDT方法，在训练和测试数据上都具有最好的预测性能，表明所提策略能够同时降低输入特征维度和提升预测模型泛化性能的能力。
针对二噁英(DXN)难以实时检测的问题，基于实际城市固废焚烧过程数据，本文建立了基于随机森林(RF)和梯度提升树(GBDT)的混合集成DXN排放浓度预测模型，其创新性体现在：通过RF构建的首层DXN子模型和GBDT构建多个DXN子模型，同时进行维数约简和降低模型预测误差。基于MSWI过程的真实数据的仿真实验结果表明了所提方法在预测效果上优于单一的RF和GBDT预测模型。
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Claims (5)
- 一种二噁英排放浓度预测方法，其特征在于，包括以下步骤：步骤1、通过训练样本与输入特征随机采样模块，对训练样本集{X∈R N×M,y∈R N×1}进行有放回的N次随机采样并随机选择固定数量的输入特征，生成训练子集其中，
表示与采集DXN化验样品同时段的MSWI过程的炉膛温度、活性炭喷射量、烟囱排放气体浓度、炉排速度、一次风\二次风流量由过程控制系统所采集的过程变量所组成的输入数据，其中N为训练样本数量，M为过程变量数量；
表示在MSWI过程末端，即在烟囱排放处进行在线采集离线化验的DXN排放浓度组成的输出数据；
步骤2、通过基于RF的DXN子模型构建模块，利用生成的训练子集建立基于RF的DXN子模型
将DXN排放浓度预测值
与测量值
进行相减，得到预测误差
步骤3、通过基于GBDT的DXN子模型构建模块，以输出的误差作为输出数据真值，和训练子集输入数据
组成新的训练子集
针对每个训练子集进行I次迭代后，构建I×J个基于GDBT的DXN子模型
步骤4、通过基于简单平均的DXN集成预测模块，将基于RF的DXN子模型和基于GBDT的DXN子模型
进行简单平均，建立最终的DXN排放浓度预测模型。
- 如权利要求1所述的二噁英排放浓度预测方法，其特征在于，所述训练样本与输入特征随机采样模块的具体工作过程为：采用自助采样法(Bootstrap)与随机子空间法(RSM)对MSWI过程数据进行处理，利用Bootstrap抽取与训练样本子集的样本数量相同的训练子集，随后引入RSM机制随机选择部分特征，最终生成包含N个样本和M j个特征的J个训练子集，训练子集的产生过程可表示为：
其中，{X j,y j}表示第jth个训练子集；表示第jth个训练子集的第nth个输入和输出样本对；m＝1,L,M j，M j表示第jth个训练子集所包含的输入特征数量，通常存在M j<<M。
- 如权利要求2所述的二噁英排放浓度预测方法，其特征在于，所述基于RF的DXN子模型构建模块的具体工作过程为：以第jth个训练子集为例描述构建过程，
首先去除因随机采样造成的训练子集中所存在的重复样本，并将其标记为
以第mth个输入特征x j,m作为切分变量，以第n selth个样本所对应的值
作为切分点，将输入特征空间切分为两个区域R 1和R 2，
基于以下准则遍历寻找最佳切分变量编号和切分点取值，
其中，和
分别表示第jth个训练子集在R 1和R 2区域的DXN排放浓度的测量值；C 1和C 2分别表示在R 1和R 2两个区域的DXN排放浓度测量值的均值，
基于上述准则，首先通过遍历所有输入特征找到最优切分变量编号和切分点的取值，并将输入特征空间划分为两个区域；然后对每个区域重复上述过程，直到叶子点所包含的训练样本数量少于预先设定的阈值θ RF；最终将输入特征空间划分为K个区域，将这些区域分别标记为R 1,L,R k,L,R K，所述K也表示CART回归树的叶子节点数，采用CART回归树构建的基于RF的DXN子模型可表示为：
其中，
其中，表示区域R k所包含的训练样本数量；
表示第jth个训练子集在R k区域的第
个DXN排放浓度测量值；I(·)为指示函数，在
时存在I(·)＝1，否则存在I(·)＝0，
第jth个训练子集构建的基于RF的DXN子模型的预测误差为，
其中，(e j,0) n表示基于第nth个训练样本的DXN排放浓度预测误差，重复上述过程，得到采用CART回归树构建的J个基于RF的DXN子模型通过将这些子模型的预测输出
与DXN测量值
相减，获得输出误差
- 如权利要求3所述的二噁英排放浓度预测方法，其特征在于，所述基于GBDT的DXN子模型构建模块的具体工作过程为：通过构建多个“串联”的弱学习器模型的方式实现，其中，多个弱学习器模型的训练子集的输入数据保持不变，除第1个子模型的训练子集的输出数据真值为基于RF的子模型的预测值与测量值的误差外，其它子模型均以前一次迭代的GBDT子模型的预测误差作为训练子集的输出数据真值，以第jth个基于GBDT的DXN子模型的构建为例，假定共有I个基于GBDT的DXN子模型需要构建，并且均采用CART回归树构建，首先，构建第1个子模型其可表示为，
其中，表示第1个基于GBDT的DXN子模型的预测输出，
上述子模型的损失函数的定义如下，
其中，表示第jth个训练子集中的第nth个样本的预测值，
然后，计算子模型的输出残差e j,1，如下所示，
接着，e j,1作为基于GBDT的第2个DXN子模型的训练子集的输出数据真值。类似的，第2个DXN子模型可表示为，
其中，(e j,1) n表示针对第nth个样本的基于GBDT的第1个DXN子模型的预测误差，重复上述过程，可知基于GBDT的第ith(i≤I)个DXN子模型可标记为其残差计算如下所示，
在迭代I-1次之后，第Ith个子模型的训练子集的输出数据真值为，
其中，为第(I-1)th个子模型
的预测输出。
进而，第Ith个子模型可表示为，
其中，(e j,I-1) n表示针对第nth个样本的基于GBDT的第(I-1)th个DXN子模型的预测误差，因此，基于第jth个训练子集构建的全部I个基于GBDT的DXN子模型可表示为其相应的输出可表示为
- 如权利要求4所述的二噁英排放浓度预测方法，其特征在于，所述基于简单平均的DXN集成预测模块的具体工作流程为：由上述过程可知，数量为J的基于RF的DXN子模型可表示为这些模型以并行方式构建；数量为J×I的基于GBDT的DXN子模型可表示为
这些模型同时以串行和并行方式构建，
针对第jth个训练子集，构建了1个基于RF的和I个基于GBDT的DXN子模型，这些子模型以串行方式产生，其预测输出之和作为第jth个训练子集的总体输出，可表示为，
由于J个训练子集间是并行的，通过简单平均加权方式对上述DXN子模型进行合并，最后DXN排放浓度集成预测模型f DXN(·)可表示如下：
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