METHOD FOR DETECTING A DIOXIN EMISSION CONCENTRATION OF A MUNICIPAL SOLID WASTE INCINERATION PROCESS BASED ON MULTI-LEVEL FEATURE SELECTION

Abstract

A method for detecting a dioxin emission concentration of a municipal solid waste incineration process based on multi-level feature selection. A grate furnace-based MSWI process is divided into a plurality of sub-processes. A correlation coefficient value, a mutual information value and a comprehensive evaluation value between each of original input features of the sub-processes and the DXN emission concentration are obtained, thereby obtaining first-level features. The first-level features are selected and statistically processed by adopting a GAPLS-based feature selection algorithm and according to redundancy between different features, thereby obtaining second-level features. Third-level features are obtained according to the first-level features and statistical results of the second-level features. A PLS algorithm-based DXN detection model is established based on model prediction performance and the third-level features. The obtained PLS algorithm-based DXN detection model is applied to detect the DXN emission concentration of the MSWI process.

Claims

1. A method for detecting a dioxin (DXN) emission concentration in a municipal solid waste incineration (MSWI) process based on multi-level feature selection, comprising: 1) dividing a grate furnace-based municipal solid waste incineration (MSWI) process into a plurality of sub-processes based on an incineration process; wherein the plurality of sub-processes comprise an incineration treatment sub-process, a boiler operation sub-process, a flue gas treatment sub-process, a steam electric power generation sub-process, a stack emission sub-process and a common resource supply sub-process; 2) obtaining a correlation coefficient value and a mutual information value between each of original input features of the sub-processes and the DXN emission concentration; and obtaining a comprehensive evaluation value of candidate input features according to the obtained correlation coefficient value and the obtained mutual information value, thereby completing the selection of first-level features of all of the sub-processes; 3) selecting and statistically processing the first-level features by adopting a feature selection algorithm based on genetic algorithm-based partial least squares (GAPLS) and according to redundancy between different features, thereby completing the selection of second-level features of all of the sub-processes; 4) performing a third-level feature selection according to the first-level features and statistical results of the second-level features within a preset threshold range, thereby completing the selection of third-level features of all of the sub-processes; and 5) establishing a partial least squares (PLS) algorithm-based DXN detection model according to model prediction performance and the third-level features; and detecting the DXN emission concentration by the obtained PLS algorithm-based DXN detection model.

2. The method of claim 1, further comprising: arranging the first-level features in series after the step of obtaining the first-level features of all of the sub-processes so as to obtain the first-level features based on a single feature correlation.

3. The method of claim 2, wherein the DXN detection model comprises input data and output data; wherein the input data is expressed as XR.sup.NP and comprises N samples as row data and P variables as column data; the input data is derived from the sub-processes of the MSWI process; monitoring data of an i-th sub-process is obtained by using a programmable logic controller (PLC) device or a distributed control system (DCS) device installed on site and is expressed as X.sub.iR.sup.NP.sup.i; and X.sub.iR.sup.NP.sup.i is input data from the i-th sub-process and satisfies Equations (1) and (2);
X=[X.sub.1, . . . , X.sub.i, . . . , X.sub.I]={X.sub.i}.sub.i=1.sup.I(1)
P=P.sub.1+ . . . +P.sub.i+ . . . +P.sub.I=.sub.i=1.sup.IP.sub.i(2) wherein I represents the number of the sub-processes P.sub.t and represents the number of input features in the i-th sub-process; X.sub.t is expressed as: $\begin{array}{cc}\begin{array}{c}{X}_i=.Math.\left[{\left\{{\left(x_n^1\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,{\left\{{\left(x_n^{p_i}\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,{\left\{{\left(x_n^{P_i}\right)}_i\right\}}_{n=1}^N\right]\\ =.Math.\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{P_i}\right)}_i\right]\\ =.Math.{\left\{{\left(x^{p_i}\right)}_i\right\}}_{p_i=1}^{P_i}\end{array}& \left(3\right)\end{array}$ wherein (x.sup.p.sup.i).sub.i represents a p.sub.i-th input feature of the i-th sub-process; and x.sup.P.sup.i={x.sub.n.sup.P.sup.i}.sub.n=1.sup.N represents a column vector; and wherein the output data is expressed as y={y.sub.n}.sub.n=1.sup.NR.sup.N1, and comprises N samples; and represents a predicted value.

4. The method of claim 3, wherein the step of obtaining the correlation coefficient value comprises: 1.1) calculating an original correlation coefficient value between each of the original input features and the DXN emission concentration, wherein an original correlation coefficient value between a p-th input feature (x.sup.p.sup.i).sub.i={x.sub.n.sup.p.sup.i).sub.i}.sub.n=1.sup.N of the i-th sub-process and the DXN emission concentration is calculated according to $\begin{array}{cc}{\left({}_{\mathrm{corr\_ori}}^{p_i}\right)}_i=\frac{\underset{n=1}{\overset{N}{.Math.}}.Math.\left[\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right).Math.\left(y_n-\stackrel{\_}{y}\right)\right]}{\sqrt{\underset{n=1}{\overset{N}{.Math.}}.Math.{\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right)}^2}.Math.\sqrt{\underset{n=1}{\overset{N}{.Math.}}.Math.{\left(y_n-\stackrel{\_}{y}\right)}^2}}& \left(4\right)\end{array}$ wherein x.sub.p.sub.i represents an average value of the p-th input feature of the i-th sub-process; and y represents an average value of N modeling samples of the DXN emission concentration; 1.2) preprocessing the original correlation coefficient value (.sub.corr_ori.sup.p.sup.i).sub.i as follows:
(.sub.corr.sup.p.sup.i).sub.i=(.sub.corr_ori.sup.p.sup.i).sub.i|(5) wherein || represents an absolute value; 1.3) repeating steps (1.1)-(1.2) until correlation coefficient values of all of the original input features are obtained; and recording the obtained correlation coefficient values as {.sub.corr.sup.p.sup.i}.sub.P.sub.i.sub.=1.sup.P.sup.i; 1.4) setting a weight factor of the i-th sub-process as f.sub.i.sup.corr; calculating a threshold .sub.i.sup.corr configured to select correlation coefficient-based input features according to $\begin{array}{cc}{}_i^{\mathrm{corr}}=f_i^{\mathrm{corr}}.Math.\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i& \left(6\right)\end{array}$ wherein a maximum value (f.sub.i.sup.corr).sub.max and a minimum value (f.sub.i.sup.corr).sub.min of f.sub.i.sup.corr are calculated according to Equation (7): $\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{corr}}\right)}_{\max }.Math.\frac{\max \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\\ {\left(f_i^{\mathrm{corr}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\end{array}& \left(7\right)\end{array}$ wherein max () is a function for finding a maximum value; and min() is a function for finding a minimum value; 1.5) selecting the p-th input feature of the i-th sub-process according to rules as follows: $\begin{array}{cc}{}_i^{p_i}=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i{}_i^{\mathrm{corr}}\\ 0,& \mathrm{else}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i<{}_i^{\mathrm{corr}}\end{array}& \left(8\right)\end{array}$ wherein .sub.i.sup.corr is taken as a threshold; 1.6) selecting a feature (x.sup.p.sup.i).sub.i in .sub.i.sup.p.sup.i=1 as a correlation coefficient-selected candidate feature; and recording the correlation coefficient-selected candidate feature as ${\left(x^{{\left(p_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i;$ 1.7) performing steps (1.1)-(1.6) for all of the original input features of the i-th sub-process; and recording the selected candidate features as: $\begin{array}{cc}{\left(X_{\mathrm{corr}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i\right]& \left(9\right)\end{array}$ wherein (P.sub.i).sub.corr.sup.sel represents the number of correlation coefficient-selected process variables of the i-th sub-process; and (x.sub.corr.sup.sel).sub.i represents a correlation coefficient-selected candidate feature set selected from the input features of the i-th sub-process; and 1.8) repeating steps (1.1)-(1.7) for all the sub-processes; and recording correlation coefficient measurement-selected features as {(X.sub.corr.sup.sel).sub.i}.sub.i=1.sup.I.

5. The method of claim 4, wherein the step of obtaining the mutual information value comprises: 2.1) calculating a mutual information value between each of the original input features and the DXN emission concentration, wherein a mutual information value between the p-th input feature (x.sup.p.sup.i), of the i-th sub-process and the DXN emission concentration is calculated according to $\begin{array}{cc}{\left({}_{\mathrm{mi}}^{p_i}\right)}_1=\underset{n=1}{\overset{N}{.Math.}}.Math.\underset{n=1}{\overset{N}{.Math.}}.Math.\left\{p_{\mathrm{rob}}\left({\left(x_n^{p_i}\right)}_i,y_n\right).Math.\log \left(\frac{p_{o.Math.b}\left({\left(x_n^{p_i}\right)}_i,y_n\right)}{p_{\mathrm{rob}}\left({\left(x_n^{p_i}\right)}_i\right).Math.p_{\mathrm{rob}}\left(y_n\right)}\right)\right\}& \left(10\right)\end{array}$ wherein p.sub.rob((x.sub.n.sup.p.sup.i).sub.i,y.sub.n) represents a joint probability density; and p.sub.rob((x.sub.n.sup.p.sup.i).sub.i) and p.sub.rob(y.sub.n) each represent a marginal probability density; 2.2) repeating step (2.1) until mutual information values of all of the original input features are obtained; and recording the obtained mutual information values as {.sub.mi.sup.p.sup.i}.sub.p.sub.i.sub.=1.sup.p.sup.i; 2.3) setting a weight factor of the i-th sub-process as f.sub.i.sup.mi, and calculating a threshold .sub.t.sup.mi configured to select the input features based on the mutual information value according to $\begin{array}{cc}{}_i^{\mathrm{mi}}=f_i^{\mathrm{mi}}.Math.\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{m.Math.i}^{p_i}\right)}_i& \left(11\right)\end{array}$ wherein a maximum value (f.sub.i.sup.mi).sub.max and a minimum value (f.sub.t.sup.mi).sub.min of f.sub.t.sup.mi are calculated according to $\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{mi}}\right)}_{\max }.Math.\frac{\max \left({\left({}_{\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i}\\ {\left(f_i^{\mathrm{mi}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i}\end{array}& \left(1.Math.2\right)\end{array}$ wherein max() is a function for finding a maximum value; and min() is a function for finding a minimum value; 2.4) selecting the p-th input feature of the i-th sub-process according to rules as follows: $\begin{array}{cc}{}_i^{p_i}=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i{}_i^{\mathrm{mi}}\\ 0,& \mathrm{else}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i<{}_i^{\mathrm{mi}}\end{array}& \left(13\right)\end{array}$ wherein .sub.i.sup.mi is taken as a threshold; 2.5) selecting a feature (x.sup.p.sup.i).sub.i of .sub.i.sup.p.sup.i=1 as a mutual information value-selected candidate feature; recording the mutual information value-selected candidate feature as ${\left(x^{{\left(p_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i;$ 2.6) performing steps (2.1)-(2.5) for all of the input features of the i-th sub-process; and recording the selected candidate features as: $\begin{array}{cc}{\left(X_{\mathrm{mi}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i\right]& \left(14\right)\end{array}$ wherein (P.sub.i).sub.mi.sup.sel represents the number of mutual information value-selected features in the i-th sub-process; and (X.sub.mi.sup.sel).sub.i represents a candidate feature set selected based on a mutual information value measurement from the input features of the i-th sub-process; and 2.7) repeating steps (2.1)-(2.6) for all the sub-processes; and recording mutual information value measurement-selected features as {(X.sub.mi.sup.sel).sub.i}.sub.i=1.sup.I.

6. The method of claim 5, wherein the step of obtaining the comprehensive evaluation value comprises: 3.1) for the i-th sub-process, taking the intersection of the mutual information-selected features (X.sub.mi.sup.sel).sub.t and the correlation coefficient-selected features (X.sub.corr.sup.sel).sub.t according to Equation (15), thereby obtaining a comprehensive evaluation value-selected candidate feature set, $\begin{array}{cc}{\left(X_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}\right)}_i={\left(X_{\mathrm{mi}}^{\mathrm{sel}}\right)}_i.Math.{\left(X_{\mathrm{corr}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i\right]& \left(15\right)\end{array}$ wherein represents the intersection; $x_i^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}$ represents a (p.sub.i).sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process; and a correlation coefficient value of the (p.sub.i).sub.corr_mi.sup.sel-th candidate feature is ${\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i.Math.\text{;}$ and a mutual information value of the (p.sub.i).sub.corr_mi.sup.sel-th candidate feature is ${\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i.Math.\text{;}$ 3.2) performing normalization according to Equations (16) and (17) so as to eliminate size differences of the correlation coefficient value and mutual information value of the different input features; $\begin{array}{cc}{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{norm}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.m.Math.i}^{\mathrm{sel}}}\right)}_i=\frac{{\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}{\underset{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{.Math.}}.Math.{\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}& \left(16\right)\\ {\left({}_{\mathrm{mi}.Math.\_.Math.\mathrm{norm}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i=\frac{{\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}{\underset{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{.Math.}}.Math.{\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}& \left(17\right)\end{array}$ wherein ${\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{norm}}^{p_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i$ represents a standardized correlation coefficient value of the p.sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process; and ${\left({}_{\mathrm{mi}.Math.\_.Math.\mathrm{norm}}^{p_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i$ represents a standardized mutual information value of the p.sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process; 3.3) defining the comprehensive evaluation value of the candidate input features as ${}_i^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}},$ expressing as ${}_i^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}$ as $\begin{array}{cc}{}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}=k_i^{\mathrm{corr}}.Math.{}_{\mathrm{corr}.Math.\_.Math.\mathrm{norm}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}+k_i^{\mathrm{mi}}.Math.{}_{\mathrm{mi}.Math.\_.Math.\mathrm{norm}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}& \left(18\right)\end{array}$ wherein k.sub.1.sup.corr and k.sub.i.sup.mi each represent a proportional coefficient; and k.sub.i.sup.corr+k.sub.i.sup.mi=1; and 3.4) repeating steps (3.1)-(3.3) until comprehensive evaluation values of all of the candidate input features are obtained; and recording the obtained comprehensive evaluation values as ${\left\{{}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right\}}_{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}^{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}.$

7. The method of claim 6, wherein k.sub.i.sup.corr is equal to 0.5; and k.sub.i.sup.mi is equal to 0.5.

8. The method of claim 6, wherein the step of obtaining the comprehensive evaluation value further comprises: 4.1) setting a weight factor of the i-th sub-process as f.sub.i.sup.corr_mi; calculating a threshold .sub.i.sup.1stsel configured to select the input features based on the comprehensive evaluation value according to $\begin{array}{cc}{}_i^{1.Math.\mathrm{stsel}}=f_i^{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}.Math.\frac{1}{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{.Math.}}.Math.{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i& \left(19\right)\end{array}$ wherein a maximum value (f.sub.i.sup.corr_mi).sub.max and a minimum value (f.sub.i.sup.corr_mi).sub.min of f.sub.i.sup.corr_mi are calculated according to $.Math.\left(20\right)$ $\{\begin{array}{c}{\left(f_i^{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}\right)}_{\max }=\frac{\max \left({\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i\right)}{\frac{1}{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{.Math.}}.Math.{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}\\ {\left(f_i^{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i\right)}{\frac{1}{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{.Math.}}.Math.{\left({}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}\right)}_i}\end{array}$ 4.2) selecting a (p.sub.i).sub.corr_mi.sup.sel-candidate input feature of the i-th sub-process according to rules as follows: $\begin{array}{cc}{}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.{}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}{}_i^{1.Math.\mathrm{stsel}}\\ 0,& \mathrm{else}.Math..Math.{}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}<{}_i^{1.Math.\mathrm{stsel}}\end{array}& \left(21\right)\end{array}$ wherein .sub.i.sup.1stsel is taken as a threshold; 4.3) performing steps (4.1)-(4.2) for all the original candidate input features; selecting variables of ${}^{{\left(p_i\right)}_{\mathrm{corr}.Math.\_.Math.\mathrm{mi}}^{\mathrm{sel}}}=1$ as comprehensive evaluation value-selected input features; and expressing the variables as: $\begin{array}{cc}{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{p_i^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{P_i^{\mathrm{sel}}}\right)}_i\right]& \left(22\right)\end{array}$ wherein (X.sub.1st.sup.sel).sub.i represents first-level features of the i-th sub-process selected using a comprehensive evaluation value measurement from the candidate feature set selected by a correlation coefficient method and a mutual information method; and 4.4) repeating steps (4.1)-(4.3) until the first-level features of all the sub-processes is obtained.

9. The method of claim 8, wherein the step of arranging the first-level features in series comprises: arranging the first-level features in series to obtain the first-level features x.sub.1st.sup.sel based on the single feature correlation; $\begin{array}{cc}{X}_{1.Math.\mathrm{st}}^{\mathrm{sel}}=\left[{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_1,\mathrm{.Math.}.Math.,{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_i,\mathrm{.Math.}.Math.,{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_I\right]=\left[x^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,x^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,x^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right]& \left(23\right)\end{array}$ wherein $x^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}$ represents a p.sub.lst.sup.sel-th feature in a first-level feature selection set; $P_{1.Math.\mathrm{st}}^{\mathrm{sel}}=\underset{i=1}{\overset{I}{.Math.}}.Math..Math.P_i^{\mathrm{sel}}$ represents the number of all of the first-level features; and X.sub.1st.sup.sel represents single feature correlation-based first-level feature obtained by serially combining the first-level features of all of the sub-processes.

10. The method of claim 8, wherein a strategy of second-level feature selection comprises: inputting the first-level features X.sub.1st.sup.sel; running the GAPLS algorithm J times; outputting the second-level features X.sub.2nd.sup.sel).sub.j and then outputting the number of times that the respective first-level input features are selected; and statistically processing the second-level features that are selected J.sub.sel times, wherein when a GAPLS model prediction error is smaller than a prediction error average obtained by running the GAPLS algorithm J times, a second-level feature is selected; recording the number of times that a p.sub.1st.sup.sel-th feature is selected as $f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}};$ accordingly, recording all p.sub.1st.sup.sel-th features of the first-level features as ${\left\{f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}};$ wherein J is the number of times that the GAPLS algorithm runs; J.sub.sel is the number of GAPLS models prediction errors of which are smaller than a prediction error average; and (X.sub.2nd.sup.sel).sub.j represents multiple feature redundancy-based second-level features selected by jth run of the GAPLS algorithm.

11. The method of claim 10, wherein the step of the second-level feature selection comprises: 5.1) setting the number of times that the GAPLS algorithm runs as J; setting GAPLS algorithm parameters; initializing a population size, maximum genetic algebra, mutation probability, a crossover method and a number of latent variables of the PLS algorithm; and setting j=1 and starting the selection of the second-level features; 5.2) determining whether the GAPLS algorithm runs J times; if yes, proceeding to step (5.11); if no, proceeding to step (5.3); 5.3) performing binary encoding for features, wherein a length of a chromosome is the number of input features; 1 implies that a feature is selected; and 0 implies that no feature is selected; 5.4) performing random initialization on population; 5.5) evaluating the fitness of the population; and calculating a root mean square error of cross-validation (RMSECV) using a leave-one-out cross-validation method; 5.6) determining whether a termination condition of the maximum genetic algebra is reached, if no, proceeding to step (5.7); if yes, proceeding to step (5.9); 5.7) performing genetic operations comprising selection, crossover and variation, wherein the selection is performed through an elite substitution strategy, that is, individuals with poor fitness are replaced with individuals with good fitness; the crossover is performed through single point crossover; and the genetic variation is performed through single point mutation; 5.8) obtaining a new population and proceeding to step (5.5); 5.9) obtaining an optimal individual after running the GAPLS algorithm times; and performing decoding to obtain selected second-level features and recording the selected second-level features as (X.sub.2nd.sup.sel).sub.j; 5.10) setting j=j+1; and proceeding to step (5.2); 5.11) calculating an average value of root mean square errors (RMSE) of a prediction model obtained by running the GAPLS algorithm J times; recording the number of the root mean square errors of the GAPLS model that are larger than the average value as J.sub.sel; processing the second-level features that are selected J.sub.sel times by counting the number of times that the P.sub.1st.sup.sel-th feature in the first-level features is selected, $\begin{array}{cc}{\left\{{\left(x_{2.Math.\mathrm{nd}}^{\mathrm{sel}}\right)}_j\right\}}_{j=1}^{J_{\mathrm{sel}}}.Math.\left\{f_{\mathrm{num}}^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right\}={\left\{f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}},1f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}{J}_{\mathrm{sel}}& \left(24\right)\end{array}$ wherein $f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}$ is the number of times that the p.sub.1st.sup.sel-th feature in the first-level features is selected.

12. The method of claim 11, wherein the population size is 20; the maximum genetic algebra is 40; a maximum number of latent variables of the PLS algorithm is 6; and the mutation probability is 0.005.

13. The method of claim 11, wherein the step of the third-level feature selection comprises: according to the number of times ${\left\{f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}$ that all the p.sub.1st.sup.sel-th features in the first-level features are selected, setting a scale factor as f.sub.DXN.sup.RMSE; determining a lower limit of a threshold configured to select the third-level features as .sub.DXN.sup.downlimit; calculating .sub.DXN.sup.downlimit according to: $\begin{array}{cc}{}_{\mathrm{DXN}}^{\mathrm{downlimit}}=\mathrm{floor}.Math.\left\{f_{\mathrm{DXN}}^{\mathrm{RMSE}}.Math.\frac{1}{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right)& \left(25\right)\end{array}$ wherein floor () represents a function that returns integers; calculating a maximum value (f.sub.DXN.sup.RMSE).sub.max and a minimum value (f.sub.DXN.sup.RMSE).sub.min of f.sub.DXN.sup.RMSE according to $\begin{array}{cc}\{\begin{array}{c}{\left(f_{\mathrm{DXN}}^{\mathrm{RMSE}}\right)}_{\max }=\frac{\max \left(f_{\mathrm{num}}^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right)}{\frac{1}{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}}\\ {\left(f_{\mathrm{DXN}}^{\mathrm{RMSE}}\right)}_{\min }=\frac{\min \left(f_{\mathrm{num}}^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right)}{\frac{1}{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}}\end{array}& \left(26\right)\end{array}$ finding a maximum value of the number of times that all the p.sub.1st.sup.sel-th features in the first-level features are selected based on an upper limit .sub.DXN.sup.uplimit of the threshold configured to select the third-level features, $\begin{array}{cc}{}_{\mathrm{DXN}}^{\mathrm{uplimit}}=\max \left(f_{\mathrm{num}}^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right)& \left(27\right)\end{array}$ recording the threshold as .sub.DXN.sup.3rd, wherein the threshold .sub.DXN.sup.3rd is between .sub.DXN.sup.downlimit and .sub.DXN.sup.uplimit; and performing the third-level feature selection according to $\begin{array}{cc}{}^p=\{\begin{array}{cc}1,\mathrm{if}.Math.& f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}{}_{\mathrm{DXN}}^{3.Math.\mathrm{rd}}\\ 0,\mathrm{else}& f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}<{}_{\mathrm{DXN}}^{3.Math.\mathrm{rd}}\end{array}& \left(28\right)\end{array}$ wherein $f_{\mathrm{num}}^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}}$ represents the number of times that the p.sub.1st.sup.sel-th feature in the first-level features is selected by running the GAPLS algorithm J times; .sup.p represents a threshold selection criterion for selecting the third-level features; sequentially storing feature variables of .sup.p=1 in X.sub.3rd.sup.sel_temp, and calculating the RMSE, wherein X.sub.3rd.sup.sel_temp serves as input variables in the establishment of the PLS algorithm-based DXN detection model; and X.sub.3rd.sup.sel represents the third-level features selected from X.sub.1st.sup.sel based on a feature selection threshold .sub.3rd and prior knowledge.

14. The method of claim 13, wherein the step of establishing the PLS algorithm-based DXN detection model comprises: increasing values of the threshold .sub.DXN.sup.3rd between .sub.DXN.sup.downlimit and .sub.DXN.sup.uplimit one by one; so as to establish a plurality of first temporary PLS algorithm-based DXN detection models; selecting a second temporary PLS algorithm-based DXN detection model from the plurality of first temporary PLS algorithm-based DXN detection models, wherein the second temporary PLS algorithm-based DXN detection model has a minimum value of RMSE; checking the input features of the DXN emission concentration detection model to determine whether the input features comprise concentrations of CO, HCL, O.sub.2 and NO.sub.x emitted from a chimney; and removing features in the common resource supply sub-process; if the input features do not include concentrations of CO, HCL, O.sub.2 and NO.sub.x, additionally selecting the third-level features to obtain selected three-level features X.sub.3rd.sup.sel, thereby varying the number of features that are selected and establishing the PLS algorithm-based DXN detection model based on prior knowledge.

15. The method of claim 1, wherein variables of the PLS algorithm-based DXN detection model have 287 dimensions.

16. The method of claim 1, wherein weight factors f.sub.i.sup.corr, f.sub.i.sup.mi and f.sub.i.sup.corr_mi of feature selection of the correlation coefficient value and the mutual information value of the first-level features are 0.8.

17. The method of claim 1, wherein there are 132 feature variables selected by the comprehensive evaluation value; for the selected 132 process variables based on the single feature correlation, an optimal process variable combination is determined using the GAPLS algorithm so as to remove redundant features.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0109] The present application will be further described below with reference to the accompanying drawings, so that the present application is more understandable. The accompanying drawings disclosed herein are merely illustrative and not intended to limit the present application.

[0110] FIG. 1 is a flowchart illustrating a grate furnace-based MSWI process.

[0111] FIG. 2 is a flowchart of a method for detecting a DXN emission concentration in a MSWI process based on multi-level feature selection according to an embodiment of the present application.

[0112] FIG. 3 schematically shows a strategy for detecting the DXN emission concentration according to an embodiment of the present application.

[0113] FIG. 4 shows a relationship between sub-processes of MSWI as well as detection data acquisition according to an embodiment of the present application.

[0114] FIG. 5 is a schematic diagram of a second-level feature selection strategy based on multi-feature redundancy according to an embodiment of the present application.

[0115] FIG. 6 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in an incineration treatment sub-process according to an embodiment of the present application.

[0116] FIG. 7 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in a boiler operation sub-process according to an embodiment of the present application.

[0117] FIG. 8 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in a flue gas treatment sub-process according to an embodiment of the present application.

[0118] FIG. 9 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in a steam electric power generation sub-process according to an embodiment of the present application.

[0119] FIG. 10 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in a stack emission sub-process according to an embodiment of the present application.

[0120] FIG. 11 shows correlation coefficient values, mutual information values and comprehensive evaluation values of process variables selected in a common resource supply sub-process according to an embodiment of the present application.

[0121] FIG. 12 is a table showing correlation measurement results of process variables of different sub-processes according to an embodiment of the present application.

[0122] FIG. 13 is a table showing the number of process variables selected based on the comprehensive evaluation values according to an embodiment of the present application.

[0123] FIG. 14 is a table of statistical RMSE results obtained by running the GAPLS algorithm J times according to an embodiment of the present application.

[0124] FIG. 15 is a table showing the number of times that process variables are selected based on multiple feature selection according to an embodiment of the present application.

[0125] FIG. 16 is a table showing process variable selected based on model prediction performance according to an embodiment of the present application.

[0126] FIG. 17 is a table showing LV contribution rates of PLS models based on different input features according to an embodiment of the present application.

[0127] FIG. 18 is a table showing statistical results of the PLS models based on different input features according to an embodiment of the present application.

[0128] In the drawings: 1, unloading hall; 2, storage tank; 3, claw; 4, incinerator feed hopper; 5, grate; 6, slag tank; 7, steam turbine set; 8, reactor; 9, lime storage tank; 10, activated carbon storage tank; 11, fly ash storage bin; 12, bag dust collector; 13, mixer; 14, water tank; 15, draft fan; and 16, chimney.

DETAILED DESCRIPTION OF EMBODIMENTS

[0129] The present application will be further described below with reference to the accompanying drawings to clearly and completely illustrate the technical solutions of the embodiments. It is apparent that the embodiments below are merely preferred embodiments of the present application and are not intended to limit the invention. Any other embodiments made by those skilled in the art based on the embodiments disclosed herein without sparing any creative efforts should fall within the scope of the invention.

[0130] FIG. 2 shows a flowchart illustrating a method for detecting a DXN emission concentration in a MSWI process based on multi-level feature selection according to an embodiment of the present application.

[0131] The method includes the following steps.

[0132] S101) A grate furnace-based municipal solid waste incineration (MSWI) process is divided into a plurality of sub-processes based on incineration process. The plurality of sub-processes include an incineration treatment sub-process, a boiler operation sub-process, a flue gas treatment sub-process, a steam electric power generation sub-process, a stack emission sub-process and a common resource supply sub-process.

[0133] S102) A correlation coefficient value and a mutual information value between each of original input features of the sub-process and the DXN emission concentration are obtained. Then a comprehensive evaluation value of candidate input features is obtained according to the obtained correlation coefficient value and the obtained mutual information value, thereby obtaining first-level features of all of the sub-processes.

[0134] S103) The first-level features are selected and statistically processed by adopting a GAPLS-based feature selection algorithm and according to redundancy between different features, thereby obtaining second-level features of all of the sub-processes.

[0135] S104) The first-level features and the second-level features are screened based on statistical results within a preset threshold range, thereby obtaining the third-level features of all of the sub-processes

[0136] S105) A DXN detection model based on a partial least squares (PLS) algorithm is obtained according to model prediction performance and the third-level features. The DXN emission concentration is detected by the obtained PLS algorithm-based DXN detection model.

[0137] Specifically, the goal of feature selection in the present application is to improve the prediction performance and interpretability of a soft sensing model. The concentration detection method of the present application belongs to environmental protection fields, particularly to complex industrial process parameter detection. In the present embodiment, a method for detecting a dioxin (DXN) emission concentration in a MSWI process based on multi-level feature selection is provided. Firstly, from the perspective of the correlation between a single input feature and the DXN emission concentration, a comprehensive evaluation value index is constructed by combining the correlation coefficient and the mutual information, so as to realize the first-level feature selection of process variables of a monitored sub-process in the MSWI process. Secondly, from the perspective of multiple feature redundancy and feature selection robustness, running the GAPLS-based feature selection algorithm multiple times is performed to achieve the second-level feature selection based on the selected first-level features. Finally, by the combination of the number of times that previously selected features are selected, the model prediction performance and mechanism, the third-level feature selection is achieved based on the selected second-level features. The DXN emission concentration detection model can be established based on the obtained features. The method provided herein is verified to be effective by multi-year DXN monitoring data of an incineration plant.

[0138] Compared to the prior art, in the method of the present embodiment, feature selection of input features is performed for each sub-process of the MSWI process, so as to detect the DXN emission concentration of the MSWI process. The method has good interpretability, conforms to DXN emission characteristics of the MSWI process and provides support for subsequent optimization control research.

[0139] Specifically, the method further includes a step of arranging the first-level features in series after obtaining the first-level features of a 1 of the sub-processes, so as to obtain the first-level features based on single feature correlation.

[0140] Specifically, the DXN detection model includes input data and output data.

[0141] The input data is expressed as XR.sup.NP and includes N samples as row data and P variables as column data. The input data is derived from respective sub-processes of the MSWI process. Monitoring data of an i-th sub-process is obtained by using a programmable logic controller (PLC) device or a distributed control system (DCS) device installed on site and is expressed as X.sub.iR.sup.NP.sup.i. X.sub.iR.sup.NP.sup.i is input data from the i-th sub-process and satisfies Equations (1) and (2):

X=[X.sub.1, . . . , X.sub.i, . . . , X.sub.I]={X.sub.i}.sub.i=1.sup.I(1)

P=P.sub.1+ . . . +P.sub.i+ . . . +P.sub.I=.sub.i=1.sup.IP.sub.i(2) [0142] where I represents the number of the sub-processes, and P.sub.i represents the number of the input features in the i-th sub-process; [0143] X.sub.i is expressed as:

[00043]$\begin{array}{cc}\begin{array}{c}{X}_i=.Math.\left[{\left\{{\left(x_n^1\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,{\left\{{\left(x_n^{p_i}\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,{\left\{{\left(x_n^{P_i}\right)}_i\right\}}_{n=1}^N\right]\\ =.Math.\left[{\left(x^1\right)}_i.Math.\mathrm{.Math.}.Math.,{\left(x^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{P_i}\right)}_i\right]\\ =.Math.{\left\{{\left(x^{p_i}\right)}_i\right\}}_{p_i=1}^{P_i}\end{array}& \left(3\right)\end{array}$ [0144] where (x.sup.P.sup.i).sub.i represents a p.sub.i-th input feature of the i-th sub-process; and x.sup.p.sup.i={x.sub.n.sup.p.sup.i}.sub.n=1.sup.N represents a column vector.

[0145] The output data is expressed as y={y.sub.n}.sub.n=1.sup.NR.sup.N1 and includes N samples; and represents a predicted value.

[0146] Specifically, the step of obtaining the correlation coefficient value is performed through the following steps. [0147] 1.1) An original correlation coefficient value between each of the original input features and the DXN emission concentration is calculated. For example, an original correlation coefficient value between a p-th input feature (x.sup.p.sup.i).sub.i={(x.sub.n.sup.p.sup.i.sub.i}.sub.n=1.sup.N of the i-th sub-process and the DXN emission concentration is calculated according to

[00044]$\begin{array}{cc}{\left({}_{\mathrm{corr\_ori}}^{p_i}\right)}_i=\frac{\underset{n=}{\overset{N}{.Math.}}.Math.\left[\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right).Math.\left(y_n-\stackrel{\_}{y}\right)\right]}{\sqrt{\underset{n=}{\overset{N}{.Math.}}.Math.{\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right)}^2}.Math.\sqrt{\underset{n=}{\overset{N}{.Math.}}.Math.{\left(y_n-\stackrel{\_}{y}\right)}^2}}& \left(4\right)\end{array}$ [0148] where x.sub.p.sub.i represents an average value of the p-th input feature of the i-th sub-process; and y represents an average value of N modeling samples of the DXN emission concentration. [0149] 1.2) The original correlation coefficient value (.sub.corr_ori.sup.p.sup.i).sub.i is preprocessed as follows:

(.sub.corr.sup.p.sup.i).sub.i=|(.sub.corr_ori.sup.p.sup.i).sub.i|(5) [0150] where || represents an absolute value. [0151] 1.3) Steps (1.1)-(1.2) are repeated until correlation coefficients of all of the original input features are obtained. The obtained correlation coefficients are recorded as {.sub.corr.sup.p.sup.i}.sub.p.sub.i.sub.=1.sup.P.sup.i. [0152] 1.4) A weight factor of the i-th sub-process is set as f.sub.i.sup.corr. A threshold .sub.i.sup.corr configured to select input features based on the correlation coefficients is calculated according to

[00045]$\begin{array}{cc}{}_i^{\mathrm{corr}}=f_i^{\mathrm{corr}}.Math.\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,& \left(6\right)\end{array}$ [0153] where a maximum value (f.sub.i.sup.corr).sub.max and a minimum value (f.sub.i.sup.corr).sub.min of f.sub.i.sup.corr are calculated according to Equation (7):

[00046]$\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{corr}}\right)}_{\max }=\frac{\max \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i,\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\\ {\left(f_i^{\mathrm{corr}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i,\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\end{array}& \left(7\right)\end{array}$ [0154] where max() is a function for finding a maximum value; and min() is a function for finding a minimum value. [0155] 1.5) The p-th input feature of the i-th sub-process is selected according to rules as follows:

[00047]$\begin{array}{cc}{}_i^{p_i}=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i{}_i^{\mathrm{corr}}\\ 0,& \mathrm{else}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i<{}_i^{\mathrm{corr}}\end{array}& \left(8\right)\end{array}$ [0156] where .sub.i.sup.corr is taken as a threshold. [0157] 1.6) A feature in (x.sup.p.sup.i).sub.i in .sub.t.sup.p.sup.i=1 is selected as a correlation coefficient-selected candidate feature. The correlation coefficient-selected candidate feature is recorded as

[00048]${\left(x^{{\left(p_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i.$ [0158] 1.7) Steps (1.1)-(1.6) are performed for all of the original input features of the i-th sub-process. The selected candidate features are recorded as:

[00049]$\begin{array}{cc}{\left(X_{\mathrm{corr}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{corr}}^{\mathrm{sel}}}\right)}_i\right]& \left(9\right)\end{array}$ [0159] where (P.sub.i).sub.corr.sup.sel represents the number of correlation coefficient-selected process variables of the i-th sub-process; and (X.sub.corr.sup.sel).sub.i represents a correlation coefficient-selected candidate feature set from the input features of the i-th sub-process. [0160] 1.8) Steps (1.1)-(1.7) are repeated for all the sub-processes. Correlation coefficient measurement-selected features are recorded as {(X.sub.corr.sup.sel).sub.i}.sub.i=1.sup.I.

[0161] Specifically, the step of obtaining the mutual information value includes the following steps. [0162] 2.1) A mutual information value between each of the original input features and the DXN emission concentration is calculated. For example, a mutual information value between the p-th input feature (x.sup.p.sup.i).sub.i of the i-th sub-process and the DXN emission concentration is calculated according to

[00050]$\begin{array}{cc}{\left({}_{\mathrm{mi}}^{p_i}\right)}_i=\underset{n=1}{\overset{N}{.Math.}}.Math.\underset{n=1}{\overset{N}{.Math.}}.Math.\left\{p_{\mathrm{rob}}\left({\left(x_n^{p_i}\right)}_i,y_n\right).Math.\log \left(\frac{p_{\mathrm{rob}}\left({\left(x_n^{p_i}\right)}_i,y_n\right)}{p_{\mathrm{rob}}\left({\left(x_n^{p_i}\right)}_i\right).Math.p_{\mathrm{rob}}\left(y_n\right)}\right)\right\}& \left(10\right)\end{array}$ [0163] where p.sub.rob((x.sub.n.sup.p.sup.i).sub.i,y.sub.n) represents a joint probability density; and p.sub.rob((x.sub.n.sup.p.sup.i) and p.sub.rob(y.sub.n) each represent a marginal probability density. [0164] 2.2) Step (2.1) is repeated for all of the original input features until mutual information values of all of the original input features are obtained. The obtained mutual information values are recorded as {.sub.mi.sup.p.sup.i}.sub.p.sub.i.sub.=1.sup.P.sup.i. [0165] 2.3) A weight factor of the i-th sub-process is set as f.sub.i.sup.mi. A threshold .sub.i.sup.mi configured to select the input features based on the mutual information value is calculated according to

[00051]$\begin{array}{cc}{}_i^{m.Math.i}=f_i^{m.Math.i}.Math.\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i& \left(11\right)\end{array}$ [0166] where a maximum value (f.sub.i.sup.mi).sub.max and a minimum value (f.sub.i.sup.mi).sub.min of f.sub.i.sup.mi are calculated according to Equation (12):

[00052]$\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{mi}}\right)}_{\max }=\frac{\max \left({\left({}_{\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i}\\ {\left(f_i^{\mathrm{mi}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{mi}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i}\end{array}& \left(12\right)\end{array}$ [0167] wherein max() is a function for finding a maximum value; and min() is a function for finding a minimum value. [0168] 2.4) The p-th input feature of the i-th sub-process is selected according to rules as follows:

[00053]$\begin{array}{cc}{}_i^{p_i}=\{\begin{array}{cc}1,& {\mathrm{if}.Math..Math.\left({}_{\mathrm{mi}}^{p_i}\right)}_i.Math.{}_i^{\mathrm{mi}}\\ 0,& \mathrm{else}.Math..Math.{\left({}_{\mathrm{mi}}^{p_i}\right)}_i<{}_i^{\mathrm{mi}}\end{array}& \left(13\right)\end{array}$ [0169] where .sub.i.sup.mi is taken as a threshold. [0170] 2.5) A feature (x.sup.p.sup.i).sub.i of .sub.i.sup.p.sup.i=1 is selected as a mutual information value-selected candidate feature. The mutual information value-selected candidate feature is recorded as

[00054]${\left(x^{{\left(p_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i.$ [0171] 2.6) Steps (2.1)-(2.5) are performed for all of the input features of the i-th sub-process. The selected candidate features are recorded as:

[00055]$\begin{array}{cc}{\left(X_{\mathrm{mi}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{mi}}^{\mathrm{sel}}}\right)}_i\right]& \left(14\right)\end{array}$ [0172] where (P.sub.i).sub.mi.sup.sel represents the number of mutual information value-selected features in the i-th sub-process; and (X.sub.mi.sup.sel).sub.i represents a candidate feature set selected based on a mutual information value measurement from the input features of the i-th sub-process. [0173] 2.7) Steps (2.1)-(2.6) are repeated for all the sub-processes. Mutual information value measurement-selected features are recorded as {(X.sub.mi.sup.sel).sub.i}.sub.t=1.sup.I.

[0174] Specifically, the step of obtaining the comprehensive evaluation value is performed through the following steps. [0175] 3.1) For the i-th sub-process, the intersection of the mutual information-selected features (X.sub.mi.sup.sel).sub.i and the correlation coefficient-selected features (X.sub.corr.sup.sel).sub.i is performed according to Equation (15), thereby obtaining a comprehensive evaluation value-selected candidate feature set

[00056]$\begin{array}{cc}{\left(X_{\mathrm{corr\_mi}}^{\mathrm{sel}}\right)}_i={\left(X_{\mathrm{mi}}^{\mathrm{sel}}\right)}_i.Math.{\left(X_{\mathrm{corr}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{{\left(P_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}\right)}_i\right].& \left(15\right)\end{array}$ [0176] where represents the intersection;

[00057]$x_i^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}$

represents a (p.sub.i).sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process; and a correlation coefficient value of the (p.sub.i).sub.corr_mi.sup.sel-th candidate feature is

[00058]${\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}\right)}_i;$

and a mutual information value of the (p.sub.i).sub.corr_mi.sup.sel-th candidate feature is

[00059]${\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}\right)}_i.$ [0177] 3.2) Normalization is performed according to Equations (16) and (17) so as to eliminate size differences of the correlation coefficient value and mutual information value of the different input features;

[00060]$\begin{array}{cc}{\left({}_{\mathrm{corr\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i=\frac{{\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}{\underset{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}& \left(16\right)\\ {\left({}_{\mathrm{mi}.Math.\mathrm{\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i=\frac{{\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}{\underset{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{.Math.}}.Math..Math.{\left({}_{\mathrm{mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}& \left(17\right)\end{array}$ [0178] where

[00061]${\left({}_{\mathrm{corr}.Math.\mathrm{\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i$

represents a standardized correlation coefficient value of the p.sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process; and

[00062]${\left({}_{\mathrm{mi}.Math.\mathrm{\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i$

represents a standardized mutual information value of the p.sub.corr_mi.sup.sel-th candidate feature of the i-th sub-process. [0179] 3.3) The comprehensive evaluation value of the candidate input features are defined as

[00063]${}_i^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}},$

and are expressed as follows:

[00064]$\begin{array}{cc}{}_{\mathrm{corr}.Math.\mathrm{\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}=k_i^{\mathrm{corr}}.Math.{}_{\mathrm{corr}.Math.\mathrm{\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}+k_i^{\mathrm{mi}}.Math.{}_{\mathrm{mi}.Math.\mathrm{\_norm}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}& \left(18\right)\end{array}$ [0180] where k.sub.i.sup.corr and k.sub.i.sup.mi each represent a proportional coefficient; and k.sub.i.sup.corr+k.sub.i.sup.mi=1. [0181] 3.4) Steps (3.1)-(3.3) are repeated for the respective candidate input features until comprehensive evaluation values of all of the candidate input features are obtained. The obtained comprehensive evaluation values are recorded as

[00065]${\left\{{}_{\mathrm{corr}.Math.\mathrm{\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right\}}_{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}^{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}.$

[0182] Specifically, k.sub.i.sup.corr is equal to 0.5; and k.sub.i.sup.mi is equal to 0.5.

[0183] Specifically, the step of obtaining the comprehensive evaluation value of the candidate input features according to the correlation coefficient value and the mutual information value is performed through the following steps. [0184] 4.1) A weight factor of the i-th sub-process is set as f.sub.i.sup.corr_mi. A threshold .sub.i.sup.1stsel configured to select the input features based on the comprehensive evaluation value is calculated as follows:

[00066]$\begin{array}{cc}{}_i^{1.Math.\mathrm{st}.Math..Math.\mathrm{sel}}=f_i^{\mathrm{corr\_mi}}.Math.\frac{1}{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}.Math.\mathrm{\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i& \left(19\right)\end{array}$ [0185] where a maximum value (f.sub.i.sup.corr_mi).sub.max and a minimum value (f.sub.i.sup.corr_mi).sub.min of f.sub.t.sup.corr_mi are calculated according to Equation (20):

[00067]$\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{corr\_mi}}\right)}_{\max }=\frac{\begin{array}{c}\max ({\left({}_{\mathrm{corr\_mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,\\ {\left({}_{\mathrm{corr\_mi}}^{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i)\end{array}}{\frac{1}{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}\\ {\left(f_i^{\mathrm{corr\_mi}}\right)}_{\min }=\frac{\begin{array}{c}\min ({\left({}_{\mathrm{corr\_mi}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,\\ {\left({}_{\mathrm{corr\_mi}}^{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i)\end{array}}{\frac{1}{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}.Math.\underset{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}=1}{\overset{{\left(P_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}\right)}_i}\end{array}.& \left(20\right)\end{array}$ [0186] 4.2) A (p.sub.i).sub.corr_mi.sup.sel-th candidate input feature of the i-th sub-process is selected according to rules as follows:

[00068]$\begin{array}{cc}{}^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.{}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}{}_i^{1.Math.\mathrm{st}.Math..Math.\mathrm{sel}}\\ 0,& \mathrm{else}.Math..Math.{}_{\mathrm{corr\_mi}}^{{\left(p_i\right)}_{\mathrm{corr\_m}.Math.i}^{\mathrm{sel}}}<{}_i^{1.Math.\mathrm{st}.Math..Math.\mathrm{sel}}\end{array}& \left(21\right)\end{array}$ [0187] where .sub.t.sup.1stsel is taken as a threshold. [0188] 4.3) Steps (4.1)-(4.2) are performed for all the original candidate input features. Variables of

[00069]${}^{{\left(p_i\right)}_{\mathrm{corr\_mi}}^{\mathrm{sel}}}=1$

are selected as comprehensive evaluation value-selected input features, and recorded as:

[00070]$\begin{array}{cc}{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_i=\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{p_i^{\mathrm{sel}}}\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{P_i^{\mathrm{sel}}}\right)}_i\right]& \left(22\right)\end{array}$ [0189] where (x.sub.1st.sup.sel).sub.i represents first-level features of the i-th sub-process selected by a comprehensive evaluation value measurement from the candidate feature set selected by a correlation coefficient method and a mutual information method. [0190] 4.4) Steps (4.1)-(4.3) are repeated until the first-level features of all the sub-processes are obtained.

[0191] Specifically, the step of arranging the first-level features in series is performed through the following steps.

[0192] The first-level features are arranged in series to obtain the first-level features X.sub.1st.sup.sel based on the single feature correlation;

[00071]$\begin{array}{cc}{X}_{1.Math.\mathrm{st}}^{\mathrm{sel}}=\left[{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_1,\mathrm{.Math.}.Math.,.Math.{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_i,.Math.\mathrm{.Math.}.Math.,.Math.{\left(X_{1.Math.\mathrm{st}}^{\mathrm{sel}}\right)}_I\right].Math..Math.=.Math.\left[x^{1_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,x^{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,x^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}\right]& \left(23\right)\end{array}$ [0193] where

[00072]$x^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}$

represents a p.sub.1st.sup.sel-th feature in a first-level feature selection set;

[00073]$P_{1.Math.\mathrm{st}}^{\mathrm{sel}}.Math.\underset{i=1}{\overset{I}{.Math.}}.Math..Math.P_i^{\mathrm{sel}}$

represents the number of all of the first-level features; and X.sub.1st.sup.sel represents single feature correlation-based first-level feature obtained by serially combining the first-level features of all of the sub-processes.

[0194] Specifically, a strategy of selecting the second-level features is described as follows.

[0195] The first-level features X.sub.1st.sup.sel are inputted into a GAPLS algorithm. After running the GAPLS algorithm J times, the second-level features (X.sub.2nd.sup.sel).sub.j are outputted. Then the number of times that the respective inputted first-level features are selected is outputted. The second-level features that are selected J.sub.sel times are statistically processed. When a GAPLS model prediction error is smaller than a prediction error average obtained by running the GAPLS algorithm J times, a second-level feature is selected.

[0196] The number of times that a p.sub.1st.sup.sel-th feature is selected is recorded as

[00074]$f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}};$

accordingly, all P.sub.1st.sup.sel-th features of the first-level features are recorded as

[00075]${\left\{f_{\mathrm{num}}^{p_{j.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}.$

[0197] J is the number of times that the GAPLS algorithm runs. J.sub.sel is the number of GAPLS models prediction errors of which are smaller than a prediction error average. (X.sub.2nd.sup.sel).sub.j represents multiple feature redundancy-based second-level features selected by jth run of the GAPLS algorithm.

[0198] Specifically, the step of selecting the second-level features is performed through the following steps.

[0199] 5.1) The number of times that the GAPLS algorithm runs is set as J. GAPLS algorithm parameters are set. Population size, maximum genetic algebra, mutation probability, a crossover method and a number of latent variables of the PLS algorithm are initialized. j=1 is set and the selection of the second-level features is started.

[0200] 5.2) Whether the GAPLS algorithm runs J times is determined. If yes, step (5.11) continues; if no, step (5.3) continues.

[0201] 5.3) Binary encoding for features is performed. A length of a chromosome is the number of input features. 1 implies that a feature is selected; and 0 implies that no feature is selected.

[0202] 5.4) Random initialization on population is performed.

[0203] 5.5) The fitness of the population is evaluated. A root mean square error of cross-validation (RMSECV) is calculated using a leave-one-out cross-validation method.

[0204] 5.6) Whether a termination condition of the maximum genetic algebra is reached is determined. If no, step (5.7) continues. If yes, step (5.9) continues.

[0205] 5.7) Genetic operations including selection, crossover and variation are performed. The selection is performed through an elite substitution strategy, that is, individuals with poor fitness are replaced with individuals with good fitness. The crossover is performed through single point crossover. The genetic variation is performed through single point mutation;

[0206] 5.8) A new population is obtained and step (5.5) continues.

[0207] 5.9) An optimal individual is obtained by running the GAPLS algorithm J times. Decoding is performed to obtain selected second-level features. The selected second-level features are recorded as (X.sub.2nd.sup.sel).sub.j.

[0208] 5.10) Let j=j+1, and step (5.2) continues.

[0209] 5.11) An average value of root mean square errors (RMSE) of a prediction model is calculated by running the GAPLS algorithm J times. The number of the root mean square errors of the GAPLS model that are larger than the average value is recorded as J.sub.sel. The second-level features that are selected J.sub.sel so times are processed by counting the number of times that the P.sub.1st.sup.sel-th feature in the first-level features is selected,

[00076]$\begin{array}{cc}{\left\{\left(X_{2.Math.\mathrm{nd}}^{\mathrm{sel}}\right)\right\}}_{j=1}^J.Math.\left\{f_{\mathrm{num}}^{1_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right\}={\left\{f_{\mathrm{num}}^{p_{j.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}},.Math..Math.1f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}{J}_{\mathrm{sel}}& \left(24\right)\end{array}$ [0210] where

[00077]$f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}$

is the number of times that the p.sub.1st.sup.sel-th feature in the first-level features is selected.

[0211] Specifically, the population size is 20. The maximum genetic algebra is 40. A maximum number of latent variables of the PLS algorithm is 6. The mutation probability is 0.005.

[0212] Specifically, the step of selecting the third-level features is performed through the following steps.

[0213] According to the number of times

[00078]${\left\{f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right\}}_{p_{1.Math.\mathrm{st}}^{\mathrm{sel}}=1}^{P_{1.Math.\mathrm{st}}^{\mathrm{sel}}}$

that all the p.sub.1st.sup.sel-th features in the first-level features are selected, a scale factor is set as f.sub.DXN.sup.RMSE. A lower limit of a threshold configured to select the third-level features recorded as .sub.DXN.sup.downlimit and calculated according to:

[00079]$\begin{array}{cc}{}_{\mathrm{DXN}}^{\mathrm{downlimit}}=\mathrm{floor}.Math..Math.\left(f_{\mathrm{DXN}}^{\mathrm{RMSE}}.Math.\frac{1}{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right)& \left(25\right)\end{array}$ [0214] where floor() indicates a function that returns integers. A maximum value (f.sub.DXN.sup.RMSE).sub.max and a minimum value (f.sub.DXN.sup.RMSE).sub.min of f.sub.DXN.sup.RMSE are calculated according to

[00080]$\begin{array}{cc}\{\begin{array}{c}{\left(f_{\mathrm{DXN}}^{\mathrm{RMSE}}\right)}_{\max }=\frac{\max \left(f_{\mathrm{num}}^{1_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right)}{\frac{1}{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}}\\ {\left(f_{\mathrm{DXN}}^{\mathrm{RMSE}}\right)}_{\min }=\frac{\min \left(f_{\mathrm{num}}^{1_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right)}{\frac{1}{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}.Math.\underset{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}=1}{\overset{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}{.Math.}}.Math..Math.f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}}\end{array}& \left(26\right)\end{array}$

[0215] A maximum value of the number of times that all the p.sub.1st.sup.sel-th features in the first-level features are selected is found based on an upper limit .sub.DXN.sup.uplimit of the threshold configured to select the third-level features,

[00081]$\begin{array}{cc}{}_{\mathrm{DXN}}^{\mathrm{uplimit}}=\max \left(f_{\mathrm{num}}^{1_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}},\mathrm{.Math.}.Math.,f_{\mathrm{num}}^{P_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}\right)& \left(27\right)\end{array}$

[0216] The threshold is recorded as .sub.DXN.sup.3rd and is between .sub.DXN.sup.downlimit and .sub.DXN.sup.uplimit. The third-level features are obtained according to

[00082]$\begin{array}{cc}{}^p=\{\begin{array}{cc}1,& \mathrm{if}.Math..Math.f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}{}_{\mathrm{DXN}}^{3.Math..Math.\mathrm{rd}}\\ 0,& \mathrm{else}.Math..Math.f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}<{}_{\mathrm{DXN}}^{3.Math..Math.\mathrm{rd}}\end{array},& \left(28\right)\end{array}$ [0217] where

[00083]$f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}$

represents the number of times that the p.sub.1st.sup.sel-th feature in the first-level features is selected by running the GAPLS algorithm J times; .sup.p represents a threshold selection criterion for selecting the third-level features.

[0218] Feature variables of .sup.p=1 are sequentially stored in X.sub.3rd.sup.sel_temp. The RMSE is calculated. X.sub.3rd.sup.sel_temp serves as input variables in the establishment of the PLS algorithm-based DXN detection model. X.sub.3rd.sup.sel represents the third-level features selected from X.sub.1st.sup.sel based on a feature selection threshold .sub.3rd and prior knowledge.

[0219] Specifically, the step of establishing the DXN detection model based on the PLS algorithm is implemented through the following steps.

[0220] Values of the threshold .sub.DXN.sup.3rd between .sub.DXN.sup.downlimit and .sub.DXN.sup.uplimit are increased one by one so as to establish a plurality of first temporary PLS algorithm-based DXN detection model.

[0221] A second temporary PLS algorithm-based DXN detection model is selected from the plurality of first temporary PLS algorithm-based DXN detection models. The second temporary PLS algorithm-based DXN detection model has a minimum value of RMSE.

[0222] Checking the input features of the DXN emission concentration detection model is performed to determine whether the input features comprises concentrations of CO, HCL, O.sub.2 and NO.sub.x emitted from a chimney. At the same time, features in the common resource supply Rib-process are removed. If the input features do not include concentrations of CO, HCL, O.sub.2 and NO.sub.x, the third-level features are additionally selected to obtain selected three-level features X.sub.3rd.sup.sel, thereby varying the number of features that are selected and establishing the PLS algorithm-based DXN detection model based on prior knowledge.

[0223] Specifically, variables of the PLS algorithm-based DXN detection model have 287 dimensions.

[0224] Specifically, weight factors f.sub.i.sup.corr, f.sub.i.sup.mi and f.sub.t.sup.corr_mi of feature selection of the correlation coefficient value and the mutual information value of the first-level features are 0.8.

[0225] Specifically, there are 132 feature variables selected by the comprehensive evaluation value. For the selected 132 process variables based on the single feature correlation, an optimal combination of the process variables is determined using the GAPLS algorithm so as to remove redundant features.

[0226] The present embodiment provides a method for detecting a dioxin (DXN) emission concentration in a MSWI process based on multi-level feature selection, which is implemented through the following specific steps.

[0227] A municipal solid waste incineration (MSWI) process is divided into six sub-processes based on an incineration process. The six sub-processes include an incineration treatment sub-process, a boiler operation sub-process, a flue gas treatment sub-process, a steam electric power generation sub-process, a stack emission sub-process and a common resource supply sub-process. FIG. 3 schematically shows a DXN emission concentration detection strategy according to an embodiment of the present application.

[0228] In the present application, the input data of the DXN detection model is expressed as XR.sup.NP and includes N samples as row data and P variables as column data. The input data is derived from respective sub-processes of the MSWI process. Monitoring data of an i-th sub-process is obtained by using a programmable logic controller (PLC) device or a distributed control system (DCS) device installed on site and is expressed as X.sub.iR.sup.NP.sup.i, which is input data from the i-th Rib-process and satisfies Equations (1) and (2);

X=[X.sub.1, . . . , X.sub.t, X.sub.I]={X.sub.i}.sub.i=1.sup.I(1)

P=P.sub.1+ . . . +P.sub.i+ . . . +P.sub.I=.sub.i=1.sup.IP.sub.i(2).

[0229] I represents the number of the sub-processes. P.sub.i represents the number of input features in the i-th sub-process, and the input features are variables derived from the monitoring data.

[0230] Accordingly, output data of the DXN detection model is expressed as y={y.sub.n}.sub.n=1.sup.NR.sup.N1 and includes Nsamples as row data.

[0231] Obviously, the input/output data of the model is quite different in a time scale, and thus NP.

[0232] In order to make the following description understandable, X.sub.t is modified as:

[00084]$\begin{array}{cc}\begin{array}{c}{X}_i=.Math.\left[{\left\{{\left(x_n^1\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,{\left\{{\left(x_n^{p_i}\right)}_i\right\}}_{n=1}^N,\mathrm{.Math.}.Math.,.Math.{\left\{{\left(x_n^{P_i}\right)}_i\right\}}_{n=1}^N\right].Math..Math.\\ =.Math.\left[{\left(x^1\right)}_i,\mathrm{.Math.}.Math.,{\left(x^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left(x_n^{P_i}\right)}_i\right]\\ =.Math.{\left\{{\left(x^{p_i}\right)}_i\right\}}_{p_i=1}^{P_i},\end{array}& \left(3\right)\end{array}$ [0233] where (x.sup.p.sup.t).sub.i represents the p.sub.i-th input feature of the i-th sub-process, and x.sup.p.sup.i={x.sub.n.sup.p.sup.i}.sub.n=1.sup.N represents a column vector.

[0234] The present application provides a DXN emission concentration detection strategy for a MSWI process based on multi-level feature selection. FIG. 4 shows a relationship between the sub-processes of MSWI as well as detection data acquisition according to an embodiment of the present application.

[0235] As shown in FIG. 4, (x.sub.corr.sup.sel).sub.i represents a correlation coefficient-selected candidate feature set selected from the input features of the i-th sub-process. (X.sub.mi.sup.sel).sub.t represents a mutual information measurement-selected candidate feature set for the input features of the i-th sub-process. (X.sub.1st.sup.sel).sub.t represents a candidate feature set selected based on a mutual information value measurement from the selected first-level features of the i-th sub-process. X.sub.1st.sup.sel represents the single feature correlation-based first-level features obtained by serially combining the first-level features of all the sub-processes. (X.sub.2nd.sup.sel).sub.j represents the multi-feature redundancy-based second-level features selected by running the GAPLS algorithm J times.

[00085]$f_{\mathrm{num}}^{p_{1.Math..Math.\mathrm{st}}^{\mathrm{sel}}}$

represents the number of times that the p.sub.1st.sup.sel-th feature in the first-level features is selected. X.sub.3rd.sup.sel represents a third-level feature selected from X.sub.1st.sup.sel in the light of a feature selection threshold .sub.3rd and prior knowledge. M.sub.parx represents parameters of the detection model. represents a predicted value.

[0236] In the method of the present embodiment, the algorithm is realized through the following steps.

[0237] 1. First-Level Feature Selection Based on Single Feature Correlation

[0238] 1.1 Single Feature Correlation Measurement Based on Correlation Coefficient

[0239] Step 1.1) An original correlation coefficient value between each of the original input features and the DXN emission concentration is calculated. For example, an original correlation coefficient value between a p-th input feature (x.sup.p.sup.i).sub.i={(x.sub.n.sup.p.sup.i).sub.i}.sub.n=1.sup.N of the i-th sub-process and the DXN emission concentration is calculated according to

[00086]$\begin{array}{cc}{\left({}_{\mathrm{corr\_ori}}^{p_i}\right)}_i=\frac{\underset{n=1}{\overset{N}{.Math.}}.Math.\left[\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right).Math.\left(y_n-\stackrel{\_}{y}\right)\right]}{\sqrt{\underset{n=1}{\overset{N}{.Math.}}.Math.{\left({\left(x_n^{p_i}\right)}_i-{\stackrel{\_}{x}}_{p_i}\right)}^2}.Math.\sqrt{\underset{n=1}{\overset{N}{.Math.}}.Math.{\left(y_n-\stackrel{\_}{y}\right)}^2}}& \left(4\right)\end{array}$ [0240] where x.sub.p.sub.i represents an average value of the p-th input feature of the i-th sub-process; and y represents an average value of N modeling samples of the DXN emission concentration.

[0241] Step 1.2) The original correlation coefficient value (.sub.corr_ori.sup.p.sup.i).sub.i is preprocessed as follows:

(.sub.corr.sup.p.sup.i).sub.i=|(.sub.corr_ori.sup.p.sup.i).sub.i|(5) [0242] where || represents an absolute value.

[0243] Step 1.3) Steps (1.1)-(1.2) are repeated for respective original input features until correlation coefficients for all of the original input features are obtained and recorded as {.sub.corr.sup.p.sup.i}.sub.P.sub.i.sub.=1.sup.P.sup.i.

[0244] Step 1.4) A weight factor of the i-th sub-process is set as f.sub.i.sup.corr. A threshold .sub.i.sup.corr configured to select input features based on the correlation coefficients is calculated according to:

[00087]$\begin{array}{cc}{}_i^{\mathrm{corr}}=f_i^{\mathrm{corr}}.Math.\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{p_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,& \left(6\right)\end{array}$ [0245] where a maximum value (f.sub.i.sup.corr).sub.max and a minimum value (f.sub.i.sup.corr).sub.min of f.sub.i.sup.corr are calculated according to Equation (7):

[00088]$\begin{array}{cc}\{\begin{array}{c}{\left(f_i^{\mathrm{corr}}\right)}_{\max }=\frac{\max \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\\ {\left(f_i^{\mathrm{corr}}\right)}_{\min }=\frac{\min \left({\left({}_{\mathrm{corr}}^1\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{p_i}\right)}_i,\mathrm{.Math.}.Math.,{\left({}_{\mathrm{corr}}^{P_i}\right)}_i\right)}{\frac{1}{p_i}.Math.\underset{p_i=1}{\overset{P_i}{.Math.}}.Math..Math.{\left({}_{\mathrm{corr}}^{p_i}\right)}_i}\end{array},& \left(7\right)\end{array}$ [0246] where max() represents a function for finding a maximum value; and min() represents a function for finding a minimum value.