### 1. Introduction

### 2. Establishment of Comprehensive Evaluation Index System of Thermal Power Plants Cleaner Production

### 3. Comprehensive Evaluation Model of Cleaner Production Based on AHP and LSSVM Optimized by GS

### 3.1. AHP

### 3.2. LSSVM

*x*

*,*

_{k}*y*

*) |*

_{k}*k*= 1,2,...,

*n*}, in which

*x*

*∈*

_{k}*R*

*is the input data, and*

^{n}*y*

*∈*

_{k}*R*

*is the output data.*

^{n}*ϕ*(•) is the nonlinear mapping function which transfers the samples into much higher dimensional feature space

*φ*(

*x*

*). Thus, the optimal decision function is established in the high-dimensional feature space [11]:*

_{k}*x*

*,*

_{i}*y*

*}(*

_{i}*i*= 1,2, ···,

*N*), the optimization problem of LSSVM can be defined as Eq. (2):

##### (2)

$$\underset{\omega ,b,e}{\text{min}}(\omega ,e)=\frac{1}{2}{\omega}^{T}\omega +\frac{1}{2}C\sum _{i=1}^{n}{\xi}_{i}^{2}$$*ω*equals

*n*-dimensional weight vector;

*ξ*

*represents the training error;*

_{i}*C*> 0 is the regularization parameter that makes a balance between the training error and model complexity.

*σ*

^{2}is the kernel width.

*C*is associated with tolerable error. The larger

*C*allows smaller errors. In addition, the kernel width

*σ*is related to the input spatial extent or width of learning samples. The larger the sample input space is, the greater the values are.

### 3.3. Parameter Optimization Based on GS

#### 3.3.1. Cross validation (CV)

*K*-1 subsets are used as training sets, therefore

*K*models can be obtained. Here, the average of classification precision derived from

*K*validation sets is regarded as the classifier performance, wherein

*K*≥ 2 and

*K*starts from 3 actually. Only when the number of original data is small,

*K*= 2. K-CV can effectively address the problems of over-learning or less-learning and obtain convincing results.

#### 3.3.2. GS

### 3.4. Approaches of Comprehensive Evaluation Model

Collect the data of the established index system from five thermal power plants and apply dimensionless processing to them.

Calculate the weights of the indexes based on AHP. The judgment matrixes are obtained through expert scoring method and consistency check is carried out here to test the rationality.

Measure the comprehensive evaluation values of cleaner production of each thermal power plants on the foundation of processed results above.

15 samples are selected as a training set, and the remaining data of 10 samples are used as a test set. The radial basis function (RBF) is exploited as the kernel function in this paper. Simultaneously, the determination of these two parameters, regularization parameter

*C*and the kernel width*σ*is generally based on GS and CV.

_{2}

*C*and log

_{2}

*σ*into a few grids, as well as all samples into

*k*groups by cross validation.

*C*and

*σ*are fixed on the grid, afterwards

*k*–1 groups, namely training samples are taken into the proposed approach to achieve the optimal evaluation model. Mean square errors (MSE) of

*n*samples are calculated as follows:

*ŷ*

*and*

_{i}*y*

*are the actual and forecasted evaluation results, respectively.*

_{i}### 4. Case Study

### 4.1. Calculation of Index Weights

### 4.2. Calculation of Sample Output Value

##### (6)

$${y}_{i}=\frac{\text{max\hspace{0.17em}}{x}_{i}+\text{min\hspace{0.17em}}{x}_{i}-{x}_{i}}{\text{max\hspace{0.17em}}{x}_{i}}$$*E*equals the expected output value,

*s*represents the score of each index and

*w*is the weight. The final 25 expected output values are presented in Table2.

### 4.3. Training of Comprehensive Evaluation Model

#### 4.3.1. Parameter optimization

_{2}

*C*and log

_{2}

*σ*is [−10, 10], and mesh width is set to 0.4. Five-fold cross validation is implemented on the training samples. The results are illustrated in the contour map and 3D view plot of GS, which are, respectively shown in Fig. 1 and Fig. 2.

*C*and kernel width parameter

*σ*are 3.0314 and 0.0272, respectively. Correspondingly, MSE of cross-validation equals 0.0027.

#### 4.3.2. Training results of comprehensive evaluation model

*C**, σ* and training samples are taken into LSSVM model so that the trained evaluation model is obtained. To examine the performance of this approach, the RE and the mean absolute percentage error (MAPE) are proposed to measure the evaluation accuracy. The formulas are defined as follows:

*y*

*and*

_{i}*ŷ*

*represent the expected output and evaluation result, respectively.*

_{i}### 4.4. Test and Analysis of Results

*C*= 20,

*σ*= 5. The test results are shown in Table 4.