CO emission predictions in municipal solid waste incineration based on reduced depth features and long short-term memory optimization

Abstract

Carbon monoxide (CO) is a toxic gas emitted during municipal solid waste incineration (MSWI). Its emission prediction is conducive to pollutant reduction and optimized control of MSWI. The variables of MSWI exhibit redundant and interdependent correlations with CO emissions. Furthermore, the mapping relationship is difficult to characterize. Therefore, the work proposed a CO emission prediction method based on reduced depth features and long short-term memory (LSTM) optimization. The particle design for reduced depth feature and LSTM optimization was initially developed—incorporating an adaptive threshold range for feature selection based on the inherent characteristics of modeling data. Secondly, the nonlinear depth features were extracted using ultra-one-dimensional convolution and subsequently fed into an LSTM model for prediction construction. The hyperparameters of the convolutional layer and LSTM were updated based on the loss function. The generalization performance of the model was used as the fitness function of the optimization. Finally, the particle swarm optimization (PSO) was used to adaptively reduce depth features and model’s hyperparameters. The rationality and effectiveness of the proposed method were validated using the benchmark dataset and CO dataset of MSWI. R² of the testing datasets for RB and CO were 0.9097 ± 3.64E-04 and 0.7636 ± 3.19E-03, respectively, by repeating 30 times.

Appendices

Appendix A

Calculation process for the LSTM model

$N = 1$ and ${\mathbf{h}}_{n - 1} = 0$ at the initial sample calculation. The specific process is shown as follows:

(1) The empty set ${\mathbf{C}}_{n}$ is the memory unit. Forget gate ${\mathbf{f}}_{n}$ determines the output ratio of the sample on ${\mathbf{C}}_{n}$ to the input.

$$ {\mathbf{F}}_{n} = {\mathbf{f}}_{n} \odot {\mathbf{C}}_{n} $$

(35)

$$ {\mathbf{f}}_{n} = \sigma \left( {{\mathbf{U}}_{{\text{f}}}^{{}} \cdot {\mathbf{h}}_{n - 1} + {\mathbf{W}}_{{\text{f}}}^{{}} \cdot {\mathbf{X}}_{n}^{{{\text{exa}}}} + {\mathbf{b}}_{{\text{f}}}^{{}} } \right) $$

(36)

where ${\mathbf{U}}_{{\text{f}}}$ and ${\mathbf{W}}_{{\text{f}}}$ are the weight of ${\mathbf{h}}_{n - 1}$ and ${\mathbf{X}}_{n}^{{{\text{exa}}}}$, respectively; ${\mathbf{b}}_{{\text{f}}}$ is the bias; $\sigma \left( \cdot \right)$ is the sigmoid activation function; $\odot$ is the Hadamard product.

(2) ${\tilde{\mathbf{C}}}_{n}$ is the candidate value for calculating the current input state.

$$ {\tilde{\mathbf{C}}}_{n} = {\text{tanh}}\left( {{\mathbf{U}}_{{\text{c}}}^{{}} \cdot {\mathbf{h}}_{n - 1} + {\mathbf{W}}_{{\text{c}}}^{{}} \cdot {\mathbf{X}}_{n}^{{{\text{exa}}}} + {\mathbf{b}}_{{\text{c}}}^{{}} } \right) $$

(37)

where ${\mathbf{U}}_{{\text{c}}}$ and ${\mathbf{W}}_{{\mathbf{c}}}$ are the weight of ${\mathbf{h}}_{n - 1}$ and ${\mathbf{X}}_{n}^{{{\text{exa}}}}$, respectively; ${\mathbf{b}}_{{\mathbf{c}}}$ is the bias; $\tanh \left( \cdot \right)$ is the tanh activation function.

(3) Input gate ${\mathbf{i}}_{n}$ controls the proportion of the nth sample input stored to ${\mathbf{C}}_{n}$.

$$ {\mathbf{i}}_{n} = \sigma \left( {{\mathbf{U}}_{{\text{i}}}^{{}} \cdot {\mathbf{h}}_{n - 1} + {\mathbf{W}}_{{\text{i}}}^{{}} \cdot {\mathbf{X}}_{n}^{{{\text{exa}}}} + {\mathbf{b}}_{{\text{i}}}^{{}} } \right) $$

(38)

$$ {\mathbf{I}}_{n} = {\mathbf{i}}_{n} \odot {\tilde{\mathbf{C}}}_{n} $$

(39)

where ${\mathbf{U}}_{{\text{i}}}$ and ${\mathbf{W}}_{{\text{i}}}$ are the weight of ${\mathbf{h}}_{n - 1}$ and ${\mathbf{X}}_{n}^{{{\text{exa}}}}$, respectively; ${\mathbf{b}}_{{\text{i}}}$ is bias.

(4) The resulting value is stored in ${\mathbf{C}}_{n}$.

$$ {\mathbf{C}}_{n} = {\mathbf{F}}_{n} + {\mathbf{I}}_{n} $$

(40)

The first sample output ${\mathbf{C}}_{n}$ is ${\mathbf{I}}_{n}$, i.e., ${\mathbf{C}}_{n} = {\mathbf{I}}_{n} ,{\mathbf{F}}_{n} = 0$.

(5) The nth sample ${\mathbf{h}}_{n}$ and the proportion of ${\mathbf{o}}_{n}$ stored in output gate control ${\mathbf{C}}_{n}$ are calculated.

$$ {\mathbf{h}}_{n} = {\mathbf{o}}_{n} \odot \tanh \left( {{\mathbf{C}}_{n} } \right) $$

(41)

$$ {\mathbf{o}}_{n} = \sigma \left( {{\mathbf{U}}_{{\text{o}}}^{{}} \cdot {\mathbf{h}}_{n - 1} + {\mathbf{W}}_{{\text{o}}}^{{}} \cdot {\mathbf{X}}_{n}^{{{\text{exa}}}} + {\mathbf{b}}_{{\text{o}}}^{{}} } \right) $$

(42)

where ${\mathbf{U}}_{{\text{o}}}$ and ${\mathbf{W}}_{{\text{o}}}$ are the weight of ${\mathbf{h}}_{n - 1}$ and ${\mathbf{X}}_{n}^{{{\text{exa}}}}$, respectively; ${\mathbf{b}}_{{\text{o}}}$ is the bias.

(6) The output of the nth sample is calculated as $\hat{y}^{\prime}_{n}$.

$$ \hat{y}^{\prime}_{n} = \sigma \left( {{\mathbf{W}}_{{{\text{out}}}}^{{}} \cdot {\mathbf{h}}_{n} } \right) = \sigma \left( {\hat{y}^{\prime\prime}_{n} } \right) $$

(43)

where ${\mathbf{W}}_{{{\text{out}}}}$ is the weight corresponding to the implied layer.

The process is the same for the remaining sample input. Output ${\mathbf{\hat{y}^{\prime}}}$ is denoted by

$$ {\mathbf{\hat{y}^{\prime}}} = \left\{ {\hat{y}^{\prime}_{n} ,\hat{y}^{\prime}_{n + 1} , \cdots ,\hat{y}^{\prime}_{n + N - 1} } \right\} $$

(44)

Appendix B

Analysis of model hyperparameters

Univariate sensitivity analysis is performed for hyperparameters such as $\theta_{{{\text{MI}}}}$, $\theta_{{{\text{convlayers}}}}$, $\theta_{{{\text{Epochs}}}}$, $\theta_{{{\text{learningrate}}}}$, and $\theta_{{{\text{dropout}}}}$. That is, each time a single hyperparameter is changed, other values maintain the optimal values in the above model. Table 7 shows the intervals in the hyperparameters.

Table 7 Intervals for the hyperparameters of the MI-1DCNN-LSTM model

(1) MI threshold: The higher the $\theta_{{{\text{MI}}}}$, the fewer the selected feature variables. Figure 

Fig. 11

Relationship between $\theta_{{{\text{MI}}}}$ and R² for the MI-1DCNN-LSTM model

11 shows its relationship to R².

(1) RB dataset: The model performance is improved with gradually increased $\theta_{{{\text{MI}}}}$, and the number of corresponding input features decreases. Stability tends to transpire after reaching a certain value. Consequently, higher $\theta_{{{\text{MI}}}}$ is selected; (2) CO dataset: R² increases first and then decreases with increased $\theta_{{{\text{MI}}}}$. Adaptive $\theta_{{{\text{MI}}}}$ should be selected. There are differences in MI thresholds for different datasets.

(2) Convolutional layer number: The network will converge slowly or will not converge if $\theta_{{{\text{convlayers}}}}$ is small. The network will be stronger if $\theta_{{{\text{convlayers}}}}$ is large. Slow training speed and overfitting of the network model are easy to happen and impair the prediction effect. The number of convolutional layers should be selected according to the data characteristics. The upper limit is ten layers based on experience. Figure 

Fig. 12

Relationship between $\theta_{{{\text{convlayers}}}}$ and R² for MI-1DCNN-LSTM model

12 shows its relationship to R².

(1) RB dataset: The model performance increases with increased $\theta_{{{\text{convlayers}}}}$. However, a downward trend is found after reaching a certain value. (2) CO dataset: R² first decreases and then increases. Finally, it decreases with increased $\theta_{{{\text{convlayers}}}}$. Therefore, appropriate $\theta_{{{\text{convlayers}}}}$ should be chosen. Different datasets should choose the appropriate number of convolutional layers.

(3) Iteration number: Increasing $\theta_{{{\text{Epochs}}}}$ increases model’s weight updates and prediction accuracy. Figure 

Fig. 13

Relationship between $\theta_{{{\text{Epochs}}}}$ and R.² for MI-1DCNN-LSTM model

13a, b shows the results of setting iteration number in (50, 3000) and successive changes in units of 50. Figure 13c, d presents the results of setting iteration number in (50, 500) and successive changes in units of 5.

(1) RB dataset: Model performance merely improves with increased $\theta_{{{\text{Epochs}}}}$ within (50, 3000). R² increases within (50, 500)with performance degradation. Larger $\theta_{{{\text{Epochs}}}}$ should be selected to stabilize model performance. (2) CO dataset: Model performance is better with increased $\theta_{{{\text{Epochs}}}}$ within (50, 3000), and R² changes little. R² shows an upward trend within (50, 500), but there are some performance degradation points. Thus, appropriate $\theta_{{{\text{Epochs}}}}$ should be selected to stabilize model performance. There are differences in the iteration number requirements of different datasets.

(4) Learning rate: Suitable $\theta_{{{\text{learningrate}}}}$ can converge the objective function to a local minimum at a suitable time. The initial value of the learning rate of most networks should be 0.01 and 0.001. The range of the learning rate is (0.01, 0.1), and the step size is changed successively in 0.01 units. (Fig. 

Fig. 14

Relationship between $\theta_{{{\text{learningrate}}}}$ and R² for the MI-1DCNN-LSTM model

14a, b). The range is (0.001, 0.03), and the step size is changed successively in units of 0.001 (Fig. 14c, d).

(1) RB dataset: Model performance first increases with increased $\theta_{{{\text{learningrate}}}}$ and then decreases sharply within (0.01, 0.1). Stable $\theta_{{{\text{learningrate}}}}$ should be selected. Model performance increases and then decreases with increased $\theta_{{{\text{learningrate}}}}$ within (0.001, 0.03). Therefore, appropriate $\theta_{{{\text{learningrate}}}}$ should be selected. (2) CO dataset: Model performance decreases significantly with increased $\theta_{{{\text{learningrate}}}}$ within (0.01, 0.1), indicating that smaller $\theta_{{{\text{learningrate}}}}$ is suitable. R² fluctuates largely at the early and later stages within (0.001, 0.03); thus, smaller $\theta_{{{\text{learningrate}}}}$ should be selected. Different dataset’s $\theta_{{{\text{learningrate}}}}$ has different influence ranges on model performance. Consequently, suitable $\theta_{{{\text{learningrate}}}}$ should be selected.

(5) Dropout rate: It probably stop the activation values of certain neurons. The model is more generalized. $\theta_{{{\text{dropout}}}}$ is within (0.1,0.9) in the work, and Fig. 

Fig. 15

Relationship between $\theta_{{{\text{dropout}}}}$ and R² for MI-1DCNN-LSTM model

15 shows its relationship with R².

(1) RB dataset: Model performance first improves and then decreases with increased $\theta_{{{\text{dropout}}}}$. It fluctuates greatly after reaching a certain value, indicating that moderate $\theta_{{{\text{dropout}}}}$ should be selected;

(2) CO dataset: R² decreases with increased $\theta_{{{\text{dropout}}}}$; thus, smaller $\theta_{{{\text{dropout}}}}$ should be selected. Different datasets have different requirements for dropout rates.

In summary, distinct hyperparameters exhibit different performance for varying datasets. It is reasonable to use PSO for the global optimized selection of these hyperparameters.