# Predicting Higher Heating Value of Sewage Sludges via Artificial Neural Network Based on Proximate and Ultimate Analyses

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Source of Sample

#### 2.2. Sample Preparation

#### 2.3. Sample Characterization

#### 2.4. Back Propagation Neural Network

_{ij}. The output yi was determined by the following equation:

_{i}is the input value of the i-th neuron and f(ξ

_{i}) is activation function.

_{r}is the measured value of output neurons.

_{i}is the fixed parameters in the (1, +∞).

#### 2.5. Statistical Analysis

^{2}) [37]. The equations of the relevant indexes are as follows:

_{i}is the measured value.

## 3. Results

#### 3.1. Proximate and Ultimate Analyses of Sewage Sludge

#### 3.2. Modeling Back Propagation Neural Network Model

^{2}, which means that the model had the highest accuracy. This may be because the data of the proximate and ultimate analysis represent the characteristics of sewage sludge, thus combining the data of both parts in building the model allows the model to predict HHV in a state that was closer to the nature of sewage sludge itself and therefore, the prediction accuracy of the model was the highest. In this study, the proximate and ultimate analyses data of sewage sludge were used as input parameters. Kolmogorov’s theorem has theoretically proved that a three-layer neural network can approximate any continuous function with arbitrary accuracy, thus a three-layer network structure was chosen for this study. A simple diagram for the model structure established in this study is shown in Figure 4.

^{−3}, 10

^{−3}, 10

^{−4}, 10

^{−5}and 10

^{−6}were selected for comparison, as shown in Figure 7. It could be seen that the R

^{2}was the same for the target error level of 10

^{−5}and 10

^{−6}, but the latter was more computationally intensive; therefore, the optimal target error level was considered to be 10

^{−5}.

## 4. Discussion

^{2}of the BPNN model in both the training (0.979) and test (0.975) groups were quite high and the corresponding values of MSE (0.161), RMSE (0.401), MAD (0.319) and MAPM (3.260) were small, which indicated that the BPNN model had a high accuracy. Furthermore, it can be observed that the differences between the training and test groups for each of the indexes were small, which reflected the high reliability of the BPNN model. Gülce Çakman et al. [33] constructed an ANN model based on the Levenberg–Marquardt algorithm to predict the HHV of biochar, with R

^{2}of 0.99 for both the training and test groups. Amir Dashti et al. [42] built four different ANN models, where the ANFIS model with a BP algorithm had an R

^{2}of 0.97 for both training and test groups, which was similar to the current study. This indicates that the BPNN model had a high accuracy and can be used to predict the HHV of sewage sludge.

^{2}(0.975). The reason for the superiority of the BPNN model over the other models may be that most of the models were modeled only based on the proximate or ultimate analysis, which would exclude some of the factors related to HHV and thus lead to poor prediction accuracy. Additionally, there was an irrelevance between the proximate and ultimate analysis of sewage sludge and its HHV and the linear model was not usable as the best option for predicting the HHV of sewage sludge. After checking other statistical results (MSE, RMSE, MAD and MAPE), it was further shown that the accuracy of the BPNN model was higher than other models. This was because the BPNN model had the lowest index for all the indicators (MSE = 0.198, RMSE = 0.444, MAD = 0.385 and MAPE = 4.081). This study clearly shows that the developed BPNN model was most suitable for predicting the HHV of sewage sludge.

## 5. Conclusions

^{2}of MSE, RMSE, MAD and MAPE were 0.209, 0.457, 0.375, 4.651 and 0.975, respectively. Several previously proposed empirical models were selected for comparison with the BPNN model. The results show that the BPNN model predicts an HHV (MAD = 0.385, MAPE = 4.081 and R

^{2}= 0.975) more accurately than the other models. The results of this study show that the non-linear model built by an artificial neural network can replace the oxygen bomb calorimeter to measure the HHV of sewage sludge and provide a more convenient option for subsequent methods of recovering energy from sewage sludge (pyrolysis, anaerobic digestion, etc.). In the future, we will expand the database by collecting different types of sewage sludge and explore the performance of other ANN models in predicting sewage sludge HHV to find the most suitable model.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Correlation between HHV and proximate analysis data: (

**a**) indicates the correlation between moisture and HHV; (

**b**) indicates the correlation between ash and HHV; (

**c**) indicates the correlation between VM and HHV; (

**d**) indicates the correlation between FC and HHV.

**Figure 3.**Correlation between HHV and ultimate analysis data: (

**a**) indicates the correlation between carbon and HHV; (

**b**) indicates the correlation between hydrogen and HHV; (

**c**) indicates the correlation between oxygen and HHV; (

**d**) indicates the correlation between nitrogen and HHV; (

**e**) indicates the correlation between sulfur and HHV.

**Figure 5.**Performance comparison with different hidden layers: (

**a**) indicates the situation where the learning rate is 0.01; (

**b**) indicates the situation where the learning rate is 0.10; (

**c**) indicates the situation where the learning rate is 0.15; (

**d**) indicates the situation where the learning rate is 0.20.

**Figure 6.**Performance of the network with different hidden layers: (

**a**) indicates the situation where the hidden layers are 12; (

**b**) indicates the situation where the hidden layers are 13.

**Figure 7.**Network simulation results with different target error level: (

**a**) indicates the situation where the target error level is 5 × 10

^{−3}; (

**b**) indicates the situation where the target error level is 10

^{−3}; (

**c**) indicates the situation where the target error level is 10

^{−4}; (

**d**) indicates the situation where the target error level is 10

^{−5}; (

**e**) indicates the situation where the target error level is 10

^{−6}.

**Figure 8.**Comparison of predicted HHV and experimental HHV: (

**a**) training group data; (

**b**) testing group data; (

**c**) all data.

**Table 1.**Characteristics of sewage sludge from different wastewater treatment plants (average for each source).

Sample | Source City | HHV (MJ/kg) | Proximate Analysis | Ultimate Analysis | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

M_{ad}(%) | Ash_{d}(%) | VM_{d}(%) | FC_{d} ^{1}(%) | C_{daf}(%) | H_{daf}(%) | O_{daf} ^{1}(%) | N_{daf}(%) | S_{daf}(%) | |||

A1 | Xuzhou | 12.794 | 1.50 | 33.81 | 58.07 | 8.12 | 46.50 | 9.49 | 35.40 | 7.46 | 0.37 |

A2 | Suqian | 5.328 | 2.66 | 61.95 | 29.38 | 8.67 | 36.08 | 9.63 | 37.23 | 11.84 | 0.77 |

A3 | Suqian | 7.743 | 2.37 | 51.42 | 42.00 | 6.59 | 40.98 | 8.52 | 37.48 | 9.91 | 0.54 |

A4 | Lianyungang | 12.020 | 2.92 | 36.77 | 55.73 | 7.50 | 45.60 | 10.16 | 34.11 | 7.94 | 0.44 |

A5 | Lianyungang | 12.260 | 1.37 | 35.89 | 55.76 | 8.34 | 47.89 | 8.23 | 35.16 | 7.57 | 0.37 |

A6 | Yancheng | 7.416 | 2.49 | 49.53 | 42.56 | 7.91 | 37.71 | 9.65 | 40.15 | 9.48 | 0.50 |

A7 | Huaian | 7.661 | 2.63 | 49.11 | 42.06 | 8.83 | 35.41 | 10.50 | 41.15 | 9.76 | 0.58 |

A8 | Huaian | 5.852 | 2.26 | 60.16 | 33.35 | 6.49 | 40.23 | 8.44 | 33.91 | 13.35 | 0.58 |

B1 | Taizhou | 8.011 | 3.06 | 49.52 | 41.78 | 8.71 | 39.46 | 10.38 | 36.55 | 9.99 | 0.52 |

B2 | Yangzhou | 8.372 | 1.79 | 45.72 | 45.72 | 8.56 | 40.33 | 9.62 | 39.41 | 8.63 | 0.47 |

B3 | Zhenjiang | 14.800 | 2.47 | 24.71 | 67.16 | 8.13 | 43.35 | 10.22 | 38.31 | 6.91 | 0.37 |

B4 | Zhenjiang | 7.155 | 2.72 | 57.67 | 36.29 | 6.04 | 36.83 | 11.57 | 35.89 | 11.23 | 0.66 |

B5 | Nantong | 9.281 | 2.78 | 47.93 | 43.92 | 8.15 | 45.08 | 9.59 | 32.64 | 9.49 | 0.57 |

B6 | Nantong | 7.718 | 2.76 | 56.37 | 36.90 | 6.73 | 47.74 | 8.88 | 25.53 | 13.60 | 0.57 |

C1 | Nanjing | 10.213 | 2.81 | 44.04 | 46.90 | 9.06 | 42.10 | 10.05 | 34.60 | 10.42 | 0.55 |

C2 | Changzhou | 11.230 | 1.77 | 41.13 | 50.89 | 7.99 | 45.70 | 10.74 | 33.11 | 8.78 | 0.41 |

C3 | Wuxi | 9.794 | 2.17 | 47.02 | 44.77 | 8.21 | 43.74 | 9.42 | 33.76 | 10.61 | 0.50 |

C4 | Wuxi | 10.935 | 2.59 | 41.37 | 49.77 | 8.86 | 41.50 | 10.44 | 37.26 | 8.45 | 0.48 |

C5 | Suzhou | 14.005 | 2.12 | 27.89 | 62.61 | 9.50 | 49.68 | 8.21 | 30.78 | 9.86 | 0.63 |

C6 | Suzhou | 15.069 | 2.81 | 24.39 | 66.44 | 9.17 | 44.18 | 10.52 | 33.40 | 9.98 | 0.98 |

_{d}Drying base;

_{ad}Air-drying base;

_{daf}Dry ash-free base;

^{1}Obtained by the “difference-subtraction method”.

Sample | Clustering Categories | Distance | Sample | Clustering Categories | Distance |
---|---|---|---|---|---|

A1 | 1 | 4.580 | B2 | 3 | 3.385 |

C5 | 1 | 6.443 | C3 | 3 | 4.079 |

A5 | 1 | 7.884 | C1 | 3 | 4.240 |

A4 | 1 | 8.364 | B1 | 3 | 4.841 |

C6 | 1 | 8.989 | B5 | 3 | 5.813 |

B3 | 1 | 9.979 | A3 | 3 | 6.256 |

A8 | 2 | 2.250 | A6 | 3 | 6.473 |

B4 | 2 | 5.740 | C4 | 3 | 7.512 |

A2 | 2 | 8.260 | A7 | 3 | 8.462 |

B6 | 2 | 11.549 | C2 | 3 | 10.181 |

Different Sizes of Data | MSE | RMSE | MAD | MAPE | R^{2} |
---|---|---|---|---|---|

Train | 0.161 | 0.401 | 0.319 | 3.260 | 0.979 |

Test | 0.209 | 0.457 | 0.375 | 4.651 | 0.975 |

All | 0.198 | 0.444 | 0.385 | 4.081 | 0.975 |

Input Parameters | Equation | Reference |
---|---|---|

Proximate analysis (FC, VM, Ash) | HHV = 353.6FC + 155.9VM − 7.8Ash | Jigisha Parikh et al. [44] |

HHV = 255.75VM + 283.88FC − 2386.38 | Puchong Thipkhunthod et al. [27] | |

Ultimate analysis (C, H, O, N, S) | HHV = 430.2C − 186.7H−127.4N + 178.6S + 184.2O − 2379.9 | Puchong Thipkhunthod et al. [27] |

HHV = 349.1C + 1178.3H + 100.5S − 103.4O − 15.1N − 21.1Ash | S. A. Channiwala et al. [45] |

Models | MSE | RMSE | MAD | MAPE | R^{2} |
---|---|---|---|---|---|

Jigisha Parikh et al. [44] | 2.262 | 1.504 | 1.188 | 15.546 | 0.722 |

Puchong Thipkhunthod et al. [27] | 5.161 | 2.272 | 2.198 | 24.574 | 0.365 |

Puchong Thipkhunthod et al. [27] | 1.588 | 1.178 | 1.104 | 11.862 | 0.797 |

S. A. Channiwala et al. [45] | 2.591 | 1.610 | 1.531 | 15.743 | 0.688 |

The BPNN model in this study | 0.198 | 0.444 | 0.385 | 4.081 | 0.975 |

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## Share and Cite

**MDPI and ACS Style**

Yang, X.; Li, H.; Wang, Y.; Qu, L.
Predicting Higher Heating Value of Sewage Sludges via Artificial Neural Network Based on Proximate and Ultimate Analyses. *Water* **2023**, *15*, 674.
https://doi.org/10.3390/w15040674

**AMA Style**

Yang X, Li H, Wang Y, Qu L.
Predicting Higher Heating Value of Sewage Sludges via Artificial Neural Network Based on Proximate and Ultimate Analyses. *Water*. 2023; 15(4):674.
https://doi.org/10.3390/w15040674

**Chicago/Turabian Style**

Yang, Xuanyao, He Li, Yizhuo Wang, and Linyan Qu.
2023. "Predicting Higher Heating Value of Sewage Sludges via Artificial Neural Network Based on Proximate and Ultimate Analyses" *Water* 15, no. 4: 674.
https://doi.org/10.3390/w15040674