# Prediction of WEEE Recycling in China Based on an Improved Grey Prediction Model

^{*}

## Abstract

**:**

## 1. Introduction

- According to the characteristics of the sample data, a non-linear grey Bernoulli model (NGBM (1,1)) is constructed, particle swarm optimization (PSO) is applied to optimize parameters, and the PSO-NGBM (1,1) model has higher prediction accuracy compared with the traditional grey prediction model (GM (1,1)), grey Verhulst model (GVM (1,1)), discrete grey prediction model (DGM (1,1)) and non-homogeneous grey prediction model (NGM (1,1,k));
- Using particle swarm optimization (PSO) to optimize the background value coefficient, it is verified that the PSO optimization algorithm is applicable for improving the prediction accuracy of various grey prediction models;
- The PSO-NGBM (1,1) model was used to forecast the WEEE recycling quantity and recycling value from 2021 to 2023, unlike previous studies, which showed an upward trend. The WEEE recycling quantity will show a slight decrease in the short term, and the recycling value will show a steady increase. This finding has implications for government policy formulation and enterprise optimization of development strategies in the context of COVID-19.

## 2. Literature Review

#### 2.1. Related Research on WEEE Recycling Prediction

#### 2.2. Grey Prediction Model and Its Optimization

_{2}emissions in China. Zhang et al. [48] proposed a fractional-order cumulative NGM (1,1,k) model based on optimal background values by optimizing the model parameters using the PSO algorithm. Hu [49] used a genetic algorithm to optimize the background value coefficients for a multivariate grey prediction model constructed for the bankruptcy prediction problem. Zhi et al. [50] proposed a method that combines a nonlinear grey Bernoulli model (NGBM (1,1)) with a genetic algorithm. Yuan et al. [51] combined an adaptive artificial fish swarm algorithm and metabolic method to select optimal parameters and established an optimized nonlinear grey Bernoulli model (AF-MNGBM (1,1)). Kong and Ma [52] simultaneously applied genetic algorithm (GA), particle swarm optimization algorithm (PSO), grey wolf optimization algorithm (GWO), and the novel ant-lion optimization algorithm (ALO) for a comparative study of the optimization effect of the parameters of the nonlinear grey Bernoulli model (NGBM (1,1)).

## 3. Methodology

#### 3.1. Nonlinear Grey Bernoulli Model (NGBM (1,1))

#### 3.2. Particle Swarm Optimization Algorithm (PSO)

#### 3.3. Improved Grey Prediction Model

## 4. Empirical Analysis

#### 4.1. Data

#### 4.2. Example Analysis

## 5. Result and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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Notation | Interpretation |
---|---|

$i$ | Particle number |

$d$ | Particle dimension number |

$k$ | Number of iterations |

$w$ | Inertia weight |

${c}_{1}$ | Individual learning factor |

${c}_{2}$ | Group learning factor |

${r}_{1}$,${r}_{2}$ | Random number in the interval [0,1] to increase the randomness of the search |

${V}_{id}^{k}$ | Velocity vector of particle $i$ in the $d$th dimension in the $k$th iteration |

${X}_{id}^{k}$ | Position vector of particle $i$ in the $d$th dimension in the $k$th iteration |

${P}_{best}^{k}$ | The optimal solution obtained by the search of the $i$th particle (individual) after the $k$th iteration |

${G}_{best}^{k}$ | The optimal solution in the whole particle population after the $k$th iteration |

Nomenclature | Parameter |
---|---|

Population size | 100 |

Number of iterations | 1000 |

$\mathrm{Inertia}\mathrm{weights}w$ | 1.0 |

$\mathrm{Random}\mathrm{number}{r}_{1},{r}_{2}$ | [0,1] |

$\mathrm{Learning}\mathrm{factor}{c}_{1}$ | 1.5 |

$\mathrm{Learning}\mathrm{factor}{c}_{2}$ | 1.5 |

$\mathrm{Range}\mathrm{for}r$ | (−1,1) |

$\mathrm{Range}\mathrm{for}p$ | (0,1) |

Year | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 |
---|---|---|---|---|---|---|---|---|---|

Recycling Quantity (10 thousand units) | 8264 | 11,430 | 13,583 | 15,274 | 16,055 | 16,370 | 16,550 | 17,100 | 16,600 |

Recycling Value (100 million yuan) | 57.2 | 69.8 | 78.4 | 78.3 | 94.4 | 125.1 | 133 | 128.7 | 135 |

Year | Recovery Quantity (10 Thousand Units) | GM (1,1) | GVM (1,1) | DGM (1,1) | NGM (1,1,k) | NGBM(1,1) | PSO-NGBM (1,1) |
---|---|---|---|---|---|---|---|

2012 | 8264 | 8264 | 8264 | 8264 | 8264 | 8264 | 8264 |

2013 | 11,430 | 12,604 | 5791 | 12,625 | 7878 | 10,540 | 11,430 |

2014 | 13,583 | 13,437 | 9048 | 12,876 | 11,730 | 13,264 | 13,635 |

2015 | 15,274 | 14,326 | 12,982 | 13,721 | 13,951 | 15,084 | 15,022 |

2016 | 16,055 | 15,273 | 16,518 | 14,622 | 15,230 | 16,198 | 15,889 |

2017 | 16,370 | 16,283 | 18,083 | 15,582 | 15,968 | 16,767 | 16,394 |

2018 | 16,550 | 17,360 | 16,808 | 16,605 | 16,393 | 16,920 | 16,635 |

MAE | 563.75 | 2182.5 | 818.69 | 1158.9 | 329.86 | 82.64 | |

RMSE | 714.43 | 2947.8 | 1001.1 | 1633 | 421.72 | 120.39 | |

MAPE (%) | 3.98% | 16.09% | 5.7% | 8.85% | 2.42% | 0.53% | |

2019 | 17,100 | 18,507 | 13,408 | 17,695 | 16,638 | 16,757 | 16,677 |

2020 | 16,600 | 19,731 | 9451 | 18,857 | 16,779 | 16,363 | 16,568 |

MAE | 2269 | 5420.5 | 1426 | 320.5 | 290 | 227.5 | |

RMSE | 2427.22 | 5689.42 | 1650.47 | 350.35 | 294.80 | 299.96 | |

MAPE (%) | 13.54% | 32.33% | 8.54% | 1.89% | 1.72% | 1.33% |

Year | Recovery Value (100 Million Yuan) | GM (1,1) | GVM (1,1) | DGM (1,1) | NGM (1,1,k) | NGBM (1,1) | PSO-NGBM (1,1) |
---|---|---|---|---|---|---|---|

2012 | 57.2 | 57.2 | 57.2 | 57.2 | 57.2 | 57.2 | 57.2 |

2013 | 69.8 | 72.89 | 28.67 | 73.23 | 55.89 | 58.43 | 68.29 |

2014 | 78.4 | 80.45 | 41.55 | 74.27 | 69.85 | 75.28 | 78.29 |

2015 | 78.3 | 88.78 | 58.54 | 81.91 | 82.81 | 89.97 | 87.77 |

2016 | 94.4 | 97.98 | 79.28 | 90.33 | 94.85 | 102.7 | 97.33 |

2017 | 125.1 | 108.13 | 101.8 | 99.62 | 106.03 | 113.68 | 107.23 |

2018 | 133 | 119.34 | 122.15 | 109.86 | 116.42 | 123.05 | 117.64 |

2019 | 128.7 | 131.7 | 135.19 | 121.16 | 126.07 | 130.98 | 128.67 |

2020 | 135 | 145.35 | 136.87 | 133.6181 | 135.03 | 137.59 | 140.41 |

MAE | 7.02 | 17.26 | 8.09 | 7.3 | 6.75 | 5.85 | |

RMSE | 8.99 | 22.05 | 12.03 | 10.18 | 8.07 | 8.72 | |

MAPE (%) | 6.45% | 20.04% | 7.08% | 7.43% | 7.14% | 5.26% |

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**MDPI and ACS Style**

Xiao, Q.; Wang, H.
Prediction of WEEE Recycling in China Based on an Improved Grey Prediction Model. *Sustainability* **2022**, *14*, 6789.
https://doi.org/10.3390/su14116789

**AMA Style**

Xiao Q, Wang H.
Prediction of WEEE Recycling in China Based on an Improved Grey Prediction Model. *Sustainability*. 2022; 14(11):6789.
https://doi.org/10.3390/su14116789

**Chicago/Turabian Style**

Xiao, Qiang, and Hongshuang Wang.
2022. "Prediction of WEEE Recycling in China Based on an Improved Grey Prediction Model" *Sustainability* 14, no. 11: 6789.
https://doi.org/10.3390/su14116789