Fractional grey model based on non-singular exponential kernel and its application in the prediction of electronic waste precious metal content.

Precious metal recovery is the main economic power of electronic waste (e-waste) recovery. The prediction of e-waste and its precious metal content is of great significance to the realisation of China's circular economy. In this work, the generation mechanism of e-waste is firstly deduced to determine model characteristics suitable for its prediction. Fractional derivative grey models base on a weak singular power kernel function (PFGM(q,1)) and a non-singular exponential kernel function (EFGM(q,1)) are established. Compared with the PFGM(q,1), the EFGM(q,1) has the advantages of simpler solution, lower calculation complexity and wider scope of application. Next, some data are selected to verify the validity. The EFGM(q,1) is used to predict mobile phone, laptop, desktop and television waste, and the weight of printed circuit boards (PCBs) in the waste and content of precious metals in these PCBs are calculated. Finally, the trend of e-waste and its precious metal contents are analysed and discussed based on the calculation results.

[1]  Deepali Sinha Khetriwal,et al.  Regional E-waste Monitor: East and Southeast Asia , 2016 .

[2]  Callie W. Babbitt,et al.  Forecasting electronic waste flows for effective circular economy planning , 2019 .

[3]  Xinping Xiao,et al.  A novel fractional grey system model and its application , 2016 .

[4]  Alessandra Magrini,et al.  A model for estimation of potential generation of waste electrical and electronic equipment in Brazil. , 2012, Waste management.

[5]  Xianpeng Wang,et al.  Grey-Lotka-Volterra model for the competition and cooperation between third-party online payment systems and online banking in China , 2020, Appl. Soft Comput..

[6]  R. Qiu,et al.  Recovering full metallic resources from waste printed circuit boards: A refined review , 2020 .

[7]  Chang Wang,et al.  The present and future availability of high-tech minerals in waste mobile phones: Evidence from China , 2018, Journal of Cleaner Production.

[8]  Yingjie Yang,et al.  Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China , 2018 .

[9]  Sifeng Liu,et al.  Grey system model with the fractional order accumulation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[10]  Jun Nakatani,et al.  Time-series product and substance flow analyses of end-of-life electrical and electronic equipment in China. , 2014, Waste management.

[11]  E. Pindza,et al.  Grey Lotka–Volterra models with application to cryptocurrencies adoption , 2019, Chaos, Solitons & Fractals.

[12]  Bert Bras,et al.  Modeling obsolete computer stock under regional data constraints: An Atlanta case study , 2007 .

[13]  Anjian Wang,et al.  Dynamic material flow analysis of zinc resources in China , 2013 .

[14]  Dingyu Xue,et al.  Continuous fractional-order grey model and electricity prediction research based on the observation error feedback , 2016 .

[15]  C. Duan,et al.  Metals recovery from dust derived from recycling line of waste printed circuit boards , 2017 .

[16]  Britt-Marie Steenari,et al.  Analysis of the metal content of small-size Waste Electric and Electronic Equipment (WEEE) printed circuit boards—part 1: Internet routers, mobile phones and smartphones , 2017, Resources, Conservation and Recycling.

[17]  He Xu,et al.  Survey and analysis of consumers' behaviour of waste mobile phone recycling in China , 2014 .

[18]  F. Beolchini,et al.  An innovative biotechnology for metal recovery from printed circuit boards , 2020 .

[19]  M. Caputo,et al.  A new Definition of Fractional Derivative without Singular Kernel , 2015 .

[20]  Hardi Mohammed,et al.  A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design , 2020, Neural Computing and Applications.

[21]  Emmanouil Stiakakis,et al.  Estimation of computer waste quantities using forecasting techniques , 2016 .

[22]  Yaoguo Dang,et al.  Using a self-adaptive grey fractional weighted model to forecast Jiangsu’s electricity consumption in China , 2020 .

[23]  Nannan Ma,et al.  Optimize production allocation for the oil-gas field basing on a novel grey model , 2019, Journal of Natural Gas Geoscience.

[24]  Wenqing Wu,et al.  The conformable fractional grey system model. , 2018, ISA transactions.

[26]  Dingyu Xue,et al.  An actual load forecasting methodology by interval grey modeling based on the fractional calculus. , 2017, ISA transactions.

[27]  Qiang Wang,et al.  Forecasting U.S. shale gas monthly production using a hybrid ARIMA and metabolic nonlinear grey model , 2018, Energy.

[28]  C. Fitzpatrick,et al.  Future E-waste Scenarios , 2019 .

[29]  Xin Ma,et al.  A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China , 2019, Energy.

[30]  Huiming Duan,et al.  A novel car-following inertia gray model and its application in forecasting short-term traffic flow , 2020 .

[31]  Wenqing Wu,et al.  Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption , 2018, Energy.

[32]  Takashi Kameya,et al.  A preliminary categorization of end-of-life electrical and electronic equipment as secondary metal resources. , 2011, Waste management.

[33]  Surendra M. Gupta,et al.  Estimation of electronic waste using optimized multivariate grey models. , 2019, Waste management.

[34]  Yong Wang,et al.  The novel fractional discrete multivariate grey system model and its applications , 2019, Applied Mathematical Modelling.

[35]  Jianxin Yang,et al.  Estimation of retired mobile phones generation in China: A comparative study on methodology. , 2015, Waste management.

[36]  T. Moyo,et al.  Assessing alternative pre-treatment methods to promote metal recovery in the leaching of printed circuit boards , 2020 .

[37]  Yong Geng,et al.  An overview of e-waste management in China , 2015 .

[38]  Miloš Polák,et al.  Estimation of end of life mobile phones generation: the case study of the Czech Republic. , 2012, Waste management.

[39]  Zhao Min,et al.  Prediction and Analysis of WEEE in China Based on the Gray Model , 2016 .