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PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.

The grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.

The introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.

With high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.

This is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

The purpose of this study is to make a prediction of China's energy consumption structure from the perspective of compositional data and construct a novel grey model for forecasting compositional data.

Due to the existing grey prediction model based on compositional data cannot effectively excavate the evolution law of correlation dimension sequence of compositional data. Thus, the adaptive discrete grey prediction model with innovation term based on compositional data is proposed to forecast the integral structure of China's energy consumption. The prediction results from the new model are then compared with three existing approaches and the comparison results indicate that the proposed model generally outperforms existing methods. A further prediction of China's energy consumption structure is conducted into a future horizon from 2021 to 2035 by using the model.

China's energy structure will change significantly in the medium and long term and China's energy consumption structure can reach the long-term goal. Besides, the proposed model can better mine and predict the development trend of single time series after the transformation of compositional data.

The paper considers the dynamic change of grey action quantity, the characteristics of compositional data and the impact of new information about the system itself on the current system development trend and proposes a novel adaptive discrete grey prediction model with innovation term based on compositional data, which fills the gap in previous studies.

In order to accurately forecast nonlinear and complex characteristics of solar power generation in China, a novel discrete grey model with time-delayed power term (abbreviated as TDDGM(1,1,tα) is proposed in this paper.

Firstly, the time response function is deduced by using mathematical induction, which overcomes the defects of the traditional grey model. Then, the genetic algorithm is employed to determine the optimal nonlinear parameter to improve the flexibility and adaptability of the model. Finally, two real cases of installed solar capacity forecasting are given to verify the proposed model, showing its remarkable superiority over seven existing grey models.

Given the reliability and superiority of the model, the model TDDGM(1,1,tα) is applied to forecast the development trend of China's solar power generation in the coming years. The results show that the proposed model has higher prediction accuracy than the comparison models.

This paper provides a scientific and efficient method for forecasting solar power generation in China with nonlinear and complex characteristics. The forecast results can provide data support for government departments to formulate solar industry development policies.

The main contribution of this paper is to propose a novel discrete grey model with time-delayed power term, which can handle nonlinear and complex time series more effectively. In addition, the genetic algorithm is employed to search for optimal parameters, which improves the prediction accuracy of the model.