The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.

A non-resonant piezoelectric sensor for measuring power-frequency (50 Hz or 60 Hz) electric currents is proposed to be applied in electric power systems. The device consists of a magnetic circuit, two piezoelectric plates, and fixed plates. The magnetic circuit is made up of three NdFeB magnets and two permalloy yokes. The high sensitivity of the device is attributed to the magnetic field concentration and the induced shear stresses. A prototype has been fabricated and the feasibility of the self-powered sensor was validated. The average sensitivity reaches 28.56 mV/A in the range of 1 A to 10 A, and the accuracy is 0.02089 mV at a current of 3.5 A. A current variation of 0.02 A is distinguished under the non-resonant condition of 50 Hz. The self-powered, highly sensitive, non-resonant, and high-resolution characteristics make the device favorable for measuring real-time electric currents in electric power systems.

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The living energy consumption of residents has become an important technical index to promote the economic and social development strategy. The country’s medium- and short-term living energy consumption is featured with both a certainty of annual increment and an uncertainty of random variation. Thus, it can be seen as a typical grey system and shall be suitable for the grey prediction model. In order to explore the future development trend of China’s per capita living energy consumption, this paper establishes a novel grey model based on the discrete grey model with time power term and the fractional accumulation (FDGM (1, 1, tα) for short) for forecasting China’s per capita living energy consumption, which makes the existing model to adapt to different time series by adjusting fractional order accumulation parameter and power term. In order to verify the feasibility and effectiveness of the novel model, the proposed and eight other existing grey prediction models are applied to the case of China’s per capita living energy consumption. The results show that the proposed model is more suitable for predicting China’s per capita energy consumption than the other eight grey prediction models. Finally, the proposed model based on metabolism mechanism is used to predict China’s per capita living energy consumption from 2018 to 2029, which can provide a reference for energy companies or government decision makers.

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