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Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.

The purpose of this paper is to propose an extensiveness intelligent hybrid model to short-term load electricity forecast that can simultaneously model the seasonal complicated nonlinear uncertain patterns in the data. For this purpose, a fuzzy seasonal version of the multilayer perceptrons (MLP) is developed.

In this paper, an extended fuzzy seasonal version of classic MLP is proposed using basic concepts of seasonal modeling and fuzzy logic. The fundamental goal behind the proposed model is to improve the modeling comprehensiveness of traditional MLP in such a way that they can simultaneously model seasonal and fuzzy patterns and structures, in addition to the regular nonseasonal and crisp patterns and structures.

Eventually, the effectiveness and predictive capability of the proposed model are examined and compared with its components and some other models. Empirical results of the electricity load forecasting indicate that the proposed model can achieve more accurate and also lower risk rather than classic MLP and some other fuzzy/nonfuzzy, seasonal nonseasonal, statistical/intelligent models.

One of the most appropriate modeling tools and widely used techniques for electricity load forecasting is artificial neural networks (ANNs). The popularity of such models comes from their unique advantages such as nonlinearity, universally, generality, self-adaptively and so on. However, despite all benefits of these methods, owing to the specific features of electricity markets and also simultaneously existing different patterns and structures in the electrical data sets, they are insufficient to achieve decided forecasts, lonely. The major weaknesses of ANNs for achieving more accurate, low-risk results are seasonality and uncertainty. In this paper, the ability of the modeling seasonal and uncertain patterns has been added to other unique capabilities of traditional MLP in complex nonlinear patterns modeling.

To predict the passenger volume reasonably and accurately, this paper fills the gap in the research of quarterly data forecast of railway passenger volume. The research results can also provide references for railway departments to plan railway operation lines reasonably and efficiently.

This paper intends to establish a seasonal cycle first order univariate grey model (GM(1,1) model) combing with a seasonal index. GM (1,1) is termed as the trend equation to fit the railway passenger volume in China from 2014 to 2018. The railway passenger volume in 2019 is used as the experimental data to verify the forecasting effect of the proposed model. The forecasting results of the seasonal cycle GM (1,1) model are compared with the traditional GM (1,1) model, seasonal grey model (SGM(1,1)), Seasonal Autoregressive Integrated Moving Average (SARIMA) model, moving average method and exponential smoothing method. Finally, the authors forecast the railway passenger volume from 2020 to 2022.

The quarterly data of national railway passenger volume have a clear tendency of cyclical fluctuations and show an annual growth trend. According to the comparison of the modeling results, the authors know that the seasonal cycle GM (1,1) model has the best prediction effect with the mean absolute percentage error of 1.32%. It is much better than the other models, reflecting the feasibility of the proposed model.

As the previous grey prediction model could not solve the series prediction problem with seasonal fluctuation, and there are few research studies on quarterly railway passenger volume forecasting, GM (1,1) model is taken as the trend equation and combined with the seasonal index to construct a combination forecasting model for accurate forecasting results in this study. Besides, considering the impact of the epidemic on passenger volume, the authors introduce a disturbance factor to deal with the forecasting results in 2020, making the modeling results more scientific, practical and referential.

Aiming to address the forecasting dilemma of seasonal air quality, the authors design the novel self-adaptive seasonal adjustment factor to extract the seasonal fluctuation information about the air quality index. Based on the novel self-adaptive seasonal adjustment factor, the novel seasonal grey forecasting models are established to predict the air quality in China.

This paper constructs a novel self-adaptive seasonal adjustment factor for quantifying the seasonal difference information of air quality. The novel self-adaptive seasonal adjustment factor reflects the periodic fluctuations of air quality. Therefore, it is employed to optimize the data generation of three conventional grey models, consisting of the GM(1,1) model, the discrete grey model and the fractional-order grey model. Then three novel self-adaptive seasonal grey forecasting models, including the self-adaptive seasonal GM(1,1) model (SAGM(1,1)), the self-adaptive seasonal discrete grey model (SADGM(1,1)) and the self-adaptive seasonal fractional-order grey model (SAFGM(1,1)), are put forward for prognosticating the air quality of all provinces in China .

The experiment results confirm that the novel self-adaptive seasonal adjustment factors promote the precision of the conventional grey models remarkably. Simultaneously, compared with three non-seasonal grey forecasting models and the SARIMA model, the performance of self-adaptive seasonal grey forecasting models is outstanding, which indicates that they capture the seasonal changes of air quality more efficiently.

Since air quality is affected by various factors, subsequent research may consider including meteorological conditions, pollutant emissions and other factors to perfect the self-adaptive seasonal grey models.

Given the problematic air pollution situation in China, timely and accurate air quality forecasting technology is exceptionally crucial for mitigating their adverse effects on the environment and human health. The paper proposes three self-adaptive seasonal grey forecasting models to forecast the air quality index of all provinces in China, which improves the adaptability of conventional grey models and provides more efficient prediction tools for air quality.

The self-adaptive seasonal adjustment factors are constructed to characterize the seasonal fluctuations of air quality index. Three novel self-adaptive seasonal grey forecasting models are established for prognosticating the air quality of all provinces in China. The robustness of the proposed grey models is reinforced by integrating the seasonal irregularity. The proposed methods acquire better forecasting precisions compared with the non-seasonal grey models and the SARIMA model.

The purpose of this paper, because of the complexity of demand time series and the need to construct a more accurate hybrid model that can model all relationships in data, is to propose a parallel-series hybridization of seasonal neural networks and statistical models for demand time series forecasting.

The main idea of proposed model is centered around combining parallel and series hybrid methodologies to use the benefit of unique advantages of both hybrid strategies as well as intelligent and classic seasonal time series models simultaneously for achieving results that are more accurate for the first time. In the proposed model, in contrast of traditional parallel and series hybrid strategies, it can be generally shown that the performance of the proposed model will not be worse than components.

Empirical results of forecasting two well-known seasonal time series data sets, including the total production value of the Taiwan machinery industry and the sales volume of soft drinks, indicate that the proposed model can effectively improve the forecasting accuracy achieved by either of their components used in isolation. In addition, the proposed model can achieve more accurate results than parallel and series hybrid model with same components. Therefore, the proposed model can be used as an appropriate alternative model for seasonal time series forecasting, especially when higher forecasting accuracy is needed.

To the best of the authors’ knowledge, the proposed model, for first time and in contrast of traditional parallel and series hybrid strategies, is developed.

Given the effects of natural and social factors, data on both the supply and demand sides of electricity will produce obvious seasonal fluctuations. The purpose of this article is to propose a new dynamic seasonal grey model based on PSO-SVR to forecast the production and consumption of electric energy.

In the model design, firstly, the parameters of the SVR are initially optimized by the PSO algorithm for the estimation of the dynamic seasonal operator. Then, the seasonal fluctuations in the electricity demand data are eliminated using the dynamic seasonal operator. After that, the time series after eliminating of the seasonal fluctuations are used as the training set of the DSGM(1, 1) model, and the corresponding fitted, and predicted values are calculated. Finally, the seasonal reduction is performed to obtain the final prediction results.

This study found that the electricity supply and demand data have obvious seasonal and nonlinear characteristics. The dynamic seasonal grey model based on PSO-SVR performs significantly better than the comparative model for hourly and monthly data as well as for different time durations, indicating that the model is more accurate and robust in seasonal electricity forecasting.

Considering the seasonal and nonlinear fluctuation characteristics of electricity data. In this paper, a dynamic seasonal grey model based on PSO-SVR is established to predict the consumption and production of electric energy.

A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.

Firstly, this paper constructs a new accumulation operation that embodies the new information priority by using a hyperparameter. Then, a new AGSM is constructed by using a new grey action quantity, nonlinear Bernoulli operator, discretization operation, moving average trend elimination method and the proposed new accumulation operation. Subsequently, the marine predators algorithm is used to quickly obtain the hyperparameters used to build the AGSM. Finally, comparative analysis experiments and ablation experiments based on China's quarterly GDP confirm the validity of the proposed model.

AGSM can be degraded to some classical grey prediction models by replacing its own structural parameters. The proposed accumulation operation satisfies the new information priority rule. In the comparative analysis experiments, AGSM shows better prediction performance than other competitive algorithms, and the proposed accumulation operation is also better than the existing accumulation operations. Ablation experiments show that each component in the AGSM is effective in enhancing the predictive performance of the model.

A new AGSM with new information priority accumulation operation is proposed.

This chapter presents an Excel-based regression analysis to forecast seasonal demand for U.S. Imported Beer sales data. The following seasonal regression models are presented and interpreted including a simple yearly model, a quarterly model, a semi-annual model, and a monthly model. The results of the models are compared and a discussion of each model's efficacy is provided. The yearly model does the best at forecasting U.S. Import Beer sales. However, the yearly does not provide a window into shorter-term (i.e., monthly) forecasting periods and subsequent peaks and valleys in demand. Although the monthly seasonal regression model does not explain as much variance in the data as the yearly model it fits the actual data very well. The monthly model is considered a good forecasting model based on the significance of the regression statistics and low mean absolute percentage error. Therefore, it can be concluded that the monthly seasonal model presented is doing an overall good job of forecasting U.S. Import Beer Sales and assisting managers in shorter time frame forecasting.