Time Response Function Research Articles

Predicting China’s Energy Consumption and CO2 Emissions by Employing a Novel Grey Model

The accurate prediction of China’s energy consumption and CO2 emissions is important for the formulation of energy and environmental policies and achieving carbon neutrality. This paper proposes a new weighted error evaluation criterion that emphasizes the importance of new data, thereby enabling more accurate capture of the variation characteristics of new data and reflecting the principle of new information priority. By optimizing the development coefficient, grey action, and parameters in the time response formula of the traditional GM(1,1), a novel optimized model, OGMW(1,1), is constructed. The accuracy of the new model is verified by three cases from the literature. The future trends of primary energy, oil, and coal consumption and CO2 emissions in China are predicted over the next five years. The conclusions are as follows: First, the new weighted error evaluation criteria are effective and reasonable and can indicate whether a grey model can reliably use the most recent information for modeling. Second, based on the new error evaluation criteria, the development coefficient, ash action, and parameter C in the time response function can be optimized. The results show that the optimization method is reasonable. Third, compared with the traditional models GM, GMO, and ARIMA, the OGMW(1,1) provides better simulation and prediction accuracy, and new information can be prioritized more effectively. Fourth, the forecasting results indicate that China will increase its consumption of primary energy, oil, and coal, as well as its CO2 emissions. Notably, the growth rates of primary energy and oil consumption are high at approximately 22.7% and 25%, coal consumption will increase slightly, and CO2 emissions will increase by approximately 11%.

A novel dynamic structural adaptive multivariable grey model and its application in China's solar energy generation forecasting

Accurately predicting China's solar energy generation is crucial for energy planning and environmental protection. However, the nonlinearity and complexity of the data pose challenges to prediction. This article proposes a dynamic structural adaptive multivariate grey model to overcome these challenges. The model constructs a dynamic nonlinear correction function with an uncertain structure that can adaptively adjust to the data characteristics. Additionally, the Gaussian function is utilized to derive the time response function, overcoming the mechanism defects present in traditional multivariate grey models. The whale optimization algorithm is applied to optimize the background value of the model, improving accuracy. The model is compatible with 14 classical models via parameter changes and has strong compatibility. The results show that the fitting error and test error of the model are 0.23 % and 1.95 % respectively, which is significantly better than the other 11 methods, indicative of strong robustness and accuracy. The forecast indicates that China's solar energy generation will experience a consistent upward trajectory from 2023 to 2030, with an average annual growth rate of 12.11 %. This study significantly contributes to the advancement of the theory of multivariate grey dynamic prediction and provides essential data support for strategic planning within China's solar power industry.

A grey prediction model optimized by meta-heuristic algorithms and its application in forecasting carbon emissions from road fuel combustion

In Cameroon, predicting CO2 emissions from road transports is crucial since it contributes in formulating the government's energy plans and strategies. In this perspective, this paper proposes an optimized wavelet transform hausdorff multivariate grey model (OWTHGM(1,N)) that addresses some of the weaknesses of the classical GM(1,N) model such as inaccurate prediction and poor stability. In all, three improvements have been made to the classical GM(1,N): First, all inputs are filtered using the wavelet transform, thereby denoising variables that could hamper modelling; second, a new time response function is established using the Hausdorff derivative; and finally, the use of Rao's algorithm to optimise the model's parameters as well as the ξ-order accumulated value of the observation data described by the Hausdorff derivative. In order to demonstrate the effectiveness of OWTHGM(1,N), it is applied to predict CO2 emissions from road transport. The new model produces predictions with 1.27 % MAPE and 79.983 RMSE, and is therefore more accurate than competing models. OWTHGM(1,N) could therefore serve a reliable forecasting tool and used to monitor the evolution of CO2 emissions in Cameroon. The forecast results also serve as a sound foundation for the formulation of energy consumption strategies and environmental policies.

An extensive conformable fractional grey model and its application

In order to expand the applicability of the conventional conformable fractional grey model, an extensive conformable fractional grey model, abbreviated as ECFGM(1,1), is proposed by the introduction of the extensive conformable fractional accumulation. Specifically, the improvements of the proposed model can be outlined as follows. First, the extensive fractional accumulation and difference are designed for accumulated generating operation and its reverse calculation, respectively. Second, based on the extensive form, the parameter estimation and time response function of the ECFGM(1,1) model are deduced, thereinto, the particle swarm optimization algorithm is employed to determine the optimal fractional order for the newly-designed model. It is worthy noting that an algorithm framework by the Monte Carlo simulation and parameter sensitivity analysis is conducted to assess the robustness of the proposed model. To validate this model’s efficacy, the novel technique is adopted to forecast China’s primary energy consumption compared with a series of competitive models. The numerical results indicate the newly-proposed model is superior to all competitors in terms of MAPE and RMSE values, thus, the proposed ECFGM(1,1) model is considered a powerful and promising method for enhancing the existing fractional grey models.

Forecasting China’s total renewable energy capacity using a novel dynamic fractional order discrete grey model

Accurately forecasting renewable energy capacity is crucial for informing national energy policies and promoting sustainable socio-economic growth. This study proposes a novel dynamic fractional-order discrete grey model (DFDGM (1,1)) for forecasting China's total renewable energy capacity. The model constructs a dynamic fractional time delay polynomial, which enhances the adaptability of the model to different sample sizes. The time response function of model is directly derived from the discrete equation, preventing errors caused by the transition from discreteness to continuity. Furthermore, the proposed model represents the unified form of six grey models, effectively expanding the model's application domain and scope. The method introduces a double error approach to facilitate optimal parameter selection, successfully addressing overfitting and randomness challenges in parameter selection. Empirical studies show that the proposed model outperforms eleven other methods, with fitting and forecasting errors of 0.39% and 1.13%, respectively. Finally, the proposed model forecasts the future development trend of China’s total renewable energy capacity. In general, this research not only improves the precision of predictions but also progresses the dynamic theory in prediction studies.

Forecasting CO2 emissions from road fuel combustion using grey prediction models: A novel approach

This paper proposes an optimized wavelet transform Hausdorff multivariate grey model (OWTHGM(1,N)) that addresses some of the weaknesses of the conventional GM(1,N) model such as inaccurate prediction and poor stability. Three improvements have been made: First, all inputs are filtered using a wavelet transform; second, a new time response function is established using the Hausdorff derivative; and finally, the use of Rao's algorithm to optimise the model's parameters as well as the ξ-order accumulated value of the observation data described by the Hausdorff derivative. In order to demonstrate the effectiveness of OWTHGM(1,N), it is applied to predict CO2 emissions from road fuel combustion. The new model scores 1.27% MAPE and 79.983 RMSE, and is therefore more accurate than competing models. OWTHGM(1,N) could therefore serve a reliable forecasting tool and used to monitor the evolution of CO2 emissions in Cameroon. The forecast results also serve as a sound foundation for the formulation of energy consumption strategies and environmental policies.• Modification, extension and optimization of grey multivariate model is done.• The model is very generic can be applied to a wide variety of energy sectors.• OWTHGM(1,N) is a valid forecasting tool that can be used to track CO2 emissions.

A novel data-driven seasonal multivariable grey model for seasonal time series forecasting

Rapid growth in solar power generation, accompanied by random fluctuations, has important implications for the security, stability, and productivity of the grid. Therefore, accurate predictions of solar power generation provide an essential benchmark for relevant institutions to conduct grid planning and power dispatch. Thereby, a novel data-driven seasonal multivariable grey model is proposed for simulating seasonal fluctuations and non-linear trends in solar power generation. To be specific, the novel model contains the following refinements: first, the seasonal factors and time-power item are introduced to modify the insensitivity of traditional multivariable grey models to seasonal fluctuations and non-linear trends. Second, to enhance the generalizability and adaptability of the model, the parameter associated with the time-power item is determined by using the genetic algorithm. Third, on the premise of proving the model’s requirements for period length and sample size, the derivation of the time response function is expounded. For illustration and verification purposes, comprehensive experimental studies are conducted with quarterly and monthly time series samples. In addition, forecasts of the novel model are compared with five prevailing models, including grey prediction models, traditional econometric technology, and artificial intelligence. Case studies indicate that this novel model exhibits improved generalizability, stability, and reliability in the face of quarterly or monthly time series data, confirming it as an auspicious and powerful tool for future solar power generation forecasting.

Spatial and time characteristics of a four-wave radiation converter in a parabolic waveguide with resonant nonlinearity

Spatial and temporal characteristics of a degenerate four-wave converter in a multimode waveguide with resonant nonlinearity in a scheme with counter-pumping waves are analyzed using the time response function and the point spread function. For single-mode pump waves with equal mode numbers, the dependences of the time response width on the waveguide length, the intensity of the first pump waves, and the mode number in the mode expansion of the object wave amplitude are obtained for the four-wave converter. The greatest contribution to the object wave amplitude is shown to be from the waveguide mode whose number coincides with the mode number of single-mode pump waves. For the stationary model, taking into account the spatial structure of the Gaussian pump wave leads to a monotonous decrease with a decrease in the pump beam width, followed by a constant value of the PSF module width. With single-mode pump waves with equal mode numbers, An increase in the mode number of the pump waves leads to a redistribution of energy concentrated in the side maxima of the point signal image and improvement in the quality of the wavefront reversal for a model with single-mode pump waves with equal mode numbers.

Forecasting methodology with structural auto-adaptive intelligent grey models

Accurate mid- and long-term petroleum products (PP) consumption forecasting is vital for strategic reserve management and energy planning. In order to address the issue of energy forecasting, a novel structural auto-adaptive intelligent grey model (SAIGM) is developed in this paper. To start with, a novel time response function for predictions that corrects the main weaknesses of the traditional grey model is established. Then, the optimal parameter values are calculated using SAIGM to increase adaptability and flexibility to deal with a variety of forecasting dilemmas. The viability and performance of SAIGM are examined with both ideal and real-world data. The former is constructed from algebraic series while the latter is made up Cameroon's PP consumption data. With its ingrained structural flexibility, SAIGM yields forecasts with RMSE of 3.10 and 1.54% MAPE. The proposed model performs better than competing intelligent grey systems that have been developed to date and is thus a valid forecasting tool that can be used to track the growth of Cameroon's PP demand.•The ability of SAIGM enhances the forecasting power of intelligent grey models to fully extracting the laws of a system, no matter the data specifications.•SAIGM is extended to include quasi-exponential series by addressing structural flexibility and parametrization concerns.•Input attributes determination and data preprocessing are not required for the proposed model.

An improved grey multivariable time-delay prediction model with application to the value of high-tech industry

To analyse the time lag effects between independent variables and dependent variables, we propose a discrete time-delay grey multivariable modelDMTGM1,Nτ. There are three improvements in this new model compared to the existing models. First, the time lag parameters are assigned different values for each independent variable. A linear correction term expands the new model. Second, with the given time lag, the least square method can be used to calculate the parameter vector. The time response function of DMTGM1,Nτ is generated, which has the advantage of eliminating the jumping errors between discrete and continuous functions over the existing grey forecasting models. Third, all of the feasible combinations of the time lag parameters are compared by using a traversal algorithm to identify the best values with the minimized mean absolute percentage error (MAPE). In three different case studies, the performance of the new model is evaluated and compared to that of a number of mainstream grey models as well as non-grey models. According to the findings, the newly designed model performs significantly better than the compared models.

A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

Due to the sensitivity of spaceborne atomic clock to many factors, the variation law of satellite clock bias (SCB) can be regarded as a grey system. The GM (1,1) model is a most classical and basic model of grey system, which has been successfully applied in SCB prediction. Moreover, many improved models have been proposed and widely used in various forecasts since GM (1,1) was generated. However, the prediction performance of these models is not obviously improved compared with the classical models in clock bias prediction. In view of this, a new GM (1,1) model has been come up with in this paper by optimising fitting model and initial condition. The new fitting model is obtained by differentiating time response function of winterisation, and the new initial condition is generated through one or more components of the original clock bias sequence. The authors employ GPS rapid and precise SCB provided by the International GNSS Service (IGS) for prediction experiments. The results show that the new GM (1,1) model is effective and feasible, and its prediction accuracy and stability are enormously better than that of the classical GM (1,1) model, especially for ultra-short-term prediction.

A Conformable Fractional Discrete Grey Model CFDGM (1,1) and its Application

An accurate forecast of the area of drought disaster is vitally important for the government to take appropriate measures to prevent disaster. In the current study, a new conformable fractional discrete grey model is applied to study the trend of the area affected by drought disasters. Firstly, the new model, abbreviated as CFDGM(1,1), is proposed with the definitions of the conformable fractional operator and the classical GM(1,1) model. Then the recursive expression of the time response function is obtained by the grey basic form, and the linear system parameters are confirmed by the linear least squares method. Further, the Salp Swarm Algorithm is chosen to determine the optimal conformable fractional order. Finally, the area of drought disaster is studied by the new model and others, where the results show the new model has a good performance among these models.

A Unified Grey Riccati Model

The grey Riccati model (GRM) is a generalization of the grey Verhulst model (GVM). Both the GRM and GVM generally perform well in simulating and forecasting the raw sequences with a bell-shaped or single peak feature. Although there are several methods to solve the Riccati differential equation, the existing time response functions of the GRM are generally complicated. In order to reduce the computational complexity of the time response function, this study attempts to transform the Riccati equation into a Bernoulli equation with the help of a known particular solution. Then, a unified time response function of the GRM is obtained by the proposed methodology. The simulation results demonstrate that the proposed unified grey Riccati model performs the same as the grey generalized Verhulst model (a kind of grey Riccati model) and is better than the traditional grey Verhulst model. The fact also reveals that the newly developed grey Riccati model is reasonable and effective.

Forecasting clean energy generation volume in China with a novel fractional Time-Delay polynomial discrete grey model

Clean energy, represented by hydropower, wind power, and nuclear power, plays a crucial role in addressing the issue of power shortage and promoting the transition of the energy structure. Scientific and accurate forecasting of clean energy generation volume can provide the necessary reference for relevant authorities to formulate reasonable energy policies. This paper proposes a novel fractional time-delay polynomial discrete grey model, FTDP-DGM(1,1), for forecasting clean energy generation volume in China. Firstly, both the structural parameters and the time response function are derived directly from the discrete equation. Secondly, the genetic algorithm is employed to determine the optimal value of the nonlinear parameter in the model, with the optimization objective of minimizing the mean absolute percentage error. Then, the proposed model is applied to the simulation and prediction of hydro, wind, and nuclear energy generation volume in China. The results show the validity and superiority of the model. Finally, out-of-sample forecasts are performed, and the forecasting results show that the proposed model has good performance with values of 1.29%, 2.94%, and 2.32% for mean absolute percentage error(MAPE), respectively. It is expected that in 2021–2025, China's hydro, wind, and nuclear power generation volume will continue to grow at a rate of 1.45%, 10.74%, and 10.66% respectively. Based on the forecast results, policy recommendations are suggested.

A novel discrete grey model with time-delayed power term and its application in solar power generation volume forecasting

PurposeIn 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 is proposed in this paper.Design/methodology/approachFirstly, 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.FindingsGiven the reliability and superiority of the model, the model 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.Practical implicationsThis 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.Originality/valueThe 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.

A Novel Robust Grey Model and Its Application

Previous studies paid attention to improving the predicted capability of the classical grey model, but its robustness is still unclear and not explored, in particular when these exhibit outliers in the time series, which is due to measurement error, uncorrected record, and censored date. In this study, we proposed a novel robust grey model. The novel robust grey model adopts the median regression method to address these problems caused by outliers, which provides the robust parameters. The analytical expression for the time response function and the forecasting values is derived by the grey system technique and mathematical tool. With annual observational data of Chinese electricity demand, we examine the fitness capability of the novel robust grey model, by comparing it with the classical grey model. Also, we adopt the bootstrapping test to further illustrate the sensitivity for the new robust grey model when there are outliers in the time series. To our knowledge, it is the first to introduce the bootstrapping test to the literature related to the grey model and to focus on the robustness of the grey model. The computational results suggest that the new robust grey model has higher precision than the classical grey model, but it is also very robust to outliers, whose accuracy and robustness are better than the classical grey model. Finally, we apply the novel grey model to forecast the future values in Chinese electricity demand during the year 2022 to 2025. This new model proposed in this study estimates that the Chinese electricity demand would continue to increase after the year of 2022, arriving at 10.446×105 million kW·h in the year of 2025 approximately.

Petroleum products consumption forecasting based on a new structural auto-adaptive intelligent grey prediction model

The demand for petroleum products has risen rapidly over the last two decades, owing mostly to the residential, transports and industrial sectors. Precise mid and long-term petroleum products consumption prediction is therefore of crucial importance for energy planning and management of strategic reserves. Thus, a new structural auto-adaptive intelligent grey model (SAIGM) is proposed as a solution to this problem. Initially, a novel time response function for predictions is theoretically determined, which addresses the standard grey model's main weaknesses. Subsequently, SAIGM is employed to determine the optimum parameter values to improve the adaptability and flexibility to confront diverse forecasting issues. Altogether, the proposed model offers a triple contribution. Firstly, SAIGM improves the predictive capabilities of intelligent grey models by making it capable of fully extracting the laws of evolution of a system, regardless of time series characteristics. Secondly, structural inflexibility and parametrization issues are addressed, so that SAIGM does not only apply to pure exponential series. Thirdly, the proposed model does not need to preprocess data nor determine the characteristics of input data. Consequently, SAIGM decreases the reliance on modeling knowledge from the standpoint of expert systems. A case study is used to check the feasibility and superiority of SAIGM. Simulation results are compared with recent intelligent grey-based models. The new model appears to benefit from its structural flexibility, since it can generate forecasts with MAPE as low as 1.54% and RMSE of 3.10. Hence, SAIGM outperforms the majority of grey models and intelligent systems known so far

A new multivariable grey model and its application to energy consumption in China

Based on the nonlinearity of energy consumption systems and the influence of multiple factors, this paper presents a nonlinear multivariable grey prediction model with parameter optimization and estimates the parameters and the approximate time response function of the model. Next, a genetic algorithm is applied to optimize the nonlinear terms of the novel model to seek the optimal parameters, and the modelling steps are outlined. Then, to assess the effectiveness of the novel model, this paper adopts Chinese oil, gas, coal and clean energy as research objects, and three classical grey forecasting models and one time series method are chosen for comparison. The results indicate that the new model attains a high simulation and prediction accuracy, basically higher than that of the three grey prediction models and the time series method.

An Improved Grey Model with Time Power and Its Application

The grey system model with time power, which is often called the GM(1,1,tα), appeals considerable interest of research due to its effectiveness in time series forecasting. Aimed to improve further the GM(1,1,tα) model, this paper introduces a new whitening equation with variable coefficient into the original whitening equation which extends applicable scope; as a result, an improved grey model with time power, namely, OGM(1,1,tα), is proposed. Firstly, the time response function of the novel model and the restored values of original series are deduced through grey modelling techniques. Secondly, the variable coefficient in the whitening equation and the time power are determined by particle swarm optimization algorithm. Two empirical examples are then used to verify the validity of the novel model. Finally, the novel model is applied to predict the oil consumption of China from 2004 to 2018. Results show the novel model outperforms other commonly‐used competitive models, which can well serve a benchmark model for scholars and decision‐makers.

Forecasting nuclear energy consumption in China and America: An optimized structure-adaptative grey model

Forecasting nuclear energy accurately is vital to ensure reliable electricity supply and alleviate environmental degradation problems. However, it is difficult to model the nuclear time series due to its complexity, nonlinearity, and uncertainty. To this end, this paper put forward an optimized structure-adaptive grey model by theoretically providing the generalized time response function and accurately modifying the background value based on Simpson's rule. Moreover, Monte-Carlo Simulation and probability density analysis (PDA) are employed to analyze the proposed model's merits, revealing its robustness and reliability. For validation and verification purposes, the optimized model is implemented to predict nuclear energy consumption in China and America, compared to seven benchmark models involving other prevalent grey models, conventional econometric technology, and artificial intelligence. Experimental results from two cases consistently demonstrate that the novel technique significantly outperforms the competitors from two different perspectives of PDA and level accuracy. Besides, further discussion over different forecasting horizons reveals that this new model can still deliver accurate forecasts with solid robustness and high reliability. Consequently, the proposed model is validated as a practical and promising model for forecasting nuclear energy consumption.