Multivariable Grey Model Research Articles

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.

Damage detection of Kevlar woven fabric using optical fiber multimode interferometer

Kevlar woven fabric is crucial for the lightweight design of aerospace structures due to its unique advantages. However, it is susceptible to damage during operation, making effective damage detection essential for ensuring structural reliability. Nevertheless, conventional sensors used for damage detection have limitations such as complex manufacturing processes and weight. To address this issue, this paper proposed a simple singlemode-multimode-singlemode (SMS) optical fiber sensor to collect vibration signals and construct a damage recognition model based on natural frequency in order to identify the size of damages in Kevlar woven fabrics. To achieve a highly linear and accurate sensor, a length determination criterion for multimode optical fiber segments based on quasi-image, notch, and transmission spectrum loss was proposed. An optical sensor was fabricated based on this criterion. The feasibility and sensitivity of the sensor for vibration signal measurement were verified by constructing a vibration signal measurement device. An experimental study was conducted to detect damage in Kevlar tapes, where the natural frequency changes measured by the SMS sensor were integrated with an optimized multi-variable gray model for damage size detection. The experimental results indicate that the estimated error in damage size is 0.71%. The damage identification system proposed in this paper offers a simple and cost-effective solution for measuring damage in flexible structures using fiber optic sensors.

Multi-step carbon emissions forecasting using an interpretable framework of new data preprocessing techniques and improved grey multivariable convolution model

As China stands at a critical juncture in its transition towards a low-carbon future, the precise prediction and analysis of provincial carbon emissions have emerged as paramount tasks. Focusing on forecasting in this intricate and vital domain, an updated grey multivariable convolution model is designed by employing the unified new-information-oriented accumulating generation operator (UNAGO) technique to process raw sequences. Equipped with UNAGO's hyper-parameters that enable the independent scaling effects and prioritize new information, the newly-designed model offers high flexibility and adaptability for handling complex provincial carbon emissions. Subsequently, four different restricted carbon emission sequences are utilized as case studies for validation purposes, and the new model's performance is scrutinized against five contrasting methods across three prediction forecasting horizons. Comparative experimental results reveal the new model's superior level of accuracy in predicting carbon emissions across four different provinces, with MAPE values of <4 % and 10 % in the in-sample and out-of-sample periods, respectively. Furthermore, rigorous evaluations with Diebold-Mariano (DM) and Probability Density Analysis (PDA) tests confirm the model's robust and general forecasting capabilities.

Forecasting the output of high-tech industry in China: A novel nonlinear grey time-delay multivariable model with variable lag parameters

Under the rapidly developing economy in China, accurate forecasting holds vital significance for policymaking and operational planning within the high-tech industry. However, the influencing factors affecting the output, accompanied by the time-delay effect, could be nonlinear, and uncertain. Thereby, this paper proposes a new nonlinear grey multivariable model with time-varying lag parameters. To be specific, the newly designed time delay function and power exponent are introduced, which can significantly enhance the adaptability and flexibility of the proposed method. The Grey Wolf Optimization algorithm is utilized to calculate the dynamic time lag parameters and power exponent to improve the prediction reliability. Furthermore, this new approach is applied to predict the high-tech industry’s output in China, Shanghai Municipality, and the Eastern Region, with due consideration given to the time-delay effect between input factors and outputs. To assess its efficacy, some leading models are selected for comparison to the proposed model. Furthermore, the utilization of Monte-Carlo simulation, the Probability Density Analysis, and the simulations are used to demonstrate the robustness and stability of this new method. The findings show that the proposed model is a feasible and applicable approach for prediction, exhibiting outstanding accuracy.

Modeling, prediction and analysis of natural gas consumption in China using a novel dynamic nonlinear multivariable grey delay model

Accurately predicting natural gas consumption is essential for developing a clean, low-carbon, safe, and efficient energy system. Therefore, this paper integrates the idea of the extended logistic model into multivariable grey prediction theory. Considering the delay effect and nonlinear characteristics of the system, a novel dynamic nonlinear multivariate grey delay prediction model is constructed. Meanwhile, the algorithmic framework for solving the parameters of the new model is provided to identify and optimize the parameters of the time-delay effect of the model. The genetic algorithm was identified as the best matching optimization algorithm for the new model. Furthermore, the new model is applied to fitting and forecasting China's natural gas consumption, and the validity of the model is fully verified. Compared with other forecasting models, the new model has a lower average relative error in the fitting and forecasting stage, and, in particular, achieves a better forecasting effect with the lowest MAPEpre value (0.001 % for one-step ahead, 0.005 % for two-step ahead, and 0.746 % for three-step ahead). Moreover, the model is employed to forecast China's natural gas consumption for the next five years, providing a robust foundation for government policies related to the supply of natural gas.

The nonlinear multi-variable grey Bernoulli model and its applications

This work uses the vector-valued Bernoulli equation to build a nonlinear multi-variable grey Bernoulli model, which is available to describe the nonlinear relationship between the output variables. By using Pade´ approximation, the proposed model can be implemented with high time efficiency. Additionally, the Sine Cosine Algorithm is employed to determine the Bernoulli exponent, thereby enhancing prediction accuracy. To evaluate the predictive performance of the proposed model, three case studies using three real-world data sets with different features of predicting per capita household income, fuel prices and crude oil prices are carried out. The results are compared with three existing grey multi-input multi-output models. Experimental results demonstrate that the proposed model excels in handling nonlinear relationships between variables and has strong robustness against noise, consistently delivering lower error values, demonstrating superior predictive performance.

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.

Small-batch product quality prediction using a novel discrete Choquet fuzzy grey model with complex interaction information

With manufacturing focused on multi-variety and small-batch intelligent production, the challenge is to guarantee and ensure good product quality. This paper proposes a novel small-batch product quality prediction approach considering complex interaction information. In this paper, first, to handle the complex nonlinear correlations among the manufacturing process variables, a kernel principal components analysis is used to extract the major features from the high-dimensional data. Second, we combine the discrete multivariate grey model and generalized discrete Choquet fuzzy integral to propose a discrete Choquet fuzzy grey model so as to capture the complex interaction information among the process variables. Next, an adjoint sensitivity analysis is applied to characterize the changes in the process variables on the predicted product quality index. We conduct an experiment on six semiconductor products made in China to validate the proposed model against a library of nine other methods. Our model yields an average reduction of 11.02% on MAPE, 20.47% on MSE, 13.56% on STD, and an average increase of 46.37% on EVS for six types of products. Our results inform that the proposed model is suitable for predicting manufacturing product quality when the process variables interact significantly, and we can prioritize the process variables for remedial action accordingly.

Improving electricity demand forecasting accuracy: a novel grey-genetic programming approach using GMC(1,N) and residual sign estimation

PurposeThis paper addresses the challenges associated with forecasting electricity consumption using limited data without making prior assumptions on normality. The study aims to enhance the predictive performance of grey models by proposing a novel grey multivariate convolution model incorporating residual modification and residual genetic programming sign estimation.Design/methodology/approachThe research begins by constructing a novel grey multivariate convolution model and demonstrates the utilization of genetic programming to enhance prediction accuracy by exploiting the signs of forecast residuals. Various statistical criteria are employed to assess the predictive performance of the proposed model. The validation process involves applying the model to real datasets spanning from 2001 to 2019 for forecasting annual electricity consumption in Cameroon.FindingsThe novel hybrid model outperforms both grey and non-grey models in forecasting annual electricity consumption. The model's performance is evaluated using MAE, MSD, RMSE, and R2, yielding values of 0.014, 101.01, 10.05, and 99% respectively. Results from validation cases and real-world scenarios demonstrate the feasibility and effectiveness of the proposed model. The combination of genetic programming and grey convolution model offers a significant improvement over competing models. Notably, the dynamic adaptability of genetic programming enhances the model's accuracy by mimicking expert systems' knowledge and decision-making, allowing for the identification of subtle changes in electricity demand patterns.Originality/valueThis paper introduces a novel grey multivariate convolution model that incorporates residual modification and genetic programming sign estimation. The application of genetic programming to enhance prediction accuracy by leveraging forecast residuals represents a unique approach. The study showcases the superiority of the proposed model over existing grey and non-grey models, emphasizing its adaptability and expert-like ability to learn and refine forecasting rules dynamically. The potential extension of the model to other forecasting fields is also highlighted, indicating its versatility and applicability beyond electricity consumption prediction in Cameroon.

A novel fractional multivariate grey prediction model for forecasting hydroelectricity consumption

PurposeThis study aims to enhance the prediction accuracy of hydroelectricity consumption in China, with a focus on addressing the challenges posed by complex and nonlinear characteristics of the data. A novel grey multivariate prediction model with structural optimization is proposed to overcome the limitations of existing grey forecasting methods.Design/methodology/approachThis paper innovatively introduces fractional order and nonlinear parameter terms to develop a novel fractional multivariate grey prediction model based on the NSGM(1, N) model. The Particle Swarm Optimization algorithm is then utilized to compute the model’s hyperparameters. Subsequently, the proposed model is applied to forecast China’s hydroelectricity consumption and is compared with other models for analysis.FindingsTheoretical derivation results demonstrate that the new model has good compatibility. Empirical results indicate that the FMGM(1, N, a) model outperforms other models in predicting the hydroelectricity consumption of China. This demonstrates the model’s effectiveness in handling complex and nonlinear data, emphasizing its practical applicability.Practical implicationsThis paper introduces a scientific and efficient method for forecasting hydroelectricity consumption in China, particularly when confronted with complexity and nonlinearity. The predicted results can provide a solid support for China’s hydroelectricity resource development scheduling and planning.Originality/valueThe primary contribution of this paper is to propose a novel fractional multivariate grey prediction model that can handle nonlinear and complex series more effectively.

Research and application of a novel grey multivariable model in port scale prediction under the impact of Free Trade Zone

Purpose Considering the impact of the Free Trade Zone (FTZ) policy on forecasting the port cargo throughput, this paper constructs a fractional grey multivariate forecasting model to improve the prediction accuracy of port cargo throughput and realize the coordinated development of FTZ policymaking and port construction.Design/methodology/approach Considering the effects of data randomization, this paper proposes a novel self-adaptive grey multivariate prediction model, namely FDCGM(1,N). First, fractional-order accumulative generation operation (AGO) is introduced, which integrates the policy impact effect. Second, the heuristic grey wolf optimization (GWO) algorithm is used to determine the optimal nonlinear parameters. Finally, the novel model is then applied to port scale simulation and forecasting in Tianjin and Fujian where FTZs are situated and compared with three other grey models and two machine learning models.Findings In the Tianjin and Fujian cases, the new model outperforms the other comparison models, with the least mean absolute percentage error (MAPE) values of 6.07% and 4.16% in the simulation phase, and 6.70% and 1.63% in the forecasting phase, respectively. The results of the comparative analysis find that after the constitution of the FTZs, Tianjin’s port cargo throughput has shown a slow growth trend, and Fujian’s port cargo throughput has exhibited rapid growth. Further, the port cargo throughput of Tianjin and Fujian will maintain a growing trend in the next four years.Practical implications The new multivariable grey model can effectively reduce the impact of data randomness on forecasting. Meanwhile, FTZ policy has regional heterogeneity in port development, and the government can take different measures to improve the development of ports.Originality/value Under the background of FTZ policy, the new multivariable model can be used to achieve accurate prediction, which is conducive to determining the direction of port development and planning the port layout.

Damping accumulative NDAGM(1,N, α) power model and its applications

PurposeIn this essay, a new NDAGM(1,N,α) power model is recommended to resolve the hassle of the distinction between old and new information, and the complicated nonlinear traits between sequences in real behavior systems.Design/methodology/approachFirstly, the correlation aspect sequence is screened via a grey integrated correlation degree, and the damped cumulative generating operator and power index are introduced to define the new model. Then the non-structural parameters are optimized through the genetic algorithm. Finally, the pattern is utilized for the prediction of China’s natural gas consumption, and in contrast with other models.FindingsBy altering the unknown parameters of the model, theoretical deduction has been carried out on the newly constructed model. It has been discovered that the new model can be interchanged with the traditional grey model, indicating that the model proposed in this article possesses strong compatibility. In the case study, the NDAGM(1,N,α) power model demonstrates superior integrated performance compared to the benchmark models, which indirectly reflects the model’s heightened sensitivity to disparities between new and old information, as well as its ability to handle complex linear issues.Practical implicationsThis paper provides a scientifically valid forecast model for predicting natural gas consumption. The forecast results can offer a theoretical foundation for the formulation of national strategies and related policies regarding natural gas import and export.Originality/valueThe primary contribution of this article is the proposition of a grey multivariate prediction model, which accommodates both new and historical information and is applicable to complex nonlinear scenarios. In addition, the predictive performance of the model has been enhanced by employing a genetic algorithm to search for the optimal power exponent.

An innovative information accumulation multivariable grey model and its application in China's renewable energy generation forecasting

Reducing greenhouse gas emissions is urgent for the global community with rising climates. Considering the importance of renewable energy in mitigating climate warming, forecasting renewable energy generation is vital for the Chinese government's future low-carbon and green development plan. This paper proposes a novel multivariable grey model based on historical data on China's renewable energy generation and three industries. A novel information accumulation mechanism with two adaptive factors is designed to improve the traditional multivariable grey modeling defect. Based on the proposed mechanism, this paper optimizes the initial and background values and nonlinear model structure with the whale optimization algorithm. The forecasting results show that the fitting MAPE is 1.13%, comprehensive MAPE is 2.60%, MSE is 50.86, and RMSE is 7.13, which significantly improve the forecasting accuracy of traditional GM(1,N) and are better than other compared models. The forecasting results show that China's renewable energy generation will gradually increase to 5834.02 TWh. The Chinese government should keep the previous Five-Year Plans rising trend of the three industries in the future Five-Year Plans to support renewable energy industries. In China's future energy system, it is necessary to promote incentive policies and capital investment for actively accelerated development to make renewable energy the leading force.

Prediction of water consumption in Beijing based on the multi-variable grey model with adjacent accumulation

Abstract With the rapid development of the social economy, the importance of water resources is becoming increasingly prominent. Urban water demand in Beijing has been growing rapidly. Accurate water consumption forecasting is of utmost importance for reasonable allocation and optimization of water supply systems. In this study, an innovative multi-variable grey prediction model with adjacent accumulation (AOGM(1,N)) is proposed to predict Beijing's annual water consumption for four different water usage scenarios (domestic water, agricultural water, industrial water, and environmental water) by incorporating the adjacent accumulation into the optimized grey model. Grey relational analysis is used to select the key influence factors. The adjustable parameter of the prediction model is chosen by using the particle swarm optimization algorithm. By comparing with other models in the existing literature, the proposed AOGM(1,N) model has evidently superior prediction performance based on the error indicators, which supports the novel method's merits and validity. This study could help us better understand water usage and be applied to the planning and management problems of urban water supply systems.

A novel dynamic grey multivariate prediction model for multiple cumulative time-delay shock effects and its application in energy emission forecasting

Energy emission systems are often influenced by external information and policy shock. However, conventional grey models ignore the existence of the impact of multiple shock events and cumulative time-delay effects, which are crucial for achieving accurate forecasts. From a dynamic perspective, we aim to establish a multivariable grey prediction model considering the impact of multiple shock events, namely MSGTDM(1,N) model. Specifically, to accurately describe the impact of different types of external shocks on the system, three kinds of nonlinear dynamic shock functions are designed, including growth dynamic shock function, decline dynamic shock function, and slope dynamic shock function. Based on this, multi-dimensional instantaneous shock utility terms and cumulative time-delay utility terms are constructed to accurately measure shock effects. And Whale Optimization Algorithm is employed to determine the optimal parameters of the shock functions through comprehensive comparative analysis. The findings affirm the MSGTDM(1,N) model's higher predictive accuracy and validity. Consequently, the forecast results of China's carbon emissions from coal and natural gas consumption in 2022–2025 provide a reliable basis for adjusting the energy structure and implementing the “dual-carbon” policy effectively.

Impact of population and primary energy consumption on air pollutants of 67 countries

Air pollution is one of the most pressing environmental issues in the world today. To predict the air quality of 67 countries, considering the influence factors including population and primary energy consumption, an unequal-order exponential cumulative grey multivariate model is proposed to predict the PM2.5 concentrations. The prediction results show that South and Southeast Asia are the most polluted regions in Asia. Eastern and Central Europe are the most polluted regions in Europe. North and West Africa are the most polluted regions in Africa. In terms of air quality, Oceania is the best continent. Air quality in North America is likely to deteriorate in the coming years. The situation in South America is also not optimistic. The results of this study can provide the government with a basis to adjust the local environmental policy in order to improve air quality. The public can deal with air pollution and take appropriate precautions.

Novel method for total organic carbon content prediction based on non-equigap multivariable grey model

Predicting total organic carbon content plays a crucial role in shale gas reservoir evaluation. To address multi-variable, imperfect logging data and non-equigap characteristics, this study developed a multi-variable grey derivative model for predicting the total organic carbon content trend. To begin with, the non-equigap factor is introduced and the parameter identification of the new model is established on the basis of least square method. Then, to reduce fluctuations in the original data, the weighted geometric average weakening operator is introduced. In addition, considering the system stability, the derivation method is used to calculate the time response formula of the model. Furthermore, two validation cases are provided to verify the validity of this novel model. Finally, the model is applied to the Fuling shale gas field in China for practical forecasting. Compared to other models, such as the grey model, statistical model, and artificial intelligence model, the proposed model achieved higher prediction accuracy in the three cases. Specifically, this model obtained 95.62%, 95.88% and 94.55% prediction accuracy for total organic carbon content. Results that the new model effectively addresses the limitations of previous studies that focus on single-parameter or equal spacing issues.

Projection of ecological water consumption under carbon emission in Chinese provinces

Under the background of “double carbon”, ecological water has become one of the significant resources to ensure the healthy and sustainable development of the regional ecological environment. And the ecological water consumption prediction is a prerequisite for optimizing water supply structures. Considering the impact of CO2 emissions on ecological water consumption, the FGM(1,1) model was firstly used to predict CO2 emissions considered as an impact factor in this paper. Then, an adjacent accumulative grey multivariate convolution model (AGMC(1,N)) was combined with the Average Weakening Buffer Operator (AWBO) to predict the annual ecological water consumption of 30 provinces (municipalities and autonomous regions) in China. The results show that the AGMC(1,N) model combined with the AWBO has better prediction effect. In addition, in the next decade, only six provinces in the northern region will have a decreasing trend in ecological water consumption. However, the other provinces are showing an upward trend. The ecological water consumption trends deviate from the CO2 emission trends in 12 provinces. The research results are beneficial for the formulation of the ecological water consumption policies and the achievement of the dual carbon goals.

Characteristics and incidence of infections in patients with multiple myeloma treated by bispecific antibodies: a national retrospective study

ObjectivesBispecific antibodies (BsAbs) are an effective treatment used in relapsed or refractory multiple myeloma. Despite a well-tolerated safety profile, infectious events appear to be frequent in clinical trials. Real-world data on epidemiology, characteristics, risk factors, and outcomes of infections in patients treated with BsAb are still needed. MethodsA retrospective, multicentre study in BsAb-treated patients with multiple myeloma was performed in 14 French centres from December 2020 to February 2023. The primary objective was to describe the incidence of infections that required hospitalization, specific treatment, or adaptation in BsAb administration. ResultsAmong 229 patients with multiple myeloma treated with BsAb, 153 (67%) received teclistamab, 47 (20%) received elranatamab, and 29 (13%) talquetamab. We reported a total of 234 infections, including 123 (53%) of grade of ≥3. Predominant infections affected the respiratory tract (n = 116, 50%) followed by bacteraemias (n = 36, 15%). The hospitalization rate was 56% (n = 131), and 20 (9%) infections resulted in death. Global cumulative incidence of the first infection was 70% in all patients, 73% in patients treated with B-cell maturation antigen-targeting, and 51% with GPRC5D-targeting BsAb. In univariate analyses, corticosteroids for cytokine release syndrome (CRS)/immune effector cell-associated neurotoxicity syndrome (ICANS) were associated with a higher risk of first infection (HR = 2.13; 95% CI, 1.38–3.28), whereas GPRC5D-targeting BsAb and anti-bacterial prophylaxis were associated with a lower risk (HR = 0.53; 95% CI, 0.3–0.94 and HR = 0.65; 95% CI, 0.46–0.9). Fine and Gray multivariate model found that only corticosteroids for CRS/ICANS were correlated with a higher risk of first infection (HR = 2.01; 95% CI, 1.27–3.19). DiscussionsThe implementation of preventive measures that aim to mitigate the risk of infection under BsAb is pivotal, notably in patients who received corticosteroids for CRS/ICANS.

The research on a novel multivariate grey model and its application in carbon dioxide emissions prediction.

Accurate small-sample prediction is an urgent, very difficult, and challenging task due to the quality of data storage restricted in most realistic situations, especially in developing countries. The grey model performs well in small-sample prediction. Therefore, a novel multivariate grey model is proposed in this study, called FBNGM (1, N, r), with afractional order operator, which can increase the impact of new information and background value coefficient to achieve high prediction accuracy. The utilization of an intelligence optimization algorithm to tune the parameters of the multivariate grey model is an improvement over the conventional method, as it leads to superior accuracy. This study conducts two sets of numerical experiments on CO2 emissions to evaluate the effectiveness of the proposed FBNGM (1, N, r) model. The FBNGM (1, N, r) model has been shown through experiments to effectively leverage all available data and avoid the problem of overfitting. Moreover, it can not only obtain higher prediction accuracy than comparison models but also further confirm the indispensable importance of various influencing factors in CO2 emissions prediction. Additionally, the proposed FBNGM (1, N, r) model is employed to forecast CO2 emissions in the future, which can be taken as a reference for relevant departments to formulate policies.