Purpose Accurate energy data prediction holds significant practical importance for optimizing energy structures and informing governmental energy decision making. Due to the uncertainty inherent in energy sequences, this paper proposes a hybrid model combining seasonal–trend decomposition and a nonlinear time-delay grey model. Design/methodology/approach The trend variations inherent in the data are obtained through signal decomposition techniques, and higher weights are assigned to new information within the model. Prediction results are restored via seasonal factors, and the optimal parameter values are obtained using the PSO algorithm. Findings An analysis of the model’s various characteristics is conducted. By fitting and forecasting China’s natural gas production data and comparing the results with those of four other benchmark models, the validity of the model is verified. Originality/value This study extends trend decomposition and seasonal factor restoration by incorporating nonlinear terms, lagged terms and new information priority, enabling the model to better adapt to dynamic trend changes and significantly improve prediction accuracy for time series with prominent dynamic trends and seasonal variations.

Purpose It is necessary but difficult to accurately predict the water levels in front of sluice gates of an open channel water transfer project due to the complex interactions among hydraulic structures. The existing methods have certain shortcomings. For example, although one-dimensional hydrodynamic simulation is technically feasible, little is known about hydrodynamic models for prediction. Another example is that, neural networks can hardly predict the information of nonmonitoring sections. To these problems, this paper presents a novel GRA-NARX and hydrodynamic coupled prediction model (H-GRA-NARX-HPM) that is based on the GRA-NARX (gray relation analysis-nonlinear auto-regressive exogenous) neural network with automatic hyperparameter calibration. Design/methodology/approach Firstly, the GRA is used to determine the correlations of influencing factors and find the optimal influencing factors. Secondly, the selected factors are taken as the input variables of the NARX neural network. Finally, the GRA-NARX neural network with automatic hyperparameter calibration (H-GRA-NARX model) provides accurate 24-h water level prediction to be used as the boundary condition of the hydrodynamic model, and then the H-GRA-NARX-HPM is constructed. Findings The section from the inlet sluice gate of Tang River aqueduct to the outlet sluice gate of Zhang River inverted siphon in the Middle Route of the South-to-North Water Transfer Project, China, is taken as the study area. The water levels before the outlet sluice gate of Anyang River inverted siphon on February 22, 2018 and February 26, 2018, are predicted by the H-GRA-NARX-HPM and then compared with those of the prediction models (GRA-BP-HPM, GRA-NARX-HPM) that use GRA-BP(gray relation analysis-back-propagation) neural network and GRA-NARX neural network prediction information as boundary conditions. The results show that the H-GRA-NARX-HPM has the highest accuracy with MAE values of 0.0028 m and 0.0141 m and MSE values of 1.636 × 10-5 and 2.658 × 10-4 on February 22 and February 26, respectively. In order to verify the universality and applicability of the model, the section from the inlet sluice gate of Ming River aqueduct to the outlet sluice gate of Qili River inverted siphon is taken as another study area. The water levels before the outlet sluice gate of Nansha River inverted siphon on March 18, 2018 and March 19, 2018, are predicted by the H-GRA-NARX-HPM and then also compared with GRA-BP-HPM and GRA-NARX-HPM. The results show that the H-GRA-NARX-HPM has the highest accuracy as well. Originality/value The main contribution of this paper is to propose a novel GRA-NARX and hydrodynamic coupled prediction model (H-GRA-NARX-HPM) which can overcome the main limitations of the individual modelling approaches.

Purpose This article aims to address the challenges of data scarcity, individual differences and multidimensional nonlinear relationships in complex equipment cost prediction. A fusion prediction model based on the residual category merging operator (RCMO) and the non-equidistant GM(1,1) model is proposed to improve prediction accuracy and generalization ability. Design/methodology/approach By constructing “virtual time factors,” multiple dimensions of cost-influencing factors are integrated into a single sequence. Combined with the non-equidistant GM(1,1) model to handle non-uniformly spaced data, the residual classification mechanism is introduced and the RCMO is designed to generate virtual similar samples, optimizing the robustness of the model. Findings In the rocket cost case, the non-equidistant RCMO-GM(1,1) model has an average relative error of 0.02650, significantly better than the multiple linear regression model (0.39237) and I-GM(0, N) model (0.11969) and can effectively capture nonlinear trends and complex patterns, demonstrating stronger adaptability and reliability. Research limitations/implications Although this model demonstrates a remarkable advantage in prediction accuracy, it has not yet been fully optimized in handling dynamic data updates. In the future, it is possible to explore the introduction of dynamic data update mechanisms to further enhance the robustness and applicability of the model. Originality/value This model solves the problems of data scarcity and individual differences through multi-factor fusion and residual correction mechanisms, providing a high-precision and stable tool for complex equipment cost prediction, and has broad engineering application potential.

PurposePeople engagement is critical to continuous improvement programmes’ performance and success. This study proposes a combined ISO standard-Grey system approach to assess the level of adoption of people engagement practices in continuous improvement programmes. To exemplify the use of this approach, this research analyses the level of adoption of these practices in Brazilian organizations in the manufacturing sector.Design/methodology/approachThe combined ISO standard-grey system approach is based on the ISO 10018:2022 standard and two grey system techniques (grey target and grey fixed weight clustering). The exemplification used industry experts from Brazil.FindingsThe approach developed presents ten people engagement practices in continuous improvement programmes to be assessed. To perform this assessment, a five-linguistic-terms scale is proposed. The exemplification of the approach application for Brazilian reality indicated that the adoption of the analysed practices is at an intermediate level in the country, with possibilities for improvement.Originality/valueThis research presents in detail an interesting method for assessing the adoption level of people engagement practices in continuous improvement programmes and contributes to debates regarding how these programmes can achieve success, primarily through company employees’ participation and engagement.

PurposeIn order to express the intrinsic information of interval grey number reasonably, this paper discusses the information measure index and its property of interval grey number.Design/methodology/approachFirstly, based on the generalized greyness and generalized whiteness of interval grey number, the definitions of the generalized grey information quantity, the generalized white information quantity and total information quantity of interval grey number are given, and the basic properties of the information quantity of interval grey number are analyzed. After that, in order to express the information dynamics of interval grey number, the concepts of generalized grey information density, generalized white information density and background information density of interval grey number are given, and the internal relationship between them is analyzed. Then, according to the principle of difference information, the definition of information difference quantity of interval grey numbers is given, and its property and the relationship between information difference quantity and greyness (whiteness) distance are analyzed, and a grey pattern recognition model based on grey information difference quantity is presented. Finally, the grey pattern recognition model is applied to the decision-making of artillery weapon procurement.FindingsThe results show that the generalized grey (white) information quantity of interval grey number is relative, normative, connected, gradual change, opposites, unity and justice, and is conserved. The generalized grey information density and generalized white information density of an interval grey number can better reflect the information dynamics of an interval grey number. The effect of the grey (white) information difference quantity is equivalent to that of the greyness (whiteness) distance. The grey pattern recognition model based on generalized grey information can make full use of the intrinsic information of interval grey numbers, and the application examples show that it is feasible and effective.Practical implicationsThe concepts and properties of the generalized grey (white) information quantity, generalized grey (white) information density and information difference quantity proposed in this paper not only provide a theoretical basis for the dialectical analysis of grey and white information evolution for interval grey numbers, but also provide a new thinking for the study of methods such as grey relational analysis, grey decision-making, grey pattern recognition and grey forecast from the perspective of information.Originality/valueThe paper succeeds in revealing some basic properties of the information quantity of interval grey number, such as the principle of information conservation and the relationship between information densities and so on, and gives a grey pattern recognition model based on grey information difference quantity, which provide a theoretical basis for the rational use of the information contained in interval grey number.

PurposeThis paper aims to propose a capacity assessment approach for production with uncertainty, focusing on single batch machine production with interval grey processing time.Design/methodology/approachBased on the interval grey number and its mathematical operations, single batch machine production with uncertain grey processing time is defined as the research object. The uncertain processing times generation methods are then developed, which rely on specific definitions and historical data. A capacity assessment approach tailored to this production mode is subsequently proposed, and its validity is demonstrated through multiple real-world cases from one aerospace composite material manufacturer.FindingsThe proposed capacity assessment approach provides reliable results for various types of single batch machine production tasks. For tasks with a small number of jobs or significant variations in job sizes, assessment results can be obtained in the first stage, known as model assessment. For the remaining production tasks, reliable results can be achieved through the second stage, heuristic assessment.Research limitations/implicationsIn this paper, the proposed capacity assessment approach is validated based on single batch machine production. To enhance its applicability in more actual production scenarios, the approach needs to extend to more production modes. The mathematical model and heuristic algorithm proposed in this paper have certain limitations and need to be further designed to suit the other production modes.Originality/valueThis paper provides a novel capacity assessment approach for uncertain production. And it helps to promote the application of grey system theory in real-world production management.

PurposeIn many instances, the data exhibits periodic and trend characteristics. However, indices like the Digital Economy Development Index (DEDI), which pertains to science, technology, policy and economy, may occasionally display erratic behaviors due to external influences. Thus, to address the unique attributes of the digital economy, this study integrates the principle of information prioritization with nonlinear processing techniques to accurately forecast rapid and anomalous data.Design/methodology/approachThe proposed method utilizes the new information priority GM(1,1) model alongside an optimized BP neural network model achieved through the gradient descent technique (GD-BP). Initially, the provincial Digital Economic Development Index (DEDI) is derived using the entropy weight approach. Subsequently, the original GM(1,1) time response equation undergoes alteration of the initial value, and the time parameter is fine-tuned using Particle Swarm Optimization (PSO). Next, the GD-BP model addresses the residual error. Ultimately, the prediction outcome of the grey combination forecasting model (GCFM) is derived by merging the findings from both the NIPGM(1,1) model and the GD-BP approach.FindingsUsing the DEDI of Jiangsu Province as a case study, researchers demonstrate the effectiveness of the grey combination forecasting model. This model achieves a mean absolute percentage error of 0.33%, outperforming other forecasting methods.Research limitations/implicationsFirst of all, due to the limited data access, it is impossible to obtain a more comprehensive dataset related to the DEDI of Jiangsu Province. Secondly, according to the test results of the GCFM from 2011 to 2020 and the forecasting results from 2021 to 2023, it can be seen that the results of the GCFM are consistent with the actual development situation, but it cannot guarantee the correctness of the long-term forecasting, so the combination forecasting model is only suitable for short-term forecasting.Originality/valueThis article proposes a grey combination prediction model based on the principles of new information priority and nonlinear processing.

PurposeThe purpose of this paper is to optimize the degradation test for products subject to multiple types of inherent stresses and external random shocks. The mechanism that shows how the variables to be optimized influence the considered multiple objectives is also aimed to be explored by using the grey incidence analysis (GIA) model.Design/methodology/approachThe Gamma process is employed to model the influences of different types of stresses and external random shocks. The GIA model is introduced to transfer multiple considered objectives as a comprehensive degree of grey incidence. The particle swarm optimization is integrated to search the globally optimal value of the characteristic variables to be optimized.FindingsThe acceleration of tested stresses and external random shocks both make the engineering systems become more vulnerable to the inherent degradation. And, the Kriging model can provide guidance of searching the optimal values of test characteristic variables and mitigate the computation burden. The grey incidence model can make the optimization focused and improve the optimality of objective values.Originality/valueThe proposed method can effectively overcome the drawbacks brought by the limitation of test data and can specify the dependence strength between the inherent degradation and external random shock. The computation cost and accuracy of optimization can be simultaneously ensured by the proposed model.

PurposeThis paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.Design/methodology/approachFirstly, 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.FindingsAGSM 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.Originality/valueA new AGSM with new information priority accumulation operation is proposed.

PurposeThis study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.Design/methodology/approachIn this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.FindingsThe results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.Originality/valueThe paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.