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Aiming at the traditional multivariate grey forecasting model only considers the modelling of real numbers; therefore, the purpose of this paper is to construct an MGM(1, m) model based on the interval grey number sequences according to the grey modelling theory.

First, the multivariable grey number sequences are transformed into the kernel and grey radius sequences which are two feature sequences of interval grey number sequences. Then the MGM(1, m) model for kernel sequences and grey radius sequences are established, respectively. Finally, the simulation and prediction of the upper and lower bounds of the interval grey number sequences are realized by the reductive calculation of the predicted values of the kernel and grey radius.

The model is applied to the prediction of visibility and relative humidity, the identification factors of the haze. The results show that the model has high accuracy on the simulation and prediction of multivariable grey number sequences, which is reasonable and practical.

The main contribution of this paper is to propose a method to simulate and forecast the multivariable grey number sequence that is to establish the prediction models for the whitening sequences of multivariable grey number sequences which are kernel and grey radius sequences and extend the possibility boundary of kernel by grey radius. The model can reflect the development trend of multivariable grey number sequence accurately. When the grey information is continuously complemented, the multivariable grey number prediction model is transformed into the traditional MGM(1, m) model. Therefore, the MGM(1, m) model based on interval grey number sequence is the generalisation and expansion of the traditional MGM(1, m) model.

In 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.

The 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.

Using 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.

First 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.

This article proposes a grey combination prediction model based on the principles of new information priority and nonlinear processing.

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

This paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.

In order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.

The proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.

Based on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

In recent years, online public opinion reversal incidents have been occurring frequently, which has increased the complexity of the evolution of online public opinion, and they have become a difficult issue for public opinion management and control. It is of great significance to explore the regularity of online public opinion reversal.

Combined with the grey characteristics of online public opinion information, a grey graphical evaluation review technique (G-GERT) network model is constructed based on kernel and grey degree, and the frequency, probability and time of online public opinion reversal nodes are calculated using C-marking method and Z-marking method.

Throughout the online public opinion reversal events, there are all repeated outbreak nodes occurring, so the authors regard the repeated occurrence of outbreak nodes as reversal. According to the average frequency, probability and time of repeated outbreak nodes in the G-GERT network model, the authors predict the corresponding key information of reversal. It can simulate the evolution process of public opinion events accurately.

The G-GERT network model based on kernel and grey degree reveals the regulation of public opinion reversal, predicts the frequency, probability and time of reversal nodes, which are the most concerned and difficult issues for decision-makers. The model provides the decision basis and reference for government decision-making departments.

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

The purpose of this study is to explore the interfacial adhesion between superhydrophobic coatings FC-X (X = 1%, 2%, 3%, 4% and 5%) and the concrete substrate, along with the impact of FC-X on the water repellency characteristics of the concrete substrate.

One synthetic step was adopted to prepare novel F-SiO₂ NP hybrid fluororesin coating. The impact of varying mass fractions of F-SiO₂ NPs on the superhydrophobicity of FC-X was analyzed and subsequently confirmed through water contact angle (WCA) measurements. Superhydrophobic coatings were simply applied to the concrete substrate using a one-step spraying method. The interfacial adhesion between FC-X and the concrete substrate was analyzed using tape pasting tests and abrasion resistance measurements. The influence of FC-X on the water repellency of the concrete substrate was investigated through measurements of water absorption, impermeability and electric flux.

FC-4% exhibits excellent superhydrophobicity, with a WCA of 157.5° and a sliding angle of 2.3°. Compared to control sample, FC-X exhibits better properties, including chemical durability, wear resistance, adhesion strength, abrasion resistance, water resistance and impermeability.

This study offers a thorough investigation into the practical implications of enhancing the durability and water repellency of concrete substrates by using superhydrophobic coatings, particularly FC-4%, which demonstrates exceptional superhydrophobicity alongside remarkable chemical durability, wear resistance, adhesion strength, abrasion resistance, water resistance and impermeability.

Through the examination of the interfacial adhesion between FC-X and the concrete substrate, along with an assessment of FC-X’s impact on the water repellency of the concrete, this paper provides valuable insights into the practical application of superhydrophobic coatings in enhancing the durability and performance of concrete materials.

The purpose of this study is to prepare a polydopamine (PDA)–palygorskite (Pal) hybrid-reinforced epoxy coating with high adhesion strength on wet concrete surface.

One synthetic step was adopted to prepare novel PDA–Pal hybrid epoxy coating. The process and product were analyzed and confirmed by FIRT, thermogravimetric analysis and scanning electron microscopy. The mass fraction of PDA–Pal hybrid affecting the adhesion strength of epoxy coating was analyzed and confirmed by pull-off test.

PDA–Pal hybrid mass fractions of 0, 1, 3 and 5 were added to the coatings. For a 5 Wt.% PDA–Pal hybrid content, the adhesive strengths on the saturated or underwater concrete surfaces increased to 4.0 and 2.5 MPa, respectively. In addition, the tensile mechanical property of the epoxy coating improved significantly after PDA–Pal addition.

This new epoxy coating hybrid by PDA–Pal could be applied as a concrete protective layer near water or in wet or damp environments.

Introduction of PDA–Pal hybrid to prepare epoxy coating with high adhesion strength on wet concrete surface has not been systematically studied previously.