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With the manufacturing reshoring to the US, increasing attention are focus on its energy consumption and environmental effects and accurate prediction of carbon emissions is vital to controlling growth from the source. Considering the slowing growth in carbon emissions with the Gompertz's law, this paper establishes a Gompertz differential equation. According to the differential information principle and fractional accumulation operator, this differential equation is transformed into a fractional accumulation grey Gompertz model. Furthermore, the chaotic whale optimization algorithm is used to optimize the order of accumulation generation and the grey background value in the proposed model. Then the Gompertz's datasets and six validation cases about carbon emissions are used to show that the proposed model demonstrates better accuracy in all cases and efficiency in the carbon emissions forecasting with several existing models. Three case studies indicate that the proposed model can fit the trend of American industrial carbon emissions better. The model results also reveal the recent policy changes have promoted the uptrend of the industrial and the total carbon emissions in the U.S. The future forecasting suggests that U.S. carbon emission is estimated to be 17.01% (in total emissions) or 17.89% (in industrial emission) percent below 2005 levels by 2025 under current policies, falling short of its commitment submitted to the United Nations Framework Convention on Climate Change.

Considering the effective service life characteristics of products in the background of product sales, this study first designs a generalized fractional-order accumulation generation matrix covering the effective accumulation percentage, replaces this matrix with the first-order accumulation generation operation in classical GMP(1,1), and establishes the definition equation of fractional-order accumulation GMP(1,1) [abbreviated as GFAGMP(1,1,D)] model. Second, the study derives the level ratio of the model via two other forms of the model [GFAGMP(1,1,M) and GFAGMP(1,1,H)] using integral and power function transformation, which is combined with the power function transformation and the relationship between the GFAGMP(1,1) model and the generalized the GM(1,1) model. The optimization model of accumulation generation matrix order $r$, effective accumulation percentage index $p$. and power exponent $m$ . is established, and the parameter optimization of the model is completed through particle swarm optimization. Finally, the simulation results of different grey models are compared with the actual sales data of Chinese refrigerators. This comparison demonstrates the feasibility and effectiveness of the GFAGMP(1,1) model in forecasting the home-appliance supply chain demand in China.

This study aims to reflect the information coverage grey number and the interaction between attributes in grey relational decision making. Therefore, a multi-attribute decision method based on the grey information coverage interaction relational degree (GIRD) is proposed. Firstly, this paper defines the information coverage grey number, and establishes the GIRD model by using the Choquet fuzzy integral and grey relational principle. It proves that the proposed model not only is the general and unified form of the point relational degree, interval relational degree, mixed relational degree and grey fuzzy integral relational degree, but also can effectively deal with the interaction between attributes. Further, a decision making example of evaluating the industrial operation quality for 14 cities in Hunan province of China is provided to high-light the implementation, availability, and feasibility of the proposed decision model.

This paper proposes a novel grey spatiotemporal model and quantitatively analyzes the spillover and momentum effects of the COVID-19 lockdown policy on the concentration of PM2.5 (particulate matter of diameter less than 2.5 μm) in Wuhan during the COVID-19 pandemic lockdown from 23 January to 8 April 2020 inclusive, and the post-pandemic period from 9 April 2020 to 17 October 2020 inclusive. The results suggest that the stringent lockdowns lead to a reduction in PM2.5 emissions arising from a momentum effect (9.57-18.67%) and a spillover effect (7.07-27.60%).

This study develops a neural network (NN) model to explore the nonlinear relationship between crash frequency and risk factors. To eliminate the possibility of over-fitting and to deal with the black-box characteristic, a network structure optimization algorithm and a rule extraction method are proposed. A case study compares the performance of the trained and modified NN models with that of the traditional negative binomial (NB) model for analyzing crash frequency on road segments in Hong Kong. The results indicate that the optimized NNs have somewhat better fitting and predictive performance than the NB models. Moreover, the smaller training/testing errors in the optimized NNs with pruned input and hidden nodes demonstrate the ability of the structure optimization algorithm to identify the insignificant factors and to improve the model generalization capacity. Furthermore, the rule-set extracted from the optimized NN model can reveal the effect of each explanatory variable on the crash frequency under different conditions, and implies the existence of nonlinear relationship between factors and crash frequency. With the structure optimization algorithm and rule extraction method, the modified NN model has great potential for modeling crash frequency, and may be considered as a good alternative for road safety analysis.

Greenhouse gas emissions bring severe challenges to the global climate, and CO2 emission prediction can provide decision support for atmospheric environmental governance and regional sustainable development. However, previous studies only focused on forecasting accuracy and neglected modeling mechanisms. To solve this problem, this paper proposes a novel fractional grey Riccati model (FGRM(1,1) model), which combines the Environmental Kuznets Curve hypothesis and differential information principle. The least-squares parameter estimation and mathematics analytical methods are utilized to obtain model parameters and the discrete response function, and the bare bone fireworks algorithm is introduced and designed to obtain the optimal fractional order. 20 data sets from M-competition are studied for confirming the effectiveness of the proposed model, and the performance test shows that it has higher stability and accuracy. Finally, the proposed model is employed to estimate and forecast the CO2 emissions of the United States, China, and Japan. Compared with three types of classical models without considering modeling mechanisms, the results show that the FGRM(1,1) model demonstrates better estimation in all cases and efficiency in short-term carbon emission forecasting. Results also indicated that these three countries all will reduce their carbon emissions gradually in future and the carbon emissions under current policies are estimated to be 0.31% (Japan), 4.52% (U.S.) and 4.49% (China) below 2020 levels by 2025, respectively.

To fully display the modeling mechanism of the novel fractional order grey model (FGM (q,1)), this paper decomposes the data matrix of the model into the mean generation matrix, the accumulative generation matrix and the raw data matrix, which are consistent with the fractional order accumulative grey model (FAGM (1,1)). Following this, this paper decomposes the accumulative data difference matrix into the accumulative generation matrix, the q-order reductive accumulative matrix and the raw data matrix, and then combines the least square method, finding that the differential order affects the model parameters only by affecting the formation of differential sequences. This paper then summarizes matrix decomposition of some special sequences, such as the sequence generated by the strengthening and weakening operators, the jumping sequence, and the non-equidistance sequence. Finally, this paper expresses the influences of the raw data transformation, the accumulation sequence transformation, and the differential matrix transformation on the model parameters as matrices, and takes the non-equidistance sequence as an example to show the modeling mechanism.

This study proposes a Bayesian spatio-temporal interaction approach for hotspot identification by applying the full Bayesian (FB) technique in the context of macroscopic safety analysis. Compared with the emerging Bayesian spatial and temporal approach, the Bayesian spatio-temporal interaction model contributes to a detailed understanding of differential trends through analyzing and mapping probabilities of area-specific crash trends as differing from the mean trend and highlights specific locations where crash occurrence is deteriorating or improving over time. With traffic analysis zones (TAZs) crash data collected in Florida, an empirical analysis was conducted to evaluate the following three approaches for hotspot identification: FB ranking using a Poisson-lognormal (PLN) model, FB ranking using a Bayesian spatial and temporal (B-ST) model and FB ranking using a Bayesian spatio-temporal interaction (B-ST-I) model. The results show that (a) the models accounting for space-time effects perform better in safety ranking than does the PLN model, and (b) the FB approach using the B-ST-I model significantly outperforms the B-ST approach in correctly identifying hotspots by explicitly accounting for the space-time variation in addition to the stable spatial/temporal patterns of crash occurrence. In practice, the B-ST-I approach plays key roles in addressing two issues: (a) how the identified hotspots have evolved over time and (b) the identification of areas that, whilst not yet hotspots, show a tendency to become hotspots. Finally, it can provide guidance to policy decision makers to efficiently improve zonal-level safety.

Of the grey models proposed for making predictions based on small sample data, the GM(1,1) model is the most important because of its low demands of data distribution, simple operation, and calculation requirements. However, the classical GM(1,1) model has two disadvantages: it cannot reflect the new information priority principle, and, if it is necessary to obtain the ideal effect of modeling, the original data must meet the class ratio test. This paper presents a new fractional grey model, FGM(q, 1), which is an extension of the GM(1,1) model in that first-order differential equations are transformed into fractional differential equations. Decomposition of the data matrix parameters during the process of solution shows that the new model follows the new information priority principle. For modeling, the mean absolute percentage error (MAPE) is established as the objective function of the optimization model, and a particle swarm algorithm is used to calculate the accumulation number and the order of the differential equation that can minimize the MAPE. Finally, the results from three groups of data modeling show that, compared with other classical grey models, FGM(q, 1) has higher modeling precision, can overcome the GM(1,1) model class ratio test restrictions and has a wider adaptability.

Nonlinear Grey Bernoulli Model (NGBM(1,1)) and its derivative model utilize the specific power exponent function to manifest the nonlinear characteristics of the energy consumption data pattern. Because the modeling constraint conditions and the data processing mechanism are rarely considered in parameter optimization of NGBM(1,1) the aim of this paper is just to establish a novel NGBM(1,1) optimization model with constraints using Box–Cox transformation (BC-NGBM*), in which the constraint conditions of the power index in the power function transformation are discussed according to the principle of difference information and the data processing mechanism. Parameter optimization of BC-NGBM* would be solved collectively using Quantum Adiabatic Evolution (QAE) algorithm. 143 data sets from M4-competition are studied for confirming the effectiveness of BC-NGBM* with QAE algorithm Finally, using data from 2010 to 2018, BC-NGBM* is used to forecast biomass energy consumption in China, the United States, Brazil, and Germany. The proposed model demonstrates high accuracy in all cases and is efficient for short-term biomass energy consumption forecasting.

Accurately forecasting energy demand can better predict future changes in energy demand. This study is aimed to develop more accurate clean energy prediction model from two perspectives of the modeling mechanisms and improvements on the model structure. For this purpose, a novel Riccati–Bernoulli differential equation is established through social practice theory, supply–demand relationship, and the preference of consumption in the energy economy. Considering the limited information in observation data, this differential equation is then transformed into a grey Riccati–Bernoulli model (GRBM(1,1)) according to the differential information principle. With the response function solved on the basis of polynomial equation theory and the power exponent optimized combining the modified flower pollination algorithm, the main process of GRBM(1,1) can be summarized. The four validation examples are provided for confirming the effectiveness and reliability of the new model by comparing with other existing models. Finally, the proposed model is employed to estimate and forecast the clean energy consumption in China and India. The results show that the proposed model demonstrates better estimation in all cases and efficiency in short-term clean energy consumption forecasting. Therefore, by using this optimum model, China’s preference coefficient in total energy consumption is 0.7103, lower than that of India (0.8799), and China’s preference coefficient in clean energy consumption is 0.9665, higher than that of Indian (0.7155), which means China has less interest to increase total energy consumption but more interest in popularizing the clean energy.

Boundary effect refers to the issue of ambiguous allocation of crashes occurred on or near the boundaries of neighboring zones in zonal safety analysis. It results in bias estimates for associate measure between crash occurrence and possible zonal factors. It is a fundamental problem to compensate for the boundary effect and enhance the model predictive performance. Compared to conventional approaches, it might be more reasonable to assign the boundary crashes according to the crash predisposing agents, since the crash occurrence is generally correlated to multiple sources of risk factors. In this study, we proposed a novel iterative aggregation approach to assign the boundary crashes, according to the ratio of model-based expected crash number in adjacent zones. To verify the proposed method, a case study using a dataset of 738 Traffic Analysis Zones (TAZs) from the county of Hillsborough in Florida was conducted. Using Bayesian spatial models (BSMs), the proposed approach demonstrated the capability in reasonably compensating for the boundary effect with better model estimation and predictive performance, as compared to three conventional approaches (i.e., half and half ratio method, one to one ratio method, and exposure ratio method). Results revealed that several factors including the number of intersections, road segment length with 35 mph speed limit, road segment length with 65 mph speed limit and median household income, were sensitive to the boundary effect.

Heterogeneity is an essential characteristic in car-following behaviours, which can be defined as the differences between the car-following behaviours of driver/vehicle combination under comparable conditions. This paper proposes a visual imaging model (VIM) with relaxed assumption on (1) a driver's perfect perception for the states of the neighbouring vehicles (e.g. spacing, velocity, etc.) and (2) uniform reaction to vehicles with different sizes in most existing car-following models. VIM utilises the visual imaging information subtended by the preceding vehicle as the stimuli drivers react to, and can generate greater stimuli from the preceding vehicle with larger apparent size (i.e. vehicle width × vehicle height) under short gap distance with the follower, but less change in stimuli from the distant leading vehicle under various apparent sizes. The NGSIM data containing vehicle type/size information is used to evaluate VIM at different levels. At the level of single trajectory pair, the calibrated VI...

Purpose – The purpose of this paper is to elevate the accuracy when predicting the gross domestic product (GDP) on research and development (R&D) and to develop the grey delay Lotka-Volterra model. Design/methodology/approach – Considering the lag effects between input in R&D and output in GDP, this paper estimated the delay value via grey delay relation analysis. Taking the delay into original Lotka-Volterra model and combining with the thought of grey theory and grey transform, the authors proposed grey delay Lotka-Volterra model, estimated the parameter of model and gave the discrete time analytic expression. Findings – Collecting the actual data of R&D and GDP in Wuhan China from 1995 until 2008, this paper figure out that the delay between R&D and GDP was 2.625 year and found the dealy time would would gradually be reduced with the economy increasing. Practical implications – Constructing the grey delay Lotka-Volterra model via above data, this paper shown that the precision was satisfactory when fitting the data of R&D and GDP. Comparing the forecasts with the actual data of GDP in Wuhan from 2009 until 2012, the error was small. Social implications – The result shows that R&D and GDP would be both growing fast in future. Wuhan will become a city full of activity. Originality/value – Considering the lag between R&D and GDP, this work estimated the delay value via a grey delay relation analysis and constructed a novel grey delay Lotka-Volterra model.

To predict the number of newborns, we establish an non-equigap stage sequence GM (1,1) model. Above all, we construct a non-equigap cumulative operator and calculate the optimal multiplier. Then we use the genetic algorithms to solve the model. On this basis, we improve it and obtain the GM(1,1,α) model. We make a contrast of the predicted number of newborns in two models above and the data in the traditional GM(1,1) model.