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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.

This paper aims to overcome the problem that the single structure of the driving term of the grey prediction model is not adapted to the complexity and diversity of the actual modeling objects, which leads to poor modeling results.

Firstly, the nonlinear law between the raw data and time point is fully mined by expanding the nonlinear term and the range of order. Secondly, through the synchronous optimization of model structure and parameter, the dynamic adjustment of the model with the change of the modeled object is realized. Finally, the objective optimization of nonlinear driving term and cumulative order of the model is realized by particle swarm optimization PSO algorithm.

The model can achieve strong compatibility with multiple existing models through parameter transformation. The synchronous optimization of model structure and parameter has a significant improvement over the single optimization method. The new model has a wide range of applications and strong modeling capabilities.

A novel grey prediction model with structure variability and optimizing parameter synchronization is proposed.

The highlights of the paper are as follows:

1. A new grey prediction model with a unified nonlinear structure is proposed.

2. The new model can be fully compatible with multiple traditional grey models.

3. The new model solves the defect of poor adaptability of the traditional grey models.

4. The parameters of the new model are optimized by PSO algorithm.

5. Cases verify that the new model outperforms other models significantly.

A new grey prediction model with a unified nonlinear structure is proposed.

The new model can be fully compatible with multiple traditional grey models.

The new model solves the defect of poor adaptability of the traditional grey models.

The parameters of the new model are optimized by PSO algorithm.

Cases verify that the new model outperforms other models significantly.

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

The purpose of this paper is to develop a novel multivariate fractional grey model termed GM(a, n) based on the classical GM(1, n) model. The new model can provide accurate prediction with more freedom, and enrich the content of grey theory.

The GM(α, n) model is systematically studied by using the grey modelling technique and the forward difference method. The optimal fractional order a is computed by the genetic algorithm. Meanwhile, a stochastic testing scheme is presented to verify the accuracy of the new GM(a, n) model.

The recursive expressions of the time response function and the restored values of the presented model are deduced. The GM(1, n), GM(a, 1) and GM(1, 1) models are special cases of the model. Computational results illustrate that the GM(a, n) model provides accurate prediction.

The GM(a, n) model is used to predict China’s total energy consumption with the raw data from 2006 to 2016. The superiority of the GM(a, n) model is more freedom and better modelling by fractional derivative, which implies its high potential to be used in energy field.

It is the first time to investigate the multivariate fractional grey GM(α, n) model, apply it to study the effects of China’s economic growth and urbanization on energy consumption.

The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with the unified fractional grey generation operator.

By systematically studying the properties of the fractional accumulating operator and the reducing operator, and analyzing the sensitivity of the order value, a unified expression of the fractional operators is given. The FDGM(1,1) model with the unified fractional grey generation operator is established. The relationship between the order value and the modeling error distribution is studied.

The expression of the fractional accumulating generation operator and the reducing generation operator can be unified to a simple expression. For −1<r < 1, the fractional grey generation operator satisfies the principle of new information priority. The DGM(1,1) model is a special case of the FDGM(1,1) model with r = 1.

The sensitivity of the unified operator is verified through random numerical simulation method, and the theoretical proof was not yet possible.

The FDGM(1,1) model has a higher modeling accuracy and modeling adaptability than the DGM(1,1) by optimizing the order.

The expression of the fractional accumulating generation operator and the reducing generation operator is firstly unified. The FDGM(1,1) model with the unified fractional grey generation operator is firstly established. The unification of the fractional accumulating operator and the reducing operator improved the theoretical basis of grey generation operator.

Accurate prediction of seasonal power consumption trends with impact disturbances provides a scientific basis for the flexible balance of the long timescale power system. Consequently, it fosters reasonable scheduling plans, ensuring the safety of the system and improving the economic dispatching efficiency of the power system.

First, a new seasonal grey buffer operator in the longitudinal and transverse dimensional perspectives is designed. Then, a new seasonal grey modeling approach that integrates the new operator, full real domain fractional order accumulation generation technique, grey prediction modeling tool and fruit fly optimization algorithm is proposed. Moreover, the rationality, scientificity and superiority of the new approach are verified by designing 24 seasonal electricity consumption forecasting approaches, incorporating case study and amalgamating qualitative and quantitative research.

Compared with other comparative models, the new approach has superior mean absolute percentage error and mean absolute error. Furthermore, the research results show that the new method provides a scientific and effective mathematical method for solving the seasonal trend power consumption forecasting modeling with impact disturbance.

Considering the development trend of longitudinal and transverse dimensions of seasonal data with impact disturbance and the differences in each stage, a new grey buffer operator is constructed, and a new seasonal grey modeling approach with multi-method fusion is proposed to solve the seasonal power consumption forecasting problem.

The highlights of the paper are as follows:

1. A new seasonal grey buffer operator is constructed.

2. The impact of shock perturbations on seasonal data trends is effectively mitigated.

3. A novel seasonal grey forecasting approach with multi-method fusion is proposed.

4. Seasonal electricity consumption is successfully predicted by the novel approach.

5. The way to adjust China's power system flexibility in the future is analyzed.

A new seasonal grey buffer operator is constructed.

The impact of shock perturbations on seasonal data trends is effectively mitigated.

A novel seasonal grey forecasting approach with multi-method fusion is proposed.

Seasonal electricity consumption is successfully predicted by the novel approach.

The way to adjust China's power system flexibility in the future is analyzed.

The purpose of this paper is to design a multi-sensory anthropomorphic prosthetic hand and a grasping controller that can detect the slip and automatically adjust the grasping force to prevent the slip.

To improve the dexterity, sensing, controllability and practicability of a prosthetic hand, a modular and multi-sensory prosthetic hand was presented. In addition, a slip prevention control based on the tactile feedback was proposed to improve the grasp stability. The proposed controller identifies slippages through detecting the high-frequency vibration signal at the sliding surface in real time and the discrete wavelet transform (DWT) was used to extract the eigenvalues to identify slippages. Once the slip is detected, a direct-feedback method of adjusting the grasp force related with the sliding times was used to prevent it. Furthermore, the stiffness of different objects was estimated and used to improve the grasp force control. The performances of the stiffness estimation, slip detection and slip control are experimentally evaluated.

It was found from the experiment of stiffness estimation that the accuracy rate of identification of the hard metal bottle could reach to 90%, while the accuracy rate of identification of the plastic bottles could reach to 80%. There was a small misjudgment rate in the identification of hard and soft plastic bottles. The stiffness of soft plastic bottles, hard plastic bottles and metal bottles were 0.64 N/mm, 1.36 N/mm and 32.55 N/mm, respectively. The results of slip detection and control show that the proposed prosthetic hand with a slip prevention controller can fast and effectively detect and prevent the slip for different disturbances, which has a certain application prospect.

Due to the small size, low weight, high integration and modularity, the prosthetic hand is easily applied to upper-limb amputees. Meanwhile, the method of the slip prevention control can be used for upper-limb amputees to complete more tasks stably in daily lives.

A multi-sensory anthropomorphic prosthetic hand is designed, and a method of stable grasps control based on slip detection by a tactile sensor on the fingertip is proposed. The method combines the stiffness estimation of the object and the real-time slip detection based on DWT with the design of the proportion differentiation robust controller based on a disturbance observer and the force controller to achieve slip prevention and stable grasps. It is verified effectively by the experiments and is easy to be applied to commercial prostheses.

China is by far the world’s largest energy consumer and importer. Reasonably forecasting the trend of China’s total energy consumption (CTEC) is of great significance. The purpose of this paper is to propose a new-structure grey system model (NSGM (1, 1)) to forecast CTEC.

Two matrices for computing the parameters of NSGM (1, 1) were defined and the specific calculation formula was derived. Since the NSGM (1, 1) model increases the number of its background values, which improves the smoothness effect of the background value and weakens the effects of extreme values in the raw sequence on the model’s performance; hence it has better simulation and prediction performances than traditional grey models. Finally, NSGM (1, 1) was used to forecast China’s total energy consumption during 2016-2025. The forecast showed CTEC will grow rapidly in the next ten years.

Therefore, in order to meet the target of keeping CTEC under control at 4.8 billion tons of standard coal in 2020, Chinese government needs to take necessary measures such as transforming the economic development pattern and enhancing the energy utilization efficiency.

A new-structure grey forecasting model, NSGM (1, 1), is proposed in this paper, which improves the smoothness and weakens the effects of extreme values and has a better structure and performance than those of other grey models. The authors successfully employ the new model to simulate and forecast CTEC. The research findings could aid Chinese government in formulating energy policies and help energy exporters make rational energy yield plans.

This paper aims to present the design and experiment of a modular multisensory prosthetic hand for applications. Design and experiment of a modular multisensory hand for prosthetic applications.

This paper reveals more details focusing on the appearance, mechanism design, electrical design and control of the prosthetic hand considering anthropomorphism, dexterity, sensing and controllability. The finger is internally integrated with the actuator, the transmission mechanism, the sensors and the controller as a modular unit. Integrated with multiple sensors, the prosthetic hand can not only perceive the position, the contact force and the temperature of the environment like a human hand but also provide the foundation for the practical control.

The experiments show that the prosthetic hand can accurately control the contact force to achieve stable grasps based on the sensors feedback and a simple and effective force-tracking impedance control algorithm. In addition, the experiments based on the cosmesis validate not only the cosmesis functionality but also the control performance for a prosthesis–cosmesis system.

Because of the small size, low weight, high integration, modularity and controllability, the prosthetic hand is easily applied to upper-limb amputees. Meanwhile, the finger as a modular unit is easy to be fixed, maintained and applied to a partial upper-limb amputee.

Each modular finger of the prosthetic hand integrated with the actuator, the transmission mechanism, the sensors and the controller as a whole can independently control the position and the force. The cosmetic glove design can provide pretty appearance without compromising the control performance.