scholarly journals An Improved Nonhomogeneous Grey Model with Fractional-Order Accumulation and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shuanghua Liu ◽  
Qin Qi ◽  
Zhiming Hu
Keyword(s):  
Optimal Parameter ◽  
Mean Value ◽  
Grey Model ◽  
Mean Value Theorem ◽  
Percentage Error ◽  
Proposed Model ◽  
Whale Optimization ◽  
Competing Models ◽  
High Prediction ◽  
Better Than

The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.

scholarly journals A New Information Priority Accumulated Grey Model with Hyperbolic Sinusoidal Term and its Application

2021 ◽  
Vol 1 (2) ◽  
pp. 5-19
Author(s):  
Xue Tian ◽  
Wenqing Wu ◽  
Xin Ma ◽  
Peng Zhang
Keyword(s):  
Natural Gas ◽  
Fossil Fuels ◽  
Optimal Parameter ◽  
Estimation Method ◽  
Least Square ◽  
Grey Model ◽  
Grey Forecasting ◽  
New Information ◽  
Proposed Model ◽  
Whale Optimization

Compared to fossil fuels, natural gas is cleaner energy, which has developed rapidly in recent years. Studying the urban supply of natural gas has implications for the development of natural gas. In this paper, the new information priority accumulation method is integrated into the grey forecasting model with the hyperbolic sinusoidal driving term, and then the new grey model is used to predict the urban natural gas supply. The system's linear parameters are calculated by the least square estimation method, and the optimal parameter of the new information accumulated priority is determined by the Whale Optimization Algorithm. Finally, the supply of urban gas is forecasted using the proposed model, and comparative analyses with the four other forecasting models are presented.  

A novel fractional discrete nonlinear grey Bernoulli model for forecasting the wind turbine capacity of China

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wen-ze Wu ◽  
Wanli Xie ◽  
Chong Liu ◽  
Tao Zhang
Keyword(s):  
Wind Turbine ◽  
Nonlinear Coefficient ◽  
Predictive Performance ◽  
Prediction Performance ◽  
New Method ◽  
Grey Model ◽  
Content Type ◽  
Proposed Model ◽  
Whale Optimization ◽  
Turbine Capacity

PurposeA new method for forecasting wind turbine capacity of China is proposed through grey modelling technique.Design/methodology/approachFirst of all, the concepts of discrete grey model are introduced into the NGBM(1,1) model to reduce the discretization error from the differential equation to its discrete forms. Then incorporating the conformable fractional accumulation into the discrete NGBM(1,1) model is carried out to further improve the predictive performance. Finally, in order to effectively seek the emerging coefficients, namely, fractional order and nonlinear coefficient, the whale optimization algorithm (WOA) is employed to determine the emerging coefficients.FindingsThe empirical results show that the newly proposed model has a better prediction performance compared to benchmark models; the wind turbine capacity from 2019 to 2021 is expected to reach 275954.42 Megawatts in 2021. According to the forecasts, policy suggestions are provided for policy-makers.Originality/valueBy combing the fractional accumulation and the concepts of discrete grey model, a new method to improve the prediction performance of the NGBM(1,1) model is proposed. The newly proposed model is firstly applied to predict wind turbine capacity of China.

scholarly journals An Improved Nonequidistant Grey Model Based on Simpson Formula and Its Application

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhiming Hu ◽  
Chong Liu
Keyword(s):  
Prediction Accuracy ◽  
Prediction Models ◽  
Prediction Performance ◽  
Grey System Theory ◽  
Grey Model ◽  
Grey Prediction ◽  
Grey System ◽  
Proposed Model ◽  
Grey Models ◽  
High Prediction

Grey prediction models have been widely used in various fields of society due to their high prediction accuracy; accordingly, there exists a vast majority of grey models for equidistant sequences; however, limited research is focusing on nonequidistant sequence. The development of nonequidistant grey prediction models is very slow due to their complex modeling mechanism. In order to further expand the grey system theory, a new nonequidistant grey prediction model is established in this paper. To further improve the prediction accuracy of the NEGM (1, 1, t2) model, the background values of the improved nonequidistant grey model are optimized based on Simpson formula, which is abbreviated as INEGM (1, 1, t2). Meanwhile, to verify the validity of the proposed model, this model is applied in two real-world cases in comparison with three other benchmark models, and the modeling results are evaluated through several commonly used indicators. The results of two cases show that the INEGM (1, 1, t2) model has the best prediction performance among these competitive models.

Non-equidistant non-homogenous grey prediction model with fractional accumulation and its application

2021 ◽  
pp. 1-14
Author(s):  
Jia-Nian Zhu ◽  
Xu-Chong Liu ◽  
Chong Liu
Keyword(s):  
Prediction Model ◽  
Prediction Accuracy ◽  
Prediction Models ◽  
Grey Prediction ◽  
Grey Prediction Model ◽  
Model Based ◽  
Whale Optimization ◽  
High Prediction ◽  
Best Parameters ◽  
Better Than

Non-equidistant non-homogenous grey model (abbreviated as NENGM (1,1, k) model) is a grey prediction model suitable for predicting time series with non-equal intervals. It is widely used in various fields of society due to its high prediction accuracy and strong adaptability. In order to further improve the prediction accuracy of the NENGM (1,1, k) model, the NENGM (1,1, k) model is optimized in terms of the cumulative order and background value of the NENGM (1,1, k) model, and a NENGM (1,1, k) model based on double optimization is established (abbreviated as FBNENGM (1,1, k) model), and the whale optimization algorithm is used to solve the best parameters of the model. In order to verify the feasibility and validity of the FBNENGM (1,1, k) model, the FBNENGM (1,1, k) model and other four prediction models are applied to three cases respectively, and three indexes commonly used to evaluate the performance of prediction models are used to distinguish. The results show that the prediction accuracy of the FBNENGM (1,1, k) model based on double optimization is better than other prediction models.

Vibration signal diagnosis and analysis of rotating machine by utilizing cloud computing

2021 ◽  
Vol 10 (1) ◽  
pp. 404-413
Author(s):  
Zhe Mi ◽  
Tiangang Wang ◽  
Zan Sun ◽  
Rajeev Kumar
Keyword(s):  
Cloud Computing ◽  
Vibration Signal ◽  
Absolute Error ◽  
Mean Value ◽  
Percentage Error ◽  
Inference System ◽  
Computing Platform ◽  
Fault Prognosis ◽  
Adaptive Neurofuzzy Inference System ◽  
Better Than

Abstract Vibration signal diagnosis and analysis plays an important role in the industrial machinery since it enhances the machinery performance under supervision. The information regarding the future condition is given by vibration diagnosis techniques which is growing interest for the scientific and industrial communities. Information for failure diagnostic and prediction are provided by the motor vibration through signal processing. The development of mechanical systems fault prognosis and in the last decades, research is done at a very rapid rate. The examination of vibration signal monitoring is done in this paper with the aid of Cyber-Physical Systems (CPS) and Cloud Technology (CT). The machines maintenance strategies are implemented by using the data collected from machines which are based on the fault prognosis. The cloud computing platform is presented in this paper which is having three layers and the unlabelled data is received to generate an interpreted online decision. Feature extraction of the vibration signal is obtained in terms of range, mean value, root mean square value, and standard deviation and crest values. The performance of the model is evaluated by utilizing the classical statistical metrics such as RMSE Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) of the vibration signal. It is obtained that the proposed technique is 25% and 90% better than the Adaptive Neurofuzzy Inference System and the Single Modeling System respectively in terms of RMSE. The performance in terms of MAPE, then the proposed technique outperforms the existing Adaptive Neurofuzzy Inference System and the Single Modeling System by 8 % and 60% respectively. The presented technique is better than the existing Adaptive Neurofuzzy Inference System and the Single Modeling techniques by average of 15% and 30 % respectively.

scholarly journals A novel particle swarm optimization-based grey model for the prediction of warehouse performance

2021 ◽  
Author(s):  
Md Rakibul Islam ◽  
Syed Mithun Ali ◽  
Amir Mohammad Fathollahi-Fard ◽  
Golam Kabir
Keyword(s):  
Particle Swarm Optimization ◽  
Supply Chain ◽  
Particle Swarm ◽  
Control Measures ◽  
Data Availability ◽  
Grey Model ◽  
Percentage Error ◽  
Swarm Optimization ◽  
Forecasting Error ◽  
Proposed Model

Abstract Warehouses constitute a key component of supply chain networks. An improvement to the operational efficiency and the productivity of warehouses is crucial for supply chain practitioners and industrial managers. Overall warehouse efficiency largely depends on synergic performance. The managers preemptively estimate the overall warehouse performance (OWP), which requires an accurate prediction of a warehouse’s key performance indicators (KPIs). This research aims to predict the KPIs of a ready-made garment (RMG) warehouse in Bangladesh with a low forecasting error in order to precisely measure OWP. Incorporating advice from experts, conducting a literature review, and accepting the limitations of data availability, this study identifies 13 KPIs. The traditional grey method (GM)—the GM (1, 1) model—is established to estimate the grey data with limited historical information but not absolute. To reduce the limitations of GM (1, 1), this paper introduces a novel particle swarm optimization (PSO)-based grey model—PSOGM (1, 1)—to predict the warehouse’s KPIs with less forecasting error. This study also uses the genetic algorithm (GA)-based grey model—GAGM (1, 1)—the discrete grey model—DGM (1, 1)—to assess the performance of the proposed model in terms of the mean absolute percentage error and other assessment metrics. The proposed model outperforms the existing grey models in projecting OWP through the forecasting of KPIs over a 5-month period. To find out the optimal parameters of the PSO and GA algorithms before combining them with the grey model, this study adopts the Taguchi design method. Finally, this study aims to help warehouse professionals make quick OWP estimations in advance to take control measures regarding warehouse productivity and efficiency.

Implementasi Metode Winter untuk Forecasting Pertumbuhan Jumlah Penduduk: Studi Kasus Wilayah Provinsi NTB

2020 ◽  
Vol 3 (1) ◽  
pp. 51-61
Author(s):  
Syaharuddin ◽  
Abdul Adhiim Rizky ◽  
Lutfi Jauhari ◽  
Siti Fatimah ◽  
Wahyu Ningsih ◽  
...  
Keyword(s):  
Time Series Data ◽  
Optimal Parameter ◽  
Series Data ◽  
Percentage Error ◽  
Average Error ◽  
Ratio Data ◽  
Female Data ◽  
Forecasting System ◽  
Conducting Research ◽  
And Gender

This research aims to analyse the acceleration of population growth based on gender in West Nusa Tenggara Province (NTB) using the Forecasting system by constructing the winter's method in the shape of the Multiple Forecasting System (G-MFS) based on Matlab by calculating the period indicator for accuracy to find time series data in the year 2020-2029. At the simulation stage, researchers used the population and gender ratio data in NTB Province in 2009-2019. The method used in conducting research is to use the winter's method. The evaluation of Forecasting results is done by calculating the average error value using the Mean Absolute Percentage Error (MAPE) method. From this study obtained the most optimal parameter value on male data namely ʌ, β and γ sequential values of 0.9, 0.5 and 0.9 while in female data, the value of ʌ, β and γ respectively, 0.2, 0.1 and 0.5. Then with the value of the parameter obtained MAPE value in male data of 1.7785% and in female data of 0.89034%.

scholarly journals On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1303
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Faraidun Kadir Hamasalh
Keyword(s):  
Time Scale ◽  
Initial Value Problems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Discrete Fractional Calculus ◽  
Initial Value ◽  
Forward Difference ◽  
The Mean ◽  
Monotonicity Analysis ◽  
Monotonicity Results

Monotonicity analysis of delta fractional sums and differences of order υ∈(0,1] on the time scale hZ are presented in this study. For this analysis, two models of discrete fractional calculus, Riemann–Liouville and Caputo, are considered. There is a relationship between the delta Riemann–Liouville fractional h-difference and delta Caputo fractional h-differences, which we find in this study. Therefore, after we solve one, we can apply the same method to the other one due to their correlation. We show that y(z) is υ-increasing on Ma+υh,h, where the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and then, we can show that y(z) is υ-increasing on Ma+υh,h, where the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) for each z∈Ma+h,h. Conversely, if y(a+υh) is greater or equal to zero and y(z) is increasing on Ma+υh,h, we show that the delta Riemann–Liouville fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to zero, and consequently, we can show that the delta Caputo fractional h-difference of order υ of a function y(z) starting at a+υh is greater or equal to −1Γ(1−υ)(z−(a+υh))h(−υ)y(a+υh) on Ma,h. Furthermore, we consider some related results for strictly increasing, decreasing, and strictly decreasing cases. Finally, the fractional forward difference initial value problems and their solutions are investigated to test the mean value theorem on the time scale hZ utilizing the monotonicity results.

scholarly journals Contactless Video-Based Heart Rate Monitoring of a Resting and an Anesthetized Pig

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 442
Author(s):  
Meiqing Wang ◽  
Ali Youssef ◽  
Mona Larsen ◽  
Jean-Loup Rault ◽  
Daniel Berckmans ◽  
...  
Keyword(s):  
Heart Rate ◽  
Estimation Error ◽  
Well Being ◽  
Absolute Error ◽  
Mean Value ◽  
Video Data ◽  
Window Functions ◽  
The Face ◽  
Short Time ◽  
Better Than

Heart rate (HR) is a vital bio-signal that is relatively easy to monitor with contact sensors and is related to a living organism’s state of health, stress and well-being. The objective of this study was to develop an algorithm to extract HR (in beats per minute) of an anesthetized and a resting pig from raw video data as a first step towards continuous monitoring of health and welfare of pigs. Data were obtained from two experiments, wherein the pigs were video recorded whilst wearing an electrocardiography (ECG) monitoring system as gold standard (GS). In order to develop the algorithm, this study used a bandpass filter to remove noise. Then, a short-time Fourier transform (STFT) method was tested by evaluating different window sizes and window functions to accurately identify the HR. The resulting algorithm was first tested on videos of an anesthetized pig that maintained a relatively constant HR. The GS HR measurements for the anesthetized pig had a mean value of 71.76 bpm and standard deviation (SD) of 3.57 bpm. The developed algorithm had 2.33 bpm in mean absolute error (MAE), 3.09 bpm in root mean square error (RMSE) and 67% in HR estimation error below 3.5 bpm (PE3.5). The sensitivity of the algorithm was then tested on the video of a non-anaesthetized resting pig, as an animal in this state has more fluctuations in HR than an anaesthetized pig, while motion artefacts are still minimized due to resting. The GS HR measurements for the resting pig had a mean value of 161.43 bpm and SD of 10.11 bpm. The video-extracted HR showed a performance of 4.69 bpm in MAE, 6.43 bpm in RMSE and 57% in PE3.5. The results showed that HR monitoring using only the green channel of the video signal was better than using three color channels, which reduces computing complexity. By comparing different regions of interest (ROI), the region around the abdomen was found physiologically better than the face and front leg parts. In summary, the developed algorithm based on video data has potential to be used for contactless HR measurement and may be applied on resting pigs for real-time monitoring of their health and welfare status, which is of significant interest for veterinarians and farmers.

scholarly journals On a hybrid version of the Vinogradov mean value theorem

2021 ◽  
Vol 163 (1) ◽  
pp. 1-17
Author(s):  
C. Chen ◽  
I. E. Shparlinski
Keyword(s):  
Mean Value ◽  
Mean Value Theorem
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