exponential regression
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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 195
Author(s):  
Matvey Pavlyutin ◽  
Marina Samoyavcheva ◽  
Rasul Kochkarov ◽  
Ekaterina Pleshakova ◽  
Sergey Korchagin ◽  
...  

To predict the spread of the new coronavirus infection COVID-19, the critical values of spread indicators have been determined for deciding on the introduction of restrictive measures using the city of Moscow as an example. A model was developed using classical methods of mathematical modeling based on exponential regression, the accuracy of the forecast was estimated, and the shortcomings of mathematical methods for predicting the spread of infection for more than two weeks. As a solution to the problem of the accuracy of long-term forecasts for more than two weeks, two models based on machine learning methods are proposed: a recurrent neural network with two layers of long short-term memory (LSTM) blocks and a 1-D convolutional neural network with a description of the choice of an optimization algorithm. The forecast accuracy of ML models was evaluated in comparison with the exponential regression model and one another using the example of data on the number of COVID-19 cases in the city of Moscow.


2021 ◽  
Vol 1 (2) ◽  
pp. 60-68
Author(s):  
Ferta Monamaulisa Septyari

Palm oil is one of the leading export commodities of Indonesia. Knowing demand in advance can help policy-makers better prepare for the situation. India is one of the major importers of Indonesian palm oil. The study forecasted the Indonesian palm oil's exports to India from till 2025 using the grey forecasting model EGM (1,1, α, θ). The comparative analyses with Linear regression and exponential regression showed that the grey forecasting technique is relatively more accurate to forecast palm oil exports despite huge uncertainty in the data trend. The secondary data on Indonesian palm oil exports to India from 2011-2018 was obtained from the Indonesian Central Statistics Agency (BPS). Mean absolute percentage error was used for error measurement. Despite uncertainty in data, the results show an increasing trend in palm oil exports.  


2021 ◽  
Vol 1 (2) ◽  
pp. 33-46
Author(s):  
Cliford Septian Candra ◽  
Jason Adrian ◽  
Varren Christian Lim

Indonesia's trade balance with China has remained negative since 2010. The current study forecasts Indonesia's trade deficit with China for five years using the Even Grey Forecasting model EGM (1,1,α,θ). The sample was conducted by collecting the data of traded deficits for the past ten years. Data were collected from the official websites of Indonesia's Central Bureau of Statistics of (BPS), Ministry of Trade, among others. By building upon the literature, the study argues that trade deficits might have occurred from internal and external factors, such as the lack of infrastructure, the depreciation of the Rupiah (Indonesian currency) against the U.S. dollar, and the ASEAN-China Free Trade Agreement. Comparative analysis with Linear Regression (LR), Exponential Regression (ER), and Exponential Triple Smoothing (ETS) revealed the superiority of the grey forecasting model for trade deficit prediction. The study found that the trade deficit was minimum during the COVID-19 pandemic. It also showed an increasing trade deficit in the post-COVID period. The study concludes with some recommendations for Indonesia to minimize the trade deficit.  


Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1371
Author(s):  
Katarzyna Peta ◽  
Michał Mendak ◽  
Tomasz Bartkowiak

The aim of this study is first to determine the effect of the discharge energy on the surface microgeometry of aluminum samples created by electrical discharge machining (EDM). Secondly, an additional purpose is to demonstrate the differences between the geometric multiscale methods: length-, area-scale, and curvature. Eleven samples were manufactured using discharge energies ranging from 0.486 mJ to 1389.18 mJ and, subsequently, measured with focus variation microscopy. Standard ISO and multiscale parameters were calculated and used for surface discrimination and regression analysis. The results of linear, logarithmic, and exponential regression analyses revealed a strong correlation (R2 > 0.9) between the geometrical features of the surface topography and the discharge energy. The approach presented in this paper shows that it is possible to shape surface microgeometry by changing the energy of electrical discharges, and these dependencies are visible in various scales of observation. The similarities of the results produced by curvature and length-scale methods were observed, despite the significant differences in the essence of those methods.


Author(s):  
Ujjval B. Vyas ◽  
Varsha A. Shah ◽  
Athul Vijay P.K. ◽  
Nikunj R. Patel

Purpose The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and SoC relationships accurately, with reduced memory requirement. Design/methodology/approach Incremental OCV test under constant temperature provides a data set of OCV and SoC. This data set is subjected to polynomial, Gaussian and the proposed Gaussian exponential equations. The unknown coefficients of these equations are obtained by least residual algorithm and differential evolution–based fitting algorithms for charging, discharging and average OCV. Findings Root mean square error (RMSE) of the proposed equation for differential evolution–based fitting technique is 35% less than second-order Gaussian and 74% less than a fifth-order polynomial equation for average OCV with a 16.66% reduction in number of coefficients, thereby reducing memory requirement. Originality/value The knee structure in the OCV and SoC relationship is accurately represented by Gaussian first-order equation, and the exponential equation can accurately describe the linear relation. Therefore, this paper proposes a Gaussian exponential equation that accurately represents the OCV as a function of SoC. The results obtained from the proposed regression methodology are compared with the polynomial and Gaussian regression in terms of RMSE, mean average, variance and number of coefficients.


2021 ◽  
Author(s):  
Mahmoud Alipour ◽  
Seyed Mohammad Reza Hashemi Gholpayeghani

Abstract One of the most challenging discussions about EEG is the chaotic nature of this biological signal. In the present study, we attempt to provide an analysis to demonstrate sleep EEG chaoticity. We model changes of sleep attractor dynamic in phase space by exponential regression. Our model demonstrates that the sleep attractor is the sleep cycle attractor whose size shrinks during successive cycles by presenting a new definition of the sleep cycle. We study the EEG dynamics of different sleep stages by presenting two new features based on phase space properties. We show that each stage has a unique chaotic attractor. We model geometric changes of these attractors during successive sleep cycles. Our model achieves an accuracy, sensitivity, and specificity of 89.15%, 82.84%, and 81.62% classifying sleep stages.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sasan Adeli ◽  
Vahid Najafi moghaddam Gilani ◽  
Mohammad Kashani Novin ◽  
Ehsan Motesharei ◽  
Reza Salehfard

The main objective of this paper was to investigate the relationship between PCI and IRI values of the rural road network. To this end, 6000 pavement sections of the rural road network in Iran were selected. Road surface images and roughness linear profiles were collected using an automated car to calculate PCI and IRI, respectively. Three exponential regression models were developed and validated in three different IRI intervals. Analysis of the results indicated that exponential regression was the best model to relate IRI and PCI. In these models, R2 values were found to be acceptable, equal to 0.75, 0.76, and 0.59 for roads with good, fair, and very poor qualities, respectively, indicating a good relationship between IRI and PCI. Moreover, validation results showed that the model had a high accuracy. Also, the relation between IRI and PCI became weaker as a result of increasing the level of road surface roughness, which can be caused by the increase in the number and severity of failures. Furthermore, two failures of rail R.C. and rutting were rarely observed in the studied roads. Therefore, the proposed model is more applicable for roads without the mentioned failures and asphalt-pavement rural road network.


Author(s):  
Thomas Apusiga Adongo ◽  
Felix K. Abagale ◽  
Wilson A. Agyare

Abstract Effective management of reservoir sedimentation requires models which can predict sedimentation of the reservoirs. In this study, linear regression, non-linear exponential regression and artificial neural network models have been developed for the forecasting of annual storage capacity loss of reservoirs in the Guinea Savannah Ecological Zone (GSEZ) of Ghana. Annual rainfall, inflows, trap efficiency and reservoir age were input parameters for the models whilst the output parameter was the annual sediment volume in the reservoirs. Twenty (20) years of reservoirs data with 70% data used for model training and 30% used for validation. The ANN model, the feed-forward, back-propagation algorithm Multi-Layer Perceptron model structure which best captured the pattern in the annual sediment volumes retained in the reservoirs ranged from 4-6-1 at Karni to 4-12-1 at Tono. The linear and nonlinear exponential regression models revealed that annual sediment volume retention increased with all four (4) input parameters whilst the rate of sedimentation in the reservoirs is a decreasing function of time. All the three (3) models developed were noted to be efficient and suitable for forecasting annual sedimentation of the studied reservoirs with accuracies above 76%. Forecasted sedimentation up to year 2038 (2019–2038) using the developed models revealed the total storage capacities of the reservoirs to be lost ranged from 13.83 to 50.07%, with 50% of the small and medium reservoirs filled with sediment deposits if no sedimentation control measures are taken to curb the phenomenon.


2021 ◽  
Vol 1 (1) ◽  
pp. 38-47
Author(s):  
Fitrah Amalia Arsy

Toyota Avanza car is a popular four-wheeler among Indonesia middle-class customers. The current study aims to forecast the demand for Toyota Avanza cars in Indonesia in the next six years using the grey forecasting model EGM (1,1, α, θ). The comparative analysis of the results obtained from the grey model with those of Linear Regression, Exponential Regression, and Exponential Triple Smoothing techniques revealed the superiority of the grey model as it produced most accurate forecasts. The accuracy was measured through the Mean Absolute Percentage Error. The results revealed, the car sales are likely to decline in the future. Although forecasts are never completely accurate, forecasting can provide a reference for developing strategy to meet future demand. The results are important for Toyota Avanza car manufacturers in Indonesia.  


2021 ◽  
Vol 1 (1) ◽  
pp. 29-43
Author(s):  
Valentina Boamah

Oil plays a vital role in the economic growth and sustainability of industries and their corporations. The current study sought to forecast oil demand in Ghana for the next decade. The variables analyzed in this study were Petroleum and other liquids, motor gasoline, distillate fuel, and liquefied petroleum gases (LPG). The study utilized three univariate models; thus, linear regression, exponential regression, and exponential smoothing for forecasting various oil components. The linear regression model was deemed a better fit for the analysis of most of the variables. Furthermore, the findings revealed that the LPG growth rate is faster and requires less time to double in numbers than the other energy sources. Also, the exponential smoothing model was ineffective and inefficient. Overall, the demand for oil components analyzed will follow an increasing pattern from 2017 to 2027.  


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