Theil Inequality Coefficient Research Articles

Very short-term wind power forecasting for real-time operation using hybrid deep learning model with optimization algorithm

This paper proposes a new hybrid deep learning model to enhance the accuracy of forecasting very short-term wind power generation. The proposed model comprises a convolutional layer, a long-short-term memory (LSTM) unit, and fully connected neural network. Convolution layer can automatically learn complicated features from the raw input, whereas the LSTM layers can retain useful information through which gradient information may flow over extended periods. To obtain the best performance from the forecasting model, a random search optimization technique has been developed for tuning hyper-parameters of the model developed. The 5 min datasets from the White Rock wind farm, Australia are used to investigate the effectiveness of the proposed model as wind farms are participating in spot electricity market. To compare the effectiveness, the proposed model is compared with the existing models, such as convolution neural network (CNN), LSTM, gated recurrent unit (GRU), bidirectional LSTM (BiLSTM), artificial neural network (ANN), and support vector machine (SVM). The root-mean-square error (RMSE), mean absolute error (MAE), and Theil’s inequality coefficient (TIC) are used to analyze and compare the performances of the predictive models. Based on RMSE and MAE, the proposed model exhibits a higher accuracy of approximately 23.79% and 28.63% compared to other forecasting methods, respectively.

Optimizing pantograph fractional differential equations: A Haar wavelet operational matrix method

In this study, we developed an operational matrix method of integration using Haar wavelets to solve both linear and nonlinear pantograph fractional differential equations by taking Atangana's beta derivative. The proposed method utilizes an operational matrix and truncated Haar wavelet series to transform linear and nonlinear problems into objective functions. These objective functions are then minimized using differential evolution optimization. Illustrative examples demonstrate convergence and validation of the proposed method. The proposed method yields exceptional numerical outcomes in terms of competitiveness and accuracy when compared to exact solutions. In addition, performance metrics, including the mean absolute deviation, root mean squared error, P2norm, P∞ norm, Theil's inequality coefficient, variance account for, coefficient of determination, and Nash-Sutcliffe efficiency, were calculated for a varying number of collocation points. The results indicate that the Haar wavelet operational matrix method is a straightforward and efficient method for solving pantograph fractional differential equations.

Predicting daily heating energy consumption in residential buildings through integration of random forest model and meta-heuristic algorithms

This research utilizes a sophisticated hybrid model integrating the Random Forest algorithm with meta-heuristic optimization techniques to estimate heating energy consumption in residential buildings. The study addresses key variables including architectural characteristics, occupancy, and ambient temperature. The primary objective is to enhance the prediction accuracy of heating energy consumption using a novel approach combining Random Forest with various meta-heuristic algorithms. The study employs six combinations of the Random Forest algorithm and meta-heuristic optimizers. To mitigate overfitting, K-Fold cross-validation is implemented during model training. The model's performance is evaluated using five statistical indices: coefficient of determination (R2), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Relative Absolute Error (RAE), and Theil Inequality Coefficient (TIC). Results demonstrate the hybrid model's high predictive accuracy, with the Arithmetic Optimization Algorithm enhancing Random Forest's performance significantly. Notable statistical achievements include R2 = 0.977201, RMSE = 0.1179, MAE = 0.0573, RAE = 0.0930, and TIC = 0.0187. Additionally, the Ant Lion Optimizer shows excellent convergence, achieving a TIC value of 0.014986 after 101 iterations. The proposed hybrid model significantly outperforms traditional methods in predicting residential heating energy consumption. The integration of Random Forest with advanced meta-heuristic algorithms offers a robust framework for enhancing prediction accuracy in energy consumption modeling.

Bioeconomics of juvenile seahorse (Hippocampus erectus) culture: Optimal harvest time

AbstractThe culture of seahorses Hippocampus erectus in captivity represents a window of opportunity for the diversification of the aquaculture activity in the ornamental industry. In this study, we have constructed a bioeconomic model to evaluate the optimal harvest time (OHT) over a culture period of 562 days. The bioeconomic model was integrated with three submodels: biological, technological, and economic. Three different mortality rates were used for different periods in culture, registering a higher survival in the period from 0 to 60 days with a rate of 53.4%. The sensitivity analysis showed that the mortality rate in this period was the parameter with the greatest influence on the benefits. The Von Bertalanffy growth model was indicated to describe the growth of H. erectus given its statistical significance using Theil's inequality coefficient, registering parameters of (L∞ = 141.62 mm) and (k = 0.0049 month‐1). The bioeconomic model determined the OHT in the 4th month of culture, the time when the maximum profit is recorded. It is concluded that the culture presents challenges to be addressed although the bioeconomic model allows for demonstrating the OHT.

Multi-model ensemble successfully predicted atmospheric methane consumption in soils across the complex landscape

Multi-model ensemble successfully predicted atmospheric methane consumption in soils across the complex landscape

주택시장과 거시경제변수들 간의 장기적 균형관계 연구

This paper was empirically conducted to compare the explanatory power of the Vector Error Correction Model (VECM) and Vector Autoregressive Model (VAR Model) in predicting the long-term equilibrium relationship between housing prices and macroeconomic variables. The analysis period spans from January 1987 to July 2023. The analysis results are as follows. First, it is found that there exists one cointegration relationship among housing prices, stock prices, liquidity, 5-year yield of government housing bonds, and income. Therefore, the VECM model can be applied to analyze the long- and short-term equilibrium relationship. Secondly, the estimation results of the VECM model revealed the presence of the following long-term relationships: a negative (-) relationship between housing prices and stock prices, a positive (+) relationship with liquidity, a negative (-) relationship with the 5-year yield of government housing bonds, and a positive (+) relationship with income. This aligns with the expected theoretical signs. Thirdly, the Root Mean Square Error (RMSE) and Theil's Inequality Coefficient, which indicate the predictive and explanatory power of the VECM and VAR models, respectively, showed that the VECM model outperformed the VAR model with smaller values for both metrics. Therefore, when a cointegration relationship exists between housing prices and macroeconomic variables, it is necessary to apply the VECM model rather than the VAR model for analysis.

COMPARATIVE PERFORMANCE OF ARIMA, SARIMA AND GARCH MODELS IN MODELLING AND FORECASTING UNEMPLOYMENT AMONG ASEAN-5 COUNTRIES

Unemployment, especially after the COVID-19 pandemic, is a critical issue for any country as it has economic and social ramifications. Consequently, forecasting unemployment becomes an essential task as it can guide government policy. Time series data are frequently influenced by outliers (unexpected events), and some outliers may exist with extreme observation to reduce the forecasting effectiveness of robust estimators. This study compared the performance of Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA) and Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models in modelling and forecasting unemployment rates during the COVID-19 pandemic among the ASEAN-5 countries. These countries include Malaysia, Singapore, Thailand, the Philippines and Indonesia. The monthly unemployment data from January 2010 to December 2021 were applied for all cases, except Thailand, until December 2020. Each adequate model from both forecasting mechanisms underwent forecasting. Their performance was compared based on root mean squared error (RMSE), mean absolute error (MAE), Theil inequality coefficient and symmetric mean absolute percentage error (SMAPE). Static forecasting from the ARIMA and SARIMA models was found to perform better than the GARCH model in modelling and forecasting the unemployment rate among ASEAN-5 countries during the pandemic period.

A computational solution of relativistic Thomas-Fermi equation of an atom with exponential collocation genetic algorithm optimization

An Exponential Collocation Genetic Algorithm Optimization (ECGAO) is considered for solving the relativistic Thomas-Fermi equation of the statistical model of an atom. The governing model equation has been transformed into an optimization problem by collocation technique using exponential basis. Then, fitness function is formulated in terms of nonlinear coupled residual equations. The fitness values achieved remained of the order of10−4. The improvement in the ionization energy values for the heavier atoms from the ECGAO came with the small percentage error for Z=80,86and92 as 1.418630%, 0.301381% and 0.018417% respectively. The accuracy and stability of the proposed method were verified using Mean Absolute Deviation (MAD), Theil's Inequality Coefficient (TIC), and Mean Fitness Value (MFV). Approximately 74% of the trial runs have successfully achieved these low statistical error indices values (in the order of10−4to10−3) for the relativistic Thomas-Fermi model. After several experimentations, we have determined that the optimal values for crossover fraction, elite count, and migration fraction interval as 0.4, 16, 0.6, and 10, respectively. The proposed methodology is computationally consistent and more accurate for scientific investigations of the relativistic Thomas-Fermi equation.

An Integrated Model of Deep Learning and Heuristic Algorithm for Load Forecasting in Smart Grid

Accurate load forecasting plays a crucial role in the effective energy management of smart cities. However, the smart cities’ residents’ load profile is nonlinear, having high volatility, uncertainty, and randomness. Forecasting such nonlinear profiles requires accurate and stable prediction models. On this note, a prediction model has been developed by combining feature preprocessing, a multilayer perceptron, and a genetic wind-driven optimization algorithm, namely FPP-MLP-GWDO. The developed hybrid model has three parts: (i) feature preprocessing (FPP), (ii) a multilayer perceptron (MLP), and (iii) a genetic wind-driven optimization (GWDO) algorithm. The MLP is the key part of the developed model, which uses a multivariate autoregressive algorithm and rectified linear unit (ReLU) for network training. The developed hybrid model known as FPP-MLP-GWDO is evaluated using Dayton Ohio grid load data regarding aspects of accuracy (the mean absolute percentage error (MAPE), Theil’s inequality coefficient (TIC), and the correlation coefficient (CC)) and convergence speed (computational time (CT) and convergence rate (CR)). The findings endorsed the validity and applicability of the developed model compared to other literature models such as the feature selection–support vector machine–modified enhanced differential evolution (FS-SVM-mEDE) model, the feature selection–artificial neural network (FS-ANN) model, the support vector machine–differential evolution algorithm (SVM-DEA) model, and the autoregressive (AR) model regarding aspects of accuracy and convergence speed. The findings confirm that the developed FPP-MLP-GWDO model achieved an accuracy of 98.9%, thus surpassing benchmark models such as the FS-ANN (96.5%), FS-SVM-mEDE (97.9%), SVM-DEA (97.5%), and AR (95.7%). Furthermore, the FPP-MLP-GWDO significantly reduced the CT (299s) compared to the FS-SVM-mEDE (350s), SVM-DEA (240s), FS-ANN (159s), and AR (132s) models.

The Czech Republic’s Economy since the 1990s and Its Development Forecasts: Selected Macroeconomic Indicators

Using a comparative developmental analysis of wage levels and other indicators, the present paper aims to capture the changes in the economy and measurable aspects of living standards in the Czech Republic since the beginning of the then Czechoslovakia’s transformation process launched in the early 1990s. To model the trend, analysis of the relevant time series was performed, exponential smoothing as an adaptive approach to trend modeling being applied. Interpolation and extrapolation criteria were used to verify the suitability of the selected exponential equalization; the Durbin-Watson test, determination index, residual autocorrelation functions, t-tests and Theil inequality coefficient were employed as well. The variables analyzed are the average wage, GDP and the rates of inflation and unemployment, supplemented by the minimum wage and the subsistence minimum. The data used come from the official website of the Czech Statistical Office. They were processed using SPSS and SAS statistical software and a Microsoft Excel spreadsheet. The results show economic downturns and gradual recoveries accompanied by repeated freezing and starting wage growth. High inflation rates in the transition from a centrally planned to a market economy or the GDP decline at the beginning of the financial crisis are evident, the labor market reacting with some delay, as reflected in the rise in the unemployment rate after the currency crisis in the late 1990s, and in average wage trends during the decline of the economic crisis in the early 2010s. The purpose of this research is also to predict further wage level and macroeconomic aggregate developments until 2023. This study aspires to be the starting point for subsequent research, comparing the original forecasts with the reality of further economic development interrupted by the COVID-19 pandemic.

A reliable stochastic computational procedure to solve the mathematical robotic model

The current work presents the numerical solutions of the robotic system in the process of coronavirus. The stochastic performances using the modeling of Gudermannian neural networks (GDMNNs) are provided along with the global search genetic algorithm (GA) and rapid interior-point scheme (IPS), i.e., GDMNNs-GAIPS. An error function using the differential form of the model is created and then optimized by applying the hybridization of GA-IPS. The correctness and accuracy of the stochastic procedure GDMNNs-GAIPS is examined by using the comparison of the proposed and reference results. The reliability and substantiation of the proposed GDMNNs-GAIPS is authenticated by using the statistical operators based on the mean square error, Theil inequality coefficient and variance account for. Forty numbers of independent trials along with ten numbers of hidden neurons have been used to solve the mathematical model of robotic system to detect the positive cases of COVID-19.

Predicting the Total Construction Spending of Health Care by Using SARIMA Model: United States Case

This study aims to determine the optimal model to predict the Total Construction Spending of Health Care by using the Seasonal Autoregressive Integrated Moving Average Model (SARIMA). SARIMA Model was performed during 22 years from January 2002 to December 2023 of Total Construction Spending of HealthCare (SHC), Millions of Dollars, from Federal Reserve Economic Data. The researcher concluded that the estimated model of the first-order difference for the logarithm of the SHC (DLSHC) series is SARIMA (1,1,2) (0,1,2)12. With coefficients: C = 0.003845, AR (1) = 0.970015, MA (1) = -1.147784, MA (2) = 0.219215, MA (12) = -0.89710 & MA (24) = -0.227258. This Model has more than 50% of the coefficients that are statistically significant at the 5% level. The jointly significant F-statistic value equals (3.893122) with a P-value (0.000981), S.E. of regression equals (0.019284). The ability to predict SARIMA (1, 1, 2) (0,1,2)12 Model is satisfactory, with a highly predictive power, with Theil Inequality Coefficient equals (0.000898) and Biaproportion equals (0.000087).

Integrating thermodynamics and mathematical modelling to investigate the stoichiometry and kinetics of sulphide oxidation-nitrate reduction with a special focus on partial autotrophic denitrification

In the present study, the stoichiometry of the Sulphur Oxidizing-Nitrate Reducing (SO-NR) process, with a focus on Partial Autotrophic Denitrification (PAD), has been evaluated through a thermodynamic-based study whereas a model-based approach has been adopted to assess process kinetics. Experimental data on process performance and biomass yields were available from a previous work achieving efficient PAD, where a biomass yield of 0.113 gVSS/gS was estimated. First, the free Gibbs energy dissipation method has been implemented, in order to provide a theoretical framework exploring the boundaries for sulphur oxidizing biomass yields. Second, a screening of available mathematical models describing SO-NR process was conducted and five published models were selected, in order to assess the most suitable model structure for describing the observed PAD kinetics. To the best of our knowledge, none of reported biomass yields are estimated in systems operating PAD as the main process and, analogously, none of the proposed models have been applied to case studies aiming at partial denitrification only. The work showed that the very low biomass yield of 0.117 ± 0.007 gVSS/gS, observed in a PAD system in our previous work, suggests that the conditions applied to achieve partial denitrification resulted in a high energy-dissipating metabolism compared to complete denitrification applications. Models’ analysis revealed that nitrite accumulation can be described by a classical Monod kinetics if different μmax are adopted for each intermediate reaction, with Theil Inequality Coefficient values lower than 0.21 for both NO3− and NO2−. Nonetheless, adopting Haldane-type kinetics for nitrite uptake inferred higher identifiability to the model structure, resulting in confidence intervals below ±10% for all the parametric estimations. The thermodynamic and modelling outcomes support the experimental results obtained in the reference study and the critical comparison of model suitability to represent PAD process is believed pivotal to pave the way to its real-scale implementation.

The ASM2d model with two-step nitrification can better simulate biological nutrient removal systems enriched with complete ammonia oxidizing bacteria (comammox Nitrospira)

The discovery of comammox Nitrospira, a complete ammonia-oxidizing microorganism belonging to the genus Nitrospira, has brought new insights into the nitrification process in wastewater treatment plants (WWTPs). The applicability of Activated Sludge Model No. 2 d with one-step nitrification (ASM2d-OSN) or two-step nitrification (ASM2d-TSN) for the simulation of the biological nutrient removal (BNR) processes of a full-scale WWTP in the presence of comammox Nitrospira was studied. Microbial analysis and kinetic parameter measurements showed comammox Nitrospira was enriched in the BNR system operated under low dissolved oxygen (DO) and long sludge retention time (SRT). The relative abundance of Nitrospira under the conditions of stage I (DO = 0.5 mg/L, SRT = 60 d) was about twice of that under stage II conditions (DO = 4.0 mg/L, SRT = 26 d), and the copy number of the comammox amoA gene for stage I was 33 times higher than that for stage II. Compared to the ASM2d-OSN model, the ASM2d-TSN model simulated the performance of the WWTP under stage I conditions better, and the Theil inequality coefficient values of all the tested water quality parameters were lower than using ASM2d-OSN. These results indicate that an ASM2d model with two-step nitrification is a better choice for the simulation of WWTPs with the presence of comammox.

Prediction of Surface Settlement in Shield-Tunneling Construction Process Using PCA-PSO-RVM Machine Learning

Surface settlement is one of the key engineering issues during shield construction process. In order to accurately predict surface settlement, this paper proposes a new machine learning method based on relevance vector machine (RVM), principal component analysis (PCA), and particle swarm optimization (PSO). Taking Beijing Metro Line 6 as a case study, the PCA-PSO-RVM model is used to make the prediction and compared with the prediction results of the RVM model using the same samples. In order to evaluate the reliability of the model, three evaluation indexes including mean relative error (MRE), root mean square error (RMSE), and Theil inequality coefficient (TIC) were calculated, and sensitivity analysis was carried out on them. The results show that the minimum relative error between PCA-PSO-RVM and the actual value is only 0.06%. The calculated MRE, RMSE, and TIC are 0.17%, 0.0714 mm, and 0.027%, respectively, which shows that PCA-PSO-RVM model has higher prediction accuracy, smaller deviations, and higher reliability compared with the three other models. Through sensitivity analysis, it is found that the weighted average internal friction angle (φ) has the most significant impact on the surface settlement, which should be focused on in relevant research.

Time series forecasting based on a novel ensemble‐based network and variational mode decomposition

AbstractStatistical and computational intelligence methods contain weaknesses in handling nonlinearity, non‐stationarity and noise. This research develops a novel decomposition ensemble‐based network named VMD‐DENetwork for time series forecasting over different horizons. A robust decomposition technique called variational mode decomposition (VMD) is applied to decompose the input sequence into several intrinsic modes in a non‐recursive manner. The optimal number of intrinsic modes is selected based on a comprehensive analysis to ensure the stability of the framework. The proposed DENetwork is developed based on stacking architecture and constitutes heterogeneous learners to model the nonlinear and complex relationships. It combines a convolutional neural network, long short‐term memory and an extreme learning machine. A firefly optimization algorithm is adopted for utilizing hyperparameters of the proposed model to enhance the efficiency of VMD‐DENetwork. The forecasting performance is verified by using six real‐world data sets from the New York Mercantile and International Petroleum Exchange. The final obtained results are compared with several peer‐advanced algorithms using the root mean squared error (RMSE), mean absolute error (MAE), Theil inequality coefficient (TIC) and correlation coefficient (R) metrics. The experimental results confirm that the proposed model demonstrates outstanding prediction performance. The employed optimization algorithm is compared with three frequently used bio‐inspired optimization algorithms, and their performance is tested using standard CEC benchmarks.

Hybrid Model for Stock Market Volatility

Empirical evidence suggests that the traditional GARCH-type models are unable to accurately estimate the volatility of financial markets. To improve on the accuracy of the traditional GARCH-type models, a hybrid model (BSGARCH (1, 1)) that combines the flexibility of B-splines with the GARCH (1, 1) model has been proposed in the study. The lagged residuals from the GARCH (1, 1) model are fitted with a B-spline estimator and added to the results produced from the GARCH (1, 1) model. The proposed BSGARCH (1, 1) model was applied to simulated data and two real financial time series data (NASDAQ 100 and S&P 500). The outcome was then compared to the outcomes of the GARCH (1, 1), EGARCH (1, 1), GJR-GARCH (1, 1), and APARCH (1, 1) with different error distributions (ED) using the mean absolute percentage error (MAPE), the root mean square error (RMSE), Theil’s inequality coefficient (TIC) and QLIKE. It was concluded that the proposed BSGARCH (1, 1) model outperforms the traditional GARCH-type models that were considered in the study based on the performance metrics, and thus, it can be used for estimating volatility of stock markets.

Computational-based partitioning and Strong [formula omitted]-cut based novel method for intuitionistic fuzzy time series forecasting

In this article, we propose a computational-based partitioning (CBP) and Strong α,β-cut based novel intuitionistic fuzzy time series (IFTS) forecasting method. Construction of intervals, intuitionistic fuzzification of time series data, appropriate intuitionistic fuzzy logical relationships (IFLRs), and procedure of defuzzification are critical issues that affect the forecasting accuracy of any IFTS method. A Computational-based partitioning approach uses basic statistical parameters to determine the number of intervals and constructing of intervals without specialized knowledge of the domain. For intuitionistic fuzzification of time series data, all those intuitionistic fuzzy sets are taken having both non-zero membership and non-membership grade. A Strong α,β-cut are used to choose apposite IFLRs that deliver importance in investigating the tendency of time series data. We also propose a defuzzification approach to get the numerical values. In this article, two popular historical time series datasets are used to demonstrate the supremacy of the proposed forecasting method. Root mean square error (RMSE) and mean absolute percentage error (MAPE) are used to verify the performance of the proposed method. Verification of the validity of the proposed forecasting method is authenticated by using the values of the Theil inequality coefficient (U) and tracking signal (TS).

A novel approach for the fractionation of organic components and microbial degraders in ADM1 and model validation based on the methanogenic potential

The anaerobic digestion model No 1 (ADM1), with fixed fractions of the substrate components, is currently used to simulate methane production during the anaerobic digestion (AD) of waste activated sludge (WAS). However, the goodness-of-fit for the simulation is not ideal due to the different characteristics of WAS from different regions. In this study, a novel methodology based on a modern instrumental analysis and 16S rRNA gene sequence analysis for the fractionation of organic components and microbial degraders in the WAS is investigated to modify the fractions of the components in the ADM1. The combination of Fourier transform infrared (FTIR), X-ray photoelectron spectroscopy (XPS), and nuclear magnetic resonance (NMR) analyses were used to achieve a rapid and accurate fractionation of the primary organic matters in the WAS that was verified using both the sequential extraction method and the excitation-emission matrix (EEM). The protein, carbohydrate, and lipid contents in the four different sludge samples measured using the above combined instrumental analyses were 25.0 – 50.0%, 2.0 – 10.0%, and 0.9 – 2.3%. The microbial diversity based on 16S rRNA gene sequence analysis was utilized to re-set the initial fractions of the microbial degraders in the ADM1. A batch experiment was utilized to further calibrate the kinetic parameters in the ADM1. Based on the above optimization of the stoichiometric and kinetic parameters, the ADM1 with full parameter modification for WAS (ADM1-FPM) simulated the methane production of the WAS very well with a Theil's inequality coefficient (TIC) of 0.049, which was increased by 89.8% than that of the default ADM1 fit. The proposed approach, with its rapid and reliable performance, demonstrated a strong application potential for the fractionation of organic solid waste and the modification of ADM1, which contributed to a better simulation of methane production during the AD of organic solid wastes.

Analysis and Forecasting of Rice Production Behavior in Bangladesh

This research looks at how numerous factors, including the price of rice, area, improved seed distribution, areas irrigated by different improved methods, and fertilizer, influence rice production in Bangladesh. This study employed the autoregressive distributed lag (ARDL) model to investigate the short-run and long-run effects of each exogenous variable on rice production. In this research work, auto regressive integrated moving average (ARIMA) and hybrid ARIMA-(general autoregressive conditional heteroskedastic) GRACH were used to forecast rice production in Bangladesh from 1983 to 2030. The parameters of price of rice, area irrigated by different improved methods, area, and fertilizer were found to have a significant and positive impact on rice production in this study, both in the short run and the long run, according to the ARDL model. According to the lowest Root Mean Squared Error, Mean Absolute Error and Theil Inequality Coefficient criteria, the linear hybrid ARIMA (11, 1, 11)–EGARCH (1, 1)–M model performed better in predicting the rice production in Bangladesh. IUBAT Review—A Multidisciplinary Academic Journal, 5 (1): 1-14