Hybrid Neuro-fuzzy Model Research Articles

Hybrid neuro-fuzzy models for assessing the optimum moisture content of lime cement-treated soil

Hybrid neuro-fuzzy models for assessing the optimum moisture content of lime cement-treated soil

Improving Significant Wave Height Prediction Using a Neuro-Fuzzy Approach and Marine Predators Algorithm

This study investigates the ability of a new hybrid neuro-fuzzy model by combining the neuro-fuzzy (ANFIS) approach with the marine predators’ algorithm (MPA) in predicting short-term (from 1 h ahead to 1 day ahead) significant wave heights. Data from two stations, Cairns and Palm Beach buoy, were used in assessing the considered methods. The ANFIS-MPA was compared with two other hybrid methods, ANFIS with genetic algorithm (ANFIS-GA) and ANFIS with particle swarm optimization (ANFIS-PSO), in predicting significant wave height for multiple lead times ranging from 1 h to 1 day. The multivariate adaptive regression spline was investigated in deciding the best input for prediction models. The ANFIS-MPA model generally offered better accuracy than the other hybrid models in predicting significant wave height in both stations. It improved the accuracy of ANFIS-PSO and ANFIS-GA by 8.3% and 11.2% in root mean square errors in predicting a 1 h lead time in the test period.

Water Quality Prediction of the Yamuna River in India Using Hybrid Neuro-Fuzzy Models

The potential of four different neuro-fuzzy embedded meta-heuristic algorithms, particle swarm optimization, genetic algorithm, harmony search, and teaching–learning-based optimization algorithm, was investigated in this study in estimating the water quality of the Yamuna River in Delhi, India. A cross-validation approach was employed by splitting data into three equal parts, where the models were evaluated using each part. The main aim of this study was to find an accurate prediction model for estimating the water quality of the Yamuna River. It is worth noting that the hybrid neuro-fuzzy and LSSVM methods have not been previously compared for this issue. Monthly water quality parameters, total kjeldahl nitrogen, free ammonia, total coliform, water temperature, potential of hydrogen, and fecal coliform were considered as inputs to model chemical oxygen demand (COD). The performance of hybrid neuro-fuzzy models in predicting COD was compared with classical neuro-fuzzy and least square support vector machine (LSSVM) methods. The results showed higher accuracy in COD prediction when free ammonia, total kjeldahl nitrogen, and water temperature were used as inputs. Hybrid neuro-fuzzy models improved the root mean square error of the classical neuro-fuzzy model and LSSVM by 12% and 4%, respectively. The neuro-fuzzy models optimized with harmony search provided the best accuracy with the lowest root mean square error (13.659) and mean absolute error (11.272), while the particle swarm optimization and teaching–learning-based optimization showed the highest computational speed (21 and 24 min) compared to the other models.

Novel hybrid neuro-fuzzy model to anticipate the heat transfer in a heat exchanger equipped with a new type of self-rotating tube insert.

In this investigation, a combination of the wingsuit flying search (WFS) and teaching-learning-based optimization (TLBO) algorithms is developed as a new combinatorial optimization algorithm. The proposed combinatorial algorithm is tested over some well-known benchmark functions and then integrated with the artificial neural network (ANN) to construct a novel hybrid model. After that, the obtained hybrid model is employed to anticipate the experimentally obtained values of the average Nusselt number (Nu), average friction coefficient (f) as well as thermal-hydraulic performance ratio (η), in a heat exchanger equipped with a new type of self-rotating tube insert, against governing parameters. The insert is placed in the tube side of the water heater to heat natural gas. The proposed insert consists of various numbers of self-rotating modules. Indeed, the rotating insert is introduced to create effective secondary sweeping flow on the inner side of the tube. Since this type of tube insert simultaneously provides heat transfer enhancement and undesired pressure drop, a thermal-hydraulic performance ratio is defined to consider both of them. The governing parameters are the number of inserts (0≤N≤30), reservoir's temperature (40 °C ≤ TR≤50 °C) as well as Reynolds number (6 × 103≤Re≤18 × 103). It was found that the WFS-TLBO enhances the effectiveness of the main ANN in anticipating the Nusselt number (Nu), average friction coefficient (f) as well as performance ratio (η). Moreover, introducing the WFS-TLBO algorithm into the neural network provides an enhancement in the effectiveness of the hybrid models based on the single WFS and TLBO algorithms in anticipating the same parameters.

New generation neurocomputing learning coupled with a hybrid neuro-fuzzy model for quantifying water quality index variable: A case study from Saudi Arabia

Ensuring availability in terms of quality and quantity and sustainable management of safe, affordable drinking water is one of the integral parts of envisioning the 2030 Sustainable Development Goals (SDGs). Saudi Arabia faces many challenges in terms of water supply, inadequate water resources, and distribution due to low rainfall throughout the year. An uncertain water quality index (WQI) has been quantified to monitor water resource quality and management. The current study developed six different computational models WQI, namely: Generalized regression neural network (GRNN), Elman Neural Network (Elm NN, considered as a new generation learning tool), Feed Forward Neural Network (FFNN), Support Vector Machine (SVM), Linear Regression (LR), and Neuro-Fuzzy (NF). The experimental data were collected from 40 sampling locations. The obtained physicochemical variables (pH, EC, Turb, TDS, COD, Cl, NH3, PO4−, N/NO3−, SO4−, and TPC) were subjected to feature sensitivity technique, and the model combinations were determined based on sensitivity analysis and principal component analysis (PCA). Goodness-of-fit, error criteria, and mean bias coupled with visualization methods were used to assess the accuracy of the models. The quantified results showed that the NF model surpassed the other models and provided the highest accuracy. NF produced the highest R2 value of 0.9989 and lowest MAD = 0.0590, MAPE = 13%, and BIAS = −0.0003. The outcomes indicate that the water quality at a few locations requires minor treatment. The techniques employed validated the application of computing intelligence for optimum decision-making.

Simulation of time-series groundwater parameters using a hybrid metaheuristic neuro-fuzzy model.

The estimation of qualitative and quantitative groundwater parameters is an essential task. In this regard, artificial intelligence (AI) techniques are extensively utilized as accurate, trustworthy, and cost-effective tools. In the present paper, two hybrid neuro-fuzzy models are implemented for the prediction of groundwater level (GWL) fluctuations, as well as variations of Cl - and HCO3 - in the Karnachi well, Kermanshah, Iran in monthly intervals within a 13-year period from 2005 to 2018. In order to develop AI models, the adaptive neuro-fuzzy inference system (ANFIS), firefly algorithm (FA), and wavelet transform (WT) are used. In other words, two hybrid models including ANFIS-FA (adaptive neuro-fuzzy inference system-firefly algorithm) and WANFIS-FA (wavelet-adaptive neuro-fuzzy inference system-firefly algorithm) are utilized for the estimation of the quantitative and qualitative parameters. Firstly, influencing lags of the time-series of the qualitative and quantitative parameters are identified using the autocorrelation function. Then, four and eight separate models are developed for the approximation of GWLs and qualitative parameters (i.e. Cl - and HCO3 -), respectively. It is worth to mention that about 75% of observed values are assigned to train the hybrid AI models, while the rest (i.e. 25%) to test them. Sensitivity analysis results reveal that the WANFIS-FA models display more acceptable performance than the ANFIS-FA ones. Also, the estimations of MAE, NSC, and SI for the simulation of HCO3 - by the superior model of the WANFIS-FA are obtained to be 0.040, 0.988, and 0.022, respectively. In addition, the lags (t-1), (t-2), (t-3), and (t-4) are ascertained as the most effective time-series lags for the estimation of Cl - .

Estimating reference evapotranspiration using hybrid adaptive fuzzy inferencing coupled with heuristic algorithms

Hybrid heuristic algorithm (HA), an innovative technique in the machine learning field, enhances the accuracy of reference evapotranspiration (ETo) prediction, which is of paramount significance for regional water management, agricultural planning, and irrigation designing. However, the new hybrid HA techniques, namely Moth-Flame Optimization Algorithm (MFO) and Water Cycle Optimization Algorithm (WCA) are rarely applied to estimate ETo in the earlier literature. Therefore, this study assessed prediction and the estimation abilities of a novel hybrid adaptive neuro-fuzzy inference system (ANFIS-WCAMFO) for monthly ETo of Dhaka and Mymensing stations with data-limited humid regions of south-central Bangladesh. Prediction precision of the ANFIS-WCAMFO model is compared with other state-of-art models, i.e., ANFIS-WCA and ANFIS-MFO using a 4-fold cross-validation method including root-mean-square-error (RMSE), mean absolute error (MAE), and Nash-Sutcliffe efficiency (NSE), and coefficient of determination (R2). Nine input combinations of meteorological datasets, including extraterrestrial radiation (Ra), solar radiation (Rs), maximum and minimum temperatures (Tmax and Tmin), relative humidity (RH), and wind speed (U2), were employed for model training and testing purposes. The ANFIS-WCAMFO performed superior to the other state-of-arts methods in estimating monthly ETo in all input combinations. The ANFIS-WCA, ANFIS-MFO, and ANFIS-WCAMFO hybrid models for estimating ETo improved RMSE as 2.7%, 6.9%, and 15.1% for Dhaka station and 0.6%, 7.3%, 12.4% for Mymensingh station, respectively. The use of the Ra variable with the temperature inputs considerably improved the models’ accuracy in ETo; improvements in RMSE, MAE, NSE, and R2 of the hybrid ANFIS-WCMFO models were 26.6%, 30.9%, 17.6%, and 8.2% for Dhaka station and by 28.8%, 34.2%, 18.8% and 22.1% for Mymensingh station, respectively. The proposed hybrid neuro-fuzzy model has been suggested as a promising technique due to high predictive accuracy and less error for monthly ETo prediction in a data-limited tropical humid region.

A hybrid PSO-ANFIS model for predicting unstable zones in underground roadways

The problem of roof failure in underground coal mines is responsible for many fatalities, injuries, downtimes, and delays in production planning. Currently, the support systems in underground roadways are mainly designed based on the miners’ experience or, at worst, on trial and error. Nonetheless, the excessive roof displacements may lead to undesirable instabilities that have adverse effects on the mining operations. The uncontrolled roof failures are the major cause of calamitous consequences in Tabas underground coal mine, northeast of Iran, which brought about many disasters in recent years, from the threat of personnel’s safety to the postponement of coal production. Therefore, this research aims at developing a hybrid neuro-fuzzy model to approximate the unknown nonlinear relationship between the maximum roof displacements (dmax) and geomechanical features at Tabas longwall mine. After designing several hybrid models, the Particle Swarm Optimization (PSO) algorithm could significantly improve the performance of the Adaptive Neuro-Fuzzy Inference System (ANFIS). The results of three hybrid neuro-fuzzy models show that the optimization process in PSO is superior in comparison with Genetic Algorithm (GA) and Simulated Annealing (SA). According to the results, the determination coefficients (R2) between the measured and predicted values of dmax for PSO-ANFIS, SA-ANFIS, GA-ANFIS, and ANFIS were respectively obtained as 0.944, 0.907, 0.882, and 0.887. The associated error indicated that the PSO-ANFIS model could yield the best performance when encountered with unseen data. Compared to the ANFIS, the PSO-ANFIS model demonstrated an increase of about 6% in R2, and a decrease of about 34% in the Root Mean Square Error (RMSE). Therefore, our strategy in this research is to predict the dmax at first, and then to establish two milestones as 33% of the dmax for timely installing standing support systems, and 66% of the dmax for announcing an alarm threshold in potentially unstable zones. This may be useful to derive a reasonable judgment for predicting the unstable zones, and implementing preventive measures ahead of time in longwall roadways.

Implementation of hybrid neuro-fuzzy and self-turning predictive model for the prediction of concrete carbonation depth: A soft computing technique

Carbonation is one of the critical problems that affects the durability of reinforced concrete; it is a reaction between CO2 gas and Ca (OH)2 when H2O is available, which forms powdery CaCO3 that alters the microstructure of the concrete by reducing its pH level and initiating corrosion that reduces the structure's service life. This study provides experimental information on the carbonation depths of samples from 10 separate existing reinforced concrete structures, where five are located in the inland area (Nicosia), while the other five are in the coastal area (Kyrenia) of the Turkish Republic of North Cyprus. The study found that the inland buildings have a higher depth of carbonation compared to the coastal buildings. The building structures in North Cyprus exhibit a higher rate of carbonation than the expected threshold within their life span. Constant values of B were yielded, which is useful in predicting carbonation depth. Using AI, the potential Hybrid Neuro-fuzzy model, which is comprised of an Adaptive Neuro-fuzzy Inference System (ANFIS), Extreme Learning Machine (ELM), Support Vector Machine (SVM) and a Conventional Multilinear Regression (MLR) model, were employed for the estimation of carbonation depth using experimental data, including age, compressive strength, current density, and carbonation constant. Four different performance indexes were used to verify the modelling accuracy, namely Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Nash- Coefficient (NSE), and Correlation Coefficient (CC). The results indicated that the AI models (ANFIS, ELM, SVM) performed better than the linear model (MLR) with NSE-values higher than 0.97 in both the testing and training stages. The results also indicated that the prediction skills of ANFIS-M2 increased the performance accuracy of ELM-M2, SVM-M2, and MLR-M2, and the ANFIS-M1 model performed better than ELM-1, SVM-1 and MLR-1 models in terms of prediction accuracy. The final outcomes indicated the capability of the non-linear models (ANFIS, ELM, and SVM) in the prediction of Cd.

Performance evaluation of sediment ejector efficiency using hybrid neuro-fuzzy models

ABSTRACT Sediment transport in the ejector is highly stochastic and non-linear in nature, and its accurate estimation is a complex and challenging mission. This study attempts to investigate the sediment removal estimation of sediment ejector using newly developed hybrid data-intelligence models. The proposed models are based on the hybridization of adaptive neuro-fuzzy inference systems (ANFIS) with different metaheuristic algorithms, namely, particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), and ant colony optimization (ACO). The proposed models are constructed with various related input variables such as sediment concentration, flow depth, velocity, sediment size, Froude number, extraction ratio, number of tunnels and sub-tunnels, and flow depth at upstream of the sediment ejector. The estimation capacity of the developed hybrid models is assessed using several statistical evaluation indices. The modeling results obtained for the studied ejector sediment removal estimation demonstrated an optimistic finding. Among the developed hybrid models, ANFIS-PSO model exhibited the best predictability potential with maximum correlation coefficient values CC Train = 0.915 and CCTest = 0.916.

A Hybrid Neuro-Fuzzy and Feature Reduction Model for Classification

The evolvement of the fuzzy system has shown influential and successful in many universal approximation capabilities and applications. This paper proposes a hybrid Neuro-Fuzzy and Feature Reduction (NF-FR) model for data analysis. This proposed NF-FR model uses a feature-based class belongingness fuzzification process for all the patterns. During the fuzzification process, all the features are expanded based on the number of classes available in the dataset. It helps to deal with the uncertainty issues and assists the Artificial Neural Network- (ANN-) based model to achieve better performance. However, the complexity of the problem increases due to this expansion of input features in the fuzzification process. These expanded features may not always contribute significantly to the model. To overcome this problem, feature reduction (FR) is used to filter out the insignificant features, resulting the network less computational cost. These reduced significant features are used in the ANN-based model to classify the data. The effectiveness of this proposed model is tested and validated with ten benchmark datasets (both balanced and unbalanced) to demonstrate the performance of the proposed NF-FR model. The performance comparison of the NF-FR model with other counterparts has been carried out based on various performance measures such as classification accuracy, root means square error, precision, recall, and f-measure for quantitative analysis of the results. The obtained simulated results have been tested using the Friedman, Holm, and ANOVA tests under the null hypothesis for statistical validity and correctness proof of the results. The result analysis and statistical analysis show that the NF-FR model has achieved a considerable improvement in accuracy and is found to be efficient in eliminating redundant and noisy information.

A Novel Neuro-Fuzzy Model for Multivariate Time-Series Prediction

Time series forecasting can be a complicated problem when the underlying process shows high degree of complex nonlinear behavior. In some domains, such as financial data, processing related time-series jointly can have significant benefits. This paper proposes a novel multivariate hybrid neuro-fuzzy model for forecasting tasks, which is based on and generalizes the neuro-fuzzy model with consequent layer multi-variable Gaussian units and its learning algorithm. The model is distinguished by a separate consequent block for each output, which is tuned with respect to the its output error only, but benefits from extracting additional information by processing the whole input vector including lag values of other variables. Numerical experiments show better accuracy and computational performance results than competing models and separate neuro-fuzzy models for each output, and thus an ability to implicitly handle complex cross correlation dependencies between variables.

Prediction of river flow using hybrid neuro-fuzzy models

The complex nature of hydrological phenomena, like rainfall and river flow, causes some limitations for some admired soft computing models in order to predict the phenomenon. Evolutionary algorithms (EA) are novel methods that used to cover the weaknesses of the classic training algorithms, such as trapping in local optima, poor performance in networks with large parameters, over-fitting, and etc. In this study, some evolutionary algorithms, including genetic algorithm (GA), ant colony optimization for continuous domain (ACOR), and particle swarm optimization (PSO), have been used to train adaptive neuro-fuzzy inference system (ANFIS) in order to predict river flow. For this purpose, classic and hybrid ANFIS models were trained using river flow data obtained from upstream stations to predict 1-, 3-, 5-, and 7-day ahead river flow of downstream station. The best inputs were selected using correlation coefficient and a sensitivity analysis test (cosine amplitude). The results showed that PSO improved the performance of classic ANFIS in all the periods such that the averages of coefficient of determination, R2, root mean square error, RMSE (m3/s), mean absolute relative error, MARE, and Nash-Sutcliffe efficiency coefficient (NSE) were improved up to 0.19, 0.30, 43.8, and 0.13%, respectively. Classic ANFIS was only capable to predict river flow in 1-day ahead while EA improved this ability to 5-day ahead. Cosine amplitude method was recognized as an appropriate sensitivity analysis method in order to select the best inputs.

A Neuro‐Fuzzy Crime Prediction Model Based on Video Analysis

A hybrid neuro-fuzzy model for predicting crime in a wide area such as a town or district in presented. The model is built using what we describe as crime indicator events extracted from simulated wide area surveillance network. The framework principally involves two phases, namely video analysis and crime modeling phases. In video analysis a concept based approach for video event detection is used to detect crime indicator events. Based on the extracted indicators with other related variables, a fuzzy inference system capable of learning is constructed in the second phase. The model is constructed using Violent scene detection (VSD) 2014 dataset and testing is done using UCR-Videoweb dataset. The experimental results show that the proposed method is quite demonstrative and promising.

Copper potential mapping in Kerman copper bearing belt by using ANFIS method and the input evidential layer analysis

Earth science information used in mineral potential mapping has an empirical component comprising an exploration database and a conceptual component comprising an expert knowledge base. The hybrid neuro-fuzzy model combines conceptual and empirical components of available earth science information for predictive mineral potential mapping effectively. This paper describes a neuro-fuzzy model, which combines exploration data in the regional scale for copper potential mapping in Kerman copper bearing belt in south of Iran. Data layers or evidential maps are in six datasets namely lithology, tectonic, airborne geophysics, ferric alteration, hydroxide alteration, and geochemistry. The modeling result was 1044 pixels selected as favorable in order to continue the copper exploration in the study area; in other words, approximately 11.7 % of the area was selected. Fifty six known deposits out of 86 ones, equal to 65 % of all, were located in favorable zone. Other main goals of this study were to determine how each input affects favorable output. For this purpose, the histogram of each normalized input data with its favorable output was drawn. The histograms of each input dataset for favorable output showed that each information layer has a certain behavioral pattern. These behavioral patterns can be considered as regional copper exploration criteria.

Intelligent multiagent coordination based on reinforcement hierarchical neuro-fuzzy models.

This paper presents the research and development of two hybrid neuro-fuzzy models for the hierarchical coordination of multiple intelligent agents. The main objective of the models is to have multiple agents interact intelligently with each other in complex systems. We developed two new models of coordination for intelligent multiagent systems, which integrates the Reinforcement Learning Hierarchical Neuro-Fuzzy model with two proposed coordination mechanisms: the MultiAgent Reinforcement Learning Hierarchical Neuro-Fuzzy with a market-driven coordination mechanism (MA-RL-HNFP-MD) and the MultiAgent Reinforcement Learning Hierarchical Neuro-Fuzzy with graph coordination (MA-RL-HNFP-CG). In order to evaluate the proposed models and verify the contribution of the proposed coordination mechanisms, two multiagent benchmark applications were developed: the pursuit game and the robot soccer simulation. The results obtained demonstrated that the proposed coordination mechanisms greatly improve the performance of the multiagent system when compared with other strategies.

Neuro-fuzzy system to predict permeability and porosity from well log data: A case study of Hassi R׳Mel gas field, Algeria

Characterization of shaly sand reservoirs by well log data is a usual way of describing oil/gas field reservoirs. Over the last few years, several studies have been conducted in the field of petroleum engineering by applying artificial intelligence. This work represents a petrophysical-based method that uses well logs and core plug data to predict well log data recorded at depth in a shaly sand reservoir of Triassic Formation in Hassi R׳Mel field, Algeria. In the study of oil reservoirs, the prediction of absolute permeability is a fundamental key in reservoir descriptions and has a direct impact, in particular, on effective completion designs, successful water injection programs and more efficient reservoir management. The Triassic Formations of Hassi R׳Mel fields are composed of sandstones and shaly sands with dolomites. Logs from 10 wells are the starting point for the reservoir characterization. This paper presents a hybrid neuro-fuzzy model based on the use of data from four wells regarding porosity and permeability estimation. A fuzzy logic approach is used to calibrate the calculated permeability and core permeability; and a neural network was developed in this model, based on the data available from the field. Fuzzy analysis is based on fuzzy logic and is used to choose the best well logs with regard to core porosity and permeability data. A neural network is used as a nonlinear regression method to develop transformation between the selected well logs and core measurements. Porosity and permeability are predicted in these wells through linear regression; and back-propagation models are constructed and their reliabilities are compared according to the regression coefficients for predictions in un-cored sections. This investigative hybrid neuro-fuzzy method becomes a powerful tool for the estimation of reservoir properties from well logs in oil and natural gas development projects.

A Hybrid Neuro-fuzzy Model to Forecast Inflation

One of the key issues in constructing monetary policy is accurate prediction of the inflation level. The complex behavior and non-linear nature of the financial markets makes it hard to forecast the inflation rate precisely. This paper introduces a hybrid model that attempts to forecast the inflation rate with a combination of a subtractive clustering technique and a fuzzy inference neural network to overcome the shortcomings of the individual methodologies. Selected macroeconomic factors were used to predict the historical CPI data from the US Markets. The results of the proposed hybrid model are measured in RMSE.

Neuro-fuzzy modeling based genetic algorithms for identification of geochemical anomalies in mining geochemistry

Abstract A genetic algorithm (GA)-based neuro-fuzzy approach is used for identification of geochemical anomalies by implementing a Takagi, Sugeno and Kang (TSK) type fuzzy inference system in a 5-layered feed-forward adaptive artificial neural network. This paper investigates the effectiveness of GA-based neuro-fuzzy for separating zone dispersed mineralization (ZDM) from blind mineralization, and its application for identification of geochemical anomalies in the arid landscape of the Lut metallogenic province in eastern Iran. Other classification algorithms such as metallometry, zonality, criteria, and back-propagation artificial neural network classifiers are also used for comparison. The genetic operators are carefully designed to optimize the artificial neural network, avoiding premature convergence and permutation problems. The results show that the GA-based hybrid neuro-fuzzy model can provide accurate results in comparison with those results obtained by other techniques. Neuro-fuzzy and GA-based neuro-fuzzy techniques appear to be well-suited for routine exploration geochemistry applications. In conjunction with statistics and conventional mathematical methods, hybrid approaches can be developed and may prove a step forward in the practice of applied geochemistry.

Mid-Term Energy Demand Forecasting by Hybrid Neuro-Fuzzy Models

This paper proposes a structure for long-term energy demand forecasting. The proposed hybrid approach, called HPLLNF, uses the local linear neuro-fuzzy (LLNF) model as the forecaster and utilizes the Hodrick–Prescott (HP) filter for extraction of the trend and cyclic components of the energy demand series. Besides, the sophisticated technique of mutual information (MI) is employed to select the most relevant input features with least possible redundancies for the forecast model. Each generated component by the HP filter is then modeled through an LLNF model. Starting from an optimal least square estimation, the local linear model tree (LOLIMOT) learning algorithm increases the complexity of the LLNF model as long as its performance is improved. The proposed HPLLNF model with MI-based input selection is applied to the problem of long-term energy forecasting in three different case studies, including forecasting of the gasoline, crude oil and natural gas demand over the next 12 months. The obtained forecasting results reveal the noteworthy performance of the proposed approach for long-term energy demand forecasting applications.