Modeling and Characterization of a Photovoltaic Array Based on Actual Performance Using Cascade-Forward Back Propagation Artificial Neural Network

This paper presents a new method for predicting hourly ambient temperature series for Malaysia using generalized regression neural network (GRNN). MATLAB was used to develop the GRNN using the weather records for Malaysia. The developed model has five inputs and one output. The inputs of the proposed model are hour, day, month, sunshine ratio, and relative humidity, meanwhile ambient temperature is the output. To evaluate the accuracy of the GRNN, three statistical parameters, namely, the mean absolute percentage error (MAPE), mean bias error (MBE), and root mean square error (RMSE) are considered. The GRNN results give an accurate prediction of ambient temperatures for the selected testing months with average values of MAPE, MBE, and RMSE of 2.65%, 4.05%, and 0.347%, respectively. The advantage of the proposed method is that it is able to predict ambient temperature at sites where there is no ambient temperature-measuring instrument installed.

Solar energy, in the recent decades has gained a great attention due to its clean, simple and easy adaptable process. The effective utilization of solar energy is possible only if proper data of incident solar radiation is available. There are number of solar models based on different climatical factors, for the assessment of radiation on plane and sloped surfaces are available in the literature but the selection of best possible model is a challenging task. Here, different isotropic and anisotropic solar models have been utilized for the estimation of overall radiation incident on the sloped surface in Karachi then estimation was compared with the experimental values. The models selected for this study includes Liu and Jordan, Koronakis, Badescue, Hay and Davies, Temps and Coulson and HDKR. The predicted values and measured values are compared by using different statistical techniques like Mean Absolute Percentage Error (MAPE), Mean Biased Error (MBE), Root Mean Square Error (RMSE) and t-stats. The outcomes revealed that isotropic models are more suitable model than the anisotropic models. Among all models, Badescue is the best suitable model for the estimation of radiations on sloped surfaces with lowest value of MBE, RMSE and t-stats while Temps and Coulson model, on the basis of MAPE, MBE, RMSE and t-stats is the most inappropriate correlation for the assessment of solar radiations on sloped surface. Overall, for the solar radiation estimation on any sloped plane in Karachi isotropic models have shown a good agreement.

The fluctuations in solar irradiance and temperature throughout the year require an accurate methodology for forecasting the generated current of a PV system based on its specifications. The optimal technique must effectively manage rapid weather fluctuations while maintaining high accuracy in forecasting the performance of a PV panel. This work presents a comparative examination of supervised learning algorithms optimized with particle swarm optimization for estimating photovoltaic output current. The empirical formula’s measured currents are compared with outputs from various neural networks techniques, including feedforward neural networks (FFNNs), the general regression network known as GRNN, cascade forward neural networks also known as CFNNs, and adaptive fuzzy inference systems known as ANFISs, all optimized for enhanced accuracy using the particle swarm optimization (PSO) method. The ground data utilized for these models comprises hourly irradiations and temperatures from 2023, sourced from several places in South Africa. The accuracy levels indicated by statistical error margins from the root mean square error (RMSE), mean bias error (MBE), and mean absolute percentage error (MAPE) imply a universal enhancement in the algorithms’ precision upon optimization.

Model evaluation is essential for ensuring the reliability, transparency, and practical usefulness of simulations in energy systems, environmental modeling, and sustainability science. However, the frequent misuse, misinterpretation, and isolated application of common performance metrics particularly root mean square error (RMSE), mean absolute percentage error (MAPE), and R 2 continue to undermine model credibility and lead to misleading conclusions. This study (i) reviews and defines five widely used evaluation metrics (mean absolute error [MAE], RMSE, mean bias error [MBE], MAPE, and R 2 ), including their mathematical foundations and conceptual meaning, (ii) compares their characteristics, strengths, and limitations, and (iii) provides context‐specific guidelines for selecting appropriate indicators based on modeling objectives and data behavior. Using a combined methodology consisting of a structured literature review, a controlled illustrative dataset, and sensitivity analysis, the study demonstrates how each metric responds to outliers and zero‐observation values. Results show that RMSE and MAE increase more under outlier conditions, MAPE becomes undefined when observed values reach zero, and R 2 collapses from 0.82 to below 0.05 when data irregularities are introduced. These findings highlight critical vulnerabilities that can distort evaluation if metrics are used in isolation. The study contributes a consolidated comparative framework, practical recommendations for multimetric reporting, and guidance for improving evaluation transparency in energy, environmental, and sustainability applications. Adopting a context‐aware, multimetric strategy enhances credibility, interpretability, and policy relevance of model‐based assessments in support of sustainable development goals (SDGs).

Globally, wind energy if properly harnessed, could serve as a source of energy generation in Africa. This study compared the performance of two Machine Learning (ML) algorithms (Linear regression and Random Forest) in predicting wind speed in five major cities in Africa (Yaoundé, Pretoria, Nairobi, Cairo and Abuja). Wind data were collected between January 1, 2000, and December 31, 2022, using the Solar Radiation Data Archive. The data preprocessing was carried out with 80% of the data used for training and 20% for validation. The performance of these ML algorithms was evaluated using Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) and coefficient of determination (R2). The result shows that Nairobi (3.814795 m/s) closely followed by Cairo (3.606453 m/s) has the highest mean wind speed while Yaoundé (1.090512 m/s) has the lowest. Based on the performance metrics used, the two Machine Learning algorithms were competitive. Still, the Linear Regression (LR) algorithm outperformed the Random Forest Algorithm in predicting wind speed in all the selected major African cities. In Yaoundé (RMSE = 0.3892, MAE= 0.3001, MAPE =0.5030), Pretoria (RMSE=1.2339, MAE=0.9480, MAPE=0.7450) Nairobi (RMSE= 0.4223, MAE =0.6499, MAPE =0.1872), Nairobi (RMSE=0.6499, MAE=0.5171, MAPE =0.1872), Cairo (RMSE =1.0909, MAE =0.8544, MAPE =0.3541) and Abuja (RMSE = 0.70245, MAE =0.5441, MAPE= 0.4515) the Linear regression algorithms was found to outperformed Random Forest Regression. Therefore, the Linear regression algorithm is more reliable in predicting wind speed compared with the Random Forest regression.

Estimation of Monthly Mean Daily Global Solar Radiation over Bangkok, Thailand Using Artificial Neural Networks

In this research work a relationship has been identified between electrical resistivity (ρ) and total dissolved solid (TDS), to delineate subsurface TDS in groundwater in study area. TDS data have been collected from twenty-three wells spread across study area. At seventy locations vertical electrical soundings (VES) surveys were carried out. Quadratic least square technique has been used to generate an empirical model for TDS and ρ with a significant high coefficient of determination (R2) value of 0.73. Developed empirical model was validated using statistical tests and found to be very near to observed values. The statistical tests for validation of model, revealed that predicted and observed TDS values are also strongly correlated with R2 value (0.89), whereas other statistical tests (Standard Error of Estimate (SEE), Root mean square error (RMSE), Relative-RMSE (R-RMSE), Percent RMSC (%RMSE), t-statistic test, Volume Error (VE), Normalized RMSE (N-RMSE), Mean absolute error (MAE), Mean bias error (MBE), Mean absolute percent error (MAPE), Average index ratio (IR) and Percent of error (PE) have also revealed that established model have a good capability to predict TDS on the basis of ρ. On the basis of developed empirical model, groundwater TDS mapping has been carryout using ArcGIS within study area and delineated as fresh, brackish and saline zones.KeywordsCoastal aquiferTotal dissolved solidsVertical electrical soundingStatistical test

Predicting dam inflow is critical for human life safety, water resource management, and hydroelectric power generation. While machine learning (ML) models address complex, nonlinear hydrological problems, quantum machine learning (QML) offers greater potential to overcome classical computational limits. This study compares a hybrid quantum neural network (HQNN) with the following two classical models: bidirectional CNN-LSTM and support vector regression (SVR). These models were evaluated to predict monthly inflow to the Mile Mughan Dam, a transboundary hydroelectric and irrigation dam located on the Aras River between Azerbaijan and Iran, using a 14-year dataset (2010–2023) under two scenarios. In total, 70% of data was used for training and 30% for testing. The first scenario encompassed meteorological variables plus three months of inflow lags, and the second included inflow lags only. Model performance was assessed using Coefficient of Determination (R2), Root Mean Squared Error (RMSE), Nash–Sutcliffe efficiency (NSE), Mean Absolute Percentage Error (MAPE), and graphical plots. HQNN showed superior performance across all metrics. In Scenario 1, HQNN achieved R2 = 0.915, RMSE = 37.318 MCM, NSE = 0.908, MAPE = 8.343%; CNN-BiLSTM had R2 = 0.867, RMSE = 46.506 MCM, NSE = 0.858, MAPE = 10.795%; SVR had R2 = 0.846, RMSE = 52.372 MCM, NSE = 0.821, MAPE = 12.772%. In Scenario 2, HQNN maintained strong performance (R2 = 0.855, RMSE = 48.56 MCM, NSE = 0.845, MAPE = 9.979%) and outperformed CNN-BiLSTM (R2 = 0.810, RMSE = 56.126 MCM, NSE = 0.793, MAPE = 11.456%) and SVR (R2 = 0.801, RMSE = 60.336 MCM, NSE = 0.761, MAPE = 12.901%). In Scenario 1 and Scenario 2, HQNN increased the prediction accuracy by 19.76% and 13.47%, respectively, compared to the CNN-BiLSTM model. These results confirm HQNN’s reliability in both multivariate and univariate modeling.

The stream flow generation method is necessary for predicting yearly bed change at an ungauged stream in Monsoon region where there is no hydrologic and hydraulic information. This study developed the stream flow generation method of daily mean flow for each month over a year for bed change simulation at an ungauged stream. The hydraulic geometries of cross-sections and the corresponding bankfull indicators of the Byeongseong river of 4 km reach were analyzed to estimate the bankfull discharge. The estimated bankfull discharge of the target reach was 77.50 m3/s, and the total annual discharge estimated 3720 m3/s through the correlation equation with the bankfull discharge. The measured total annual discharge of the Byeongseong river was 3887.30 m3/s, which is greater by 167.30 m3/s of 4.3% relative error. The volume and bed changes over a year by the Center for Computational Hydroscience and Engineering Two-Dimension (CCHE2D) model simulated using the measured discharge during 2013 and 2014 coincided with the surveyed in the same period. Estimated total annual discharge was used for the scenarios of stream flow generation. The generated stream flow using the flow apportioned to each month on the basis of the flow percentage in an adjacent stream simulated the river bed most appropriately. The generated stream flow using the flow based on the monthly rainfall percentage of the rainfall station in the target stream basin also simulated river bed well, which is confirmed as an alternative. Quantitatively, the root mean square error (RMSE), mean bias error (MBE), and mean absolute percentage error (MAPE) in-depth change of thalweg between the measured and the simulated were found to be 0.25 m, 0.04 m, and 0.44%, respectively. The result of the simulated cross-sectional river bed change for target reach coincided well with the surveyed. The proposed method is highly applicable to generate the stream flow for analyzing the yearly bed change at an ungauged stream in Monsoon region.

본 연구는 Deep Neural Network(DNN)을 이용하여 광주-기아 챔피언스 필드의 일일 관중 수를 예측함으로써 이를 통해 구단과 관련기업의 마케팅 자료제공 및 구장 내 부대시설의 재고관리에 자료로 쓰임을 목적으로 수행 되었다. 본 연구 에서는 Artificial Neural Network(ANN)의 종류인 DNN 모델을 이용하였으며 DNN 모델의 과적합을 막기 위해 Dropout 과 Batch normalization 적용한 모델을 바탕으로 총 4종류를 설계하였다. 각각 10개의 DNN을 만들어 예측값의 Root Mean Square Error(RMSE)와 Mean Absolute Percentage Error(MAPE)의 평균값을 낸 모델과 예측값의 평균으로 RMSE와 MAPE를 평가한 Ensemble 모델을 만들었다. 모델의 학습 데이터는 2008년부터 2017년까지의 관중 수 데이터를 수집하여 수집된 데이터의 80%를 무작위로 선정하였으며, 나머지 20%는 테스트 데이터로 사용하였다. 총 100회의 데이터 선정, 모델구성 그리고 학습 및 예측을 한 결과 Ensemble 모델은 DNN 모델의 예측력이 가장 우수하게 나왔으며, 다중선 형회귀 모델 대비 RMSE는 15.17%, MAPE는 14.34% 높은 예측력을 보이고 있다.In this paper, we used the Deep Neural Network (DNN) to predict the number of daily spectators of Gwangju -KIA Champions Field in order to provide marketing data for the team and related businesses and for managing the inventories of the facilities in the stadium. In this study, the DNN model, which is based on an artificial neural network (ANN), was used, and four kinds of DNN model were designed along with dropout and batch normalization model to prevent overfitting. Each of four models consists of 10 DNNs, and we added extra models with ensemble model. Each model was evaluated by Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The learning data from the model randomly selected 80% of the collected data from 2008 to 2017, and the other 20% were used as test data. With the result of 100 data selection, model configuration, and learning and prediction, we concluded that the predictive power of the DNN model with ensemble model is the best, and RMSE and MAPE are 15.17% and 14.34% higher, correspondingly, than the prediction value of the multiple linear regression model.

This article uses machine learning techniques as fuzzy and neuro-fuzzy ANFISs, to develop and compare prediction models capable of relating pregnant women’s exposure to air pollutants, such as Nitrogen Dioxide and Particulate Matter, the mother’s age, and the number of prenatal consultations to the incidence of premature birth. In the current literature, studies can be found that relate prematurity to the exposure of pregnant women to NO2, O3, and PM10; to Toluene and benzene, mainly in the window 5 to 10 days before birth; and to PM10 in the week before birth. Both models used logistic regression to quantify the effects of pollutants as a result of premature birth. Datasets from Brazil—Departamento de Informatica do Sistema Único de Saúde (DATASUS) and Companhia Ambiental do Estado de São Paulo (CETESB)—were used, covering the period from 2016 to 2018 and comprising women living in the city of São José dos Campos (SP), Brazil. In order to evaluate and compare the different techniques used, evaluation metrics were calculated, such as correlation (r), coefficient of determination (R2), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), and Mean Absolute Error (MAE). These metrics are widely used in the literature due to their ability to evaluate the robustness and efficiency of prediction models. For the RMSE, MAPE, MSE, and MAE metrics, lower values indicate that prediction errors are smaller, demonstrating better model accuracy and confidence. In the case of (r) and R2, a positive and strong result indicates alignment and better performance between the real and predicted data. The neuro-fuzzy ANFIS model showed superior performance, with a correlation (r) of 0.59, R2 = 0.35, RMSE = 2.83, MAPE = 5.35%, MSE = 8.00, and MAE = 1.70, while the fuzzy model returned results of r = 0.20, R2 = 0.04, RMSE = 3.29, MSE = 10.81, MAPE = 6.67%, and MAE = 2.01. Therefore, the results from the ANFIS neuro-fuzzy system indicate greater prediction capacity and precision in relation to the fuzzy system. This superiority can be explained by integration with neural networks, allowing data learning and, consequently, more efficient modeling. In addition, the findings obtained in this study have potential for the formulation of public health policies aimed at reducing the number of premature births and promoting improvements in maternal and neonatal health.

Solar radiation is the principal and fundamental energy for many physical, chemical and biological processes. Estimation of solar radiation from other measured meteorological variables offers an important alternative in the absence of availability of measured solar radiation data. In this paper, we validate and assess four commonly used air temperature-based models including the Hargreaves and Samani, Hargreaves, Bristow & Campbell and Chen model and a local regression model, developed using long-term data from 14 sites in Yangtze River basin in China. We present the two-step method to estimate solar radiation from the commonly measured air temperature. The model performance is evaluated using root mean square error (RMSE), relative root mean square error (RRMSE), mean absolute bias error (MABE) and mean absolute percentage error (MAPE). Results show that the two-step method gives good performance and significantly outperforms the temperature-based models. The parameters determination equations of the two-step method are proposed to solve the difficult problem in parameter calibration at the site where no long-term observations of solar radiation and sunshine duration are available. It is found that the two-step method using the parameters determined by the proposed equations gives good performance, with the averaged R-2 of 0.881, RRMSE of 15.04% and MAPE of 12.67%. Therefore, the two-step method with the parameters determined by the proposed equations could be used to estimate solar radiation in Yangtze River basin. It is believed to be useful for the site where no measured solar radiation and sunshine duration data is available, whereas the air temperatures are common measured.

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Solar radiation modelling using ANNs for different climates in China

Electricity consumption prediction plays a vital role in intelligent energy management systems, and it is essential for electricity power supply companies to have accurate short and long-term energy predictions. In this study, a deep-ensembled neural network was used to anticipate hourly power utilization, providing a clear and effective approach for predicting power consumption. The dataset comprises of 13 files, each representing a different region, and ranges from 2004 to 2018, with two columns for the date, time, year and energy expenditure. The data was normalized using minmax scalar, and a deep ensembled (long short-term memory and recurrent neural network) model was used for energy consumption prediction. This proposed model effectively trains long-term dependencies in sequence order and has been assessed using several statistical metrics, including root mean squared error (RMSE), relative root mean squared error (rRMSE), mean absolute bias error (MABE), coefficient of determination (R2), mean bias error (MBE), and mean absolute percentage error (MAPE). Results show that the proposed model performs exceptionally well compared to existing models, indicating its effectiveness in accurately predicting energy consumption.