Statistical Error Parameters Research Articles

On the evaluation of surface tension of biodiesel

Over time, with the increase in population and the subsequent increase in energy consumption and also due to the non-renewability of fossil fuels, the study of alternative fuels has increased. One of these fuels is biodiesel, which is a suitable alternative to fossil fuels such as diesel and received much attention from researchers today. For this reason, measuring the physical properties of biodiesel is of great importance. Due to the high cost and time-consuming nature of laboratory methods, numerical methods are used to estimate material properties. The novelty of this research was the use of two white box models, including Group method of data handling (GMDH) and Gene expression programming (GEP), which work on the basis of artificial intelligence. By using these models, two simple mathematical equations with high accuracy were presented to predict the surface tension of biodiesel. These models can be used at different temperatures and molecular weights. To do modeling, 78 laboratory data available in the literature were gathered and the data were randomly divided into two groups, train and test, in a ratio of 80 and 20. The input parameters include mass fraction of fatty acid ethyl esters and temperature (T), and esters are divided into three groups according to their molecular weight: less than 200 (Mw1), between 200 and 300 (Mw2), and greater than 300 (Mw3). The statistical error parameters were calculated for the two models developed in this research and after comparing the results, it was found that the GMDH model estimates the surface tension of biodiesel with a higher accuracy. The average absolute relative error for GMDH and GEP models was reported as 0.97 and 1.89, respectively. Also, other statistical error parameters of GMDH such as RMSE, SD, and R2 for the GMDH model were obtained as 0.444, 0.000233, and 0.9233, respectively. Moreover, sensitivity analysis showed that temperature has the highest impact on the surface tension of biodiesel, which is also an inverse effect. Finally, suspicious laboratory and outlier data points were identified using the Leverage technique. According to this analysis, only five data points were identified as outliers and suspicious laboratory data.

Accuracy of Weather Radar Products for Rainfall Estimation in North Sumatra Region

The weather radar is a remote sensing-based observation tool that identifies and records rainfall. Remote sensing is a technology that determines atmospheric conditions, measures rainfall, and performs other functions. However, the accuracy of weather radar products concerning rainfall estimation need to be evaluated. This research aims to investigate the accuracy of weather radar products for rainfall estimation in North Sumatra. We analyzed the raw weather radar data using RAINBOW software for data processing. We presented the accuracy evaluation between weather data and observation data using several statistical error parameters such as the Mean Absolute Error (MAE), Mean Error (ME), and Pearson Correlation (r). The results indicate that the CMAX radar product estimates rainfall better than the PPI and CAPPI products. The CMAX product has the lowest error value and higher correlation coefficient (r), indicating its superior rainfall estimation performance.

Cross section empirical formulation for (n, 2n) nuclear reactions on natural isotopes from Z= 21 to Z= 79 for neutron energy range, 8–20 MeV

Neutron induced reactions with different target materials and isotopes are very important for completion of nuclear data base as well as for many applications. Since the experimental determinations of the reaction cross sections for such reactions are not always available, attempts were made to introduce empirical or semi empirical formulae. In this work, new empirical formulation for (n, 2n) nuclear reactions on natural isotopes for neutron energies range 8–20 MeV, based on some published experimental works. The deuced formulae are then used to calculate the excitation functions for the (n,2n) on target isotopes having atomic numbers in the range 21–79. The cross section values for many reactions, having previously measured values, are determined and inter-comparison with the experimental and the TENDL-2019 database values are given using some statistical error parameters. Special attention was made to some Lanthanide isotopes. The results showed satisfied predictions in most cases.

Terminal settling velocity of solids in the pseudoplastic non-Newtonian liquid system – Experiment and ANN modeling

The terminal settling velocity (TSV) of solid particles is experimentally determined in fluidizing columns. In monodispersed (single component) systems, the bed expansion behavior has been experimented with using pseudoplastic liquids. The terminal velocity is calculated from the plot of bed voidage (ε) vs. liquid velocity and extrapolating to ε = 1.0. An empirical correlation is developed for determining the TVS with acceptable statistical accuracy. Successful applicability of ANN modeling has been reported. After comparing with existing literature, it was found that the present work yielded better results (based on the statistical error parameters) than the previous literature.

Wind speed and power forecasting of a utility-scale wind farm with inter-farm wake interference and seasonal variation

Forecasting skills for a wind farm would significantly degrade if the complex wake effects of the upstream wind farms are excluded, especially when they are spatially close to each other. In this study, the Weather Research and Forecasting (WRF) model has been used to predict wind speed and power for a wind farm in Pakistan in the presence of wake interference from neighboring wind farms for two different seasons. Forecasting is done for two different cases i.e. without and with inter-farm wake effects, and different statistical error parameters were evaluated based on the real observations. A significant reduction in errors was observed in the latter case. For instance, the mean absolute errors in wind speed prediction were reduced by 7.7% and 14% in June (summer) and January (winter) respectively, by the inclusion of inter-farm wake effects. Similarly, an improved forecast of power output was obtained by incorporating the interaction of upstream wind farms i.e. a reduction of 15% and 26% in the normalized mean absolute error in power output values was observed for June and January, respectively. However, the prediction accuracy of power output substantially deteriorated in the winter season.

Optimal estimations of directional wave conditions for nearshore field studies

Accurate directional wave conditions at shallow water are crucial for nearshore field studies and necessary as boundary conditions for morphodynamic models. However, obtaining reliable results for all wave parameters can be challenging, particularly regarding wave direction. Here, the accuracy of two global hindcast models and propagation of measured wave conditions using linear wave theory or the SWAN wave model (forced by integrated wave parameters or 2D spectra) is assessed to obtain directional wave conditions at shallow water for Castelldefels beach, northwestern Mediterranean Sea. Results are analyzed using different statistical error parameters and for different wave climates (shore-normal, shore-oblique and bimodal). The analysis shows that global hindcast models correctly predict the trends in wave height and mean wave period but predictions for mean wave direction are only accurate for shore-normal waves. Linear wave theory provides good results for wave height but underestimates refraction, resulting in significant errors in mean wave direction for shore-oblique waves. Finally, SWAN forced with 2D spectra results in the most accurate predictions for all wave parameters. When using integrated wave parameters as boundary conditions, the results for wave height and mean period stay the same whilst the errors in peak period and mean direction worsen for shore-oblique and bimodal wave climates. The reason is that for these wave conditions the directional spectrum constructed out of integrated wave parameters does not resemble the actual directional spectrum.

Statistical comparison of two modeling methods on pressurized hot water extraction of vitamin C and phenolic compounds from Moringa oleifera leaves

Moringa oleifera is an excellent source of bioactive compounds which exhibit nutritional and medicinal properties. Pressurized hot water extraction is known as a green, environmentally, faster and efficient extraction technique. However, it is facing a challenge with the degradation of thermolabile compounds at higher temperature. This research was performed to investigate the influence of extraction temperature, time and flow rate of pressurized hot water extraction in the recovery of Vitamin C and phenolic compounds from Moringa oleifera leaves. Response surface methodology (RSM) and artificial neural network (ANN) were used as estimates and predictive models with maximum responses. The optimal pressurized hot water extraction conditions were identified at: 91°C for temperature, 60 min for extraction time and 0.3 mL min−1 for flow rate, giving a predicted concentration of 3.92 ± 0.30, 4.74 ± 0.32 and 0.357 ± 0.19 g per 100 g of dry powder for kaempferol, quercetin and vitamin C, respectively. Evaluation of the two models through the statistical error parameters showed that ANN model gave a good predictive and estimation capabilities than RSM. Therefore, ANN can be recommended for use optimization method in the pressure hot water extraction.

GMDH-based prediction of shear strength of FRP-RC beams with and without stirrups

In the present study, group method of data handling networks (GMDH) are adopted and evaluated for shear strength prediction of both FRP-reinforced concrete members with and without stirrups. Input parameters considered for the GMDH are altogether 12 influential geometrical and mechanical parameters. Two available and very recently collected comprehensive datasets containing 112 and 175 data samples are used to develop new models for two cases with and without shear reinforcement, respectively. The proposed GMDH models are compared with several codes of practice. An artificial neural network (ANN) model and an ANFIS based model are also developed using the same databases to further assessment of GMDH. The accuracy of the developed models is evaluated by statistical error parameters. The results show that the GMDH outperforms other models and successfully can be used as a practical and effective tool for shear strength prediction of members without stirrups (R2=0.94) and with stirrups (R2=0.95). Furthermore, the relative importance and influence of input parameters in the prediction of shear capacity of reinforced concrete members are evaluated through parametric and sensitivity analyses.

Derivation of New Equations for Prediction of Principal Ground-Motion Parameters using M5′ Algorithm

In this study, M5′ model tree is used to develop a model for prediction of peak time-domain strong ground motion parameters. The main advantages of model trees are that can be easily developed and their formulas are simple and understandable. Selected data from Pacific Earthquake Engineering Research Center (PEER) are used to train the proposed model. Earthquake magnitude, earthquake source to site distance, average shear-wave velocity, and faulting mechanisms are used as input parameters. The developed M5′ based formulas are compared with those of well-known empirical and soft computing based models. The accuracy of the model is evaluated by statistical error parameters.

Development and assessment of different modeling approaches for size-mass estimation of mango fruits (Mangifera indica L., cv. ‘Nam Dokmai’)

To meet consumer demands, the need for quick and accurate methods for quality assessment of fresh fruits is increasing constantly. This study presents a comparison of three different models for mass estimation of mango fruits (cv. ‘Nam Dokmai’) calculated by simple linear regression (SLR), multiple linear regression (MLR) and artificial neural network (ANN). Three dimensions (length, maximum width, and maximum thickness) were manually measured and included as parameters for model building. Calibration and validation were carried out on independent data sets with 820 samples (2010–2012) and 61 samples (2014), respectively. This allowed it to establish a high-performance model that can be used for further mass-size estimation in a machine-vision system. For the SLR, an existing equation for mass estimation was modified to calculate an adjusted coefficient for accurate mass estimation. A MLR model was proposed to obtain the intercept, the slopes of the three parameters length, maximum width and maximum thickness as well as the random error. In addition, an ANN model was used as it allows the network to learn linear and nonlinear relationships between inputs and outputs. Performance evaluation of three different models was based on a compilation of different statistical error parameters and goodness-of-fit measures and the outcomes of the models were compared. ANN was found to be the most accurate and robust model for mass estimation with a root mean squared error (RMSE) of 6.55g, mean absolute percentage error (MAPE) of 1.62%, and coefficient of efficiency (E) of 0.99 after validation. Therefore, it can be applied for mass estimation of mango fruits with highest accuracy and success rate of 96.7% compared to the other models in this study.

Neuro-Fuzzy GMDH-Based Evolutionary Algorithms to Predict Flow Discharge in Straight Compound Channels

In this study, neuro-fuzzy-based group method of data handling (NF-GMDH) as an adaptive learning network is used to predict the flow discharge in straight compound channels. The NF-GMDH network is developed by using the particle swarm optimization (PSO) and gravitational search algorithm (GSA). The depth ratio (ratio of water depth in floodplain to that in main channel), coherence parameter, and the discharge ratio [ratio of flow discharge calculated from vertical divided channel method (VDCM) to the bank full discharge] are considered as input parameters to represent a functional relationship between input and output parameters. The performances of training and testing stages for NF-GMDH models were quantified in terms of statistical error parameters. Also, the results of performances were compared with those obtained by using linear genetic programming, nonlinear regression methods, and VDCM. Evaluation of the proposed model demonstrated that NF-GMDH-GSA network provides a more accurate prediction than the NF-GMDH-PSO network. Finally, statistical error parameters indicated that the NF-GMDH networks as a new soft-computing tool produced better prediction of flow discharge in comparison with linear genetic programming, nonlinear regression methods, and VDCM.

Modeling of global horizontal irradiance in the United Arab Emirates with artificial neural networks

This paper employs ANN (Artificial Neural Network) models to estimate GHI (global horizontal irradiance) for three major cities in the UAE (United Arab Emirates), namely Abu Dhabi, Dubai and Al-Ain. City data are then used to develop a comprehensive global GHI model for other nearby locations in the UAE. The ANN models use MLP (Multi-Layer Perceptron) and RBF (Radial Basis Function) techniques with comprehensive training algorithms, architectures, and different combinations of inputs. The UAE models are tested and validated against individual city models and data available from the UAE Solar Atlas with good agreement as attested by the computed statistical error parameters.The optimal ANN model is MLP-based and requires four mean daily weather parameters; namely, maximum temperature, wind speed, sunshine hours, and relative humidity. The computed statistical error parameters for the optimal MLP-ANN model in relation to the measured three-cities mean data (referred to as UAE data) are MBE (mean bias error) = −0.0003 kWh/m2, RMSE = 0.179 kWh/m2, R2 = 99%, NSE (Nash-Sutcliffe model Efficiency coefficient) = 99%, and t-statistic = 0.005 at 5% significance level. Results prove the suitability of the ANN models for estimating the monthly mean daily GHI in different locations of the UAE.

Wellhead Choke Performance in Oil Well Pipeline Systems Based on Genetic Programming

AbstractThe accurate determination of choke performance in oil pipelines is considered a main challenge for petroleum engineers. This study introduces a new correlation based on genetic programming (GP) to describe choke performance in both critical and subcritical flow conditions in pipeline flow regimes. The GP model is developed using field data collected from various Iranian oil well pipelines. Statistical error parameters are used to compare the accuracy of results obtained from the new correlation with other empirical models. The GP model predicted the choke performance for critical flow condition with relatively lower error (normalized mean square error = 0.006) and higher accuracy (R=0.993%). In addition, the results of the model in a subcritical flow regime showed that the GP model could be applied effectively and yield high accuracy for choke performance pipeline forecasting.

Estimation of Hourly Temperature at a Site and its Impact on Energy Yield of a PV Module

This paper discusses a method for estimating the hourly temperature at a location, if the ambient maximum and minimum temperatures of a particular day, along with the maximum temperature on the previous day and the minimum temperature of the following day, are known. The impact of estimated temperature on the energy yield of a photovoltaic (PV) module is also discussed with the help of a mathematical model. Algorithms have been developed for relevant computations and implemented using MATLAB. Hourly meteorological data of Bhopal and Trivandrum, India, have been considered for studying, analyzing, and validating the results. A PV module (BP 3215) manufactured by BP Solar Ltd. has been considered for analyzing the results in terms of energy generation. The statistical error parameters calculated for the estimated hourly temperature indicate a reasonable degree of accuracy of estimation. The values of mean absolute error (MAE) and root mean square error (RMSE) are superior to those of other models and that of R2 is comparable. The estimated values of yearly and monthly average of hourly temperature are invariably found to be more than the corresponding measured values. At these two locations, there is a reasonable linear fit between monthly averages of hourly temperature, calculated from the estimated and measured values of hourly temperature. The deviation between the two values of annual energy generated, one calculated from the estimated values and the other from the measured values of hourly temperature, is nominal. Thus, the estimated values of hourly temperature can be used for energy estimation and feasibility analysis of PV system, with a fair degree of accuracy.

Modeling of desorption of Alfalfa ( Medicago sativa) stems and leaves

The equilibrium moisture content of agricultural products is necessary to optimize drying process and helps to keep the quality of the product during the period of storage. The main aim of this research was to find the best model which could define well, the exchange of moisture between alfalfa ( Medicago sativa) and the surrounding air. The desorption isotherms of alfalfa (stem and leaf) were determined separately by using the saturated salt solutions method at three temperatures (25, 50 and 70 °C) within a range of 5–90% relative humidity. Experimental curves of desorption isotherms were fitted to modified equations of Henderson, Halsey, Oswin and Chung-Pfost as well as the GAB model and then evaluated visually by using residual plots and also by some statistical error parameters. The modified Halsey model was found to be the most suitable for describing the relationship between equilibrium moisture content, relative humidity and temperature.

Equilibrium Moisture Content Equations for some Medicinal and Aromatic Plants

In this research, the most commonly used equilibrium moisture content (EMC) and equilibrium relative humidity (ERH) equations are compared on their ability to best fit the published sorption data for selected medicinal and aromatic plants. A non-linear regression technique is used to fit data subsets. In order to compare the performance of the EMC/ERH equations, three statistical error parameters are used. The best-fitted equations which provide a sound basis for future work on drying and storage of medicinal and aromatic plants are given.