Levenberg-Marquardt Learning Algorithm Research Articles

Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm

Abstract The aim of this research is to provide a new computer-assisted approach for predicting thermophoresis particle decomposition on three-dimensional Casson nanofluid flow that passed over a stretched surface (thermophoresis particle decomposition on three-dimensional Casson nanofluid flow; TPD-CNF). In order to understand the flow behavior of nanofluid flow model, an optimized Levenberg–Marquardt learning algorithm with backpropagation neural network (LMLA-BPNN) has been designed. The mathematical model of TPD-CNF framed with appropriate assumptions and turned into ordinary differential equations via suitable similarity transformations are used. The bvp4c approach is used to collect the data for the LMLA-BPNN, which is used for parameters related with the TPD-CNF model controlling the velocity, temperature, and nanofluid concentration profiles. The proposed algorithm LMLA-BPNN is used to evaluate the obtained TDP-CNF model performance in various instances, and a correlation of the findings with a reference dataset is performed to check the validity and efficacy of the proposed algorithm for the analysis of nanofluids flow composed of sodium alginate nanoparticles dispersed in base fluid water. Statistical tools such as Mean square error, State transition dynamics, regression analysis, and error dynamic histogram investigations all successfully validate the suggested LMLA-BPNN for solving the TPD-CNF model. LMLA-BPNN networks have been used to numerically study the impact of different parameters of interest, such as Casson parameter, power-law index, thermophoretic parameter, and Schmidt number on flow profiles (axial and transverse), and energy and nanofluid concentration profiles. The range, i.e., 10−4–10−5 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks.

Investigating the Impacts of Tropospheric Parameters on Received Signal Strength of the Mobile Communication System

Abstract Radio communication systems are crucial for information transmission, but they face challenges like interference and fading, which significantly impact network efficiency. Understanding propagation-related issues is crucial for optimizing networks. This study examined the influence of tropospheric parameters on the Received Signal Strength (RSS) of the Globacom communication system in Rivers State. Four tropospheric variables (air temperature, relative humidity, atmospheric pressure, and wind speed) are collected from the River State University of Science and Technology (RSUST) Environmental and Climatic Observatory Program. The results of the correlation analysis indicated a direct linear correlation between air temperature and RSS. In contrast, wind speed displayed an indirect relationship, while the remaining parameters demonstrated an inverse linear relationship. Multiple linear regression (MLR) and multiple linear perceptron (MLP) models were developed to accurately predict the impacts of tropospheric parameters on RSS. A supervised-learning three-layered MLP feed-forward neural network was employed, consisting of 10 distinct MLP NN models. The Levenberg-Marquardt (LM) learning algorithm was used in training and validating the MLP NN models. The MLP 4-40-1 model showed an exceptional understanding of the non-linear relationship between the tropospheric parameters and RSS. The MLR model exhibited a weaker correlation coefficient of 0.2164, while the MLP demonstrated a stronger correlation coefficient of 0.7942. Additionally, the MLP 4-40-1 model outperformed the MLR model in terms of Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), achieving an accuracy of 0.2480 RMSE and 12.9963% MAPE, while the MLR model had 1.6880 RMSE and 27.3787% MAPE. These findings highlight the efficiency of the MLP 4-40-1 model in estimating the exact relationship between the tropospheric parameters and the signal strength of the mobile network in Rivers State. The study provides valuable insights into optimizing network design and emphasizes the significance of including tropospheric parameters in enhancing mobile communication performance.

Multilayer Perceptron Artificial Neural Network (Mlpann) Model to Predict Temperature During Rotary Drilling

In this paper, a multilayer perceptron neural network has been used to represent temperature measurement during rotary drilling of five types of rock samples. To forecast the temperature at various thermocouple depths, the experimentally collected data was standardized. Indicators of model performance was also obtained in order to assess the correctness of the model. One hidden layer and one output layer were employed with MLPANN, which has ten input parameters (bit diameter (DD), Spindle Speed (SS), Penetration Rate (PR), thrust, and torque) and rock properties. Levenberg Marquardt learning algorithm with transfer function of logsig is the most optimal neuron number of 10-16-1 was successfully forecasting the temperature with a correlation of 0.9936 and 0.9941 for training and testing algorithm during drilling after analysis based on the trial-and- error approach to identify the optimum algorithm. Ten input parameters, a logsig sigmoid transfer function, and the trainlm algorithm in this study provide good prediction ability with tolerable accuracy.

SMART MINING: JOINT MODEL FOR PARAMETRIZATION OF COAL EXCAVATION PROCESS BASED ON ARTIFICIAL NEURAL NETWORKS

<p>In the present paper we propose a new artificial neural network model for the estimation of coal cutting resistance and excavator performance as a nonlinear relationship between the examined input (excavator movement angle in the left and right direction, slice height and thickness, coal unit weight, compressive and shear strength) and output factors (excavator effective capacity, maximum current/power/force/energy consumption, linear and areal cutting resistance). We analyze the dataset collected from three open-pit coal mines in Serbia: Field D, Tamnava Eastern Field and Tamnava Western Field (all part of the Kolubara coal basin). The model is developed using a multilayer feed-forward neural network, with a Levenberg-Marquardt learning algorithm. Results of the preformed analysis indicate satisfying statistical accuracyof the developed model (R>0.9). Additionally, we analyze the individual effects of input factors on the properties of coal cutting resistance and performance of the excavator, by invokling the multiple linear regression. As a result, we single out the statististically significant and physically possible interactions between the individual controlling factors</p>

Application of Artificial Intelligence for Modeling the Internal Environment Condition of Polyethylene Greenhouses

Accurate temperature prediction and modeling are critical for effective management of agricultural greenhouses. By optimizing control and minimizing energy waste, farmers can maintain optimal environmental conditions, leading to improved crop yields and reduced financial losses. In this study, multiple models, including Multiple Linear Regression (MLR), Radial Basis Function (RBF), and Support Vector Machine (SVM), were compared to predict greenhouse air temperature. External parameters, such as air temperature (Tout), relative humidity (Hout), wind speed (W), and solar radiation (S), were used as inputs for these models, and the output was the inside temperature. The results showed that the RBF model with the LM (Levenberg–Marquardt) learning algorithm outperformed the other models, achieving the lowest error and the highest coefficient of determination (R2) value. The RBF model produced RMSE, MAPE, and R2 values of 1.32 °C, 3.23%, and 0.931, respectively. These results demonstrate that the RBF model with the LM learning algorithm can reliably predict greenhouse air temperatures for the next two hours. The ANN model can be applied to optimize time management and reduce energy losses, improving the overall efficiency of greenhouse operations.

An approach towards building robust neural networks models using multilayer perceptron through experimentation on different photovoltaic thermal systems

The study is aimed at training an artificial neural network to determine the specific Photo voltaic thermal (PV/T) system that will function optimally in a specific environmental situation by optimizing the input parameters. In this regard, four different PV/T systems based on the arrangement of the tubes and the presence of the copper absorber sheet, namely, vertically oscillating tube, vertically oscillating sheet tube, rectangular spiral tube and horizontally oscillating tube PV/T’s were considered. In the experimental study, wind velocity, solar irradiation, ambient temperature, relative humidity, and inlet temperature to the PV/T are considered the influencing factors. The response factors for evaluating the performance of the PV/T system were temperature outlet and power output. Water was used as the working fluid for the thermal management of the systems for all four test cases. The investigation discloses that the rectangular spiral tube photovoltaic thermal system is the best among the studied systems as it maintains both average thermal efficiency and average electrical efficiency at 50.7% and 12.15%, respectively, considering the trade-off between electrical and thermal efficiency. The ideal design can then be selected for a specific area that will be more appropriate with its environmental fluctuations by approximating the production for each scenario. The artificial neural network was designed to be capable of being successfully trained for this application based on Artificial Neural Network (ANN), Multilayer Perceptron using Levenberg Marquardt learning algorithm through MATLAB software based on the experimental data. The ANN model for the rectangular spiral tube PV/T system achieved an exceptional overall R-value of 0.99843 among the proposed prediction models. For the artificial neural network model formulated for vertically oscillating tube, vertically oscillating sheet tube and horizontally oscillating tube PV/T system, the R-value was found to be 0.99807, 0.9943, and 0.99593, respectively. In the training phase, the MSE for vertically oscillating tube, vertically oscillating sheet tube, rectangular spiral tube and horizontally oscillating tube PV/T’s using the multilayer perceptron artificial neural network models were found to be 1.1328, 3.5082, 0.3134 and 1.1328, respectively. For the same PV/T’s models, the MSE values for Cross validation phase were found to be 1.8497, 3.9072, 5.1419, and 4.6402, respectively. Finally, the suggested linear prediction models assist in quickly and easily determining the ideal conditions for every solar system while lowering the error in furcating future results.

Isolated UIPC-intertied AC-DC microgrids operation with novel dynamic flexible loads model

This work discusses the islanding operation of hybrid microgrids (HµGs) interconnected by a unified interphase power controller (UIPC). It is illustrated that considering islanding operation of HµG, the problem of power dispatch among intertied AC and DC µGs, as well as voltage and frequency control, can be handled by UIPC. The power dispatch among various AC and DC µGs using UIPC is analyzed and formulated through defining a simple demand condition function (DCF). A new control structure is proposed for the series power converter of the UIPC which enjoys the robustness of sliding mode control (SMC) concept and adopts a new energy management system (EMS) with embedded decision-making. This provides a fast, robust, and simple power flow control unit which acts as a general supervisory system for the UIPC and islanding operation of HµG. Also, a novel generalized dynamic model for flexible loads has been proposed. These loads have been directly controlled through UIPC supervisory system here. The analytical response of the proposed flexible load model is discussed and further developed using the nonlinear autoregressive-moving-average artificial neural network (ANN) model. The Levenberg-Marquardt learning algorithm is used to train the network based on the model estimation error. Besides, a new model predictive-based optimal control scheme is proposed for the flexible load. Simulation results using MATLAB support the usefulness of the proposed UIPC-based islanded HµG platform.

Road adhesion coefficient estimation by multi-sensors with LM-MMSOFNN algorithm

Accurate and efficient road adhesion coefficient estimation is the premise for the proper functioning of vehicle active safety control system. With the increased application of distributed drive vehicles and on-board sensors, a multi-module self-organizing feedforward neural network (LM-MMSOFNN) based on improved Levenberg-Marquardt (LM) learning algorithm is proposed for online road adhesion coefficient estimation. In this method, the vehicle dynamics model and the Dugoff tire model were well established, and the input and output variables of the neural network model were obtained by Principal Component Analysis (PCA) method. To improve the estimation accuracy, Extended Kalman Filter (EKF) and Moving Average (MA) were used to denoise the measured signal. On this basis, a road adhesion coefficient estimation model based on multi-module self-organizing neural network was established. Both sides of road adhesion coefficients are calculated by multi-module self-organizing neural network simultaneously. Through the increase and decrease of self-organizing neurons and the improved LM learning algorithm, the computational complexity and system hardware storage are reduced, and the algorithm exhibits a good adaptability to different roads. Simulation and vehicle experiments show that the proposed method can fully extract multi-sensor information and adapt to the different road characteristics changes under driving condition. As compared with Kmeans method, it has higher estimation accuracy and stronger adaptability to varying speed.

Experimental evaluation and modeling the mass and temperature of dried mint in greenhouse solar dryer; Application of machine learning method

This study is aimed to model the temperature and mass of dried mint in a Quonset type of Greenhouse Solar Dryer (GSD). The inputs including ambient air temperature (◦C), ambient air humidity (%) and solar radiation (Wm-2) and output data including temperature (◦C) and mass (gr) of dried mint were collected from a Quonset GSD. Artificial Neural Network (ANN) models including Multilayer Perceptron (MLP) and Radial Bias Function (RBF) and also, Gaussian Process Regression (GPR) by k-fold cross validation method were used for modeling. Levenberg-Marquardt (LM) learning algorithm with Sigmoid-Tangent transfer function by different combinations of neurons in the hidden layer were assessed for ANN models. The results showed that MLP and GPR have higher error than RBF model for predicting the temperature and mass of dried mint. The results of RBF optimization indicated that 3-15-1 and 3-18-1 topologies with using 60 and 50% of total dataset for training steps and having 0.4 and 0.3 spread factor values can predict the temperature and mass of dried mint with Mean Absolute Percentage Error (MAPE) of 1.4 and 1.82%, respectively. The results of t, F, and Kolmogorov–Smirnov tests indicated that there is no significant difference between actual and RBF output values.

Comparison of Artificial Neural Network and Polynomial Approximation Models for Reflectance Spectra Reconstruction

Knowledge of surface reflection of an object is essential in many technological fields, including graphics and cultural heritage. Compared to direct multi- or hyper-spectral capturing approaches, commercial RGB cameras allow for a high resolution and fast acquisition, so the idea of mapping this information into a reflectance spectrum (RS) is promising. This study compared two modelling approaches based on a training set of RGB-reflectance pairs, one implementing artificial neural networks (ANN) and the other one using multivariate polynomial approximation (PA). The effect of various parameters was investigated: the ANN learning algorithm-standard backpropagation (BP) or Levenberg-Marquardt (LM), the number of hidden layers (HLs) and neurons, the degree of multivariate polynomials in PA, the number of inputs, and the training set size on both models. In the two-layer ANN with significantly fewer inputs than outputs, a better MSE performance was found where the number of neurons in the first HL was smaller than in the second one. For ANNs with one and two HLs with the same number of neurons in the first layer, the RS reconstruction performance depends on the choice of BP or LM learning algorithm. RS reconstruction methods based on ANN and PA are comparable, but the ANN models' better fine-tuning capabilities enable, under realistic constraints, finding ANNs that outperform PA models. A profiling approach was proposed to determine the initial number of neurons in HLs-the search centre of ANN models for different training set sizes.

Designing of the Artificial Neural Network Model Trained by Using the Different Learning Algorithms to Classify the Electrocardiographic Signals

An artificial neural network model trained by using various learning algorithms is designed to classify the electrocardiographic signals in this study. The model of artificial neural network is constructed on the structure consisting of a multilayered perceptron based on the feed forward back propagation. A data pool is built by using a dataset consists of 66 electrocardiographic data’s taken from the MIT BIH arrhythmia database to perform the training and testing processes of artificial neural network model. The training process of artificial neural network model is performed with 46 electrocardiographic data and then the accuracy of the model is tested via 20 electrocardiographic data. The artificial neural network is trained by 3 different learning algorithms to achieve a robust model. The performance of the learning algorithms used for training the model of the artificial neural network is evaluated according to percentage error. It illustrates that the artificial neural network model trained by Levenberg–Marquardt learning algorithm obtains the better classification result than other learning algorithms. The proposed artificial neural network model can be successfully used to classify the electrocardiographic signals.

Application of machine learning to determine the shear stress and filtration loss properties of nano-based drilling fluid

A detailed understanding of the drilling fluid rheology and filtration properties is essential to assuring reduced fluid loss during the transport process. As per literature review, silica nanoparticle is an exceptional additive to enhance drilling fluid rheology and filtration properties enhancement. However, a correlation based on nano-SiO2-water-based drilling fluid that can quantify the rheology and filtration properties of nanofluids is not available. Thus, two data-driven machine learning approaches are proposed for prediction, i.e. artificial-neural-network and least-square-support-vector-machine (LSSVM). Parameters involved for the prediction of shear stress are SiO2 concentration, temperature, and shear rate, whereas SiO2 nanoparticle concentration, temperature, and time are the inputs to simulate filtration volume. A feed-forward multilayer perceptron is constructed and optimised using the Levenberg–Marquardt learning algorithm. The parameters for the LSSVM are optimised using Couple Simulated Annealing. The performance of each model is evaluated based on several statistical parameters. The predicted results achieved R2 (coefficient of determination) value higher than 0.99 and MAE (mean absolute error) and MAPE (mean absolute percentage error) value below 7% for both the models. The developed models are further validated with experimental data that reveals an excellent agreement between predicted and experimental data.

Specific heat capacity prediction of hybrid nanofluid using artificial neural network and its heat transfer application

Currently, many industries aim to improve the heat transfer system to reduce cost and carbon emission. For improving heat exchanger apparatus, the convectional working fluid such as water can be replaced by hybrid nanofluid. The hybrid nanofluid is a suspension of nanoparticles into conventional base fluids to improve its properties. Generally, different combinations of nanoparticle and base fluid can variably enhance the specific heat capacity for removing heat from the system. In this study, the artificial neural network was thus employed to develop the prediction model for predicting specific heat capacity using feedforward and cascade forward propagation networks with Levenberg–Marquardt learning algorithm. The best artificial neural network (ANN) model topology was selected to predict specific heat capacity of hybrid nanofluid with R value of 0.9919, 0.9473 and 0.9673 for training, validating and testing, respectively. Then, the specific heat capacity value from ANN model was applied to evaluate and analyze the heat transfer rates. The hybrid nanofluid with Al2O3 and CuO in water exhibited the best heat removing medium in heat exchanger application.

다층신경망 학습 알고리즘 변화에 따른 건물 냉방부하 예측 모델의 성능 비교 평가

Purpose: In this study, among the methods of applying machine learning when predicting the load of a building, the cooling load of a building was predicted using a neural network model. To investigate the appropriateness of the learning algorithm of the multi-layer neural network model, the main purpose is to compare the predictive performance according to the change in the learning algorithm. Method: Among the learning algorithms applicable to multilayer neural networks, a total of 16 algorithms were used to predict the cooling load and compare the prediction results. The input variables of the input layer of the neural network model are outdoor dry bulb temperature, outdoor humidity, and Seasonally Data. The training period is 70% and the test period was 30%. The number of layers in the hidden layer is 3, the number of neurons is 20, and Epochs is 100. CvRMSE and MBE are used as performance index of the prediction model. The maximum, minimum, average, and standard deviation of the 20 prediction results are calculated, and the prediction performance according to the change in the learning algorithm was compared. Result: As a result of analyzing the predictive performance for each learning algorithm, the predictive performance according to the learning algorithm was different. Considering the results and deviations of the two indicators of predictive performance comprehensively, the model using the Levenberg-Marquardt (LM) learning algorithm is judged to have the best predictive performance.

Automatic Modulation Recognition Using Minimum-Phase Reconstruction Coefficients and Feed-Forward Neural Network

Identification of signal waveforms is highly critical in 5G communications and other state-of-the-art radio technologies such as cognitive radios. For instance, to achieve efficient demodulation and spectrum sensing, cognitive radios need to implement automatic modulation recognition (AMR) of detected signals. Although many works have been reported in the literature on the subject, most of them have mainly focused on the additive white Gaussian noise (AWGN) channel. However, addressing the AWGN channel, only, does not sufficiently emulate real-time wireless communications. In this paper, we created datasets of six modulation schemes in GNU Radio. Wireless signal impairment issues such as center frequency offset, sample rate offset, AWGN, and multipath fading effects were applied for the dataset creation. Afterward, we developed AMR models by training different artificial neural network (ANN) architectures using real cepstrum coefficients (RCC), and minimum-phase reconstruction coefficients (MPRC) extracted from the created signals. Between these two features, MPRC features have the best performance, and the ANN architecture with Levenberg-Marquardt learning algorithm, as well as logsig and purelin activation functions in the hidden and output layers, respectively, gave the best performance of 98.7% accuracy, 100% sensitivity, and 99.33% specificity when compared with other algorithms. This model can be leveraged in cognitive radio for spectrum sensing and automatic selection of signal demodulators.

Detection of Foreign Materials in Wheat Kernels Using Regional Colour Descriptors

Present paper reports the development of an automated machine vision system for detection of foreign materials in wheat kernels using regional color descriptors. The said system was executed in the form of an integrated flowing pipeline after having proper choice of different possible alternatives at different stages of image processing. A new type of surface colour descriptor is also proposed in this work to define wheat kernel uniquely. The fifteen-element colour descriptor is executed after having thorough comparison of six different colour spaces, each having 72 separate quantifiable components. The fifteen elements of the proposed colour-descriptor, extracted from each segmented region of the sample image, are concatenated in the form of an input to the neural classifier. The neural classifier is trained with Levenberg-Marquardt (LM) learning algorithm to achieve extremely fast convergence. The recognition rate of the executed classifier is found to be more than 99.2% for detection of impurity in unconnected wheat kernels. The results of present investigations are quite promising. The proposed pipeline has potential future in the field of machine vision based quality inspection of wheat and other cereal grains.

Comparison of ANFIS and ANN modeling for predicting the water absorption behavior of polyurethane treated polyester fabric

Nowadays, the polyurethane and its derivatives are highly applied as a surface modification material onto the textile substrates in different forms to enhance the functional properties of the textile materials. The primary purpose of this study is to develop prediction models to model the absorption property of the textile substrate using the Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Network (ANN) methods. In this study, polyurethane (PU) along with acrylic binder was applied on the dyed polyester knitted fabric to develop and validate the prediction models. Through the morphological study, it was evident that the solution prepared with the polyurethane and the acrylic binder was effectively coated onto the fabric surface. The ANFIS model was constructed by considering binder (ml) and PU (%) as input parameters, whereas absorbency (%) was the only output parameter. On the other hand, the system was trained with 70% data for constructing the ANN model whereas testing and validation were done with 15% data, respectively. To train the network, feed-forward backpropagation with Levenberg–Marquardt learning algorithm was used. The coefficient of determination (R2) was found to be 0.98 and 0.93 for ANFIS and ANN model, respectively. Both prediction models exhibited an excellent mean absolute error percentage (0.76% for the ANFIS model and 1.18% for the ANN model). Furthermore, an outstanding root-mean-square error (RMSE) of 0.61% and 1.28% for ANFIS and ANN models was observed. These results suggested an excellent performance of the developed models to predict the absorption property of the polyurethane and acrylic binder treated fabric. Besides, these models can be taken as a basis to develop prediction models for specific types of functional applications of the textile materials to eliminate heaps of trial and error efforts of the textile industries, which eventually be helpful in the scalable production of functional textiles.

Finite Element-Based Machine Learning Method to Predict Breast Displacement during Running

This paper presents an effective method to simulate the dynamic deformation of the breasts when a sports bra is worn during physical activity. A subject-specific finite element (FE) model of a female subject is established, and the accuracy of the material coefficients of the model is analyzed. An FE model of the sports bra is also built based on a commercially-available compression sports bra with a vest style. Then, an FE contact model between the body and bra is developed and validated, and the results applied to train a neural network model for predicting breast displacement based on bra straps with different tensile moduli. In this study, a four-layer neural network with a backpropagation algorithm (a Levenberg-Marquardt learning algorithm) is used. A comparison of the FE and machine learning results shows that machine learning can well predict the dynamic displacement of the breasts in a more time-efficient and convenient manner.

Shear Stress and Filtration Loss Properties Assessment of Nano-Silica Water-Based Drilling Fluid Using Machine Learning Approaches

AbstractA complete overview of the rheology and filtration properties of drilling fluids is essential to ensure an efficient transport process with minimized fluid loss. Silica nanoparticle is an excellent additive for rheology and filtration properties enhancement. Existing correlations are not available for nano-SiO2-water-based drilling fluid that can extensively quantify the rheology or filtration loss of nanofluids. Thus, two data-driven machine learning approaches are proposed for prediction, i.e., artificial neural network (ANN) and least square support vector machine (LSSVM). Parameters involved in the prediction of shear stress are SiO2 concentration, temperature, and shear rate, whereas SiO2 nanoparticle concentration, temperature, and time are the inputs to simulate filtration volume. A feed-forward multilayer perceptron is constructed and optimized using the Levenberg–Marquardt learning algorithm. The parameters for the LSSVM are optimized using couple simulated annealing (CSA). The performance of each model is evaluated based on several statistical parameters. The predicted results achieved R2 (coefficient of determination) value higher than 0.99 and mean absolute error (MAE) and mean absolute percentage error (MAPE) value below 7% for both the models. The developed models are further validated with experimental data that reveals an excellent agreement between predicted and experimental data.

Investigation of the Efficiency of Small-Scale NF/RO Seawater Desalination by Using Artificial Neural Network Modeling

An attempt is conducted in this paper to develop an artificial neural network (ANN) model for predicting the efficiency of small-scale NF/RO seawater desalination, then applied to the simulation of permeate flow rate and water recovery. A feed-forward back-propagation neural network with the Levenberg-Marquardt learning algorithm is considered. The performance of ANN compared to the multiple linear regression (MLR) is based on the calculated value of the coefficient of determination (R2). For ANN, R2 permeate flow rate was 0.997, and R2 permeate water recovery was 0.999, and for MLR, R2 permeate flow rate was 0.508, and R2 permeate water recovery was 0.713. It was observed that ANN performed better than the MLR.