Modeling the Electrochemical Synthesis of Zinc Oxide Nanoparticles Using Artificial Neural Networks

The aim of this work is to use multilayered perceptron artificial neural networks (MLP-ANN) and multiple linear regressions (MLR) models to predict the dynamic adsorption of the complex system of adsorbent-adsorbate in solid-liquid phase. A set of 1859 data points were used. For the (MLP-ANN), nine neurons were used in the input layer, sixteen neurons at hidden layer and one was used in the output layer. Levenberg Marquardt learning (LM) algorithm, logarithmic sigmoid transfer function and linear transfer function were used at the hidden and output layer respectively. The comparison of the obtained results in term of root mean square error (RMSE) and correlation coefficient (R) using the (MLP-ANN) and MLR models revealed the superiority of the (MLP-ANN) model in predicting of dynamic adsorption process. The statistic results showed a correlation coefficient R = 0.991 with root mean square error RMSE= 0.0521for the (MLP-ANN) model and R= 0.80 with RMSE=0.237for the MLR model. Thus, it can be suggested that the artificial neural network model gave far better and more significant results.

Introduction Atmospheric corrosion is the main cause of metallic heritage degradation when they are exposed to relative humidity, temperature cycle and air contaminants. Corrosivity maps are one of the preventive strategies for atmospheric corrosion mitigation, but they do not provide enough information about corrosion mechanism, besides that long experimentation periods are required [1]. Moreover, electrochemical techniques are alternatives to speed up results, but their relationship with constantly changing environmental variables is difficult to control.Currently, Artificial Intelligence has been introduced in corrosion engineering studies, because of its capability to make predictions based on big data. Also, experimental data of Electrochemical Impedance Spectroscopy had been used in Artificial Neural Network training to obtain Nyquist Diagrams [2]. The objective of this work is to obtain computational models of Artificial Neural Networks to predict atmospheric corrosion in Bronze with nanostructured patina with SiO2, in marine environments. Method Environmental parameters were taken from database previously reported [3,4], and from Civil Protection Secretariat of Veracruz. Whilst electrochemical evaluation consists in Polarization Resistance and Electrochemical Impedance Spectroscopy; they were carried out in a Gamry Interface 1000 Potentiostat with a Saturated Calomel Reference Electrode (SCE) and a graphite bar as counter electrode in an agar gelled cell. Meanwhile, working electrode was bronze with nanostructured patina with SiO2. Two patina were prepared, the first with CuSO4 solution (0.015 mol L-1) and the second applying a CuNO3 solution (20% wt).The 13 variables used in the database for Artificial Neural Networks (ANN) training were: exposure time, chloride concentration, sulfur compounds concentration, relative humidity, precipitation level, windspeed, temperature, nanocoating presence, corrosion potential, corrosion rate, frequency, real and imaginary component of impedance. The values of each variable were treated with measures of central tendency and dispersion, as well as correlation matrix and histograms, which allowed to find a relationship between variables, and choosing the inputs for ANN. The prediction models consisted in 5, 9, 10 and 12 neurons in the input layer (R5E, R9E, R10E and R12E, respectively), a hidden layer, and Zima as only neuron in the output layer. The number of neurons in hidden layer varied from 1 to 8 until the highest coefficient of determination was achieved. The computational model was performed using the toolbox in MATLAB with a feedforward ANN. It is worth mention that the hidden and output layers used a hyperbolic tangent and a linear transfer function, respectively, and a Levenberg-Marquardt algorithm as training function was used in the models. Results and Conclusions Figure 1 presents the coefficient of determination (R2) and root mean squared error (RMSE) with different ANN architectures. In the four models, the highest value was reached with 8 neurons in the hidden layer. Then, the linear regressions for R5E, R9E, R10E and R12E models and 8 neurons in the input layer were compared in Figure 2. In that sense, the Nyquist Diagrams in Figure 3 were simulated with the R9E and R12E models. Also, they were compared with experimental Nyquist Diagrams for Bronze with patina of CuSO4 and CuNO3, with and without SiO2 nanoparticles, at 56 days of exposure in marine atmospheres. The simulations demonstrated how an ANN model with 12 neurons in the input layer, 8 neurons in the hidden layer and 1 neuron in the output layer can be used as a corrosion prediction model of bronze with nanostructured patina with SiO2.

Artificial neural network models (ANNs) were used in this study to predict reference evapotranspiration ( ETo) using climatic data from the meteorological station at the test station in Kafr El-Sheikh Governorate as inputs and reference evaporation values computed using the Penman–Monteith (PM) equation. These datasets were used to train and test seven different ANN models that included different combinations of the five diurnal meteorological variables used in this study, namely, maximum and minimum air temperature ( Tmax and Tmin), dew point temperature ( Tdw), wind speed ( u), and precipitation (P), how well artificial neural networks could predict ETo values. A feed- forward multi-layer artificial neural network was used as the optimization algorithm. Using the tansig transfer function, the final architected has a 6-5-1 structure with 6 neurons in the input layer, 5 neurons in the hidden layer, and 1 neuron in the output layer that corresponds to the reference evapotranspiration. The root mean square error ( RMSE) of 0.1295 mm∙day –1 and the correlation coefficient ( r) of 0.996 are estimated by artificial neural network ETo models. When fewer inputs are used, ETo values are affected. When three separate variables were employed, the RMSE test values were 0.379 and 0.411 mm∙day –1 and r values of 0.971 and 0.966, respectively, and when two input variables were used, the RMSE test was 0.595 mm∙day –1 and the r of 0.927. The study found that including the time indicator as an input to all groups increases the prediction of ETo values significantly, and that including the rain factor has no effect on network performance. Then, using the Penman–Monteith method to estimate the missing variables by using the ETo calculator the normalised root mean squared error ( NRMSE) reached about 30% to predict ETo if all data except temperature is calculated, while the NRMSE reached about of 13.6% when used ANN to predict ETo using variables of temperature only.

The purpose of this study is to develop an artificial neural network (ANN) model for performance prediction of a variable compression ratio gasoline port fuel injection spark ignition engine. For ANN modeling, a large experimental data set was generated in which at random 85% was assigned for training the network, and 15% that are not included during the training process was used for testing the network. A multilayer perception feed forward neural network was used to predict the correlation between input and output layer. The input layer consists of engine speed, throttle position, spark timing, and compression ratio. Whereas, the output layer consists of torque, brake power and indicated mean effective pressure (IMEP). Neurons in the hidden layer were varied and optimized based on a specified goal error. A standard supervised back propagation learning algorithm was used in which the error between the target and network output was calculated and minimized. In the hidden and output layers, a non-linear tan-sigmoid and a linear transfer function were used, respectively, for input-output mapping. The performance of the network was evaluated by statistical parameters like correlation coefficient (R), mean relative error (MRE) and root mean square error (RMSE). It was found from the test data that the R and MRE values are lies in between 0.99853 to 0.99875 and 0.42% to 0.58%, respectively. Whereas, RMSE value for all performance parameters was found to be very low. Hence, this study reveals that the application of ANN modeling has the ability to predict the performance of a variable compression ratio gasoline engine and is the best alternative tool over all classical modeling techniques.

It is important to correctly predict the microclimate of a greenhouse for control and crop management purposes. Accurately forecasting temperatures in greenhouses has been a focus of research because internal temperature is one of the most important factors influencing crop growth. Artificial Neural Networks (ANNs) are a powerful tool for making forecasts. The purpose of our research was elaboration of a model that would allow to forecast changes in temperatures inside the heated foil tunnel using ANNs. Experimental research has been carried out in a heated foil tunnel situated on the property of the Agricultural University of Krakow. Obtained results have served as data for ANNs. Conducted research confirmed the usefulness of ANNs as tools for making internal temperature forecasts. From all tested networks, the best is the three-layer Perceptron type network with 10 neurons in the hidden layer. This network has 40 inputs and one output (the forecasted internal temperature). As the networks input previous historical internal temperature, external temperature, sun radiation intensity, wind speed and the hour of making a forecast were used. These ANNs had the lowest Root Mean Square Error (RMSE) value for the testing data set (RMSE value = 3.7 °C).

In the present study, deep learning neural network model has been employed in many engineering problems including heat transfer prediction. The main consideration of this document is to predict the performance of the boiling heat transfer in helical coils under terrestrial gravity conditions and compare with actual experimental data. Total of 877 data sample has been used in the present neural model. Artificial new Neural Network (ANN) model developed in Python environment with Multi-layer Perceptron (MLP) using four parameters (helical coils dimensions, mass flow rate, heating power, inlet temperature) and one parameter (outlet temperature) has been used in the input layer and output layer in order. Levenberg-Marquardt (LM) algorithm using L2 Regularization to find out the optimal model. A typical feed-forward neural network model composed of three layers, with 30 numbers of neurons in each hidden layer, has been found as optimal based on statistical error analysis. The 4-30-30-1 neural model predicts the characteristics of the helical coil with the accuracy of 98.16 percent in the training stage and 96.68 percent in the testing stage. The result indicated that the proposed ANN model successfully predicts the heat transfer performance in helical coils and can be applied for others operation concerned with heat transfer prediction for future works

In this study, a three-layer feed-forward back propagation network with Levenberg-Marquardt (LM) learning algorithm was applied to predict adsorption of phenol onto activated carbon (AC). Batch experiments were carried out to obtain experimental data. The neural network was trained considering the amount of adsorbent, initial concentration of phenol, temperature, contact time and pH as input parameters and the final concentration of phenol as a desired parameter. Different transfer functions for hidden and output layers and different number of neurons in a hidden layer were tested to optimize the network structure. An empirical equation for final concentration of phenol was developed by using the weights of optimized network. Accuracy of the developed ANN model was also measured using statistical parameters, such as mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE) and correlation coefficient (R2). Results showed that MAE, MSE, RMSE, and R2 values of the ANN model were 0.1540, 0.0565, 0.2378, and 0.9998, respectively, which indicate high accuracy of the ANN model. In the equilibrium study, predicted results of the ANN model were also compared with experimental data and the results of other conventional isotherm models.

Daily reference evapotranspiration estimates by artificial neural networks technique and empirical equations using limited input climate variables

This work aims to develop an ANN model to predict the dynamic adsorption of complex system of adsorbent- adsorbate in solid-liquid phase on different parameters through an adsorption column. Nine neurons were used in the input layer, fourteen neurons and ten neurons were used respectively in the first and the second hidden layer. One neuron was used in the output layer. A set of 2007 data points were used for testing the neural network. Levenberg Marquardt learning (LM) algorithm, logarithmic sigmoid transfer function and linear transfer function were used for the hidden and output layer respectively. Results with the ANN showed a correlation coefficient R2 = 0.9976 and 0.9969 respectively for total database and for validation phase between simulated data and those obtained from the literature with a root mean square error RMSE = 0.0268 and 0.0305for total database and for validation phase respectively. Moreover, to determine the most suitable model, Thomas and Bohart-Adams models were applied. The comparison between root mean square error (RMSE), sum of the absolute error (SAE), Chi-square statistic test (X2) and correlation coefficient (R2) showed that the neural network model gave far better. In general, the developed model provides the highest agreement vector values of [R2,\(\begin{equation}\label{eq1}\alpha, \beta\end{equation}\)] with a root mean square error value (RMSE) closed to zero.

Knowledge of pore-water pressure responses to rainfall is vital in slope failure and slope hydrological studies. The performance of four artificial neural network (ANN) training algorithms was evaluated to identify the training algorithm appropriate for modeling the dynamics of soil pore-water pressure responses to rainfall patterns using multilayer perceptron (MLP) ANN. The ANN model comprised eight neurons in the input layer, four neurons in the hidden layer, and a single neuron in the output layer representing an 8-4-1 ANN architecture. The training algorithms evaluated include the gradient descent, gradient descent with momentum, scaled conjugate gradient, and Levenberg-Marquardt (LM). The performance of the training algorithms was evaluated using standard performance evaluation measures—root mean square error, coefficient of efficiency, and the time and number of epochs required to reach a predefined accuracy. It was found that all the training algorithms could be used in the prediction of po...

In this work, the Artificial Neural Networks (ANN) are used to model a chaotic system. A method based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to determine the best parameters of a Multilayer Perceptron (MLP) artificial neural network. Using NSGA-II, the optimal connection weights between the input layer and the hidden layer are obtained. Using NSGA-II, the connection weights between the hidden layer and the output layer are also obtained. This ensures the necessary learning to the neural network. The optimized functions by NSGA-II are the number of neurons in the hidden layer of MLP and the modelling error between the desired output and the output of the neural model. After the construction and training of the neural model, the selected model is used for the prediction of the chaotic system behaviour. This method is applied to model the chaotic system of Mackey-Glass time series prediction problem. Simulation results are presented to illustrate the proposed methodology.

وقوع متناوب دوره های کم آبی و پرآبی درحوضه آبریز زرینه رود علاوه بر تأثیر روی وضعیت کمی آب های سطحی، باعث تغییراتی در کیفیت آب این حوضه شده است. لذا، مدل بندی و پیش بینی پارامترهای کیفی آب رودخانه زرینه رود در دوره های کم آبی و پرآبی، یکی از ضرورت های تحقیقاتی در این رودخانه پرآب شمال غرب ایران بوده است. در این مطالعه، روش های شبکه های عصبی مصنوعی به ازای پنج الگوریتم آموزشی مختلف و سامانه استنتاجی عصبی-فازی تطبیقی مبتنی بر مدل دسته بندی تفریقی، جهت تخمین میزان جامدات محلول TDS به کار گرفته شدند. بدین منظور از داده های کیفیت آب هفت ایستگاه هیدرومتری در حوضه آبریز مذکور با طول دوره آماری 18 ساله (1389-1372) استفاده گردید. ابتدا دوره مطالعاتی مذکور بر اساس میزان جریان در رودخانه به دو دوره کم آبی و پرآبی تفکیک شده، سپس در یک آنالیز اولیه آماری، پارامترهای مؤثر اصلی در تخمین TDS تعیین و برای مدل بندی استفاده گردید. برای مدل بندی 75 درصد داده ها برای کالیبره کردن و 25 درصد برای ارزیابی مدل استفاده شده است. ارزیابی عملکرد مدل های به کار رفته بر اساس آزمون های آماری مختلف، ضریب همبستگی، ریشه میانگین مربعات خطا و میانگین قدر مطلق خطا انجام گرفت. نتایج حاصل حاکی از عملکرد قابل قبول هر دو روش شبکه های عصبی مصنوعی با الگوریتم آموزشی لونبرگ-مارگارت و سامانه استنتاجی عصبی-فازی تطبیقی در دوره های کم آبی و پرآبی بود. مقایسه عملکرد روش های به کار گرفته شده، نشان داد که عملکرد روش عصبی-فازی تطبیقی در هر دو دوره مطالعاتی بهتر از شبکه های عصبی مصنوعی می‏باشد.

The main purpose of the present study is to develop some artificial neural network (ANN) models for the prediction of limit pressure (PL) and pressuremeter modulus (EM) for clayey soils. Moisture content, plasticity index, and SPT values are used as inputs in the ANN models. To get plausible results, the number of hidden layer neurons in all models is varied between 1 and 5. In addition, both linear and nonlinear activation functions are considered for the neurons in output layers while a nonlinear activation function is employed for the neurons in the hidden layers of all models. Logistic activation function is used as a nonlinear activation function. During the modeling studies, total eight different ANN models are constructed. The ANN models having two outputs produced the worst results, independent from activation function. However, for PL, the best results are obtained from the feed-forward neural network with five neurons in the hidden layer, and logistic activation function is employed in the output neuron. For EM, the best model producing the most acceptable results is Elman recurrent network model, which has 4 neurons in the neurons in the hidden layer, and linear activation function is used for the output neuron. Finally, the results show that the ANN models produce the more accurate results than the regression-based models. In the literature, when empirical equations based on regression analysis were used, the best root mean square error (RMSE) values obtained to date for PL and EM have been 0.43 and 5.65, respectively. In this study, RMSE values for PL and EM were found to be 0.20 and 2.99, respectively, by using ANN models. It was observed that using ANN approach drastically increases the prediction accuracy in terms of RMSE criterion.

Evaporation is one of the main essential components of the hydrologic cycle. The study of this parameter has significant consequences for knowing reservoir level forecasts and water resource management. This study aimed to test the three artificial neural networks (feed-forward, Elman and nonlinear autoregressive network with exogenous inputs (NARX) models) and multiple linear regression to predict the rate of evaporation in the Boudaroua reservoir using the calculated values obtained from the energy budget method. The various combinations of meteorological data, including solar radiation, air temperature, relative humidity, and wind speed, are used for the training and testing of the model’s studies. The architecture that was finally chosen for three types of neural networks has the 4-10-1 structure, with contents of 4 neurons in the input layer, 10 neurons in the hidden layer and 1 neuron in the output layer. The calculated evaporation rate presents a typical annual cycle, with low values in winter and high values in summer. Moreover, air temperature and solar radiation were identified as meteorological variables that mostly influenced the rate of evaporation in this reservoir, with an annual average equal to 4.67 mm∙d –1. The performance evaluation criteria, including the coefficient of determination (R 2), root mean square error ( RMSE) and mean absolute error ( MAE) approved that all the networks studied were valid for the simulation of evaporation rate and gave better results than the multiple linear regression (MLR) models in the study area.

Prediction of suspended sediment discharge in a catchments area is very important because it can be used to evaluation the erosion hazard, management of its water resources, water quality, hydrology project management (dams, reservoirs, and irrigation) and to determine the extent of the damage that occurred in the catchments. Multiple Linear Regression analysis and artificial neural network can be used to predict the amount of daily suspended sediment discharge. Regression analysis using the least square method, whereas artificial neural networks using Radial Basis Function (RBF) and feedforward multilayer perceptron with three learning algorithms namely Levenberg-Marquardt (LM), Scaled Conjugate Descent (SCD) and Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFGS). The number neuron of hidden layer is three to sixteen, while in output layer only one neuron because only one output target. The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R2 ) and coefficient of efficiency (CE) of the multiple linear regression (MLRg) value Model 2 (6 input variable independent) has the lowest the value of MAE and RMSE (0.0000002 and 13.6039) and highest R2 and CE (0.9971 and 0.9971). When compared between LM, SCG and RBF, the BFGS model structure 3-7-1 is the better and more accurate to prediction suspended sediment discharge in Jenderam catchment. The performance value in testing process, MAE and RMSE (13.5769 and 17.9011) is smallest, meanwhile R2 and CE (0.9999 and 0.9998) is the highest if it compared with the another BFGS Quasi-Newton model (6-3-1, 9-10-1 and 12-12-1). Based on the performance statistics value, MLRg, LM, SCG, BFGS and RBF suitable and accurately for prediction by modeling the non-linear complex behavior of suspended sediment responses to rainfall, water depth and discharge. The comparison between artificial neural network (ANN) and MLRg, the MLRg Model 2 accurately for to prediction suspended sediment discharge (kg/day) in Jenderan catchment area.