\documentclass[two column,10pt,a4paper]{article} \usepackage{graphicx} \usepackage{cuted} \usepackage{float} \begin{document} \title{Artificial Neural Network optimization of process parameters to determine hardness of matal/ceramic nanocmposites produced by high energy ball milling} \author{A. Irannejad, Assistant Professor \footnotemark[1] \\ \texttt{E-mail:Irannejhad@uk.ac.ir} \and H .zadsirjan, Student member \footnotemark[2] \\ \texttt{E-mail:H.Zadsirjan@eng.uk.ac.ir}\and S.Abbasloo, Student member \footnotemark[3] \\ \texttt{E-mail:Samad-Abbasloo@yahoo.com}} \date{13 . ‎Jan 2016} \maketitle \footnotemark[1]\footnotemark[2]\footnotemark[3]Department of Material Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.\\ \twocolumn[ \begin{@twocolumnfalse} \begin{abstract} In recent years, artificial neural networks (ANN) have been used as an interdisciplinary tool in many applications. There are various training algorithms used in neural network applications. In this study, it is aim to investigate the effect of the amount of reinforcement, milling time, BPR, speed, sintering temperature, sintering time performance of the neural networks on the prediction of hardness behaviour of particulate reinforced Carbon black-AlB-MgB2-Fe-AlN-Ti-Sic-Tio2 metal matrix composites (MMCs). Hardness was one of the output developed from the proposed network. Effects of adding different ceramics as reinforcement particles to Al metal matrix have been investigated by using artificial neural networks. The maximum absolute relative error for predicted values does not exceed 1.49 percentage. By comparing the predicted values with the experimental data, it was demonstrated that the well-trained feed forward back propagation ANN model is a powerful tool for prediction of effect of physical and mechanical properties of composites. \end{abstract} \end{@twocolumnfalse} ] \section{Introduction} \label{section. Intro} Aluminum alloys have a wide diversity of industrial applications because of their light weight, high electric conductivity, and corrosion resistance [1]. However, the use of aluminum and its alloys in advanced applications are limited due to their low stiffness, resistance to wear and tear, and low yield strength. Furthermore, industry demands advanced materials and technology for the preparation of these materials, which include aerospace, automotive, and defense applications. It is attractive to use aluminum based metal matrix composites (MMCs) in structural applications because of their excellent stiffness-to-weight and strength-toweight ratios[2][3]. However, the disadvantage for these composites is their high production cost[4][5]. Metal matrix composites (MMCs) have received considerable attention because of their superior properties as compared to those of most conventional materials. MMCs exhibit a high specific strength, stiffness and wear resistance, in addition to a service temperature capability, that is much higher than that of other materials or composites. They are also excellent thermal conductors.They typically include ceramic particles to improve their mechanical properties. The high strength to weight ratio of MMC enables it to be applied extensively in the aerospace industry. In particular, particle-reinforced metal matrix composites are attractive highly versatile engineering materials having attractive combinations of density, strength, stiffness, reliability and structural efficiency. Particle reinforced aluminum composites are being recognized as an important class of engineering material that is making significant progress. The attractiveness in preferringand choosing a discontinuously reinforced MMC, for many applications stems from an improvement in specific modulus, that is, the density compensated increase in elastic modulus [4]. In addition, which include low density, high specific stiffness, and controlled coefficient of thermal expansion, superior dimensional stability and increased tensile strength. It has been determined that the addition of ceramic particles to aluminum improves its strength, wear resistance, and corrosion resistance[6]. Mechanical alloying (MA) or high energy ball milling as a powder processing technique involves repeated deformation, welding and fracturing of powder particles. MA has been widely used to synthesize a variety of materials, such as supersaturated solid solutions, (nonequilibrium) intermetallic compounds, or to the formation of stable or unstable carbides, borides, nitrides, silicides, etc.[7][8][9]. It is well known that the addition of ceramic hard particles to metal alloys increases the hardness during high energy ball milling. But, it is essential to have an optimal milling parameters (in this study, sintering time,sintering temperature and compact pressure were also considered as milling parameters) to achieve excellent mechanical properties.Mechanical milling is a useful powder processing technique that can improve the homogeneous distribution of ceramic reinforcement particles in the matrix material. Various researchers have successfully investigated and reported the dispersion of alloying the diverse hard reinforcements such as SiC [10], Al2O3 [11], TiC [12], AlN [13], Al4C3 [14] and NbC [15] on the aluminum based MMCs through the mechanical milling technique. Recently, artificial neural networks have taken a great deal of attention as a prediction and modeling tool in many research areas; such as electronics, automotive, robotics, medical diagnosis, chemistry, etc. Artificial neural networks can be used in such applications as prediction, classification, recognition, and modeling the manufacturing of engineering materials. . It is a promising field of research in predicting experimental trends and has become increasingly popular in the last few years as they can often solve problems much faster compared to other approaches with the additional ability to learn from small experimental data [16][17][18][19][20][21][22]. Its working principle can be resembled the human brain due to its functions in two ways: (i) the neural network through a learning process acquires knowledge and (ii) the connection strengths, which are known as synaptic weights, between interneurons are used to store the knowledge. The neural network theory deals with learning from a previous obtained data, which is named as training or learning set, and then to check the system success using test data. In this study, artificial neural networks are used in the prediction of experimental processes in material science. The aim of this study to investigate prediction performance of hardness of composites. \section{Principle of artificial neural network} \label{section. principle} ANN is a network containing layers of neurons and connections between them.The basic neural cell models is shown in Fig. 1. Neuron is the smallest computing element of a network. Each neuron in each layer receives one input signal from all neurons of its previous layer and sends one output signal to all neurons in its next layer. The following takes place in each neuron; all input signals are multiplied by a corresponding weight factor which shows the strength of that input then added to a separate bias factor. ‎\begin{figure}[H]‎ \centering \includegraphics[width=13.8cm,height=8.93cm]{photo_2016-01-12_19-37-571234faer1.jpg}‎ \end{figure} The result goes into an activation or transfer function. The most common characteristics of applications which are solved by the ANNs are [23]: 1. A large database is available. 2. Existing mathematical approaches show poor capability in finding precise solution for the problem. 3. Incompleteness, noisiness or complexity of the dataset. In order to develop an appropriate ANN in the specific field, three main works have to be done; first, a data set of inputs and targets should be prepared for training and testing the network. Second, a good architecture should be specified. Architecture determines the number of layers and neurons in each layer and transfer function for each layer. Third task is to determine parameters of the network i.e. weights and biases. In the present work, network architectures including MLP was designed and used. MLP neural networks are feed-forward networks that consist of a number of layers of neurons, with the output from each neuron propagating to the input of each neuron of the next layer. and finally \subsection{Experimental design} \label{section. principle.Exprimental} A specific number of experimental results is always needed to develop a well functioning ANN model in the field of material research [24]. At first in this research work, it was obligatory to distinguish the most prominent factors in the MA process. Amount of reinforcement, milling time, BPR, speed, sintering temperature, sintering time control were chosen as the prime parameters [25]. The collected data from the articles [26][27][28][29][30][31][32][33][33] are listed in Table 1. The hardness of several MA-synthesized nano-composites has been considered as the main objective or cost function of this study for prediction As we know, the crystallite size and the lattice strain of the Al matrix that directly influence the mechanical properties of the fabricated nanocomposite were chosen as the characteristics of the nanocomposite [34]. The ranges of the parameters are given in the Table 2. Further details about the values presented in Table 1, have been listed in the Table 3. \begin{center} Table 1 \end{center} \begin{center} Table 2 \begin{tabular}{|c|c|} \hline % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... Input & Output \\ \hline Amount of reinforcement & 0-50 \\ \hline Milling time (h) & 1-40 \\ \hline BPR & 3-35 \\ \hline Vial spinning rate (rpm) & 270-450 \\ \hline sintering temperature (k) & ambient-1173 \\ \hline sintering time ( min ) & 5-360 \\ \hline \end{tabular} \end{center} \begin{strip} \begin{center} Table 3 \begin{tabular}{|c|c|c|c|c|} \hline % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... Symbol & Type of mill & Type of vial & Type of ball & Type of atmosphere \\ \hline 1 & SPEX 8000 & Hardened steel & Hardened steel & Argon \\ \hline 2 & Fritsch & WC & WC & Toluene \\ \hline 3 & Planetary ball mill & Stainless Steel & Cr steel & Air \\ \hline 4 & Attritor & - & Stainless Steel & Acetone \\ \hline 5 & RETSCH & - & Steel & - \\ \hline 6 & Planetary ball mill & M200 & - & Agate\\ \hline 7 & Zoz & Simoloyer & - & - \\ \hline \end{tabular} \end{center} \end{strip} \section{Neural network design} \label{section. Neural} As sigmoid activation function is used in training algorithm, all numbers in training and test sets have been normalized between 0 and 1 because of its characteristic feature. Feed forward neural networks were used in all cases. The performance analysis were done from the viewpoint of training duration, error minimization and prediction achievement. Then, training processes results were interpreted with graphics. \subsection{Network training and testing} \label{section. Neural.Network} Among 77 experimental set, 62 data sets allotted for training, and 15 for testing. A neural network is implemented with three layer feedforward structure with an input layer, a two hidden layer and an output layer. The designed neural network has 6 input and 1 output neurons. Number of neurons in the hidden layer include 8 neurons for first hidden layer and 14 neurons for secound hidden layer. Each designed neural networks using various training algorithms were tested by those ways: (i) using the test data, which were not used during the training procedure. Because of that during the training process neural network used the training set and had information about the characteristic of the data in training set. It is clear that the neural network will give the better result for any data in training set than for any data in test set. (ii) Mean square error (MSE), which is statistical and scientific error computation method, was used to analyze the error. (iii) The neural network predictions were directly compared with the experimental obtained data to evaluate the learning performance. The multilayer network structure (6–8–14–1) gives the minimum mean square error, so this structure is finally used for the ANNs prediction system. \section{Results and discussion} \label{section. Reaults} Fig. 2, 3 shows the comparison made between the experimental and predicted data set of training, validation, testing and combined set. Fig. 2, 3 is corresponds to the output parameter of hardness. All the mention output having good coincidence exists between the experimental and predicted output system, also Fig. 2, 3 confirms that all the data having good fit due to the well training. So the trained network system gives the output with minimum percentage of error and also used to predict the unknown value for the future. Regression coefficient (R) value calculates the correlation between the output and target. Fig. 2 shows the training and validation combined set of all having the R value is one, which means that there is little error in the selected network structure (6–8–14–1). The results in terms of various performance statistics from all the ANN models and error are presented in Table 4. In Fig. 4, obtained MSE values for training data were given for each training algorithm. The obtained error values for different number of neurons in the hidden layer were analyzed and given, graphically. This figure also gives information about the accuracy of each training algorithm depending on the number of neurons in the hidden layer. MSE is a good criterion to have information about learning performance. The iterations were continued until it is decided that the minimum MSE error is obtained. \section{Conclusion} \label{section.conclu} In this study, an artificial neural network (ANN) model with the back-propagation learning algorithm was established to predict the hardness properties of Al copmosite. The trained networks for the Al composites were developed with minimum mean square error. Fine agreement between the experimental and predicted results from using the neural networks. The results show that the average absolute relative error of hardness between the ANN prediction results and experimental data is 1.49%. Therefore, the MLP model proposed in this article can be used as an accurate model for the prediction of hardness of Al composites. \section{Reference} \label{section.Ref} \end{document}