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Neural. Network. Design. 2nd Edition. Hagan. Demuth. Beale. De Jesús .. Powerpoint format or PDF) for each chapter are available on the web at. Martin T. Hagan, Howard B. Demuth, Mark H. Beale, Orlando De Jes s NEURAL NETWORK DESIGN (2nd Edition) provides a clear and detailed A free page eBook version of the book ( MB PDF) can be downloaded from here. Neural Network Design - Hagan; Demuth; Beale - Ebook download as PDF File . pdf) or read book online.

Moghadassi; F. Hosseini; A. However, the success estimation of such correlations depends mainly on the range of data which have originated. Therefore new models are highly required. The data sets were collected from Perry's Chemical Engineers' Handbook.

In physics and thermodynamics, an equation of state is a relation between state variables temperature, pressure, volume, or internal energy. The most prominent use of an equation of state is to estimate the state of gases and liquids. One of the simplest equations of state for this purpose is the ideal gas law, which is roughly accurate for gases at low pressures and high temperatures. However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation of gas to liquid.

Therefore, a number of much more accurate equations of state such as Vander Waals, Redlich Kwong, and Peng Robinson have been developed for gases and liquids. At present, there is no single equation of state that accurately estimates the properties of all substances under all conditions. Therefore the new attempts have been made to develop an alternative to a simple equation of state which can be used for all conditions. ANN is a model based on some experimental results that is proposed to predict the required data because of avoiding more experiments.

This model provides a connection between input and output variables and bypass underlying complexity inside the system. The ability to learn the behavior of the data generated by a system certifies versatility of neural network Valles, Speed, simplicity, and capacity to learn are the advantages of ANN compared to classical methods. This model has been widely applied to estimate the physical and thermodynamic properties of chemical compounds. ANN has recently been used to predict some pure substances and petroleum fraction's properties Bozorgmehry et al.

Defining the ANN and selecting the best ANN predictor to predict the compressibility factor z in desired temperature and pressure ranges instead of empirically derived correlations are the main focus of this work. Finally results of the ANN model is evaluated against with the unseen data and then compared with the empirical models.

ANN is an especially efficient algorithm to approximate any function with finite number of discontinuities by learning the relationships between input and output vectors Bozorgmehry et al. These algorithms can learn from the experiments, and also are fault tolerant in the sense that they are able to handle noisy and incomplete data. The ANNs are able to deal with non-linear problems, and once trained can perform estimation and generalization rapidly Sozen et al.

They have been used to solve complex problems that are difficult to be solved if not impossible by the conventional approaches, such as control, optimization, pattern recognition, classification, and so on, Specially it is desired to have the minimum difference between the predicted and observed actual outputs Richon and Laugier, Artificial neural networks are biological inspirations based on the various brain functionality characteristics.

They are composed of many simple elements called neurons that are interconnected by links and act like axons to determine an empirical relationship between the inputs and outputs of a given system. Multiple layers arrangement of a typical interconnected neural network is shown in Figure 1. It consists of an input layer, an output layer, and one hidden layer with different roles.

Each connecting line has an associated weight. Artificial neural networks are trained by adjusting these input weights connection weights , so that the calculated outputs may be approximated by the desired values. The output from a given neuron is calculated by applying a transfer function to a weighted summation of its input to give an output, which can serve as input to other neurons, as follows Gharbi, The model fitting parameters wijk are the connection weights.

The nonlinear activation transfer functions Fk may have many different forms. The classical ones are threshold, sigmoid, Gaussian and linear function, etc Lang, , for more details of various activation functions see Bulsari The training process requires a proper set of data i.

During training the weights and biases of the network are iteratively adjusted to minimize the network performance function Demuth and Beale, In this paper the back propagation learning algorithm, which is one of the most commonly used algorithms is designed to predict the PVT properties.

Back propagation is a multilayer feed-forward network with hidden layers between the input and output Osman and Al-MArhoun, The simplest implementation of back propagation learning is the network weights and biases updates in the direction of the negative gradient that the performance function decreases most rapidly.

An iteration of this algorithm can be written as follows Gharbi, The process details flowchart to find the optimal model is shown in Figure 2.

LM is the fastest training algorithm for networks of moderate size and it has the memory reduction feature to be used when the training set is large. One of the most important general purpose back propagation training algorithms is SCG Lang , ; Demuth and Beale, The neural nets learn to recognize the patterns of the data sets during the training process. Neural nets teach themselves the patterns of the data set letting the analyst to perform more interesting flexible work in a changing environment.

These three networks are representative of the types of networks that are presented in the remainder of the text. In addition, the pattern recognition problem presented here provides a common thread of experience throughout the book. Much of the focus of this book will be on methods for training neural networks to perform various tasks.

In Chapter 4 we introduce learning algorithms and present the first practical algorithm: the perceptron learning rule.

The perceptron network has fundamental limitations, but it is important for historical reasons and is also a useful tool for introducing key concepts that will be applied to more powerful networks in later chapters.

One of the main objectives of this book is to explain how neural networks operate. For this reason we will weave together neural network topics with important introductory material.

For example, linear algebra, which is the core of the mathematics required for understanding neural networks, is reviewed in Chapters 5 and 6. The concepts discussed in these chapters will be used extensively throughout the remainder of the book.

Chapters 7, and 15—19 describe networks and learning rules that are heavily inspired by biology and psychology. They fall into two categories: associative networks and competitive networks. Chapters 7 and 15 introduce basic concepts, while Chapters 16—19 describe more advanced networks. Chapters 8—14 and 17 develop a class of learning called performance learning, in which a network is trained to optimize its performance.

Chapters 8 and 9 introduce the basic concepts of performance learning. Chapters 10— 13 apply these concepts to feedforward neural networks of increasing power and complexity, Chapter 14 applies them to dynamic networks and Chapter 17 applies them to radial basis networks, which also use concepts from competitive learning. Chapters 20 and 21 discuss recurrent associative memory networks.

These networks, which have feedback connections, are dynamical systems. Chapter 20 investigates the stability of these systems.

Chapter 21 presents the Hopfield network, which has been one of the most influential recurrent networks. Chapters 22—27 are different than the preceding chapters.

Previous chapters focus on the fundamentals of each type of network and their learning rules. The focus is on understanding the key concepts. In Chapters 22—27, we discuss some practical issues in applying neural networks to real world problems.

Chapter 22 describes many practical training tips, and Chapters 23—27 present a series of case studies, in which neural networks are applied to practical problems in function approximation, probability estimation, pattern recognition, clustering and prediction. The computer exercises can be performed with any available programming language, and the Neural Network Design Demonstrations, while helpful, are not critical to understanding the material covered in this book. Many of the important features of neural networks become apparent only for large-scale problems, which are computationally intensive and not feasible for hand calculations.

With MATLAB, neural network algorithms can be quickly implemented, and large-scale problems can be tested conveniently. These interactive demonstrations illustrate important concepts in each chapter.

All demonstrations are easily accessible from a master menu. The icon shown here to the left identifies references to these demonstrations in the text.

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