Search results for: feed forward and feedback multi-context neural network.

Authors: Travis Wiens, Greg Schoenau, Rich Burton

Abstract:

It is well known that a linear dynamic system including a delay will exhibit limit cycle oscillations when a bang-bang sensor is used in the feedback loop of a PID controller. A similar behaviour occurs when a delayed feedback signal is used to train a neural network. This paper develops a method of predicting this behaviour by linearizing the system, which can be shown to behave in a manner similar to an integral controller. Using this procedure, it is possible to predict the characteristics of the neural network driven limit cycle to varying degrees of accuracy, depending on the information known about the system. An application is also presented: the intelligent control of a spark ignition engine.

Keywords: Control and automation, artificial neural networks, limit cycle

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Authors: Oi Mean Foong, Tan Jung Low, Satrio Wibowo

Abstract:

Hand gesture is one of the typical methods used in sign language for non-verbal communication. It is most commonly used by people who have hearing or speech problems to communicate among themselves or with normal people. Various sign language systems have been developed by manufacturers around the globe but they are neither flexible nor cost-effective for the end users. This paper presents a system prototype that is able to automatically recognize sign language to help normal people to communicate more effectively with the hearing or speech impaired people. The Sign to Voice system prototype, S2V, was developed using Feed Forward Neural Network for two-sequence signs detection. Different sets of universal hand gestures were captured from video camera and utilized to train the neural network for classification purpose. The experimental results have shown that neural network has achieved satisfactory result for sign-to-voice translation.

Keywords: Hand gesture detection, neural network, signlanguage, sequence detection.

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Authors: E. Giovanis

Abstract:

In this paper we present a Feed-Foward Neural Networks Autoregressive (FFNN-AR) model with genetic algorithms training optimization in order to predict the gross domestic product growth of six countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final optimum weights from input-hidden layer of the training process. The forecasts are compared with those of the ordinary autoregressive model and we conclude that the proposed regression-s forecasting results outperform significant those of autoregressive model. Moreover this technique can be used in Autoregressive-Moving Average models, with and without exogenous inputs, as also the training process with genetics algorithms optimization can be replaced by the error back-propagation algorithm.

Keywords: Autoregressive model, Feed-Forward neuralnetworks, Genetic Algorithms, Gross Domestic Product

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Authors: Myungsook Klassen

Abstract:

Training neural networks to capture an intrinsic property of a large volume of high dimensional data is a difficult task, as the training process is computationally expensive. Input attributes should be carefully selected to keep the dimensionality of input vectors relatively small. Technical indexes commonly used for stock market prediction using neural networks are investigated to determine its effectiveness as inputs. The feed forward neural network of Levenberg-Marquardt algorithm is applied to perform one step ahead forecasting of NASDAQ and Dow stock prices.

Keywords: Stock Market Prediction, Neural Networks, Levenberg-Marquadt Algorithm, Technical Indexes

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Authors: Apinan Aurasopon, Worawat Sa-ngiavibool

Abstract:

This paper proposes a feed-forward control in a halfbridge resonant dc link inverter. The configuration of feed-forward control is based on synchronous sigma-delta modulation and the halfbridge resonant dc link inverter consists of two inductors, one capacitor and two power switches. The simulation results show the proposed technique can reject non-ideal dc bus improving the total harmonic distortion.

Keywords: Feed-forward control, Resonant dc link inverter, Synchronous sigma-delta modulation.

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Authors: Alireza Vakili, Mohsen Danesh Mesgaran, Majid Abdollazade

Abstract:

In this study four Holstein steers with rumen fistula fed 7 kg of dry matter (DM) of diets differing in concentrate to alfalfa hay ratios as 60:40, 70:30, 80:20, and 90:10 in a 4 × 4 latin square design. The pH of the ruminal fluid was measured before the morning feeding (0.0 h) to 8 h post feeding. In this study, a two-layered feed-forward neural network trained by the Levenberg-Marquardt algorithm was used for modelling of ruminal pH. The input variables of the network were time, concentrate to alfalfa hay ratios (C/F), non fiber carbohydrate (NFC) and neutral detergent fiber (NDF). The output variable was the ruminal pH. The modeling results showed that there was excellent agreement between the experimental data and predicted values, with a high determination coefficient (R2 >0.96). Therefore, we suggest using these model-derived biological values to summarize continuously recorded pH data.

Keywords: Ruminal pH, Artificial Neural Network (ANN), Non Fiber Carbohydrate, Neutral Detergent Fiber.

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Authors: Supriya Pal, Kalyan Adhikari, Somnath Mukherjee, Sudipta Ghosh

Abstract:

This study presents the application of artificial neural network for modeling the phenolic compound migration through vertical soil column. A three layered feed forward neural network with back propagation training algorithm was developed using forty eight experimental data sets obtained from laboratory fixed bed vertical column tests. The input parameters used in the model were the influent concentration of phenol(mg/L) on the top end of the soil column, depth of the soil column (cm), elapsed time after phenol injection (hr), percentage of clay (%), percentage of silt (%) in soils. The output of the ANN was the effluent phenol concentration (mg/L) from the bottom end of the soil columns. The ANN predicted results were compared with the experimental results of the laboratory tests and the accuracy of the ANN model was evaluated.

Keywords: Modeling, Neural Networks, Phenol, Soil media

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Authors: Mughal Yar M, Israr Ul Haq, Bushra Noman

Abstract:

The stem cells have ability to differentiated themselves through mitotic cell division and various range of specialized cell types. Cellular differentiation is a way by which few specialized cell develops into more specialized.This paper studies the fundamental problem of computational schema for an artificial neural network based on chemical, physical and biological variables of state. By doing this type of study system could be model for a viable propagation of various economically important stem cells differentiation. This paper proposes various differentiation outcomes of artificial neural network into variety of potential specialized cells on implementing MATLAB version 2009. A feed-forward back propagation kind of network was created to input vector (five input elements) with single hidden layer and one output unit in output layer. The efficiency of neural network was done by the assessment of results achieved from this study with that of experimental data input and chosen target data. The propose solution for the efficiency of artificial neural network assessed by the comparatative analysis of “Mean Square Error" at zero epochs. There are different variables of data in order to test the targeted results.

Keywords: Computational shcmin, meiosis, mitosis, neuralnetwork, Stem cell SOM;

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Authors: Ε. Giovanis

Abstract:

In this paper we present an autoregressive model with neural networks modeling and standard error backpropagation algorithm training optimization in order to predict the gross domestic product (GDP) growth rate of four countries. Specifically we propose a kind of weighted regression, which can be used for econometric purposes, where the initial inputs are multiplied by the neural networks final optimum weights from input-hidden layer after the training process. The forecasts are compared with those of the ordinary autoregressive model and we conclude that the proposed regression-s forecasting results outperform significant those of autoregressive model in the out-of-sample period. The idea behind this approach is to propose a parametric regression with weighted variables in order to test for the statistical significance and the magnitude of the estimated autoregressive coefficients and simultaneously to estimate the forecasts.

Keywords: Autoregressive model, Error back-propagation Feed-Forward neural networks, , Gross Domestic Product

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Authors: S. A. Gawish, F. A. Khalifa, R. M. Mostafa

Abstract:

This paper presents Simulation and experimental study aimed at investigating the effectiveness of an adaptive artificial neural network stabilizer on enhancing the damping torque of a synchronous generator. For this purpose, a power system comprising a synchronous generator feeding a large power system through a short tie line is considered. The proposed adaptive neuro-control system consists of two multi-layered feed forward neural networks, which work as a plant model identifier and a controller. It generates supplementary control signals to be utilized by conventional controllers. The details of the interfacing circuits, sensors and transducers, which have been designed and built for use in tests, are presented. The synchronous generator is tested to investigate the effect of tuning a Power System Stabilizer (PSS) on its dynamic stability. The obtained simulation and experimental results verify the basic theoretical concepts.

Keywords: Adaptive artificial neural network, power system stabilizer, synchronous generator.

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Authors: Wenbin Zhang, Hantian Wu, Jian Tang

Abstract:

An artificial neural network is a mathematical model inspired by biological neural networks. There are several kinds of neural networks and they are widely used in many areas, such as: prediction, detection, and classification. Meanwhile, in day to day life, people always have to make many difficult decisions. For example, the coach of a soccer club has to decide which offensive player to be selected to play in a certain game. This work describes a novel Neural Network using a combination of the General Regression Neural Network and the Probabilistic Neural Networks to help a soccer coach make an informed decision.

Keywords: General Regression Neural Network, Probabilistic Neural Networks, Neural function.

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Authors: S. M. Ali, N. R. Dhar

Abstract:

Tool wear and surface roughness prediction plays a significant role in machining industry for proper planning and control of machining parameters and optimization of cutting conditions. This paper deals with developing an artificial neural network (ANN) model as a function of cutting parameters in turning steel under minimum quantity lubrication (MQL). A feed-forward backpropagation network with twenty five hidden neurons has been selected as the optimum network. The co-efficient of determination (R2) between model predictions and experimental values are 0.9915, 0.9906, 0.9761 and 0.9627 in terms of VB, VM, VS and Ra respectively. The results imply that the model can be used easily to forecast tool wear and surface roughness in response to cutting parameters.

Keywords: ANN, MQL, Surface Roughness, Tool Wear.

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Authors: H. F. A. Abdul Ghani, R. R. Porle

Abstract:

Speech to text in Malay language is a system that converts Malay speech into text. The Malay language recognition system is still limited, thus, this paper aims to investigate the performance of ten Malay words obtained from the online Malay news. The methodology consists of three stages, which are preprocessing, feature extraction, and speech classification. In preprocessing stage, the speech samples are filtered using pre emphasis. After that, feature extraction method is applied to the samples using Mel Frequency Cepstrum Coefficient (MFCC). Lastly, speech classification is performed using Feedforward Neural Network (FFNN). The accuracy of the classification is further investigated based on the hidden layer size. From experimentation, the classifier with 40 hidden neurons shows the highest classification rate which is 94%.  

Keywords: Feed-Forward Neural Network, FFNN, Malay speech recognition, Mel Frequency Cepstrum Coefficient, MFCC, speech-to-text.

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Authors: K.Sedhuraman, S.Himavathi, A.Muthuramalingam

Abstract:

The performance of sensor-less controlled induction motor drive depends on the accuracy of the estimated speed. Conventional estimation techniques being mathematically complex require more execution time resulting in poor dynamic response. The nonlinear mapping capability and powerful learning algorithms of neural network provides a promising alternative for on-line speed estimation. The on-line speed estimator requires the NN model to be accurate, simpler in design, structurally compact and computationally less complex to ensure faster execution and effective control in real time implementation. This in turn to a large extent depends on the type of Neural Architecture. This paper investigates three types of neural architectures for on-line speed estimation and their performance is compared in terms of accuracy, structural compactness, computational complexity and execution time. The suitable neural architecture for on-line speed estimation is identified and the promising results obtained are presented.

Keywords: Sensorless IM drives, rotor speed estimators, artificial neural network, feed- forward architecture, single neuron cascaded architecture.

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Authors: Vipul M. Patel, Hemantkumar B. Mehta

Abstract:

Technological innovations in electronic world demand novel, compact, simple in design, less costly and effective heat transfer devices. Closed Loop Pulsating Heat Pipe (CLPHP) is a passive phase change heat transfer device and has potential to transfer heat quickly and efficiently from source to sink. Thermal performance of a CLPHP is governed by various parameters such as number of U-turns, orientations, input heat, working fluids and filling ratio. The present paper is an attempt to predict the thermal performance of a CLPHP using Artificial Neural Network (ANN). Filling ratio and heat input are considered as input parameters while thermal resistance is set as target parameter. Types of neural networks considered in the present paper are radial basis, generalized regression, linear layer, cascade forward back propagation, feed forward back propagation; feed forward distributed time delay, layer recurrent and Elman back propagation. Linear, logistic sigmoid, tangent sigmoid and Radial Basis Gaussian Function are used as transfer functions. Prediction accuracy is measured based on the experimental data reported by the researchers in open literature as a function of Mean Absolute Relative Deviation (MARD). The prediction of a generalized regression ANN model with spread constant of 4.8 is found in agreement with the experimental data for MARD in the range of ±1.81%.

Keywords: ANN models, CLPHP, filling ratio, generalized regression, spread constant.

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Authors: Hassan Berbia, Faissal Elbouanani, Rahal Romadi, Mostafa Belkasmi

Abstract:

This paper introduces two decoders for binary linear codes based on Metaheuristics. The first one uses a genetic algorithm and the second is based on a combination genetic algorithm with a feed forward neural network. The decoder based on the genetic algorithms (DAG) applied to BCH and convolutional codes give good performances compared to Chase-2 and Viterbi algorithm respectively and reach the performances of the OSD-3 for some Residue Quadratic (RQ) codes. This algorithm is less complex for linear block codes of large block length; furthermore their performances can be improved by tuning the decoder-s parameters, in particular the number of individuals by population and the number of generations. In the second algorithm, the search space, in contrast to DAG which was limited to the code word space, now covers the whole binary vector space. It tries to elude a great number of coding operations by using a neural network. This reduces greatly the complexity of the decoder while maintaining comparable performances.

Keywords: Block code, decoding, methaheuristic, genetic algorithm, neural network

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Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

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In this paper, novel techniques in increasing the accuracy and speed of convergence of a Feed forward Back propagation Artificial Neural Network (FFBPNN) with polynomial activation function reported in literature is presented. These technique was subsequently used to determine the coefficients of Autoregressive Moving Average (ARMA) and Autoregressive (AR) system. The results obtained by introducing sequential and batch method of weight initialization, batch method of weight and coefficient update, adaptive momentum and learning rate technique gives more accurate result and significant reduction in convergence time when compared t the traditional method of back propagation algorithm, thereby making FFBPNN an appropriate technique for online ARMA coefficient determination.

Keywords: Adaptive Learning rate, Adaptive momentum, Autoregressive, Modeling, Neural Network.

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Authors: Anjan Kumar Kakati, M. Chandrasekaran, Amitava Mandal, Amit Kumar Singh

Abstract:

End milling process is one of the common metal cutting operations used for machining parts in manufacturing industry. It is usually performed at the final stage in manufacturing a product and surface roughness of the produced job plays an important role. In general, the surface roughness affects wear resistance, ductility, tensile, fatigue strength, etc., for machined parts and cannot be neglected in design. In the present work an experimental investigation of end milling of aluminium alloy with carbide tool is carried out and the effect of different cutting parameters on the response are studied with three-dimensional surface plots. An artificial neural network (ANN) is used to establish the relationship between the surface roughness and the input cutting parameters (i.e., spindle speed, feed, and depth of cut). The Matlab ANN toolbox works on feed forward back propagation algorithm is used for modeling purpose. 3-12-1 network structure having minimum average prediction error found as best network architecture for predicting surface roughness value. The network predicts surface roughness for unseen data and found that the result/prediction is better. For desired surface finish of the component to be produced there are many different combination of cutting parameters are available. The optimum cutting parameter for obtaining desired surface finish, to maximize tool life is predicted. The methodology is demonstrated, number of problems are solved and algorithm is coded in Matlab®.

Keywords: End milling, Surface roughness, Neural networks.

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Authors: M.R. Mustafa, M.H. Isa, R.B. Rezaur

Abstract:

Prediction of highly non linear behavior of suspended sediment flow in rivers has prime importance in the field of water resources engineering. In this study the predictive performance of two Artificial Neural Networks (ANNs) namely, the Radial Basis Function (RBF) Network and the Multi Layer Feed Forward (MLFF) Network have been compared. Time series data of daily suspended sediment discharge and water discharge at Pari River was used for training and testing the networks. A number of statistical parameters i.e. root mean square error (RMSE), mean absolute error (MAE), coefficient of efficiency (CE) and coefficient of determination (R2) were used for performance evaluation of the models. Both the models produced satisfactory results and showed a good agreement between the predicted and observed data. The RBF network model provided slightly better results than the MLFF network model in predicting suspended sediment discharge.

Keywords: ANN, discharge, modeling, prediction, suspendedsediment,

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Authors: Pradyumna Kumar Sahoo, Prasanta Kumar Satpathy

Abstract:

This paper aims at finding a suitable neural network for monitoring congestion level in electrical power systems. In this paper, the input data has been framed properly to meet the target objective through supervised learning mechanism by defining normal and abnormal operating conditions for the system under study. The congestion level, expressed as line congestion index (LCI), is evaluated for each operating condition and is presented to the NN along with the bus voltages to represent the input and target data. Once, the training goes successful, the NN learns how to deal with a set of newly presented data through validation and testing mechanism. The crux of the results presented in this paper rests on performance comparison of a multi-layered feed forward neural network with eleven types of back propagation techniques so as to evolve the best training criteria. The proposed methodology has been tested on the standard IEEE-14 bus test system with the support of MATLAB based NN toolbox. The results presented in this paper signify that the Levenberg-Marquardt backpropagation algorithm gives best training performance of all the eleven cases considered in this paper, thus validating the proposed methodology.

Keywords: Line congestion index, critical bus, contingency, neural network.

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Authors: Vishnu Pratap Singh Kirar

Abstract:

Artificial Neural Network (ANN) can be trained using back propagation (BP). It is the most widely used algorithm for supervised learning with multi-layered feed-forward networks. Efficient learning by the BP algorithm is required for many practical applications. The BP algorithm calculates the weight changes of artificial neural networks, and a common approach is to use a twoterm algorithm consisting of a learning rate (LR) and a momentum factor (MF). The major drawbacks of the two-term BP learning algorithm are the problems of local minima and slow convergence speeds, which limit the scope for real-time applications. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and criteria for evaluating convergence are required to facilitate the application of the three terms BP algorithm. Although these two seem to be closely related, as described later, we summarize various improvements to overcome the drawbacks. Here we compare the different methods of convergence of the new three-term BP algorithm.

Keywords: Neural Network, Backpropagation, Local Minima, Fast Convergence Rate.

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Authors: H. Sadjadian , H.D. Taghirad Member, A. Fatehi

Abstract:

In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

Keywords: Forward Kinematics, Neural Networks, Numerical Solution, Parallel Manipulators.

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Authors: M. P. Nanda Kumar, K. Dheeraj

Abstract:

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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Authors: S. Janpong, K-L. Areerak, K-N. Areerak

Abstract:

This paper aims to present the reviews of the application of neural network in shunt active power filter (SAPF). From the review, three out of four components of SAPF structure, which are harmonic detection component, compensating current control, and DC bus voltage control, have been adopted some of neural network architecture as part of its component or even substitution. The objectives of most papers in using neural network in SAPF are to increase the efficiency, stability, accuracy, robustness, tracking ability of the systems of each component. Moreover, minimizing unneeded signal due to the distortion is the ultimate goal in applying neural network to the SAPF. The most famous architecture of neural network in SAPF applications are ADALINE and Backpropagation (BP).

Keywords: Active power filter, neural network, harmonic distortion, harmonic detection and compensation, non-linear load.

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Authors: B. Chandra, P. Paul Varghese

Abstract:

Crypto System Identification is one of the challenging tasks in Crypt analysis. The paper discusses the possibility of employing Neural Networks for identification of Cipher Systems from cipher texts. Cascade Correlation Neural Network and Back Propagation Network have been employed for identification of Cipher Systems. Very large collection of cipher texts were generated using a Block Cipher (Enhanced RC6) and a Stream Cipher (SEAL). Promising results were obtained in terms of accuracy using both the Neural Network models but it was observed that the Cascade Correlation Neural Network Model performed better compared to Back Propagation Network.

Keywords: Back Propagation Neural Networks, CascadeCorrelation Neural Network, Crypto systems, Block Cipher, StreamCipher.

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Authors: Namal A. Senanayake, A. Beg, Withana C. Prasad

Abstract:

This paper analyzes the patterns of the Monte Carlo data for a large number of variables and minterms, in order to characterize the circuit path length behavior. We propose models that are determined by training process of shortest path length derived from a wide range of binary decision diagram (BDD) simulations. The creation of the model was done use of feed forward neural network (NN) modeling methodology. Experimental results for ISCAS benchmark circuits show an RMS error of 0.102 for the shortest path length complexity estimation predicted by the NN model (NNM). Use of such a model can help reduce the time complexity of very large scale integrated (VLSI) circuitries and related computer-aided design (CAD) tools that use BDDs.

Keywords: Monte Carlo data, Binary decision diagrams, Neural network modeling, Shortest path length estimation.

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Authors: Christian Endisch, Christoph Hackl, Dierk Schröder

Abstract:

This paper presents an exact pruning algorithm with adaptive pruning interval for general dynamic neural networks (GDNN). GDNNs are artificial neural networks with internal dynamics. All layers have feedback connections with time delays to the same and to all other layers. The structure of the plant is unknown, so the identification process is started with a larger network architecture than necessary. During parameter optimization with the Levenberg- Marquardt (LM) algorithm irrelevant weights of the dynamic neural network are deleted in order to find a model for the plant as simple as possible. The weights to be pruned are found by direct evaluation of the training data within a sliding time window. The influence of pruning on the identification system depends on the network architecture at pruning time and the selected weight to be deleted. As the architecture of the model is changed drastically during the identification and pruning process, it is suggested to adapt the pruning interval online. Two system identification examples show the architecture selection ability of the proposed pruning approach.

Keywords: System identification, dynamic neural network, recurrentneural network, GDNN, optimization, Levenberg Marquardt, realtime recurrent learning, network pruning, quasi-online learning.

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Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

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Authors: Hemashree Bordoloi, Kandarpa Kumar Sarma

Abstract:

Rotation or tilt present in an image capture by digital means can be detected and corrected using Artificial Neural Network (ANN) for application with a Face Recognition System (FRS). Principal Component Analysis (PCA) features of faces at different angles are used to train an ANN which detects the rotation for an input image and corrected using a set of operations implemented using another system based on ANN. The work also deals with the recognition of human faces with features from the foreheads, eyes, nose and mouths as decision support entities of the system configured using a Generalized Feed Forward Artificial Neural Network (GFFANN). These features are combined to provide a reinforced decision for verification of a person-s identity despite illumination variations. The complete system performing facial image rotation detection, correction and recognition using re-enforced decision support provides a success rate in the higher 90s.

Keywords: Rotation, Face, Recognition, ANN.

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Authors: Lina Yan, Jingjing Di, Ke Wang

Abstract:

A new basis function neural network algorithm is proposed for numerical integration. The main idea is to construct neural network model based on spline basis functions, which is used to approximate the integrand by training neural network weights. The convergence theorem of the neural network algorithm, the theorem for numerical integration and one corollary are presented and proved. The numerical examples, compared with other methods, show that the algorithm is effective and has the characteristics such as high precision and the integrand not required known. Thus, the algorithm presented in this paper can be widely applied in many engineering fields.

Keywords: Numerical integration, Spline basis function, Neural network algorithm

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