Search results for: constrained input

Authors: Qin Ding, Jim Gasvoda

Abstract:

Clustering is the process of subdividing an input data set into a desired number of subgroups so that members of the same subgroup are similar and members of different subgroups have diverse properties. Many heuristic algorithms have been applied to the clustering problem, which is known to be NP Hard. Genetic algorithms have been used in a wide variety of fields to perform clustering, however, the technique normally has a long running time in terms of input set size. This paper proposes an efficient genetic algorithm for clustering on very large data sets, especially on image data sets. The genetic algorithm uses the most time efficient techniques along with preprocessing of the input data set. We test our algorithm on both artificial and real image data sets, both of which are of large size. The experimental results show that our algorithm outperforms the k-means algorithm in terms of running time as well as the quality of the clustering.

Keywords: Clustering, data mining, genetic algorithm, image data.

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Authors: B. Janani, S. Thiruvenkadam

Abstract:

In this work, the system evaluates the impact of considering a stochastic approach on the day ahead basis Unit Commitment. Comparisons between stochastic and deterministic Unit Commitment solutions are provided. The Unit Commitment model consists in the minimization of the total operation costs considering unit’s technical constraints like ramping rates, minimum up and down time. Load shedding and wind power spilling is acceptable, but at inflated operational costs. The evaluation process consists in the calculation of the optimal unit commitment and in verifying the fulfillment of the considered constraints. For the calculation of the optimal unit commitment, an algorithm based on the Benders Decomposition, namely on the Dual Dynamic Programming, was developed. Two approaches were considered on the construction of stochastic solutions. Data related to wind power outputs from two different operational days are considered on the analysis. Stochastic and deterministic solutions are compared based on the actual measured wind power output at the operational day. Through a technique capability of finding representative wind power scenarios and its probabilities, the system can analyze a more detailed process about the expected final operational cost.

Keywords: Benders’ decomposition, network constrained AC unit commitment, stochastic programming, wind power uncertainty.

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Authors: Mohammad Hasan Raouf, Ahmad Rouhani, Mohammad Abedini, Ebrahim Rasooli Anarmarzi

Abstract:

In this paper the application of a hierarchical fuzzy system (HFS) based on MPSS and SVC in multi-machine environment is studied. Also the effect of communication lines active power variance signal between two ΔP_Tie-line regions, as one of the inputs of hierarchical fuzzy multi-input PSS and SVC (HFMPSS & SVC), on the increase of low frequency oscillation damping is examined. In the MPSS, to have better efficiency an auxiliary signal of reactive power deviation (ΔQ) is added with ΔP+ Δω input type PSS. The number of rules grows exponentially with the number of variables in a classic fuzzy system. To reduce the number of rules the HFS consists of a number of low-dimensional fuzzy systems in a hierarchical structure. Phasor model of SVC is described and used in this paper. The performances of MPSS and ΔP_Tie-line based HFMPSS and also the proposed method in damping inter-area mode of oscillation are examined in response to disturbances. The efficiency of the proposed model is examined by simulating a four-machine power system. Results show that the proposed method is performing satisfactorily within the whole range of disturbances and reduces the cost of system.

Keywords: Communication lines active power variance signal, Hierarchical fuzzy system (HFS), Multi-input power system stabilizer (MPSS), Static VAR compensator (SVC).

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Authors: Jung–Min Yang

Abstract:

Solvability of the model matching problem for input/output switched asynchronous sequential machines is discussed in this paper. The control objective is to determine the existence condition and design algorithm for a corrective controller that can match the stable-state behavior of the closed-loop system to that of a reference model. Switching operations and correction procedures are incorporated using output feedback so that the controlled switched machine can show the desired input/output behavior. A matrix expression is presented to address reachability of switched asynchronous sequential machines with output equivalence with respect to a model. The presented reachability condition for the controller design is validated in a simple example.

Keywords: Asynchronous sequential machines, corrective control, model matching, input/output control.

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Authors: Steven W. Su , Hung Nguyen, Rob Jarman, Joe Zhu, David Lowe, Peter McLean, Shoudong Huang, Nghia T. Nguyen, Russell Nicholson, Kaili Weng

Abstract:

This paper proposed a nonlinear model predictive control (MPC) method for the control of gantry crane. One of the main motivations to apply MPC to control gantry crane is based on its ability to handle control constraints for multivariable systems. A pre-compensator is constructed to compensate the input nonlinearity (nonsymmetric dead zone with saturation) by using its inverse function. By well tuning the weighting function matrices, the control system can properly compromise the control between crane position and swing angle. The proposed control algorithm was implemented for the control of gantry crane system in System Control Lab of University of Technology, Sydney (UTS), and achieved desired experimental results.

Keywords: Model Predictive Control, Control constraints, Input nonlinearity compensation, Overhead gantry crane.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.

Keywords: Fast Code/Data Detection, Neural Networks, Cross Correlation, real/complex values.

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Authors: Moe Moe Htun, Khin Htar Nwe

Abstract:

In this paper, parallel interface for microprocessor trainer was implemented. A programmable parallel–port device such as the IC 8255A is initialized for simple input or output and for handshake input or output by choosing kinds of modes. The hardware connections and the programs can be used to interface microprocessor trainer and a personal computer by using IC 8255A. The assembly programs edited on PC-s editor can be downloaded to the trainer.

Keywords: Parallel I/O ports, parallel interface, trainer, two 8255 ICs.

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Authors: Mariyam Arif, Ye Liu, Israr Ul Haq, Ahsan Ashfaq

Abstract:

High cost of fossil fuels and intensifying installations of alternate energy generation sources are intimidating main challenges in power systems. Making accurate load forecasting an important and challenging task for optimal energy planning and management at both distribution and generation side. There are many techniques to forecast load but each technique comes with its own limitation and requires data to accurately predict the forecast load. Artificial Neural Network (ANN) is one such technique to efficiently forecast the load. Comparison between two different ranges of input datasets has been applied to dynamic ANN technique using MATLAB Neural Network Toolbox. It has been observed that selection of input data on training of a network has significant effects on forecasted results. Day-wise input data forecasted the load accurately as compared to year-wise input data. The forecasted load is then distributed among the six generators by using the linear programming to get the optimal point of generation. The algorithm is then verified by comparing the results of each generator with their respective generation limits.

Keywords: Artificial neural networks, demand-side management, economic dispatch, linear programming, power generation dispatch.

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Authors: Yi Zhang, Quan Zhou, Jun Li, Yanlang Hu

Abstract:

Scheduling algorithm is a key technology in satellite switching system with input-buffer. In this paper, a new scheduling algorithm and its realization are proposed. Based on Crossbar switching fabric, the algorithm adopts serial scheduling strategy and adjusts the output port arbitrating strategy for the better equity of every port. Consequently, it increases the matching probability. The algorithm can greatly reduce the scheduling delay and cell loss rate. The analysis and simulation results by OPNET show that the proposed algorithm has the better performance than others in average delay and cell loss rate, and has the equivalent complexity. On the basis of these results, the hardware realization and simulation based on FPGA are completed, which validate the feasibility of the new scheduling algorithm.

Keywords: Scheduling algorithm, input-buffer, serial scheduling, hardware design.

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Authors: S. Safi, M. Frikel, M. M'Saad, A. Zeroual

Abstract:

This paper describes a blind algorithm for estimating a time varying and frequency selective fading channel. In order to identify blindly the impulse response of these channels, we have used Higher Order Statistics (HOS) to build our algorithm. In this paper, we have selected two theoretical frequency selective channels as the Proakis-s 'B' channel and the Macchi-s channel, and one practical frequency selective fading channel called Broadband Radio Access Network (BRAN A). The simulation results in noisy environment and for different data input channel, demonstrate that the proposed method could estimate the phase and magnitude of these channels blindly and without any information about the input, except that the input excitation is i.i.d (Identically and Independent Distributed) and non-Gaussian.

Keywords: Frequency response, system identification, higher order statistics, communication channels, phase estimation.

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Authors: Reza Hossseynie, Amir Jafari

Abstract:

This paper presents a method for steering velocity bounded mobile robots in environments with partially known stationary obstacles. The exact location of obstacles is unknown and only a probability distribution associated with the location of the obstacles is known. Kinematic model of a 2-wheeled differential drive robot is used as the model of mobile robot. The presented control strategy uses the Artificial Potential Field (APF) method for devising a desired direction of movement for the robot at each instant of time while the Constrained Directions Control (CDC) uses the generated direction to produce the control signals required for steering the robot. The location of each obstacle is considered to be the mean value of the 2D probability distribution and similarly, the magnitude of the electric charge in the APF is set as the trace of covariance matrix of the location probability distribution. The method not only captures the challenges of planning the path (i.e. probabilistic nature of the location of unknown obstacles), but it also addresses the output saturation which is considered to be an important issue from the control perspective. Moreover, velocity of the robot can be controlled during the steering. For example, the velocity of robot can be reduced in close vicinity of obstacles and target to ensure safety. Finally, the control strategy is simulated for different scenarios to show how the method can be put into practice.

Keywords: Steering, obstacle avoidance, mobile robots, constrained directions control, artificial potential field.

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Authors: Yizhi Gai, Yukinori Kobayashi, Yohei Hoshino, Takanori Emaru

Abstract:

Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

Keywords: Motion control, flexible robotic arm, CEVEPSO, ball throwing robot.

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Authors: Hanif Che Lah, Wee Leong Son, Rozita Borhan

Abstract:

This paper is about method to produce a stable and accurate constant output pulse width regardless of the amplitude, period and pulse width variation of the input signal source. The pulse generated is usually being used in numerous applications as the reference input source to other circuits in the system. Therefore, it is crucial to produce a clean and constant pulse width to make sure the system is working accurately as expected.

Keywords: Amplitude, Constant Pulse Width, Frequency Divider, Pulse Generator.

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Authors: Jae Wook Shin, Ju-man Song, Hyun-Taek Choi, Poo Gyeon Park

Abstract:

This paper introduces a new variable step-size APA with decorrelation of AR input process is based on the MSD analysis. To achieve a fast convergence rate and a small steady-state estimation error, he proposed algorithm uses variable step size that is determined by minimising the MSD. In addition, experimental results show that the proposed algorithm is achieved better performance than the other algorithms.

Keywords: adaptive filter, affine projection algorithm, variable step size.

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Authors: Apratim Roy, A. B. M. H. Rashid

Abstract:

In this paper, a double balanced radio frequency multiplier is presented which is customized for transmitted reference ultra wideband (UWB) receivers. The multiplier uses 90nm model parameters and exploits compensating transistors to provide controllable gain for a Gilbert core. After performing periodic and quasiperiodic non linear analyses the RF mixer (multiplier) achieves a voltage conversion gain of 16 dB and a DSB noise figure of 8.253 dB with very low power consumption. A high degree of LO to RF isolation (in the range of -94dB), RF to IF isolation (in the range of -95dB) and LO to IF isolation (in the range of -143dB) is expected for this design with an input-referred IP3 point of -1.93 dBm and an input referred 1 dB compression point of -10.67dBm. The amount of noise at the output is 7.7 nV/√Hz when the LO input is driven by a 10dBm signal. The mixer manifests better results when compared with other reported multiplier circuits and its Zero-IF performance ensures its applicability as TR-UWB multipliers.

Keywords: UWB, Transmitted Reference, Controllable Gain, RFMixer, Multiplier.

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Authors: Sanda Win, Tin Shein, Khin Maung Latt

Abstract:

This document describes an electronic speed control designed to drive two DC motors from a 6 V battery pack to be controlled by a commercial universal infrared remote control hand set. Conceived for a tank-like vehicle, one motor drives the left side wheels or tracks and the other motor drives the right side. As it is shown here, there is a left-right steering input and a forward– backward throttles input, like would be used on a model car. It is designed using a microcontroller PIC16F873A.

Keywords: Assembly Language, Direction Control, SpeedControl, PIC 16F 873A

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Authors: Salah Al-Din I. Badran, Samad Ahmadi, Dylan Menzies, Ismail Shahin

Abstract:

This paper describes a new efficient blind source separation method; in this method we uses a non-uniform filter bank and a new structure with different sub-bands. This method provides a reduced permutation and increased convergence speed comparing to the full-band algorithm. Recently, some structures have been suggested to deal with two problems: reducing permutation and increasing the speed of convergence of the adaptive algorithm for correlated input signals. The permutation problem is avoided with the use of adaptive filters of orders less than the full-band adaptive filter, which operate at a sampling rate lower than the sampling rate of the input signal. The decomposed signals by analysis bank filter are less correlated in each sub-band than the input signal at full-band, and can promote better rates of convergence.

Keywords: Blind source separation (BSS), estimates, full-band, mixtures, Sub-band.

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Authors: Hassan Jassim Motlak

Abstract:

A novel design technique employing CMOS Current Feedback Operational Amplifier (CFOA) is presented. The feature of consumption very low power in designing pseudo-OTA is used to decreasing the total power consumption of the proposed CFOA. This design approach applies pseudo-OTA as input stage cascaded with buffer stage. Moreover, the DC input offset voltage and harmonic distortion (HD) of the proposed CFOA are very low values compared with the conventional CMOS CFOA due to the symmetrical input stage. P-Spice simulation results are obtained using 0.18μm MIETEC CMOS process parameters and supply voltage of ±1.2V, 50μA biasing current. The p-spice simulation shows excellent improvement of the proposed CFOA over existing CMOS CFOA. Some of these performance parameters, for example, are DC gain of 62. dB, openloop gain bandwidth product of 108 MHz, slew rate (SR+) of +71.2V/μS, THD of -63dB and DC consumption power (PC) of 2mW.

Keywords: Pseudo-OTA used CMOS CFOA, low power CFOA, high-performance CFOA, novel CFOA.

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

Abstract:

In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: P. Joyce Beryl Princess, Y. Harold Robinson

Abstract:

Image Processing is a structure of Signal Processing for which the input is the image and the output is also an image or parameter of the image. Image Resolution has been frequently referred as an important aspect of an image. In Image Resolution Enhancement, images are being processed in order to obtain more enhanced resolution. To generate highly resoluted image for a low resoluted input image with high PSNR value. Stationary Wavelet Transform is used for Edge Detection and minimize the loss occurs during Downsampling. Inverse Discrete Wavelet Transform is to get highly resoluted image. Highly resoluted output is generated from the Low resolution input with high quality. Noisy input will generate output with low PSNR value. So Noisy resolution enhancement technique has been used for adaptive sub-band thresholding is used. Downsampling in each of the DWT subbands causes information loss in the respective subbands. SWT is employed to minimize this loss. Inverse Discrete wavelet transform (IDWT) is to convert the object which is downsampled using DWT into a highly resoluted object. Used Image denoising and resolution enhancement techniques will generate image with high PSNR value. Our Proposed method will improve Image Resolution and reached the optimized threshold.

Keywords: Image Processing, Inverse Discrete wavelet transform, PSNR.

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Authors: Alexey V. Klyuev, Valery P. Samarin, Viktor F. Klyuev

Abstract:

A power measurement algorithm of the input mix components of the noise signal and narrowband interference is considered using functional transformations of the input mix in the postdetection processing channel. The algorithm efficiency analysis has been carried out for different interference-to-signal ratio. Algorithm performance features have been explored by numerical experiment results.

Keywords: Noise signal, continuous narrowband interference, signal power, spectrum width, detection.

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Authors: Ling-fei Xu, Qi Zhao, Yan-ru Chen, Mu-chun Zhou, Meng Zhang, Shi-xue Xu

Abstract:

SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we found that there exist some regular in the characteristic curve of the flame from the mouse of pudding. And we can use SVM to predict end point of the BOF, just single spectrum intensity should be required as the input parameter. Moreover, its compatibility for the input space is better than the BP network.

Keywords: SVM, predict, BOF, single spectrum intensity.

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Authors: Dawei Wang, Rujing Wang, Ying Li, Baozi Wei

Abstract:

FAQ system can make user find answer to the problem that puzzles them. But now the research on Chinese FAQ system is still on the theoretical stage. This paper presents an approach to semantic inference for FAQ mining. To enhance the efficiency, a small pool of the candidate question-answering pairs retrieved from the system for the follow-up work according to the concept of the agriculture domain extracted from user input .Input queries or questions are converted into four parts, the question word segment (QWS), the verb segment (VS), the concept of agricultural areas segment (CS), the auxiliary segment (AS). A semantic matching method is presented to estimate the similarity between the semantic segments of the query and the questions in the pool of the candidate. A thesaurus constructed from the HowNet, a Chinese knowledge base, is adopted for word similarity measure in the matcher. The questions are classified into eleven intension categories using predefined question stemming keywords. For FAQ mining, given a query, the question part and answer part in an FAQ question-answer pair is matched with the input query, respectively. Finally, the probabilities estimated from these two parts are integrated and used to choose the most likely answer for the input query. These approaches are experimented on an agriculture FAQ system. Experimental results indicate that the proposed approach outperformed the FAQ-Finder system in agriculture FAQ retrieval.

Keywords: FAQ, Semantic Inference, Ontology.

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Authors: Ming-Hui Lee, Tsung-Chien Chen, Tsu-Ping Yu, Horng-Yuan Jang

Abstract:

The innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux of the multilayer materials as presented in this paper. The feasibility of this method can be verified by adopting the temperature measurement experiment. The experiment modular may be designed by using the copper sample which is stacked up 4 aluminum samples with different thicknesses. Furthermore, the bottoms of copper samples are heated by applying the standard heat source, and the temperatures on the tops of aluminum are measured by using the thermocouples. The temperature measurements are then regarded as the inputs into the presented method to estimate the heat flux in the bottoms of copper samples. The influence on the estimation caused by the temperature measurement of the sample with different thickness, the processing noise covariance Q, the weighting factor γ , the sampling time interval Δt , and the space discrete interval Δx , will be investigated by utilizing the experiment verification. The results show that this method is efficient and robust to estimate the unknown time-varying heat input of the multilayer materials.

Keywords: Multilayer Materials, Input Estimation Method, IHCP, Heat Flux.

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Authors: Sheroz Khan, I. Adam, A. H. M. Zahirul Alam, Mohd Rafiqul Islam, Othman O. Khalifa

Abstract:

This paper attempts to model and design a simple fuzzy logic controller with Variable Reference. The Variable Reference (VR) is featured as an adaptability element which is obtained from two known variables – desired system-input and actual system-output. A simple fuzzy rule-based technique is simulated to show how the actual system-input is gradually tuned in to a value that closely matches the desired input. The designed controller is implemented and verified on a simple heater which is controlled by PIC Microcontroller harnessed by a code developed in embedded C. The output response of the PIC-controlled heater is analyzed and compared to the performances by conventional fuzzy logic controllers. The novelty of this work lies in the fact that it gives better performance by using less number of rules compared to conventional fuzzy logic controllers.

Keywords: Fuzzy logic controller, Variable reference, Adaptability, Rule-based.

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Authors: Alexey V. Klyuev, Valery P. Samarin, Viktor F. Klyuev, Andrey V. Klyuev

Abstract:

A power measurement algorithm of the input mix components of the noise signal and pulse interference is considered. The algorithm efficiency analysis has been carried out for different interference-to-signal ratio. Algorithm performance features have been explored by numerical experiment results.

Keywords: Noise signal, pulse interference, signal power, spectrum width, detection.

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Authors: Azeddine Ghodbane, David Bensoussan, Maher Hammami

Abstract:

In this study, we introduce an alternative adaptive architecture that enhances both time and frequency performance, helpfully mitigating the effects of disturbances from the input plant and external disturbances affecting the output. To facilitate superior performance in both the time and frequency domains, we have developed a user-friendly interactive design methods using the GeoGebra platform.

Keywords: Control theory, decentralized control, sensitivity theory, input-output stability theory, robust multivariable feedback control design.

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Authors: Lewis E. Hibell, Honghai Liu, David J. Brown

Abstract:

This paper presents the use of a newly created network structure known as a Self-Delaying Dynamic Network (SDN) to create a high resolution image from a set of time stepped input frames. These SDNs are non-recurrent temporal neural networks which can process time sampled data. SDNs can store input data for a lifecycle and feature dynamic logic based connections between layers. Several low resolution images and one high resolution image of a scene were presented to the SDN during training by a Genetic Algorithm. The SDN was trained to process the input frames in order to recreate the high resolution image. The trained SDN was then used to enhance a number of unseen noisy image sets. The quality of high resolution images produced by the SDN is compared to that of high resolution images generated using Bi-Cubic interpolation. The SDN produced images are superior in several ways to the images produced using Bi-Cubic interpolation.

Keywords: Image Enhancement, Neural Networks, Multi-Frame.

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Authors: Inder K. Purohit, M. Nazrul Islam, K. Vijayan Asari, Mohammad A. Karim

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A new target detection technique is presented in this paper for the identification of small boats in coastal surveillance. The proposed technique employs an adaptive progressive thresholding (APT) scheme to first process the given input scene to separate any objects present in the scene from the background. The preprocessing step results in an image having only the foreground objects, such as boats, trees and other cluttered regions, and hence reduces the search region for the correlation step significantly. The processed image is then fed to the shifted phase-encoded fringe-adjusted joint transform correlator (SPFJTC) technique which produces single and delta-like correlation peak for a potential target present in the input scene. A post-processing step involves using a peak-to-clutter ratio (PCR) to determine whether the boat in the input scene is authorized or unauthorized. Simulation results are presented to show that the proposed technique can successfully determine the presence of an authorized boat and identify any intruding boat present in the given input scene.

Keywords: Adaptive progressive thresholding, fringe adjusted filters, image segmentation, joint transform correlation, synthetic discriminant function

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Authors: Tao Dai, Andy Adler, Behnam Shahrrava

Abstract:

This paper presents a forgetting factor scheme for variable step-size affine projection algorithms (APA). The proposed scheme uses a forgetting processed input matrix as the projection matrix of pseudo-inverse to estimate system deviation. This method introduces temporal weights into the projection matrix, which is typically a better model of the real error's behavior than homogeneous temporal weights. The regularization overcomes the ill-conditioning introduced by both the forgetting process and the increasing size of the input matrix. This algorithm is tested by independent trials with coloured input signals and various parameter combinations. Results show that the proposed algorithm is superior in terms of convergence rate and misadjustment compared to existing algorithms. As a special case, a variable step size NLMS with forgetting factor is also presented in this paper.

Keywords: Adaptive signal processing, affine projection algorithms, variable step-size adaptive algorithms, regularization.

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