Search results for: Lattice reduction aided detection

Authors: Andreas Theissler, Ian Dear

Abstract:

In the automotive industry test drives are being conducted during the development of new vehicle models or as a part of quality assurance of series-production vehicles. The communication on the in-vehicle network, data from external sensors, or internal data from the electronic control units is recorded by automotive data loggers during the test drives. The recordings are used for fault analysis. Since the resulting data volume is tremendous, manually analysing each recording in great detail is not feasible. This paper proposes to use machine learning to support domainexperts by preventing them from contemplating irrelevant data and rather pointing them to the relevant parts in the recordings. The underlying idea is to learn the normal behaviour from available recordings, i.e. a training set, and then to autonomously detect unexpected deviations and report them as anomalies. The one-class support vector machine “support vector data description” is utilised to calculate distances of feature vectors. SVDDSUBSEQ is proposed as a novel approach, allowing to classify subsequences in multivariate time series data. The approach allows to detect unexpected faults without modelling effort as is shown with experimental results on recordings from test drives.

Keywords: Anomaly detection, fault detection, test drive analysis, machine learning.

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Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

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Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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Authors: K. C. Meher, R. K. Swain, C. K. Chanda

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This paper presents the performance analysis of dynamic search space reduction (DSR) based gravitational search algorithm (GSA) to solve dynamic economic dispatch of thermal generating units with valve point effects. Dynamic economic dispatch basically dictates the best setting of generator units with anticipated load demand over a definite period of time. In this paper, the presented technique is considered that deals an inequality constraints treatment mechanism known as DSR strategy to accelerate the optimization process. The presented method is demonstrated through five-unit test systems to verify its effectiveness and robustness. The simulation results are compared with other existing evolutionary methods reported in the literature. It is intuited from the comparison that the fuel cost and other performances of the presented approach yield fruitful results with marginal value of simulation time.

Keywords: Dynamic economic dispatch, dynamic search space reduction strategy, gravitational search algorithm, ramp rate limits, valve-point effects.

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Authors: M. R. Ghasemi, R. Ghiasi, H. Varaee

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Surrogate model has received increasing attention for use in detecting damage of structures based on vibration modal parameters. However, uncertainties existing in the measured vibration data may lead to false or unreliable output result from such model. In this study, an efficient approach based on Monte Carlo simulation is proposed to take into account the effect of uncertainties in developing a surrogate model. The probability of damage existence (PDE) is calculated based on the probability density function of the existence of undamaged and damaged states. The kriging technique allows one to genuinely quantify the surrogate error, therefore it is chosen as metamodeling technique. Enhanced version of ideal gas molecular movement (EIGMM) algorithm is used as main algorithm for model updating. The developed approach is applied to detect simulated damage in numerical models of 72-bar space truss and 120-bar dome truss. The simulation results show the proposed method can perform well in probability-based damage detection of structures with less computational effort compared to direct finite element model.

Keywords: Enhanced ideal gas molecular movement, Kriging, probability-based damage detection, probability of damage existence, surrogate modeling, uncertainty quantification.

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Authors: Sarah Odofin, Zhiwei Gao, Sun Kai

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Operations, maintenance and reliability of wind turbines have received much attention over the years due to the rapid expansion of wind farms. This paper explores early fault diagnosis technique for a 5MW wind turbine system subjected to multiple faults, where genetic optimization algorithm is employed to make the residual sensitive to the faults, but robust against disturbances. The proposed technique has a potential to reduce the downtime mostly caused by the breakdown of components and exploit the productivity consistency by providing timely fault alarms. Simulation results show the effectiveness of the robust fault detection methods used under Matlab/Simulink/Gatool environment.

Keywords: Disturbance robustness, fault monitoring and detection, genetic algorithm and observer technique.

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Authors: Jiri Barta, Jiri F. Urbanek

Abstract:

This paper deals with a protection of the national and European infrastructure. It is issue nowadays. The paper deals with the perspectives and possibilities of "smart solutions" to critical infrastructure protection. The research project deals with computers aided technologies are used from the perspective of new, better protection of selected infrastructure objects. Protection is focused on communication and information channels. These communication and information channels are very important for the functioning of the system of protection of critical infrastructure elements.

Keywords: Interoperability, Communication systems, Controlling Process, Critical Infrastructure, Crisis Workplaces. Continuity.

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Authors: S. Liangwongsan, A. Oonsivilai

Abstract:

Nowadays, hard disk is one of the most popular storage components. In hard disk industry, the hard disk drive must pass various complex processes and tested systems. In each step, there are some failures. To reduce waste from these failures, we must find the root cause of those failures. Conventionall data analysis method is not effective enough to analyze the large capacity of data. In this paper, we proposed the Hough method for straight line detection that helps to detect straight line defect patterns that occurs in hard disk drive. The proposed method will help to increase more speed and accuracy in failure analysis.

Keywords: Hough Transform, Failure Analysis, Media, Hard Disk Drive

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Authors: K. Idir, H. Merouani, Y. Tlili.

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An effective method for the early detection of breast cancer is the mammographic screening. One of the most important signs of early breast cancer is the presence of microcalcifications. For the detection of microcalcification in a mammography image, we propose to conceive a multiagent system based on a dual irregular pyramid. An initial segmentation is obtained by an incremental approach; the result represents level zero of the pyramid. The edge information obtained by application of the Canny filter is taken into account to affine the segmentation. The edge-agents and region-agents cooper level by level of the pyramid by exploiting its various characteristics to provide the segmentation process convergence.

Keywords: Dual Pyramid, Image Segmentation, Multi-agent System, Region/Edge Cooperation.

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Authors: S. Padmapriya

Abstract:

Vehicular Adhoc Networks (VANETs), a subset of Mobile Adhoc Networks (MANETs), refers to a set of smart vehicles used for road safety. This vehicle provides communication services among one another or with the Road Side Unit (RSU). Security is one of the most critical issues related to VANET as the information transmitted is distributed in an open access environment. As each vehicle is not a source of all messages, most of the communication depends on the information received from other vehicles. To protect VANET from malicious action, each vehicle must be able to evaluate, decide and react locally on the information received from other vehicles. Therefore, message verification is more challenging in VANET because of the security and privacy concerns of the participating vehicles. To overcome security threats, we propose Monitoring Algorithm that detects malicious nodes based on the pre-selected threshold value. The threshold value is compared with the distrust value which is inherently tagged with each vehicle. The proposed Monitoring Algorithm not only detects malicious vehicles, but also isolates the malicious vehicles from the network. The proposed technique is simulated using Network Simulator2 (NS2) tool. The simulation result illustrated that the proposed Monitoring Algorithm outperforms the existing algorithms in terms of malicious node detection, network delay, packet delivery ratio and throughput, thereby uplifting the overall performance of the network.

Keywords: VANET, security, malicious vehicle detection, threshold value, distrust value.

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Authors: E. Kaygan, A. Gatto

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An investigation of adaptable winglets for morphing aircraft control and performance is described in this paper. The concepts investigated consist of various winglet configurations fundamentally centred on a baseline swept wing. The impetus for the work was to identify and optimize winglets to enhance controllability and the aerodynamic efficiency of a small unmanned aerial vehicle. All computations were performed with Athena Vortex Lattice modelling with varying degrees of twist, swept, and dihedral angle considered. The results from this work indicate that if adaptable winglets were employed on small scale UAV’s improvements in both aircraft control and performance could be achieved.

Keywords: Aircraft, rolling, wing, winglet.

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Authors: Wajdi Ghezaiel, Amel Ben Slimane Rahmouni, Ezzedine Ben Braiek

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Many applications of speech communication and speaker identification suffer from the problem of co-channel speech. This paper deals with a multi-resolution dyadic wavelet transform method for usable segments of co-channel speech detection that could be processed by a speaker identification system. Evaluation of this method is performed on TIMIT database referring to the Target to Interferer Ratio measure. Co-channel speech is constructed by mixing all possible gender speakers. Results do not show much difference for different mixtures. For the overall mixtures 95.76% of usable speech is correctly detected with false alarms of 29.65%.

Keywords: Co-channel speech, usable speech, multi-resolutionanalysis, speaker identification

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Authors: B. Rebekka, B. Malarkodi

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This paper describes an approach to detect the transmitted signals for 2×2 Multiple Input Multiple Output (MIMO) setup using roulette wheel based ant colony optimization technique. The results obtained are compared with classical zero forcing and least mean square techniques. The detection rates achieved using this technique are consistently larger than the one achieved using classical methods for 50 number of attempts with two different antennas transmitting the input stream from a user. This paves the path to use alternative techniques to improve the throughput achieved in advanced networks like Long Term Evolution (LTE) networks.

Keywords: MIMO, ant colony optimization, roulette wheel, soft computing, LTE.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

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Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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Authors: S. Cagin, X. Fischer, E. Delacourt, N. Bourabaa, C. Morin, D. Coutellier, B. Carré, S. Loumé

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The complexity of scavenging by ports and its impact on engine efficiency create the need to understand and to model it as realistically as possible. However, there are few empirical scavenging models and these are highly specialized. In a design optimization process, they appear very restricted and their field of use is limited. This paper presents a comparison of two methods to establish and reduce a model of the scavenging process in 2-stroke diesel engines. To solve the lack of scavenging models, a CFD model has been developed and is used as the referent case. However, its large size requires a reduction. Two techniques have been tested depending on their fields of application: The NTF method and neural networks. They both appear highly appropriate drastically reducing the model’s size (over 90% reduction) with a low relative error rate (under 10%). Furthermore, each method produces a reduced model which can be used in distinct specialized fields of application: the distribution of a quantity (mass fraction for example) in the cylinder at each time step (pseudo-dynamic model) or the qualification of scavenging at the end of the process (pseudo-static model).

Keywords: Diesel engine, Design optimization, Model reduction, Neural network, NTF algorithm, Scavenging.

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Authors: Mamoun F. Abdel-Hafez

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In this paper, the detection of a fault in the Global Positioning System (GPS) measurement is addressed. The class of faults considered is a bias in the GPS pseudorange measurements. This bias is modeled as an unknown constant. The fault could be the result of a receiver fault or signal fault such as multipath error. A bias bank is constructed based on set of possible fault hypotheses. Initially, there is equal probability of occurrence for any of the biases in the bank. Subsequently, as the measurements are processed, the probability of occurrence for each of the biases is sequentially updated. The fault with a probability approaching unity will be declared as the current fault in the GPS measurement. The residual formed from the GPS and Inertial Measurement Unit (IMU) measurements is used to update the probability of each fault. Results will be presented to show the performance of the presented algorithm.

Keywords: Estimation and filtering, Statistical data analysis, Faultdetection and identification.

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Authors: N. Hammid, F. Bouarab-Dahmani, T. Berkane

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Since its appearance, the MOOC (massive open online course) is gaining more and more intention of the educational communities over the world. Apart from the current MOOCs design and purposes, the creators of MOOC focused on the importance of the connection and knowledge exchange between individuals in learning. In this paper, we present a conceptual model for massive open online blended courses where teachers over the world can collaborate and exchange their experience to get a common efficient content designed as a MOOC opened to their students to live a better learning experience. This model is based on disciplines’ concepts capitalization and the detection of the obstacles met by their students when faced with problem situations (exercises, projects, case studies, etc.). This detection is possible by analyzing the frequently of semantic errors committed by the students. The participation of teachers in the design of the course and the attendance by their students can guarantee an efficient and extensive participation (an important number of participants) in the course, the learners’ motivation and the evaluation issues, in the way that the teachers designing the course assess their students. Thus, the teachers review, together with their knowledge, offer a better assessment and efficient connections to their students.

Keywords: MOOC, Massive Open Online Courses, Online learning, E-learning, Blended learning.

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Authors: K. Varesi

Abstract:

This paper proposes a Particle Swarm Optimization (PSO) based technique for the optimal allocation of Distributed Generation (DG) units in the power systems. In this paper our aim is to decide optimal number, type, size and location of DG units for voltage profile improvement and power loss reduction in distribution network. Two types of DGs are considered and the distribution load flow is used to calculate exact loss. Load flow algorithm is combined appropriately with PSO till access to acceptable results of this operation. The suggested method is programmed under MATLAB software. Test results indicate that PSO method can obtain better results than the simple heuristic search method on the 30-bus and 33- bus radial distribution systems. It can obtain maximum loss reduction for each of two types of optimally placed multi-DGs. Moreover, voltage profile improvement is achieved.

Keywords: Distributed Generation (DG), Optimal Allocation, Particle Swarm Optimization (PSO), Power Loss Minimization, Voltage Profile Improvement.

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Authors: Amir Hossein Pakshir, A. Hossein Pour, N. Jahandar, Ali Paydar

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Roundabout work on the principle of circulation and entry flows, where the maximum entry flow rates depend largely on circulating flow bearing in mind that entry flows must give away to circulating flows. Where an existing roundabout has a road hump installed at the entry arm, it can be hypothesized that the kinematics of vehicles may prevent the entry arm from achieving optimum performance. Road humps are traffic calming devices placed across road width solely as speed reduction mechanism. They are the preferred traffic calming option in Malaysia and often used on single and dual carriageway local routes. The speed limit on local routes is 30mph (50 km/hr). Road humps in their various forms achieved the biggest mean speed reduction (based on a mean speed before traffic calming of 30mph) of up to 10mph or 16 km/hr according to the UK Department of Transport. The underlying aim of reduced speed should be to achieve a 'safe' distribution of speeds which reflects the function of the road and the impacts on the local community. Constraining safe distribution of speeds may lead to poor drivers timing and delayed reflex reaction that can probably cause accident. Previous studies on road hump impact have focused mainly on speed reduction, traffic volume, noise and vibrations, discomfort and delay from the use of road humps. The paper is aimed at optimal entry and circulating flow induced by road humps. Results show that roundabout entry and circulating flow perform better in circumstances where there is no road hump at entrance.

Keywords: Road hump, Roundabout, Speed Reduction

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Authors: Levente Varga, Dávid Deritei, Mária Ercsey-Ravasz, Răzvan Florian, Zsolt I. Lázár, István Papp, Ferenc Járai-Szabó

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One of the major shortcomings of widely used scientometric indicators is that different disciplines cannot be compared with each other. The issue of cross-disciplinary normalization has been long discussed, but even the classification of publications into scientific domains poses problems. Structural properties of citation networks offer new possibilities, however, the large size and constant growth of these networks asks for precaution. Here we present a new tool that in order to perform cross-field normalization of scientometric indicators of individual publications relays on the structural properties of citation networks. Due to the large size of the networks, a systematic procedure for identifying scientific domains based on a local community detection algorithm is proposed. The algorithm is tested with different benchmark and real-world networks. Then, by the use of this algorithm, the mechanism of the scientometric indicator normalization process is shown for a few indicators like the citation number, P-index and a local version of the PageRank indicator. The fat-tail trend of the article indicator distribution enables us to successfully perform the indicator normalization process.

Keywords: Citation networks, scientometric indicator, cross-field normalization, local cluster detection.

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Authors: Leili Nosrati, Alireza Nemaney Pour

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Although e-mail is the most efficient and popular communication method, unwanted and mass unsolicited e-mails, also called spam mail, endanger the existence of the mail system. This paper proposes a new algorithm called Dynamic Weighted Majority Concept Drift Detection (DWM-CDD) for content-based filtering. The design purposes of DWM-CDD are first to accurate the performance of the previously proposed algorithms, and second to speed up the time to construct the model. The results show that DWM-CDD can detect both sudden and gradual changes quickly and accurately. Moreover, the time needed for model construction is less than previously proposed algorithms.

Keywords: Concept drift, Content-based filtering, E-mail, Spammail.

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Authors: J. Ramos, V. Gil, A. F. Torres

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In this research (using induction furnace process) nodular iron with three different percentages of copper (residual, 0.5% and 1,2%) was obtained. Chemical analysis was performed by mass spectrometry and microstructures were characterized by Optical Microscopy (ASTM E3) and Scanning Electron Microscopy (SEM). The study of mechanical behavior was carried out in a mechanical test machine (ASTM E8) and a Pin on disk tribometer (ASTM G99) was used to assess wear resistance. It is observed that the dissolution of copper in crystal lattice increases the pearlite structure improving the wear and hardness behavior, but producing a contrary effect on the energy absorption.

Keywords: Ferritic and perlite structure, mechanical properties, nodular iron, wear.

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Authors: Ionel D. Craiu, Mihai Nedelcu

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Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: Damage detection, generalized beam theory, inverse finite element method, shape sensing.

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Authors: Antonis Sideris, Elias Chlis Kalogeropoulos, Konstantia Moirogiorgou

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The present study proposes a methodology for the efficient daily management of fleet vehicles and construction machinery. The application covers the area of remote monitoring of heavy-duty vehicles operation parameters, where specific sensor data are stored and examined in order to provide information about the vehicle’s health. The vehicle diagnostics allow the user to inspect whether maintenance tasks need to be performed before a fault occurs. A properly designed machine learning model is proposed for the detection of two different types of faults through classification. Cross validation is used and the accuracy of the trained model is checked with the confusion matrix.

Keywords: Fault detection, feature selection, machine learning, predictive maintenance.

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Authors: Livier Serna, Xavier Fischer, Fouad Bennis

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In this paper, a decision aid method for preoptimization is presented. The method is called “negotiation", and it is based on the identification, formulation, modeling and use of indicators defined as “negotiation indicators". These negotiation indicators are used to explore the solution space by means of a classbased approach. The classes are subdomains for the negotiation indicators domain. They represent equivalent cognitive solutions in terms of the negotiation indictors being used. By this method, we reduced the size of the solution space and the criteria, thus aiding the optimization methods. We present an example to show the method.

Keywords: Optimization Model Reduction, Pre-Optimization, Negotiation Process, Class-Making, Cognition Based VirtualExploration.

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Authors: Hyun-Koo Kim, Sangmoon Lee, Ho-Youl Jung, Ju H. Park

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We present a system that finds road boundaries and constructs the virtual lane based on fusion data from a laser and a monocular sensor, and detects forward vehicle position even in no lane markers or bad environmental conditions. When the road environment is dark or a lot of vehicles are parked on the both sides of the road, it is difficult to detect lane and road boundary. For this reason we use fusion of laser and vision sensor to extract road boundary to acquire three dimensional data. We use parabolic road model to calculate road boundaries which is based on vehicle and sensors state parameters and construct virtual lane. And then we distinguish vehicle position in each lane.

Keywords: Vehicle Detection, Adaboost, Haar-like Feature, Road Boundary Detection

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Authors: I. L. Ahmad, M. Mohamed, N. A. Ab. Ghani

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This paper presents the work of signal discrimination specifically for Electrocardiogram (ECG) waveform. ECG signal is comprised of P, QRS, and T waves in each normal heart beat to describe the pattern of heart rhythms corresponds to a specific individual. Further medical diagnosis could be done to determine any heart related disease using ECG information. The emphasis on QRS Complex classification is further discussed to illustrate the importance of it. Pan-Tompkins Algorithm, a widely known technique has been adapted to realize the QRS Complex classification process. There are eight steps involved namely sampling, normalization, low pass filter, high pass filter (build a band pass filter), derivation, squaring, averaging and lastly is the QRS detection. The simulation results obtained is represented in a Graphical User Interface (GUI) developed using MATLAB.

Keywords: ECG, Pan Tompkins Algorithm, QRS Complex, Simulation

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Authors: Eugene Y. C. Wong, Henry Y. K. Lau, Mardjuki Raman

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CO₂ emissions from maritime transport operations represent a substantial part of the total greenhouse gas emission. Vessels are designed with better energy efficiency. Minimizing CO₂ emission in maritime operations plays an important role in supply chain decarbonisation. This paper reviews the initiatives on slow steaming operations towards the reduction of carbon emission. It investigates the relationship and impact among slow steaming cost reduction, carbon emission reduction, and shipment delay. A scenario-based cost-driven decision support model is developed to facilitate the selection of the optimal slow steaming options, considering the cost on bunker fuel consumption, available speed, carbon emission, and shipment delay. The incorporation of the social cost of cargo is reviewed and suggested. Additional measures on the effect of vessels sizes, routing, and type of fuels towards decarbonisation are discussed.

Keywords: Slow steaming, carbon emission, maritime logistics, sustainability, green supply chain.

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Authors: Seyed Mostafa Torabi

Abstract:

A Wireless sensor network (WSN) consists of a set of battery-powered nodes, which collaborate to perform sensing tasks in a given environment. Each node in WSN should be capable to act for long periods of time with scrimpy or no external management. One requirement for this independent is: in the presence of adverse positions, the sensor nodes must be capable to configure themselves. Hence, the nodes for determine the existence of unusual events in their surroundings should make use of position awareness mechanisms. This work approaches the problem by considering the possible unusual events as diseases, thus making it possible to diagnose them through their symptoms, namely, their side effects. Considering these awareness mechanisms as a foundation for highlevel monitoring services, this paper also shows how these mechanisms are included in the primal plan of an intrusion detection system.

Keywords: Awareness Mechanism, Intrusion Detection, Independent, Wireless Sensor Network

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Authors: Yiqin Lin, Wenbo Li

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Dimensionality reduction and feature extraction are of crucial importance for achieving high efficiency in manipulating the high dimensional data. Two-dimensional discriminant locality preserving projection (2D-DLPP) and two-dimensional discriminant supervised LPP (2D-DSLPP) are two effective two-dimensional projection methods for dimensionality reduction and feature extraction of face image matrices. Since 2D-DLPP and 2D-DSLPP preserve the local structure information of the original data and exploit the discriminant information, they usually have good recognition performance. However, 2D-DLPP and 2D-DSLPP only employ single-sided projection, and thus the generated low dimensional data matrices have still many features. In this paper, by combining the discriminant supervised LPP with the bidirectional projection, we propose the bidirectional discriminant supervised LPP (BDSLPP). The left and right projection matrices for BDSLPP can be computed iteratively. Experimental results show that the proposed BDSLPP achieves higher recognition accuracy than 2D-DLPP, 2D-DSLPP, and bidirectional discriminant LPP (BDLPP).

Keywords: Face recognition, dimension reduction, locality preserving projection, discriminant information, bidirectional projection.

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Authors: S. Swain, P. S. Khuntia

Abstract:

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

Keywords: Convex Optimization, Kharitonov Stability Criterion, Model Reduction, Robust Stability.

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