Search results for: localization average error

Authors: Kelong Zheng, Jinsong Hu,

Abstract:

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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Authors: Jalal Karam

Abstract:

In real-field applications, the correct determination of voice segments highly improves the overall system accuracy and minimises the total computation time. This paper presents reliable measures of speech compression by detcting the end points of the speech signals prior to compressing them. The two different compession schemes used are the Global threshold and the Level- Dependent threshold techniques. The performance of the proposed method is tested wirh the Signal to Noise Ratios, Peak Signal to Noise Ratios and Normalized Root Mean Square Error parameter measures.

Keywords: Wavelets, End-points Detection, Compression.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Sulaiman Yunus

Abstract:

The need for modeling response to urban fire disaster cannot be over emphasized, as recurrent fire outbreaks have gutted most cities of the world. This necessitated the need for a prompt and efficient response system in order to mitigate the impact of the disaster. Promptness, as a function of time, is seen to be the fundamental determinant for efficiency of a response system and magnitude of a fire disaster. Delay, as a result of several factors, is one of the major determinants of promptgness of a response system and also the magnitude of a fire disaster. Response Delay Model (RDM) intends to bridge the gap in urban fire disaster response system through incorporating and synchronizing the delay moments in measuring the overall efficiency of a response system and determining the magnitude of a fire disaster. The model identified two delay moments (pre-notification and Intra-reflex sequence delay) that can be elastic and collectively plays a significant role in influencing the efficiency of a response system. Due to variation in the elasticity of the delay moments, the model provides for measuring the length of delays in order to arrive at a standard average delay moment for different parts of the world, putting into consideration geographic location, level of preparedness and awareness, technological advancement, socio-economic and environmental factors. It is recommended that participatory researches should be embarked on locally and globally to determine standard average delay moments within each phase of the system so as to enable determining the efficiency of response systems and predicting fire disaster magnitudes.

Keywords: Delay moment, fire disaster, reflex sequence, response, response delay moment.

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Authors: Rujijan Vichivanives

Abstract:

This research aims to create a knowledge-based system as a database for self-healthcare analysis, diagnosis of simple illnesses, and the use of Thai herbs instead of modern medicine by using principles of Thai traditional medication theory. These were disseminated by website network programs within Suan Sunandha Rajabhat University. The population used in this study was divided into two groups: the first group consisted of four experts of Thai traditional medication and the second group was 300 website users. The methods used for collecting data were paper questionnaires and poll questionnaires on the website. The statistics used for analyzing data was at an average level. The results were divided into three parts: the first part was the development of a knowledge-based system and the second part was applied programs on website. Both parts could be fulfilled and achieved according to the set goal. The third part was the evaluation of the study: The evaluation of the viewpoints of the experts towards website designs were evaluated at a good level of 4.20. The satisfaction evaluation of the users was found at a good level of average satisfactory level at 4.24. It was found that the young population of those under the age of 16 had less cares about their health than the population of other teenagers, working age adults and those of older age. The research findings should be extended in order to encourage the lifestyle modifications to people of all ages by using the self-healthcare principles.

Keywords: Developing, Herbs, Knowledge-based system, Medical treatment.

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Authors: Jun Su Ha

Abstract:

Various advanced technologies will be adopted in Advanced Control Rooms (ACRs) of advanced Nuclear Power Plants (NPPs), which is thought to increase operators’ performance. However, potential human factors issues coupled with digital technologies might be troublesome. Human factors issues in ACRs are identified and strategies (or countermeasures) for evaluating and analyzing each of issues are addressed in this study.

 

Keywords: Advanced control room, human factor issues, human performance, human error, nuclear power plant.

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Authors: S. H. Oudjana, A. Hellal, I. Hadj Mahammed

Abstract:

Photovoltaic power generation forecasting is an important task in renewable energy power system planning and operating. This paper explores the application of neural networks (NN) to study the design of photovoltaic power generation forecasting systems for one week ahead using weather databases include the global irradiance, and temperature of Ghardaia city (south of Algeria) using a data acquisition system. Simulations were run and the results are discussed showing that neural networks Technique is capable to decrease the photovoltaic power generation forecasting error.

Keywords: Photovoltaic Power Forecasting, Regression, Neural Networks.

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Authors: Bhavneet Sidhu, Hardeep Singh, Amit Chhabra

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The world of wireless telecommunications is rapidly evolving. Technologies under research and development promise to deliver more services to more users in less time. This paper presents the emerging technologies helping wireless systems grow from where we are today into our visions of the future. This paper will cover the applications and characteristics of emerging wireless technologies: Wireless Local Area Networks (WiFi-802.11n), Wireless Personal Area Networks (ZigBee) and Wireless Metropolitan Area Networks (WiMAX). The purpose of this paper is to explain the impending 802.11n standard and how it will enable WLANs to support emerging media-rich applications. The paper will also detail how 802.11n compares with existing WLAN standards and offer strategies for users considering higher-bandwidth alternatives. The emerging IEEE 802.15.4 (ZigBee) standard aims to provide low data rate wireless communications with high-precision ranging and localization, by employing UWB technologies for a low-power and low cost solution. WiMAX (Worldwide Interoperability for Microwave Access) is a standard for wireless data transmission covering a range similar to cellular phone towers. With high performance in both distance and throughput, WiMAX technology could be a boon to current Internet providers seeking to become the leader of next generation wireless Internet access. This paper also explores how these emerging technologies differ from one another.

Keywords: MIMO technology, WiFi, WiMAX, ZigBee.

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Authors: J. H. Park, S. C. Jeong, J. H. Koo, H. Y. Jung, S. M. Lee

Abstract:

We propose an integral tracking control method for a piezoelectric actuator system. The proposed method achieves the output tracking without requiring any hysteresis observer or schemes to compensate the hysteresis effect. With the proposed control law, the system is converted into the standard singularly perturbed model. Using Tikhonov-s theorem, we guarantee that the tracking error can be reduced to arbitrarily small bound. A numerical example is given to illustrate the effectiveness of our proposed method.

Keywords: Piezoelectric actuator, tracking control, hysteresis effect.

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Authors: Biao Qin, Jin Huang

Abstract:

In this paper, together with some improved Lyapunov-Krasovskii functional and effective mathematical techniques, several sufficient conditions are derived to guarantee the error system is globally asymptotically stable with H∞ performance, in which both the time-delay and its time variation can be fully considered. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. A numerical example is provided to illustrate the usefulness and effectiveness of the obtained results.

Keywords: H∞ performance, Neural networks, State estimation.

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Authors: Shagufta Tabassum

Abstract:

The study of dielectric properties in a binary mixture of liquids is very useful to understand the liquid structure, molecular interaction, dynamics, and kinematics of the mixture. Time-domain reflectometry (TDR) is a powerful tool for studying the cooperation and molecular dynamics of the H-bonded system. Here we discuss the basic calibration and normalization procedure for TDR measurements. Our aim is to explain different types of error occur during TDR measurements and how to minimize it.

Keywords: time domain reflectometry measurement technique, cable and connector loss, oscilloscope loss, normalization technique

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Authors: J. S. Kim

Abstract:

This paper presents a 0.13-µm Complementary Metal-Oxide Semiconductor (CMOS) vector modulator for beamforming system. The vector modulator features a 360° phase and gain range of -10 dB to 10 dB with a root mean square phase and amplitude error of only 2.2° and 0.45 dB, respectively. These features make it a suitable for wireless backhaul system in the 5 GHz industrial, scientific, and medical (ISM) bands. It draws a current of 20.4 mA from a 1.2 V supply. The total chip size is 1.87x1.34 mm².

Keywords: CMOS, vector modulator, beamforming, wireless backhaul, ISM.

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Authors: M. Israil Hossain, T. P. Tiwari, Ashrafuzzaman Gulandaz, Nusrat Jahan

Abstract:

Two-wheel tractor (power tiller) is a common tillage tool in Bangladesh agriculture for easy access in fragmented land with affordable price of small farmers. Traditional maize sheller needs to be carried from place to place by hooking with two-wheel tractor (2WT) and set up again for shelling operation which takes longer time for preparation of maize shelling. The mobile maize sheller eliminates the transportation problem and can start shelling operation instantly any place as it is attached together with 2WT. It is counterclockwise rotating cylinder, axial flow type sheller, and grain separated with a frictional force between spike tooth and concave. The maize sheller is attached with nuts and bolts in front of the engine base of 2WT. The operating power of the sheller comes from the fly wheel of the engine of the tractor through ‘V” belt pulley arrangement. The average shelling capacity of the mobile sheller is 2.0 t/hr, broken kernel 2.2%, and shelling efficiency 97%. The average maize shelling cost is Tk. 0.22/kg and traditional custom hire rate is Tk.1.0/kg, respectively (1 US$=Tk.78.0). The service provider of the 2WT can transport the mobile maize sheller long distance in operator’s seating position. The manufacturers started the fabrication of mobile maize sheller. This mobile maize sheller is also compatible for the other countries where 2WT is available for farming operation.

Keywords: Cost effective, mobile maize sheller, maize shelling capacity, small farmers, two-wheel tractor.

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Authors: Youngpo Lee, Sanghun Kim, Youngyoon Lee, Seokho Yoon

Abstract:

Due to its capability to resist jamming signals, chirp spread spectrum (CSS) technique has attracted much attention in the area of wireless communications. However, there has been little rigorous analysis for the performance of the CSS communication system in jamming environments. In this paper, we present analytic results on the performance of a CSS system by deriving symbol error rate (SER) expressions for a CSS M-ary phase shift keying (MPSK) system in the presence of broadband and tone jamming signals, respectively. The numerical results show that the empirical SER closely agrees with the analytic result.

Keywords: CSS, DM, jamming, broadband jamming, tone jamming.

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Authors: Ali Fadhil Naser, Wang Zonglin

Abstract:

The main objectives of this study are to inspect and identify any damage of jaimusi highway prestressed concrete bridge after repair and strengthening of damaged structural members and to evaluate the performance of the bridge structural members by adopting static load test. Inspection program after repair and strengthening includes identifying and evaluating the structural members of bridge such as T-shape cantilever structure, hanging beams, corbels, external tendons, anchor beams, sticking steel plate, and piers. The results of inspection show that the overall state of the bridge structural member after repair and strengthening is good. The results of rebound test of concrete strength show that the average strength of concrete is 46.31Mpa. Whereas, the average value of concrete strength of anchor beam is 49.82Mpa. According to the results of static load test, the experimental values are less than theoretical values of internal forces, deflection, and strain, indicating that the stiffness of the experimental structure, overall deformation and integrity satisfy the designed standard and the working performance is good, and the undertaking capacity has a certain surplus. There is not visible change in the length and width of cracks and there are not new cracks under experimental load.

Keywords: Jiamusi Bridge, Damage inspection, deflection, strain.

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Authors: M. A. Masnadi-Shirazi, S. A. Banani

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In this paper a comprehensive algorithm is presented to alleviate the undesired simultaneous effects of target maneuvering, observed glint noise distribution, and colored noise spectrum using online colored glint noise parameter estimation. The simulation results illustrate a significant reduction in the root mean square error (RMSE) produced by the proposed algorithm compared to the algorithms that do not compensate all the above effects simultaneously.

Keywords: Glint noise, IMM, Kalman Filter, Kinematics, Target Tracking.

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Authors: Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine

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This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Keywords: Gauss-Legendre, Clenshaw-Curtis, quadrature, Peano kernel, irregular sampling.

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Authors: C. B. Vishwakarma

Abstract:

The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature.

Keywords: Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error.

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Authors: Shuki Dror

Abstract:

This work discusses an innovative methodology for deployment of service quality characteristics. Four groups of organizational features that may influence the quality of services are identified: human resource, technology, planning, and organizational relationships. A House of Service Quality (HOSQ) matrix is built to extract the desired improvement in the service quality characteristics and to translate them into a hierarchy of important organizational features. The Mean Square Error (MSE) criterion enables the pinpointing of the few essential service quality characteristics to be improved as well as selection of the vital organizational features. The method was implemented in an engineering supply enterprise and provides useful information on its vital service dimensions.

Keywords: HOQ, organizational features, service quality.

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Authors: Sorin Soviany, Cristina Soviany, Mariana Jurian

Abstract:

The paper presents a multimodal approach for biometric authentication, based on multiple classifiers. The proposed solution uses a post-classification biometric fusion method in which the biometric data classifiers outputs are combined in order to improve the overall biometric system performance by decreasing the classification error rates. The paper shows also the biometric recognition task improvement by means of a carefully feature selection, as much as not all of the feature vectors components support the accuracy improvement.

Keywords: biometric fusion, multiple classifiers

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Authors: A. Chowdhury, P. Egodawatta, J. M. McGree, A. Goonetilleke

Abstract:

Hydrologic models are increasingly used as tools to predict stormwater quantity and quality from urban catchments. However, due to a range of practical issues, most models produce gross errors in simulating complex hydraulic and hydrologic systems. Difficulty in finding a robust approach for model calibration is one of the main issues. Though automatic calibration techniques are available, they are rarely used in common commercial hydraulic and hydrologic modelling software e.g. MIKE URBAN. This is partly due to the need for a large number of parameters and large datasets in the calibration process. To overcome this practical issue, a framework for automatic calibration of a hydrologic model was developed in R platform and presented in this paper. The model was developed based on the time-area conceptualization. Four calibration parameters, including initial loss, reduction factor, time of concentration and time-lag were considered as the primary set of parameters. Using these parameters, automatic calibration was performed using Approximate Bayesian Computation (ABC). ABC is a simulation-based technique for performing Bayesian inference when the likelihood is intractable or computationally expensive to compute. To test the performance and usefulness, the technique was used to simulate three small catchments in Gold Coast. For comparison, simulation outcomes from the same three catchments using commercial modelling software, MIKE URBAN were used. The graphical comparison shows strong agreement of MIKE URBAN result within the upper and lower 95% credible intervals of posterior predictions as obtained via ABC. Statistical validation for posterior predictions of runoff result using coefficient of determination (CD), root mean square error (RMSE) and maximum error (ME) was found reasonable for three study catchments. The main benefit of using ABC over MIKE URBAN is that ABC provides a posterior distribution for runoff flow prediction, and therefore associated uncertainty in predictions can be obtained. In contrast, MIKE URBAN just provides a point estimate. Based on the results of the analysis, it appears as though ABC the developed framework performs well for automatic calibration.

Keywords: Automatic calibration framework, approximate Bayesian computation, hydrologic and hydraulic modelling, MIKE URBAN software, R platform.

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Authors: D.Elleuch, T.Damak

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In this paper, the performance of two adaptive observers applied to interconnected systems is studied. The nonlinearity of systems can be written in a fractional form. The first adaptive observer is an adaptive sliding mode observer for a Lipchitz nonlinear system and the second one is an adaptive sliding mode observer having a filtered error as a sliding surface. After comparing their performances throughout the inverted pendulum mounted on a car system, it was shown that the second one is more robust to estimate the state.

Keywords: Adaptive observer, Lipchitz system, Interconnected fractional nonlinear system, sliding mode.

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Authors: Salah Gariani, Taher Dao, Khaled Jegandi

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Wiper inserts are widely used nowadays, particularly in turning and milling operations, due to their unique geometric characteristics that generate superb surface finish and improve productivity. Wiper inserts can produce double the feed rate while preserving comparable surface roughness compared to that produced by conventional cutting tools. This paper reports an experimental investigation of surface quality generated in the precision dry turning of 6060 Aluminium alloy using conventional and wiper inserts at different cutting conditions. The Taguchi L9 array, Analysis of Means (AOM) and variance (ANOVA) were employed in the development of the experimental design and to optimise the process parameter identified: average surface roughness (Ra). The experimental results show that the wiper inserts substantially improved the surface quality of the machined samples by a factor of two compared to those for the conventional insert under all cutting conditions. The ANOVA and AOM analysis showed that the type of insert is the most significant factor affecting surface roughness, with a Percentage Contribution Ratio (PCR) value of 67.41%. Feed rate also significantly affected surface roughness but contributed less to its variation. No significant difference was found between values of Ra using wiper inserts under dry and wet cooling modes when turning 6060 Aluminium alloy.

Keywords: 6060 Aluminium alloy, conventional and wiper carbide tools, dry turning, average surface roughness.

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Authors: V. Sandeep Kumar, S. Anuradha

Abstract:

The high Peak to Average Power Ratio (PAR) in Filter Bank Multicarrier with Offset Quadrature Amplitude Modulation (FBMC-OQAM) can significantly reduce power efficiency and performance. In this paper, we address the problem of PAPR reduction for FBMC-OQAM systems using Tone Reservation (TR) technique. Due to the overlapping structure of FBMCOQAM signals, directly applying TR schemes of OFDM systems to FBMC-OQAM systems is not effective. We improve the tone reservation (TR) technique by employing sliding window with Active Constellation Extension for the PAPR reduction of FBMC-OQAM signals, called sliding window tone reservation Active Constellation Extension (SW-TRACE) technique. The proposed SW-TRACE technique uses the peak reduction tones (PRTs) of several consecutive data blocks to cancel the peaks of the FBMC-OQAM signal inside a window, with dynamically extending outer constellation points in active(data-carrying) channels, within margin-preserving constraints, in order to minimize the peak magnitude. Analysis and simulation results compared to the existing Tone Reservation (TR) technique for FBMC/OQAM system. The proposed method SW-TRACE has better PAPR performance and lower computational complexity.

Keywords: FBMC-OQAM, peak-to-average power ratio, sliding window, tone reservation Active Constellation Extension.

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Authors: Lily Ingsrisawang, Supawadee Ingsriswang, Saisuda Somchit, Prasert Aungsuratana, Warawut Khantiyanan

Abstract:

This paper presents the methodology from machine learning approaches for short-term rain forecasting system. Decision Tree, Artificial Neural Network (ANN), and Support Vector Machine (SVM) were applied to develop classification and prediction models for rainfall forecasts. The goals of this presentation are to demonstrate (1) how feature selection can be used to identify the relationships between rainfall occurrences and other weather conditions and (2) what models can be developed and deployed for predicting the accurate rainfall estimates to support the decisions to launch the cloud seeding operations in the northeastern part of Thailand. Datasets collected during 2004-2006 from the Chalermprakiat Royal Rain Making Research Center at Hua Hin, Prachuap Khiri khan, the Chalermprakiat Royal Rain Making Research Center at Pimai, Nakhon Ratchasima and Thai Meteorological Department (TMD). A total of 179 records with 57 features was merged and matched by unique date. There are three main parts in this work. Firstly, a decision tree induction algorithm (C4.5) was used to classify the rain status into either rain or no-rain. The overall accuracy of classification tree achieves 94.41% with the five-fold cross validation. The C4.5 algorithm was also used to classify the rain amount into three classes as no-rain (0-0.1 mm.), few-rain (0.1- 10 mm.), and moderate-rain (>10 mm.) and the overall accuracy of classification tree achieves 62.57%. Secondly, an ANN was applied to predict the rainfall amount and the root mean square error (RMSE) were used to measure the training and testing errors of the ANN. It is found that the ANN yields a lower RMSE at 0.171 for daily rainfall estimates, when compared to next-day and next-2-day estimation. Thirdly, the ANN and SVM techniques were also used to classify the rain amount into three classes as no-rain, few-rain, and moderate-rain as above. The results achieved in 68.15% and 69.10% of overall accuracy of same-day prediction for the ANN and SVM models, respectively. The obtained results illustrated the comparison of the predictive power of different methods for rainfall estimation.

Keywords: Machine learning, decision tree, artificial neural network, support vector machine, root mean square error.

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Authors: Amer Ibrahim Falah Al-Omari

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In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.

Keywords: Product estimator, auxiliary variable, simple random sampling, extreme ranked set sampling

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Authors: Young-Seok Choi

Abstract:

We propose two affine projection algorithms (APA) with variable regularization parameter. The proposed algorithms dynamically update the regularization parameter that is fixed in the conventional regularized APA (R-APA) using a gradient descent based approach. By introducing the normalized gradient, the proposed algorithms give birth to an efficient and a robust update scheme for the regularization parameter. Through experiments we demonstrate that the proposed algorithms outperform conventional R-APA in terms of the convergence rate and the misadjustment error.

Keywords: Affine projection, regularization, gradient descent, system identification.

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Authors: Deng Zengming, Wang Mingjiang

Abstract:

As 3D video is explored as a hot research topic in the last few decades, free-viewpoint TV (FTV) is no doubt a promising field for its better visual experience and incomparable interactivity. View synthesis is obviously a crucial technology for FTV; it enables to render images in unlimited numbers of virtual viewpoints with the information from limited numbers of reference view. In this paper, a novel hybrid synthesis framework is proposed and blending priority is explored. In contrast to the commonly used View Synthesis Reference Software (VSRS), the presented synthesis process is driven in consideration of the temporal correlation of image sequences. The temporal correlations will be exploited to produce fine synthesis results even near the foreground boundaries. As for the blending priority, this scheme proposed that one of the two reference views is selected to be the main reference view based on the distance between the reference views and virtual view, another view is chosen as the auxiliary viewpoint, just assist to fill the hole pixel with the help of background information. Significant improvement of the proposed approach over the state-of –the-art pixel-based virtual view synthesis method is presented, the results of the experiments show that subjective gains can be observed, and objective PSNR average gains range from 0.5 to 1.3 dB, while SSIM average gains range from 0.01 to 0.05.

Keywords: View synthesis, Gaussian mixture model, hybrid framework, fusion method.

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Authors: Ruili Zhou, Yuesheng Zhu

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In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.

Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM

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Authors: Seyedvahid Najafi, Viliam Makis

Abstract:

In recent years, maintenance optimization has attracted special attention due to the growth of industrial systems complexity. Maintenance costs are high for many systems, and preventive maintenance is effective when it increases operations' reliability and safety at a reduced cost. The novelty of this research is to consider general repair in the modeling of multi-unit series systems and solve the maintenance problem for such systems using the semi-Markov decision process (SMDP) framework. We propose an opportunistic maintenance policy for a series system composed of two main units. Unit 1, which is more expensive than unit 2, is subjected to condition monitoring, and its deterioration is modeled using a gamma process. Unit 1 hazard rate is estimated by the proportional hazards model (PHM), and two hazard rate control limits are considered as the thresholds of maintenance interventions for unit 1. Maintenance is performed on unit 2, considering an age control limit. The objective is to find the optimal control limits and minimize the long-run expected average cost per unit time. The proposed algorithm is applied to a numerical example to compare the effectiveness of the proposed policy (policy Ⅰ) with policy Ⅱ, which is similar to policy Ⅰ, but instead of general repair, replacement is performed. Results show that policy Ⅰ leads to lower average cost compared with policy Ⅱ. 

Keywords: Condition-based maintenance, proportional hazards model, semi-Markov decision process, two-unit series systems.

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