Search results for: Estimation algorithms

Authors: Hongkui Li, Tongli Lu , Jianwu Zhang

Abstract:

This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.

Keywords: Clutch drag torque, wet DCT, dynamic viscosity, recursive least squares.

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Authors: Taeung Yoon, Youngpo Lee, Chonghan Song, Na Young Ha, Seokho Yoon

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Ren et al. presented an efficient carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM), which has an estimation range as large as the bandwidth of the OFDM signal and achieves high accuracy without any constraint on the structure of the training sequence. However, its detection probability of the integer frequency offset (IFO) rapidly varies according to the fractional frequency offset (FFO) change. In this paper, we first analyze the Ren-s method and define two criteria suitable for detection of IFO. Then, we propose a novel method for the IFO estimation based on the maximum-likelihood (ML) principle and the detection criteria defined in this paper. The simulation results demonstrate that the proposed method outperforms the Ren-s method in terms of the IFO detection probability irrespective of a value of the FFO.

Keywords: Orthogonal frequency division multiplexing, integer frequency offset, estimation, training symbol

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Authors: Mahmoud R. Shaghaghian

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Genetic Algorithms (GAs) are direct searching methods which require little information from design space. This characteristic beside robustness of these algorithms makes them to be very popular in recent decades. On the other hand, while this method is employed, there is no guarantee to achieve optimum results. This obliged designer to run such algorithms more than one time to achieve more reliable results. There are many attempts to modify the algorithms to make them more efficient. In this paper, by application of fractal dimension (particularly, Box Counting Method), the complexity of design space are established for determination of mutation and crossover probabilities (Pm and Pc). This methodology is followed by a numerical example for more clarification. It is concluded that this modification will improve efficiency of GAs and make them to bring about more reliable results especially for design space with higher fractal dimensions.

Keywords: Genetic Algorithm, Fractal Dimension, BoxCounting Method, Weierstrass-Mandelbrot function.

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Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.

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Authors: Pradya Pornnimitkul, Suwich Kunaruttanapruk, Bamrung Tau Sieskul, Somchai Jitapunkul

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In this paper, we investigate a blind channel estimation method for Multi-carrier CDMA systems that use a subspace decomposition technique. This technique exploits the orthogonality property between the noise subspace and the received user codes to obtain channel of each user. In the past we used Singular Value Decomposition (SVD) technique but SVD have most computational complexity so in this paper use a new algorithm called URV Decomposition, which serve as an intermediary between the QR decomposition and SVD, replaced in SVD technique to track the noise space of the received data. Because of the URV decomposition has almost the same estimation performance as the SVD, but has less computational complexity.

Keywords: Channel estimation, MC-CDMA, SVD, URV.

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Authors: Marco Intelvi, Apolinar Picado, Joaquín Martínez

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In this work, simulation algorithms for contact drying of agitated particulate materials under vacuum and at atmospheric pressure were developed. The implementation of algorithms gives a predictive estimation of drying rate curves and bulk bed temperature during contact drying. The calculations are based on the penetration model to describe the drying process, where all process parameters such as heat and mass transfer coefficients, effective bed properties, gas and liquid phase properties are estimated with proper correlations. Simulation results were compared with experimental data from the literature. In both cases, simulation results were in good agreement with experimental data. Few deviations were identified and the limitations of the predictive capabilities of the models are discussed. The programs give a good insight of the drying behaviour of the analysed powders.

Keywords: Agitated bed, Atmospheric pressure, Penetrationmodel, Vacuum

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Authors: Karandeep Singh, Baibing Li

Abstract:

Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, control systems, observer systems, unscented Kalman filter, nonlinear vehicle dynamics.

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Authors: Sepehr Aslani, Homayoun Mahdavi-Nasab

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Automated motion detection and tracking is a challenging task in traffic surveillance. In this paper, a system is developed to gather useful information from stationary cameras for detecting moving objects in digital videos. The moving detection and tracking system is developed based on optical flow estimation together with application and combination of various relevant computer vision and image processing techniques to enhance the process. To remove noises, median filter is used and the unwanted objects are removed by applying thresholding algorithms in morphological operations. Also the object type restrictions are set using blob analysis. The results show that the proposed system successfully detects and tracks moving objects in urban videos.

Keywords: Optical flow estimation, moving object detection, tracking, morphological operation, blob analysis.

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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: Ramin Javadzadeh., Zahra Afsahi, MohammadReza Meybodi

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The Artificial immune systems algorithms are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Artificial Immune System Algorithm is introduced for the first time to overcome its problems of artificial immune system. That use of the small size of a local search around the memory antibodies is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the standard artificial immune system algorithms

Keywords: Artificial immune system, Cellular Automata, Cellular learning automata, Cellular learning automata, , Local search, Optimization.

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Authors: Hyeon-Cheol Lee

Abstract:

The adaptive power control of Code Division Multiple Access (CDMA) communications using Remote Radio Head (RRH) between multiple Unmanned Aerial Vehicles (UAVs) with a link-budget based Signal-to-Interference Ratio (SIR) estimate is applied to four inner loop power control algorithms. It is concluded that Base Station (BS) can calculate not only UAV distance using linearity between speed and Consecutive Transmit-Power-Control Ratio (CTR) of Adaptive Step-size Closed Loop Power Control (ASCLPC), Consecutive TPC Ratio Step-size Closed Loop Power Control (CS-CLPC), Fixed Step-size Power Control (FSPC), but also UAV position with Received Signal Strength Indicator (RSSI) ratio of RRHs.

Keywords: speed estimation, adaptive power control, link-budget, SIR, multi-bit quantizer, RRH

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: Karima Siham Aoubid, Mohamed Boulemden

Abstract:

The development of the signal compression algorithms is having compressive progress. These algorithms are continuously improved by new tools and aim to reduce, an average, the number of bits necessary to the signal representation by means of minimizing the reconstruction error. The following article proposes the compression of Arabic speech signal by a hybrid method combining the wavelet transform and the linear prediction. The adopted approach rests, on one hand, on the original signal decomposition by ways of analysis filters, which is followed by the compression stage, and on the other hand, on the application of the order 5, as well as, the compression signal coefficients. The aim of this approach is the estimation of the predicted error, which will be coded and transmitted. The decoding operation is then used to reconstitute the original signal. Thus, the adequate choice of the bench of filters is useful to the transform in necessary to increase the compression rate and induce an impercevable distortion from an auditive point of view.

Keywords: Compression, linear prediction analysis, multiresolution analysis, speech signal.

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Authors: C. Rajan, K. Geetha, C. Rasi Priya, R. Sasikala

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Nature is a great source of inspiration for solving complex problems in networks. It helps to find the optimal solution. Metaheuristic algorithm is one of the nature-inspired algorithm which helps in solving routing problem in networks. The dynamic features, changing of topology frequently and limited bandwidth make the routing, challenging in MANET. Implementation of appropriate routing algorithms leads to the efficient transmission of data in mobile ad hoc networks. The algorithms that are inspired by the principles of naturally-distributed/collective behavior of social colonies have shown excellence in dealing with complex optimization problems. Thus some of the bio-inspired metaheuristic algorithms help to increase the efficiency of routing in ad hoc networks. This survey work presents the overview of bio-inspired metaheuristic algorithms which support the efficiency of routing in mobile ad hoc networks.

Keywords: Ant colony optimization algorithm, Genetic algorithm, naturally inspired algorithms and particle swarm optimization algorithm.

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Authors: M. Soryani, N. Rafat

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Dealing with hundreds of features in character recognition systems is not unusual. This large number of features leads to the increase of computational workload of recognition process. There have been many methods which try to remove unnecessary or redundant features and reduce feature dimensionality. Besides because of the characteristics of Farsi scripts, it-s not possible to apply other languages algorithms to Farsi directly. In this paper some methods for feature subset selection using genetic algorithms are applied on a Farsi optical character recognition (OCR) system. Experimental results show that application of genetic algorithms (GA) to feature subset selection in a Farsi OCR results in lower computational complexity and enhanced recognition rate.

Keywords: Feature Subset Selection, Genetic Algorithms, Optical Character Recognition.

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Authors: Roelien Goede

Abstract:

Data Structures and Algorithms is a module in most Computer Science or Information Technology curricula. It is one of the modules most students identify as being difficult. This paper demonstrates how programming a solution for Sudoku can make abstract concepts more concrete. The paper relates concepts of a typical Data Structures and Algorithms module to a step by step solution for Sudoku in a human type as opposed to a computer oriented solution.

Keywords: Data Structures, Algorithms, Sudoku, ObjectOriented Programming, Programming Teaching, Education.

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Authors: T. Song, T. Shimamoto

Abstract:

In this paper a fast motion estimation method for H.264/AVC named Triplet Search Motion Estimation (TS-ME) is proposed. Similar to some of the traditional fast motion estimation methods and their improved proposals which restrict the search points only to some selected candidates to decrease the computation complexity, proposed algorithm separate the motion search process to several steps but with some new features. First, proposed algorithm try to search the real motion area using proposed triplet patterns instead of some selected search points to avoid dropping into the local minimum. Then, in the localized motion area a novel 3-step motion search algorithm is performed. Proposed search patterns are categorized into three rings on the basis of the distance from the search center. These three rings are adaptively selected by referencing the surrounding motion vectors to early terminate the motion search process. On the other hand, computation reduction for sub pixel motion search is also discussed considering the appearance probability of the sub pixel motion vector. From the simulation results, motion estimation speed improved by a factor of up to 38 when using proposed algorithm than that of the reference software of H.264/AVC with ignorable picture quality loss.

Keywords: Motion estimation, VLSI, image processing, search patterns

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Authors: J. Arneric, A. Rozga

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In this paper usefulness of quasi-Newton iteration procedure in parameters estimation of the conditional variance equation within BHHH algorithm is presented. Analytical solution of maximization of the likelihood function using first and second derivatives is too complex when the variance is time-varying. The advantage of BHHH algorithm in comparison to the other optimization algorithms is that requires no third derivatives with assured convergence. To simplify optimization procedure BHHH algorithm uses the approximation of the matrix of second derivatives according to information identity. However, parameters estimation in a/symmetric GARCH(1,1) model assuming normal distribution of returns is not that simple, i.e. it is difficult to solve it analytically. Maximum of the likelihood function can be founded by iteration procedure until no further increase can be found. Because the solutions of the numerical optimization are very sensitive to the initial values, GARCH(1,1) model starting parameters are defined. The number of iterations can be reduced using starting values close to the global maximum. Optimization procedure will be illustrated in framework of modeling volatility on daily basis of the most liquid stocks on Croatian capital market: Podravka stocks (food industry), Petrokemija stocks (fertilizer industry) and Ericsson Nikola Tesla stocks (information-s-communications industry).

Keywords: Heteroscedasticity, Log-likelihood Maximization, Quasi-Newton iteration procedure, Volatility.

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Authors: Somayeh Komeylian

Abstract:

The direction of arrival (DoA) estimation is the crucial aspect of the radar technologies for detecting and dividing several signal sources. In this scenario, the antenna array output modeling involves numerous parameters including noise samples, signal waveform, signal directions, signal number, and signal to noise ratio (SNR), and thereby the methods of the DoA estimation rely heavily on the generalization characteristic for establishing a large number of the training data sets. Hence, we have analogously represented the two different optimization models of the DoA estimation; (1) the implementation of the decision directed acyclic graph (DDAG) for the multiclass least-squares support vector machine (LS-SVM), and (2) the optimization method of the deep neural network (DNN) radial basis function (RBF). We have rigorously verified that the LS-SVM DDAG algorithm is capable of accurately classifying DoAs for the three classes. However, the accuracy and robustness of the DoA estimation are still highly sensitive to technological imperfections of the antenna arrays such as non-ideal array design and manufacture, array implementation, mutual coupling effect, and background radiation and thereby the method may fail in representing high precision for the DoA estimation. Therefore, this work has a further contribution on developing the DNN-RBF model for the DoA estimation for overcoming the limitations of the non-parametric and data-driven methods in terms of array imperfection and generalization. The numerical results of implementing the DNN-RBF model have confirmed the better performance of the DoA estimation compared with the LS-SVM algorithm. Consequently, we have analogously evaluated the performance of utilizing the two aforementioned optimization methods for the DoA estimation using the concept of the mean squared error (MSE).

Keywords: DoA estimation, adaptive antenna array, Deep Neural Network, LS-SVM optimization model, radial basis function, MSE.

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Authors: S. Prabha, K. Duraiswamy, J. Indhumathi

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Search engine plays an important role in internet, to retrieve the relevant documents among the huge number of web pages. However, it retrieves more number of documents, which are all relevant to your search topics. To retrieve the most meaningful documents related to search topics, ranking algorithm is used in information retrieval technique. One of the issues in data miming is ranking the retrieved document. In information retrieval the ranking is one of the practical problems. This paper includes various Page Ranking algorithms, page segmentation algorithms and compares those algorithms used for Information Retrieval. Diverse Page Rank based algorithms like Page Rank (PR), Weighted Page Rank (WPR), Weight Page Content Rank (WPCR), Hyperlink Induced Topic Selection (HITS), Distance Rank, Eigen Rumor, Distance Rank Time Rank, Tag Rank, Relational Based Page Rank and Query Dependent Ranking algorithms are discussed and compared.

Keywords: Information Retrieval, Web Page Ranking, search engine, web mining, page segmentations.

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Authors: Seda Yavuz, Anıl Çelebi, Aysun Taşyapı Çelebi, Oğuzhan Urhan

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Nowadays, demand for using real-time video transmission capable devices is ever-increasing. So, high resolution videos have made efficient video compression techniques an essential component for capturing and transmitting video data. Motion estimation has a critical role in encoding raw video. Hence, various motion estimation methods are introduced to efficiently compress the video. Low bit‑depth representation based motion estimation methods facilitate computation of matching criteria and thus, provide small hardware footprint. In this paper, a hardware implementation of a two-bit transformation based low-complexity motion estimation method using local binary pattern approach is proposed. Image frames are represented in two-bit depth instead of full-depth by making use of the local binary pattern as a binarization approach and the binarization part of the hardware architecture is explained in detail. Experimental results demonstrate the difference between the proposed hardware architecture and the architectures of well-known low-complexity motion estimation methods in terms of important aspects such as resource utilization, energy and power consumption.

Keywords: Binarization, hardware architecture, local binary pattern, motion estimation, two-bit transform.

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Authors: Najmeh Abedzadeh, Matthew Jacobs

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An intrusion detection system (IDS) is a software application that monitors malicious activities and generates alerts if any are detected. However, most network activities in IDS datasets are normal, and the relatively few numbers of attacks make the available data imbalanced. Consequently, cyber-attacks can hide inside a large number of normal activities, and machine learning algorithms have difficulty learning and classifying the data correctly. In this paper, a comprehensive literature review is conducted on different types of algorithms for both implementing the IDS and methods in correcting the imbalanced IDS dataset. The most famous algorithms are machine learning (ML), deep learning (DL), synthetic minority over-sampling technique (SMOTE), and reinforcement learning (RL). Most of the research use the CSE-CIC-IDS2017, CSE-CIC-IDS2018, and NSL-KDD datasets for evaluating their algorithms.

Keywords: IDS, intrusion detection system, imbalanced datasets, sampling algorithms, big data.

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Authors: Nazleeni Samiha Haron, Anang Hudaya Muhamad Amin, Mohd Hilmi Hasan, Izzatdin Abdul Aziz, Wirdhayu Mohd Wahid

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In any distributed systems, process scheduling plays a vital role in determining the efficiency of the system. Process scheduling algorithms are used to ensure that the components of the system would be able to maximize its utilization and able to complete all the processes assigned in a specified period of time. This paper focuses on the development of comparative simulator for distributed process scheduling algorithms. The objectives of the works that have been carried out include the development of the comparative simulator, as well as to implement a comparative study between three distributed process scheduling algorithms; senderinitiated, receiver-initiated and hybrid sender-receiver-initiated algorithms. The comparative study was done based on the Average Waiting Time (AWT) and Average Turnaround Time (ATT) of the processes involved. The simulation results show that the performance of the algorithms depends on the number of nodes in the system.

Keywords: Distributed Systems, Load Sharing, Process Scheduling, AWT and ATT

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Authors: Felix Baumann, Aleksandar Milutinovic, Dieter Roller

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Up to this point business process management projects in general and business process modelling projects in particular could not rely on a practical and scientifically validated method to estimate cost and effort. Especially the model development phase is not covered by a cost estimation method or model. Further phases of business process modelling starting with implementation are covered by initial solutions which are discussed in the literature. This article proposes a method of filling this gap by deriving a cost estimation method from available methods in similar domains namely software development or software engineering. Software development is regarded as closely similar to process modelling as we show. After the proposition of this method different ideas for further analysis and validation of the method are proposed. We derive this method from COCOMO II and Function Point which are established methods of effort estimation in the domain of software development. For this we lay out similarities of the software development process and the process of process modelling which is a phase of the Business Process Management life-cycle.

Keywords: Cost Estimation, Effort Estimation, Process Modelling, Business Process Management, COCOMO.

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Authors: Abdolreza Hatamlou, Yusef Farhang, Mohammad Reza Meybodi

Abstract:

Variable ordering heuristics are used in constraint satisfaction algorithms. Different characteristics of various variable ordering heuristics are complementary. Therefore we have tried to get the advantages of all heuristics to improve search algorithms performance for solving constraint satisfaction problems. This paper considers combinations based on products and quotients, and then a newer form of combination based on weighted sums of ratings from a set of base heuristics, some of which result in definite improvements in performance.

Keywords: Constraint Satisfaction Problems, Variable Ordering Heuristics, Combination, Search Algorithms

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Authors: Fituri H Belgassem, Abdulbasit Nigrat, Seddeeq Ghrari

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In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

Keywords: Piece wise linear transforms, Fast transforms, Fast algorithms.

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Authors: Adil Salam, Nadia Bhuiyan, Gerard J. Gouw

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The Canadian aerospace industry faces many challenges. One of them is the difficulty in estimating costs. In particular, the design effort required in a project impacts resource requirements and lead-time, and consequently the final cost. This paper presents the findings of a case study conducted for recognized global leader in the design and manufacturing of aircraft engines. The study models parametric cost estimation relationships to estimate the design effort of integrated blade-rotor low-pressure compressor fans. Several effort drivers are selected to model the relationship. Comparative analyses of three types of models are conducted. The model with the best accuracy and significance in design estimation is retained.

Keywords: Effort estimation, design, aerospace.

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

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This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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