Search results for: Asymptotic error constant

Authors: Mamoun F. Abdel-Hafez

Abstract:

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: Yukiko Sasaki Alam

Abstract:

This research aims at finding out the causes that led to wrong lexical selections in machine translation (MT) rather than categorizing lexical errors, which has been a main practice in error analysis. By manually examining and analyzing lexical errors outputted by a MT system, it suggests what knowledge would help the system reduce lexical errors.

Keywords: Error analysis, causes of errors, machine translation, outputs evaluation.

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Authors: Miroslav H. Hristov, Velizar A. Vassilev, Georgi K. Dukendjiev

Abstract:

Due to the constant development of measurement systems and the aim for computerization, unavoidable improvements are made for the main disadvantages of air gauges. With the appearance of the air-electronic measuring devices, some of their disadvantages are solved. The output electrical signal allows them to be included in the modern systems for measuring information processing and process management. Producer efforts are aimed at reducing the influence of supply pressure and measurement system setup errors. Increased accuracy requirements and preventive error measures are due to the main uses of air electronic systems - measurement of geometric dimensions in the automotive industry where they are applied as modules in measuring systems to measure geometric parameters, form, orientation and location of the elements.

Keywords: Air-electronic, geometrical parameters, improvement, measurement systems.

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Authors: Liang Zhao, Guangwen Wang, Guichang Liu

Abstract:

Constant potometer is an important component of pipeline anti-corrosion systems in the chemical industry. Based on Internet of Things (IoT) technology, Programmable Logic Controller (PLC) technology and database technology, this paper developed a set of a constant potometer remote monitoring management system. The remote monitoring and remote adjustment of the working status of the constant potometer are realized. The system has real-time data display, historical data query, alarm push management, user permission management, and supporting Web access and mobile client application (APP) access. The actual engineering project test results show the stability of the system, which can be widely used in cathodic protection systems.

Keywords: Internet of Things, pipe corrosion protection, potentiostat, remote monitoring.

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Authors: Hichem Sassi, Tawfik Najeh, Noureddine Liouane

Abstract:

Information of nodes’ locations is an important criterion for lots of applications in Wireless Sensor Networks. In the hop-based range-free localization methods, anchors transmit the localization messages counting a hop count value to the whole network. Each node receives this message and calculates its own distance with anchor in hops and then approximates its own position. However the estimative distances can provoke large error, and affect the localization precision. To solve the problem, this paper proposes an algorithm, which makes the unknown nodes fix the nearest anchor as a reference and select two other anchors which are the most accurate to achieve the estimated location. Compared to the DV-Hop algorithm, experiment results illustrate that proposed algorithm has less average localization error and is more effective.

Keywords: Wireless Sensors Networks, Localization problem, localization average error, DV–Hop Algorithm, MATLAB.

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Authors: Hongyu Wei, Wenliang Chen, Lin Gao

Abstract:

Incremental forming is a complex forming process with continuously local cumulative deformation taking place during its process, and springback that forming quality affected by would occur. The springback evaluation method based on forming error compensation also was proposed, which it can be defined as the difference between theory and the actual amount of compensation along the measured direction. According to forming error compensation evaluation method, experiments was designed and implemented. And from the results that obtained it can be show, the magnitude of springback average (δE) of formed parts was very small, and the forming precision could be significantly improved by adopting compensation method. Based on double tensile stress state in the main deformation area, a hypothesis that there is little springback be arisen by bending behavior on the formed parts that was proposed.

Keywords: Sheet metal, incremental forming, springback, forming error compensation, geometric accuracy

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Authors: Young-San Shin, Seongsoo Lee

Abstract:

Hall sensor is widely used to measure rotation angle. When the Hall voltage is measured for linear displacement, it is converted to angular displacement using arctangent function, which requires a large lookup table. In this paper, a lookup table reduction technique is presented for angle measurement. When the input of the lookup table is small within a certain threshold, the change of the outputs with respect to the change of the inputs is relatively small. Thus, several inputs can share same output, which significantly reduce the lookup table size. Its error analysis was also performed, and the threshold was determined so as to maintain the error less than 1°. When the Hall voltage has 11-bit resolution, the lookup table size is reduced from 1,024 samples to 279 samples.

Keywords: Hall sensor, angle measurement, lookup table, arctangent.

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Authors: P. Bárta

Abstract:

Increasing demand on the performance of Subsea Production Systems (SPS) suggests a need for more detailed investigation of fluid behavior taking place in subsea equipment. Complete CFD cool down analyses of subsea equipment are very time demanding. The objective of this paper is to investigate a Locked CFD approach, which enables significant reduction of the computational time and at the same time maintains sufficient accuracy during thermal cool down simulations. The result comparison of a dead leg simulation using the Full CFD and the three LCFD-methods confirms the validity of the locked flow field assumption for the selected case. For the tested case the LCFD simulation speed up by factor of 200 results in the absolute thermal error of 0.5 °C (3% relative error), speed up by factor of 10 keeps the LCFD results within 0.1 °C (0.5 % relative error) comparing to the Full CFD.

Keywords: CFD, Locked Flow Field, Speed up of CFD simulation time, Subsea

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

Abstract:

This paper introduces an original method of parametric optimization of the structure for multimodal decisionlevel fusion scheme which combines the results of the partial solution of the classification task obtained from assembly of the mono-modal classifiers. As a result, a multimodal fusion classifier which has the minimum value of the total error rate has been obtained.

Keywords: Сlassification accuracy, fusion solution, total error rate.

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Authors: Vinod B. Suryawanshi, Ajit D. Kelkar

Abstract:

Composite materials, due to their unique properties such as high strength to weight ratio, corrosion resistance, and impact resistance have huge potential as structural materials in automotive, construction and transportation applications. However, these properties often come at higher cost owing to complex design methods, difficult manufacturing processes and raw material cost. Traditionally, tapered laminated composite structures are manufactured using autoclave manufacturing process by ply drop off technique. Autoclave manufacturing though very powerful suffers from high capital investment and higher energy consumption. As per the current trends in composite manufacturing, Out of Autoclave (OoA) processes are looked as emerging technologies for manufacturing the structural composite components for aerospace and defense applications. However, there is a need for improvement among these processes to make them reliable and consistent. In this paper, feasibility of using out of autoclave process to manufacture the variable thickness cantilever beam is discussed. The minimum weight design for the composite beam is obtained using constant stress beam concept by tailoring the thickness of the beam. Ply drop off techniques was used to fabricate the variable thickness beam from glass/epoxy prepregs. Experiments were conducted to measure bending stresses along the span of the cantilever beam at different intervals by applying the concentrated load at the free end. Experimental results showed that the stresses in the bean at different intervals were constant. This proves the ability of OoA process to manufacture the constant stress beam. Finite element model for the constant stress beam was developed using commercial finite element simulation software. It was observed that the simulation results agreed very well with the experimental results and thus validated design and manufacturing approach used.

Keywords: Beams, Composites, Constant Stress, Structures.

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Authors: S.A.M. Yatim, Z.B. Ibrahim, K.I. Othman, F. Ismail

Abstract:

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precision and computation time. The strategy involves constant, halving or increasing the step size by 1.9 times the previous step size. Decision of changing the step size is determined by the local truncation error (LTE). Numerical results are provided to support the enhancement of method applied.

Keywords: Backward differentiation formulae, block backwarddifferentiation formulae, stiff ordinary differential equation, variablestep size.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai

Abstract:

One of the main objectives of order reduction is to design a controller of lower order which can effectively control the original high order system so that the overall system is of lower order and easy to understand. In this paper, a simple method is presented for controller design of a higher order discrete system. First the original higher order discrete system in reduced to a lower order model. Then a Proportional Integral Derivative (PID) controller is designed for lower order model. An error minimization technique is employed for both order reduction and controller design. For the error minimization purpose, Differential Evolution (DE) optimization algorithm has been employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the desired response and actual response pertaining to a unit step input. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specification. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete System, Model Order Reduction, PIDController, Integral Squared Error, Differential Evolution.

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Authors: Wararit Panichkitkosolkul

Abstract:

The unit root tests based on the robust estimator for the first-order autoregressive process are proposed and compared with the unit root tests based on the ordinary least squares (OLS) estimator. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of Type I error and powers of the unit root tests are estimated via Monte Carlo simulation. Simulation results show that all unit root tests can control the probability of Type I error for all situations. The empirical power of the unit root tests based on the robust estimator are higher than the unit root tests based on the OLS estimator.

Keywords: Autoregressive, Ordinary least squares, Type I error, Power of the test, Monte Carlo simulation.

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Authors: Vitalice K. Oduol, C. Ardil

Abstract:

The paper examines the performance of bit-interleaved parity (BIP) methods in error rate monitoring, and in declaration and clearing of alarms in those transport networks that employ automatic protection switching (APS). The BIP-based error rate monitoring is attractive for its simplicity and ease of implementation. The BIP-based results are compared with exact results and are found to declare the alarms too late, and to clear the alarms too early. It is concluded that the standards development and systems implementation should take into account the fact of early clearing and late declaration of alarms. The window parameters defining the detection and clearing thresholds should be set so as to build sufficient hysteresis into the system to ensure that BIP-based implementations yield acceptable performance results.

Keywords: Automatic protection switching, bit interleaved parity, excessive bit error rate

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Authors: Khairul Jauhari, Achmad Widodo, Ismoyo Haryanto

Abstract:

In this article, the radial displacement error correction capability of a high precision spindle grinding caused by unbalance force was investigated. The spindle shaft is considered as a flexible rotor mounted on two sets of angular contact ball bearing. Finite element methods (FEM) have been adopted for obtaining the equation of motion of the spindle. In this paper, firstly, natural frequencies, critical frequencies, and amplitude of the unbalance response caused by residual unbalance are determined in order to investigate the spindle behaviors. Furthermore, an optimization design algorithm is employed to minimize radial displacement of the spindle which considers dimension of the spindle shaft, the dynamic characteristics of the bearings, critical frequencies and amplitude of the unbalance response, and computes optimum spindle diameters and stiffness and damping of the bearings. Numerical simulation results show that by optimizing the spindle diameters, and stiffness and damping in the bearings, radial displacement of the spindle can be reduced. A spindle about 4 μm radial displacement error can be compensated with 2 μm accuracy. This certainly can improve the accuracy of the product of machining.

Keywords: Error correction, High precision grinding, Optimization, Radial displacement, Spindle.

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

Abstract:

An alternative approach to the use of Discrete Fourier Transform (DFT) for Magnetic Resonance Imaging (MRI) reconstruction is the use of parametric modeling technique. This method is suitable for problems in which the image can be modeled by explicit known source functions with a few adjustable parameters. Despite the success reported in the use of modeling technique as an alternative MRI reconstruction technique, two important problems constitutes challenges to the applicability of this method, these are estimation of Model order and model coefficient determination. In this paper, five of the suggested method of evaluating the model order have been evaluated, these are: The Final Prediction Error (FPE), Akaike Information Criterion (AIC), Residual Variance (RV), Minimum Description Length (MDL) and Hannan and Quinn (HNQ) criterion. These criteria were evaluated on MRI data sets based on the method of Transient Error Reconstruction Algorithm (TERA). The result for each criterion is compared to result obtained by the use of a fixed order technique and three measures of similarity were evaluated. Result obtained shows that the use of MDL gives the highest measure of similarity to that use by a fixed order technique.

Keywords: Autoregressive Moving Average (ARMA), MagneticResonance Imaging (MRI), Parametric modeling, Transient Error.

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Authors: Huang Shengqin, Xiao Hong

Abstract:

LES with mixed subgrid-scale model has been used to simulate aerodynamic performance of hypersonic configuration. The simulation was conducted to replicate conditions and geometry of a model which has been previously tested. LES Model has been successful in predict pressure coefficient with the max error 1.5% besides afterbody. But in the high Mach number condition, it is poor in predict ability and product 12.5% error. The calculation error are mainly conducted by the distribution swirling. The fact of poor ability in the high Mach number and afterbody region indicated that the mixed subgrid-scale model should be improved in large eddied especially in hypersonic separate region. In the condition of attach and sideslip flight, the calculation results have waves. LES are successful in the prediction the pressure wave in hypersonic flow.

Keywords: Hypersonic, LES, mixed Subgrid-scale model, experiment.

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Authors: Vai Kuong Sin, Chon Kit Chio

Abstract:

In this paper, the two-dimensional reversed stagnationpoint flow is solved by means of an anlytic approach. There are similarity solutions in case the similarity equation and the boundary condition are modified. Finite analytic method are applied to obtain the similarity velocity function.

Keywords: reversed stagnation-point flow, similarity solutions, asymptotic solution

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

Abstract:

 A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: Forecasting model, Steel demand uncertainty, Hierarchical Bayesian framework, Exponential smoothing method.

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Authors: Rafsan Al Mamun, Md. Motaharul Islam, Rabana Tajrin, Nabiha Noor, Shafinaz Qader

Abstract:

In an attempt to enrich the lives of billions of people by providing proper information, security and a way of communicating with others, the need for efficient and improved satellites is constantly growing. Thus, there is an increasing demand for better error detection and correction (EDAC) schemes, which are capable of protecting the data onboard the satellites. The paper is aimed towards detecting and correcting such errors using a special algorithm called the Hamming Code, which uses the concept of parity and parity bits to prevent single-bit errors onboard a satellite in Low Earth Orbit. This paper focuses on the study of Low Earth Orbit satellites and the process of generating the Hamming Code matrix to be used for EDAC using computer programs. The most effective version of Hamming Code generated was the Hamming (16, 11, 4) version using MATLAB, and the paper compares this particular scheme with other EDAC mechanisms, including other versions of Hamming Codes and Cyclic Redundancy Check (CRC), and the limitations of this scheme. This particular version of the Hamming Code guarantees single-bit error corrections as well as double-bit error detections. Furthermore, this version of Hamming Code has proved to be fast with a checking time of 5.669 nanoseconds, that has a relatively higher code rate and lower bit overhead compared to the other versions and can detect a greater percentage of errors per length of code than other EDAC schemes with similar capabilities. In conclusion, with the proper implementation of the system, it is quite possible to ensure a relatively uncorrupted satellite storage system.

Keywords: Bit-flips, Hamming code, low earth orbit, parity bits, satellite, single error upset.

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Authors: H. Katkhuda, B. Hanayneh, N. Shatarat

Abstract:

The main objective of this paper is to determine the isolated effect of silica fume on tensile, compressive and flexure strengths on high strength lightweight concrete. Many experiments were carried out by replacing cement with different percentages of silica fume at different constant water-binder ratio keeping other mix design variables constant. The silica fume was replaced by 0%, 5%, 10%, 15%, 20% and 25% for a water-binder ratios ranging from 0.26 to 0.42. For all mixes, split tensile, compressive and flexure strengths were determined at 28 days. The results showed that the tensile, compressive and flexure strengths increased with silica fume incorporation but the optimum replacement percentage is not constant because it depends on the water–cementitious material (w/cm) ratio of the mix. Based on the results, a relationship between split tensile, compressive and flexure strengths of silica fume concrete was developed using statistical methods.

Keywords: Silica fume, Lightweight, High strength concrete, and Strength.

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Authors: Roman Novak, Matjaz Vencelj

Abstract:

The angular distribution of Compton scattering of two quanta originating in the annihilation of a positron with an electron is investigated as a quantum key distribution (QKD) mechanism in the gamma spectral range. The geometry of coincident Compton scattering is observed on the two sides as a way to obtain partially correlated readings on the quantum channel. We derive the noise probability density function of a conceptually equivalent prepare and measure quantum channel in order to evaluate the limits of the concept in terms of the device secrecy capacity and estimate it at roughly 1.9 bits per 1 000 annihilation events. The high error rate is well above the tolerable error rates of the common reconciliation protocols; therefore, the proposed key agreement protocol by public discussion requires key reconciliation using classical error-correcting codes. We constructed a prototype device based on the readily available monolithic detectors in the least complex setup.

Keywords: Compton scattering, gamma-ray polarization, quantumcryptography, quantum key distribution

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Authors: M. Govindarajan

Abstract:

Text Mining is around applying knowledge discovery techniques to unstructured text is termed knowledge discovery in text (KDT), or Text data mining or Text Mining. In decision tree approach is most useful in classification problem. With this technique, tree is constructed to model the classification process. There are two basic steps in the technique: building the tree and applying the tree to the database. This paper describes a proposed C5.0 classifier that performs rulesets, cross validation and boosting for original C5.0 in order to reduce the optimization of error ratio. The feasibility and the benefits of the proposed approach are demonstrated by means of medial data set like hypothyroid. It is shown that, the performance of a classifier on the training cases from which it was constructed gives a poor estimate by sampling or using a separate test file, either way, the classifier is evaluated on cases that were not used to build and evaluate the classifier are both are large. If the cases in hypothyroid.data and hypothyroid.test were to be shuffled and divided into a new 2772 case training set and a 1000 case test set, C5.0 might construct a different classifier with a lower or higher error rate on the test cases. An important feature of see5 is its ability to classifiers called rulesets. The ruleset has an error rate 0.5 % on the test cases. The standard errors of the means provide an estimate of the variability of results. One way to get a more reliable estimate of predictive is by f-fold –cross- validation. The error rate of a classifier produced from all the cases is estimated as the ratio of the total number of errors on the hold-out cases to the total number of cases. The Boost option with x trials instructs See5 to construct up to x classifiers in this manner. Trials over numerous datasets, large and small, show that on average 10-classifier boosting reduces the error rate for test cases by about 25%.

Keywords: C5.0, Error Ratio, text mining, training data, test data.

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Authors: K. Kouzi

Abstract:

In order to have stable and high performance of direct torque and flux control (DTFC) of double star induction motor drive (DSIM), proper on-line adaptation of the stator resistance is very important. This is inevitably due to the variation of the stator resistance during operating conditions, which introduces error in estimated flux position and the magnitude of the stator flux. Error in the estimated stator flux deteriorates the performance of the DTFC drive. Also, the effect of error in estimation is very important especially at low speed. Due to this, our aim is to overcome the sensitivity of the DTFC to the stator resistance variation by proposing on-line fuzzy estimation stator resistance. The fuzzy estimation method is based on an on-line stator resistance correction through the variations of the stator current estimation error and its variations. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of the suggested algorithm control is to avoid the drive instability that may occur in certain situations and ensure the tracking of the actual stator resistance. The validity of the technique and the improvement of the whole system performance are proved by the results.

Keywords: Direct torque control, dual stator induction motor, fuzzy logic estimation, stator resistance adaptation.

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Authors: Mochammad Dewo, Sumarsono Sudarto

Abstract:

The Exponential Triple Smoothing Algorithm approach nowadays, which is used to anticipate the export value of Indonesia's two major commodities, coal and palm oil, has a Mean Percentage Absolute Error (MAPE) value of 30-50%, which may be considered as a "reasonable" forecasting mistake. Forecasting errors of more than 30% shall have a domino effect on industrial output, as extra production adds to raw material, manufacturing and storage expenses. Whereas, reaching an "excellent" classification with an error value of less than 10% will provide new investors and exporters with confidence in the commercial development of related sectors. Industrial growth will bring out a positive impact on economic development. It can be applied for other commodities if the forecast error is less than 10%. The purpose of this project is to create a forecasting technique that can produce precise forecasting results with an error of less than 10%. This research analyzes forecasting methods such as ARIMA (Autoregressive Integrated Moving Average), ANN (Artificial Neural Network) and LSTM (Long-Short Term Memory). By providing a MAPE of 1%, this study reveals that ANN is the most successful strategy for forecasting coal and palm oil commodities in Indonesia.

Keywords: ANN, Artificial Neural Network, ARIMA, Autoregressive Integrated Moving Average, export value, forecast, LSTM, Long Short Term Memory.

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Authors: Il Young Song, Du Yong Kim, Vladimir Shin

Abstract:

This paper reports on a receding horizon filtering for mobile robot systems with cross-correlated sensor noises and uncertainties. Also, the effect of uncertain parameters in the state of the tracking error model performance is considered. A distributed fusion receding horizon filter is proposed. The distributed fusion filtering algorithm represents the optimal linear combination of the local filters under the minimum mean square error criterion. The derivation of the error cross-covariances between the local receding horizon filters is the key of this paper. Simulation results of the tracking mobile robot-s motion demonstrate high accuracy and computational efficiency of the distributed fusion receding horizon filter.

Keywords: Distributed fusion, fusion formula, Kalman filter, multisensor, receding horizon, wheeled mobile robot

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Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

Abstract:

Financial forecasting is an example of signal processing problems. A number of ways to train/learn the network are available. We have used Levenberg-Marquardt algorithm for error back-propagation for weight adjustment. Pre-processing of data has reduced much of the variation at large scale to small scale, reducing the variation of training data.

Keywords: Gradient descent method, jacobian matrix.Levenberg-Marquardt algorithm, quadratic error surfaces,

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Authors: E. Keramaris, V. Kanakoudis

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In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: Sharp-crested weir, weir height, flow measurement, open channel flow.

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Authors: Renzo Carta, Francesco Desogus

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Variations in the growth rate constant of the Listeria monocytogenes bacterial species were determined at 37°C in irradiated environments and compared to the situation of a nonirradiated environment. The bacteria cells, contained in a suspension made of a nutrient solution of Brain Heart Infusion, were made to grow at different frequency (2.30e2.60 GHz) and power (0e400 mW) values, in a plug flow reactor positioned in the irradiated environment. Then the reacting suspension was made to pass into a cylindrical cuvette where its optical density was read every 2.5 minutes at a wavelength of 600 nm. The obtained experimental data of optical density vs. time allowed the bacterial growth rate constant to be derived; this was found to be slightly influenced by microwave power, but not by microwave frequency; in particular, a minimum value was found for powers in the 50e150 mW field.

Keywords: Growth rate constant, irradiated environment, Listeria monocytogenes, microwaves, plug flow reactor.

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Authors: Andres G. Victorio, Montita Rungswang

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A free-trade agreement is found to increase Thailand-s agricultural imports from New Zealand, despite the short span of time for which the agreement has been operational. The finding is described by autoregressive estimates that correct for possible unit roots in the data. The agreement-s effect upon imports is also estimated while considering an error-correction model of imports against gross domestic product.

Keywords: Agricultural imports, free trade, unit roots, cointegration, error correction.

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