Search results for: joint probability density matrix
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2828

Search results for: joint probability density matrix

1268 Real-Time Testing of Steel Strip Welds based on Bayesian Decision Theory

Authors: Julio Molleda, Daniel F. García, Juan C. Granda, Francisco J. Suárez

Abstract:

One of the main trouble in a steel strip manufacturing line is the breakage of whatever weld carried out between steel coils, that are used to produce the continuous strip to be processed. A weld breakage results in a several hours stop of the manufacturing line. In this process the damages caused by the breakage must be repaired. After the reparation and in order to go on with the production it will be necessary a restarting process of the line. For minimizing this problem, a human operator must inspect visually and manually each weld in order to avoid its breakage during the manufacturing process. The work presented in this paper is based on the Bayesian decision theory and it presents an approach to detect, on real-time, steel strip defective welds. This approach is based on quantifying the tradeoffs between various classification decisions using probability and the costs that accompany such decisions.

Keywords: Classification, Pattern Recognition, ProbabilisticReasoning, Statistical Data Analysis.

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1267 Application of Artificial Neural Network in Assessing Fill Slope Stability

Authors: An-Jui. Li, Kelvin Lim, Chien-Kuo Chiu, Benson Hsiung

Abstract:

This paper details the utilization of artificial intelligence (AI) in the field of slope stability whereby quick and convenient solutions can be obtained using the developed tool. The AI tool used in this study is the artificial neural network (ANN), while the slope stability analysis methods are the finite element limit analysis methods. The developed tool allows for the prompt prediction of the safety factors of fill slopes and their corresponding probability of failure (depending on the degree of variation of the soil parameters), which can give the practicing engineer a reasonable basis in their decision making. In fact, the successful use of the Extreme Learning Machine (ELM) algorithm shows that slope stability analysis is no longer confined to the conventional methods of modeling, which at times may be tedious and repetitive during the preliminary design stage where the focus is more on cost saving options rather than detailed design. Therefore, similar ANN-based tools can be further developed to assist engineers in this aspect.

Keywords: Landslide, limit analysis, ANN, soil properties.

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1266 On Convergence Property of MINRES Method for Solving a Complex Shifted Hermitian Linear System

Authors: Guiding Gu, Guo Liu

Abstract:

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

Keywords: complex shifted linear system, Hermitian matrix, MINRES method.

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1265 Simulation of Large Deformations of Rubbers by the RKPM Method

Authors: M. Foroutan, H. Dalayeli, M. Sadeghian

Abstract:

In this paper processes including large deformations of a rubber with hyperelastic material behavior are simulated by the RKPM method. Due to the loss of kronecker delta properties in the mesh less shape functions, the imposition of essential boundary conditions consumes significant CPU time in mesh free computations. In this work transformation method is used for imposition of essential boundary conditions. A RKPM material shape function is used in this analysis. The support of the material shape functions covers the same set of particles during material deformation and hence the transformation matrix is formed only once at the initial stages. A computer program in MATLAB is developed for simulations.

Keywords: RKPM, large deformations, transformation, essentialboundary conditions.

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1264 Process Parameters Optimization for Pulsed TIG Welding of 70/30 Cu-Ni Alloy Welds Using Taguchi Technique

Authors: M. P. Chakravarthy, N. Ramanaiah, B. S. K.Sundara Siva Rao

Abstract:

Taguchi approach was applied to determine the most influential control factors which will yield better tensile strength of the joints of pulse TIG welded 70/30 Cu-Ni alloy. In order to evaluate the effect of process parameters such as pulse frequency, peak current, base current and welding speed on tensile strength of Pulsed current TIG welded 70/30 Cu-Ni alloy of 5 mm thickness, Taguchi parametric design and optimization approach was used. Through the Taguchi parametric design approach, the optimum levels of process parameters were determined at 95% confidence level. The results indicate that the Pulse frequency, peak current, welding speed and base current are the significant parameters in deciding the tensile strength of the joint. The predicted optimal values of tensile strength of Pulsed current Gas tungsten arc welding (PC GTAW) of 70/30 Cu-Ni alloy welds are 368.8MPa.

Keywords: 70/30 Cu-Ni alloy, pulsed current GTAW, mechanical properties, Taguchi technique, analysis of variance.

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1263 Digital filters for Hot-Mix Asphalt Complex Modulus Test Data Using Genetic Algorithm Strategies

Authors: Madhav V. Chitturi, Anshu Manik, Kasthurirangan Gopalakrishnan

Abstract:

The dynamic or complex modulus test is considered to be a mechanistically based laboratory test to reliably characterize the strength and load-resistance of Hot-Mix Asphalt (HMA) mixes used in the construction of roads. The most common observation is that the data collected from these tests are often noisy and somewhat non-sinusoidal. This hampers accurate analysis of the data to obtain engineering insight. The goal of the work presented in this paper is to develop and compare automated evolutionary computational techniques to filter test noise in the collection of data for the HMA complex modulus test. The results showed that the Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES) approach is computationally efficient for filtering data obtained from the HMA complex modulus test.

Keywords: HMA, dynamic modulus, GA, evolutionarycomputation.

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1262 Sampling Effects on Secondary Voltage Control of Microgrids Based on Network of Multiagent

Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

Abstract:

This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: Microgrids, secondary control, multiagent, sampling, LMI.

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1261 Oxide Based Resistive Random Access Memory Device for High Density Non Volatile Memory Applications

Authors: Z. Fang, X. P. Wang, G. Q. Lo, D. L. Kwong

Abstract:

In this work, we demonstrated vertical RRAM device fabricated at the sidewall of contact hole structures for possible future 3-D stacking integrations. The fabricated devices exhibit polarity dependent bipolar resistive switching with small operation voltage of less than 1V for both set and reset process. A good retention of memory window ~50 times is maintained after 1000s voltage bias.

Keywords: Bipolar switching, non volatile memory, resistive random access memory, 3-D stacking.

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1260 New Iterative Algorithm for Improving Depth Resolution in Ionic Analysis: Effect of Iterations Number

Authors: N. Dahraoui, M. Boulakroune, D. Benatia

Abstract:

In this paper, the improvement by deconvolution of the depth resolution in Secondary Ion Mass Spectrometry (SIMS) analysis is considered. Indeed, we have developed a new Tikhonov- Miller deconvolution algorithm where a priori model of the solution is included. This is a denoisy and pre-deconvoluted signal obtained from: firstly, by the application of wavelet shrinkage algorithm, secondly by the introduction of the obtained denoisy signal in an iterative deconvolution algorithm. In particular, we have focused the light on the effect of the iterations number on the evolution of the deconvoluted signals. The SIMS profiles are multilayers of Boron in Silicon matrix.

Keywords: DRF, in-depth resolution, multiresolution deconvolution, SIMS, wavelet shrinkage.

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1259 Gel-Based Autologous Chondrocyte Implantation (GACI) in the Knee: Multicentric Short Term Study

Authors: Shaival Dalal, Nilesh Shah, Dinshaw Pardiwala, David Rajan, Satyen Sanghavi, Charul Bhanji

Abstract:

Autologous Chondrocyte Implantation (ACI) is used worldwide since 1998 to treat cartilage defect. GEL based ACI is a new tissue-engineering technique to treat full thickness cartilage defect with fibrin and thrombin as scaffold for chondrocytes. Purpose of this study is to see safety and efficacy of gel based ACI for knee cartilage defect in multiple centres with different surgeons. Gel-based Autologous Chondrocyte Implantation (GACI) has shown effectiveness in treating isolated cartilage defect of knee joint. Long term results are still needed to be studied. This study was followed-up up to two years and showed benefit to patients. All enrolled patients with a mean age of 28.5 years had an average defect size of3 square centimeters, and were grade IV as per ICRS grading. All patients were followed up several times and at several intervals at 6th week, 8th week, 11th week, 17th week, 29th week, 57th week after surgery. The outcomes were measured based on the IKDC (subjective and objective) and MOCART scores.

Keywords: Knee, chondrocyte, autologous chondrocyte implantation, gel.

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1258 A Balanced Cost Cluster-Heads Selection Algorithm for Wireless Sensor Networks

Authors: Ouadoudi Zytoune, Youssef Fakhri, Driss Aboutajdine

Abstract:

This paper focuses on reducing the power consumption of wireless sensor networks. Therefore, a communication protocol named LEACH (Low-Energy Adaptive Clustering Hierarchy) is modified. We extend LEACHs stochastic cluster-head selection algorithm by a modifying the probability of each node to become cluster-head based on its required energy to transmit to the sink. We present an efficient energy aware routing algorithm for the wireless sensor networks. Our contribution consists in rotation selection of clusterheads considering the remoteness of the nodes to the sink, and then, the network nodes residual energy. This choice allows a best distribution of the transmission energy in the network. The cluster-heads selection algorithm is completely decentralized. Simulation results show that the energy is significantly reduced compared with the previous clustering based routing algorithm for the sensor networks.

Keywords: Wireless Sensor Networks, Energy efficiency, WirelessCommunications, Clustering-based algorithm.

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1257 Seismic Fragility of Weir Structure Considering Aging Degradation of Concrete Material

Authors: HoYoung Son, DongHoon Shin, WooYoung Jung

Abstract:

This study presented the seismic fragility framework of concrete weir structure subjected to strong seismic ground motions and in particular, concrete aging condition of the weir structure was taken into account in this study. In order to understand the influence of concrete aging on the weir structure, by using probabilistic risk assessment, the analytical seismic fragility of the weir structure was derived for pre- and post-deterioration of concrete. The performance of concrete weir structure after five years was assumed for the concrete aging or deterioration, and according to after five years’ condition, the elastic modulus was simply reduced about one–tenth compared with initial condition of weir structures. A 2D nonlinear finite element analysis was performed considering the deterioration of concrete in weir structures using ABAQUS platform, a commercial structural analysis program. Simplified concrete degradation was resulted in the increase of almost 45% of the probability of failure at Limit State 3, in comparison to initial construction stage, by analyzing the seismic fragility.

Keywords: Weir, FEM, concrete, fragility, aging

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1256 On the outlier Detection in Nonlinear Regression

Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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1255 Richtmyer-Meshkov Instability and Gas-Particle Interaction of Contoured Shock-Tube Flows: A Numerical Study

Authors: Yi Liu

Abstract:

In this paper, computational fluid dynamics (CFD) is utilized to characterize a prototype biolistic delivery system, the biomedical device based on the contoured-shock-tube design (CST), with the aim at investigating shocks induced flow instabilities within the contoured shock tube. The shock/interface interactions, the growth of perturbation at an interface between two fluids of different density are interrogated. The key features of the gas dynamics and gas-particle interaction are discussed

Keywords: Simulation, Shock wave, Particle, Interface, Supersonic, Richtmyer-Meshkov Instability

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1254 Factor Resistance Comparison of a Long Shaft in 955 and 1055 John Deere Grain Combine

Authors: M. Azadbakht, M. E. Shayan, H. Jafari, E. Ghajarjazi, A. Kiapei

Abstract:

Transmission shafts are affected by various forces, for example, during acceleration or sudden breaks, bending during transportation, vertical forces that lead to cuts. One of the main failures in combines is breaking shaft which repairmen refer it. Structural resistance of canal against torque is very important in the beginning of the movement. For analyzing stress, a typical sample from a type of combine was selected, called JD955 combine. Long shaft in this combine was analyzed with finite element method by Ansys13 generic package under static load. Conducted analysis showed that there is a maximum stress in contact surfaces of indentations and also in place of changing diameter. Safety factor value is low in parts of the shaft and this increases the probability of failure at these points. To improve the conditions with the least cost and an approach of product improvement, using alternative alloy is important.

Keywords: John Deere, Ansys, Shaft, Stress, Grain Combine harvester, Finite element, Failure.

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1253 An Intelligent System Framework for Generating Activity List of a Project Using WBS Mind map and Semantic Network

Authors: H. Iranmanesh, M. Madadi

Abstract:

Work Breakdown Structure (WBS) is one of the most vital planning processes of the project management since it is considered to be the fundamental of other processes like scheduling, controlling, assigning responsibilities, etc. In fact WBS or activity list is the heart of a project and omission of a simple task can lead to an irrecoverable result. There are some tools in order to generate a project WBS. One of the most powerful tools is mind mapping which is the basis of this article. Mind map is a method for thinking together and helps a project manager to stimulate the mind of project team members to generate project WBS. Here we try to generate a WBS of a sample project involving with the building construction using the aid of mind map and the artificial intelligence (AI) programming language. Since mind map structure can not represent data in a computerized way, we convert it to a semantic network which can be used by the computer and then extract the final WBS from the semantic network by the prolog programming language. This method will result a comprehensive WBS and decrease the probability of omitting project tasks.

Keywords: Expert System, Mind map, Semantic network, Work breakdown structure,

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1252 Reducing Power in Error Correcting Code using Genetic Algorithm

Authors: Heesung Lee, Joonkyung Sung, Euntai Kim

Abstract:

This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.

Keywords: Error correcting codes, genetic algorithm, non-linearpower optimization, Hamming code, Hsiao code.

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1251 Puff Noise Detection and Cancellation for Robust Speech Recognition

Authors: Sangjun Park, Jungpyo Hong, Byung-Ok Kang, Yun-keun Lee, Minsoo Hahn

Abstract:

In this paper, an algorithm for detecting and attenuating puff noises frequently generated under the mobile environment is proposed. As a baseline system, puff detection system is designed based on Gaussian Mixture Model (GMM), and 39th Mel Frequency Cepstral Coefficient (MFCC) is extracted as feature parameters. To improve the detection performance, effective acoustic features for puff detection are proposed. In addition, detected puff intervals are attenuated by high-pass filtering. The speech recognition rate was measured for evaluation and confusion matrix and ROC curve are used to confirm the validity of the proposed system.

Keywords: Gaussian mixture model, puff detection and cancellation, speech enhancement.

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1250 Argon/Oxygen Plasma Surface Modification of Biopolymers for Improvement of Wettability and Wear Resistance

Authors: Binnur Sagbas

Abstract:

Artificial joint replacements such as total knee and total hip prosthesis have been applied to the patients who affected by osteoarthritis. Although different material combinations are used for these joints, biopolymers are most commonly preferred materials especially for acetabular cup and tibial component of hip and knee joints respectively. The main limitation that shortens the service life of these prostheses is wear. Wear is complicated phenomena and it must be considered with friction and lubrication. In this study, micro wave (MW) induced argon+oxygen plasma surface modification were applied on ultra-high molecular weight polyethylene (UHMWPE) and vitamin E blended UHMWPE (VE-UHMWPE) biopolymer surfaces to improve surface wettability and wear resistance of the surfaces. Contact angel measurement method was used for determination of wettability. Ball-on-disc wear test was applied under 25% bovine serum lubrication conditions. The results show that surface wettability and wear resistance of both material samples were increased by plasma surface modification.

Keywords: Artificial joints, plasma surface modification, UHMWPE, vitamin E, wear.

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1249 A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation

Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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1248 On Four Models of a Three Server Queue with Optional Server Vacations

Authors: Kailash C. Madan

Abstract:

We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

Keywords: A three server queue, Bernoulli schedule server vacations, queue size distribution at a random epoch, steady state.

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1247 Implicit Force Control of a Position Controlled Robot – A Comparison with Explicit Algorithms

Authors: Alexander Winkler, Jozef Suchý

Abstract:

This paper investigates simple implicit force control algorithms realizable with industrial robots. A lot of approaches already published are difficult to implement in commercial robot controllers, because the access to the robot joint torques is necessary or the complete dynamic model of the manipulator is used. In the past we already deal with explicit force control of a position controlled robot. Well known schemes of implicit force control are stiffness control, damping control and impedance control. Using such algorithms the contact force cannot be set directly. It is further the result of controller impedance, environment impedance and the commanded robot motion/position. The relationships of these properties are worked out in this paper in detail for the chosen implicit approaches. They have been adapted to be implementable on a position controlled robot. The behaviors of stiffness control and damping control are verified by practical experiments. For this purpose a suitable test bed was configured. Using the full mechanical impedance within the controller structure will not be practical in the case when the robot is in physical contact with the environment. This fact will be verified by simulation.

Keywords: Damping control, impedance control, robot force control, stability, stiffness control.

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1246 Angle of Arrival Detection with Fifth Order Phase Operators

Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, a fifth order propagator operators are proposed for estimating the Angles Of Arrival (AOA) of narrowband electromagnetic waves impinging on antenna array when its number of sensors is larger than the number of radiating sources.

The array response matrix is partitioned into five linearly dependent phases to construct the noise projector using five different propagators from non diagonal blocks of the spectral matrice of the received data; hence, five different estimators are proposed to estimate the angles of the sources. The simulation results proved the performance of the proposed estimators in the presence of white noise comparatively to high resolution eigen based spectra.

Keywords: DOA, narrowband, antenna, propagator, high resolution. Array, operator, angular, spectrum, goniometry.

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1245 Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm

Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

Abstract:

Cubic equations of state like Redlich–Kwong (RK)  EOS have been proved to be very reliable tools in the prediction of  phase behavior. Despite their good performance in compositional  calculations, they usually suffer from weaknesses in the predictions  of saturated liquid density. In this research, RK equation was  modified. The result of this study show that modified equation has  good agreement with experimental data.

 

Keywords: Equation of state, modification, ammonia, genetic algorithm.

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1244 A Proposed Technique for Software Development Risks Identification by using FTA Model

Authors: Hatem A. Khater, A. Baith Mohamed, Sara M. Kamel

Abstract:

Software Development Risks Identification (SDRI), using Fault Tree Analysis (FTA), is a proposed technique to identify not only the risk factors but also the causes of the appearance of the risk factors in software development life cycle. The method is based on analyzing the probable causes of software development failures before they become problems and adversely affect a project. It uses Fault tree analysis (FTA) to determine the probability of a particular system level failures that are defined by A Taxonomy for Sources of Software Development Risk to deduce failure analysis in which an undesired state of a system by using Boolean logic to combine a series of lower-level events. The major purpose of this paper is to use the probabilistic calculations of Fault Tree Analysis approach to determine all possible causes that lead to software development risk occurrence

Keywords: Software Development Risks Identification (SDRI), Fault Tree Analysis (FTA), Taxonomy for Software Development Risks (TSDR), Probabilistic Risk Assessment (PRA).

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1243 Data Quality Enhancement with String Length Distribution

Authors: Qi Xiu, Hiromu Hota, Yohsuke Ishii, Takuya Oda

Abstract:

Recently, collectable manufacturing data are rapidly increasing. On the other hand, mega recall is getting serious as a social problem. Under such circumstances, there are increasing needs for preventing mega recalls by defect analysis such as root cause analysis and abnormal detection utilizing manufacturing data. However, the time to classify strings in manufacturing data by traditional method is too long to meet requirement of quick defect analysis. Therefore, we present String Length Distribution Classification method (SLDC) to correctly classify strings in a short time. This method learns character features, especially string length distribution from Product ID, Machine ID in BOM and asset list. By applying the proposal to strings in actual manufacturing data, we verified that the classification time of strings can be reduced by 80%. As a result, it can be estimated that the requirement of quick defect analysis can be fulfilled.

Keywords: Data quality, feature selection, probability distribution, string classification, string length.

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1242 Damage Strain Analysis of Parallel Fiber Eutectic

Authors: Jian Zheng, Xinhua Ni, Xiequan Liu

Abstract:

According to isotropy of parallel fiber eutectic, the no- damage strain field in parallel fiber eutectic is obtained from the flexibility tensor of parallel fiber eutectic. Considering the damage behavior of parallel fiber eutectic, damage variables are introduced to determine the strain field of parallel fiber eutectic. The damage strains in the matrix, interphase, and fiber of parallel fiber eutectic are quantitatively analyzed. Results show that damage strains are not only associated with the fiber volume fraction of parallel fiber eutectic, but also with the damage degree.

Keywords: Parallel fiber eutectic, no-damage strain, damage strain, fiber volume fraction, damage degree.

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1241 Development of an Elastic Functionally Graded Interphase Model for the Micromechanics Response of Composites

Authors: Trevor Sabiston, Mohsen Mohammadi, Mohammed Cherkaoui, Kaan Inal

Abstract:

A new micromechanics framework is developed for long fibre reinforced composites using a single fibre surrounded by a functionally graded interphase and matrix as a representative unit cell. The unit cell is formulated to represent any number of aligned fibres by a single fibre. Using this model the elastic response of long fibre composites is predicted in all directions. The model is calibrated to experimental results and shows very good agreement in the elastic regime. The differences between the proposed model and existing models are discussed.

Keywords: Computational mechanics, functionally graded interphase, long fibre composites, micromechanics.

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1240 The Effects of Extracorporeal Shockwave Therapy on Pain, Function, Range of Motion and Strength in Patients with Plantar Fasciitis

Authors: P. Sanzo

Abstract:

Ten percent of the population will develop plantar fasciitis (PF) during their lifetime. Two million people are treated yearly accounting for 11-15% of visits to medical professionals. Treatment ranges from conservative to surgical intervention. The purpose of this study was to assess the effects of extracorporeal shockwave therapy (ECSWT) on heel pain, function, range of motion (ROM), and strength in patients with PF. One hundred subjects were treated with ECSWT and measures were taken before and three months after treatment. There was significant differences in visual analog scale scores for pain at rest (p=0.0001); after activity (p= 0.0001) and; overall improvement (p=0.0001). There was also significant improvement in Lower Extremity Functional Scale scores (p=0.0001); ankle plantarflexion (p=0.0001), dorsiflexion (p=0.001), and eversion (p=0.017),and first metatarsophalangeal joint flexion (p=0.002) and extension (p=0.003) ROM. ECSWT is an effective treatment improving heel pain, function and ROM in patients with PF.

Keywords: Extracorporeal shockwave therapy, shockwave therapy, plantar fasciitis, heel pain, function, range of motion, strength.

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1239 Implicit Two Step Continuous Hybrid Block Methods with Four Off-Steps Points for Solving Stiff Ordinary Differential Equation

Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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