Search results for: Fault Prediction Modeling.

Authors: Omer Nebil Yaveroglu, Tolga Can

Abstract:

In this study, a high accuracy protein-protein interaction prediction method is developed. The importance of the proposed method is that it only uses sequence information of proteins while predicting interaction. The method extracts phylogenetic profiles of proteins by using their sequence information. Combining the phylogenetic profiles of two proteins by checking existence of homologs in different species and fitting this combined profile into a statistical model, it is possible to make predictions about the interaction status of two proteins. For this purpose, we apply a collection of pattern recognition techniques on the dataset of combined phylogenetic profiles of protein pairs. Support Vector Machines, Feature Extraction using ReliefF, Naive Bayes Classification, K-Nearest Neighborhood Classification, Decision Trees, and Random Forest Classification are the methods we applied for finding the classification method that best predicts the interaction status of protein pairs. Random Forest Classification outperformed all other methods with a prediction accuracy of 76.93%

Keywords: Protein Interaction Prediction, Phylogenetic Profile, SVM , ReliefF, Decision Trees, Random Forest Classification

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Authors: Sun-Young Jang, Sung-Ah Kim, Dongyoun Shin

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Current real-estate value estimation, difficult for laymen, usually is performed by specialists. This paper presents an automated estimation process based on big data and machine-learning technology that calculates influences of building conditions on real-estate price measurement. The present study analyzed actual building sales sample data for Nonhyeon-dong, Gangnam-gu, Seoul, Korea, measuring the major influencing factors among the various building conditions. Further to that analysis, a prediction model was established and applied using RapidMiner Studio, a graphical user interface (GUI)-based tool for derivation of machine-learning prototypes. The prediction model is formulated by reference to previous examples. When new examples are applied, it analyses and predicts accordingly. The analysis process discerns the crucial factors effecting price increases by calculation of weighted values. The model was verified, and its accuracy determined, by comparing its predicted values with actual price increases.

Keywords: Big data, building-value analysis, machine learning, price prediction.

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Authors: Anthony Spiteri Staines

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This paper examines the modeling and analysis of a cruise control system using a Petri net based approach, task graphs, invariant analysis and behavioral properties. It shows how the structures used can be verified and optimized.

Keywords: Software Engineering, Real Time Analysis andDesign, Petri Nets, Task Graphs, Parallelism.

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Authors: Farhad Kolahan, Mohammad Bironro

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This paper addresses modeling and optimization of process parameters in powder mixed electrical discharge machining (PMEDM). The process output characteristics include metal removal rate (MRR) and electrode wear rate (EWR). Grain size of Aluminum powder (S), concentration of the powder (C), discharge current (I) pulse on time (T) are chosen as control variables to study the process performance. The experimental results are used to develop the regression models based on second order polynomial equations for the different process characteristics. Then, a genetic algorithm (GA) has been employed to determine optimal process parameters for any desired output values of machining characteristics.

Keywords: Regression modeling, PMEDM, GeneticAlgorithm, Optimization.

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Authors: G. Das, S. Das, P. Purkait, A. Dasgupta, M. Kumar

Abstract:

Properly sized capacitor banks are connected across induction motors for several reasons including power factor correction, reducing distortions, increasing capacity, etc. Total harmonic distortion (THD) and power factor (PF) are used in such cases to quantify the improvements obtained through connection of the external capacitor banks. On the other hand, one of the methods for assessing the motor internal condition is by the use of Park-s pattern analysis. In spite of taking adequate precautionary measures, the capacitor banks may sometimes malfunction. Such a minor fault in the capacitor bank is often not apparently discernible. This may however, give rise to substantial degradation of power factor correction performance and may also damage the supply profile. The case is more severe with the fact that the Park-s pattern gets distorted due to such external capacitor faults, and can give anomalous results about motor internal fault analyses. The aim of this paper is to present simulation and hardware laboratory test results to have an understanding of the anomalies in harmonic distortion and Park-s pattern analyses in induction motors due to capacitor bank defects.

Keywords: Capacitor bank, harmonic distortion, induction motor, Park's pattern, PSCAD simulation.

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Authors: Ahmed S. Al-Abdulwahab

Abstract:

Generation system reliability assessment is an important task which can be performed using deterministic or probabilistic techniques. The probabilistic approaches have significant advantages over the deterministic methods. However, more complicated modeling is required by the probabilistic approaches. Power generation model is a basic requirement for this assessment. One form of the generation models is the well known capacity outage probability table (COPT). Different analytical techniques have been used to construct the COPT. These approaches require considerable mathematical modeling of the generating units. The unit-s models are combined to build the COPT which will add more burdens on the process of creating the COPT. Decimal to Binary Conversion (DBC) technique is widely and commonly applied in electronic systems and computing This paper proposes a novel utilization of the DBC to create the COPT without engaging in analytical modeling or time consuming simulations. The simple binary representation , “0 " and “1 " is used to model the states o f generating units. The proposed technique is proven to be an effective approach to build the generation model.

Keywords: Decimal to Binary, generation, reliability.

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Authors: Peter Antwi Buah, Yingbin Zhang, Jianxian He, Chenlin Xiang, Delali Atsu Y. Bakah

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Near-fault ground motions with velocity pulses are considered to cause significant damage to structures or slopes compared to ordinary ground motions without velocity pulses. The double pulsed pulse-like ground motion is well known to be stronger than the single pulse. This research has numerically justified this perspective by studying the dynamic response of a homogeneous rock slope subjected to four pulse-like and two non-pulse-like ground motions using the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) software. Two of the pulse-like ground motions just have a single pulse. The results show that near-fault ground motions with velocity pulses can cause a higher dynamic response than regular ground motions. The amplification of the peak ground acceleration (PGA) in horizontal direction increases with the increase of the slope elevation. The seismic response of the slope under double pulse ground motion is stronger than that of the single pulse ground motion. The PGV amplification factor under the effect of the non-pulse-like records is also smaller than those under the pulse-like records. The velocity pulse strengthens the earthquake damage to the slope, which results in producing a stronger dynamic response.

Keywords: Velocity pulses, dynamic response, PGV magnification effect, elevation effect, double pulse.

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Authors: Phumelele P. Kubheka, Pius A. Owolawi, Gbolahan Aiyetoro

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Twitter is one of the most popular social media platforms where users share their opinions on different subjects. Twitter can be considered a great source for mining text due to the high volumes of data generated through the platform daily. Many industries such as telecommunication companies can leverage the availability of Twitter data to better understand their markets and make an appropriate business decision. This study performs topic modeling on Twitter data using Latent Dirichlet Allocation (LDA). The obtained results are benchmarked with another topic modeling technique, Latent Semantic Indexing (LSI). The study aims to retrieve topics on a Twitter dataset containing user tweets on South African Telcos. Results from this study show that LSI is much faster than LDA. However, LDA yields better results with higher topic coherence by 8% for the best-performing model in this experiment. A higher topic coherence score indicates better performance of the model.

Keywords: Big data, latent Dirichlet allocation, latent semantic indexing, Telco, topic modeling, Twitter.

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Authors: Gionata Carmignani, Mario G. C. A. Cimino, Franco Failli

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Business Processes (BPs) are the key instrument to understand how companies operate at an organizational level, taking an as-is view of the workflow, and how to address their issues by identifying a to-be model. In last year’s, the BP Model and Notation (BPMN) has become a de-facto standard for modeling processes. However, this standard does not incorporate explicitly the Problem- Solving (PS) knowledge in the Process Modeling (PM) results. Thus, such knowledge cannot be shared or reused. To narrow this gap is today a challenging research area. In this paper we present a framework able to capture the PS knowledge and to improve a workflow. This framework extends the BPMN specification by incorporating new general-purpose elements. A pilot scenario is also presented and discussed.

Keywords: Business Process Management, BPMN, Problem Solving, Process mapping.

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Authors: Mohamed A. Khlifi, Badr M. Alshammari

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This paper discusses the general methods to saturation in the steady-state, two axis (d & q) frame models of synchronous machines. In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon), is demonstrated. For that purpose, distinct methods of saturation modeling of dumper synchronous machine with cross-saturation are identified, and detailed models synthesis in d-q axes. A number of models are given in the final developed form. The procedure and the novel models are verified by a critical application to prove the validity of the method and the equivalence between all developed models is reported. Advantages of some of the models over the existing ones and their applicability are discussed.

Keywords: Cross-magnetizing, models synthesis, synchronous machine, saturated modeling, state-space vectors.

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Authors: I. M. Abd Rahim, H. Abdul Rahim, R. Ghazali

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There is numerous non-invasive blood glucose measurement technique developed by researchers, and near infrared (NIR) is the potential technique nowadays. However, there are some disagreements on the optimal wavelength range that is suitable to be used as the reference of the glucose substance in the blood. This paper focuses on the experimental data collection technique and also the analysis method used to analyze the data gained from the experiment. The selection of suitable linear and non-linear model structure is essential in prediction system, as the system developed need to be conceivably accurate.

Keywords: Invasive, linear, near-infrared (Nir), non-invasive, non-linear, prediction system.

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Authors: Yasuo Obikane

Abstract:

This work is to study a roll of the fluctuating density gradient in the compressible flows for the computational fluid dynamics (CFD). A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups: group proportional to the mean velocity, and that proportional to the mean strain rate, and that proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vorticity in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.

Keywords: Turbulence Modeling , Density Gradient Correlation, Compressible

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Authors: Rafayel A. Azizyan, Aram E. Gevogyan, Valeri B. Arakelyan, Emil S. Gevorgyan

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The mathematical modeling of different biological processes is usually used to predict or assess behavior of systems in which these processes take place. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions with ping-pong mechanism, which play an important role in different biochemical pathways. Besides that, three models of competitive inhibition were designed using different software packages. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions with ordered pingpong mechanism in the presence of competitive inhibitors, as well as to describe in details the inhibition effects. The simulation of the models with certain kinetic parameters allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of competitive inhibition. Simultaneous presence of two inhibitors, competitive to the S1 and S2 substrates have been studied. Moreover, we have found the pattern of simultaneous influence of both inhibitors.

Keywords: Mathematical modeling, bi-substrate enzymatic reactions, ping-pong mechanism, competitive inhibition.

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Authors: Anwar Jarndal

Abstract:

In this paper, a genetic-neural-network (GNN) based large-signal model for GaN HEMTs is presented along with its parameters extraction procedure. The model is easy to construct and implement in CAD software and requires only DC and S-parameter measurements. An improved decomposition technique is used to model self-heating effect. Two GNN models are constructed to simulate isothermal drain current and power dissipation, respectively. The two model are then composed to simulate the drain current. The modeling procedure was applied to a packaged GaN-on-Si HEMT and the developed model is validated by comparing its large-signal simulation with measured data. A very good agreement between the simulation and measurement is obtained.

Keywords: GaN HEMT, computer-aided design & modeling, neural networks, genetic optimization.

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Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

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This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: Availability Analysis, Markov Process, Performance Modeling, Steady State Availability.

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Authors: Fajaruddin Mustakim, Motohiro Fujita

Abstract:

This paper present the study carried out of accident analysis, black spot study and to develop accident predictive models based on the data collected at rural roadway, Federal Route 50 (F050) Malaysia. The road accident trends and black spot ranking were established on the F050. The development of the accident prediction model will concentrate in Parit Raja area from KM 19 to KM 23. Multiple non-linear regression method was used to relate the discrete accident data with the road and traffic flow explanatory variable. The dependent variable was modeled as the number of crashes namely accident point weighting, however accident point weighting have rarely been account in the road accident prediction Models. The result show that, the existing number of major access points, without traffic light, rise in speed, increasing number of Annual Average Daily Traffic (AADT), growing number of motorcycle and motorcar and reducing the time gap are the potential contributors of increment accident rates on multiple rural roadway.

Keywords: Accident Trends, Black Spot Study, Accident Prediction Model

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Authors: Yun-Pang Flötteröd, Jakob Erdmann

Abstract:

The human behaviors during evacuations are quite complex. One of the critical behaviors which affect the efficiency of evacuation is route choice. Therefore, the respective simulation modeling work needs to function properly. In this paper, Simulation of Urban Mobility’s (SUMO) current dynamic route modeling during evacuation, i.e. the rerouting functions, is examined with a real case study. The result consistency of the simulation and the reality is checked as well. Four influence factors (1) time to get information, (2) probability to cancel a trip, (3) probability to use navigation equipment, and (4) rerouting and information updating period are considered to analyze possible traffic impacts during the evacuation and to examine the rerouting functions in SUMO. Furthermore, some behavioral characters of the case study are analyzed with use of the corresponding detector data and applied in the simulation. The experiment results show that the dynamic route modeling in SUMO can deal with the proposed scenarios properly. Some issues and function needs related to route choice are discussed and further improvements are suggested.

Keywords: Evacuation, microscopic traffic simulation, rerouting, SUMO.

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Authors: N. Boutra, N. Ravot, J. Benoit, O. Picon

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Submarine power cables used for offshore wind farms electric energy distribution and transmission are subject to numerous threats. Some of the risks are associated with transport, installation and operating in harsh marine environment. This paper describes the feasibility of an electromagnetic low frequency sensing technique for submarine power cable failure prediction. The impact of a structural damage shape and material variability on the induced electric field is evaluated. The analysis is performed by modeling the cable using the finite element method, we use sensitivity analysis in order to identify the main damage characteristics affecting electric field variation. Lastly, we discuss the results obtained.

Keywords: Electromagnetism, defect, finite element method, sensitivity analysis, submarine power cables.

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Authors: Lambros V. Skarlas, Grigorios N. Beligiannis, Efstratios F. Georgopoulos, Adam V. Adamopoulos

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The aim of this contribution is to present a new approach in modeling the electrical activity of the human heart. A recurrent artificial neural network is being used in order to exhibit a subset of the dynamics of the electrical behavior of the human heart. The proposed model can also be used, when integrated, as a diagnostic tool of the human heart system. What makes this approach unique is the fact that every model is being developed from physiological measurements of an individual. This kind of approach is very difficult to apply successfully in many modeling problems, because of the complexity and entropy of the free variables describing the complex system. Differences between the modeled variables and the variables of an individual, measured at specific moments, can be used for diagnostic purposes. The sensor fusion used in order to optimize the utilization of biomedical sensors is another point that this paper focuses on. Sensor fusion has been known for its advantages in applications such as control and diagnostics of mechanical and chemical processes.

Keywords: Artificial Neural Networks, Diagnostic System, Health Condition Modeling Tool, Heart Diagnostics Model, Heart Electricity Model.

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Authors: Mahesh Chudasama, Harit Raval

Abstract:

Conical sections and shells of metal plates manufactured by 3-roller conical bending process are widely used in the industries. The process is completed by first bending the metal plates statically and then dynamic roller bending sequentially. It is required to have an analytical model to get maximum bending force, for optimum design of the machine, for static bending stage. Analytical models assuming various stress conditions are considered and these analytical models are compared considering various parameters and reported in this paper. It is concluded from the study that for higher bottom roller inclination, the shear stress affects greatly to the static bending force whereas for lower bottom roller inclination it can be neglected.

Keywords: Roller-bending, static-bending, stress-conditions, analytical-modeling.

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Authors: Sema Kurtuluş, Kemal Kurtuluş

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The objective of this paper is to review and assess the methodological issues and problems in marketing research, data and knowledge mining in Turkey. As a summary, academic marketing research publications in Turkey have significant problems. The most vital problem seems to be related with modeling. Most of the publications had major weaknesses in modeling. There were also, serious problems regarding measurement and scaling, sampling and analyses. Analyses myopia seems to be the most important problem for young academia in Turkey. Another very important finding is the lack of publications on data and knowledge mining in the academic world.

Keywords: Marketing research, data mining, knowledge mining, research modeling, analyses.

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Authors: S. Balaji, E. Golden Julie, Y. Harold Robinson

Abstract:

The context aware adaptive routing protocol is presented for unicast communication in intermittently connected mobile ad hoc networks (MANETs). The selection of the node is done by the Kalman filter prediction theory and it also makes use of utility functions. The context aware adaptive routing is defined by spray and wait technique, but the time consumption in delivering the message is too high and also the resource wastage is more. In this paper, we describe the spray and focus routing scheme for avoiding the existing problems.

Keywords: Context aware adaptive routing, Kalman filter prediction, spray and wait, spray and focus, intermittent networks.

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Authors: Tien-Shun Chan, Yung-Chung Chang, Cheng-Yu Chu, Wen-Hui Chen, Yuan-Lin Chen, Shun-Chong Wang, Chang-Chun Wang

Abstract:

98% of the energy needed in Taiwan has been imported. The prices of petroleum and electricity have been increasing. In addition, facility capacity, amount of electricity generation, amount of electricity consumption and number of Taiwan Power Company customers have continued to increase. For these reasons energy conservation has become an important topic. In the past linear regression was used to establish the power consumption models for chillers. In this study, grey prediction is used to evaluate the power consumption of a chiller so as to lower the total power consumption at peak-load (so that the relevant power providers do not need to keep on increasing their power generation capacity and facility capacity). In grey prediction, only several numerical values (at least four numerical values) are needed to establish the power consumption models for chillers. If PLR, the temperatures of supply chilled-water and return chilled-water, and the temperatures of supply cooling-water and return cooling-water are taken into consideration, quite accurate results (with the accuracy close to 99% for short-term predictions) may be obtained. Through such methods, we can predict whether the power consumption at peak-load will exceed the contract power capacity signed by the corresponding entity and Taiwan Power Company. If the power consumption at peak-load exceeds the power demand, the temperature of the supply chilled-water may be adjusted so as to reduce the PLR and hence lower the power consumption.

Keywords: Gery system theory, grey prediction, chller.

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Authors: Farhad Asadi, S. Hossein Sadati

Abstract:

This paper presents a prediction performance of feedforward Multilayer Perceptron (MLP) and Echo State Networks (ESN) trained with extended Kalman filter. Feedforward neural networks and ESN are powerful neural networks which can track and predict nonlinear signals. However, their tracking performance depends on the specific signals or data sets, having the risk of instability accompanied by large error. In this study we explore this process by applying different network size and leaking rate for prediction of nonlinear or chaotic signals in MLP neural networks. Major problems of ESN training such as the problem of initialization of the network and improvement in the prediction performance are tackled. The influence of coefficient of activation function in the hidden layer and other key parameters are investigated by simulation results. Extended Kalman filter is employed in order to improve the sequential and regulation learning rate of the feedforward neural networks. This training approach has vital features in the training of the network when signals have chaotic or non-stationary sequential pattern. Minimization of the variance in each step of the computation and hence smoothing of tracking were obtained by examining the results, indicating satisfactory tracking characteristics for certain conditions. In addition, simulation results confirmed satisfactory performance of both of the two neural networks with modified parameterization in tracking of the nonlinear signals.

Keywords: Feedforward neural networks, nonlinear signal prediction, echo state neural networks approach, leaking rates, capacity of neural networks.

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Authors: F. Hosseinpour, H. Hajihosseini

Abstract:

Simulation is a very helpful and valuable work tool in manufacturing. It can be used in industrial field allowing the system`s behavior to be learnt and tested. Simulation provides a low cost, secure and fast analysis tool. It also provides benefits, which can be reached with many different system configurations. Topics to be discussed include: Applications, Modeling, Validating, Software and benefits of simulation. This paper provides a comprehensive literature review on research efforts in simulation.

Keywords: Manufacturing, modeling, simulation, training.

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Authors: S. Esfandeh, M. Sedighizadeh

Abstract:

Weather systems use enormously complex combinations of numerical tools for study and forecasting. Unfortunately, due to phenomena in the world climate, such as the greenhouse effect, classical models may become insufficient mostly because they lack adaptation. Therefore, the weather forecast problem is matched for heuristic approaches, such as Evolutionary Algorithms. Experimentation with heuristic methods like Particle Swarm Optimization (PSO) algorithm can lead to the development of new insights or promising models that can be fine tuned with more focused techniques. This paper describes a PSO approach for analysis and prediction of data and provides experimental results of the aforementioned method on realworld meteorological time series.

Keywords: Weather, Climate, PSO, Prediction, Meteorological

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Authors: E. Nemati Lay, M. Peymani, E. Sanjari

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Prediction of viscosity of natural gas is an important parameter in the energy industries such as natural gas storage and transportation. In this study viscosity of different compositions of natural gas is modeled by using an artificial neural network (ANN) based on back-propagation method. A reliable database including more than 3841 experimental data of viscosity for testing and training of ANN is used. The designed neural network can predict the natural gas viscosity using pseudo-reduced pressure and pseudo-reduced temperature with AARD% of 0.221. The accuracy of designed ANN has been compared to other published empirical models. The comparison indicates that the proposed method can provide accurate results.

Keywords: Artificial neural network, Empirical correlation, Natural gas, Viscosity

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Authors: Jatinder Kumar, Ajay Bansal

Abstract:

The present study deals with the modeling and simulation of flow through an annular reactor at different hydrodynamic conditions using computational fluid dynamics (CFD) to investigate the flow behavior. CFD modeling was utilized to predict velocity distribution and average velocity in the annular geometry. The results of CFD simulations were compared with the mathematically derived equations and already developed correlations for validation purposes. CFD modeling was found suitable for predicting the flow characteristics in annular geometry under laminar flow conditions. It was observed that CFD also provides local values of the parameters of interest in addition to the average values for the simulated geometry.

Keywords: Annular reactor, computational fluid dynamics (CFD), hydrodynamics, Rhodamine B

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Authors: Raquel M. de Sousa, Sofiane Labidi, Allan Kardec D. Barros, Alex O. Barradas Filho, Aldalea L. B. Marques

Abstract:

Several parameters are established in order to measure biodiesel quality. One of them is the iodine value, which is an important parameter that measures the total unsaturation within a mixture of fatty acids. Limitation of unsaturated fatty acids is necessary since warming of higher quantity of these ones ends in either formation of deposits inside the motor or damage of lubricant. Determination of iodine value by official procedure tends to be very laborious, with high costs and toxicity of the reagents, this study uses artificial neural network (ANN) in order to predict the iodine value property as an alternative to these problems. The methodology of development of networks used 13 esters of fatty acids in the input with convergence algorithms of back propagation of back propagation type were optimized in order to get an architecture of prediction of iodine value. This study allowed us to demonstrate the neural networks’ ability to learn the correlation between biodiesel quality properties, in this caseiodine value, and the molecular structures that make it up. The model developed in the study reached a correlation coefficient (R) of 0.99 for both network validation and network simulation, with Levenberg-Maquardt algorithm.

Keywords: Artificial Neural Networks, Biodiesel, Iodine Value, Prediction.

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Authors: M. Morri, A. Soualmia, P. Belleudy

Abstract:

Vegetation affects the mean and turbulent flow structure. It may increase flood risks and sediment transport. Therefore, it is important to develop analytical approaches for the bed shear stress on vegetated bed, to predict resistance caused by vegetation. In the recent years, experimental and numerical models have both been developed to model the effects of submerged vegetation on open-channel flow. In this paper, different analytic models are compared and tested using the criteria of deviation, to explore their capacity for predicting the mean velocity and select the suitable one that will be applied in real case of rivers. The comparison between the measured data in vegetated flume and simulated mean velocities indicated, a good performance, in the case of rigid vegetation, whereas, Huthoff model shows the best agreement with a high coefficient of determination (R2=80%) and the smallest error in the prediction of the average velocities.

Keywords: Analytic Models, Comparison, Mean Velocity, Vegetation.

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