Search results for: line ampacity prediction

Authors: Xiang-Yao Zheng, Jen-Cheng Wang, Joe-Air Jiang

Abstract:

Improving the line ampacity while using existing power grids is an important issue that electricity dispatchers are now facing. Using the information provided by the dynamic thermal rating (DTR) of transmission lines, an overhead power grid can operate safely. However, dispatchers usually lack real-time DTR information. Thus, this study proposes a long-short-term memory (LSTM)-based method, which is one of the neural network models. The LSTM-based method predicts the DTR of lines using the weather data provided by Central Weather Bureau (CWB) of Taiwan. The possible thermal bottlenecks at different locations along the line and the margin of line ampacity can be real-time determined by the proposed LSTM-based prediction method. A case study that targets the 345 kV power grid of TaiPower in Taiwan is utilized to examine the performance of the proposed method. The simulation results show that the proposed method is useful to provide the information for the smart grid application in the future.

Keywords: electricity dispatch, line ampacity prediction, dynamic thermal rating, long-short-term memory neural network, smart grid

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: A. Hadjadj, S. Maamir

Abstract:

Since the advent of the law 86/14 concerning the
exploitation of the national territory by foreign companies in
partnership with the Algerian oil and gas company, the problem of
hydrocarbons metering in the sharing production come out.
More generally, good management counting hydrocarbons can
provide data on the production wells, the field and the reservoir for
medium and long term planning, particularly in the context of the
management and field development.
In this work, we are interested in the transactional metering which
is a very delicate and crucial period in the current context of the new
hydrocarbon’s law characterized by assets system between the
various activities of Sonatrach and its foreign partners.
After a state of the art on hydrocarbons metering devices in
Algeria and elsewhere, we will decline the advantages and
disadvantages of each system, and then we describe the problem to
try to reach an optimal solution.

Keywords: transactional metering, flowmeter orifice, heat flow, Sonatrach

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Authors: Aasheesh Raturi, Vimal Kothiyal, P. D. Semalty

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We studied mechanical properties of Eucalyptus tereticornis using FT-NIR spectroscopy. Firstly, spectra were pre-processed to eliminate useless information. Then, prediction model was constructed by partial least squares regression. To study the influence of pre-processing on prediction of mechanical properties for NIR analysis of wood samples, we applied various pretreatment methods like straight line subtraction, constant offset elimination, vector-normalization, min-max normalization, multiple scattering. Correction, first derivative, second derivatives and their combination with other treatment such as First derivative + straight line subtraction, First derivative+ vector normalization and First derivative+ multiplicative scattering correction. The data processing methods in combination of preprocessing with different NIR regions, RMSECV, RMSEP and optimum factors/rank were obtained by optimization process of model development. More than 350 combinations were obtained during optimization process. More than one pre-processing method gave good calibration/cross-validation and prediction/test models, but only the best calibration/cross-validation and prediction/test models are reported here. The results show that one can safely use NIR region between 4000 to 7500 cm-1 with straight line subtraction, constant offset elimination, first derivative and second derivative preprocessing method which were found to be most appropriate for models development.

Keywords: FT-NIR, mechanical properties, pre-processing, PLS

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Authors: Marian Dragomir, Alin Dragomir

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In the paper, two fault location algorithms are presented for transmission lines which use the line parameters to estimate the distance to the fault. The first algorithm uses only the measurements from one end of the line and the positive and zero sequence parameters of the line, while the second one uses the measurements from both ends of the line and only the positive sequence parameters of the line. The algorithms were tested using a transmission grid transposed in MATLAB. In a first stage it was established a fault location base line, where the algorithms mentioned above estimate the fault locations using the exact line parameters. After that, the positive and zero sequence resistance and reactance of the line were calculated again for different ground resistivity values and then the fault locations were estimated again in order to compare the results with the base line results. The results show that the algorithm which uses the zero sequence impedance of the line is the most sensitive to the line parameters modifications. The other algorithm is less sensitive to the line parameters modification.

Keywords: estimation algorithms, fault location, line parameters, simulation tool

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Authors: Kamalpreet Kaur, Renu Dhir

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Climate prediction is an essential component of climate research, which helps evaluate possible effects on economies, communities, and ecosystems. Climate prediction involves short-term weather prediction, seasonal prediction, and long-term climate change prediction. Climate prediction can use the information gathered from satellites, ground-based stations, and ocean buoys, among other sources. The paper's four architectures, such as ResNet50, VGG19, Inception-v3, and Xception, have been combined using an ensemble approach for overall performance and robustness. An ensemble of different models makes a prediction, and the majority vote determines the final prediction. The various architectures such as ResNet50, VGG19, Inception-v3, and Xception efficiently classify the dataset RSI-CB256, which contains satellite images into cloudy and non-cloudy. The generated ensembled S-E model (Sar-ensembled model) provides an accuracy of 99.25%.

Keywords: climate, satellite images, prediction, classification

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Authors: B. Sir, M. Podhoranyi, S. Kuchar, T. Kocyan

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Rainfall-runoff models play important role in hydrological predictions. However, the model is only one part of the process for creation of flood prediction. The aim of this paper is to show the process of successful prediction for flood event (May 15–May 18 2014). The prediction was performed by rainfall runoff model HEC–HMS, one of the models computed within Floreon+ system. The paper briefly evaluates the results of automatic hydrologic prediction on the river Olše catchment and its gages Český Těšín and Věřňovice.

Keywords: flood, HEC-HMS, prediction, rainfall, runoff

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Authors: N. H. Adenan, M. S. M. Noorani

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River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to developed an efficient water management system to optimize the allocation water resources.

Keywords: river flow, nonlinear prediction method, phase space, local linear approximation

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Authors: Yu Zhao, Min Zhang, Yuanqian Wang, Qiuyu Yu

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The prediction of aesthetics of apparel is helpful for the development of a new type of apparel. This study is to build the quantitative relationship between the aesthetics and its design parameters. In particular, women’s pants have been preliminarily studied. This aforementioned relationship has been carried out by statistical analysis. The contributions of this study include the development of a more personalized apparel design mechanism and the provision of some empirical knowledge for the development of other products in the aspect of aesthetics.

Keywords: aesthetics, crease line, cropped straight leg pants, knee width

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Authors: Muhammet Baldan, Emel Timuçin

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Generally, absorption and bioavailability increase if solubility increases; therefore, it is crucial to predict them in drug discovery applications. Molecular descriptors and Molecular properties are traditionally used for the prediction of water solubility. There are various key descriptors that are used for this purpose, namely Drogan Descriptors, Morgan Descriptors, Maccs keys, etc., and each has different prediction capabilities with differentiating successes between different data sets. Another source for the prediction of solubility is structural features; they are commonly used for the prediction of solubility. However, there are little to no studies that combine three or more properties or descriptors for prediction to produce a more powerful prediction model. Unlike available models, we used a combination of those features in a random forest machine learning model for improved solubility prediction to better predict and, therefore, contribute to drug discovery systems.

Keywords: solubility, molecular descriptors, machine learning, random forest

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Authors: Mehmet Savsar

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Several factors affect productivity of Food Processing Assembly Lines (FPAL). Engineers and line managers usually do not recognize some of these factors and underutilize their production/assembly lines. In this paper, a special food processing assembly line is studied in detail, and procedures are presented to illustrate how productivity and efficiency of such lines can be increased. The assembly line considered produces ten different types of freshly prepared salads on the same line, which is called mixed model assembly line. Problems causing delays and inefficiencies on the line are identified. Line balancing and related tools are used to increase line efficiency and minimize balance delays. The procedure and the approach utilized in this paper can be useful for the operation managers and industrial engineers dealing with similar assembly lines in food processing industry.

Keywords: assembly lines, line balancing, production efficiency, bottleneck

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Authors: Kefaya Qaddoum

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The aim of this study is to predict breast cancer and to construct a supportive model that will stimulate a more reliable prediction as a factor that is fundamental for public health. In this study, we utilize general regression neural networks (GRNN) to replace the normal predictions with prediction periods to achieve a reasonable percentage of confidence. The mechanism employed here utilises a machine learning system called conformal prediction (CP), in order to assign consistent confidence measures to predictions, which are combined with GRNN. We apply the resulting algorithm to the problem of breast cancer diagnosis. The results show that the prediction constructed by this method is reasonable and could be useful in practice.

Keywords: neural network, conformal prediction, cancer classification, regression

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Authors: Cristian Păuna

Abstract:

In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.

Keywords: algorithmic trading, automated trading systems, high-frequency trading, DAX Deutscher Aktienindex

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Authors: Hang Lo Lee, Ki Il Song, Hee Hwan Ryu

Abstract:

An accurate prediction of TBM(Tunnel Boring Machine) performance is very difficult for reliable estimation of the construction period and cost in preconstruction stage. For this purpose, the aim of this study is to analyze the evaluation process of various prediction models published since 2000 for TBM performance, and to select the optimal input parameters for the prediction model. A classification system of TBM performance prediction model and applied methodology are proposed in this research. Input and output parameters applied for prediction models are also represented. Based on these results, a statistical analysis is performed using the collected data from shield TBM tunnel in South Korea. By performing a simple regression and residual analysis utilizinFg statistical program, R, the optimal input parameters are selected. These results are expected to be used for development of prediction model of TBM performance.

Keywords: TBM performance prediction model, classification system, simple regression analysis, residual analysis, optimal input parameters

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Authors: Han Bing, Yin Zhenjie

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In order to analyze the status of a diesel engine, as well as conduct fault prediction, a new prediction model based on a gray system is proposed in this paper, which takes advantage of the neural network and the genetic algorithm. The proposed GBPGA prediction model builds on the GM (1.5) model and uses a neural network, which is optimized by a genetic algorithm to construct the error compensator. We verify our proposed model on the diesel faulty simulation data and the experimental results show that GBPGA has the potential to employ fault prediction on diesel.

Keywords: fault prediction, neural network, GM(1, 5) genetic algorithm, GBPGA

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Authors: Emin Gundogar, Burak Erkayman, Aysegul Yilmaz, Nusret Sazak

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When considering current competition conditions on the world, satisfying customer demands on time has become an important factor that enables the firms take a step further. Therefore, production process must be completed faster to take the competitive advantage. A balanced assembly line is the one of most important factors affecting the speed of production lines. The aim of this study is to build an assembly line to balance the assembly line and to simulate it for different scenarios through a refrigerator factory. The times of the operations is analyzed and grouped by the priorities. First, a Kilbridge & Wester heuristics is put to the model then a simulation approach is implemented to the model and the differences are observed.

Keywords: assembly line design, assembly line balancing, simulation modelling, refrigeration industry

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Authors: S. A. Naeini, A. Khalili

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Nowadays, tunnels with different applications are developed, and most of them are related to subway tunnels. The excavation of shallow tunnels that pass under municipal utilities is very important, and the surface settlement control is an important factor in the design. The study sought to analyze the settlement and also to find an appropriate model in order to predict the behavior of the tunnel in Tehran subway line-3. The displacement in these sections is also determined by using numerical analyses and numerical modeling. In addition, the Adaptive Neuro-Fuzzy Inference System (ANFIS) method is utilized by Hybrid training algorithm. The database pertinent to the optimum network was obtained from 46 subway tunnels in Iran and Turkey which have been constructed by the new Austrian tunneling method (NATM) with similar parameters based on type of their soil. The surface settlement was measured, and the acquired results were compared to the predicted values. The results disclosed that computing intelligence is a good substitute for numerical modeling.

Keywords: settlement, Subway Line, FLAC3D, ANFIS Method

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Authors: K. Jahani, J. Razavi

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Nowadays, to decrease the number of downtimes in the industries such as metal mining, petroleum and chemical industries, predictive maintenance is crucial. In order to have efficient predictive maintenance, knowing the performance of critical equipment of production line such as pumps and hydro-cyclones under variable operating parameters, selecting best indicators of this equipment health situations, best locations for instrumentation, and also measuring of these indicators are very important. In this paper, computer aided engineering (CAE) tools are implemented to study some important elements of copper process line, namely slurry pumps and cyclone to predict the performance of these components under different working conditions. These modeling and simulations can be used in predicting, for example, the damage tolerance of the main shaft of the slurry pump or wear rate and location of cyclone wall or pump case and impeller. Also, the simulations can suggest best-measuring parameters, measuring intervals, and their locations.

Keywords: computer aided engineering, predictive maintenance, fault detection, mining process line, slurry pump, hydrocyclone

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Authors: Inaki Maulida Hakim, T. Yuri M. Zagloel, Astari Wulandari

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Six sigma is a framework that is used to identify inefficiency so that the cause of inefficiency will be known and right improvement to overcome cause of inefficiency can be conducted. This paper presents result of implementing six sigma to improve piston assembly line in Manufacturing Laboratory, Universitas Indonesia. Six sigma framework will be used to analyze the significant factor of inefficiency that needs to be improved which causes bottleneck in assembly line. After analysis based on six sigma framework conducted, line balancing method was chosen for improvement to overcome causative factor of inefficiency which is differences time between workstation that causes bottleneck in assembly line. Then after line balancing conducted in piston assembly line, the result is increase in efficiency. Efficiency is shown in the decreasing of Defects per Million Opportunities (DPMO) from 900,000 to 700,000, the increasing of level of labor productivity from 0.0041 to 0.00742, the decreasing of idle time from 121.3 seconds to 12.1 seconds, and the increasing of output, which is from 1 piston in 5 minutes become 3 pistons in 5 minutes.

Keywords: assembly line, line balancing, productivity, six sigma

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: Hyun-Woo Cho

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Detection of incipient abnormal events in production processes is important to improve safety and reliability of manufacturing operations and reduce losses caused by failures. The construction of calibration models for predicting faulty conditions is quite essential in making decisions on when to perform preventive maintenance. This paper presents a multivariate calibration monitoring approach based on the statistical analysis of process measurement data. The calibration model is used to predict faulty conditions from historical reference data. This approach utilizes variable selection techniques, and the predictive performance of several prediction methods are evaluated using real data. The results shows that the calibration model based on supervised probabilistic model yielded best performance in this work. By adopting a proper variable selection scheme in calibration models, the prediction performance can be improved by excluding non-informative variables from their model building steps.

Keywords: calibration model, monitoring, quality improvement, feature selection

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Authors: Jeonghwan Jeon

Abstract:

With the advent of IPTV in the fierce competition with existing broadcasting system, it is emerged as an important issue to predict how much the adoption of IPTV service will be. This paper aims to suggest a prediction model for adopting IPTV using classification and Ranking Belief Simplex (CaRBS). A simplex plot method of representing data allows a clear visual representation to the degree of interaction of the support from the variables to the prediction of the objects. CaRBS is applied to the survey data on the IPTV adoption.

Keywords: prediction, adoption, IPTV, CaRBS

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Authors: Andrey Lebedev, Ilya Dmitrenok, JooYoung Lee, Leonard Johard

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Top-k shortest path routing problem is an extension of finding the shortest path in a given network. Shortest path is one of the most essential measures as it reveals the relations between two nodes in a network. However, in many real world networks, whose diameters are small, top-k shortest path is more interesting as it contains more information about the network topology. Many variations to compute top-k shortest paths have been studied. In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Then, we also propose a top-k distance based graph matching algorithm.

Keywords: graph matching, link prediction, shortest path, similarity

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Authors: Ali Hamad, Ibrahim Al-Drous, Saleh Al-Jufout

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This paper presents a case study of using STATCOM to enhance the performance of Al-Qatraneh 33-kV transmission line. The location of the STATCOM was identified maintaining minimum voltage drops at the 110 load nodes. The transmission line and the 110 load nodes have been modeled by MATLAB/Simulink. The suggested STATCOM and its location will increase the transmission capability of this transmission line and overcome the overload expected in the year 2020. The annual percentage loading rise has been considered as 14%. A graphical representation of the line voltages and the voltage drops at different load nodes has been illustrated.

Keywords: FACTS, MATLAB, STATCOM, transmission line, voltage drop

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Authors: Fadwa Jewilli

Abstract:

A sudden leak of a 6-inch gas line pipe after being in service for one year was observed. The pipe had been designed to transport dry gas. The failure had taken place in 6 o’clock position at the stage discharge of the flow process. Laboratory investigations were conducted to find out the cause of the pipe rupture. Visual and metallographic observations confirmed that the pipe split was due to a crack initiated in circumferential and then turned into longitudinal direction. Sever wall thickness reduction was noticed on the internal pipe surface. Scanning electron microscopy observations at the fracture surface revealed features of ductile fracture mode. Corrosion product analysis showed the traces of iron carbonate and iron sulphate. The laboratory analysis resulted in the conclusion that the pipe failed due to the effect of wet fluid (condensate) caused severe wall thickness dissolution resulted in pipe could not stand the continuation at in-service working condition.

Keywords: gas line pipe, corrosion prediction ductile fracture, ductile fracture, failure analysis

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Authors: Maurice Ntahobari, Levin Kuhlmann, Mario Boley, Zhinoos Razavi Hesabi

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For machine learning based epileptic seizure prediction, it is important for the model to be implemented in small implantable or wearable devices that can be used to monitor epilepsy patients; however, current state-of-the-art methods are complex and computationally intensive. We use Shapley Additive Explanation (SHAP) to find relevant intracranial electroencephalogram (iEEG) features and improve the computational efficiency of a state-of-the-art seizure prediction method based on the extra trees classifier while maintaining prediction performance. Results for a small contest dataset and a much larger dataset with continuous recordings of up to 3 years per patient from 15 patients yield better than chance prediction performance (p < 0.004). Moreover, while the performance of the SHAP-based model is comparable to that of the benchmark, the overall training and prediction time of the model has been reduced by a factor of 1.83. It can also be noted that the feature called zero crossing value is the best EEG feature for seizure prediction. These results suggest state-of-the-art seizure prediction performance can be achieved using efficient methods based on optimal feature selection.

Keywords: machine learning, seizure prediction, extra tree classifier, SHAP, epilepsy

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Authors: John Morales, Eduardo Orduña

Abstract:

Currently the Principal Component Analysis (PCA) theory has been used to develop algorithms regarding to Electric Power Systems (EPS). In this context, this paper presents a practical tutorial of this technique detailed their concept, on-line and off-line mathematical foundations, which are necessary and desirables in EPS algorithms. Thus, features of their eigenvectors which are very useful to real-time process are explained, showing how it is possible to select these parameters through a direct optimization. On the other hand, in this work in order to show the application of PCA to off-line and on-line signals, an example step to step using Matlab commands is presented. Finally, a list of different approaches using PCA is presented, and some works which could be analyzed using this tutorial are presented.

Keywords: practical guide; on-line; off-line, algorithms, faults

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Authors: Jae Kyung Lee, Joon Young Park

Abstract:

Maintenance on power transmission lines requires a lot of works. Sometimes they should be maintained on live-line environment with high altitude. Therefore, there always exist risks of falling from height and electric shock. To decline those risks, drones are recently applying on the electric power industry. This paper presents new operational technology while inspecting power transmission line. This paper also describes a technique for creating a flight path of a drone for transmission line inspection and a technique for controlling the drones of different types. Its technical and economical feasibilities have confirmed through experiments.

Keywords: drones, transmission line, inspection, control system

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Authors: Albert Suryaprawira

Abstract:

The Nasion-Sella Line (NSL) has been used for several years as a reference line in longitudinal growth study. Therefore this line is considered to be stable not only to evaluate treatment outcome and to predict relapse possibility but also to manage prognosis. This is a radiographic superimposition of an adult male aged 19 years who complained of difficulty in aesthetic, talking and chewing. Patient has a midface hypoplasia profile (concave). He was diagnosed to have a severe Skeletal Class III with Class III malocclusion, increased lower vertical height, and an anterior open bite. A pre-treatment cephalometric radiograph was taken to analyse the skeletal problem and to measure the amount of bone movement and the prediction soft tissue response. A panoramic radiograph was also taken to analyse bone quality, bone abnormality, third molar impaction, etc. Before the surgery, a pre-surgical cephalometric radiograph was taken to re-evaluate the plan and to settle the final amount of bone cut. After the surgery, a post-surgical cephalometric radiograph was taken to confirm the result with the plan. The superimposition using NSL as a reference line between those radiographs was performed to analyse the outcome. It is important to describe the amount of hard and soft tissue movement and to predict the possibility of relapse after the surgery. The patient also needs to understand all the surgical plan, outcome and relapse prevention. The surgical management included maxillary impaction and advancement of Le Fort I osteotomy. The evaluation using NSL as a reference was a very useful method in determining the outcome and prognosis.

Keywords: Nasion-Sella Line, midface hypoplasia, Le Fort 1, maxillary advancement

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Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani

Abstract:

This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: chaotic approach, phase space, Cao method, local linear approximation method

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