Search results for: algorithm optimisation

Authors: Mehdi Jalalpour, Mazdak Tootkaboni

Abstract:

We present a computationally efficient method for reliability-based topology optimization under material properties uncertainty, which is assumed to be lognormally distributed and correlated within the domain. Computational efficiency is achieved through estimating the response statistics with stochastic perturbation of second order, using these statistics to fit an appropriate distribution that follows the empirical distribution of the response, and employing an efficient gradient-based optimizer. The proposed algorithm is utilized for design of new structures and the changes in the optimized topology is discussed for various levels of target reliability and correlation strength. Predictions were verified thorough comparison with results obtained using Monte Carlo simulation.

Keywords: material uncertainty, stochastic perturbation, structural reliability, topology optimization

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Authors: Sanaa I. Abu Alasal, Madleen M. Esbeih, Eman R. Fayyad, Rami S. Gharaibeh, Mostafa Z. Ali, Ahmed A. Freewan, Monther M. Jamhawi

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This research proposes a novel reconstruction protocol for restoring missing surfaces and low-quality edges and shapes in photos of artifacts at historical sites. The protocol starts with the extraction of a cloud of points. This extraction process is based on four subordinate algorithms, which differ in the robustness and amount of resultant. Moreover, they use different -but complementary- accuracy to some related features and to the way they build a quality mesh. The performance of our proposed protocol is compared with other state-of-the-art algorithms and toolkits. The statistical analysis shows that our algorithm significantly outperforms its rivals in the resultant quality of its object files used to reconstruct the desired model.

Keywords: meshes, point clouds, surface reconstruction protocols, 3D reconstruction

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Authors: Fanqiang Kong, Jindong Zhang, Daiyin Zhu

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Space-time adaptive processing (STAP) techniques have been motivated as a key enabling technology for advanced airborne radar applications. In this paper, the notion of cognitive radar is extended to STAP technique, and cognitive STAP is discussed. The principle for improving signal-to-clutter ratio (SCNR) based on slow-time coding is given, and the corresponding optimization algorithm based on cyclic and power-like algorithms is presented. Numerical examples show the effectiveness of the proposed method.

Keywords: space-time adaptive processing (STAP), airborne radar, signal-to-clutter ratio, slow-time coding

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Authors: Sana Ansari, Sirus Mohammadi

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In distribution systems, shunt capacitors are used to reduce power losses, to improve voltage profile, and to increase the maximum flow through cables and transformers. This paper presents a new method to determine the optimal locations and economical sizing of fixed and/or switched shunt capacitors with a view to power losses reduction and voltage stability enhancement. General Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with Linear Programming (LP). The proposed method is tested on 33 node distribution system and the results show that the algorithm suitable for practical implementation on real systems with any size.

Keywords: power losses, voltage stability, radial distribution systems, capacitor

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Authors: Shamsundar Kulkarni

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Video capturing by non-professionals will lead to unanticipated effects. Such as image distortion, image blurring etc. Hence, many researchers study such drawbacks to enhance the quality of videos. In this paper, an algorithm is proposed to stabilize jittery videos .A stable output video will be attained without the effect of jitter which is caused due to shaking of handheld camera during video recording. Firstly, salient points from each frame from the input video are identified and processed followed by optimizing and stabilize the video. Optimization includes the quality of the video stabilization. This method has shown good result in terms of stabilization and it discarded distortion from the output videos recorded in different circumstances.

Keywords: video stabilization, point feature matching, salient points, image quality measurement

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Isa Moazen, Ali Nahvi

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Driver drowsiness is a major cause of vehicle accidents, and facial images are highly valuable to detect drowsiness. In this paper, we perform our research via a thermal camera to record drivers' facial images on a driving simulator. A robust real-time algorithm extracts the features using horizontal and vertical integration projection, contours, contour orientations, and cropping tools. The features are included four target areas on the cheeks and forehead. Qt compiler and OpenCV are used with two cameras with different resolutions. A high-resolution thermal camera is used for fifteen subjects, and a low-resolution one is used for a person. The results are investigated by four temperature plots and evaluated by observer rating of drowsiness.

Keywords: advanced driver assistance systems, thermal imaging, driver drowsiness detection, feature extraction

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Authors: Brian E. Usibe

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This paper addresses the problem of a linear crack located in the middle of a homogeneous elastic media under normal tension-compression harmonic loading. The problem of deformation of the fractured media is solved using the direct finite element numerical procedure, including the analysis of the dynamic field variables of the problem. A finite element algorithm that satisfies the unilateral Signorini contact constraint is also presented for the solution of the contact interaction of the crack faces and how this accounts for the qualitative and quantitative changes in the solution when determining the dynamic fracture parameter.

Keywords: harmonic loading, linear crack, fracture parameter, wave number, FEA, contact interaction

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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Authors: Kostas Metaxiotis, Kostas Liagkouras

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This study presents an Expert System specially designed to be used with Multiobjective Evolutionary Algorithms (MOEAs) for the solution of the portfolio selection problem. The validation of the proposed hybrid System is done by using data sets from Hang Seng 31 in Hong Kong, DAX 100 in Germany and FTSE 100 in UK. The performance of the proposed system is assessed in comparison with the Non-dominated Sorting Genetic Algorithm II (NSGAII). The evaluation of the performance is based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it. The results show that the proposed hybrid system is efficient for the solution of this kind of problems.

Keywords: expert systems, multi-objective optimization, evolutionary algorithms, portfolio selection

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Authors: Supriya H. S., Chandrakala B. M.

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Deep learning based models have been recently successful adoption for network traffic prediction. However, training a deep learning model for various prediction tasks is considered one of the critical tasks due to various reasons. This research work develops Multi-Layer Hybrid Network (MLHN) for network traffic prediction and analysis; MLHN comprises the three distinctive networks for handling the different inputs for custom feature extraction. Furthermore, an optimized and efficient parameter-tuning algorithm is introduced to enhance parameter learning. MLHN is evaluated considering the “Big Data Challenge” dataset considering the Mean Absolute Error, Root Mean Square Error and R^2as metrics; furthermore, MLHN efficiency is proved through comparison with a state-of-art approach.

Keywords: MLHN, network traffic prediction

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Authors: L. Matlawe, E. S. Idemudia

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The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modeling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they were designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: emotional abuse, employees, mental health, self-concept

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Authors: András Rövid, Takeshi Hashimoto

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The paper focuses on the problem of the point correspondence matching in stereo images. The proposed matching algorithm is based on the combination of simpler methods such as normalized sum of squared differences (NSSD) and a more complex phase correlation based approach, by considering the noise and other factors, as well. The speed of NSSD and the preciseness of the phase correlation together yield an efficient approach to find the best candidate point with sub-pixel accuracy in stereo image pairs. The task of the NSSD in this case is to approach the candidate pixel roughly. Afterwards the location of the candidate is refined by an enhanced phase correlation based method which in contrast to the NSSD has to run only once for each selected pixel.

Keywords: stereo matching, sub-pixel accuracy, phase correlation, SVD, NSSD

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Authors: M. Bassoui, M. Ferfra, M. Chrayagne

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This paper presents a qualitative modeling for the nonlinear B-H curve of the saturable magnetic materials for a transformer with shunts used in the power supply for the magnetron. This power supply is composed of a single phase leakage flux transformer supplying a cell composed of a capacitor and a diode, which double the voltage and stabilize the current, and a single magnetron at the output of the cell. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve.

Keywords: B(H) curve, fuzzy clustering, magnetron, power supply

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Boukhatem Mohamed Belkaid, Lahdi Mourad

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In this paper, we propose a new encryption system for security issues medical images. The hybrid encryption scheme is based on AES and RSA algorithms to validate the three security services are authentication, integrity, and confidentiality. Privacy is ensured by AES, authenticity is ensured by the RSA algorithm. Integrity is assured by the basic function of the correlation between adjacent pixels. Our system generates a unique password every new session of encryption, that will be used to encrypt each frame of the medical image basis to strengthen and ensure his safety. Several metrics have been used for various tests of our analysis. For the integrity test, we noticed the efficiencies of our system and how the imprint cryptographic changes at reception if a change affects the image in the transmission channel.

Keywords: AES, RSA, integrity, confidentiality, authentication, medical images, encryption, decryption, key, correlation

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Authors: Iris Vogeler, Rogerio Cichota, Armin Werner

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Dairy farms are under pressure to increase productivity while reducing environmental impacts. Effective fertiliser management practices are critical to achieve this. Determination of optimum nitrogen (N) fertilisation rates which maximise pasture growth and minimise N losses is challenging due to variability in plant requirements and likely near-future supply of N by the soil. Remote sensing can be used for mapping N nutrition status of plants and to rapidly assess the spatial variability within a field. An algorithm is, however, lacking which relates the N status of the plants to the expected yield response to additions of N. The aim of this simulation study was to develop a multi-variate model for determining N fertilisation rate for a target percentage of the maximum achievable yield based on the pasture N concentration (ii) use of an algorithm for guiding fertilisation rates, and (iii) evaluation of the model regarding pasture yield and N losses, including N leaching, denitrification and volatilisation. A simulation study was carried out using the Agricultural Production Systems Simulator (APSIM). The simulations were done for an irrigated ryegrass pasture in the Canterbury region of New Zealand. A multi-variate model was developed and used to determine monthly required N fertilisation rates based on pasture N content prior to fertilisation and targets of 50, 75, 90 and 100% of the potential monthly yield. These monthly optimised fertilisation rules were evaluated by running APSIM for a ten-year period to provide yield and N loss estimates from both nonurine and urine affected areas. Comparison with typical fertilisation rates of 150 and 400 kg N/ha/year was also done. Assessment of pasture yield and leaching from fertiliser and urine patches indicated a large reduction in N losses when N fertilisation rates were controlled by the multi-variate model. However, the reduction in leaching losses was much smaller when taking into account the effects of urine patches. The proposed approach based on biophysical modelling to develop a multi-variate model for determining optimum N fertilisation rates dependent on pasture N content is very promising. Further analysis, under different environmental conditions and validation is required before the approach can be used to help adjust fertiliser management practices to temporal and spatial N demand based on the nitrogen status of the pasture.

Keywords: APSIM modelling, optimum N fertilization rate, pasture N content, ryegrass pasture, three dimensional surface response function.

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Authors: H. Gonzalez-Rivera, J. L. Palmeros-Torres

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This paper describes the application of traditional computer vision techniques as a procedure for automatic measurement of the secondary dendrite arm spacing (SDAS) from microscopic images. The algorithm is capable of finding the lineal or curve-shaped secondary column of the main microstructure, measuring its length size in a micro-meter and counting the number of spaces between dendrites. The automatic characterization was compared with a set of 1728 manually characterized images, leading to an accuracy of −0.27 µm for the length size determination and a precision of ± 2.78 counts for dendrite spacing counting, also reducing the characterization time from 7 hours to 2 minutes.

Keywords: dendrite arm spacing, microstructure inspection, pattern recognition, polynomial regression

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Authors: Ali Mashayekh, Mahdiye Khorasani, Thomas weyh

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The demand for battery electric vehicles (BEV) is steadily increasing, and it can be assumed that electric mobility will dominate the market for individual transportation in the future. Regarding BEVs, the focus of state-of-the-art research and development is on vehicle batteries since their properties primarily determine vehicles' characteristic parameters, such as price, driving range, charging time, and lifetime. State-of-the-art battery packs consist of invariable configurations of battery cells, connected in series and parallel. A promising alternative is battery systems based on multilevel inverters, which can alter the configuration of the battery cells during operation via semiconductor switches. The main benefit of such topologies is that a three-phase AC voltage can be directly generated from the battery pack, and no separate power inverters are required. Therefore, modular battery systems based on different multilevel inverter topologies and reconfigurable battery systems are currently under investigation. Another advantage of the multilevel concept is that the possibility to reconfigure the battery pack allows battery cells with different states of charge (SoC) to be connected in parallel, and thus low-loss balancing can take place between such cells. In contrast, in conventional battery systems, parallel connected (hard-wired) battery cells are discharged via bleeder resistors to keep the individual SoCs of the parallel battery strands balanced, ultimately reducing the vehicle range. Different multilevel inverter topologies and reconfigurable batteries have been described in the available literature that makes the before-mentioned advantages possible. However, what has not yet been described is how an intelligent operating algorithm needs to look like to keep the SoCs of the individual battery strands of a modular battery system with integrated power electronics balanced. Therefore, this paper suggests an SoC balancing approach for Battery Modular Multilevel Management (BM3) converter systems, which can be similarly used for reconfigurable battery systems or other multilevel inverter topologies with parallel connectivity. The here suggested approach attempts to simultaneously utilize all converter modules (bypassing individual modules should be avoided) because the parallel connection of adjacent modules reduces the phase-strand's battery impedance. Furthermore, the presented approach tries to reduce the number of switching events when changing the switching state combination. Thereby, the ohmic battery losses and switching losses are kept as low as possible. Since no power is dissipated in any designated bleeder resistors and no designated active balancing circuitry is required, the suggested approach can be categorized as a proactive balancing approach. To verify the algorithm's validity, simulations are used.

Keywords: battery management system, BEV, battery modular multilevel management (BM3), SoC balancing

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Authors: Riona Dighe

Abstract:

This research attempts to identify an alternative approach to the measurement of Gross National Happiness (GNH). It uses artificial intelligence (AI), incorporating natural language processing (NLP) and sentiment analysis to measure GNH. We use ‘off the shelf’ NLP models responsible for the sentiment analysis of a sentence as a building block for this research. We constructed an algorithm using NLP models to derive a sentiment analysis score against sentences. This was then tested against a sample of 20 respondents to derive a sentiment analysis score. The scores generated resembled human responses. By utilising the MLP classifier, decision tree, linear model, and K-nearest neighbors, we were able to obtain a test accuracy of 89.97%, 54.63%, 52.13%, and 47.9%, respectively. This gave us the confidence to use the NLP models against sentences in websites to measure the GNH of a country.

Keywords: artificial intelligence, NLP, sentiment analysis, gross national happiness

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Authors: Yayun Hsu, Henry Horng-Shing Lu

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This paper proposes a data-driven, biology-inspired neural segmentation method of 3D drosophila Brainbow images. We use Bayesian Sequential Partitioning algorithm for probabilistic modeling, which can be used to detect somas and to eliminate cross talk effects. This work attempts to develop an automatic methodology for neuron image segmentation, which nowadays still lacks a complete solution due to the complexity of the image. The proposed method does not need any predetermined, risk-prone thresholds since biological information is inherently included in the image processing procedure. Therefore, it is less sensitive to variations in neuron morphology; meanwhile, its flexibility would be beneficial for tracing the intertwining structure of neurons.

Keywords: brainbow, 3D imaging, image segmentation, neuron morphology, biological data mining, non-parametric learning

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Authors: Khadija Raissi, Bechir Ben Gouissem

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In this paper, we perform the investigation of some routing protocols in Vehicular Ad-Hoc Network (VANET) context. Indeed, we study the efficiency of protocols like Dynamic Source Routing (DSR), Ad hoc On-demand Distance Vector Routing (AODV), Destination Sequenced Distance Vector (DSDV), Optimized Link State Routing convention (OLSR) and Vehicular Multi-hop algorithm for Stable Clustering (VMASC) in terms of packet delivery ratio (PDR) and throughput. The performance evaluation and comparison between the studied protocols shows that the VMASC is the best protocols regarding fast data transmission and link stability in VANETs. The validation of all results is done by the NS3 simulator.

Keywords: VANET, smart city, AODV, OLSR, DSR, OLSR, VMASC, routing protocols, NS3

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Authors: Damanjit Kaur, Avani Bhatia

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Color constancy is significant for human vision since color is a pictorial cue that helps in solving different visions tasks such as tracking, object recognition, or categorization. Therefore, several computational methods have tried to simulate human color constancy abilities to stabilize machine color representations. Two different kinds of methods have been used, i.e., normalization and constancy. While color normalization creates a new representation of the image by canceling illuminant effects, color constancy directly estimates the color of the illuminant in order to map the image colors to a canonical version. Color constancy is the capability to determine colors of objects independent of the color of the light source. This research work studies the most of the well-known color constancy algorithms like white point and gray world.

Keywords: color constancy, gray world, white patch, modified white patch

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Authors: Meiling Yang, Shuguo Xie, Yilong Zhu

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Nowadays, due to diverse electric products and complex electromagnetic environment, the localization and troubleshooting of the electromagnetic radiation source is urgent and necessary especially on the condition of far field. However, based on the existing DOA positioning method, the system or devices are complex, bulky and expensive. To address this issue, this paper proposes a single antenna radiation source localization method. A single antenna moves to form a virtual antenna array combined with DOA and MUSIC algorithm to position accurately, meanwhile reducing the cost and simplify the equipment. As shown in the results of simulations and experiments, the virtual antenna array DOA estimation modeling is correct and its positioning is credible.

Keywords: virtual antenna array, DOA, localization, far field

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Vahid Bayrami Rad

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Ever since humans developed a collective way of life to the development of urbanization, the concern of security has always been considered one of the most important challenges of life. To protect property, locks have always been a practical tool. With the advancement of technology, the form of locks has changed from mechanical to electric. One of the most widely used fields of using artificial intelligence is its application in the technology of surveillance security systems. Currently, the technologies used in smart anti-theft door handles are one of the most potential fields for using artificial intelligence. Artificial intelligence has the possibility to learn, calculate, interpret and process by analyzing data with the help of algorithms and mathematical models and make smart decisions. We will use Arduino board to process data.

Keywords: arduino board, artificial intelligence, image processing, solenoid lock

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Authors: Mohamed Gazzeh, Bradley Null, Fethi Tlili, Hichem Besbes

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The burgeoning global ownership of personal vehicles has posed a significant strain on urban infrastructure, notably parking facilities, leading to traffic congestion and environmental concerns. Effective parking management systems (PMS) are indispensable for optimizing urban traffic flow and reducing emissions. The most commonly deployed systems nowadays rely on computer vision technology. This paper explores the integration of radar sensors and simulation in the context of smart parking management. We concentrate on radar sensors due to their versatility and utility in automotive applications, which extends to PMS. Additionally, radar sensors play a crucial role in driver assistance systems and autonomous vehicle development. However, the resource-intensive nature of radar data collection for algorithm development and testing necessitates innovative solutions. Simulation, particularly the monoDrive simulator, an internal development tool used by NI the Test and Measurement division of Emerson, offers a practical means to overcome this challenge. The primary objectives of this study encompass simulating radar sensors to generate a substantial dataset for algorithm development, testing, and, critically, assessing the transferability of models between simulated and real radar data. We focus on occupancy detection in parking as a practical use case, categorizing each parking space as vacant or occupied. The simulation approach using monoDrive enables algorithm validation and reliability assessment for virtual radar sensors. It meticulously designed various parking scenarios, involving manual measurements of parking spot coordinates, orientations, and the utilization of TI AWR1843 radar. To create a diverse dataset, we generated 4950 scenarios, comprising a total of 455,400 parking spots. This extensive dataset encompasses radar configuration details, ground truth occupancy information, radar detections, and associated object attributes such as range, azimuth, elevation, radar cross-section, and velocity data. The paper also addresses the intricacies and challenges of real-world radar data collection, highlighting the advantages of simulation in producing radar data for parking lot applications. We developed classification models based on Support Vector Machines (SVM) and Density-Based Spatial Clustering of Applications with Noise (DBSCAN), exclusively trained and evaluated on simulated data. Subsequently, we applied these models to real-world data, comparing their performance against the monoDrive dataset. The study demonstrates the feasibility of transferring models from a simulated environment to real-world applications, achieving an impressive accuracy score of 92% using only one radar sensor. This finding underscores the potential of radar sensors and simulation in the development of smart parking management systems, offering significant benefits for improving urban mobility and reducing environmental impact. The integration of radar sensors and simulation represents a promising avenue for enhancing smart parking management systems, addressing the challenges posed by the exponential growth in personal vehicle ownership. This research contributes valuable insights into the practicality of using simulated radar data in real-world applications and underscores the role of radar technology in advancing urban sustainability.

Keywords: autonomous vehicle simulator, FMCW radar sensors, occupancy detection, smart parking management, transferability of models

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Authors: M. Jebali, M. Jemni

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This work is the part of vision based hand gesture recognition system for Natural Human Computer Interface. Hand tracking and segmentation are the primary steps for any hand gesture recognition system. The aim of this paper is to develop robust and efficient hand segmentation algorithm such as an input to another system which attempt to bring the HCI performance nearby the human-human interaction, by modeling an intelligent sign language recognition system based on prediction in the context of dialogue between the system (avatar) and the interlocutor. For the purpose of hand segmentation, an overcoming occlusion approach has been proposed for superior results for detection of hand from an image.

Keywords: HCI, sign language recognition, object tracking, hand segmentation

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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