Search results for: nonlinear systems of equations

Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: George Mahalu

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The Chua diode has been configured over time in various ways, using electronic structures like operational amplifiers (AOs) or devices with gas or semiconductors. When discussing the use of semiconductor devices, tunnel diodes (Esaki diodes) are most often considered, and more recently, transistorized configurations such as lambda diodes. The paperwork proposed here uses in the modeling a lambda diode type configuration consisting of two junction field effect transistors (JFET). The original scheme is created in the MULTISIM electronic simulation environment and is analyzed in order to identify the conditions for the appearance of evolutionary unpredictability specific to nonlinear dynamic systems with chaos-induced behavior. The chaotic deterministic oscillator is one autonomous type, a fact that places it in the class of Chua’s type oscillators, the only significant and most important difference being the presence of a nonlinear device like the one mentioned structure above. The chaotic behavior is identified both by means of strange attractor-type trajectories and visible during the simulation and by highlighting the hypersensitivity of the system to small variations of one of the input parameters. The results obtained through simulation and the conclusions drawn are useful in the further research of ways to implement such constructive electronic solutions in theoretical and practical applications related to modern small signal amplification structures, to systems for encoding and decoding messages through various modern ways of communication, as well as new structures that can be imagined both in modern neural networks and in those for the physical implementation of some requirements imposed by current research with the aim of obtaining practically usable solutions in quantum computing and quantum computers.

Keywords: chua, diode, memristor, chaos

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Authors: Yasar Pala, Safa Senaysoy, Emre Calis

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In this paper, structural behavior and improvement of buckling behavior of cold formed steel uprights with open cross-section used storage rack system are studied. As a first step, in the case of a stiffener having an inclined part on the flange, experimental and nonlinear finite element analysis are carried out for three different upright lengths. In the uprights with long length, global buckling is observed while distortional buckling and local buckling are observed in the uprights with medium length and those with short length, respectively. After this point, the study is divided into two groups. One of these groups is the case where the stiffener on the flange is folded at 90°. For this case, four different distances of the stiffener from the web are taken into account. In the other group, the case where different depth of stiffener on the web is considered. Combining experimental and finite element results, the cross-section giving the ultimate critical buckling load is selected.

Keywords: steel, upright, buckling, modes, nonlinear finite element analysis, optimization

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Authors: Yosra Baaziz, Moez Labidi

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Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: Farhad Imanshoar

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The regime or equilibrium geometry of alluvial rivers remains a topic of fundamental scientific and engineering interest. There are several approaches to analyze the problem, namely: empirical formulas, semi-theoretical methods and rational (extreme) procedures. However, none of them is widely accepted at present, due to lack of knowledge of some physical processes associated with channel formation and the simplification hypotheses imposed in order to reduce the high quantity of involved variables. The study presented in this paper shows a new approach to estimate stable width and depth of sand-bed rivers by using developed stream power equation (DSPE). At first, a new procedure based on theoretical analysis and by considering DSPE and ultimate sediment concentration were developed. Then, experimental data for regime condition in sand-bed rivers (flow depth, flow width, sediment feed rate for several cases) were gathered. Finally, the results of this research (regime equations) are compared with the field data and other regime equations. A good agreement was observed between the field data and the values resulted from developed regime equation.

Keywords: regime equations, developed stream power equation, sand-bed rivers, semi-theoretical methods

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Authors: Jaime E. Munoz, Jose C. Arcos, Oscar E. Bautista, Ivan E. Campos

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The influence of slippage phenomenon over the destabilization and atomization mechanisms induced via surface acoustic waves on a Newtonian, millimeter-sized, drop deposited on a hydrophilic substrate is studied theoretically. By implementing the Navier-slip model and a lubrication-type approach into the equations which govern the dynamic response of a drop exposed to acoustic stress, a highly nonlinear evolution equation for the air-liquid interface is derived in terms of the acoustic capillary number and the slip coefficient. By numerically solving such an evolution equation, the Spatio-temporal deformation of the drop's free surface is obtained; in this context, atomization of the initial drop into micron-sized droplets is predicted at our numerical model once the acoustically-driven capillary waves reach a critical value: the instability length. Our results show slippage phenomenon at systems with partial and complete wetting favors the formation of capillary waves at the free surface, which traduces in a major volume of liquid being atomized in comparison to the no-slip case for a given time interval. In consequence, slippage at the wall possesses the capability to affect and improve the atomization rate for a drop exposed to a high-frequency acoustic field.

Keywords: capillary instability, lubrication theory, navier-slip condition, SAW atomization

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Authors: Ju-young Hwang, Hyo-Gyoung Kwak, Hong Jae Yim

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This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical non-linearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, Prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC structures, heat transfer analysis, nonlinear analysis, after-cooling concrete model

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

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Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: Sanjay Kumar, Lillie Dewan

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The study of complex dynamic systems has advanced through various scientific approaches with the help of computer modeling. The common design trends in aerospace system design can be applied to quadcopter design. A quadcopter is a nonlinear, under-actuated system with complex aerodynamics parameters and creates challenges that demand new, robust, and effective control approaches. The flight control stability can be improved by planning and tracking the trajectory and reducing the effect of sensors and the operational environment. This paper presents a modern design Simmechanics visual modeling approach for a mechanical model of a quadcopter with three degrees of freedom. The Simmechanics model, considering inertia, mass, and geometric properties of a dynamic system, produces multiple translation and rotation maneuvers. The proportional, integral, and derivative (PID) controller is integrated with the Simmechanics model to follow a predefined quadcopter rotational trajectory for a fixed time interval. The results presented are satisfying. The simulation of the quadcopter control performed operations successfully.

Keywords: nonlinear system, quadcopter model, simscape modelling, proportional-integral-derivative controller

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: J. Fernandez de Canete

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Object-oriented modeling is spreading in the current simulation of physiological systems through the use of the individual components of the model and its interconnections to define the underlying dynamic equations. In this paper, we describe the use of both the SIMSCAPE and MODELICA simulation environments in the object-oriented modeling of the closed-loop cardiovascular system. The performance of the controlled system was analyzed by simulation in light of the existing hypothesis and validation tests previously performed with physiological data. The described approach represents a valuable tool in the teaching of physiology for graduate medical students.

Keywords: object-oriented modeling, SIMSCAPE simulation language, MODELICA simulation language, cardiovascular system

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Authors: Usamah Al-Ali

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We explore the effect of expanding space on the exoticity of the matter supporting a traversable Lorentzian wormhole of zero radial tide whose line element is given by ds2 = dt^2 − a^2(t)[ dr^2/(1 − kr2 −b(r)/r)+ r2dΩ^2 in the context of General Relativity. This task is achieved by deriving the Einstein field equations for anisotropic matter field corresponding to the considered cosmological wormhole metric and performing a classification of their solutions on the basis of a variable equations of state (EoS) of the form p = ω(r)ρ. Explicit forms of the shape function b(r) and the scale factor a(t) arising in the classification are utilized to construct the corresponding energy-momentum tensor where the energy conditions for each case is investigated. While the violation of energy conditions is inevitable in case of static wormholes, the classification we performed leads to interesting solutions in which this violation is either reduced or eliminated.

Keywords: general relativity, Einstein field equations, energy conditions, cosmological wormhole

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Authors: Milca F. Coelho, K. Bousson, Kawser Ahmed

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To accurately track an aerospace vehicle in a time-critical situation and in a highly nonlinear environment, is one of the strongest interests within the aerospace community. The tracking is achieved by estimating accurately the state of a moving target, which is composed of a set of variables that can provide a complete status of the system at a given time. One of the main ingredients for a good estimation performance is the use of efficient estimation algorithms. A well-known framework is the Kalman filtering methods, designed for prediction and estimation problems. The success of the Kalman Filter (KF) in engineering applications is mostly due to the Extended Kalman Filter (EKF), which is based on local linearization. Besides its popularity, the EKF presents several limitations. To address these limitations and as a possible solution to tracking problems, this paper proposes the use of the Ensemble Kalman Filter (EnKF). Although the EnKF is being extensively used in the context of weather forecasting and it is being recognized for producing accurate and computationally effective estimation on systems with a very high dimension, it is almost unknown by the tracking community. The EnKF was initially proposed as an attempt to improve the error covariance calculation, which on the classic Kalman Filter is difficult to implement. Also, in the EnKF method the prediction and analysis error covariances have ensemble representations. These ensembles have sizes which limit the number of degrees of freedom, in a way that the filter error covariance calculations are a lot more practical for modest ensemble sizes. In this paper, a realistic simulation of a radar tracking was performed, where the EnKF was applied and compared with the Extended Kalman Filter. The results suggested that the EnKF is a promising tool for tracking applications, offering more advantages in terms of performance.

Keywords: Kalman filter, nonlinear state estimation, optimal tracking, stochastic environment

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Authors: Mei Xutao, Nakano Kimihiko

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In order to enhance the energy harvesting efficiency, this paper presents a novel tri-stable energy harvesting system (TEHS), which is realized by the effect of magnetic force, in rotational motion to scavenge vibration energy. The device is meant to provide the power supply for wireless autonomous systems in low-frequency environment. The nonlinear TEHS is composed of the cantilever beam which is mounted on a rotating hub and partially covered by piezoelectric patch, a tip mass magnet in the end and two fixed magnets. A theoretical investigation using the Lagrangian formulation is derived to describe the motion of the energy harvesting system and the output voltage. Additionally, several numerical simulations were carried out to characterize the system under different external excitations and to validate its performance. The results demonstrated that TEHS owns a wide range of frequency of snap-through and high output voltage compared with the bi-stable energy harvesting system (BEHS). Moreover, some sets of experimental validations will be performed in the future work because the experimental setup is in the configuration now.

Keywords: piezoelectric beam, rotational motion, snap-through, tri-stable energy harvester

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Authors: Hamid Goharnejad, Milad Sadeghpoor Moalem, Mahmood Zakeri Niri, Leili Sadeghi Khalegh Abadi

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While there are many benefits to using reservoir dams, their break leads to destructive effects. From the viewpoint of International Committee of Large Dams (ICOLD), dam break means the collapse of whole or some parts of a dam; thereby the dam will be unable to hold water. Therefore, studying dam break phenomenon and prediction of its behavior and effects reduces losses and damages of the mentioned phenomenon. One of the most common types of reservoir dams is embankment dam. Overtopping in embankment dams occurs because of flood discharge system inability in release inflows to reservoir. One of the most important issues among managers and engineers to evaluate the performance of the reservoir dam rim when sliding into the storage, creating waves is large and long. In this study, the effects of floods which caused the overtopping of the dam have been investigated. It was assumed that spillway is unable to release the inflow. To determine outflow hydrograph resulting from dam break, numerical model using Flow-3D software and empirical equations was used. Results of numerical models and their comparison with empirical equations show that numerical model and empirical equations can be used to study the flood resulting from dam break.

Keywords: embankment dam break, empirical equations, Taleghan dam, Flow-3D numerical model

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Authors: Samsher Gautam, Apoorva Roy, Bhuvan Aggarwal

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Vapor absorption refrigeration systems can replace vapor compression systems in many applications as they can operate on a low-grade heat source and are environment-friendly. Widely used refrigerants such as CFCs and HFCs cause significant global warming. Natural refrigerants can be an alternative to them, among which carbon dioxide is promising for use in automotive air conditioning systems. Its inherent safety, ability to withstand high pressure and high heat transfer coefficient coupled with easy availability make it a likely choice for refrigerant. Various properties of the ionic liquid [bmim][PF₆], such as non-toxicity, stability over a wide temperature range and ability to dissolve gases like carbon dioxide, make it a suitable absorbent for a vapor absorption refrigeration system. In this paper, an absorption chiller consisting of a generator, condenser, evaporator and absorber was studied at an operating temperature of 70⁰C. A thermodynamic model was set up using the Peng-Robinson equations of state to predict the behavior of the refrigerant and absorbent pair at different points in the system. A MATLAB code was used to obtain the values of enthalpy and entropy at selected points in the system. The exergy destruction in each component and exergetic coefficient of performance (ECOP) of the system were calculated by performing an exergy analysis based on the second law of thermodynamics. Graphs were plotted between varying operating conditions and the ECOP obtained in each case. The effect of every component on the ECOP was examined. The exergetic coefficient of performance was found to be lesser than the coefficient of performance based on the first law of thermodynamics.

Keywords: [bmim][PF₆] as absorbent, carbon dioxide as refrigerant, exergy analysis, Peng-Robinson equations of state, vapor absorption refrigeration

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Authors: Semra Sirin Kiris

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Nonlinear dynamic analysis is permitted to be used for structures without any restrictions. The important issue is the selection of the design earthquake to conduct the analyses since quite different response may be obtained using ground motion records at the same general area even resulting from the same earthquake. In seismic design codes, the method requires scaling earthquake records based on site response spectrum to a specified hazard level. Many researches have indicated that this limitation about selection can cause a large scatter in response and other charecteristics of ground motion obtained in different manner may demonstrate better correlation with peak seismic response. For this reason influence of eleven different ground motion parameters on the peak displacement of reinforced concrete systems is examined in this paper. From conducting 7020 nonlinear time history analyses for single degree of freedom systems, the most effective earthquake parameters are given for the range of the initial periods and strength ratios of the structures. In this study, a hysteresis model for reinforced concrete called Q-hyst is used not taken into account strength and stiffness degradation. The post-yielding to elastic stiffness ratio is considered as 0.15. The range of initial period, T is from 0.1s to 0.9s with 0.1s time interval and three different strength ratios for structures are used. The magnitude of 260 earthquake records selected is higher than earthquake magnitude, M=6. The earthquake parameters related to the energy content, duration or peak values of ground motion records are PGA(Peak Ground Acceleration), PGV (Peak Ground Velocity), PGD (Peak Ground Displacement), MIV (Maximum Increamental Velocity), EPA(Effective Peak Acceleration), EPV (Effective Peak Velocity), teff (Effective Duration), A95 (Arias Intensity-based Parameter), SPGA (Significant Peak Ground Acceleration), ID (Damage Factor) and Sa (Spectral Response Spectrum).Observing the correlation coefficients between the ground motion parameters and the peak displacement of structures, different earthquake parameters play role in peak displacement demand related to the ranges formed by the different periods and the strength ratio of a reinforced concrete systems. The influence of the Sa tends to decrease for the high values of strength ratio and T=0.3s-0.6s. The ID and PGD is not evaluated as a measure of earthquake effect since high correlation with displacement demand is not observed. The influence of the A95 is high for T=0.1 but low related to the higher values of T and strength ratio. The correlation of PGA, EPA and SPGA shows the highest correlation for T=0.1s but their effectiveness decreases with high T. Considering all range of structural parameters, the MIV is the most effective parameter.

Keywords: earthquake parameters, earthquake resistant design, nonlinear analysis, reinforced concrete

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Authors: Hyun-Woo Cho

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Unexpected operational events or abnormalities of industrial processes have a serious impact on the quality of final product of interest. In terms of statistical process control, fault detection and diagnosis of processes is one of the essential tasks needed to run the process safely. In this work, nonlinear representation of process measurement data is presented and evaluated using a simulation process. The effect of using different representation methods on the diagnosis performance is tested in terms of computational efficiency and data handling. The results have shown that the nonlinear representation technique produced more reliable diagnosis results and outperforms linear methods. The use of data filtering step improved computational speed and diagnosis performance for test data sets. The presented scheme is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. Thus this scheme helps to reduce the sensitivity of empirical models to noise.

Keywords: fault diagnosis, nonlinear technique, process data, reduced spaces

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Authors: Aleksander Nawrat, Karol Jędrasiak, Artur Ryt, Dawid Sobel

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The goal of the article is to present a novel Multimedia Firearms Training System. The system was developed in order to compensate for major problems of existing shooting training systems. The designed and implemented solution can be characterized by five major advantages: algorithm for automatic geometric calibration, algorithm of photometric recalibration, firearms hit point detection using thermal imaging camera, IR laser spot tracking algorithm for after action review analysis, and implementation of ballistics equations. The combination of the abovementioned advantages in a single multimedia firearms training system creates a comprehensive solution for detecting and tracking of the target point usable for shooting training systems and improving intervention tactics of uniformed services. The introduced algorithms of geometric and photometric recalibration allow the use of economically viable commercially available projectors for systems that require long and intensive use without most of the negative impacts on color mapping of existing multi-projector multimedia shooting range systems. The article presents the results of the developed algorithms and their application in real training systems.

Keywords: firearms shot detection, geometric recalibration, photometric recalibration, IR tracking algorithm, thermography, ballistics

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Authors: Habib Akbarzadeh Bengar, Mohammad Asadi Kiadehi, Ali Rameeh

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The result of the past earthquakes has shown that insufficient amount of stirrups and brittle behavior of concrete lead to the shear and flexural failure in reinforced concrete (RC) members. In this paper, an analytical model proposed to predict the nonlinear behavior of RC and SFRC elements and frames. In this model, some important parameter such as shear effect, varying axial load, and longitudinal bar buckling are considered. The results of analytical model were verified with experimental tests. The results of verification have shown that the proposed analytical model can predict the nonlinear behavior of RC and SFRC members and also frames accurately. In addition, the results have shown that use of steel fibers increased bearing capacity and ductility of RC frame. Due to this enhancement in shear strength and ductility, insufficient amount of stirrups, which resulted in shear failure, can be offset with usage of the steel fibers. In addition to the steps taken, to analyze the effects of fibers percentages on the bearing capacity and ductility of frames parametric studies have been performed to investigate of these effects.

Keywords: nonlinear analysis, SFRC frame, shear failure, varying an axial load

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Kodo Sektani, Apostolos Tsouvalas, Andrei Metrikine

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The reassessment of existing movable bridges in The Netherlands has created the need for acceptance/rejection criteria to assess whether the machineries are meet certain design demands. However, the existing design code defines a different limit state design, meant for new machineries which is based on a simple linear spring-mass model. Observations show that existing bridges do not confirm the model predictions. In fact, movable bridges are nonlinear systems consisting of mechanical components, such as, gears, electric motors and brakes. Next to that, each movable bridge is characterized by a unique set of parameters. However, in the existing code various variables that describe the physical characteristics of the bridge are neglected or replaced by partial factors. For instance, the damping ratio ζ, which is different for drawbridges compared to bascule bridges, is taken as a constant for all bridge types. In this paper, a model is developed that overcomes some of the limitations of existing modelling approaches to capture the dynamics of the powertrain of a class of bridge machineries First, a semidefinite dynamic model is proposed, which accounts for stiffness, damping, and some additional variables of the physical system, which are neglected by the code, such as nonlinear braking torques. The model gives an upper bound of the peak forces/torques occurring in the powertrain during emergency braking. Second, a discrete nonlinear dynamic model is discussed, with realistic motor torque characteristics during normal operation. This model succeeds to accurately predict the full time history of the occurred stress state of the opening and closing cycle for fatigue purposes.

Keywords: Dynamics of movable bridges, Bridge machinery, Powertrains, Torque measurements

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Authors: Mahmood Khalghollah, Mohammad Tavallaeinejad, Mohammad Eghtesad

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The method of Controlled Lagrangian is an energy shaping control technique for under actuated Lagrangian systems. Energy shaping control design methods are appealing as they retain the underlying nonlinear dynamics and can provide stability results that hold over larger domain than can be obtained using linear design and analysis. In the present study, controlled lagrangian is employed for designing a controller in an under actuated rotating flexible plate system. In the system of rotating flexible plate, due to its nonlinear characteristics and coupled dynamics of rigid and flexible components, controller design is a known challenge. In this paper, controller objectives are considered to be vibration reduction of flexible component and position control of the tip of the plate. To achieve the goals, a method based on both kinetic and potential energy shaping is introduced. The stability of the closed-loop system is investigated and proved around its equilibrium points. Moreover, the proposed controller is shown to be robust against disturbance and plant uncertainties.

Keywords: controlled lagrangian, underactuated system, flexible rotating plate, disturbance

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Authors: Ana Paula P. dos Santos, Claudia R. Andrade, Edson L. Zaparoli

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Pressure loss in ductworks is an important factor to be considered in design of engineering systems such as power-plants, refineries, HVAC systems to reduce energy costs. Ductwork can be composed by straight ducts and different types of fittings (elbows, transitions, converging and diverging tees and wyes). Duct fittings are significant sources of pressure loss in fluid distribution systems. Fitting losses can be even more significant than equipment components such as coils, filters, and dampers. At the present work, a conventional 90o round elbow under turbulent incompressible airflow is studied. Mass, momentum, and k-e turbulence model equations are solved employing the finite volume method. The SIMPLE algorithm is used for the pressure-velocity coupling. In order to validate the numerical tool, the elbow pressure loss coefficient is determined using the same conditions to compare with ASHRAE database. Furthermore, the effect of Reynolds number variation on the elbow pressure loss coefficient is investigated. These results can be useful to perform better preliminary design of air distribution ductworks in air conditioning systems.

Keywords: duct fitting, pressure loss, elbow, thermodynamics

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Authors: Ali Borhani Manesh, Sirus Mohammadi

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Harmonic distortion is caused by nonlinear devices in the power system. A nonlinear device is one in which the current is not proportional to the applied voltage. Harmonic distortion is present to some degree on all power systems. Proactive monitoring of power quality disturbance levels by electricity utilities is vital to allow cost-effective mitigation when disturbances are perceived to be approaching planning levels and also to protect the security of customer installations. Ensuring that disturbance levels are within limits at the HV and EHV points of supply of the network is essential if satisfactory levels downstream are to be maintained. This paper presents discussion on a power quality monitoring campaign performed at the sub-transmission point of supply of a distribution network with the objective of benchmarking background disturbance levels prior to modifications to the substation and to ensure emissions from HV customers and the downstream MV networks are within acceptable levels. Some discussion on the difficulties involved in such a study is presented. This paper presents a survey of voltage and current harmonic distortion levels at transmission system in Kohgiloye and Boyrahmad. The effects of harmonics on capacitors and power transformers are discussed.

Keywords: power quality, harmonics, flicker, measurement, substation

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: M. Abdallah

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Urban development requires deep excavations near buildings and other structures. Deep excavation has become more a necessity for better utilization of space as the population of the world has dramatically increased. In Lebanon, some urban areas are very crowded and lack spaces for new buildings and underground projects, which makes the usage of underground space indispensable. In this paper, a numerical modeling is performed using the finite element method to study the deep excavation-diaphragm wall soil-structure interaction in the case of nonlinear soil behavior. The study is focused on a comparison of the results obtained using different support systems. Furthermore, a parametric study is performed according to the remoteness of the structure.

Keywords: deep excavation, ground anchors, interaction soil-structure, struts

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Authors: Riadh Zorgati, Thomas Triboulet

Abstract:

In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.

Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix

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