Search results for: uncertain nonlinear systems

Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Tomas Menard

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The synthesis of output-feedback control law has been investigated by many researchers since the last century. While many results exist for the case of Linear Time Invariant systems whose measurements are continuously available, nowadays, control laws are usually implemented on micro-controller, then the measurements are discrete-time by nature. This fact has to be taken into account explicitly in order to obtain a satisfactory behavior of the closed-loop system. One considers here a general class of systems corresponding to an observability normal form and which is subject to uncertainties in the dynamics and sampling of the output. Indeed, in practice, the modeling of the system is never perfect, this results in unknown uncertainties in the dynamics of the model. We propose here an output feedback algorithm which is based on a linear state feedback and a continuous-discrete time observer. The main feature of the proposed control law is that only discrete-time measurements of the output are needed. Furthermore, it is formally proven that the state of the closed loop system exponentially converges toward the origin despite the unknown uncertainties. Finally, the performances of this control scheme are illustrated with simulations.

Keywords: dynamical systems, output feedback control law, sampling, uncertain systems

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Authors: Siu-Siu Guo, Qingxuan Shi

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In this paper, single-degree-of-freedom (SDOF) systems to white noise and colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis.

Keywords: filtered noise, narrow-banded noise, nonlinear dynamic, random vibration

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Mahtab Abdollahi Sarvi, Siamak Epackachi, Ali Imanpour

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Reinforced concrete shear walls are commonly used as the lateral load-resisting system of mid- to high-rise office or residential buildings around the world. Design of such systems is often governed by wind rather than seismic effects, in particular in low-to-moderate seismic regions. The current design philosophy as per the majority of building codes under wind loads require elastic response of lateral load-resisting systems including reinforced concrete shear walls when subjected to the rare design wind load, resulting in significantly large wall sections needed to meet strength requirements and drift limits. The latter can highly influence the design in upper stories due to stringent drift limits specified by building codes, leading to substantial added costs to the construction of the wall. However, such walls may offer limited to moderate over-strength and ductility due to their large reserve capacity provided that they are designed and detailed to appropriately develop such over-strength and ductility under extreme wind loads. This would significantly contribute to reducing construction time and costs, while maintaining structural integrity under gravity and frequently-occurring and less frequent wind events. This paper aims to investigate the over-strength and ductility capacity of several imaginary office buildings located in Edmonton, Canada with a glance at earthquake design philosophy. Selected models are 10- to 25-story buildings with three types of reinforced concrete shear wall configurations including rectangular, barbell, and flanged. The buildings are designed according to National Building Code of Canada. Then fiber-based numerical models of the walls are developed in Perform 3D and by conducting nonlinear static (pushover) analysis, lateral nonlinear behavior of the walls are evaluated. Ductility and over-strength of the structures are obtained based on the results of the pushover analyses. The results confirmed moderate nonlinear capacity of reinforced concrete shear walls under extreme wind loads. This is while lateral displacements of the walls pass the serviceability limit states defined in Pre standard for Performance-Based Wind Design (ASCE). The results indicate that we can benefit the limited nonlinear response observed in the reinforced concrete shear walls to economize the design of such systems under wind loads.

Keywords: concrete shear wall, high-rise buildings, nonlinear static analysis, response modification factor, wind load

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Luis Andrey Fajardo Fajardo

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We are immersed in complex systems. The human brain, the galaxies, the snowflakes are examples of complex systems. An area of interest in Complex systems is the chaos theory. This revolutionary field of science presents different ways of study than determinism and reductionism. Here is where in junction with the Nonlinear DSP, chaos theory offer valuable techniques that establish a link between time series and complex theory in terms of complex networks, so that, the study of signals can be explored from the graph theory. Recently, some people had purposed a method to transform time series in graphs, but no one had developed a suitable implementation in Python with signals extracted from Chaotic Systems or Complex systems. That’s why the implementation in Python of an existing method to transform one dimensional chaotic signals from time domain to graph domain and some measures that may reveal information not extracted in the time domain is proposed.

Keywords: Python, complex systems, graph theory, dynamical systems

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Amar Khoukhi, Mohamed Shahab

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This paper presents the optimal control problem of mobile robot motion as a nonlinear programming problem (NLP) and solved using a direct method of numerical optimal control. The NLP is initialized with a B-Spline for which node locations are optimized using a genetic search. The system acceleration inputs and sampling periods are considered as optimization variables. Different scenarios with different objectives weights are implemented and investigated. Interesting results are found in terms of complying with the expected behavior of a mobile robot system and time-energy minimization.

Keywords: multi-objective control, non-holonomic systems, mobile robots, nonlinear programming, motion planning, B-spline, genetic algorithm

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Authors: Hendradi Hardhienata, Tony Sumaryada, Sri Setyaningsih

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Current progress in the field of nonlinear optics has enabled precise surface characterization in semiconductor materials. Nonlinear optical techniques are favorable due to their nondestructive measurement and ability to work in nonvacuum and ambient conditions. The advance of the bond hyperpolarizability models opens a wide range of nanoscale surface investigation including the possibility to detect molecular orientation at the surface of silicon and zincblende semiconductors, investigation of electric field induced second harmonic fields at the semiconductor interface, detection of surface impurities, and very recently, study surface defects such as twin boundary in wurtzite semiconductors. In this work, we show using nonlinear optical techniques, e.g. nonlinear bond models how arbitrary polarization of the incoming electric field in Rotational Anisotropy Spectroscopy experiments can provide more information regarding the origin of the nonlinear sources in zincblende and wurtzite semiconductor structure. In addition, using hyperpolarizability consideration, we describe how the nonlinear susceptibility tensor describing SHG can be well modelled using only few parameter because of the symmetry of the bonds. We also show how the third harmonic intensity feature shows considerable changes when the incoming field polarization angle is changed from s-polarized to p-polarized. We also propose a method how to investigate surface reconstruction and defects in wurtzite and zincblende structure at the nanoscale level.

Keywords: surface characterization, bond model, rotational anisotropy spectroscopy, effective hyperpolarizability

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Authors: Saied Farham-Nia, Alireza Ghaffari-Hadigheh

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Game theory is a mathematical tool to study the behaviors of a rational and strategic decision-makers, that analyze existing equilibrium in interest conflict situation and provides an appropriate mechanisms for cooperation between two or more player. Game theory is applicable for any strategic and interest conflict situation in politics, management and economics, sociology and etc. Real worlds’ decisions are usually made in the state of indeterminacy and the players often are lack of the information about the other players’ payoffs or even his own, which leads to the games in uncertain environments. When historical data for decision parameters distribution estimation is unavailable, we may have no choice but to use expertise belief degree, which represents the strength with that we believe the event will happen. To deal with belief degrees, we have use uncertainty theory which is introduced and developed by Liu based on normality, duality, subadditivity and product axioms to modeling personal belief degree. As we know, the personal belief degree heavily depends on the personal knowledge concerning the event and when personal knowledge changes, cause changes in the belief degree too. Uncertainty theory not only theoretically is self-consistent but also is the best among other theories for modeling belief degree on practical problem. In this attempt, we primarily reintroduced Expected Utility Function in uncertainty environment according to uncertainty theory axioms to extract payoffs. Then, we employed Nash Equilibrium to investigate the solutions. For more practical issues, Stackelberg leader-follower Game and Bertrand Game, as a benchmark models are discussed. Compared to existing articles in the similar topics, the game models and solution concepts introduced in this article can be a framework for problems in an uncertain competitive situation based on experienced expert’s belief degree.

Keywords: game theory, uncertainty theory, belief degree, uncertain expected value, Nash equilibrium

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Authors: Esma Birisci, Ronald McGarvey

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One of the common problems in food service industry is demand uncertainty. This research presents a multi-criteria optimization approach to identify the efficient frontier of points lying between the minimum-waste and minimum-shortfall solutions within uncertain demand environment. It also addresses correlation across demands for items (e.g., hamburgers are often demanded with french fries). Reducing overproduction food waste (and its corresponding environmental impacts) and an aversion to shortfalls (leave some customer hungry) need to consider as two contradictory objectives in an all-you-care-to-eat environment food service operation. We identify optimal production adjustments relative to demand forecasts, demand thresholds for utilization of leftovers, and percentages of demand to be satisfied by leftovers, considering two alternative metrics for overproduction waste: mass; and greenhouse gas emissions. Demand uncertainty and demand correlations are addressed using a kernel density estimation approach. A statistical analysis of the changes in decision variable values across each of the efficient frontiers can then be performed to identify the key variables that could be modified to reduce the amount of wasted food at minimal increase in shortfalls. We illustrate our approach with an application to empirical data from Campus Dining Services operations at the University of Missouri.

Keywords: environmental studies, food waste, production planning, uncertain and correlated demand

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Authors: Ali Ballouch, Nourelhouda Choukri, Zouhair Soufiani, Mohamed El Jouad, Mohamed Addou

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For several years, significant research has been developed in the areas of applications of semiconductor wide bandgap such as ZnO in optoelectronics. This oxide has the advantage of having a large exciton energy (60 meV) three times higher than that of GaN (21 meV) or ZnS (20 meV). This energy makes zinc oxide resistant for laser irradiations and very interesting for the near UV-visible optic, as well as for studying physical microcavities. A high-energy direct gap at room temperature (Eg > 1 eV) which makes it a potential candidate for emitting devices in the near UV and visible. Our work is to study the nonlinear optical properties, mainly the nonlinear third-order susceptibility of europium doped Zinc oxide thin films. The samples were prepared by chemical vapor spray method (Spray), XRD, SEM technique, THG were used for characterization. In this context, the influence of europium doping on the nonlinear optical response of the Zinc oxide was investigated. The nonlinear third-order properties depend on the physico-chemical parameters (crystallinity, strain, and surface roughness), the nature and the level of doping, temperature.

Keywords: ZnO, characterization, non-linear optical properties, optoelectronics

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Juliette Harper, Yu Yang

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Biofuels have gained significant attention recently due to the new regulations and agreements regarding fossil fuels and greenhouse gases being made by countries around the globe. One of the most common types of biofuels is biodiesel, primarily made via the transesterification reaction. We model this nonlinear process in MATLAB using the standard kinetic equations. Then, a nonlinear Model predictive control (NMPC) was developed to regulate this process due to its capability to handle process constraints. The feeding flow uncertainty and kinetic disturbances are further incorporated in the model to capture the real-world operating conditions. The simulation results will show that the proposed NMPC can guarantee the final composition of fatty acid methyl esters (FAME) above the target threshold with a high chance by adjusting the process temperature and flowrate. This research will allow further understanding of NMPC under uncertainties and how to design the computational strategy for larger process with more variables.

Keywords: NMPC, biodiesel, uncertainties, nonlinear, MATLAB

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Authors: Kang-Gyu Park, Sun-Jong Park, Hong Jae Yim, Hyo-Gyung Kwak

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This paper attempts to evaluate the effect of fire damage on concrete by using nonlinear resonance vibration method, one of the nonlinear nondestructive method. Concrete exhibits not only nonlinear stress-strain relation but also hysteresis and discrete memory effect which are contained in consolidated materials. Hysteretic materials typically show the linear resonance frequency shift. Also, the shift of resonance frequency is changed according to the degree of micro damage. The degree of the shift can be obtained through nonlinear resonance vibration method. Five exposure scenarios were considered in order to make different internal micro damage. Also, the effect of post-fire-curing on fire-damaged concrete was taken into account to conform the change in internal damage. Hysteretic non linearity parameter was obtained by amplitude-dependent resonance frequency shift after specific curing periods. In addition, splitting tensile strength was measured on each sample to characterize the variation of residual strength. Then, a correlation between the hysteretic non linearity parameter and residual strength was proposed from each test result.

Keywords: nonlinear resonance vibration method, non linearity parameter, splitting tensile strength, micro damage, post-fire-curing, fire damaged concrete

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Authors: R. K. Apalowo, D. Chronopoulos

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A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Reza E. Sedgh, Rajesh P. Dhakal

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Shear walls have been used extensively as the main lateral force resisting systems in multi-storey buildings. The recent development in performance based design urges practicing engineers to conduct nonlinear static or dynamic analysis to evaluate seismic performance of multi-storey shear wall buildings by employing distinct analytical models suggested in the literature. For practical purpose, application of macroscopic models to simulate the global and local nonlinear behavior of structural walls outweighs the microscopic models. The skill level, computational time and limited access to RC specialized finite element packages prevents the general application of this method in performance based design or assessment of multi-storey shear wall buildings in design offices. Hence, this paper organized to verify capability of nonlinear shell element in commercially available package (Sap2000) in simulating results of some specimens under monotonic and cyclic loads with very oversimplified available cyclic material laws in the analytical tool. The selection of constitutive models, the determination of related parameters of the constituent material and appropriate nonlinear shear model are presented in detail. Adoption of proposed simple model demonstrated that the predicted results follow the overall trend of experimental force-displacement curve. Although, prediction of ultimate strength and the overall shape of hysteresis model agreed to some extent with experiment, the ultimate displacement(significant strength degradation point) prediction remains challenging in some cases.

Keywords: analytical model, nonlinear shell element, structural wall, shear behavior

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Soheib Fergani

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This paper concerns with the formal asymptotic stability guarantees, analysis and evaluation of a nonlinear controlled unmanned aerial vehicles (uav) for trajectory tracking purpose. As the system has been recognised as an under-actuated non linear system, the control strategy has been oriented towards a hierarchical control. The dynamics of the system and the mission purpose make it mandatory to provide an absolute proof of the vehicle stability during the maneuvers. For this sake, this work establishes the complete theoretical proof for an implementable control oriented strategy that asymptotically stabilizes (GAS and LISS) the system and has never been provided in previous works. The considered model is reorganized into two partly decoupled sub-systems. The concidered control strategy is presented into two stages: the first sub-system is controlled by a nonlinear backstepping controller that generates the desired control inputs to stabilize the second sub-system. This methodology is then applied to a harware in the loop uav simulator (SiMoDrones) that reproduces the realistic behaviour of the uav in an indoor environment has been performed to show the efficiency of the proposed strategy.

Keywords: UAV application, trajectory tracking, backstepping, sliding mode control, input to state stability, stability evaluation

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Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh

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This paper presents a new method to design nonlinear feedback linearization controller for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA_II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.

Keywords: nonlinear dynamic model, polymer electrolyte membrane fuel cells, feedback linearization, optimal control, NSGA_II

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Tudor Barbu

Abstract:

We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Mesbaholdin Salami, Farzad Movahedi Sobhani, Mohammad Sadegh Ghazizadeh

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Evaluation of organizational performance is among the most important measures that help organizations and entities continuously improve their efficiency. Organizations can use the existing data and results from the comparison of units under investigation to obtain an estimation of their performance. The Malmquist Productivity Index (MPI) is an important index in the evaluation of overall productivity, which considers technological developments and technical efficiency at the same time. This article proposed a model based on the multistage MPI, considering limited data (Grey’s theory). This model can evaluate the performance of units using limited and uncertain data in a multistage process. It was applied by the electricity market manager to Iran’s electric power supply chain (EPSC), which contains uncertain data, to evaluate the performance of its actors. Results from solving the model showed an improvement in the accuracy of future performance of the units under investigation, using the Grey’s system theory. This model can be used in all case studies, in which MPI is used and there are limited or uncertain data.

Keywords: Malmquist Index, Grey's Theory, CCR Model, network data envelopment analysis, Iran electricity power chain

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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Authors: T. Sanches, K. Bousson

Abstract:

As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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