Search results for: second-order nonlinear neutral dynamic equation

Authors: Kelong Zheng, Jinsong Hu,

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In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Hölder continuity condition, Fréchet derivative, fifth order convergence, recurrence relations.

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Authors: Nikolay Nikolaev, Evgueni Smirnov

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This paper develops an unscented grid-based filter and a smoother for accurate nonlinear modeling and analysis of time series. The filter uses unscented deterministic sampling during both the time and measurement updating phases, to approximate directly the distributions of the latent state variable. A complementary grid smoother is also made to enable computing of the likelihood. This helps us to formulate an expectation maximisation algorithm for maximum likelihood estimation of the state noise and the observation noise. Empirical investigations show that the proposed unscented grid filter/smoother compares favourably to other similar filters on nonlinear estimation tasks.

Keywords:

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: Optimal control, stochastic systems, quantum systems, stabilization.

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Authors: T. Sanches, K. Bousson

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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 and stability.

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Authors: Shobha Sharma, Amita Dev

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Data driven dynamic logic is the high speed dynamic circuit with low area. The clock of the dynamic circuit is removed and data drives the circuit instead of clock for precharging purpose. This data driven dynamic nand gate is given static forward substrate biasing of Vsupply/2 as well as the substrate bias is connected to the input data, resulting in dynamic substrate bias. The dynamic substrate bias gives the shortest propagation delay with a penalty on the power dissipation. Propagation delay is reduced by 77.8% compared to the normal reverse substrate bias Data driven dynamic nand. Also dynamic substrate biased D3nand’s propagation delay is reduced by 31.26% compared to data driven dynamic nand gate with static forward substrate biasing of Vdd/2. This data driven dynamic nand gate with dynamic body biasing gives us the highest speed with no area penalty and finds its applications where power penalty is acceptable. Also combination of Dynamic and static Forward body bias can be used with reduced propagation delay compared to static forward biased circuit and with comparable increase in an average power. The simulations were done on hspice simulator with 22nm High-k metal gate strained Si technology HP models of Arizona State University, USA.

Keywords: Data driven nand gate, dynamic substrate biasing, nand gate, static substrate biasing.

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Authors: A. Bennassar, A. Abbou, M. Akherraz, M. Barara

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In this paper, we propose a sensorless backstepping control of induction motor (IM) associated with three levels neutral clamped (NPC) inverter. First, the backstepping approach is designed to steer the flux and speed variables to theirs references and to compensate the uncertainties. A Lyapunov theory is used and it demonstrates that the dynamic trajectories tracking are asymptotically stable. Second, we estimate the rotor flux and speed by using the adaptive Luenberger observer (ALO). Simulation results are provided to illustrate the performance of the proposed approach in high and low speeds and load torque disturbance.

Keywords: Sensorless backstepping, IM, Three levels NPC inverter, Lyapunov theory, ALO.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

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In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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Authors: Mahesh K. Chudasama, Harit K. Raval

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3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: Analytical modeling, cone frustum, dynamic bending, static bending.

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Authors: Amr R. El-Gamal, Ashraf Essa, Ayman Ismail

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The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark’s beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated.

Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.

Keywords: Hydrodynamic wave forces, tension leg platforms, tethers length, wave characteristic.

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Authors: Dae-Hee Son, Sang-Hee Kang, Soon-Ryul Nam

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In this paper, we develop a dynamic modeling of wind farms in the Jeju power system. The dynamic model of wind farms is developed to study their dynamic effects on the Jeju power system. PSS/E is used to develop the dynamic model of a wind farm composed of 1.5-MW doubly fed induction generators. The output of a wind farm is regulated based on pitch angle control, in which the two controllable parameters are speed and power references. The simulation results confirm that the pitch angle is successfully controlled, regardless of the variation in wind speed and output regulation.

Keywords: Dynamic model, Jeju power system, pitch angle control, PSS/E, wind farm.

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Authors: E. Srinivasan, D. Ebenezer

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Midpoint filter is quite effective in recovering the images confounded by the short-tailed (uniform) noise. It, however, performs poorly in the presence of additive long-tailed (impulse) noise and it does not preserve the edge structures of the image signals. Median smoother discards outliers (impulses) effectively, but it fails to provide adequate smoothing for images corrupted with nonimpulse noise. In this paper, two nonlinear techniques for image filtering, namely, New Filter I and New Filter II are proposed based on a nonlinear high-pass filter algorithm. New Filter I is constructed using a midpoint filter, a highpass filter and a combiner. It suppresses uniform noise quite well. New Filter II is configured using an alpha trimmed midpoint filter, a median smoother of window size 3x3, the high pass filter and the combiner. It is robust against impulse noise and attenuates uniform noise satisfactorily. Both the filters are shown to exhibit good response at the image boundaries (edges). The proposed filters are evaluated for their performance on a test image and the results obtained are included.

Keywords: Image filters, Midpoint filter, Nonlinear filters, Nonlinear highpass filter, Order-statistic filters, Rank-order filters.

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Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

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In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

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Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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Authors: Muhammad Rizwan Azhar, Emadadeen Ali

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In this paper, periodic force operation of a wastewater treatment process has been studied for the improved process performance. A previously developed dynamic model for the process is used to conduct the performance analysis. The static version of the model was utilized first to determine the optimal productivity conditions for the process. Then, feed flow rate in terms of dilution rate i.e. (D) is transformed into sinusoidal function. Nonlinear model predictive control algorithm is utilized to regulate the amplitude and period of the sinusoidal function. The parameters of the feed cyclic functions are determined which resulted in improved productivity than the optimal productivity under steady state conditions. The improvement in productivity is found to be marginal and is satisfactory in substrate conversion compared to that of the optimal condition and to the steady state condition, which corresponds to the average value of the periodic function. Successful results were also obtained in the presence of modeling errors and external disturbances.

Keywords: Dilution rate, nonlinear model predictive control, sinusoidal function, wastewater treatment.

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Authors: M. Mohebbi, K. Shakeri

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Since the actuator capacity is limited, in the real application of active control systems under sever earthquakes it is conceivable that the actuators saturate, hence the actuator saturation should be considered as a constraint in design of optimal controllers. In this paper optimal design of active controllers for nonlinear structures by considering actuator saturation, has been studied. The proposed method for designing optimal controllers is based on defining an optimization problem which the objective has been to minimize the maximum displacement of structure when a limited capacity for actuator has been used. To this end a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of prestressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used. To achieve the best results, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been optimized by the Distributed Genetic Algorithm (DGA). Results show the effectiveness of the proposed method in considering actuator saturation. Also based on the numerical simulations it can be concluded that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers which consider the actuator saturation.

Keywords: Active control, Actuator Saturation, Distributedgeneticalgorithms, Nonlinear.

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Authors: Farzan Namvari, Panam Zarfam

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Nowadays use of a new structural bracing system called 'Knee Bracing System' have taken the specialists attention too much. On the other hand nonlinear static analysis procedures in estimate structures performance in earthquake time have taken attention too much. One of these procedure is modal pushover analysis (MPA) procedure. The accuracy of MPA procedure for simple steel moment resisting frame has been verified and considered in Chintanapakdee and Chopra-s article in 2003. Since the accuracy of MPA procedure has not verified for semi-rigid steel frames with knee bracing, we are going to get through with this matter in this study. For this purpose, the selected structures are four frames with different heights, 5 to 20 stories, will be designed according to AISC criteria. Then MPA procedure is used for the same frames with different rigidity percentiles of connections. The results of seismic responses are compared with dynamic nonlinear response history analysis as exact procedure and accuracy of MPA procedure is evaluated. It seems that MPA procedure accuracy will come down by reduction of the rigidity percentiles of semi-rigid connections.

Keywords: Knee Bracing, Modal Pushover Analysis, SeismicBehavior, Semi-Rigid Connections.

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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Authors: Yongyoon Suh, Chulhyun Kim, Moon-soo Kim

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As the trend of manufacturing is being dominated depending on services, products and processes are more and more related with sophisticated services. Thus, this research starts with the discussion about integration of the product, process, and service in the innovation process. In particular, this paper sets out some foundations for a theory of service innovation in the field of manufacturing, and proposes the dynamic model of service innovation related to product and process. Two dynamic models of service innovation are suggested to investigate major tendencies and dynamic variations during the innovation cycle: co-innovation and sequential innovation. To structure dynamic models of product, process, and service innovation, the innovation stages in which two models are mainly achieved are identified. The research would encourage manufacturers to formulate strategy and planning for service development with product and process.

Keywords: dynamic model, service innovation, service innovation models, innovation cycle, manufacturing industry.

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Authors: Abida Harbi

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We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic boundary value problem of the form -Δu = f(u), on two overlapping sub domains with non matching grids. We consider a domain which is the union of two overlapping sub domains where each sub domain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz assumption on the nonlinearity, we establish, on each sub domain, an optimal L∞ error estimate between the discrete Schwarz sequence and the exact solution of the boundary value problem.

Keywords: Error estimates, Finite elements, Nonlinear PDEs, Schwarz method.

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Authors: B. Navayineya, J. Vaseghi Amiri, M. Alijani Ardeshir

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Hydrodynamic pressures acting on upstream of concrete dams during an earthquake are an important factor in designing and assessing the safety of these structures in Earthquake regions. Due to inherent complexities, assessing exact hydrodynamic pressure is only feasible for problems with simple geometry. In this research, the governing equation of concrete gravity dam reservoirs with effect of fluid viscosity in frequency domain is solved and then compared with that in which viscosity is assumed zero. The results show that viscosity influences the reservoir-s natural frequency. In excitation frequencies near the reservoir's natural frequencies, hydrodynamic pressure has a considerable difference in compare to the results of non-viscose fluid.

Keywords: Closed form solution, concrete dams reservoir, viscosity, dynamic loads, hydrodynamic pressure.

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Authors: K. Abuzayan, H. Alabed, J. Ezarrugh, M. Agila

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Static and dynamic balance are essential in daily and sports life. Many factors have been identified as influencing static balance control. Therefore, the aim of this study was to apply the (XCoM) method and other relevant variables (CoP, CoM, F_h, KE, P, Q, and, AI) to investigate sport related activities such as hopping and jumping. Many studies have represented the CoP data without mentioning its accuracy so several experiments were done to establish the agreement between the CoP and the projected CoM in a static condition. 5 healthy male were participated in this study (Mean ± SD:- age 24.6 years ±4.5, height 177cm ± 6.3, body mass 72.8kg ± 6.6).Results found that the implementation of the XCoM method was found to be practical for evaluating both static and dynamic balance. The general findings were that the CoP, the CoM, the XCoM, F_h, and Q were more informative than the other variables (e.g. KE, P, and AI) during static and dynamic balance. The XCoM method was found to be applicable to dynamic balance as well as static balance.

Keywords: Centre of Mass, static balance, Dynamic balance, extrapolated Centre of Mass

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Authors: Abhishek Chandra, Man Singh

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Highly stable and homogeneously dispersed amino acid coated silver nanoparticles (ANP) of ≈ 10 nm diameter, ranging from 420 to 430 nm are prepared on AgNO3 solution addition to gum of Azadirachta indica solution at 373.15 K. The amino acids were selected based on their polarity. The synthesized nanoparticles were characterized by UV-Vis, FTIR spectroscopy, HR-TEM, XRD, SEM and 1H-NMR. The coated nanoparticles were used as catalyst for the reduction of methylene blue dye in presence of Sn(II) in aqueous, anionic and cationic micellar media. The rate of reduction of dye was determined by measuring the absorbance at 660 nm, spectrophotometrically and followed the order: Kcationic > Kanionic > Kwater. After 12 min and in absence of the ANP, only 2%, 3% and 6% of the dye reduction was completed in aqueous, anionic and cationic micellar media respectively while, in presence of ANP coated by polar neutral amino acid with non-polar -R group, the reduction completed to 84%, 95% and 98% respectively. The ANP coated with polar neutral amino acid having non-polar -R group, increased the rate of reduction of the dye by 94, 3205 and 6370 folds in aqueous, anionic and cationic micellar media respectively. Also, the rate of reduction of the dye increased by three folds when the micellar media was changed from anionic to cationic when the ANP is coated by a polar neutral amino acid having a non-polar -R group.

Keywords: Silver nanoparticle, surfactant, methylene blue, amino acid.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Yanling Li, Linying Ji, Zita Oravecz, Timothy R. Brick, Michael D. Hunter, Sy-Miin Chow

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Assessing several individuals intensively over time yields intensive longitudinal data (ILD). Even though ILD provide rich information, they also bring other data analytic challenges. One of these is the increased occurrence of missingness with increased study length, possibly under non-ignorable missingness scenarios. Multiple imputation (MI) handles missing data by creating several imputed data sets, and pooling the estimation results across imputed data sets to yield final estimates for inferential purposes. In this article, we introduce dynr.mi(), a function in the R package, Dynamic Modeling in R (dynr). The package dynr provides a suite of fast and accessible functions for estimating and visualizing the results from fitting linear and nonlinear dynamic systems models in discrete as well as continuous time. By integrating the estimation functions in dynr and the MI procedures available from the R package, Multivariate Imputation by Chained Equations (MICE), the dynr.mi() routine is designed to handle possibly non-ignorable missingness in the dependent variables and/or covariates in a user-specified dynamic systems model via MI, with convergence diagnostic check. We utilized dynr.mi() to examine, in the context of a vector autoregressive model, the relationships among individuals’ ambulatory physiological measures, and self-report affect valence and arousal. The results from MI were compared to those from listwise deletion of entries with missingness in the covariates. When we determined the number of iterations based on the convergence diagnostics available from dynr.mi(), differences in the statistical significance of the covariate parameters were observed between the listwise deletion and MI approaches. These results underscore the importance of considering diagnostic information in the implementation of MI procedures.

Keywords: Dynamic modeling, missing data, multiple imputation, physiological measures.

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Hyun-Woo Cho

Abstract:

The early diagnostic decision making in industrial processes is absolutely necessary to produce high quality final products. It helps to provide early warning for a special event in a process, and finding its assignable cause can be obtained. This work presents a hybrid diagnostic schmes for batch processes. Nonlinear representation of raw process data is combined with classification tree techniques. The nonlinear kernel-based dimension reduction is executed for nonlinear classification decision boundaries for fault classes. In order to enhance diagnosis performance for batch processes, filtering of the data is performed to get rid of the irrelevant information of the process data. For the diagnosis performance of several representation, filtering, and future observation estimation methods, four diagnostic schemes are evaluated. In this work, the performance of the presented diagnosis schemes is demonstrated using batch process data.

Keywords: Diagnostics, batch process, nonlinear representation, data filtering, multivariate statistical approach

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Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

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In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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Authors: M. Polanský

Abstract:

This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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Authors: Laura Lukmanto, Harya Widiputra, Lukas

Abstract:

Studies in economics domain tried to reveal the correlation between stock markets. Since the globalization era, interdependence between stock markets becomes more obvious. The Dynamic Interaction Network (DIN) algorithm, which was inspired by a Gene Regulatory Network (GRN) extraction method in the bioinformatics field, is applied to reveal important and complex dynamic relationship between stock markets. We use the data of the stock market indices from eight countries around the world in this study. Our results conclude that DIN is able to reveal and model patterns of dynamic interaction from the observed variables (i.e. stock market indices). Furthermore, it is also found that the extracted network models can be utilized to predict movement of the stock market indices with a considerably good accuracy.

Keywords: complex dynamic relationship, dynamic interaction network, interactive stock markets, stock market interdependence.

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