Strong Nonlinear System Research Articles

Analytical solution for nonlinear vertical vibration model of mill roll system based on improved complexification averaging method

Rolling mill is the core equipment in modern iron and steel industry, and the reliability of its mill roll system (MRS) is the key to ensure the rolling process with high precision, high speed, continuity and stability. However, the MRS possesses some features such as high nonlinearity, time variability and strong coupling. The vertical vibration easily happens in its working process. Nevertheless, the mathematical model of MRS is difficult to be established and hard to be solved. In this paper, the nonlinear dynamics theory and modern signal processing method were introduced to solve this difficult problem. A two degree of freedom (DOF) nonlinear vertical vibration model of MRS was established. And the model was analytically solved by using complexification averaging (CA) method. The solution error of CA method was thoroughly analyzed. Moreover, the CA method was improved by combining the fast empirical mode decomposition (FEMD) method. Research results indicate that the improved CA method presents a significant advantage in improving the solution precision, and can be used to solve strong nonlinear vibration system (NVS) with two DOF.

On Squeezed Flow of Jeffrey Nanofluid between Two Parallel Disks

The present communication examines the magnetohydrodynamic (MHD) squeezing flow of Jeffrey nanofluid between two parallel disks. Constitutive relations of Jeffrey fluid are employed in the problem development. Heat and mass transfer aspects are examined in the presence of thermophoresis and Brownian motion. Jeffrey fluid subject to time dependent applied magnetic field is conducted. Suitable variables lead to a strong nonlinear system. The resulting systems are computed via homotopic approach. The behaviors of several pertinent parameters are analyzed through graphs and numerical data. Skin friction coefficient and heat and mass transfer rates are numerically examined.

Unified linear time-invariant model predictive control for strong nonlinear chaotic systems

It is well known that an alone linear controller is difficult to control a chaotic system, because intensive nonlinearities exist in such system. Meanwhile, depending closely on a precise mathematical modeling of the system and high computational complexity, model predictive control has its inherent drawback in controlling nonlinear systems. In this paper, a unified linear time-invariant model predictive control for intensive nonlinear chaotic systems is presented. The presented model predictive control algorithm is based on an extended state observer, and the precise mathematical modeling is not required. Through this method, not only the required coefficient matrix of impulse response can be derived analytically, but also the future output prediction is explicitly calculated by only using the current output sample. Therefore, the computational complexity can be reduced sufficiently. The merits of this method include, the Diophantine equation needing no calculation, and independence of precise mathematical modeling. According to the variation of the cost function, the order of the controller can be reduced, and the system stability is enhanced. Finally, numerical simulations of three kinds of chaotic systems confirm the effectiveness of the proposed method.

Attitude control of reentry vehicle with a pitch-control single moving mass

Since the point moving mass configuration cannot be implemented in engineering applications, a novel configuration of moving mass with large mass ratio and reaction jet is proposed. This configuration has a great advantage in engineering application as well as improving the vehicle’s maneuverability. According to the dynamic analysis, the moving mass with large mass ratio leads to the coupling between the attitude and the deflection angle of moving mass and the dynamic behavior of flight vehicle can be affected by the momentum exchange. Therefore, the moving mass cannot be regarded as a point mass. A disturbance observer is investigated for this strong coupling nonlinear system, which estimates the total disturbance which contains the nonlinear couples and un-modeled disturbances. Then, a control law based on feedback linearization is used for compensation. The simulation results show that the proposed configuration is feasible and validate the quality of the adaptive controller which ensures a good performance.

Limitations of ozone data assimilation with adjustment of NO<sub><i>x</i></sub> emissions: mixed effects on NO<sub>2</sub> forecasts over Beijing and surrounding areas

Abstract. This study investigates a cross-variable ozone data assimilation (DA) method based on an ensemble Kalman filter (EnKF) that has been used in the companion study to improve ozone forecasts over Beijing and surrounding areas. The main purpose is to delve into the impacts of the cross-variable adjustment of nitrogen oxide (NOx) emissions on the nitrogen dioxide (NO2) forecasts over this region during the 2008 Beijing Olympic Games. A mixed effect on the NO2 forecasts was observed through application of the cross-variable assimilation approach in the real-data assimilation (RDA) experiments. The method improved the NO2 forecasts over almost half of the urban sites with reductions of the root mean square errors (RMSEs) by 15–36 % in contrast to big increases of the RMSEs over other urban stations by 56–239 %. Over the urban stations with negative DA impacts, improvement of the NO2 forecasts (with 7 % reduction of the RMSEs) was noticed at night and in the morning versus significant deterioration during daytime (with 190 % increase of the RMSEs), suggesting that the negative data assimilation impacts mainly occurred during daytime. Ideal-data assimilation (IDA) experiments with a box model and the same cross-variable assimilation method confirmed the mixed effects found in the RDA experiments. In the same way, NOx emission estimation was improved at night and in the morning even under large biases in the prior emission, while it deteriorated during daytime (except for the case of minor errors in the prior emission). The mixed effects observed in the cross-variable data assimilation, i.e., positive data assimilation impacts on NO2 forecasts over some urban sites, negative data assimilation impacts over the other urban sites, and weak data assimilation impacts over suburban sites, highlighted the limitations of the EnKF under strong nonlinear relationships between chemical variables. Under strong nonlinearity between daytime ozone concentrations and NOx emissions uncertainties (with large biases in the a priori emission), the EnKF may come up with inefficient or wrong adjustments to NOx emissions. The present findings reveal that bias correction is essential for the application of the EnKF in dealing with the data assimilation problem over strong nonlinear system.

On magnetohydrodynamic three-dimensional flow of nanofluid over a convectively heated nonlinear stretching surface

This research article explores the magnetohydrodynamic (MHD) three-dimensional flow of viscous nanofluid subject to convective surface boundary condition. Flow is generated by an impermeable surface which is stretched nonlinearly. The process of heat transfer is managed through the convective surface boundary condition. Heat and mass transfer aspects are studied through the thermophoresis and Brownian motion effects. Viscous fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is presented subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Suitable transformations yield a strong nonlinear differential system. Convergent homotopic solutions for resulting nonlinear system are constructed and verified. Impacts of various influential parameters on the temperature and nanoparticles concentration are sketched and discussed. Numerical computations are performed to examine the skin-friction coefficients and local Nusselt number.

A Two-stage Parametric Identification of Strong Nonlinear Structural Systems with Incomplete Response Measurements

Compared with the identification of linear structural parameters, it is more difficult to conduct parametric identification of strong nonlinear structural systems, especially when only incomplete structural responses are available. Although the extended Kalman filter (EKF) is useful for structural identification with partial measurements of structural responses and can be extended for the identification of nonlinear structures, EKF approximates nonlinear system through Taylor series expansion and is therefore not effective for the identification of strong nonlinear structural systems. Other approaches such as the unscented Kalman filter (UKF) have been proposed for the identification of strong nonlinear problems. Based on the fact that nonlinearities exist in local areas of structures, a straightforward two-stage identification approach is proposed in this paper for the identification of strong nonlinear structural parameters with incomplete response measurements. In the first stage, the locations of nonlinearities are identified based on the EKF for the identification of the equivalent linear structures. In the second stage, the UKF is utilized to identify the parameters of strong nonlinear structural systems. Therefore, the parametric identification of strong nonlinear structural parameters is simplified by the proposed approach. Several numerical examples with different nonlinear models and locations are used to validate the proposed approach.

Fault diagnosis for manifold absolute pressure sensor(MAP) of diesel engine based on Elman neural network observer

Intake system of diesel engine is a strong nonlinear system, and it is difficult to establish accurate model of intake system; and bias fault and precision degradation fault of MAP of diesel engine can’t be diagnosed easily using model-based methods. Thus, a fault diagnosis method based on Elman neural network observer is proposed. By comparing simulation results of intake pressure based on BP network and Elman neural network, lower sampling error magnitude is gained using Elman neural network, and the error is less volatile. Forecast accuracy is between 0.015-0.017 5 and sample error is controlled within 0-0.07. Considering the output stability and complexity of solving comprehensively, Elman neural network with a single hidden layer and with 44 nodes is presented as intake system observer. By comparing the relations of confidence intervals of the residual value between the measured and predicted values, error variance and failures in various fault types. Then four typical MAP faults of diesel engine can be diagnosed: complete failure fault, bias fault, precision degradation fault and drift fault. The simulation results show: intake pressure is observable and selection of diagnostic strategy parameter reasonably can increase the accuracy of diagnosis; the proposed fault diagnosis method only depends on data and structural parameters of observer, not depends on the nonlinear model of air intake system. A fault diagnosis method is proposed not depending system model to observe intake pressure, and bias fault and precision degradation fault of MAP of diesel engine can be diagnosed based on residuals.

Darcy–Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet

The present work studies the MHD two-dimensional flow of Maxwell liquid over a stretched surface moving with linear velocity. Convective heat phenomenon characterizes the heat transfer process. Induced electric and magnetic fields are absent. The set of partial differential equations governing the Darcy–Forchheimer flow of Maxwell liquid is derived. Computations for strong nonlinear systems are presented after non-dimensionalization. Convergent relations for velocity and temperature distributions are achieved. Besides this local Nusselt number is computed and analyzed. Our findings reveal that the temperature field has an inverse relationship with the thermal relaxation parameter and Prandtl number.

Numerical Analysis of Transient Wave Propagation in Nonlinear One-Dimensional Waveguides by Using the Spectral Finite Element Method

In this paper, transient wave propagation in nonlinear one-dimensional (1D) waveguides is studied. A complete nonlinear (CN) 1D model accounting for both axial and transverse displacements is developed and geometric and material nonlinearities are separately modeled. The alternating frequency-time finite element method (AFT-FEM) is implemented for this complete 1D model. Numerical simulations are conducted and the response behaviors for axial and transverse motions are analyzed. Comparison of the responses for the geometrically nonlinear (GN) model with a corresponding linear model supports predictions made from the previous analytical studies that the geometric nonlinearity has limited influence on the response of transient transverse waves in the intermediate strain regime. On the contrary, strong nonlinear behavior appears in the response for the materially nonlinear (MN) models. Depending on the local nonlinear property of the material in the intermediate strain regime, the amplitude of the response can be significantly influenced and additional dispersion can be introduced into the response. An exploration of the interaction between the geometric nonlinearity and the material nonlinearity for a rod model in a large strain regime is also conducted and the responses are analyzed by using time-frequency analysis. The competing effect of the geometric nonlinearity and the material nonlinearity can result in a pseudolinear response in a strong nonlinear system for a given range of impact loading.

Rational design of metallic nanocavities for resonantly enhanced four-wave mixing.

Optimizing the shape of nanostructures and nano-antennas for specific optical properties has evolved to be a very fruitful activity. With modern fabrication tools a large variety of possibilities is available for shaping both nanoparticles and nanocavities; in particular nanocavities in thin metal films have emerged as attractive candidates for new metamaterials and strong linear and nonlinear optical systems. Here we rationally design metallic nanocavities to boost their Four-Wave Mixing response by resonating the optical plasmonic resonances with the incoming and generated beams. The linear and nonlinear optical responses as well as the propagation of the electric fields inside the cavities are derived from the solution of Maxwell’s equations by using the 3D finite-differences time domain method. The observed conversion-efficiency of near-infrared to visible light equals or surpasses that of BBO of equivalent thickness. Implications to further optimization for efficient and broadband ultrathin nonlinear optical materials are discussed.

Adaptive control of piezoelectric fast steering mirror for high precision tracking application

A piezoelectric fast steering mirror (PFSM) is a complex, strong coupling nonlinear system that integrates optics, mechanics, electrics, and control. Due to the existence of hysteresis nonlinearity, mechanical resonance, and all kinds of disturbances, precise tracking control of a PFSM is a challenging task. This paper presents a comprehensive study of modeling, controller design, and simulation evaluation for a PFSM system. First a general model of a PFSM system integrating mechanical dynamics, electrical dynamics, and hysteresis nonlinearity is proposed, and then a robust adaptive controller is developed under both unknown hysteresis nonlinearities and parameter uncertainties. The parameters needed directly in the formulation of the controller are adaptively estimated. The proposed control law ensures the uniform boundedness of all signals in the closed-loop system. Furthermore, a stability analysis of the control system is performed to guarantee that the output tracking error converges to zero asymptotically. Finally, simulation tests with different motion trajectories are conducted to verify the effectiveness of the proposed method.

Sensor Data Fusion by Support Vector Regression Methodology—A Comparative Study

Multisensor data fusion can be considered as a strong nonlinear system. A precise analytical solution is challenging to obtain, thus making it hard to dissect with routine diagnostic systems. Since tried-and-true logical systems are extremely difficult to undertake, soft computing methodologies are deemed having potential for such applications. This paper presents the support vector regression (SVR) methodology for sensor fusion to improve tracking ability. Radial basis function (RBF) and polynomial function are used as SVR kernel functions. The system combines Kalman filtering and soft computing principle, i.e., SVR, to structure an effective information combination method for the target framework. A radar-infrared system is proposed to adapt contextual changes and lessen the dubious unsettling influence of an information estimation from multisensory data. The experimental results show that an improvement in predictive accuracy and generalization capability can be achieved using the SVR with RBF kernel compared with the SVR with polynomial kernel approach.

Discrete-Time Nonlinear Control of VSC-HVDC System

Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO) system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.

Robust Control Method Based on Machine Learning for Boiler Combustion System

In this study, we presented a boiler combustion robust control method under load changes based on the least squares support vector machine, PID parameters are on-line adjusted and identified by LSSVM, optimum control output is obtained. The simulation result shows control performance of the intelligent control algorithm is superior to traditional control algorithm and fuzzy PID control algorithm, the study provides a new control method for strong non-linear boiler combustion control system.

Analysis of Chaotic Characteristics of the Strong Nonlinear Vibration Isolation System Based on Harmonic Balance Method

The key of studying the nonlinear system of the stationary period solutions by the HBM is solving a group of higher order multi-degree-of-freedom nonlinear equations. Aiming at this difficulty, this paper can easily get a higher harmonic balance truncation order expression of solution using a powerful symbolic computation software, and avoid the tedious derivation process. And the main subharmonic response range was accurately obtained by the EACM for solving the nonlinear equations. Meanwhile, the chaotic region was estimated through subharmonic cascade regions combined with the bifurcation of the Feigenbaum rule by solving the system. And, numerical results calculated by the Runge-Kutta method were given to verify the results of the period doubling bifurcations and chaotic region obtained by this method. It has been shown that they are in good agreement.

Modeling and Simulation of the Helicopter Control System Based on the Flight Qualities

Helicopter is a strong coupling and instability nonlinear system, of which the inherent flight qualities are poor. Helicopter model following control technology can make four control channels of helicopter with excellent tracking and decoupling characteristics. This paper applied the control method of model following control combining eigenststructure assignment to the helicopter control system. The results of simulation show that the helicopter flight qualities meet the requirements of ADS-33, the helicopter has excellent tracking and decoupling characteristics. Thus it proves that this control method is of great effectiveness.

Shape optimization design of steel shear panel dampers

Steel shear panel dampers (SSPDs) have a reasonably good and stable energy dissipation capacity, and are widely used in engineering to enhance the structural safety of buildings in large earthquakes. Efforts to improve the low cycle fatigue performance of SSPDs have focused mostly on the arrangement of the stiffeners or on the effects of the material properties. The shape of the SSPD plate has not been well investigated. This paper presents a shape optimization method for improving the low cycle fatigue performance of SSPDs. The shear plate shape of the SSPD is taken as the variable in the optimization process. The low cycle fatigue performance of the SSPD is assumed to have a negative relationship to the maximum equivalent plastic strain in the cyclic loading process. The equivalent plastic strains are obtained using the finite element software ABAQUS. The simulated annealing method is adopted for the optimization, which is capable of solving optimization problems involving strong nonlinear systems. In the optimization, four types of SSPDs with different aspect were modeled and the optimal shape of the SSPD for each case was derived. It can be found that the low cycle fatigue performance of the SSPD was significantly improved and the global optimal solution showed better performance compared to the local optimal solution.

Application of Model-Free Adaptive Controller for Multivariable System with Time Delays

The generalized MFAC control algorithm is proposed for the disadvantage of the basic MFAC controller in the strong nonlinear system with large time delays.As the same time,the algorithm is applied in the double flume liquid temperature control system,the simulation of the control system is carried out.The simulation results presents the the control structure and control algorithm track ability, anti-interference,rubustness and load adaptability meet the demand of control design.The designed system have good control qualities.

Strong and weak nonlinear dynamics: Models, classification, examples

The difference between strong and weak nonlinear systems is discussed. A classification of strong nonlinearities is given. It is based on the divergence or inanity of series expansions of the equation of state commonly used in the study of weak nonlinear phenomena. Such power or functional series cannot be used in three cases: (i) if the equation of state contains a singularity; (ii) if the series diverges for strong disturbances; (iii) if the linear term is absent, and higher nonlinearity dominates. Strong nonlinearities are known in acoustics, optics, mechanics and in quantum field theory. Mathematical models, solutions and observed phenomena are presented. For example, an equation of Heisenberg type and its generalization for strongly nonlinear wave system are given. In particular, exact solutions of new “quadratically cubic” Burgers and Riemann-Hopf equations are discovered.