Second-order Nonlinear Model Research Articles

Nonlinear Moment Matching for the Simulation-Free Reduction of Structural Systems

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019a] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.

Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a second-order nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.

Efficient computational method for joint distributions of heights and periods of nonlinear ocean waves

This paper proposes a novel method for efficient prediction of joint distributions of heights and periods of nonlinear ocean waves. The proposed novel method utilizes a transformed linear simulation which is based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial, calibrated such that the first four moments of the transformed model match the moments of the true process. This proposed novel method is utilized to predict the joint distributions of wave heights and periods of a sea state with the surface elevation data measured at the Gulfaks C platform in the North Sea, and the novel method's accuracy and efficiency are favorably validated by using comparisons with the results from an empirical joint distribution model, from a linear simulation model and from a second-order nonlinear simulation model.

A Computational Approach for Stent Elution Rate Determined Specific Drug Binding and Receptor-mediated Effects in Arterial Tissue

Background and objectiveIn the present article the effects of drug binding (both specific and nonspecific) in the porous arterial wall following stent-based drug delivery from drug-eluting stents (DESs) are investigated. A three-phase (free, extracellular matrix-bound, and specific receptor-bound) second-order nonlinear saturable reversible binding model is considered in order to describe the binding process with the constituents of the porous arterial wall. Although, there are currently some precise forms of a drug binding model in the arterial tissue in the literature, analyzed by various authors. The specific interest in this present context is in assessing to what extent modelling of specific and nonspecific binding within a single-layered homogeneous porous arterial wall is possible. A novel axi-symmetric model of drug delivery from three stent struts has been developed and is presented.

Role of Blade Flexibility on Cycloidal Rotor Hover Performance

In this paper, the aeromechanics of a cycloidal rotor (or cyclorotor) is investigated to understand the effect of blade flexibility on the performance of the rotor in hover. Toward this, experiments are conducted on cyclorotors using moderately and highly flexible blades. These studies show that, with increasing blade flexibility, the rotor thrust decreases; whereas the power consumption increases, leading to a significant drop in power loading (thrust/power). To investigate these phenomena, a coupled aeroelastic model of cyclorotor is developed by coupling an unsteady aerodynamics model with a beam-based structural model and is systematically validated with experimental results. The aerodynamic model contains rigorous modeling of various physics behind the operation of the cyclorotor, such as the nonlinear dynamic virtual camber, the effect of near and shed wakes, and the leading-edge vortex. In comparison with a second-order nonlinear structural model, inclusion of a geometrically exact structural model proves to be essential in accurate prediction of rotor deflections and performance. Based on a systematic analysis performed using the validated model, it is observed that the large torsional deflections of the blades are a key reason for the drop in thrust. The torsional deflections are mainly produced by centrifugal force and nonlinear moments due to bending curvatures.

Modeling the respiration rate of Golden papayas stored under different atmosphere conditions at room temperature

The present study aimed to measure the respiration rate of papayas (cv. Golden) stored under controlled atmosphere at room temperature, with decreasing O2 and increasing CO2 levels, in order to identify mathematical models capable of predicting respiration rate throughout storage. A model was proposed based on the Michaelis–Menten equation with uncompetitive inhibition and kinetic parameters that change during storage time. A second-order nonlinear regression model was used as reference for the mathematical approach. Nine experiments with three replicates were conducted under different controlled atmospheres to generate respiration data. A closed system method was used to measure the respiration rate at 2d intervals over 13d of storage at ambient temperature (23°C). Peel color measurements indicated total ripening of fruit stored in high O2 atmospheres, whereas ripening was minimal in atmospheres containing low O2 and high CO2 levels. The respiration rate remained at the lowest value, but gradually increased during storage at the lowest O2 level associated with the highest CO2 concentration. The nonlinear regression model obtained the lowest AICc value with VarPow variance, indicating a better fit than the Michaelis–Menten model. However, the latter, whose kinetic parameters change according to a polynomial second-order equation (MMQ), displayed a better fit than the nonlinear regression model evaluated by homoscedastic variance. Additionally, MMQ was more sensitive than nonlinear regression in detecting the real change in respiration rate in a biological system as a function of different gas compositions during storage.

Predictive path following based on adaptive line-of-sight for underactuated autonomous surface vessels

Underactuated autonomous surface vehicles (ASVs) have stringent requirements on automatically tracking a predefined path. This paper proposes a model predictive control (MPC) approach based on adaptive line-of-sight (LOS) guidance for path following of ASVs. For the controller, a second-order nonlinear Nomoto model with disturbances is proposed as the vessel dynamic motion model after reviewing and comparing different ship motion models applied for path following control. For the guidance system, a novel adaptive LOS guidance with a variable acceptance circle radius is proposed to improve the precision of reference path tracking. Specifically, the acceptance circle radius is adapted with the angle between two adjacent straight segments of a reference path. Simulation experiments illustrate that the LOS guidance system with a variable acceptance circle radius results in smaller tracking errors compared with the fixed acceptance circle radius. The proposed path following method can track reference paths well even in the face of disturbances.

Adaptive-gain fast super-twisting sliding mode fault tolerant control for a reusable launch vehicle in reentry phase

In this paper, a novel adaptive-gain fast super-twisting (AGFST) sliding mode attitude control synthesis is carried out for a reusable launch vehicle subject to actuator faults and unknown disturbances. According to the fast nonsingular terminal sliding mode surface (FNTSMS) and adaptive-gain fast super-twisting algorithm, an adaptive fault tolerant control law for the attitude stabilization is derived to protect against the actuator faults and unknown uncertainties. Firstly, a second-order nonlinear control-oriented model for the RLV is established by feedback linearization method. And on the basis a fast nonsingular terminal sliding mode (FNTSM) manifold is designed, which provides fast finite-time global convergence and avoids singularity problem as well as chattering phenomenon. Based on the merits of the standard super-twisting (ST) algorithm and fast reaching law with adaption, a novel adaptive-gain fast super-twisting (AGFST) algorithm is proposed for the finite-time fault tolerant attitude control problem of the RLV without any knowledge of the bounds of uncertainties and actuator faults. The important feature of the AGFST algorithm includes non-overestimating the values of the control gains and faster convergence speed than the standard ST algorithm. A formal proof of the finite-time stability of the closed-loop system is derived using the Lyapunov function technique. An estimation of the convergence time and accurate expression of convergence region are also provided. Finally, simulations are presented to illustrate the effectiveness and superiority of the proposed control scheme.

Prediction of height and period joint distributions for stochastic ocean waves

This article proposes a new methodology to predict the wave height and period joint distributions by utilizing a transformed linear simulation method. The proposed transformed linear simulation method is based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial, calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave height and period joint distributions of a sea state with the surface elevation data measured at an offshore site, and its accuracy and efficiency are favorably validated by using comparisons with the results from an empirical joint distribution model, from a linear simulation model and from a second-order nonlinear simulation model.

Nonlinear Growth Models as Measurement Models: A Second-Order Growth Curve Model for Measuring Potential

ABSTRACTRecent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components—ability, capacity, and availability—where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study–Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.

Nonlinear identification of the total baroreflex arc: higher-order nonlinearity

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R2 values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R2 values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R2 values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions.

A second-order nonlinear model of monolayer adsorption in refractometric chemical sensors and biosensors case of equilibrium fluctuations

In adsorption-based chemical and biological refractometric sensors the dependence of the refractive index of the sensing area on the number of adsorbed particles is used for detection and quantification of analytes. We perform stochastic analysis of equilibrium fluctuations of the adsorbed particles number for monolayer adsorption using a nonlinear second-order model. We derive an analytical expression for the power spectral density (PSD) of the refractive index change fluctuations. Our theory is applicable to sensors operating in closed volume systems with spatially uniform analyte concentration. Our analysis of fluctuations in a benzene sensor shows a significant difference between the PSD according to the derived expression and the PSD obtained by the linear adsorption model, especially for very low amounts of analyte. The developed theory is valid in a wider range of pressures and temperatures. Since signal fluctuations determine the detection limit, the presented theoretical model is applicable as a tool for the design, optimization and characterization of practical adsorption-based refractometric sensors.

Genetic optimization and experimental validation of a test cycle that maximizes parameter identifiability for a Li-ion equivalent-circuit battery model

This article presents an experimental study demonstrating the degree to which optimal experimental design can improve lithium-ion battery parameter estimation. The article is motivated by previous literature showing that lithium-ion batteries suffer from poor parameter identifiability. This makes it difficult to estimate battery parameters quickly and accurately from input–output cycling data. Previous research shows that optimizing the shape of a battery cycle for Fisher information – an identifiability metric – can improve parameter estimation speed and accuracy significantly. However, most studies demonstrating this improvement are simulation-based, rather than experimental. In contrast, the centermost goal in this article is to provide an experimental assessment of the degree to which trajectory optimization for Fisher identifiability can improve lithium-ion battery parameter estimation. We optimize battery cycling to maximize Fisher information for a nonlinear second-order model of a commercial lithium iron phosphate (LFP) cell. We implement this optimal cycle experimentally for 3 different battery cells, and compare it with two benchmark cycles representing automotive battery use. The results of this comparison are quite compelling: when parameterized using data from the optimal cycle, the cell voltage prediction signal-to-noise ratio improves significantly over the benchmarks. Moreover, only the optimized cycle produces reasonable estimates of battery parameters over the course of a 4-hour experiment.

Stabilisation of second-order nonlinear equations with variable delay

For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilisation by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.

Improve GRAPPA with Cross-sampled ACS Lines and Nonlinear Kernel Model

Among the methods of parallel magnetic resonance imaging (PMRI), Generalized Auto-calibrating Partially Parallel Acquisitions (GRAPPA) technique reconstructs the missing k-space data by a set of weights, which are derived from auto-calibration signal (ACS) lines acquired in parallel to the reduced lines. In this paper, a novel hybrid method is proposed to reconstruct by cross sampling the ACS lines orthogonal to the reduced lines and estimating weights with a second-order nonlinear model. The proposed method can mix the benefits of cross sampling and the nonlinear kernel model. The in vivo experiments demonstrate this method, named as cross-sampled nonlinear (CSNL) GRAPPA, can effectively reduce the aliasing artifacts and noises when high acceleration is desired.

Nonlinear Second-Order Model and Equilibrium Point Characteristic Analysis of DC Traction Power Supply System

According to the different features of the DC traction network transient current in the Metro, the electromagnetic transient process of traction power supply system that should be divided into the two forms of short-circuit fault and the low-frequency oscillation was proposed. While traction network short-circuit fault happens, the system model is a weakly nonlinear first-order differential equation, which feeder current is increasing exponentially and eventually stabilized. While the load current becomes low-frequency oscillation current, the system model is a nonlinear second-order differential equation. After linear processing in unique equilibrium point neighborhood, the state space equation of linear system is built, and the structural reason of low-frequency oscillation is revealed by eigenvalue analysis method. The simulation result shows that the simulation current waveforms are consistent with the recorded current waveforms and the division of transient process is reasonable.

Second-order sliding mode tracking control for the piezoelectric actuator with hysteretic nonlinearity

For the piezoelectric actuator model with hysteretic nonlinearity, a second-order sliding mode tracking controller is proposed. First, a second-order nonlinear dynamic model is introduced for the piezoelectric actuator. Next, a second order sliding mode control law with dual-phase sliding movement is designed. Then, the system stability is proved with a theorem. From theoretical analysis, the feedback control system is stable in the sense that all signals involved are bounded. The simulation results show the validity of the proposed method for this kind of nonlinear dynamic model of the piezoelectric actuator.

Mathematical Model for Wear Rate of Negative Graphite Electrode in Electrical Discharge Machining on Ti-5A1-2.5Sn

There are several electrical and non-electrical factors having the significant effect on tool wear in electrical discharge machining (EDM). It is very difficult to select the parameters correctly. Likewise, the tool wear rate is changed dramatically with workpiece material and electrode material. Until now no attempt is appeared that yields the tool wear characteristics in EDM on Ti-5Al-2.5Sn retaining Graphite as electrode. Thus, in this study a mathematical model is developed to predict the tool wear rate which will provide the opportunity of proper selection of the EDM parameters and make the EDM cost effective. To model both the linear and non-linear equation is applied using the experimental data which are obtained performing the experimentation as design of experiment. The developed model has been verified through analysis of variance (ANOVA). The second-order non-linear model is found as appropriate as compared with a linear model. It is evidenced that the proposed model can effectively predict the tool wear rate (TWR) and adequately explains the variation in the machining parameters on TWR.

Modelling and Identification of Oxygen Excess Ratio of Self-Humidified PEM Fuel Cell System

One essential parameter in fuel cell operation is oxygen excess ratio which describes comparison between reacted and supplied oxygen number in cathode. Oxygen excess ratio relates to fuel cell safety and lifetime. This paper explains development of air feed model and oxygen excess ratio calculation in commercial self-humidified PEM fuel cell system with 1 kW output power. This modelling was developed from measured data which was limited in open loop system. It was carried out to get relationship between oxygen excess ratio with stack output current and fan motor voltage. It generated fourth-order 56.26% best fit ARX linear polynomial model estimation (loss function = 0.0159, FPE = 0.0159) and second-order ARX nonlinear model estimation with 75 units of wavenet estimator with 84.95% best fit (loss function = 0.0139). The second-order ARX model linearization yielded 78.18% best fit (loss function = 0.0009, FPE = 0.0009).

Binary interactions of solitary pulses in falling liquid films

We examine binary interaction of two-dimensional solitary pulses in falling liquid films. We make use of a two-field system of equations for the local flow rate and interface position that includes (second-order) viscous dispersion effects. By applying a coherent-structure theory, we obtain a dynamical system for the separation length between the pulses. The system is re-formulated in terms of a potential function which not only allows us to predict bound-state formation but also to interpret physically this formation. Numerical results of the fully non-linear second-order model are in very good agreement with the theoretically predicted distances. In addition, we numerically show that there are different types of dynamics associated with each bound state, including an overdamped, underdamped and undamped oscillating state depending on both the initial separation length and the Reynolds number.