Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

Characterization and identification towards dynamic-based electrical modeling of lithium-ion batteries

Lithium-ion batteries are widely recognized as a crucial enabling technology for the advancement of electric vehicles and energy storage systems in the grid.The design of battery state estimation and control algorithms in battery management systems is usually based on battery models,which interpret crucial battery dynamics through the utilization of mathematical functions.Therefore,the investigation of battery dynamics with the purpose of battery system identification has garnered considerable attention in the realm of battery research.Characterization methods in terms of linear and nonlinear response of lithium-ion batteries have emerged as a prominent area of study in this field.This review has undertaken an analysis and discussion of characterization methods,with a particular focus on the motivation of battery system identification.Specifically,this work encompasses the incorporation of frequency domain nonlinear characterization methods and dynamics-based battery electrical models.The aim of this study is to establish a connection between the characterization and identification of battery systems for researchers and engineers specialized in the field of batteries,with the intention of promoting the advancement of efficient battery technology for real-world applications.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Atlantic blocking events in a simplified nonlinear baroclinic model for local finite-amplitude wave activity

为研究北大西洋阻高的形成机制,本文在局部有限振幅波活动(LWA)框架下进行了一系列数值实验.采用的数值模型能显式地描绘出两种重要的大气内部动力过程,即非线性纬向位涡通量和Rossby波包传播.模拟结果显示,这两种动力学过程均是形成大西洋阻高的重要机理.具体地,非线性纬向位涡通量和Rossby波包传播,分别是大西洋阻高南部和北部LWA形成的主导因子.因此,本研究综合了前人关于大西洋阻高的研究成果,为其形成机理提供了新的认识.

Determination of Melamine by Infrared Spectroscopy Based on Nonlinear Modeling

[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.

Nonlinear Auto-Companding Method for Behavioral Modeling of Switched-Current Circuits

A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch( Larix olgensis ) plantations in northeast China

Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.

Pre-compensation of Friction for CNC Machine Tools through Constructing a Nonlinear Model Predictive Scheme

Nonlinear friction is a dominant factor afecting the control accuracy of CNC machine tools.This paper proposes a friction pre-compensation method for CNC machine tools through constructing a nonlinear model predictive scheme.The nonlinear friction-induced tracking error is frstly modeled and then utilized to establish the nonlinear model predictive scheme,which is subsequently used to optimize the compensation signal by treating the friction-induced tracking error as the optimization objective.During the optimization procedure,the derivative of compensation signal is constrained to avoid vibration of machine tools.In contrast to other existing approaches,the proposed method only needs the parameters of Stribeck friction model and an additional tuning parameter,while fnely identifying the parameters related to the pre-sliding phenomenon is not required.As a result,it greatly facilitates the practical applicability.Both air cutting and real cutting experiments conducted on an in-house developed open-architecture CNC machine tool prove that the proposed method can reduce the tracking errors by more than 56%,and reduce the contour errors by more than 50%.

Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Nonlinear Modeling and Identification of the Electro-hydraulic Control System of an Excavator Arm Using BONL Model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.

Nonlinear Modeling of a High Precision Servo Injection Molding Machine Including Novel Molding Approach

A nonlinear mathematical model of the injection molding process for electrohydraulic servo injection molding machine (IMM) is developed.It was found necessary to consider the characteristics of asymmetric cylinder for electrohydraulic servo IMM.The model is based on the dynamics of the machine including servo valve,asymmetric cylinder and screw,and the non-Newtonian flow behavior of polymer melt in injection molding is also considered.The performance of the model was evaluated based on novel approach of molding - injection and compress molding,and the results of simulation and experimental data demonstrate the effectiveness of the model.

Support Vector Machine-Based Nonlinear System Modeling and Control

This paper provides an introduction to a support vector machine, a new kernel-based technique introduced in statistical learning theory and structural risk minimization, then presents a modeling-control framework based on SVM. At last a numerical experiment is taken to demonstrate the proposed approach's correctness and effectiveness.

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control(NMPC)scheme is an effective method of multi-objective optimization control in complex industrial systems.In this paper,a NMPC scheme for the wet limestone flue gas desulphurization(WFGD)system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme.At first,a mathematical model of the FGD process is deduced which is suitable for NMPC structure.To equipoise the model’s accuracy and conciseness,the wet limestone FGD system is separated into several modules.Based on the conservation laws,a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design.Then,by addressing economic objectives directly into the NMPC scheme,the NMPC controller can minimize economic cost and track the set-point simultaneously.The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province,China.The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time.In the meantime,the control scheme satisfies the multiobjective control requirements under complex operation conditions(e.g.,boiler load fluctuation and set point variation).The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.

Design of a Computational Heuristic to Solve the Nonlinear Liénard Differential Model

In this study,the design of a computational heuristic based on the nonlinear Liénard model is presented using the efficiency of artificial neural networks(ANNs)along with the hybridization procedures of global and local search approaches.The global search genetic algorithm(GA)and local search sequential quadratic programming scheme(SQPS)are implemented to solve the nonlinear Liénard model.An objective function using the differential model and boundary conditions is designed and optimized by the hybrid computing strength of the GA-SQPS.The motivation of the ANN procedures along with GA-SQPS comes to present reliable,feasible and precise frameworks to tackle stiff and highly nonlinear differentialmodels.The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models.The achieved numerical outcomes on multiple trials using the designed procedures are compared to authenticate the correctness,viability and efficacy.Moreover,statistical performances based on different measures are also provided to check the reliability of the ANN along with GASQPS.

Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.