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 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.

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%.

The effects of cold region meteorology and specific environment on the number of hospital admissions for chronic kidney disease:An investigate with a distributed lag nonlinear model

Objective:To explore the effects of daily mean temperature(°C),average daily air pressure(hPa),humidity(%),wind speed(m/s),particulate matter(PM)2.5(μg/m3)and PM10(μg/m3)on the admission rate of chronic kidney disease(CKD)patients admitted to the Second Affiliated Hospital of Harbin Medical University in Harbin and to identify the indexes and lag days that impose the most critical influence.Methods:The R language Distributed Lag Nonlinear Model(DLNM),Excel,and SPSS were used to analyze the disease and meteorological data of Harbin from 01 January 2010 to 31 December 2019 according to the inclusion and exclusion criteria.Results:Meteorological factors and air pollution influence the number of hospitalizations of CKD to vary degrees in cold regions,and differ in persistence or delay.Non-optimal temperature increases the risk of admission of CKD,high temperature increases the risk of obstructive kidney disease,and low temperature increases the risk of other major types of chronic kidney disease.The greater the temperature difference is,the higher its contribution is to the risk.The non-optimal wind speed and non-optimal atmospheric pressure are associated with increased hospital admissions.PM2.5 concentrations above 40μg/m3 have a negative impact on the results.Conclusion:Cold region meteorology and specific environment do have an impact on the number of hospital admissions for chronic kidney disease,and we can apply DLMN to describe the analysis.

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.

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system(VHDNS)along with the numerical treatment of artificial neural networks(ANNs)techniques supported by Levenberg-Marquardt backpropagation(LMQBP),known as ANNs-LMQBP.This mechanism is physically appropriate,where the number of infected people is increasing along with the limited health services.Furthermore,the biological effects have fadingmemories and exhibit transition behavior.Initially,the model is developed by considering the two and three categories for the humans and the vector species.The VHDNS is constructed with five classes,susceptible humans Sh(t),infected humans Ih(t),recovered humans Rh(t),infected vectors Iv(t),and susceptible vector Sv(t)based system of the fractional-order nonlinear ordinary differential equations.To solve the number of variations of the VHDNS,the numerical simulations are performed using the stochastic ANNs-LMQBP.The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training,verifying,and testing data to decrease the mean square error(MSE).An extensive analysis is provided using the correlation studies,MSE,error histograms(EHs),state transitions(STs),and regression to observe the accuracy,efficiency,expertise,and aptitude of the computing ANNs-LMQBP.

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.

Smoothed Empirical Likelihood Inference for Nonlinear Quantile Regression Models with Missing Response

In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.

Unconfined compressive strength and failure behaviour of completely weathered granite from a fault zone

Understanding the strength characteristics and deformation behaviour of the tunnel surrounding rock in a fault zone is significant for tunnel stability evaluation.In this study,a series of unconfined compression tests were conducted to investigate the mechanical characteristics and failure behaviour of completely weathered granite(CWG)from a fault zone,considering with height-diameter(h/d)ratio,dry densities(ρd)and moisture contents(ω).Based on the experimental results,a regression mathematical model of unconfined compressive strength(UCS)for CWG was developed using the Multiple Nonlinear Regression method(MNLR).The research results indicated that the UCS of the specimen with a h/d ratio of 0.6 decreased with the increase ofω.When the h/d ratio increased to 1.0,the UCS increasedωwith up to 10.5%and then decreased.Increasingρd is conducive to the improvement of the UCS at anyω.The deformation and rupture process as well as final failure modes of the specimen are controlled by h/d ratio,ρd andω,and the h/d ratio is the dominant factor affecting the final failure mode,followed byωandρd.The specimens with different h/d ratio exhibited completely different fracture mode,i.e.,typical splitting failure(h/d=0.6)and shear failure(h/d=1.0).By comparing the experimental results,this regression model for predicting UCS is accurate and reliable,and the h/d ratio is the dominant factor affecting the UCS of CWG,followed byρd and thenω.These findings provide important references for maintenance of the tunnel crossing other fault fractured zones,especially at low confining pressure or unconfined condition.

Different responses of two adjacent artificial beaches to Typhoon Hato in Zhuhai,China

Major differences in beach erosion between two neighboring artificial beaches Xiangluwan Beach(XL beach)and Meiliwan Beach(ML beach)in Zhuhai,China,were studied after Super Typhoon Hato.In this study,a fully nonlinear Boussinesq wave model(FUNWAVE)-Total Variation Diminishing(TVD)was used to distinguish the main impact factors,their relative contributions,and the hydrodynamic mechanisms underlying the different beach responses.Results show that compared to the ML beach,the main reason for the relatively weak erosion on Xiangluwan(XL)beach was the smaller beach berm height(accounting for approximately 75.9%of the erosion response).Regarding the beach with a higher berm,the stronger wave-induced undertow flow,along with the higher sediment concentration,led to a higher offshore sediment transport flux,resulting in more severe erosion relative to the beach with a smaller berm height.The second most important reason explaining the weak erosion on XL beach was the absence of seawalls(accounting for approximately 17.9%of the erosion response).Wave reflection induced by the seawall could cause higher suspended sediment concentration,resulting in a toe scouring near the seawall.The offshore submerged breakwater protected XL beach slightly(accounting for approximately 6.1%of the erosion response).Due to the higher water level induced by storm surge,most of the wave energy could penetrate through the submerged breakwater.The effect of the larger berm width of XL beach was negligible.Compared to the beach with a larger berm width,the erosion/deposition regions in the beach with a narrower berm width showed shoreward migration,without significant changes in the erosion/deposition extent.Despite of this,the larger berm width could reduce the wave energy reaching the shoreline.This study of the storm stability of artificial beaches may be applied to beach restoration design.

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.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Feedback linearization of the nonlinear model of a small-scale helicopter

In order to design a nonlinear controller for small-scale autonomous helicopters, the dynamic characteristics of a model helicopter are investigated, and an integrated nonlinear model of a small-scale helicopter for hovering control is presented. It is proved that the nonlinear system of the small-scale helicopter can be transformed to a linear system using the dynamic feedback linearization technique. Finally, simulations are carried out to validate the nonlinear controller.

Maximal and total skew information for a two-qubit system using nonlinear interaction models

Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value （Sz） at any time t. Based on （Sz）2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.

Accurate Torque Modeling With PSO-Based Recursive Robust LSSVR for a Segmented-Rotor Switched Reluctance Motor

In order to improve the reliability in torque calculation of SRM,an accurate nonlinear torque model regresses by recursive robust least squares support vector regression(RR-LSSVR)is proposed in this paper.The model is in terms of a segmented-rotor switched reluctance motor(SSRM).The characteristics of the SSRM is introduced to show its nonlinear characteristics both in magnetic and torque.Then,its mathematic model is established,and an accurate inductance measurement method and a torque calculation method are presented.After this,the principle of the RR-LSSVR and why it can adjust weights according to errors are described.The model used the RR-LSSVR algorithm shows an outstanding capability in accuracy and quickness compared with other algorithms.Finally,to further validate the accuracy of the proposed model in practical application,simulation and experiment are designed based on a 16/10 SSRM.

GA-Based Model Predictive Control of Semi-Active Landing Gear

Semi-active landing gear can provide good performance of both landing impact and taxi situation, and has the ability for adapting to various ground conditions and operational conditions. A kind of Nonlinear Model Predictive Control algorithm （NMPC） for semi-active landing gears is developed in this paper. The NMPC algorithm uses Genetic Algorithm （GA） as the optimization technique and chooses damping performance of landing gear at touch down to be the optimization object. The valve＇s rate and magnitude limitations are also considered in the controller＇s design. A simulation model is built for the semi-active landing gear＇s damping process at touchdown. Drop tests are carried out on an experimental passive landing gear systerm to validate the parameters of the simulation model. The result of numerical simulation shows that the isolation of impact load at touchdown can be significantly improved compared to other control algorithms. The strongly nonlinear dynamics of semi-active landing gear coupled with control valve＇s rate and magnitude limitations are handled well with the proposed controller.

Penalized total least squares method for dealing with systematic errors in partial EIV model and its precision estimation

When the total least squares(TLS)solution is used to solve the parameters in the errors-in-variables(EIV)model,the obtained parameter estimations will be unreliable in the observations containing systematic errors.To solve this problem,we propose to add the nonparametric part(systematic errors)to the partial EIV model,and build the partial EIV model to weaken the influence of systematic errors.Then,having rewritten the model as a nonlinear model,we derive the formula of parameter estimations based on the penalized total least squares criterion.Furthermore,based on the second-order approximation method of precision estimation,we derive the second-order bias and covariance of parameter estimations and calculate the mean square error(MSE).Aiming at the selection of the smoothing factor,we propose to use the U curve method.The experiments show that the proposed method can mitigate the influence of systematic errors to a certain extent compared with the traditional method and get more reliable parameter estimations and its precision information,which validates the feasibility and effectiveness of the proposed method.

ON CONFIDENCE REGIONS OF SEMIPARAMETRIC NONLINEAR REGRESSION MODELS(A GEOMETRIC APPROACH)

A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.

Maximal and total skew information of three-qubit system obtained using nonlinear interaction models

Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t. Beused on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the （Sx, Sv） plane. We give the condition for the occurrence of IGHZ}sy, in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.