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.

Path-Following Based on Nonlinear Model Predictive Control with Adaptive Path Preview

This paper presents a Nonlinear Model Predictive Controller(NMPC)for the path following of autonomous vehicles and an algorithm to adaptively adjust the preview distance.The prediction model includes vehicle dynamics,path following dynamics,and system input dynamics.The single-track vehicle model considers the vehicle’s coupled lateral and longitudinal dynamics,as well as nonlinear tire forces.The tracking error dynamics are derived based on the curvilinear coordinates.The cost function is designed to minimize path tracking errors and control effort while considering constraints such as actuator bounds and tire grip limits.An algorithm that utilizes the optimal preview distance vector to query the corresponding reference curvature and reference speed.The length of the preview path is adaptively adjusted based on the vehicle speed,heading error,and path curvature.We validate the controller performance in a simulation environment with the autonomous racing scenario.The simulation results show that the vehicle accurately follows the highly dynamic path with small tracking errors.The maximum preview distance can be prior estimated and guidance the selection of the prediction horizon for NMPC.

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.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

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.

Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

A nonlinear wake model of a wind turbine considering the yaw wake steering

Duo to fluctuations in atmospheric turbulence and yaw control strategies,wind turbines are often in a yaw state.To predict the far wake velocity field of wind turbines quickly and accurately,a wake velocity model was derived based on the method of momentum conservation considering the wake steering of the wind turbine under yaw conditions.To consider the shear effect of the vertical incoming wind direction,a two-dimensional Gaussian distribution function was introduced to model the velocity loss at different axial positions in the far wake region based on the assumption of nonlinear wake expansion.This work also developed a“prediction-correction”method to solve the wake velocity field,and the accuracy of the model results was verified in wake experiments on the Garrad Hassan wind turbine.Moreover,a 33-kW two-blade horizontal axis wind turbine was simulated using this method,and the results were compared with the classical wake model under the same parameters and the computational fluid dynamics(CFD)simulation results.The results show that the nonlinear wake model well reflected the influence of incoming flow shear and yaw wake steering in the wake velocity field.Finally,computation of the wake flow for the Horns Rev offshore wind farm with 80 wind turbines showed an error within 8%compared to the experimental values.The established wake model is less computationally intensive than other methods,has a faster calculation speed,and can be used for engineering calculations of the wake velocity in the far wakefield of wind turbines.

Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects

Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.

Fuzzy-Model-Based Finite Frequency Fault Detection Filtering Design for Two-Dimensional Nonlinear Systems

This article studies the fault detection filtering design problem for Roesser type two-dimensional(2-D)nonlinear systems described by uncertain 2-D Takagi-Sugeno(T-S)fuzzy models.Firstly,fuzzy Lyapunov functions are constructed and the 2-D Fourier transform is exploited,based on which a finite frequency fault detection filtering design method is proposed such that a residual signal is generated with robustness to external disturbances and sensitivity to faults.It has been shown that the utilization of available frequency spectrum information of faults and disturbances makes the proposed filtering design method more general and less conservative compared with a conventional nonfrequency based filtering design approach.Then,with the proposed evaluation function and its threshold,a novel mixed finite frequency H_(∞)/H_(-)fault detection algorithm is developed,based on which the fault can be immediately detected once the evaluation function exceeds the threshold.Finally,it is verified with simulation studies that the proposed method is effective and less conservative than conventional non-frequency and/or common Lyapunov function based filtering design methods.

Stiffness Characteristics of a Basic Nonlinear Air Spring Model

This study predicts the characteristics of a compressible polytropic air spring model. A second-order nonlinear autonomous air spring model is presented. The proposed model is based on the assumption that polytropic processes occur. Isothermal and isentropic compression and expansion of the air within the spring chambers are the two scenarios that are taken into consideration. In these situations, the air inside the spring chambers compresses and expands, resulting in nonlinear spring restoring forces. The MATLAB/Simulink software environment is used to build a numerical simulation model for the dynamic behavior of the air spring. To quantify the values of the stiffnesses of the proposed models, a numerical solution is run over time for various values of the design parameters. The isentropic process case has a higher dynamic air spring stiffness than the isothermal process case, according to the results. The size of the air spring chamber and the area of the air spring piston influence the air spring stiffness in both situations. It is demonstrated that the stiffness of the air spring increases linearly with increasing piston area and decreases nonlinearly with increasing air chamber length. As long as the ratio of the vibration’s amplitude to the air spring’s chamber length is small, there is good agreement in both scenarios between the linearized model and the full nonlinear model. This implies that linear modeling is a reasonable approximation of the complete nonlinear model in this particular scenario.

Aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders:progress of experimental models based on disease pathogenesis

Neuromyelitis optica spectrum disorders are neuroinflammatory demyelinating disorders that lead to permanent visual loss and motor dysfunction.To date,no effective treatment exists as the exact causative mechanism remains unknown.Therefore,experimental models of neuromyelitis optica spectrum disorders are essential for exploring its pathogenesis and in screening for therapeutic targets.Since most patients with neuromyelitis optica spectrum disorders are seropositive for IgG autoantibodies against aquaporin-4,which is highly expressed on the membrane of astrocyte endfeet,most current experimental models are based on aquaporin-4-IgG that initially targets astrocytes.These experimental models have successfully simulated many pathological features of neuromyelitis optica spectrum disorders,such as aquaporin-4 loss,astrocytopathy,granulocyte and macrophage infiltration,complement activation,demyelination,and neuronal loss;however,they do not fully capture the pathological process of human neuromyelitis optica spectrum disorders.In this review,we summarize the currently known pathogenic mechanisms and the development of associated experimental models in vitro,ex vivo,and in vivo for neuromyelitis optica spectrum disorders,suggest potential pathogenic mechanisms for further investigation,and provide guidance on experimental model choices.In addition,this review summarizes the latest information on pathologies and therapies for neuromyelitis optica spectrum disorders based on experimental models of aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders,offering further therapeutic targets and a theoretical basis for clinical trials.

Exploiting fly models to investigate rare human neurological disorders

Rare neurological diseases,while individually are rare,collectively impact millions globally,leading to diverse and often severe neurological symptoms.Often attributed to genetic mutations that disrupt protein function or structure,understanding their genetic basis is crucial for accurate diagnosis and targeted therapies.To investigate the underlying pathogenesis of these conditions,researchers often use non-mammalian model organisms,such as Drosophila(fruit flies),which is valued for their genetic manipulability,cost-efficiency,and preservation of genes and biological functions across evolutionary time.Genetic tools available in Drosophila,including CRISPR-Cas9,offer a means to manipulate gene expression,allowing for a deep exploration of the genetic underpinnings of rare neurological diseases.Drosophila boasts a versatile genetic toolkit,rapid generation turnover,and ease of large-scale experimentation,making it an invaluable resource for identifying potential drug candidates.Researchers can expose flies carrying disease-associated mutations to various compounds,rapidly pinpointing promising therapeutic agents for further investigation in mammalian models and,ultimately,clinical trials.In this comprehensive review,we explore rare neurological diseases where fly research has significantly contributed to our understanding of their genetic basis,pathophysiology,and potential therapeutic implications.We discuss rare diseases associated with both neuron-expressed and glial-expressed genes.Specific cases include mutations in CDK19 resulting in epilepsy and developmental delay,mutations in TIAM1 leading to a neurodevelopmental disorder with seizures and language delay,and mutations in IRF2BPL causing seizures,a neurodevelopmental disorder with regression,loss of speech,and abnormal movements.And we explore mutations in EMC1 related to cerebellar atrophy,visual impairment,psychomotor retardation,and gain-of-function mutations in ACOX1 causing Mitchell syndrome.Loss-of-function mutations in ACOX1 result in ACOX1 deficiency,characterized by very-long-chain fatty acid accumulation and glial degeneration.Notably,this review highlights how modeling these diseases in Drosophila has provided valuable insights into their pathophysiology,offering a platform for the rapid identification of potential therapeutic interventions.Rare neurological diseases involve a wide range of expression systems,and sometimes common phenotypes can be found among different genes that cause abnormalities in neurons or glia.Furthermore,mutations within the same gene may result in varying functional outcomes,such as complete loss of function,partial loss of function,or gain-of-function mutations.The phenotypes observed in patients can differ significantly,underscoring the complexity of these conditions.In conclusion,Drosophila represents an indispensable and cost-effective tool for investigating rare neurological diseases.By facilitating the modeling of these conditions,Drosophila contributes to a deeper understanding of their genetic basis,pathophysiology,and potential therapies.This approach accelerates the discovery of promising drug candidates,ultimately benefiting patients affected by these complex and understudied diseases.

A promising approach for quantifying focal stroke modeling and assessing stroke progression:optical resolution photoacoustic microscopy photothrombosis

To investigate the mechanisms underlying the onset and progression of ischemic stroke,some methods have been proposed that can simultaneously monitor and create embolisms in the animal cerebral cortex.However,these methods often require complex systems and the effect of age on cerebral embolism has not been adequately studied,although ischemic stroke is strongly age-related.In this study,we propose an optical-resolution photoacoustic microscopy-based visualized photothrombosis methodology to create and monitor ischemic stroke in mice simultaneously using a 532 nm pulsed laser.We observed the molding process in mice of different ages and presented age-dependent vascular embolism differentiation.Moreover,we integrated optical coherence tomography angiography to investigate age-associated trends in cerebrovascular variability following a stroke.Our imaging data and quantitative analyses underscore the differential cerebrovascular responses to stroke in mice of different ages,thereby highlighting the technique's potential for evaluating cerebrovascular health and unraveling age-related mechanisms involved in ischemic strokes.

Reduced mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor contributes to neurodegeneration in a model of spinal and bulbar muscular atrophy pathology

Spinal and bulbar muscular atrophy is a neurodegenerative disease caused by extended CAG trinucleotide repeats in the androgen receptor gene,which encodes a ligand-dependent transcription facto r.The mutant androgen receptor protein,characterized by polyglutamine expansion,is prone to misfolding and forms aggregates in both the nucleus and cytoplasm in the brain in spinal and bulbar muscular atrophy patients.These aggregates alter protein-protein interactions and compromise transcriptional activity.In this study,we reported that in both cultured N2a cells and mouse brain,mutant androgen receptor with polyglutamine expansion causes reduced expression of mesencephalic astrocyte-de rived neurotrophic factor.Overexpressio n of mesencephalic astrocyte-derived neurotrophic factor amelio rated the neurotoxicity of mutant androgen receptor through the inhibition of mutant androgen receptor aggregation.Conversely.knocking down endogenous mesencephalic astrocyte-derived neurotrophic factor in the mouse brain exacerbated neuronal damage and mutant androgen receptor aggregation.Our findings suggest that inhibition of mesencephalic astrocyte-derived neurotrophic factor expression by mutant androgen receptor is a potential mechanism underlying neurodegeneration in spinal and bulbar muscular atrophy.

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.

Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.