Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with NiTiNOL-steel wire ropes(NiTi-ST)is applied to a whole-spacecraft system.The NiTi-ST is used to describe the damping of the NES,which is coupled with the modified Bouc-Wen model of hysteresis.The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET)to concentrate the energy locally on the nonlinear oscillator,and then dissipates it through damping in the NES with NiTi-ST.The generalized vibration transmissibility,obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs.Finally,the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption.The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system,without changing its natural frequency.Moreover,the NES with NiTi-ST can be directly used in practical engineering applications.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

基于GFRFs的非线性系统结构故障检测方法

为了能够更加准确高效地检测非线性系统的结构是否发生故障,提出了基于系统带外部输入的非线性自回归(NARX)模型的广义频率响应函数(GFRFs)故障检测方法。根据受检系统的NARX模型参数和一阶GFRF估算出系统的高阶GFRFs,通过比较受检系统与无故障系统结构的广义频率响应函数值,实现系统结构的故障检测。根据受检系统和无故障系统的GFRFs确定系统故障损害程度指数,进一步对故障程度进行评估。通过实验与其他检测方法进行对比,验证了所提检测方法的优越性。

基于NOFRFs的非等温CSTR同步周期操作的评估优化

化学反应周期操作是利用反应非线性来提高系统性能指标的技术,对其评估与优化仍是现阶段工业应用亟待解决的关键问题.利用非线性输出频率响应函数对具有显著非线性的连续搅拌反应釜的入口浓度和入口温度同步周期操作进行评估.首先分析单个周期操作的输入对系统性能指标的单独贡献,然后确定使转化率最大化而应使用的最优相位差,最后分析入口浓度和入口温度同步周期操作的各阶交叉项的贡献.仿真结果表明:提出的方法优于传统的NFR方法和单变量NOFRFs方法,提高了周期操作评估的准确性;同时,在允许的工艺过程约束条件下进行了最优化设计,明显提高了反应物的转化率,为其他类型的化学反应过程周期操作评估和优化提供参考.

一类非线性系统的广义伴随线性方程分析研究

非线性输出频率响应函数是线性系统理论中频率响应函数在非线性系统中的一种推广,越来越多的学者已将其应用在结构损伤检测及故障诊断中.基于Volterra级数理论与由非线性微分方程描述的单输入单输出非线性系统的广义频率响应函数递归计算公式,利用多重积分性质和多维傅里叶变换,将广义频率响应函数映射到了一维频域中,推导出了一类非线性系统的广义伴随线性方程计算公式.研究表明,这类系统的第n阶非线性输出响应是以系统输入激励和前n-1阶非线性输出响应的组合函数作为广义激励作用到系统各阶广义伴随线性方程中的输出响应,最后通过求解一系列线性微分方程可得到这类非线性系统的任意阶非线性输出响应,其结果弥补了伴随线性方程无法求解这类非线性系统的不足.同时,针对广义伴随线性方程的数值计算问题,论文提出了一种耦合计算法,提高了计算非线性输出响应的精度,为非线性输出频率响应函数的计算提供了一种新思路.最后利用广义伴随线性方程与线性算子理论研究了两种典型非线性系统中非线性现象产生的原因,研究结果为非线性系统的分析与设计提供了一种有效途径.

Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions

In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system.The AVS-VI is composed of horizontal stiffness spring,positive stiffness spring,parallelogram linkage mechanism,piezoelectric actuator,acceleration sensor,viscoelastic damping,and PID active controller.Based on the AVS-VI,the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI.The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system,and the analysis results indicate that the AVS-VI is efTective in reducing the extravagant vibration of the whole-spacecraft system,where the vibration isolation is decreased up to above 65%under different acceleration excitations.Finally,different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate.

一类非线性动态系统的非参数GFRF 模型辨识(英文)

本文对一类用多项式描述的非线性动态系统提出使用ＧＦＲＦ模型类的非参数辨识算法．这种算法的显著特点是需要很小的计算量和存储空间，而且辨识精度较高．仿真结果表明这种非参数模型辨识算法是有效的，而且由辨识方法获得的模型一般具有很好的泛化能力，因而是一种具有重要应用前景的实用方法．

基于NOFRF裂纹转子非线性频谱分析

建立了裂纹转子非线性逼近模型,论述了非线性输出频域响应函数(NOFRF)及其非线性频谱分析理论,基于该理论对裂纹转子系统的各阶NOFRF进行了仿真分析,该分析结果说明了裂纹转子系统新频域成份是如何产生的,对裂纹转子的超谐波成份和亚共振现象进行了解释,并进行了试验分析,结果表明了高阶NOFRF比一阶对转子裂纹深度更敏感,为裂纹转子的精确故障诊断提供了理论基础。

基于NARMAX模型和NOFRF结构损伤检测的实验研究

非线性输出频率响应函数是由Volterra级数发展而来的频域概念,可方便在频域对非线性系统进行分析,它是频率的一维函数.本文主要介绍了利用NARMAX模型以及NOFRF对结构进行损伤检测的方法,并利用实验研究证实了该损伤检测方法的可行性.另外,由于系统非线性特性可用来做结构损伤检测,且具有对系统状态比较敏感的优点,而基于NOFRF的损伤检测方法是利用非线性方法来分析系统的状态,该方法提取出的特征属于非线性特征,所以该损伤检测方法可以用来做结构损伤检测,且具有对系统状态比较敏感的优点.

基于GFRF的二次调节流量耦联系统的频域非线性H∞控制

二次调节流量耦联系统为非线性系统,在Volterra级数描述该系统的基础上,通过SISO多项式类非线性系统的GFRF递推算式获得二次调节流量耦联系统的广义频率响应函数GFRF(generalized frequency response function).基于系统的GFRF,在频域内应用非线性控制理论为系统设计了镇定控制器和非线性H∞控制器,不仅使系统稳定,而且能达到无超调、无稳态误差.此外,在白噪声条件下证明该控制器比线性控制器抗干扰性强.

一种直升机舵机的GFRF模型辨识方法

改进了以多音组合正弦信号为持续激励信号的非线性系统GFRF非参数模型辨识方法,并成功地利用该方法辨识出某型直升机并联电动舵机的GFRF模型.实践表明,改进后的辨识方法辨识精度高且稳定,只需很小的计算量和数据存储空间,是一种有效的非线性系统辨识方法,具有重要的工程实际应用价值.

Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis

The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.

Identification of Composite-Metal Bolted Structures with Nonlinear Contact Effect

The middle layer model has been used in recent years to better describe the connection behavior in composite structures.The influencing parameters including low pre-screw and high preload have the main effects on nonlinear behavior of the connection as well as the amplitude of the excitation force applied to the structure.Therefore,in this study,the effects of connection behavior on the general structure in two sections of increasing damping and reducing the stiffness of the structures that lead to non-linear phenomena have been investigated.Due to the fact that in composite structure we are faced to the limitation of increasing screw preload which tend to structural damage,so the investigation on the hybrid connection(metal-composite)behavior is conducted.In this research,using the two-dimensional middle layer theory,the stiffness properties of the connection are modeled by normal stiffness and the connection damping is modeled using the structural damping in the shear direction.Nonlinear frequency response diagrams have been extracted twice for two different excitation forces and then proposed by a high-order multitasking approximation according to the response range of the nonlinear finite element model for stiffness and damping of the connection.The effect of increasing the amplitude of the excitation force and decreasing the preload of the screw on the nonlinear behavior of the component has been extracted.The results show that the limited presented novel component model has been accurately verified on the model obtained from the vibration experimental test and the reduction of nonlinear model updating based on that is represented.The comparison results show good agreementwith a maximumof 1.33%error.

T型橡胶减振器非线性特性分析与预压缩量设计

为研究T型橡胶减振器的结构型式和材料性能对其非线性动力学特性的影响,并提高其对飞行环境的适应能力,改善其在恶劣环境下的使用性能,提出了一种含分段线性刚度及阻尼和立方刚度的双层级非线性动力学模型。首先,对T型橡胶减振器进行了简化建模,并采用等价线性化方法,推导得到了分段线性系统的等效刚度和等效阻尼。其次,利用谐波平衡法分别数值模拟了等幅值外力载荷正弦扫频激励下分段线性刚度系统和立方刚度系统的非线性频响函数,验证了构建模型的有效性。最后,进行了T型橡胶减振系统在基础位移正弦扫频条件下的传递特性试验,并与数值计算结果进行了比对。研究结果表明,针对T型橡胶减振器,较低激励载荷即可导致结构型式的渐进软化,较高激励载荷才能引发材料性能的动态软化;该模型能够较好的模拟T型橡胶减振器具有的渐软刚度和渐小阻尼的非线性特性。此外,从航天工程应用的角度出发提出了针对大过载、强振动环境进行预压缩量设计的方法。

频率响应函数估计方法综述

回顾了近年来以线性系统为基础模型的频率响应函数估计方法的理论研究和发展现状。根据干扰误差主要成分的不同分为几个方面讨论,包括加性随机噪声、加窗泄漏引起的噪声、非线性系统失真引起的噪声等。综合论述了各种干扰误差下,各种频率响应函数估计方法的原理、特点及其在工程中的应用。最后对文章内容进行了总结并对频率响应函数估计领域的发展前景进行了探讨和展望。

基于非线性输出频响函数的NES动力学参数设计

基于非线性输出频率响应函数(Nonlinear Output Frequency Response Function,NOFRF),对引入了被动非线性消振器(Nonlinear Energy Sink,NES)的单自由度振动系统进行了分析,从频域分析的角度评价NES的振动抑制效果,对其进行动力学参数设计。首先,建立了引入NES的振动系统非线性动力学模型。然后,通过数值仿真,对单自由度系统进行了非线性输出频率响应函数分析和输出频率响应分析,从频域分析的角度解释了在原振动系统中引入NES对原系统固有频率几乎没有影响的原因。最后,通过分析NES各参数对振动抑制效果的影响,对NES进行了动力学参数设计。本文得出的分析结果对于工程领域中NES的设计具有非常重要的指导意义。

基于非线性频谱特征及核主元分析的模拟电路故障诊断方法

针对模拟电路基于非线性输出频域响应函数(NOFRF)模型进行故障特征提取时,具有维数多、数据量大的特点,提出了采用核主元分析(KPCA)和多类别支持向量机(MSVM)进行故障模式判别的新方法(KPCA-MSVM)。该方法首先采用KPCA对特征向量进行维数压缩、消除变量之间的非线性;其次构造MSVM分类器,在PSpice环境下通过蒙特卡罗仿真生成模拟电路在各种故障状态下的数据,对MSVM分类器进行训练,将训练好的MSVM分类器用于模拟电路的故障状态识别。通过对Sallen-Key带通滤波器模拟电路的故障诊断结果表明,该故障诊断方法对模拟电路参数型故障有很好的识别、定位能力并具有速度快和准确率高的特点。