Random vibration of hysteretic systems under Poisson white noise excitations

Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.

STOCHASTIC OPTIMAL CONTROL OF STRONGLY NONLINEAR SYSTEMS UNDER WIDE-BAND RANDOM EXCITATION WITH ACTUATOR SATURATION

A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.

RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.

An iterative algorithm for analysis of coupled structural-acoustic systems subject to random excitations

This paper analyzes the random response of structural-acoustic coupled systems. Most existing works on coupled structural-acoustic analysis are limited to systems under deterministic excitations due to high computational cost required by a random response analysis. To reduce the computational burden involved in the coupled random analysis, an iterative procedure based on the Pseudo excitation method has been developed. It is found that this algorithm has an overwhelming advantage in computing efficiency over traditional methods, as demonstrated by some numerical examples given in this paper.

Research on the random seismic response analysis for multi- and large-span structures to multi-support excitations

The pseudo excitation method(PEM) has been improved into a more practical form,on which the analytic formulae of seismic response power spectral density(PSD) of simplified large-span structural models have been derived.The analytic formulae and numerical computing results of seismic response PSD have been derived to study the mechanism of multi-support excitation effects,such as the wave-passage effect and incoherence effect,for the seismic response of multiand large-span structures.By using a multi-span truss as an example,the influence of multi-support excitation effects on the seismic response of such structures is studied.

Time-delayed feedback control optimization for quasi linear systems under random excitations

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces,making it challenging to carry out the research of this category of complex systems with non-smooth characteristics.To address this problem,by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation,a modified conducting process has proposed.Taking the multiple nonlinear parameters,the non-smooth parameters,and the external excitation frequency into consideration,the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed.It can be found that the system parameters can make the system stability topology change.The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo(MC)simulation.Consequently,the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Karhunen-loéve expansion for random earthquake excitations

This paper develops a trigonometric-basis-fimction based Karhunen-Loeve （KL） expansion for simulating random earthquake excitations with known covariance functions. The methods for determining the number of the KL terms and defining the involved random variables are described in detail. The simplified form of the KL expansion is given, whereby the relationship between the KL expansion and the spectral representation method is investigated and revealed. The KL expansion is of high efficiency for simulating long-term earthquake excitations in the sense that it needs a minimum number of random variables, as compared with the spectral representation method. Numerical examples demonstrate the convergence and accuracy of the KL expansion for simulating two commonly-used random earthquake excitation models and estimating linear and nonlinear random responses to the random excitations.

Modal identification to non-stationary random excitation based on wavelet transform and co-integration theory

A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.

Parametric Vibration of Submerged Floating Tunnel Tether Under Random Excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.

Vibration and acoustic radiation of bogie area under random excitation in high-speed trains

Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. Firstly, combined with line tests, a vehicle body with a length of 7 m was used as the research object. By comparing the results of experiment and simulation, the accuracy of the finite element model was verified. Secondly, the power spectral density curves at typical measuring points in bogie area were obtained by processing and calculating the line test data, which was measured when the vehicle ran at high speeds, and the standard vibration spectrum of the bogie area was obtained by the extreme envelope method. Furthermore, the random vibration test and simulation prediction analysis of the real vehicle structure were carried out to further verify the accuracy of the noise and vibration prediction model. Finally, according to the vibration and acoustic radiation theory, the indirect boundary element method was adopted to predict the acoustic response of the real vehicle. The analysis shows that the simulated power spectral density curves of acceleration and sound pressure level are highly consistent with the experimental ones, and the error between the simulated prediction and the experimental result is within the allowable range of 3 dB.

Response of train-bridge system under intensive seismic excitation by random vibration method

Earthquake is a kind of sudden and destructive random excitation in nature.It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation,the intensity of which is larger than 7,acts in train-bridge system.Firstly,the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established,where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom,while the single-span simple supported bridge subsystem is composed of 102D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support.Secondly,Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system.The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method,respectively solved by precise integral method and Newmark-βmethod through the inter-system iterative procedure.Finally,the results are compared with the case under the weak seismic excitation,and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution.In a high probability,the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.

Dynamic Characteristics of Tracked Vehicle Power Train Considering Road Random Torsional Excitation

The road random torsional excitation is one type of torque rooted from the road roughness and vehicle drive system. This paper aims to study how the road random torsional excitation affects the dynamic characteristics of vehicle power train. The method of simulating the random torsional excitation of tracked vehicle is explored at first. Secondly,the road random torsional excitations under different road roughness,vehicle speeds and pre-tensions are obtained. Thirdly,the dynamic analysis model of tracked vehicle power train is constructed with the consideration of the road random torsional excitation. Eventually,the influences of this excitation on output torque,bearing support force,vibration acceleration and dynamic shear stress of transmission shafts are intensively studied.The research conclusions are helpful to correct and refine the present virtual prototype of tracked vehicle power train.

Analysis on Pseudo Excitation of Random Vibration for Structure of Time Flight Counter

Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method（PEM）is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter（ToFC）.The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.

Modeling and Analysis of a Random Excited Double-Clamped Piezoelectric Energy Harvester

A double-clamped piezoelectric energy harvester subjected to random excitation is presented,for which corresponding analytical model is established to predict its output characteristics.With the presented theoretical natural frequency and equivalent stiffness of vibrator,the closed-form expressions of mean power and voltage acquired from the double-clamped piezoelectric energy harvester under random excitation are derived.Finally theoretical analysis is conducted for the output performance of the doubleclamped energy harvester with the change of spectrum density（SD）of acceleration,load resistance,piezoelectric coefficient and natural frequency value,which is found to closely agree with Monte Carlo simulation and experimental results.

Analyzing Nonstationary Random Response of a SDOF System under the Evolutionary Random Excitation by Wavelet Transform

For evolutionary random excitations, a general method of analyzing nonstationary random responses of systems was presented in this paper. Firstly, for the evolutionary random excitation model, the evolutionary power spectrum density function （EPSD） of a random excitation was given by wavelet transform. Based on the EPSD, the nonstationary responses of a SDOF system subjected to evolutionary random excitations were studied. The application and validity of presented method were illustrated by numerical examples. In numerical examples, the recently developed stochastic models for El Centro （1934） and Mexico City （1985） earthquakes which preserve the nonstationary evolutions of amplitude and frequency content of ground accelerations were used as excitations. The nonstationary random mean-square responses of a SDOF system under these two excitations were evaluated and compared with simulated results.

基于虚拟激励法的大跨度桥梁非平稳随机振动分析闭合解

针对大跨度结构考虑地面空间运动的非一致地震响应分析问题,结合虚拟激励法,应用傅里叶分析建立了结构非平稳随机振动响应演变功率谱分析的频域方法。建立的方法完全基于频域执行,给出了响应演变功率谱的闭合解表达式。由于实现了确定性调制过程与随机过程的有效分离,应用离散傅里叶变换进行计算不需要较高的采样分析频率就可以获得较好精度的数值结果。数值算例研究了某斜拉桥的考虑地面运动空间效应非平稳随机地震响应,与通常时频分析方法进行对比,验证了本文频域方法的正确性和有效性。

基于多粒度时间卷积网络的超短期风功率预测

针对传统风功率预测方法通常基于固定时间粒进行研究,但该类方法往往忽略了其他时间粒度对风功率的影响的问题,提出一种基于多粒度时间卷积网络(MGTCN)的超短期风功率预测方法,使用时间卷积网络来挖掘多粒度视角下的风力机数据特征,并设计多粒度特征融合模块来增强模型的鲁棒性,提高风功率预测精度。首先,利用随机森林算法(RF)得到与输出功率相关性较强的部分特征数据;然后,对筛选后的特征数据进行多粒度划分,通过时间卷积网络(TCN)提取各个粒度的独立特征。最后,使用挤压激励网络(SENet)对不同粒度特征进行自适应加权融合,得到最终预测值。采用中国某风场数据进行算例分析,结果表明相较于其他方法,所提方法在24步预测任务和6步预测任务上取得了最佳的预测性能,具有较高的准确性和稳定性。在24步预测任务上归一化均方根误差、归一化平均绝对值误差和决定系数指标分别为0.152、0.108和0.7214,在6步预测任务上各指标分别为0.1027,0.0683和0.8717。

外部随机激励干扰下掘进机振动信号多传感采集方法

掘进机运行过程中,在外部随机激励源的作用下,造成多传感器模式下的传感敏感性波动,结合振动信号不稳定,会导致采集的振动信号大幅度失真。为保证掘进机的稳定运行,提出多传感器模式下的随机激励振动信号采集方法。将掘进机看作多自由度系统,建立设备动力学模型;结合掘进机动力学特征,利用虚拟激励法构建符合外部源的随机激励函数;在建立的随机激励下,选择传感器类型和参数并安装多个传感器,设定采样频率;根据正弦稳态校准方法需求,设计校准传感器采集系统,提高传感器敏感性;在随机激励函数约束下预测传感器输出延时,计算每次测量的同步误差和误差补偿值,通过补偿确保多传感器实现振动信号的同步动态采集。实验结果表明:在多传感模式下,这种方法降低了外部的随机迟滞干扰,在随机激励作用下采集到的掘进机多传感振动信号波形与实际波形相符。

随机激励下斜拉索-梁参数振动模型及响应分析

为了揭示随机激励下斜拉索参数振动特性,考虑拉索几何非线性、倾角以及桥面梁的协同振动影响,建立了斜拉索-桥面梁耦合参数振动模型,利用相空间变换推导了索-梁结构耦合振动伊藤状态方程组,给出了高斯白噪声作用下索梁振动时程求解迭代格式,分析了拉索随机响应时程、频域、统计特性以及概率密度变化,并与高斯截断方法进行比较,考察了拉索阻尼比、初始张力、桥面梁的初始扰动以及随机激励强度对拉索振动的影响规律。结果表明:斜拉索振动迭代方法可有效求解随机激励下索-梁耦合参数振动时程,与传统的高斯截断方法的计算结果吻合;随机激励下,斜拉索“拍振”振幅具有明显的不确定性,斜拉索与桥面梁结构发生耦合振动时,两者之间存在能量传递现象;斜拉索随机激励位移响应均值具有非平稳瞬态特性,其位移均方差的稳定时间大于理想激励下的响应;斜拉索响应功率峰值对应的频率和功率谱密度旁瓣峰值衰减量基本一致,但斜拉索第一旁瓣峰值与主峰差值并不相同。斜拉索振动响应概率密度分布满足高斯分布形态,置信区间约为0.98,符合马尔科夫性质。随着阻尼比增大,拉索阻尼抑制效率降低;桥面梁初始扰动越大,拉索振动位移越大;拉索张力越大,拉索振动幅值呈非线性减小趋势,但张力进一步增大时,拉索振动幅值衰减趋于稳定;随机激励强度越大,拉索响应越大。