快速独立分量分析法识别结构模态参数研究

采用快速独立分量分析(FastICA)算法,快速、准确地识别结构模态参数.该算法以模态响应之间的独立性为依据构建出目标函数,并以此目标函数为基准采用ICA算法对结构输出信号进行分离,而得到结构振型向量.进而通过单模态识别技术-希尔伯特(Hilbert)变换,识别出结构的频率和阻尼比.最后通过白噪声激励下六层框架结构的模态参数识别,验证了快速独立分量分析算法识别结构模态参数的可行性和鲁棒性.     

Model updating of multistory shear buildings for simultaneous identification of mass,stiffness and damping matrices using two different soft-computing methods

In this research, two novel methods for simultaneous identification of mass–damping–stiffness of shear buildings are proposed. The first method presents a procedure to estimate the natural frequencies, modal damping ratios, and modal shapes of shear buildings from their forced vibration responses. To estimate the coefficient matrices of a state-space model, an auto-regressive exogenous excitation (ARX) model cooperating with a neural network concept is employed. The modal parameters of the structure are then evaluated from the eigenparameters of the coefficient matrix of the model. Finally, modal parameters are used to identify the physical/structural (i.e., mass, damping, and stiffness) matrices of the structure. In the second method, a direct strategy of physical/structural identification is developed from the dynamic responses of the structure without any eigenvalue analysis or optimization processes that are usually necessary in inverse problems. This method modifies the governing equations of motion based on relative responses of consecutive stories such that the new set of equations can be implemented in a cluster of artificial neural networks. The number of neural networks is equal to the number of degree-of-freedom of the structure. It is shown the noise effects may partially be eliminated by using high-order finite impulse response (FIR) filters in both methods. Finally, the feasibility and accuracy of the presented model updating methods are examined through numerical studies on multistory shear buildings using the simulated records with various noise levels. The excellent agreement of the obtained results with those of the finite element models shows the feasibility of the proposed methods.     

A comparative study on the identification of the dynamical model of multi-mass electrical drives using wavelet transforms

This paper deals with dynamical modelling and modal identification of a special class of electromechanical systems: the multi-mass electrical drives. The aim of the work is to investigate the usefulness and the performance of the continuous wavelet transform (CWT) for the estimation of modal parameters, such as damping ratios and natural frequencies of these electromechanical systems. For this investigation, two models of elastic drive systems are considered: the two-mass and the three-mass models. The modal analysis identification using CWT is compared to the Hilbert–Huang transform technique and evaluated in terms of accuracy and ability to estimate modal parameters with different inputs, aptitude to distinguish several modes especially in the case of closely spaced modes and resistance to noisy conditions. In view of the results of the study, the advantages and shortcomings of each technique are presented and discussed.     

A top-down approach to calibration, validation, uncertainty quantification and predictive accuracy assessment

This paper describes a “top-down” uncertainty quantification (UQ) approach for calibration, validation and predictive accuracy assessment of the SNL Validation Workshop Structural Dynamics Challenge Problem. The top-down UQ approach differs from the more conventional (“bottom-up”) approach in that correlated statistical analysis is performed directly with the modal characteristics (frequencies, mode shapes and damping ratios) rather than using the modal characteristics to derive the statistics of physical model parameters (springs, masses and viscous damping elements in the present application). In this application, a stochastic subsystem model is coupled with a deterministic subsystem model to analyze stochastic system response to stochastic forcing functions. The weak nonlinearity of the stochastic subsystem was characterized by testing it at three different input levels, low, medium and high. The calibrated subsystem models were validated with additional test data using published NASA and Air Force validation criteria. The validated subsystem models were first installed in the accreditation test bed where system response simulations involving stochastic shock-type force inputs were conducted. The validated stochastic subsystem model was then installed in the target application and simulations involving limited duration segments of stationary random vibration excitation were conducted.     

Nonlinear dynamics by mode superposition

A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram—Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly.The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matrix half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.     

System identification of torsionally coupled buildings

In this study, an extended random decrement method, which considers the correlation among measurements, was employed to reduce the measured dynamic responses of general torsionally coupled multi-story building under random excitations. The Ibrahim time domain technique was then applied to calculate the modal frequencies and damping ratios based on only a few floor response measurements. To obtain the complete mode shapes, an interpolation method was developed to estimate the mode shape values for the locations without measurements. The seismic responses at floors with and without measurements were also calculated. Numerical results through a seven-story torsionally coupled building under ambient random excitations demonstrated that the proposed method is able to identify structural dominant modal parameters accurately even with highly coupled modes and noise contamination. A small number of response measurements, no requirement for input excitation measurements and simple on-line calculations make the proposed method favorable for implementation.     

Duffing系统中Lévy噪声诱导的随机共振与相转移

研究了Lévy噪声激励下Duffing系统的随机共振与相转移问题.分析了噪声强度、阻尼系数及稳定性指标对系统随机共振的影响,结果表明减小阻尼系数有利于观测系统的随机共振现象,而稳定性指标的减小削弱了随机共振的发生.模拟了系统的稳态概率密度函数,通过调节噪声参数来观察稳态概率密度峰数的变化,进而讨论了系统的相转移现象,发现Lévy噪声的噪声强度、稳定性指标及偏斜参数均能诱导系统发生相转移,而高斯噪声激励下,噪声强度不能诱导系统发生相转移,从而反映了高斯噪声与Lévy噪声对系统的不同作用机理.     

A cohesive modeling technique for theoretical and experimental estimation of damping in serial robots with rigid and flexible links

Dynamic model incorporating damping characteristics, namely joint damping and structural damping in flexible links, of the serial robots with rigid and flexible links is presented. A novel procedure, based on the unified approach of theoretical formulation and analysis of experimental data, is proposed for the estimation of damping coefficients. First, the dynamic model of a robotic system with rigid and flexible links is presented. Next, the modifications in the dynamic model due to the considerations of damping characteristics of joints and structural damping characteristics of the flexible links are presented. A systematic methodology based on analysis of data obtained from experiments is presented for estimation and determination of damping coefficients of rigid-flexible links. The determination of joint damping coefficients, is based on the logarithmic decay of the amplitude of the oscillations of robotic links, while the structural damping coefficients are estimated mainly using the modal analysis and the method of evolving spectra. The method of evolving spectra, based on the Fast Fourier Transform of the decay of the amplitude in structural vibrations of the robot links in progressive windows is used to estimate the structural damping ratios while the critical structural coefficients are determined using the modal analysis. The methodology is illustrated through a series of simple experiments on simple robotic systems. The experimental results are then compared with the simulation results incorporating the damping coefficients determined using the proposed procedure. The comparisons leads to the validation of the proposed dynamic modeling technique, modeling of the damping characteristics, and the method proposed for estimation of damping coefficients for rigid-flexible link robotic systems.     

Inverse method based on modal analysis for characterizing the constitutive properties of thick composite plates

This paper presents a powerful method for evaluating the constitutive properties of composite laminates through a mixed numerical–experimental identification procedure based on both the extracted mode shapes and the corresponding natural frequencies of the structure. The modal quantities are measured with a precise contact-free experimental technique and extracted numerically with an accurate shell element derived from the higher order shear deformation theory. The elastic properties are estimated with a nonlinear least squares algorithm applied to modal identification criteria. With this novel approach of combining frequency and mode based error norms, the proposed identification method allows an accurate identification of both in-plane and transverse elastic properties with a single non-destructive test. The effectiveness of the procedure is highlighted by test cases on moderately thick to thick plates.     

蒙特卡罗仿真机及其应用

蒙特卡罗仿真机是通过对随机性问题采用Monte Carlo方法进行计算机仿真，从而得出待解问题的解。为了研究复杂的随机问题，文中提出了基于蒙特卡罗的随机模拟法的蒙特卡罗仿真机，并说明了它的基本原理。通过圆周率的计算，实践了蒙特卡罗仿真机的应用过程，从而显示出蒙特卡罗仿真法处理随机性问题的优越性和仿真普遍的适用性。     

Parameter identification of linear structural dynamic systems

The parameter estimations of linear multi-degree-of-freedom structural dynamic systems are carried out in time domain. Methods for estimating the system parameters and the modal parameters are presented. The equation of motion is transformed into the state space equation of the observable canonical form, and then into the auto-regressive and moving average model with auxiliary stochastic input (ARMAX) model to process the measurement data contaminated by the system noise as well as the output noise. The parameters of the ARMAX model are estimated by using the sequential prediction error method. Then, the parameters of equation of motion are recovered thereafter. In order to verify the accuracy of the estimation method, analytical simulation studies are performed for a model with two degrees of freedom on the basis of simulated data under various noise conditions. It is shown that the presented methods yield good estimates even under large noise conditions. The method is also applied to the identification of the modal parameters of a building model based on the experimental data.     

Particle filtering-based fault detection in non-linear stochastic systems

Much of the development in model-based fault detection techniques for dynamic stochastic systems has relied on the system model being linear and the noise and disturbances being Gaussian. Linearized approximations have been used in the non-linear systems case. However, linearization techniques, being approximate, tend to suffer from poor detection or high false alarm rates. A novel particle filtering based approach to fault detection in non-linear stochastic systems is developed here. One of the appealing advantages of the new approach is that the complete probability distribution information of the state estimates from particle filter is utilized for fault detection, whereas, only the mean and covariance of an approximate Gaussian distribution are used in a coventional extended Kalman filter-based approach. Another advantage of the new approach is its applicability to general non-linear system with non-Gaussian noise and disturbances. The effectiveness of this new method is demonstrated through Monte Carlo simulations and the detection performance is compared with that using the extended Kalman filter on a non-linear system.     

Peak response of non-linear oscillators under stationary white noise

The use of the advanced censored closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the stochastic averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo simulation and by other approximate formulations available in the literature.     

Modelling and identification of offshore towers with general damping

The modelling problem of offshore towers is considered. A model is proposed which includes viscous and hydrodynamic drag damping and takes into account the stochastic nature of the problem. The model is decoupled into a set of modal equations by using the complex mode theory. A technique is developed to identify the modal parameters and the complex mode shapes by using the noisy excitation and response measurements. This technique is computationally efficient and accurate in the sense of minimizing a criterion function of the estimates variance. A simulation example is presented to demonstrate the results.     

A bias-eliminated least-squares method for continuous-time model identification of closed-loop systems

Schemes for system identification based on closed-loop experiments have attracted considerable interest lately. However, most of the existing approaches have been developed for discrete-time models. In this paper, the problem of continuoustime model identification is considered. A bias correction method without noise modelling associated with the Poisson moment functionals approach is presented for indirect identification of closed-loop systems. To illustrate the performances of the proposed method, the bias-eliminated least-squares algorithm is applied to the parameter estimation of a simulated system via Monte Carlo simulations.     

Expressive Facial Gestures From Motion Capture Data

Human facial gestures often exhibit such natural stochastic variations as how often the eyes blink, how often the eyebrows and the nose twitch, and how the head moves while speaking. The stochastic movements of facial features are key ingredients for generating convincing facial expressions. Although such small variations have been simulated using noise functions in many graphics applications, modulating noise functions to match natural variations induced from the affective states and the personality of characters is difficult and not intuitive. We present a technique for generating subtle expressive facial gestures (facial expressions and head motion) semi‐automatically from motion capture data. Our approach is based on Markov random fields that are simulated in two levels. In the lower level, the coordinated movements of facial features are captured, parameterized, and transferred to synthetic faces using basis shapes. The upper level represents independent stochastic behavior of facial features. The experimental results show that our system generates expressive facial gestures synchronized with input speech.     

Finite element modal analysis of a rotating disk–spindle system in a HDD with hydrodynamic bearings considering the flexibility of a complicated supporting structure

This paper presents a method to analyze the free vibration of a rotating disk–spindle system in a HDD with hydrodynamic bearings (HDBs) considering the flexibility of a complicated base structure by using finite element method. Finite element equations of each component of a HDD spindle system from the spinning flexible disk to the flexible base plate are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between the sleeve and hydrodynamic bearings to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. The validity of the proposed method is verified by comparing the calculated damped natural frequencies and modes with the experimental results. This research also shows that the supporting structure which includes the stator, housing and base plate plays an important role in determining the natural frequencies and mode shapes of a HDD spindle system     

Identification of step response estimates utilizing continuous time subspace approach

Direct identification procedures using raw data seem to face difficulties especially when the data is corrupted with noise or the data acquisition leads to huge amount of data to be processed. This will lead to complexity in obtaining the accurate model of the system and the increase of computational load and time may also arise. In this paper, we present 2-stage identification, in which, the first stage involves a process to obtain step response estimates. A multi input multi output frequency sampling filter model is used to simulate the estimates. With the aid of finite impulse response model, maximum likelihood method and the predicted sum of square statistics, this procedure able to clean the noise that occurred at high frequency region, compressed the data into the reduced amount and obtained only meaningful parameter that describes the system. Next, at the second stage the continuous time subspace model identification is conducted using the step response estimates obtained from the first stage. Here, three continuous time subspace methods will be observed to develop a state space mathematical model; those are the MOESP, CCA and ORT methods. A Monte Carlo simulation is performed as to see the efficacy and robustness of those models in identifying the step response estimates of the observed system. Comparative analysis with respect to two-stage identification and direct identification procedure is also conducted. This is to show the significant contribution of having MIMO FSF in the overall identification procedure. From results, the developed MIMO FSF is able to compress raw MIMO data into fewer numbers, and produce cleaned and unbiased step response estimates. When it is implemented to MIMO continuous-time subspace identification, MOESP method has demonstrated good performance based on the accuracy and robustness of the developed model.     

Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method

In order to endow the expansion-based stochastic formulation with the capability of representing the characteristic behavior of stochastic systems, i.e., the non-linear dependence of the response variability on the coefficient of variation of the stochastic field, a Monte Carlo simulation-compatible stochastic field is suggested. Through a theoretical comparison of displacement vectors in the Monte Carlo method and an expansion-based scheme, it is found that the stochastic field adopted in the expansion-based scheme is not compatible with that appearing in the Monte Carlo simulation. The Monte Carlo simulation-compatible stochastic field is established by means of enforcing the compatibility between the stochastic fields in the expansion-based scheme and the Monte Carlo simulation. Employing the stochastic field suggested in this study, the response variability is reproduced with high precision even for uncertain fields with a moderately large coefficient of variation. Furthermore, the formulation proposed here can be used as an indirect Monte Carlo scheme by directly substituting the numerically simulated random fields into the covariance formula. This yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte Carlo technique.     

Updating response sensitivity models of nonlinear vibrating structures using particle filters

The problem of updating response gradients with respect to chosen system parameters based on spatially sparse measurements is considered. The measurement noise and imperfections in mathematical modeling are treated as Gaussian white noise processes. The system states are augmented by response gradients with respect to system parameters and an extended set of equations in the state space is formulated. These equations are cast in the form of Ito’s stochastic differential equations and measured data are assimilated into this model using Monte Carlo based Bayesian filtering tools. Illustrative examples include a few low dimensional dynamical systems with cubic and hereditary nonlinearities.