non-Gaussian Random Excitation Research Articles

Response analysis of nonlinear multi-degree-of-freedom systems with uncertain properties to non-Gaussian random excitations

The investigation reported in this paper is concerned with the development of an approach for response analysis of multi-degree-of-freedom (mdof) nonlinear systems with uncertain properties of large variations and under non-Gaussian nonstationary random excitations. The developed approach makes use of the stochastic central difference (SCD) method, time co-ordinate transformation (TCT), and adaptive time schemes (ATS). It is applicable to geometrically complicated systems idealized by the finite element method (FEM). For demonstration of its use and availability of results for direct comparison, a two-degree-of-freedom (tdof) nonlinear asymmetric system with uncertain natural frequencies and under Gaussian and non-Gaussian nonstationary random excitations is considered. Computed results obtained for the system with and without uncertain natural frequencies, and under Gaussian and non-Gaussian nonstationary random excitations are presented. It is concluded that the approach is relatively simple, accurate and efficient to apply.

Response Distribution of a Nonlinear System Subjected to Non-Gaussian Random Excitation with Correlation Time

Response distribution of a nonlinear system subjected to non-Gaussian excitation is investigated. The excitation is represented by its probability density and the auto-correlation function whose characteristic is governed by the correlation time. Both bimodal and Laplace distributions are considered as the non-Gaussianity of the excitation. In order to examine the influence of the non-Gaussianity and the length of correlation time of the excitation on the response, stationary response distributions of a Duffing system are simulated. It is shown that the response distribution is similar to the non-Gaussian distribution of the excitaiton when the correlation time is long.

421 相関特性を考慮した非ガウス性不規則入力を受ける非線形系の応答分布

421 相関特性を考慮した非ガウス性不規則入力を受ける非線形系の応答分布

Generation of Non-Gaussian Random Vibration Excitation Signal for Reliability Enhancement Test

AbstractDuring environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. To simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density (PSD), skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal.

Response of Systems Under Non-Gaussian Random Excitations

The approach of nonlinear filter is applied to model non-Gaussian stochastic processes defined in an infinite space, a semi-infinite space or a bounded space with one-peak or multiple peaks in their spectral densities. Exact statistical moments of any order are obtained for responses of linear systems jected to such non-Gaussian excitations. For nonlinear systems, an improved linearization procedure is proposed by using the exact statistical moments obtained for the responses of the equivalent linear systems, thus, avoiding the Gaussian assumption used in the conventional linearization. Numerical examples show that the proposed procedure has much higher accuracy than the conventional linearization in cases of strong system nonlinearity and/or high excitation non-Gaussianity.

Numerical and experimental studies of linear systems subjected to non-Gaussian random excitations

This paper presents a numerical simulation scheme for generating symmetric non-Gaussian random processes governed by prescribed kurtosis and spectral density. The generated process is represented as a continuous stationary random signal with occasional spikes superimposed on a Gaussian random background. The generated time history data records are used to simulate random excitations acting on linear single-degree-of-freedom systems. The results of the numerical simulation are compared with those measured experimentally. For a wide-band random excitation with kurtosis close to 3, the response kurtosis is found to be very sensitive to small changes in the excitation kurtosis. This is manifested by the appearance of significant spikes in the time history records when the excitation records do not display any significant spikes. The influence of the system damping is also examined for narrow-band and wide-band random excitations, and some differences are reported in the results.

Random response of catenary moored offshore vessels to non-linear wave forces

This paper investigates the response statistics of non-linearly moored vessels to non-linear wave forces. More specifically, the response of a catenary moored vessel to stationary non-Gaussian random excitation is considered in which the equation of motion is of the Duffing type. The approach adopted is based on the assumption that the response may be expressed as a second-order Volterra/Wiener series, that is, including linear and quadratic terms. This allows the response probability density function (pdf) (and mean up-crossing rate) to be calculated using previously developed techniques. The technique used to accomplish this is the Wiener-Hermite functional (WHF) approach. Given that this technique yields coupled integro-differential equations governing the Wiener response kernels which are difficult to solve, an approximate solution procedure is used which is based upon a single-term Galerkin procedure. The relationship of this method to the method of statistical quadratization is investigated, and it is shown that under certain conditions these techniques are mathematically identical. The accuracy of this technique to predict the response pdf is investigated by comparison with numerical simulation.

Application of higher order spectral analysis to cubically nonlinear system identification

In this study, digital higher-order spectral analysis and frequency-domain Volterra system models are utilized to yield a practical methodology for the identification of weakly nonlinear time-invariant systems up to third order. The primary focus is on consideration of random excitation of nonlinear systems and, thus, the approach makes extensive use of higher-order spectral analysis to determine the frequency-domain Volterra kernels, which correspond to linear, quadratic, and cubic transfer functions. Although the Volterra model is nonlinear in terms of its input, it is linear in terms of its unknown transfer functions. Thus, a least squares approach is used to determine the optimal (in a least squares sense) set of linear, quadratic, and cubic transfer functions. Of particular practical note, is the fact that the approach of this paper is valid for non-Gaussian, as well as Gaussian, random excitation. It may also be utilized for multitone inputs. The complexity of the problem addressed in this paper arises from two principal causes: (1) the necessity to work in a 3D frequency space to describe cubically nonlinear systems, and (2) the necessity to characterize the non-Gaussian random excitation by computing higher-order spectral moments up to sixth order. A detailed description of the approach used to determine the nonlinear transfer functions, including considerations necessary for digital implementation, is presented. >

A new model for non-Gaussian random excitations

Very often one is called upon to model time series data which are clearly non-Gaussian, but which retain some aspects of a Gaussian process. In the present paper, a novel methodology which helps in modelling such data is presented. The method is essentially to express the process as a series with finite number of terms, wherein the first term is a Gaussian process with zero mean and unit standard deviation. Non-Gaussian higher order correction terms are added to this such that each succeeding term is orthogonal or uncorrelated with all the previous terms. The unknown coefficients in the series representation can be expressed in terms of the estimated moments of the data. Further the autocorrelation or PSD of the data can be exactly reproduced by the non-Gaussian model. The use of the proposed model is illustrated by considering the unevenness data of railway tracks. Application to response of systems under non-Gaussian excitation is also briefly discussed.

Dynamic response of hysteretic systems to Poisson-distributed pulse trains

A single-degree-of-freedom hysteretic system subjected to a specific non-Gaussian random excitation in the form of a Poisson-distributed train of random pulses is considered. The hysteretic behaviour is described by the Bouc-Wen model of smooth hysteresis. The total hysteretic energy dissipation is assumed as a cumulative damage indicator. The state variables of the system together with the damage indicator form in that case a Poisson-driven, non-diffusive Markov vector process. Two equivalent systems are introduced by substituting the original non-analytical, non-algebraic non-linearities by equivalent linear and cubic forms in the pertinent state variables. Equations for mean responses are obtained by direct averaging of the governing equations, whereas the equations for second- and higher-order joint central moments are derived from the equivalent systems with the help of a generalized Ito's differential rule. Appearing in the equations for mean responses and for equivalent coefficients, expectations of non-algebraic functions of state variables are performed with respect to a non-Gaussian joint probability density function assumed in the form of a generalized, bivariate Gram-Charlier expansion. In the case of equivalent cubic non-linearities, the equations for moments form an infinite hierarchy which is truncated with the help of a cumulant-neglect closure technique. Mean values and variances of the response variables are evaluated by the numerical integration of equations for moments for two equivalent systems. For the sake of comparison the excitation process is also substituted by a Gaussian white noise and the usual equivalent linearization technique, combined with the Gaussian closure, is applied. The cases of non-zero-mean as well as zero-mean excitation processes are included. The case of general pulses is dealt with by a suitable augmentation of the state vector. The accuracy of the analytical techniques developed is verified against Monte Carlo simulations.

Approximate first-passage and extremes of narrow-band Gaussian and non-Gaussian random vibrations

An approximate method for estimating the probability distribution of first-passage times and extreme values of stationary narrow-band random vibrations is presented. The advantage of the method is that explicit, closed from expressions are obtained. The method is applied to the response process of a simple linear oscillator driven by both Gaussian and non-Gaussian random excitations and, by comparison with published simulation results, good agreement is obtained. For the Duffing oscillator, the results of Markov diffusion models are compared with the present method, and the agreement is fairly good.

Response of the Duffing Oscillator to a Non-Gaussian Random Excitation

Response of the Duffing Oscillator to a Non-Gaussian Random Excitation

Modeling of the nonlinear drift oscillations of moored vessels subject to non-Gaussian random sea-wave excitation

A quadratic system model based on Volterra series representation is utilized to model the nonlinear response of moored vessels subjected to random seas. The key idea is to represent the relationship between the incident sea wave (input) and corresponding sway response of the moored vessel (output) with a parallel combination of linear and quadratic transfer functions, and to estimate them by processing actual input and output data. Compared to previous approaches, we take the important step of removing the restriction that the random input must possess Gaussian statistics. The feasibility and validity of the approach is demonstrated by analyzing experimental data taken in model basin tests. We also describe some of the deleterious consequences of assuming Gaussian sea-wave excitation when in fact the excitation is non-Gaussian.

Linear systems and normality

This paper is concerned with responses of linear systems to non-Gaussian random excitation and with the measurement of the departure of the responses from Gaussian behavior. First, we show the classical Rosenblatt result and its nonapplicability to the most popular practical systems described by differential equations of first and second order. Then, using a simple measure of departure from normality (the asymmetry and excess coefficients) and performing numerical calculations, we give quantitative information about the effect of system parameters and the radius of correlation of the excitation process on the distance from normality.