Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique

1978 ◽  
Vol 45 (2) ◽  
pp. 393-399 ◽  
Author(s):  
R. N. Iyengar ◽  
P. K. Dash
Keyword(s):  
Nonlinear Systems ◽  
Random Vibration ◽  
Joint Probability ◽  
Statistical Linearization ◽  
Closure Technique ◽  
Input Variables ◽  
Non Gaussian ◽  
Joint Probability Density ◽  
Gaussian Closure ◽  
Good Agreement

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Probabilistic Inverse Simulation and its Application in Vehicle Accident Reconstruction

2013 ◽  
Author(s):  
Xiaoyun Zhang ◽  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Traffic Accident ◽  
Joint Probability ◽  
Accident Reconstruction ◽  
Direct Simulation ◽  
Inverse Simulation ◽  
Vehicle Accident ◽  
Simulation Output ◽  
Simulation Input ◽  
Input Variables ◽  
Joint Probability Density

Inverse simulation is an inverse process of direct simulation. It determines unknown input variables of the direct simulation for a given set of simulation output variables. Uncertainties usually exist, making it difficult to solve inverse simulation problems. The objective of this research is to account for uncertainties in inverse simulation in order to produce high confidence in simulation results. The major approach is the use of the maximum likelihood methodology, which determines not only unknown deterministic input variables but also the realizations of random input variables. Both types of variables are solved on the condition that the joint probability density of all the random variables is maximum. The proposed methodology is applied to a traffic accident reconstruction problem where the simulation output (accident consequences) is known and the simulation input (velocities of the vehicle at the beginning of crash) is sought.

Methods and Gaussian Criterion for Statistical Linearization of Stochastic Parametrically and Externally Excited Nonlinear Systems

1989 ◽  
Vol 56 (1) ◽  
pp. 179-185 ◽  
Author(s):  
R. J. Chang ◽  
G. E. Young
Keyword(s):  
Nonlinear Systems ◽  
Goodness Of Fit ◽  
Duffing Oscillator ◽  
A Priori ◽  
Nonlinear Oscillators ◽  
Statistical Linearization ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Non Gaussian ◽  
Parametric And External Excitations

The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented. The techniques of Gaussian linearization are first derived and the accuracy in the prediction of the stationary output variances is illustrated. The justification of using Gaussian linearization a priori is further investigated by establishing a Gaussian Criterion. The non-Gaussian effects due to system nonlinearities and/or large noise intensities in a Duffing oscillator are also illustrated. The validity of employing the Gaussian Criterion test for assuring accuracy of Gaussian linearization is supported by performing the Chi-square Gaussian goodness-of-fit test.

A First-Passage Approximation in Random Vibration

1971 ◽  
Vol 38 (1) ◽  
pp. 143-147 ◽  
Author(s):  
Ronald L. Racicot ◽  
Fred Moses
Keyword(s):  
Random Vibration ◽  
Numerical Technique ◽  
Joint Probability ◽  
Poisson Processes ◽  
Joint Probability Distribution ◽  
First Passage ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Average Size ◽  
Good Agreement

A numerical technique is described for computing approximate first-passage probabilities for single-degree-of-freedom systems. It is applicable to cases where the joint probability distribution of response at two times can be found. From these distributions, the average size of a clump of consecutive failure crossings is computed. Results are compared to previously published simulation first-passage probabilities and good agreement is found. Examples illustrate applications to Gaussian and filtered Poisson processes.

A New Approach for Response Analysis of Nonlinear Systems Under Random Excitations

1991 ◽  
Author(s):  
Ismail I. Orabi ◽  
Goodarz Ahmadi
Keyword(s):  
Nonlinear Systems ◽  
Digital Simulation ◽  
Expansion Method ◽  
Kernel Functions ◽  
Equivalent Linearization ◽  
Response Analysis ◽  
Hermite Expansion ◽  
Closure Scheme ◽  
Non Gaussian ◽  
Gaussian Closure

Abstract A new technique for response analysis of nonlinear systems subjected to non-Gaussian excitations is presented. The technique is based on a Wiener-Hermite series expansion method. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite Kernel functions is described. The resulting response statistics are compared with those obtained from Gaussian closure scheme. A Monte Carlo digital simulation study is also performed. It is shown that the Gaussian closure technique and equivalent linearization method lead to identical results which are somewhat less accurate than those obtained by the non-Gaussian closure scheme. It is also shown that the Wiener-Hermite expansion method is well suited for response analysis of nonlinear systems under non-Gaussian excitations.

Prediction of near-wall turbulence using minimal flow unit

2018 ◽  
Vol 841 ◽  
pp. 654-673 ◽  
Author(s):  
Guang Yin ◽  
Wei-Xi Huang ◽  
Chun-Xiao Xu
Keyword(s):  
Joint Probability ◽  
Flow Unit ◽  
Wall Turbulence ◽  
Minimal Flow ◽  
Velocity Fluctuations ◽  
Wall Velocity ◽  
Near Wall Turbulence ◽  
Joint Probability Density ◽  
Good Agreement ◽  
Near Wall

In the present study, direct numerical simulation (DNS) is carried out in a minimal channel at $Re_{\unicode[STIX]{x1D70F}}=2000$ to sustain healthy turbulence below $y^{+}=100$. Turbulence intensities are compared with those of the motions at the same scales as the minimal channel in the full-sized channel at $Re_{\unicode[STIX]{x1D70F}}=2003$ (Hoyas & Jiménez, Phys. Fluids, vol. 20 (10), 2008, article 101511). They show good agreement in $y^{+}<100$. The universal signals for the three velocity components similar to that in the predictive model of Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196) are extracted from the DNS data of the full-sized channel. They correspond well to the near-wall velocity fluctuations in the minimal flow unit (MFU). The predictive models for the three components of near-wall velocity fluctuations are proposed based on the MFU data. The predicted turbulence intensities as well as the joint probability density functions of velocity fluctuations agree well with the DNS results of the full-sized channel turbulence.

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