scholarly journals Random vibration analysis for coupled vehicle-track systems with uncertain parameters

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Pan Xiang ◽  
Yan Zhao ◽  
Jiahao Lin ◽  
D Kennedy ◽  
Fred W Williams
Keyword(s):  
Vibration Analysis ◽  
Random Vibration ◽  
Design Methodology ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Pseudo Excitation ◽  
Random Vibration Analysis ◽  
Excitation Method

Purpose The purpose of this paper is to present a new random vibration-based assessment method for coupled vehicle-track systems with uncertain parameters when subjected to random track irregularity. Design/methodology/approach The uncertain parameters of vehicle are described as bounded random variables. The track is regarded as an infinite periodic structure, and the dynamic equations of the coupled vehicle-track system, under mixed physical coordinates and symplectic dual coordinates, are established through wheel-rail coupling relationships. The random track irregularities at the wheel-rail contact points are converted to a series of deterministic harmonic excitations with phase lag by using the pseudo excitation method. Based on the polynomial chaos expansion of the pseudo response, a chaos expanded pseudo equation is derived, leading to the combined hybrid pseudo excitation method - polynomial chaos expansion method Findings The impact of uncertainty propagation on the random vibration analysis is assessed efficiently. According to GB5599-85, the reliability analysis for the stability index is implemented, which can grade the comfort level by the probability. Comparing to the deterministic analysis, it turns out that neglect of the parameter uncertainty will lead to potentially risky analysis results. Originality/value The proposed method is compared with Monte Carlo simulations, achieving good agreement. It is an effective means for random vibration analysis of uncertain coupled vehicle-track systems and has good engineering practicality

STOCHASTIC STRUCTURAL MODAL ANALYSIS INVOLVING UNCERTAIN PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION

2011 ◽  
Vol 03 (03) ◽  
pp. 587-606 ◽  
Author(s):  
K. SEPAHVAND ◽  
S. MARBURG ◽  
H.-J. HARDTKE
Keyword(s):  
Modal Analysis ◽  
Polynomial Chaos ◽  
Continuous Model ◽  
Polynomial Chaos Expansion ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Parameter Uncertainties ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
Key Issues

In this paper, the application of generalized polynomial chaos expansion in stochastic structural modal analysis including uncertain parameters is investigated. We review the theory of polynomial chaos and relating error analysis. A general formulation for the representation of modal problems by the polynomial chaos expansion is derived. It shows how the modal frequencies and modal shapes are influenced by the parameter uncertainties. The key issues that arise in the polynomial chaos simulation of modal analysis are discussed for two examples: a discrete 2-DOF system and continuous model of a microsensor. In both cases, the polynomial chaos expansion is used for the approximation of uncertain parameters, eigenfrequencies and eigenvectors. We emphasize the accuracy and time efficiency of the method in estimation of the stochastic modal responses in comparison with the sampling techniques, such as the Monte Carlo simulation.

UNCERTAINTY QUANTIFICATION IN STOCHASTIC SYSTEMS USING POLYNOMIAL CHAOS EXPANSION

2010 ◽  
Vol 02 (02) ◽  
pp. 305-353 ◽  
Author(s):  
K. SEPAHVAND ◽  
S. MARBURG ◽  
H.-J. HARDTKE
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Uncertainty Quantification ◽  
Stochastic Systems ◽  
Polynomial Chaos ◽  
Random Variables ◽  
Polynomial Chaos Expansion ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Generalized Polynomial

In recent years, extensive research has been reported about a method which is called the generalized polynomial chaos expansion. In contrast to the sampling methods, e.g., Monte Carlo simulations, polynomial chaos expansion is a nonsampling method which represents the uncertain quantities as an expansion including the decomposition of deterministic coefficients and random orthogonal bases. The generalized polynomial chaos expansion uses more orthogonal polynomials as the expansion bases in various random spaces which are not necessarily Gaussian. A general review of uncertainty quantification methods, the theory, the construction method, and various convergence criteria of the polynomial chaos expansion are presented. We apply it to identify the uncertain parameters with predefined probability density functions. The new concepts of optimal and nonoptimal expansions are defined and it demonstrated how we can develop these expansions for random variables belonging to the various random spaces. The calculation of the polynomial coefficients for uncertain parameters by using various procedures, e.g., Galerkin projection, collocation method, and moment method is presented. A comprehensive error and accuracy analysis of the polynomial chaos method is discussed for various random variables and random processes and results are compared with the exact solution or/and Monte Carlo simulations. The method is employed for the basic stochastic differential equation and, as practical application, to solve the stochastic modal analysis of the microsensor quartz fork. We emphasize the accuracy in results and time efficiency of this nonsampling procedure for uncertainty quantification of stochastic systems in comparison with sampling techniques, e.g., Monte Carlo simulation.

scholarly journals Discrete singular convolution–polynomial chaos expansion method for free vibration analysis of non-uniform uncertain beams

2021 ◽  
pp. 107754632098819
Author(s):  
Abdullah Seçgin ◽  
Murat Kara ◽  
Neil Ferguson
Keyword(s):  
Free Vibration ◽  
Young’S Modulus ◽  
Vibration Analysis ◽  
Polynomial Chaos ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Discrete Singular Convolution ◽  
Convolution Method

This article enhances the discrete singular convolution method for free vibration analysis of non-uniform thin beams with variability in their geometrical and material properties such as thickness, specific volume (inverse of density) and Young’s modulus. The discrete singular convolution method solves the differential equation of motion of a structure with a high accuracy using a small number of discretisation points. The method uses polynomial chaos expansion to express these variabilities simulating uncertainty in a closed form. Non-uniformity is locally provided by changing the cross section and Young’s modulus of the beam along its length. In this context, firstly natural frequencies of deterministic uniform and non-uniform beams are predicted via the discrete singular convolution. These results are compared with finite element calculations and analytical solutions (if available) for the purpose of verification. Next, the uncertainty of the beam because of geometrical and material variabilities is modelled in a global manner by polynomial chaos expansion to predict probability distribution functions of the natural frequencies. Monte Carlo simulations are then performed for validation purpose. Results show that the proposed algorithm of the discrete singular convolution with polynomial chaos expansion is very accurate and also efficient, regarding computation cost, in handling non-uniform beams having material and geometrical variabilities. Therefore, it promises that it can be reliably applied to more complex structures having uncertain parameters.

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