Wyniki wyszukiwania - BazTech

1

Stochastic finite element analysis using polynomial chaos

Drakos S., Pande G. N.

Studia Geotechnica et Mechanica

|

2016

|

Vol. 38, nr 1

33-43

EN

This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.

2

Influence of uncertainty in aerodynamic performance on the dynamic response of a two stage gear system

Tounsi M., Beyaoui M., Abboudi K., Feki N., Walha L., Haddar M.

Journal of Theoretical and Applied Mechanics

|

2016

|

Vol. 54 nr 2

601--612

EN

In this paper, the nonlinear dynamic response in a wind turbine system is considered and the quantification of uncertainty effects on the variability of this nonlinear response is investigated. Under dynamic conditions, a lumped model with 12 degrees of freedom is proposed taking into account the uncertainty associated to the power coefficient of the input aerodynamic torque. The dynamic response of the two-stage spur gear system is obtained using ODE45 solver of Matlab. The Polynomial Chaos (PC) method is used to introduce the uncertainties on the proposed model. A comparison between the two dynamic responses given by the proposed lumped dynamic model takes into account the uncertainty. It is performed on the existed model without uncertainty. Thus, the efficiency and robustness of the proposed new methodology is evaluated.

3

Application of the polynomial chaos approximation to a stochastic parametric vibrations problem

Brząkała A.

Archives of Civil and Mechanical Engineering

|

2013

|

Vol. 13, no. 2

220--228

EN

In the paper the application of the polynomial chaos expansion in case of parametric vibrations problem is presented. Hitherto this innovative approach has not been applied to such a stochastic problem. The phenomenon is described by a nonlinear ordinary differential equation with periodic coefficients. It can be observed among others in cable-stayed bridges due to periodic excitation caused by a deck or a pylon. The analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben–Ahin bridge). The characteristic of the viscous damper is considered as a log-normal random variable. The results obtained by the use of the polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation. The convergence of both methods is discussed. It is found that the polynomial chaos yields a better convergence then the Monte Carlo simulation, if resonant vibrations appear.

4

Real-time parameter estimation study for inertia properties of ground vehicles

Kolansky J., Sandu C.

Archive of Mechanical Engineering

|

2013

|

Vol. LX, nr 1

7--21

EN

Vehicle parameters have a significant impact on handling, stability, and rollover propensity. This study demonstrates two methods that estimate the inertia values of a ground vehicle in real-time. Through the use of the Generalized Polynomial Chaos (gPC) technique for propagating the uncertainties, the uncertain vehicle model outputs a probability density function for each of the variables. These probability density functions (PDFs) can be used to estimate the values of the parameters through several statistical methods. The method used here is the Maximum A-Posteriori (MAP) estimate. The MAP estimate maximizes the distribution of P(β ׀z) where β is the vector of the PDFs of the parameters and z is the measurable sensor comparison. An alternative method is the application of an adaptive filtering method. The Kalman Filter is an example of an adaptive filter. This method, when blended with the gPC theory is capable at each time step of updating the PDFs of the parameter distributions. These PDF’s have their median values shifted by the filter to approximate the actual values.

PL

Parametry pojazdu mają znaczny wpływ na jego właściwości, takie jak sterowalność, stabilność i odporność na wywrócenie. W pracy przedstawiono dwie metody estymacji parametrów inercyjnych pojazdu terenowego w czasie rzeczywistym. W modelu pojazdu z niepewnościami wyznacza się funkcje gęstości prawdopodobieństwa (PDF) dla każdej wielkości opisując propagację niepewności przez zastosowanie techniki uogólnionego chaosu wielomianowego (gPC). Funkcje te mogą być użyte do estymacji wartości parametrów przy wykorzystaniu różnych metod statystycznych. W pracy zastosowano metodę maksymalnego estymatora a posteriori (MAP). Estymator MAP maksymalizuje funkcję rozkładu P(β ׀z), gdzie β jest wektorem funkcji gęstości prawdopodobieństwa parametrów, a z jest wielkością mierzalną, otrzymaną z porównania wyjść czujników. Metodą alternatywną jest zastosowanie filtru adaptacyjnego, którego przykładem jest filtr Kalmana. Metoda ta, w połączeniu z techniką uogólnionego chaosu wielomianowego (gPC), umożliwia, w każdym kroku adaptacji, uaktualnianie funkcji gęstości prawdopodobieństwa (PDF) parametrów systemu. Działanie filtru powoduje, że mediany tych funkcji zmieniają się dążąc do rzeczywistych wartości poszukiwanych parametrów.

5

Logarithmic Sobolev inequalities and concentration of measure for convex functions and polynomial chaoses

Adamczak R.

Bulletin of the Polish Academy of Sciences. Mathematics

|

2005

|

Vol. 53, no 2

221-238

EN

We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in the spirit of Talagrand and Arcones-Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Łochowski, and present an application to exponential integrability of Rademacher chaos.