Random Variables and Random Processes,

2016 ◽  
pp. 425-440
Keyword(s):  
Random Variables ◽  
Random Processes

Plate and line segment processes

1978 ◽  
Vol 15 (03) ◽  
pp. 494-501 ◽  
Author(s):  
N. A. Fava ◽  
L. A. Santaló
Keyword(s):  
Line Segment ◽  
Integral Geometry ◽  
Random Variables ◽  
Random Processes ◽  
Line Segments ◽  
Expected Values

Random processes of convex plates and line segments imbedded in R 3 are considered in this paper, and the expected values of certain random variables associated with such processes are computed under a mean stationarity assumption, by resorting to some general formulas of integral geometry.

Reliability Analysis and Random Vibration of Nonlinear Systems Using the Adjoint Method and Projected Differentiation

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Equations Of Motion ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Vibratory System ◽  
Standard Normal ◽  
Non Gaussian ◽  
Nonlinear Equations Of Motion ◽  
Adjoint Approach

Abstract This paper proposes a new methodology for time-dependent reliability and random vibrations of nonlinear vibratory systems using a combination of a time-dependent adjoint variable (AV) method and a projected differentiation (PD) method. The proposed approach is called AV-PD. The vibratory system is excited by stationary Gaussian or non-Gaussian input random processes. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. The nonlinear equations of motion (EOM) are linearized using a Taylor expansion using the first-order derivatives of the output with respect to the input KL random variables. An adjoint approach obtains the output derivatives accurately and efficiently requiring the solution of as many sets of EOM as the number of outputs of interest, independently of the number of KL random variables. The proposed PD method then computes the autocorrelation function of each output process at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). A time-dependent reliability analysis is finally performed using a KL expansion of the output processes and Monte Carlo simulation (MCS). The number of solutions of the EOM scales only with the number of output random processes which is commonly much smaller than the number of input KL random variables. The efficiency and accuracy of the proposed approach is demonstrated using a four degree-of-freedom (DOF) half-car vibratory problem.

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