chapter 14 monte carlo simulation
DESCRIPTION
Chapter 14 Monte Carlo Simulation. 14.1 Introduction. Find several parameters Parameter follow the specific probability distribution Generate parameter following the probability distribution. 14.2 Generation of random number. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 14 Monte Carlo Simulation
14.1 Introduction
• Find several parameters
• Parameter follow the specific probability distribution
• Generate parameter following the probability distribution
14.2 Generation of random number
14.3 generation of random numbers following standard uniform
distribution
• The pseudo random number following standard uniform distribution:
mind by the limitation of computer used.
14.2.2 Random variables with nonuniform distribution
• Distribution function:
)(1 uFx x
Niux ii ..,,.........2,1;ln
14.2.3 Generation of discrete random variable
• X can take n+1 distinct values with mass function pX(xi), the cumulative distribution function is given by:
The discrete random number Xi and Xi+1 can be determined by:
i
jjXiX xpxF
0
)()(
14.3 Generation of jointly distributed random variable
14.3.1 independent variable
Density and distribution function
14.3.3 generation of correlated normal random variables
Vector of mean value
Covariance matrix
Express Xi as:
The mean values and standard deviation:
The mean values of Wj can be determined as
XaW 1
Example 14.9 the torque transmitted by a plate clutch with a single pair of friction surfaces, shown in Fig. 14.6, can be expressed as:
pressureuniformfordD
dDFfT
and
wearuniformfordDFf
T
)(4
)(4
22
33
14.4 computation of reliability
14.4.1 Sampling size and error in simulation
14.4.2 Example: reliability analysis of a straight line mechanism