Stochastic Simulation Techniques and Structural Reliability
Budget: €8 – €30 EUR
• Implement now your own random field generator, i.e., by choosing one of the
methods:
– Moving Average Method (1D),
– Turning bands (2D),
Please compute the probability of failure and the reliability index β of the following limit
state functions:
• g1(X1, X2) = 5X1 + X2 with X1 ∼ N(12, 5), X2 ∼ N(10, 9).
• g2(X1, X2) = 3X1 − X2
2 with X1 ∼ N(10, 3), X2 ∼ E(1).
• g2(X1, X2) = X4
1 + X3
2 with X1 ∼ N(0, 1), X2 ∼ N(2, 1).
Select an appropriate method from the lecture notes (not MCS!) for each limit state
function. Explain your choice. Verify the results using Monte Carlo Simulation. Include
useful figures or calculations explaining the procedure, and include figures of the Monte
Carlo Simulations in your report
methods:
– Moving Average Method (1D),
– Turning bands (2D),
Please compute the probability of failure and the reliability index β of the following limit
state functions:
• g1(X1, X2) = 5X1 + X2 with X1 ∼ N(12, 5), X2 ∼ N(10, 9).
• g2(X1, X2) = 3X1 − X2
2 with X1 ∼ N(10, 3), X2 ∼ E(1).
• g2(X1, X2) = X4
1 + X3
2 with X1 ∼ N(0, 1), X2 ∼ N(2, 1).
Select an appropriate method from the lecture notes (not MCS!) for each limit state
function. Explain your choice. Verify the results using Monte Carlo Simulation. Include
useful figures or calculations explaining the procedure, and include figures of the Monte
Carlo Simulations in your report