Calculation OF Reliability Index PDF

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Calculation OF Reliability Index...

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Brief Notes #9 CALCULATION OF RELIABILITY INDEX, β X ~ (m, Σ)

Z ~ (0, I)

1. Select initial unit vector, αo

1. Select initial unit vector, αo

2. Find z *o = βo α o where β o = min{β : βα o ∈ D F }

2. Find x *o = m + δα o ∈ Β and calculate

3. Linearize Β around z*o Let γ o be the unit external vector:

γo =

grad g( z) grad g( z)

*

zo

⎡ ∂g( z) ⎤ ⎢ ⎥ ∝ ⎢ ∂z i ⎥ ⎥ ⎢ # z *o ⎦⎥ ⎣⎢

4. Go back to step 2 with α o replaced with α 1 = γ . o Iterate until convergence in β and z* .

β o as:

(

β o = δ α To Σ −1 α o

)

1 2

3. Linearize Β at x*o . (Calculate γ as in o z space). 4. The next search direction α1 is that of the β point according to the linearized boundary. From analytical geometry, α1 ∝ Σ γ o . 5. Go back to Step 2 until convergence....