Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Algorithm 1

A flowchart of the OQNLP MultiStart algorithm.

Stage 1

Call 𝐿(𝑥0,𝑥𝑓) (𝑥0 = user initial point)

Call UPDATE LOCALS(𝑥0,𝑥𝑓,𝑤)

For 𝑖=1∶𝑛1 Do

     Call SP(𝑥𝑡(𝑖))

     Evaluate 𝑃(𝑥𝑡(𝑖),𝑤)

EndDo

𝑥𝑡^∗ = point yielding best value of 𝑃(𝑥𝑡(𝑖),𝑤) over all stage one points (𝑖=1,2,…,𝑛1).

call 𝐿(𝑥𝑡^∗,𝑥𝑓)

Call UPDATE LOCALS(𝑥𝑡^∗,𝑥𝑓,𝑤)

threshold = 𝑃(𝑥𝑡^∗,𝑤)

Stage 2

For 𝑖=1∶𝑛2 Do

     Call SP(𝑥𝑡(𝑖))

     Evaluate 𝑃(𝑥𝑡(𝑖),𝑤)

     Perform merit and distance filter tests:

     Call distance filter(𝑥𝑡(𝑖), dstatus)

     Call merit filter(𝑥𝑡(𝑖), threshold, mstatus)

     If (dstatus and mstatus = “accept”) Then

         Call 𝐿(𝑥𝑡(𝑖),𝑥𝑓)

         Call UPDATE LOCALS(𝑥𝑡(𝑖),𝑥𝑓,𝑤)

     EndIf

EndDo