Fasteners number optimization

Hello! My name is Tatiana Pogarskaia and I am one of the PhD students working for the VIM Lab. Today I would like to tell some words about my current research. The research was mostly caused by one of the projects under our collaboration with Airbus SAS Company and it is certainly connected with the airframe assembly simulation.

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During the airframe assembly process it is important to reduce the number of installed fasteners. At the same time the gap between parts has to be inside a given range (e.g., smaller than a given value) in order to provide expected quality. The gap has to be within a given range everywhere in the junction but in practice it is nearly impossible for the whole cloud of initial gaps. Thus, it is reasonable to formulate the optimization problem in probabilistic terms. For a given cloud of initial gaps and given number of fastening elements find the disposition of fasteners providing minimal number of nodes with computed gap exceeding the given level.

The worst thing it the problem can operate with more than 50 variables (fasteners positions) and it has a binary character. The simplest way to solve the kind of problems is to put a new fastener in a hole with the largest gap value, get new gap as a solution of corresponding contact problems and go on. This approach is quite logical but demands to solve contact problem when each new fastener was put. We also tried other different approaches but did not quite succeed.

We wanted to solve the problem using NOMAD software toll (designed especially for optimization and to compare results with our own software called ASRP. As far as NOMAD was developed in Montreal we decided that it was the best reason to visit the city and our colleagues from McGill University. I stayed there for 2 months and did many simulations in NOMAD.

As our problem is binary the main advantage of NOMAD is an opportunity to use derivative free optimization methods, surrogate models and a user defined search step algorithm. We created a test model of a wing to fuselage junction with 410 net nodes (205 on each part), 60 holes and used fasteners only of 1000 N force.  We also simulated several clouds of gaps (cloud of gaps is a set of different gaps with the same general paramentrs such as roughness and amplitude).

As NOMAD was able to use ASRP kernel to read the data and solve contact problem as a black-box function we managed to do optimization with the same  test model and the same test gaps using NOMAD and ASRP optimization functionality. In the picture below one can see holes (blue) and fasteners (red).

We managed to speed up the calculations twice but lost in quality so we are still trying to find a way to improve the procedure.