PSI - Issue 38

Ronald Schrank et al. / Procedia Structural Integrity 38 (2022) 30–39 Ronald Schrank / Structural Integrity Procedia 00 (2021) 000 – 000

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19 Hotspots are defined for the control arm, each contributing to the error sum. Bilinear error functions ( ) have found to be very suitable for these kind of optimization problems. Bilinearity gives a certain acceptance of damage discrepancies within defined tolerances (z min ; z max ). The error values increase much more rapidly beyond these tolerances.

Fig. 11. Bilinear error function

5.4. Constraints Additional constraints are used in numerical optimization: •

Maximum stress lower than yield strength at all hotspots • Limitation of fatigue damage at some additional hotspots These constraints can be part of the objective function as additional penalty terms. Alternatively, individuals violating constraints can be sorted out from population.

5.5. Results and performance The hybrid optimization is randomized due to several aspects, for instance • random based initialization of evolution strategy • random based mutation within evolution strategy

Generally, randomization leads to a certain dependency of the optimization result from the random seed. Different optimization runs (optimization cycles) with different random seeds give different optimization results commonly. This is a typical phenomenon of evolution strategy which normally won´t find the unique global optimum, especially in cases with a high number of optimization parameters, high complexity and existing constraints. Local optima are identified instead. Typically, they represent a sufficient solution within an acceptable run-time. 20 optimization cycles have been performed for the control arm, each requiring roughly 30000 evaluations of the objective function (fatigue damage calculations). The analysis time is approx. one hour (real time) using a single CPU. The simplified 3-channel test reproduces fatigue damages from reference (full test) at all relevant hotspots with a very good accuracy. Another optimization without any phase angels (synchronous loads) also results in a sufficient quality of damage reproduction. This benchmark clarifies capability of the new fatigue optimization method. Such high-quality optimization results had not been feasible by any other methods so far, especially by the application of the classic manual strategies.