Abstract Summary
Aging vibration-prone structures may require up-to-date proofs of their load-bearing capacity for retrofitting or life-cycle assessments. The structural vibration response is affected by naturally variable structural properties and loads, known as aleatory uncertainties. With modeling, additional epistemic uncertainties are introduced due to missing knowledge of model parameters. The model responses then include both types of uncertainties in a mixed and nested form. Quantifying these polymorphic uncertainties is particularly important in structural dynamics, where a deterministic model may significantly underestimate responses, such as resonance phenomena.
A case study was conducted to characterize the vibration behavior of a guyed mast under polymorphic uncertainties. A simplified linear structural model was built using commercially available FEM software. Polymorphic uncertainties in the input parameters were modeled and propagated using in-house code.
Aleatory uncertainties were modeled by probability theory, and a quasi-Monte Carlo simulation based on importance sampling facilitates an efficient reuse of computed samples. Epistemic uncertainties were modeled by evidence / belief function theory and their propagation was performed using approximate interval optimizations, avoiding surrogate models to avoid non-physical results. Particular emphasis was placed on computational efficiency, as the developed method is designed to be used for more complex numerical models. Statistics and aggregation of belief functions were used in conjunction with sensitivity analyses to yield explainable results.
The case study scenario is a retrofit of a guyed mast based on outdated design documents. Epistemically uncertain parameters include unknown structural damping, cross-section tolerances and material properties, the additional mass from antennas and cables, and pre-tensioning forces of the guy wires. Aleatory uncertainties arise from temperature effects on the guy wires and the viscosity of the dampers, as well as from icing in winter. The results highlight the natural variations of resonant frequencies, the characterization of resonant bands due to epistemic uncertainties, and the effectiveness of a deterministically designed Tuned Mass Damper in a structural model influenced by polymorphic uncertainties.
The developed methodology is applicable to moderately computationally expensive models of any type and does not require building surrogate models. Model runs are efficiently re-used and the uncertainty propagation can be highly parallelized. At the same computational cost, a pure stochastic treatment of uncertainties achieves slightly better variances, while concealing the influence of missing knowledge. The method reveals where enhancing knowledge about partly-known model parameters is beneficial and permits robust retrofit designs or increased confidence in life-cycle estimates.
