Quantification of Polymorphic Uncertainties in Structural Dynamics: Case Study of a Guyed Mast

Abstract

Abstract 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 is conducted to characterize the vibration behavior of a guyed mast under polymorphic uncertainties. A simplified linear structural model is built using commercially available FEM software. Polymorphic uncertainties in the input parameters are modeled and propagated using in-house code. Aleatory uncertainties are modeled by probability theory, and a quasi-Monte Carlo simulation based on weighted sampling facilitates an efficient reuse of computed samples. Epistemic uncertainties are modeled by evidence/belief function theory and their propagation is performed using interval optimizations on Radial Basis Function interpolators and quasi-Monte Carlo sequences. Particular emphasis is placed on computational efficiency, as the developed method is designed to be used for more complex numerical models. Statistics and aggregation of belief functions are used to yield explainable results. The case study scenario is a retrofit of a guyed mast based on outdated design documents. Epistemic uncertain parameters include unknown structural damping, cross-section tolerances, material properties, the additional mass from antennas and cables, and the pre-tensioning forces of the guy cables. Aleatory uncertainties arise from temperature effects on the guy cables and the viscosity of the dampers, as well as from icing in winter. The results highlight the intrinsic variations of natural frequencies, the characterization of resonance bands due to epistemic uncertainties, and the effectiveness of a deterministically designed Tuned Mass Damper (TMD) in a structural model influenced by polymorphic uncertainties. The developed methodology is applicable to moderately computationally expensive models of any type. Model runs are efficiently re-used and the uncertainty propagation can be highly parallelized. 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.