Fuzzy Arithmetical Assessment of Wave Propagation Models for Multi-Wire Cables

Abstract

To localize damages in engineering structures, such as power lines, ultrasonic wave-based techniques are widely used for Structural Health Monitoring applications. In a cylindrical waveguide, longitudinal, flexural and torsional modes may propagate. Additionally, the wave propagation is generally of dispersive nature. Since cable structures usually consist of several smaller wires, coupling in between individual wires must also be considered. Friction contact causes energy transfer and dissipation as well as mode conversion of propagating waves. Precise transient simulation of wave propagation in multi-wire cables with common FE software results in tremendous computational costs. Therefore, recent research follows a different strategy: only power flows due to propagating waves are considered. Since these models incorporate significant simplifications, a model assessment strategy through advanced fuzzy arithmetic is applied. Uncertainty in model parameters, especially due to simplification and idealization during the modeling process, is considered as epistemic uncertainty. Therefore, the effects of uncertain model parameters represented as fuzzy numbers are investigated by simulations with the use of the Transformation Method. Different models are simulated and an inverse fuzzy arithmetical technique is used to identify parameter uncertainty based on experimentally derived data. Finally, the models’ validity is verified.