PSI - Issue 52

658 Ilias N. Giannakeas et al. / Procedia Structural Integrity 52 (2024) 655–666 Ilias N. Giannakeas/ Structural Integrity Procedia 00 (2022) 000 – 000 where, ( ) = ( − ) − ( − ) , = ⁄ is the arrival time, the distance, the group velocity and = +1.1 ∙ ⁄ the wave packet duration. Then a damage index along each senor pair can be computed based on the correlation coefficient: =max( ̂ ( ) − ̂ ( )) max ( ̂ ( )) ⁄ (3) where ̂ denotes the reference or baseline signal. Once damage indexes have been computed along all sensor pairs, then is defined as: = −1 ∑ 1 (4) This HI has been selected as it is expected that as the size of the damage increases, it will intersect additional sensors pairs and therefore it will increase the value of the HI. 2.2. Damage Estimation Process In (Giannakeas et al. 2023), a mapping was constructed to link the health indicators (HI) extracted from the GWSHM system to a specific delamination size. Definition of this mapping however is challenging for two main reasons: i) finite elements fail to capture uncertainties relating to the geometry of the delamination or the complex interaction with a propagating wave and ii) data-driven methods require the collection of a large data sample to efficiently explore the input space which is not feasible for real-scale structures. To overcome this, a multi-fidelity approach was employed to combine samples generated from the numerical model with the available sample of experimental observations (Fig. 2). Let , , , and , denote the damage area, x coordinate and y coordinate of the damage, respectively. Then = ( , , , and , ) is the vector of inputs for the th impact event. The objective is to identify a mapping that will link with . A numerical model (finite elements) is used to simulate the propagation of guided waves and their interaction with damage. The simulator provides and approximation of the system’s response based on the underlying physics of the problem. Since the physics cannot capture the complete response, we consider this to be a low-fidelity estimation, denoted as ( ) . Experimental observations on the other hand offer a true representation of the structure’s response. These observations however are limited in number and are influenced by uncertainties such as material properties and noise. By fusing these two heterogenous sources of information, a stochastic model can be trained that accounts for the mismatch between the numerical and experimental observations and considers the observed uncertainties. The objective of this model is to offer a high-fidelity approximation of the system, denoted ℎ ( ) . This approximation can be written as (Higdon et al. 2008): ( )= ℎ ( )≈ ( ) + ( ) + , = 1,2, … . (5) where, ( ) captures the finite element model response, ( ) accounts for the discrepancy between the high and low fidelity approximations and ~ (0, ) is the measurement noise. 4

Fig. 2: Combination of numerical and Experimental