PSI - Issue 80

Tafara E. Makuni et al. / Procedia Structural Integrity 80 (2026) 105–116 Tafara Makuni / Structural Integrity Procedia 00 (2019) 000 – 000

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In 2017, Young et al. developed an inverse method for hydrodynamic load reconstruction using limited SG measurements in multi-phase flows. The results were found to agree well with experimental observations and measurements (Ward, et al., 2018). More recently in 2021, Araujo-Estrada et al. used an instrumented wind tunnel model of a wing with a distributed array of strain and pressure sensors to characterise the relationship between the sensor signals, and the aerodynamic variables and loads. Here the Artificial Neural Networks, ANN, based method performed well; however, the partial least-squared, PLS, approach was less accurate for aerodynamic variables and load prediction (Araujo-Estrada, et al., 2021). In 2023, Ao et al. developed a method that reconstructed the full-field strain distribution from a limited number of displacement responses. The method involved the use of a displacement to-strain transformation matrix based on blade mode shapes. This technique was validated against numerical and experimental cases, and the results demonstrated a high consistency between the measured and reconstructed results. This displacement response-based technique performs well where traditional would otherwise struggle (Ao, et al., 2023). This is because, as previously mentioned, the relationship between the aerodynamic loading and the structural response is complex (Trivailo, et al., 2006), and difficult to predict using traditional methods. Digital twinning offers us a new method that can produce an accurate structural response given the aerodynamic loading as an input for realistic flight conditions. In 2021, Wang et al. used a cantilevered circular beam, and the fin of a missile rudder in a numerical study for displacement field reconstruction and they found that the results closely matched the simulated FEA deformation (Wang, et al., 2021). In the field of wind engineering, Bucher et al. reconstructed the loading from the measured structural response on a wind mast in the time domain using an augmented impulse matrix. The accuracy and availability of the measured response was increased by projecting the problem onto the modal coordinates, for a selected number of sensors. The numerical simulations conducted compared well to the experiments results (Amiria, et al., 2017). A key challenge of developing an accurate DT is the availability of data. For load reconstruction, ideally the full pressure field is required, however, this is not possible with discrete sensors in-service or in a laboratory testing (Ao, et al., 2023). The wind tunnel study by Araujo-Estrada et al. used discrete strain and pressure measurements to perform the load reconstruction (Araujo-Estrada, et al., 2021). The DT study by Willcox et al. used 24 uniaxial SGs on the wing of the physical UAV (Kapteyn, et al., 2004) (Kapteyn, et al., 2020) (Willcox, 2021) (Kapteyn, et al., 2022). Shkarayev et al. used the 90 o rosette and uniaxial type SGs to reconstruct the load and displacements using the inverse interpolation method (Shkarayev, et al., 2002). Amiria et al. used accelerometers on the wind mast structure to obtain the structural response (Amiria, et al., 2017). Ao et al. used strain gauges and laser doppler vibrometer, LDV, to reconstruct the loading on an aerodynamic blade (Ao, et al., 2023). Trivailo et al. used strain gauges to train the NN for aerodynamic load prediction (Trivailo, et al., 2006). Other techniques such as data assimilation and transformation can be applied to enlarge the required dataset (Renganathan, et al., 2020) (Kapteyn, et al., 2022). The novelty of the approach in this work is that XFOIL is used to generate large aerodynamic datasets (low fidelity) to be used in combination with limited sensor outputs (high fidelity) to generate simplified but computationally efficient pressure distributions. These pressure distributions can then be used as input to obtain the structural response of an aerofoil section or wing. For a given aerofoil section, the DT platform takes as input three main parameters; (i) Mach number, M ∞ , (ii) angle of attack, α ∞ ; and (iii) altitude, h ; and outputs the pressure distribution. This pressure distribution can then be used to calculate the structural response. Details of this DT platform are given in the next Section. 2. DT Platform 2.1. Introducing the DT Platform An outline of the DT platform is shown in Figure 1. As explained in the previous Section, the main inputs are; M ∞ , α ∞ and h . In terms of Aerodynamics, the main output is the pressure field across the aerofoil which is then used to obtain the structural response in terms of the strain field. If the internal geometry and properties of the wing are known, it is possible to compute the stress field. If M ∞ and h are known, the Reynolds number, Re , can be calculated. In addition to this, the wing planform can be analysed to obtain a NACA 4-digit equivalent profile at the root. This profile is used as the basis to the 2D calculations conducted using XFOIL. The baseline profile used in this work is the NACA3418 based on Evektor, EV, aeroplane Cobra. Flight test data exists for this aeroplane, and the data has been used to