Improved Tangential Interpolation-based Multi-input Multi-output Modal Analysis of a Full Aircraft

Abstract

In the field of Structural Dynamics, modal analysis is the foundation of System Identification and vibration-based inspection. However, despite their widespread use, current state-of-the-art methods for extracting modal parameters from multi-input multi-output (MIMO) frequency domain data are still affected by many technical limitations. Mainly, they can be computationally cumbersome and/or negatively affected by close-in-frequency modes. The Loewner Framework (LF) was recently proposed to alleviate these problems with the limitation of working with single-input data only. This work proposes a computationally improved version of the LF, or iLF, to extract modal parameters more efficiently. Also, the proposed implementation is extended in order to handle MIMO data in the frequency domain. This new implementation is compared to state-of-the-art methods such as the frequency domain implementations of the Least Square Complex Exponential method and the Numerical Algorithm for Subspace State Space System Identification on numerical and experimental datasets. More specifically, a finite element model of a 3D Euler-Bernoulli beam is used for the baseline comparison and the noise robustness verification of the proposed MIMO iLF algorithm. Then, an experimental dataset from MIMO ground vibration tests of a trainer jet aircraft with over 91 accelerometer channels is chosen for the algorithm validation on a real-life application. Its validation is carried out with known results from a single-input multi-output dataset of the starboard wing of the same aircraft. Excellent results are achieved in terms of accuracy, robustness to noise, and computational performance by the proposed improved MIMO method, both on the numerical and the experimental datasets. The MIMO iLF MATLAB implementation is shared in the work supplementary material.

Figures (14)

• Figure 1: 8-element 3D beam: \ref{['fig:3dbeam']} is the schematic drawing of the discretised 8-element Euler-Bernoulli beam and \ref{['fig:beam_sec']} shows the beam rectangular box cross-section with the relative dimensions. Not in scale.
• Figure 2: 8-element 3D beam: Stabilisation diagrams for the model parameters identification via LF (\ref{['fig:LF_stab']}), iLF (\ref{['fig:iLF_stab']}), N4SID (\ref{['fig:N4SID_stab']}), and LSCE (\ref{['fig:LSCE_stab']}).
• Figure 3: 8-element 3D beam: Average time to identification for all methods considered for orders $k$ between 32 and 60.
• Figure 4: 8-element 3D beam: Effects of input-output noise on the identification (difference w.r.t analytical results) of $\omega_n$ (\ref{['fig:noise_w']}), $\zeta_n$ (\ref{['fig:noise_z']}), and $\mathbf{\phi}_n$ (\ref{['fig:noise_p']}) via the iLF at the minimum order $k$.
• Figure 5: 8-element 3D beam: Effects of input-output noise on the identification (difference w.r.t. analytical results) of $\omega_n$ (\ref{['fig:noise_stab_w']}), $\zeta_n$ (\ref{['fig:noise_stab_z']}), and $\mathbf{\phi}_n$ (\ref{['fig:noise_stab_p']}) via the iLF for the stable modes, such that $k$$\in$ [32,60].