Modal decomposition with a limited number of sensors: virtual sensor expansion in aeroelastic systems
Creators: name: KOSCHEL, Stephan
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400102
subject: Aerospace structures
classificationCode: 400105
subject: Flight dynamics
classificationCode: 401201
subject: Aerodynamics (excl. hypersonic aerodynamics)

description: The use of flight test measurements to assist the development of models for the prediction aeroelastic phenomena like flutter, Limit Cycle Oscillation (LCO) or buffet, has been an engineering practice since the beginning of the commercial aviation. The placement of flight sensors requires special considerations. The space inside the structure is often limited and placing sensors on the outer surface might change the aerodynamic characteristic of the aircraft. Furthermore, aircraft are often lightweight, thin, and include multiple slender structures. The description of these structures often require a large number of Degrees of Freedom (DOF), depending on the problem at hand. This implies that more sensor points are required to provide a proper representation of the structure and the structural dynamics.

Techniques to derive more information from a limited set of measurements are therefore sought-after. Modal decomposition techniques can be used for this purpose as they allows the representation of a structure response as the superposition of the corresponding structural Eigenmodes. These Eigenmodes are either determined experimentally or derived from a structural model such as the one derived via Finite Element Method (FEM). Modal decomposition techniques are used to build Reduced Order Models (ROMs) from the measured data. A modal model of the system can then be used to determine the response of the system in any arbitrary structure location in a process called Virtual Sensor Expansion (VSE). Modal decomposition techniques traditionally require more sensors than DOF of the system, which to date has limited their application to environments that allow the installation of a sufficient number of sensors, for example in civil engineering.

In this work, a novel Modal Frequency Decomposition and Reconstruction (MFDR) process is introduced. The basis of the process is the new iterative modal decomposition, which inherently includes the assumption of similarity between the measured system and the structural Eigenmodes. This similarity in the frequency domain allows a modal decomposition even if the system is under-determined, which means that the number of sensor measurements can be smaller than the number of Eigenmodes of the structure. This removes one of the major challenges involved in the application of modal decomposition techniques in the flight test analyses. The other contributions of the MFDR process are the VSE and a novel approach for the Operational Modal Analysis (OMA).

Two major applications are investigated to demonstrate the robustness of the iterative decomposition. The first application is the determination of the time histories of the system response in non-measured locations. These Virtual Sensors are then compared to the actual measurements in these locations to validate the process. It is shown that the process provides very good results if the requirements on sensor noise and sensor placement are met. These requirements are similar to traditional requirements for the modal analysis in flight tests. The impact of the sensor noise, sensor placement and model uncertainties are also investigated in analytical and numerical models. Furthermore, the method is validated against flight test data from a RAAF PC-9/A and a DSTG supplied "Generic Fighter" surrogate dataset. In both cases, the VSE of MFDR is able to predict the virtual sensors with high accuracy.

The second application that MFDR offered to perform is the Operational Modal Analysis (OMA). Modal analyses, especially in the context of flight test analyses, often includes challenges in regards to the selection of the corresponding modes. Spurious noise modes, additional excitation modes or closely-spaced physical modes make it difficult to distinguish and select the correct modes. The modal decomposition, or more precise the derived modal ROM of the measured system, allows the implementation of an additional criterion for the mode selection. The implicit assumption used here is that the measured response of the system resembles the structural Eigenmodes, at least to some degree. This simplifies the mode selection and implements a simple and easy automated OMA. Furthermore, the determined modes can be expanded to derive mode shapes in systems with a larger number of DOF than the actual measurements by using a similar expansion as in the VSE. The OMA method is validated against analytical and numerical models, as well as flight test data of the PC-9/A. The OMA of MFDR was able to provide similar results compared to commonly used OMA approaches like Frequency Domain Decomposition (FDD) and Eigensystem Realization Algorithm (ERA). The process is automated and used a smaller number of sensors compared to the FDD and ERA analyses.