Effect of broad-band phase-based motion magnification on modal parameter estimation


Operational modal analysis provides a reliable method for estimating modal parameters of structures. This approach requires only the measurement of the system’s vibratory response, displacement or acceleration, which can be captured using high-speed cameras. This approach also uses a two-dimensional point tracking (2DPT) technique to determine the displacement of the structure. Notably, 2DPT requires the use of markers coupled with an algorithm for accurate tracking of the displacement of the points. Unfortunately, the markers are highly susceptible to low signal-to-noise ratio (SNR) due to the induced sub-pixel amplitudes during their oscillatory motion. If uncontrolled, high-frequency data content makes the identification of higher modes difficult.

Phased-based motion magnification (PMM), a combination of phase-based motion estimation (PME) and motion magnification, has emerged as a robust approach for solving the above problem. Through a set of temporal and spatial filtering, PMM-based video processing algorithm is a powerful tool for enhancing the visualization properties of the resulting images and videos. To date, the use of PMM to improve the two-dimensional and three-dimensional modal parameter estimation has been reported in numerous studies. Interestingly, previous research findings revealed that a significant improvement in the modal parameter estimation could be obtained by magnifying the motion in a narrow frequency centered around the noisy mode.

Motivated by these results, Dr. Marc Eitner, Benjamin Miller (PhD candidate), Professor Jayant Sirohi and Professor Charles Tinney from The University of Texas at Austin investigated the effect of broad-band phase-based motion magnification (BPMM) on modal parameter analysis and estimation. Unlike in the previous studies where the motion was magnified in a narrow frequency band, it was magnified in a broad-frequency band containing all the active modes in this study. The objective was to improve the SNR throughout the frequency band to improve the operational modal analysis and modal parameter estimation. Their work is currently published in the journal, Mechanical Systems and Signal Processing.

In their approach, the modal parameter estimation process comprised three key elements: a 2DPT technique for monitoring the structural motion, a PMM algorithm for magnifying the high-speed images and a Complexity Pursuit algorithm for estimating the modal parameters based on the vibration data. Through a numerical experiment, the feasibility of the proposed methodology was validated. The modal analysis was conducted on a metallic nozzle, excited with pressurized air, with fluorescent markers. Then, a high-speed camera was used to measure the structural displacement derived from the vibrations, followed by the magnification of the video and subsequent extraction of the discrete motion using the respective algorithms. Finally, the modal parameters were estimated with and without the broad-band magnification of the motion.

Results demonstrated that by using the BPMM as a preprocessor, the modal analysis outcomes were significantly improved. According to Eitner the “approach is very attractive, since we chose a broad frequency band for magnification and thus need very few apriori information about the system to utilize this approach.” Moreover, magnifying the motion in a broad frequency band improved the SNR, enhancing the motion extraction and subsequently improving the analysis and modal parameter estimation. However, only the first five modes were obtained without motion magnification. In contrast, the modal shapes agreed well with the experimental results and six modes were obtained when the motion was magnified using the new methodology. Additionally, the improvement of the modal parameters exhibited a positive correlation with the magnification factor. Finally, it was noted that the method did not require system knowledge to use other than the selection of the most appropriate magnification factor.

In summary, a PMM algorithm for improving the SNR of motion in high-speed images was reported. Importantly, this approach involved motion magnification in the broad frequency band containing the active modes to improve motion extraction and modal parameter estimation. From the nozzle test, BPMM enabled the identification of the sixth mode. Moreover, the good agreement between the estimated mode shapes and the finite element analysis results confirmed the quality of the modal parameters. Therefore, Marc Eitner and colleagues study provides a promising result useful in future investigations in the same field, e.g., in developing improved methods for simulating high-speed images.

About the author

Marc Eitner was born in Germany where he studied Mechanical and Aerospace Engineering at RWTH Aachen University. He moved to Austin, Texas and obtained his PhD in the summer of 2021. His primary research focuses on experimental system identification of aeroelastic systems in high-speed flow environments. A further research interest involves the implementation of novel algorithms that facilitate video based system identification. He currently works as a research fellow at The University of Texas at Austin.

About the author

Benjamin Miller received his BS in Aerospace Engineering from The University of Texas at Austin, where he is currently working towards a PhD in Computational Science, Engineering, and Mathematics under an NDSEG fellowship. His research focuses on detection and tracking of anthropogenic space objects as structures in noise using a-contrario methods.


Eitner, M., Miller, B., Sirohi, J., & Tinney, C. (2021). Effect of broad-band phase-based motion magnification on modal parameter estimation. Mechanical Systems and Signal Processing, 146, 106995.

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