Video analysis of nonlinear systems with extended Kalman filtering for modal identification

This study proposes to carry out the experimental modal analysis of nonlinear systems under the assumption of almost invariant modal shapes by coupling video analysis from a high speed/resolution camera and extended Kalman filtering. A clamped-clamped beam with a local nonlinearity is considered, and its vibrations are measured by detecting and tracking a large set of (virtual) sensors bonded to the beam outer surface. Specific image processing and video tracking techniques are employed and detailed herein. Then, the instantaneous natural frequencies and modal amplitudes are identified by means of a data assimilation method based on extended Kalman and modal filters. Finally, the proposed method of identification is assessed using a numerical example possessing 3 degrees of freedom and a strong nonlinearity. The performance and limits of the identification process are discussed.

Automated summary

This study proposes a method for experimental modal analysis of nonlinear systems under the assumption of almost invariant modal shapes, combining video analysis from a high speed/resolution camera and extended Kalman filtering. A clamped-clamped beam with a local nonlinearity is considered and vibrations are measured using (virtual) sensors bonded to the beam outer surface. Specific image processing and video tracking techniques are employed. Instantaneous natural frequencies and modal amplitudes are identified using a data assimilation method based on extended Kalman and modal filters. The proposed method is evaluated using a numerical example and the performance and limits of the identification process are discussed.