Systems and methods for analyzing flutter test data using damped sine curve fitting with the closed form shape fit

A system comprising:

• a plurality of sensors configured to provide a flutter test data from a structure subject to one or more excitation events, the flutter test data comprising machine-readable time history data corresponding to physical measurements taken by the sensors;
• and
• a computer processor configured to receive the machine-readable time history data and to execute a process, the process including:
• performing one or more fits of a series of damped sine curves to the time history data;
• computing a Fast Fourier Transform (FFT) of a fit error of a first fit of the one or more fits of the series of damped sine curves to the time history data;
• estimating a next damped sine curve to include in the series of damped sine curves;
• performing one or more iterations of a closed form shape fit to optimize one or more mode shape terms and a first non-linear fit to optimize one or more frequency and damping and excitation level terms for the series of damped sine curves;
• perform a second nonlinear fit of the series of damped sine curves, using the optimized frequency and damping and excitation level and mode shape terms, to the time history data;
• and
• output the results of the nonlinear fit.

A non-transitory computer-readable medium comprising instructions which, in response to execution by a computer system, cause the computer system to:

• receive time history data corresponding to an excitation of a structure from a measurement taken by a sensor attached to the structure;
• formulate a linear least squares problem for the time history data from the sensor for the excitation;
• solve the linear least squares problem for the time history data from the sensor for the excitation;
• and
• extract one or more mode shape terms to obtain mode shape information about the structure from the time history data.