Eigensystem realization algorithm
The Eigensystem realization algorithm (ERA) is a system identification technique popular in civil engineering, in particular in structural health monitoring. ERA can be used as a modal analysis technique and generates a system realization using the time domain response (multi-)input and (multi-)output data. The ERA was proposed by Juang and Pappa  and has been used for system identification of aerospace structures such as the Galileo spacecraft, turbines, civil structures  and many other type of systems.
Given pulse response data form the Hankel matrix
where is the pulse response at time step . Next, perform a singular value decomposition of , i.e. . Then choose only the rows and columns corresponding to physical modes to form the matrices . Then the discrete time system realization can be given by:
- Marlon D. Hill. "An Experimental Verification of the Eigensystem Realization Algorithm for Vibration Parameter Identification" (pdf). Retrieved August 24, 2011.
- Juang, J.-N.; Pappa, R. S. (1985). "An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction". Journal of Guidance, Control, and Dynamics 8 (5).
- Pappa, Richard S., and J-N. Juang. "Galileo spacecraft modal identification using an eigensystem realization algorithm." Structures, Structural Dynamics and Materials Conference, 25 th, Palm Springs, CA. 1984.
- Sanchez-Gasca, J. J. "Computation of turbine-generator subsynchronous torsional modes from measured data using the eigensystem realization algorithm." Power Engineering Society Winter Meeting, 2001. IEEE. Vol. 3. IEEE, 2001.
- Juan Martin Caicedo; Shirley J. Dyke; Erik A. Johnson (2004). "Natural Excitation Technique and Eigensystem Realization Algorithm for Phase I of the IASC-ASCE Benchmark Problem: Simulated Data". Journal of Engineering Mechanics 130 (1). doi:10.1061/(asce)0733-9399(2004)130:1(49).
- Brownjohn, James Mark William; Moyo, Pilate; Omenzetter, Piotr; Lu, Yong (2003). "Assessment of Highway Bridge Upgrading by Dynamic Testing and Finite-Element Model Updating". Journal of Bridge Engineering 8 (3): 162–172. doi:10.1061/(ASCE)1084-0702(2003)8:3(162). ISSN 1084-0702.
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