Eigensystem realization algorithm
Encyclopedia
The Eigensystem realization algorithm (ERA) is a system identification
technique popular in civil engineering
, in particular in structural health monitoring
. ERA is a modal analysis
technique which generates a system realization using the frequency response given (multi-)input and (multi-)output data.
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:
To generate the system states
where 
is the matrix of eigenvectors for 
.
System identification
In control engineering, the field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data...
technique popular in civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...
, in particular in structural health monitoring
Structural health monitoring
The process of implementing a damage detection and characterization strategy for engineering structures is referred to as Structural Health Monitoring . Here damage is defined as changes to the material and/or geometric properties of a structural system, including changes to the boundary conditions...
. ERA is a modal analysis
Modal analysis
Modal analysis is the study of the dynamic properties of structures under vibrational excitation.Modal analysis is the field of measuring and analysing the dynamic response of structures and or fluids when excited by an input...
technique which generates a system realization using the frequency response given (multi-)input and (multi-)output data.
Algorithm
Given pulse response data form the Hankel matrix
where
is the pulse response at time step . Next, perform a singular value decompositionSingular value decomposition
In linear algebra, the singular value decomposition is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics....
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:
To generate the system states
where is the matrix of eigenvectors for .