mdof.realize module

mdof.realize.era(Y, **options)

System realization from Markov parameters (discrete impulse response data). Ho-Kalman / Eigensystem Realization Algorithm (ERA) [1] [2].

Parameters:

• Y (array) – Markov parameters. dimensions: \((p,q,nt)\), where \(p\) = number of outputs, \(q\) = number of inputs, and \(nt\) = number of Markov parameters.

• horizon (int, optional) – number of block rows in Hankel matrix = order of observability matrix. default: \(min(150, (nt-1)/2)\)

• nc (int, optional) – number of block columns in Hankel matrix = order of controllability matrix. default: \(min(150, max(nt-1-\) horizon\(, (nt-1)/2))\)

• order (int, optional) – model order. default: \(min(20,\) horizon\(/2)\)

Returns:

realization in the form of state space coefficients (A,B,C,D)

Return type:

tuple of arrays

References

[1]

Ho, Β. L., & Kálmán, R. E. (1966). Effective construction of linear state-variable models from input/output functions: Die Konstruktion von linearen Modeilen in der Darstellung durch Zustandsvariable aus den Beziehungen für Ein-und Ausgangsgrößen. at-Automatisierungstechnik, 14(1-12), 545-548. (https://doi.org/10.1524/auto.1966.14.112.545)

[2]

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), 620-627. (https://doi.org/10.2514/3.20031)

mdof.realize.era_dc(Y, **options)

System realization from Markov parameters (discrete impulse response data). Eigensystem Realization Algorithm with Data Correlations (ERA/DC) [3].

Parameters:

• Y (array) – Markov parameters. dimensions: \((p,q,nt)\), where \(p\) = number of outputs, \(q\) = number of inputs, and \(nt\) = number of Markov parameters.

• horizon (int, optional) – number of block rows in Hankel matrix = order of observability matrix. default: \(min(150, (nt-1)/2)\)

• nc (int, optional) – number of block columns in Hankel matrix = order of controllability matrix. default: \(min(150, max(nt-1-\) horizon\(, (nt-1)/2))\)

• order (int, optional) – model order. default: \(min(20,\) horizon\(/2)\)

• a (int, optional) – \((\alpha)\) number of block rows in Hankel of correlation matrix. default: 0

• b (int, optional) – \((\beta)\) number of block columns in Hankel of correlation matrix. default: 0

• l (int, optional) – initial lag for data correlations. default: 0

• g (int, optional) – lags (gap) between correlation matrices. default: 1

Returns:

realization in the form of state space coefficients (A,B,C,D)

Return type:

tuple of arrays

References

[3]

Juang, J. N., Cooper, J. E., & Wright, J. R. (1987). An eigensystem realization algorithm using data correlations (ERA/DC) for modal parameter identification. (https://ntrs.nasa.gov/citations/19870035963)

mdof.realize.srim(inputs, outputs, **options)

System realization from input and output data, with output error minimization method. System Realization Using Information Matrix (SRIM) [4].

Parameters:

• inputs (array) – input time history. dimensions: \((q,nt)\), where \(q\) = number of inputs, and \(nt\) = number of timesteps

• outputs (array) – output response history. dimensions: \((p,nt)\), where \(p\) = number of outputs, and \(nt\) = number of timesteps

• horizon (int, optional) – number of steps used for identification (prediction horizon). default: \(min(300, nt)\)

• order (int, optional) – model order. default: \(min(20,\) horizon\(/2)\)

• full (bool, optional) – if True, full SVD. default: True

• find (string, optional) – “ABCD” or “AC”. default: “ABCD”

• threads (int, optional) – number of threads used during the output error minimization method. default: 6

• chunk (int, optional) – chunk size in output error minimization method. default: 200

Returns:

realization in the form of state space coefficients (A,B,C,D)

Return type:

tuple of arrays

References

[4]

Juang, J. N. (1997). System realization using information matrix. Journal of Guidance, Control, and Dynamics, 20(3), 492-500. (https://doi.org/10.2514/2.4068)