Modal Analysis and System Identification (identification)

Created on Nov. 26, 2017 @author: Joseph C. Slater

identification.cmif(freq, H, freq_min=None, freq_max=None, plot=True)

Complex mode indicator function

Plots the complex mode indicator function

Parameters:

freq : array

The frequency vector in Hz. Does not have to start at 0 Hz.

H : array

The complex frequency response function

freq_min : float, optional

The minimum frequency to be plotted

freq_max : float, optional

The maximum frequency to be plotted

plot : boolean, optional (True)

Whether to also plot mode indicator functions

Returns:

cmifs : complex mode indicator functions

Notes

Note

Allemang, R. and Brown, D., “A Complete Review of the Complex Mode Indicator Function (CMIF) With Applications,” Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2006.

Examples

>>> import vibrationtesting as vt
>>> M = np.diag([1,1,1])
>>> K = K = np.array([[3.03, -1, -1],[-1, 2.98, -1],[-1, -1, 3]])
>>> Damping = K/100
>>> Cd = np.eye(3)
>>> Cv = Ca = np.zeros_like(Cd)
>>> Bt = np.eye(3)
>>> H_all = np.zeros((3,1000,3), dtype = 'complex128')
>>> for i in np.arange(1, 4):
...        for j in np.arange(1, 4):
...            omega, H_all[i-1,:,j-1] = vt.sos_frf(M, Damping/10, K, Bt,
...                                                 Cd, Cv, Ca, 0, 3, i,
...                                                 j, num_freqs = 1000)
>>> _ = vt.cmif(omega, H_all)

identification.mdof_cf(f, TF, Fmin=None, Fmax=None)

Curve fit to multiple degree of freedom FRF

If Fmin and Fmax are not entered, the first and last elements of TF are used.

If the first column of TF is a collocated (input and output location are the same), then the mode shape returned is the mass normalized mode shape. This can then be used to generate an identified mass, damping, and stiffness matrix as shown in the following example.

Parameters:

f: array

The frequency vector in Hz. Does not have to start at 0 Hz.

TF: array

The complex transfer function

Fmin: int

The minimum frequency to be used for curve fitting in the FRF

Fmax: int

The maximum frequency to be used for curve fitting in the FRF

Returns:

z: double

The damping ratio

nf: double

Natural frequency (Hz)

u: array

The mode shape

Notes

FRF are columns comprised of the FRFs presuming single input, multiple output z and nf are the damping ratio and natural frequency (Hz) u is the mode shape. Only one peak may exist in the segment of the FRF passed to sdofcf. No zeros may exist within this segment. If so, curve fitting becomes unreliable.

Author: Original Joseph C. Slater. Python version, Gabriel Loranger

Examples

>>> # First we need to load the sampled data which is in a .mat file
>>> import vibrationtesting as vt
>>> import scipy.io as sio
>>> data = sio.loadmat(vt.__path__[0] + '/data/case2.mat')
>>> #print(data)
>>> # Data is imported as arrays. Modify then to fit our function
>>> TF = data['Hf_chan_2']
>>> f = data['Freq_domain']
>>> # Now we are able to call the function
>>> z, nf, a = vt.mdof_cf(f,TF,500,1000)
>>> nf
192.59382330...

identification.sdof_cf(f, TF, Fmin=None, Fmax=None)

Curve fit to a single degree of freedom FRF.

Only one peak may exist in the segment of the FRF passed to sdofcf. No zeros may exist within this segment. If so, curve fitting becomes unreliable.

If Fmin and Fmax are not entered, the first and last elements of TF are used.

Parameters:

f: array

The frequency vector in Hz. Does not have to start at 0 Hz.

TF: array

The complex transfer function

Fmin: int

The minimum frequency to be used for curve fitting in the FRF

Fmax: int

The maximum frequency to be used for curve fitting in the FRF

Returns:

z: double

The damping ratio

nf: double

Natural frequency (Hz)

a: double

The numerator of the identified transfer functions

Plot of the FRF magnitude and phase.

Notes

Author: Original Joseph C. Slater. Python version, Gabriel Loranger

Examples

>>> # First we need to load the sampled data which is in a .mat file
>>> import vibrationtesting as vt
>>> import scipy.io as sio
>>> data = sio.loadmat(vt.__path__[0] + '/data/case1.mat')
>>> #print(data)
>>> # Data is imported as arrays. Modify then to fit our function.
>>> TF = data['Hf_chan_2']
>>> f = data['Freq_domain']
>>> # Now we are able to call the function
>>> z, nf, a = vt.sdof_cf(f,TF,500,1000)
>>> nf
212.092530551...