Generate stabilization diagram for modal analysis
generates a stabilization diagram in the current figure.
modalsd estimates the natural frequencies and damping
ratios from 1 to 50 modes and generates the diagram using the least-squares
complex exponential (LSCE) algorithm.
fs is the sample
rate. The frequency,
f, is a vector with a number of
elements equal to the number of rows of the frequency-response function,
frf. You can use this diagram to differentiate between
computational and physical modes.
returns a cell array
of natural frequencies,
fn = modalsd(___)
fn, identified as being stable
between consecutive model orders. The ith element contains a
length-i vector of natural frequencies of stable poles.
Poles that are not stable are returned as
NaNs. This syntax
accepts any combination of inputs from previous syntaxes.
MIMO Stabilization Diagram
Compute the frequency-response functions for a two-input/two-output system excited by random noise.
Load the data file. Compute the frequency-response functions using a 5000-sample Hann window and 50% overlap between adjoining data segments. Specify that the output measurements are displacements.
load modaldata winlen = 5000; [frf,f] = modalfrf(Xrand,Yrand,fs,hann(winlen),0.5*winlen,'Sensor','dis');
Generate a stabilization diagram to identify up to 20 physical modes.
Repeat the computation, but now tighten the criteria for stability. Classify a given pole as stable in frequency if its natural frequency changes by less than 0.01% as the model order increases. Classify a given pole as stable in damping if the damping ratio estimate changes by less than 0.2% as the model order increases.
Restrict the frequency range to between 0 and 500 Hz. Relax the stability criteria to 0.5% for frequency and 10% for damping.
modalsd(frf,f,fs,'MaxModes',20,'SCriteria',[5e-3 0.1],'FreqRange',[0 500])
Repeat the computation using the least-squares rational function algorithm. Restrict the frequency range from 100 Hz to 350 Hz and identify up to 10 physical modes.
frf — Frequency-response functions
vector | matrix | 3-D array
Frequency-response functions, specified as a vector, matrix,
or 3-D array.
frf has size p-by-m-by-n,
where p is the number of frequency bins, m is
the number of response signals, and n is the number
of excitation signals used to estimate the transfer function.
the frequency response of an oscillator.
Complex Number Support: Yes
f — Frequencies
Frequencies, specified as a vector. The number of elements of
equal the number of rows of
fs — Sample rate of measurement data
Sample rate of measurement data, specified as a positive scalar expressed in hertz.
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
'MaxModes',20,'FreqRange',[0 500] computes
up to 20 physical modes and restricts the frequency range to between
0 and 500 Hz.
FitMethod — Fitting algorithm
'lsce' (default) |
Fitting algorithm, specified as the comma-separated pair consisting of
'lsce'— Least-squares complex exponential method.
'lsrf'— Least-squares rational function estimation method. The method is described in . See Continuous-Time Transfer Function Estimation Using Continuous-Time Frequency-Domain Data (System Identification Toolbox) for more information. This algorithm typically requires less data than nonparametric approaches.
FreqRange — Frequency range
two-element vector of positive values
Frequency range, specified as the comma-separated pair consisting of
'FreqRange' and a two-element vector of
increasing, positive values contained within the range specified in
MaxModes — Maximum number of modes
50 (default) | positive integer
Maximum number of modes, specified as the comma-separated pair
'MaxModes' and a positive integer.
SCriteria — Criteria to define consecutive stable natural frequencies and damping ratios
[0.01 0.05] (default) | two-element vector of positive values
Criteria to define stable natural frequencies and damping ratios
between consecutive model degrees of freedom, specified as the
comma-separated pair consisting of
'SCriteria' and a
two-element vector of positive values.
contains the maximum fractional differences between poles to be
classified as stable. The first element of the vector applies to natural
frequencies. The second element applies to damping ratios.
fn — Natural frequencies identified as stable
Natural frequencies identified as stable, returned as a matrix.
The first i elements of the ith
row contain natural frequencies. Poles that are nonphysical or not
stable in frequency are returned as
 Brandt, Anders. Noise and Vibration Analysis: Signal Analysis and Experimental Procedures. Chichester, UK: John Wiley & Sons, 2011.
 Ozdemir, Ahmet Arda, and Suat Gumussoy. "Transfer Function Estimation in System Identification Toolbox™ via Vector Fitting." Proceedings of the 20th World Congress of the International Federation of Automatic Control, Toulouse, France, July 2017.
 Vold, Håvard, John Crowley, and G. Thomas Rocklin. “New Ways of Estimating Frequency Response Functions.” Sound and Vibration. Vol. 18, November 1984, pp. 34–38.