ii_mmif

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ii_mmif

Purpose

Standard transformations of data sets.

Syntax

[mmif,ua] = ii_mmif(xf,IDopt)
[mmif,ua] = ii_mmif(xf,IDopt,'waitbar')
amif =  ii_mmif(xf,IDopt,'amif','waitbar')
[cmif,u,v] = ii_mmif(xf,IDopt,'cmif','waitbar')
sum = ii_mmif(xf,IDopt,'sum')
ii_mmif(mmifcommand,ci,CurveName)

Description

This function supports all standard transformations of response datasets. From the iiplot gui, use iicom('CurtabStack'); then select Compute ... in the context menu to transform a given dataset. From the command line

Syntax

 ci=iicom('curveload','gartid');
 ii_mmif('mmif',ci,'Test');
 iicom('iixonly',{'mmif(Test)'});

Computed mmif are stored in the stack with name mmif(CurveName). Use command modifier 'Command-reset' to compute a mmif which has already been computed before (otherwise old result is returned).

When used with idcom, the Show ... context menu supports the automated computation of a number of transformations of XF('Test'). These mode indicator functions combine data from several input/output pairs of a MIMO transfer function in a single response that gives the user a visual indication of pole locations. You can then use the idcom e command to get a pole estimate.

This function supports standard mode indicator functions and is easily accessed through iiplot interface which computes and displays these functions for the nominal data set (XF(1)).

MMIF

The Multivariate Mode Indicator Function (MMIF) (use the iicom showmmi command) was introduced in [51]. Its introduction is motivated by the fact that, for a single mode mechanical model, the phase at resonance is close to -90^o. For a set of transfer functions such that {y(s)}=[H(s)]{u(s)}, one thus considers the ratio of real part of the response to total response

q(s,{u})=

{u} ^T [Re H^T Re H] {u}

{u} ^T [H^H H] {u}

{u} ^T [B] {u}

{u} ^T [A] {u}

(9.14)

For structures that are mostly elastic (with low damping), resonances are sharp and have properties similar to those of isolated modes. The MMIF (q) thus drops to zero.

Note that the real part is considered for force to displacement or acceleration, while for force to velocity the numerator is replaced by the norm of the imaginary part in order to maintain the property that resonances are associated to minima of the MMIF. A MMIF showing maxima indicates improper setting of IDopt.DataType.

For system with more than one input (u is a vector rather than a scalar), one uses the extrema of q for all possible real valued u which are given by the solutions of the eigenvalue problem [A] {u} q + [B] {u} = 0.

The figure below shows a particular set fo MMIF. The system has 3 inputs, so that there are 3 indicator functions. The resonances are clearly indicated by minima that are close to zero.

The second indicator function is particularly interesting to verify pole multiplicity. It presents an minima when the system presents two closely spaced modes that are excited differently by the two inputs (this is the case near 1850 Hz in the figure). In this particular case, the two poles are sufficiently close to allow identification with a single pole with a modeshape multiplicity of 2 (see id_rm) or two close modes. More details about this example are given in [8].

This particular structure is not simply elastic (the FRFs combine elastic properties and sensor/actuator dynamics linked to piezoelectric patches used for the measurement). This is clearly visible by the fact that the first MIF does not go up to 1 between resonances (which does not happen for elastic structures).

At minima, the forces associated to the MMIF (eigenvector of [A] {u} q + [B] {u} = 0) tend to excite a single mode and are thus good candidates for force appropriation of this mode [52]. These forces are the second optional output argument ua.

CMIF

The Complex Mode Indicator Function (CMIF) (use the iicom showcmi command, see [53] for a thorough discussion of CMIF uses), uses the fact that resonances of lightly damped systems mostly depend on a single pole. By computing, at each frequency point, the singular value decomposition of the response

[H(s)]_NS × NA = [U]_NS × NS [Σ]_NS × NA [V^H]_NA × NA (9.15)

one can pick the resonances of Σ and use U₁,V₁ as estimates of modal observability / controllability (modeshape / participation factor). The optional u, v outputs store the left/right singular vectors associated to each frequency point.

AMIF

ii_mmif provides an alternate mode indicator function defined by

q(s) = 1−

|Im H(s)||H(s)|^T

|H(s)||H(s)|^T

(9.16)

which has been historically used in force appropriation studies [52]. Its properties are similar to those of the MMIF except for the fact that it is not formulated for multiple inputs.

This criterion is supported by iiplot (use iicom('show amif')).

SUM, SUMI, SUMA

Those functions are based upon the sum of data from amplitude of sensors for a given input.

SUM,

S(s,k) =

∑

||H_j,k(s)||²

is the sum of the square of all sensor amplitude for each input.

SUMI,

S(s,k) =

∑

Im(H_j,k(s))²

is the sum of the square of the imaginary part of all sensors for each input.

SUMA,

S(s,k) =

∑

||H_j,k(s)||

is the sum of the amplitude of all sensors for each input.

Those functions are sometimes used as mode indicator functions and are thus supported by ii_mmif (use iicom('show sumi') for example).

NODEMIF

Undocumented.

INTEGRATE

Integrates the frequency dependent signal

I_j,k(s) =

H_j,k(0)

s²

H_j,k(s)

DOUBLEINT

Integrates twice the frequency dependent signal

I2_j,k(s) =

H_j,k(0)

s³

H_j,k(s)

s²

VEL

Computes the velocity (first derivative) of the signal. For a frequency dependent signal

V_j,k(s) = s · H_j,k(s) .

For a time dependent signal, finite differences are used

V_j,k(t_n) =

H_j,k(t_n+1) − H_j,k(t_n)

t_n+1−t_n

V_j,k(t_end) is linearly interpolated.

ACC

Computes the acceleration (second derivative) of the signal. For a frequency dependent signal

A_j,k(s) = s² · H_j,k(s) .

For a time dependent signal, finite differences are used

A_j,k(t_n) =

h_n · (H_j,k(t_n+1) − H_j,k(t_n)) − h_n+1 · (H_j,k(t_n) − H_j,k(t_n−1))

· h_n · h_n+1

with h_n+1=t_n+1−t_n and h_n+1/2=h_n+h_n+1/2.

A_j,k(t_end) and A_j,k(t₁) are linearly interpolated.

FFT,FFTSHOCK

Computes the Discrete Fourier Transform of a time signal. FFT normalizes according to the sampling period whereas FFTSHOCK normalizes according to the length of the signal (so that it is useful for shock signal analysis). The command modifier -nostat can be used to remove static component (f=0) from fft response.

IFFT,IFFTSHOCK

IFFT and IFFTSHOCK are respectively the inverse operations of FFT and FFTSHOCK (see above) for frequency dependent signals.

BANDPASS

ii_mmif('BandPass fmin fmin fmax fmax') Performs a true bandpass filtering (i.e. using fft() and ifft()) between fmin and fmax frequencies.

OCTGEN, OCTAVE

filt=ii_mmif('OctGen nth',f) compute filters to perform a 1/nth octave analysis.

As many filters as frequencies at the 1/nth octave of 1000 Hz in the range of f (vector of frequencies) are computed. Each bandpass filter is associated to a frequency f₀ and a bandwidth Bw depending on f₀. Filters are computed so that their sum is almost equal to 1. Filter computed are, for each f₀ :

H(f,f₀) =

1+ (

Bw(f₀)

f²−f₀²

)⁶

With command modifier plot, filters are plotted.

ii_mmif('octave nth',ci) performs the 1/nth octave analysis of active curve displayed in iiplot figure.

The 1/nth octave analysis consists in applying each filter on the dataset. Energy in each filtered signal is computed with 10log(S) (where S is the trapezium sum of the filtered signal, or of the square of the filtered signal if it contains complex or negative values) and associated to the center frequency of corresponding filter.

See also

iiplot, iicom, idopt, fe_sens