OPTIMAL STAGGERED PULSE EXCITING TECHNIQUE OF

OPTIMAL STAGGERED PULSE EXCITING TECHNIQUE OF
MODAL TESTING DESIGN

Ren Hui Cheng Bingxun Wu Ya Fag
Data Pmcessing Center
Data Processing Center
Northwestern Polytechnical University Northwestern Polytechnical University

Xi’m, 710072, P.R. China Xi’an, 710072, P.R. China

ABSTRACT flight flutter testing, however DSP is limited because
of the complicated response data with lower SNR and
This paper preznts an improving exciting technique closer modes. And then the other instrumental a.~
proaches are hoped, one of which is testing design.
(ref.% to optimal staggered pulse), which is siutable The triditional pulse exciting is usually used in single-
point or multi-paints at the same time, which is not
for stressing the interesting mcdes. Fisher information suitable for strwing the beresting modes. OptimaI
testing design techniques can be used to overcome
matrix and the D-optimaI testing design criterion are these shortcomings in a degree[l ,2]. Many methcds
were proprxed according to different testing purpose
proposed based on the finite element caculation. In [3,4,5]. The centrical question of the design prc-
multi-pints exciting, the optimal input delay of stag- gram aim at selecting a p*ope* cat function o* infor-
mation criterion from the view of tberetical point.
gered pulse is deduced and the corresponding charac- ln this paper, a constrained plate model far imitating
teristics are discussed by using the numerical simula- cantilever wing is used to engage in parameters identi-
tion. fication testing design. A finite element model is ap
plied to modeling. By introducing Fisher optimization
NOMENCLATURE theory, we conducted optimal design of delay time for
multi-input and enabled the Fisher information maxi-
(Xl displacement vector mum. In a physical sense, selecting appropriate delay
time facor, the energy of multi-exciting signaI are ef-
1:; [Cl input distributed matrix ficiently distributed to every interesting modes. The
CM]. [K], input “e&or main thewy deduction is given, and the simulation
[“I and testing results are presented.
mass, stiffness, damping matrices
WI medal damping matrix 2. THE OF.TIMti STAGGERED PULSE DESIGN
modal frequency m&ix
di In m&l analysis pmcw, the proper approximate
la components of matrix D models are needed for different problems. As a effi-
tqJ cient tool, the finite element analysis is usually used
components of matrix W to build the mcdel of structuraI system which general-
EOl ly has a distributed pwameter representation. And the
a vector of N flexible body modal infinite dimensional system may be approximated by a
Q amplitudes constant coefficient differential medal with finite di-
N mension , as expressed following :
modaI matrix
M components of matrix [0] where ( X)N is the system’ s displacement vector,
u* Number of mcdes included [B& is input distzibuted matrix, (U)x is input vet-
ear. CM&,XN, [C]w.w and [K&w are the mass ma-
$(“) Numb-s of sensors
the optimal input design
b(t)
ihl the optimal sensot placement design
h,(t)
lQ) matrix in Eq. (10)
CT]
kmnecker delta function
vscto* of sense* nxasure.me”t

cornpenmts of vector(h)

“ecto* of paranleters
Fisner information matrix

1. LVTRODUCTION

As u’e know, the medal analysis are greatly prom&xi
with me&In digital signal processing (DSP) tech-
nique developing. For some vibration testings such as

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trix, damping matrix, and stiffness matrix *espzc-
tively.

Let [@lNm be the normalized eigenvector matrix (et.
medal matrix), such that

(12)

where [ D ] = d> , [WI =

L d NXN

\ are diagonal matrices containing the Optimal dcsim p*og?am can b.z achived by selecting
m
the sense* placements the sense* number, exciting
L J NXN is the medal signal and d&y time of signa etc. The plate model
modal damping and frequenciw. [0&
imitating a cantilever wing is considered here to exe-
matrix of the st*uctu*e. It is a.sswned that there a*e M cute the optimal staggered pulse exciting design. lt is

se”sors and the meas”*e,,,ent he, k = 1, . ..M has the assumed that input signal is consisted of two pulse av
follows
form

(u) = bl6ctl a26ct-T))T (13)

where {V,C)~ is the vecto* associated with the location Applying the criterion (8) and (10) to the problem
of the Kth sense*, and nk (t) is a white Gau&an yields

noise p*wxss , J”CuI=J~(u) (14)

(5) II* =Arg 7 J”(u)

A vecto* of parmeters (f~) m is defined as from (11) yields

{~)~~=[~~,d,.....~.d~lT (6)

The Fisher Information Matrix T is given as follows Figure 1 indicate the variation of fisher information
value. it is seen that the information vahx is max.
[II: mutn in 17ms. this is the ease when calculating the
two medal together. Gmsidering the first mc&l
CT]= I( +)r[‘S’-z( +)dt alone, the maximum F&e* information value is in
~b)~=Cb~.....h~)r 16ms. A nunbe* of peaks appzar when considering
(7) the second modal alone. thus the optimal delay time 7
r\ 1 is given.

The criteria for optimal testing design a*e defined as 3. SIMULATION AND MODEL TFSTIGN
the maximum determinant of the Fisher matrix. For
light damping system, the optimal input design II. Figure 2 is the mcde shape of the first two modes.
and optimal sense* placement design f3* can be inde- We are only interested in these two mcdes. We select
padent& given as[5] 19” point and 9” point as both exciting and nwsw-
ing points. 19’ is at the maximum of the first mcde
(10) shap and near the node of the second mode. 9’ is at
the maximum of the second mcde and near the node
of the first mode. The forced vibration *espouse of
the system is computed. the 19” is first excited and
the 9” is excited after delay time T. table 1 indicate
the pak vallle of pave* spectrum of system *eapo”se

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when the delay time T is equal to the different value. ABLE 1
When the T is near 18ms. the perk value for the sects
and modal is maximum and ihe peak value for the
fiW modal is maximum a3 the r is near the 16ms.
The experiment system blxk diagram is presented in
?igure 3. The sensor date are processed by CF920 and
?he power spectra are given. Table 1 contain the mea-
sured peak value of power spectra. It is seen that
when the two points are excited simultanieously, only
:he first modal energy is enhanced. The first modal
energy is larger when the ? is near the 16. 2ms. The
second medal energy is larger when the T is near the
1% 2ms. Besides the two modal energy is all chanced
to some extent when the ‘r is at 18. 2ms. this agree
well with the situation in which two modal are consid-
ered simultaneously to cornput the overall fisher in-
formation value in figure I. thus by selecting differ-
ent delay time, it is enabled that the distribution of
excfting energy for the each rntial will be changed.

4. CONCLUSION

Starting from the Fisher information theory, we have
obtained the variation trend of the modal information
with the delay factor r. And the optimal criterion of r
has been given. Simulation results agee wjth the
analytical results. And the testing results manifest the
theory and the calculation. It has been indicated that
the exciting energy are efficiently distributed into in-
westin modes as the 7 js chosen appropriately.

5. REFERENCES

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variation of Fisher information for the two nxdes

T FQ.. 2 the mcde shape of the first two mcdes

;m l/II/II

0. 02 SW.

r=o. 016

variation of Fisher information for the first mcde

variation of Fisher hformation for the second male Fig. 3 experiment system block diagram
Fig. I variation of Fisher information

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