daviddong 发表于 2006-2-20 20:33

关于PolyMAX的一点介绍,转载

本帖最后由 VibInfo 于 2016-4-21 14:22 编辑

  The LMS PolyMAX method is a further evolution of

  the least-squares complex frequency-domain (LSCF)

  estimation method. That method was fi rst introduced to

  fi nd initial values for the iterative maximum likelihood

  method . The method estimates a so-called commondenominator

  transfer function model . Quickly it

  was found that these “initial values” yielded already

  very accurate modal parameters with a very small

  computational effort . The most important

  advantage of the LSCF estimator over the available and

  widely applied parameter estimation techniques is the

  fact that very clear stabilization diagrams are obtained.

  A thorough analysis of different variants of the commondenominator

  LSCF method can be found in . A

  complete background on frequency-domain system

  identifi cation can be found in .

  It was found that the identifi ed common-denominator

  model closely fi tted the measured frequency response

  function (FRF) data. However, when converting this

  model to a modal model by reducing the residues to a

  rank-one matrix using the singular value decomposition

  (SVD), the quality of the fi t decreased .

  Another feature of the common-denominator

  implementation is that the stabilization diagram can only

  be constructed using pole information (eigenfrequencies

  and damping ratios). Neither participation factors nor

  mode shapes are available at fi rst instance . The

  theoretically associated drawback is that closely spaced

  poles will erroneously show up as a single pole.

  These two reasons provided the motivation for a

  polyreference version of the LSCF method, using a socalled

  right matrix-fraction model. In this approach, also

  the participation factors are available when constructing

  the stabilization diagram. The main benefi ts of the

  polyreference method are the facts that the SVD step

  to decompose the residues can be avoided and that

  closely spaced poles can be separated. The method was

  introduced in . Here we briefl y review the theory.

  Figure 7: Comparison of the measured FRFs (green/grey)

  with FRFs synthesized from the identifi ed modal model

  (black/red). (Top) Sensor at the wing tip; (Bottom) Sensor at

  the back of the plane.

  LMS PolyMAX: Theoretical

  Foundation

  Data model

  Just like the FDPI (Frequency-domain direct parameter

  identifi cation) method1 , the LMS PolyMAX method

  uses measured FRFs as primary data. Time-domain

  methods, such as the polyreference LSCE method2 ,

  typically require impulse responses (obtained as the

  inverse Fourier transforms of the FRFs) as primary

  data. In the LMS PolyMAX method, following so-called

  right matrix-fraction model is assumed to represent the

  measured FRFs:

  p p

  =sum (z ^r)*(sum (z ^r)^-1 (1)

  r=0 r=0

  where is the matrix containing the FRFs

  between all m inputs and all l outputs; are the

  numerator matrix polynomial coeffi cients; are

  the denominator matrix polynomial coeffi cients and is

  the model order. Please note that a so-called -domain

  model (i.e. a frequency-domain model that is derived from

  a discrete-time model) is used in (1), with:

  z=exp(-j.w.deltt) (2)

  where is the sampling time.

  Equation (1) can be written down for all values of the

  frequency axis of the FRF data. Basically, the unknown

  model coeffi cients are then found as the Least-

  Squares solution of these equations (after linearization).

  More details about this procedure can be found in.

  Poles and modal participation factors

  Once the denominator coeffi cients

  Poles and modal participation factors

  are determined,

  the poles and modal participation factors are retrieved

  as the eigenvalues and eigenvectors of their companion

  matrix:

  (3)

  The modal participation factors are the last m rows

  of ; the matrix contains the

  (discrete-time) poles on its diagonal. They are

  related to the eigenfrequencies and damping

  ratios [-] as follows ( •* denotes complex conjugate):

  (4)

  This procedure is similar to what happens in the

  time-domain LSCE method and allows constructing a

  stabilization diagram for increasing model orders

  and

  using stability criteria for eigenfrequencies, damping

  ratios and modal participation factors.

  Mode shapes

  Although theoretically, the mode shapes could be derived

  from the model coeffi cients , we proceed in a

  different way.

  The mode shapes can be found by considering the socalled

  pole-residue model:

  (5)

  where n is the number of modes; denotes complex

  conjugate transpose of a matrix; are the mode

  shapes; are the modal participation factors

  and are the poles (4). are respectively the

  lower and upper residuals modeling the infl uence of the

  out-of-band modes in the considered frequency band.

  The interpretation of the stabilization diagram yields a

  set of poles and corresponding participation factors

  Since the mode shapes and the lower and upper

  residuals are the only unknowns, they are readily obtained

  by solving (5) in a linear least-squares sense. This second

  step is commonly called least-squares frequency-domain

  (LSFD) method . The same mode-shape estimation

  method is normally also used in conjunction with the

  time-domain LSCE method.

  References

   VAN DER AUWERAER H., C. LIEFOOGHE, K.

  WYCKAERT AND J. DEBILLE. Comparative study of excitation

  and parameter estimation techniques on a fully equipped car.

  In Proceedings of IMAC 11, the International Modal Analysis

  Conference, 627–633, Kissimmee (FL), USA, 1–4 February 1993

   HEYLEN W., S. LAMMENS AND P. SAS. Modal Analysis

  Theory and Testing. Department of Mechanical Engineering,

  Katholieke Universiteit Leuven, Leuven, Belgium, 1995.

   LMS INTERNATIONAL. The LMS Theory and Background

  Book, Leuven, Belgium, 2000.

   LEMBREGTS F., J. LEURIDAN, L. ZHANG AND H.

  KANDA. Multiple input modal analysis of frequency response

  functions based direct parameter identifi cation. In Proceedings of

  IMAC 4, the International Modal Analysis Conference, 589–598,

  Los Angeles (CA), USA, 1986.

   LEMBREGTS F., R. SNOEYS AND J. LEURIDAN.

  Application and evaluation of multiple input modal parameter

  estimation. International Journal of Analytical and Experimental

  Modal Analysis, 2(1), 19–31, 1987.

   BROWN D.L., R.J. ALLEMANG, R. ZIMMERMAN AND

  M. MERGEAY. Parameter estimation techniques for modal

  analysis. Society of Automotive Engineers, Paper No. 790221,

  1979.

   GUILLAUME P., P. VERBOVEN AND S. VANLANDUIT.

  Frequency-domain maximum likelihood identifi cation of modal

  parameters with confi dence intervals. In Proceedings of ISMA

  23, the International Conference on Noise and Vibration

  Engineering, Leuven, Belgium, 16–18 September 1998.

   GUILLAUME P., R. PINTELON AND J. SCHOUKENS.

  Parametric identifi cation of multivariable systems in the

  frequency domain - a survey. In Proceedings of ISMA 21, the

  International Conference on Noise and Vibration Engineering,

  1069–1082, Leuven, Belgium, 18–20 September 1996.

   VAN DER AUWERAER H., P. GUILLAUME, P.

  VERBOVEN AND S. VANLANDUIT. Application of a faststabilizing

  frequency domain parameter estimation method.

  ASME Journal of Dynamic Systems, Measurement, and Control,

  123(4), 651–658, 2001.

   VERBOVEN, P. Frequency domain system identifi cation for

  modal analysis. PhD Thesis, Vrije Universiteit Brussel, Belgium,

  2002.

   PINTELON R. AND J. SCHOUKENS. System

  Identifi cation: a Frequency Domain Approach. IEEE Press, New

  York, 2001.

   GUILLAUME P., P. VERBOVEN, S. VANLANDUIT, H.

  VAN DER AUWERAER AND B. PEETERS. A poly-reference

  implementation of the least-squares complex frequency-domain

  estimator. In Proceedings of IMAC 21, the International Modal

  Analysis Conference, Kissimmee (FL), USA, February 2003.

   PEETERS B., P. GUILLAUME, H. VAN DER AUWERAER,

  B. CAUBERGHE, P. VERBOVEN AND J. LEURIDAN.

  Automotive and aerospace applications of the LMS PolyMAX

  modal parameter estimation method. In Proceedings of IMAC

  22, Dearborn (MI), USA, January 2004.

  呵呵:)谁想要原文,发email给我吧。

  daviddongsw007@163.com

daviddong 发表于 2009-8-21 09:54

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[ 本帖最后由 daviddong 于 2009-8-21 09:56 编辑 ]

chjchchjch 发表于 2010-11-9 08:52

⊙﹏⊙b汗,,怎么下不下来啊……

yangtzebin 发表于 2010-12-15 09:47

何必搞得这么玄乎,随处可见的一篇文章,见LMS公司官网:
http://www.lmsintl.com/download.asp?id=8397BE61-F019-4DE2-B365-BB6AC320A776
题目如下:PolyMAX:A Revolution in Modal Parameter Estimation

mxlzhenzhu 发表于 2013-10-11 13:19

多谢楼上的指引!

navoleon 发表于 2014-3-9 17:22

好东西!!!!!!!!!!!!!

navoleon 发表于 2014-3-9 17:23

谢谢楼主!!!!!!!!!!!!!!

navoleon 发表于 2014-3-9 17:23

谢谢!!!!!!!!!!!!!!!!!!!!!!!
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