A direct method for model updating with incomplete measured data and without spurious modes

This paper presents a new method for finite element matrix updating problem in an undamped model. This method has a computationally convenient feature of handling the difficulty of the incomplete measured data in an algorithmic way without using standard modal expansion or reduction techniques. The completed eigenvector matrix is such that it is mass normalised with respect to the analytical mass matrix. The method is also capable of preserving the large number of eigenvalues and eigenvectors of the finite element model that are not affected by updating. The latter has an effect of preventing the appearance of spurious modes in the frequency range of interest, which is a common concern with most direct updating methods. r 2007 Elsevier Ltd. All rights reserved.

[1]  Alex Berman.  Inherently Incomplete Finite Element Model and Its Effects on Model Updating , 2000 .

[2]  David C. Zimmerman,et al.  Correcting finite element models using a symmetric eigenstructure assignment technique , 1990 .

[3]  Theodore Bartkowicz,et al.  DAMAGE DETECTION AND HEALTH MONITORING OF LARGE SPACE STRUCTURES , 1993 .

[4]  B. Datta.  Numerical Linear Algebra and Applications , 1995 .

[5]  M. Friswell,et al.  Direct Updating of Damping and Stiffness Matrices , 1998 .

[6]  Sylvan Elhay,et al.  POLE ASSIGNMENT IN VIBRATORY SYSTEMS BY MULTI-INPUT CONTROL , 2000 .

[7]  Izhak Bucher,et al.  The structural modification inverse problem: an exact solution , 1993 .

[8]  K. S. Smith,et al.  Faster, easier finite element model reduction , 1999 .

[9]  Fu-Shang Wei,et al.  Analytical dynamic model improvement using vibration test data , 1990 .

[10]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[11]  Richard Rebarber.  Feedback Control in Distributed Parameter Systems , 1990 .

[12]  Biswa Nath Datta,et al.  Feedback Control in Distributed Parameter Gyroscopic Systems: A Solution of the Partial Eigenvalue A , 2001 .

[13]  H. S. Wolff,et al.  iRun: Horizontal and Vertical Shape of a Region-Based Graph Compression , 2022, Sensors.

[14]  D. Kammer.  Optimum approximation for residual stiffness in linear system identification , 1988 .

[15]  Biswa Nath Datta,et al.  Symmetry preserving eigenvalue embedding in finite-element model updating of vibrating structures , 2006 .

[16]  Etienne Balmes,et al.  Sensors, degrees of freedom, and generalized modeshape expansion methods , 1999 .

[17]  Gene H. Golub,et al.  Matrix computations , 1983 .

[18]  D. Kammer.  Correlation considerations. Part 2: Model reduction using modal, SEREP, and hybrid , 1998 .

[19]  B. Datta.  Numerical methods for linear control systems : design and analysis , 2004 .

[20]  John E. Mottershead,et al.  Model Updating In Structural Dynamics: A Survey , 1993 .

[21]  Michael Link,et al.  UPDATING ANALYTICAL MODELS BY USING LOCAL AND GLOBAL PARAMETERS AND RELAXED OPTIMISATION REQUIREMENTS , 1998 .

[22]  Daniel J. Inman,et al.  Matching Analytical Models with Experimental Modal Data in Mechanical Systems , 1990 .

[23]  Biswa N. Datta,et al.  Contemporary Mathematics Theory and Computations of Some Inverse Eigenvalue Problems for the Quadratic Pencil , 2007 .

[24]  A. Kabe.  Stiffness matrix adjustment using mode data , 1985 .

[25]  Yoram Halevi,et al.  MODEL UPDATING IN STRUCTURAL DYNAMICS: A GENERALISED REFERENCE BASIS APPROACH , 1998 .

[26]  B. Datta,et al.  ORTHOGONALITY AND PARTIAL POLE ASSIGNMENT FOR THE SYMMETRIC DEFINITE QUADRATIC PENCIL , 1997 .

[27]  Paul Van Dooren,et al.  A rational Lanczos algorithm for model reduction , 1996, Numerical Algorithms.

[28]  Izhak Bucher,et al.  Model updating via weighted reference basis with connectivity constraints , 2003 .

[29]  Wei-Xin Ren,et al.  Damage detection by finite element model updating using modal flexibility residual , 2006 .

[30]  M. Baruch.  Optimization Procedure to Correct Stiffness and Flexibility Matrices Using Vibration Tests , 1978 .

[31]  Wen-Wei Lin,et al.  THE SPILLOVER PHENOMENON IN QUADRATIC MODEL UPDATING DRAFT AS OF August 3 , 2006 , 2005 .

[32]  F. Hemez,et al.  Updating finite element dynamic models using an element-by-element sensitivity methodology , 1993 .

[33]  David C. Zimmerman,et al.  Structural Health Monitoring of Large Structures , 1994 .

[34]  ScienceDirect.  Mechanical systems and signal processing , 1987 .

[35]  Yueh-Cheng Kuo,et al.  A New Model Updating Method for Quadratic Eigenvalue Problems , 2009 .

[36]  David J. Ewins,et al.  Adjustment or updating of models , 2000 .

[37]  Alex Berman,et al.  Optimal weighted orthogonalization of measured modes , 1979 .

[38]  Christopher Beattie,et al.  Optimal matrix approximants in structural identification , 1992 .

[39]  Olof Friberg,et al.  Updating Large Finite Element Models in Structural Dynamics , 1998 .

[40]  A. Berman,et al.  Improvement of a Large Analytical Model Using Test Data , 1983 .

[41]  M. Link,et al.  Updating of Analytical Models — Basic Procedures and Extensions , 1999 .

[42]  Menahern Baruch,et al.  Optimal Weighted Orttiogonalization of Measured Modes , 1978 .