Updating large models for mechanical systems using incomplete modal measurement

Abstract The problem of model updating for mechanical or structural systems is addressed by using incomplete modal measurement. The proposed method requires only the modal frequencies and mode shapes at some selected degrees of freedom for a few modes. The method updates the mass and stiffness matrix without imposing any parameterization and it utilizes the information from both the nominal finite-element model and the modal data. The method is computationally efficient as neither iteration nor numerical optimization is required. It does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the ones corresponding to the observed modes are needed. The method first updates the modal frequencies. Then, an efficient algorithm is presented to construct a transformation matrix. This matrix is used to correct the nominal eigenvectors so that the updated model is compatible with the measurement of the eigenvectors. A twelve-degree-of-freedom truss is used to provide insights of the proposed method. Finally, a 1600-degree-of-freedom spring-mass system is considered to illustrate the efficiency of the proposed method for large structure.

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

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

[3]  Yi-Qing Ni,et al.  Adaptive regularization parameter optimization in output-error-based finite element model updating , 2009 .

[4]  Biswa Nath Datta,et al.  Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach , 2010 .

[5]  Mark Milman,et al.  Mode shape expansion techniques for prediction : Experimental evaluation , 1996 .

[6]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[7]  James L. Beck,et al.  Structural Health Monitoring via Measured Ritz Vectors Utilizing Artificial Neural Networks , 2006, Comput. Aided Civ. Infrastructure Eng..

[8]  Raimondo Betti,et al.  Structural Health Monitoring of Bridge Cables , 2009 .

[9]  James L. Beck,et al.  Monitoring Structural Health Using a Probabilistic Measure , 2001 .

[10]  Yi-Qing Ni,et al.  Structural Damage Detection of Cable-Stayed Bridges Using Changes in Cable Forces and Model Updating , 2009 .

[11]  James L. Beck,et al.  Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies , 2004 .

[12]  James L. Beck,et al.  Statistical System Identification of Structures , 1989 .

[13]  Ka-Veng Yuen,et al.  Efficient Model Correction Method with Modal Measurement , 2010 .

[14]  Congbo Li,et al.  A system theory approach to multi-input multi-output modal parameters identification methods , 1994 .

[15]  J. Ko,et al.  Localization of damaged structural connections based on experimental modal and sensitivity analysis , 1998 .

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

[17]  James L. Beck,et al.  New Bayesian Model Updating Algorithm Applied to a Structural Health Monitoring Benchmark , 2004 .

[18]  S. Liu.  Improvement of analytical dynamic models using complex modal test data , 1992 .

[19]  Lambros S. Katafygiotis,et al.  Bayesian time–domain approach for modal updating using ambient data , 2001 .

[20]  A. Berman,et al.  Improvement of analytical dynamic models using modal test data , 1980 .

[21]  Yi-Qing Ni,et al.  Constructing input vectors to neural networks for structural damage identification , 2002 .

[22]  R. B. Testa,et al.  Modal Analysis for Damage Detection in Structures , 1991 .

[23]  Silian Lin,et al.  Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data , 2004 .

[24]  Ka-Veng Yuen,et al.  On the complexity of artificial neural networks for smart structures monitoring , 2006 .

[25]  Jer-Nan Juang,et al.  An Eigensystem Realization Algorithm in Frequency Domain for Modal Parameter Identification , 1986 .

[26]  M. Hoshiya,et al.  Structural Identification by Extended Kalman Filter , 1984 .

[27]  H. Du,et al.  Improved Inverse Eigensensitivity Method for Structural Analytical Model Updating , 1995 .

[28]  Lambros S. Katafygiotis,et al.  Efficient model updating and health monitoring methodology using incomplete modal data without mode matching , 2006 .

[29]  Lambros S. Katafygiotis,et al.  Bayesian modal updating using complete input and incomplete response noisy measurements , 2002 .

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