Finite Element Model Updating in Structural Dynamics
The Finite Element Method is used extensively to model the dynamics of structures and with care is capable of producing accurate results. Often the inaccuracies in the model will arise because of poorly known boundary conditions, unknown material properties or simplification in the modelling. For example, welded or bolted joints will not be rigid but have a finite stiffness which is difficult to predict. Or a plate containing numerous small holes may be approximated by a homogenous plate. These uncertainties in the modelling process cause the predicted dynamics of a structure to be different from the measured dynamics of the real structure. If accurate measured data is available then this data could be used to improve the numerical model in general, and the uncertain parameters of the model in particular. This is model updating.
Recently there has been considerable interest in model updating and a large number of techniques have been proposed. Broadly speaking the methods may be split according to the type of measured data they use and model parameters that are updated. The measured data may be in form of frequency response function (FRF) data or natural frequencies and mode shapes. The updating process may estimate physical parameters, complete mass, damping and stiffness matrices or groups of individual matrix elements. Research so far has concentrated on updating physical parameters using either FRF or modal data. Other aspects of model updating, such as parameter uniqueness, efficient computation, parameterisation, ill-conditioning and the use of incomplete data, are being investigated. The measured data will always be incomplete because the measurements will only be taken at a relatively small number of locations and over a limited frequency range. Issues of parameter uniqueness arise because an infinite number of parameter values can often give rise to identical measured data. The equations to identify the parameters directly will often be ill conditioned and the original finite element model is used to provide extra information and to update the parameters. The process of identification from poorly conditioned equations is called regularization.
One major challenge is to apply the technology to practical problems with a large number of degrees of freedom. Hence the need for computationally efficient programs is growing. Furthermore the key to success in model updating is the choice of parameters. These should be chosen so that the measured data is sensitive to changes in the parameters, but also there should be some indication that there may be modelling errors in the corresponding regions of the model. Good predictability of the updated model depends on choosing a small number of the most important parameters. Modelling joints is particular difficult, and equivalent models for these, often using geometric or generic parameterisations, is a significant application area.
Recently the quantification of parameter uncertainty has become an important research topic. Production techniques require that many structures made to a particular design are nominally identical. However samples taken on real structures demonstrate that there will be a significant variability from structure to structure. As for deterministic model updating, the parameters that model joints cannot be measured directly. Thus if measurements are made on multiple structures, the uncertainty in the parameters may be identified, leading to the concept of stochastic model updating and uncertainty quantification.
The papers listed below give more information.
Book and Survey Paper
Methods and General Papers
- M Link & MI Friswell, Generation of Validated Structural Dynamic Models - Results of a Benchmark Study Utilising the GARTEUR SM-AG19 Testbed. Mechanical Systems and Signal Processing, COST Action Special Issue, 17(1), January 2003, 9-20.
- C Mares, JE Mottershead & MI Friswell, Results Obtained by Minimising Natural-Frequency Errors and using Physical Reasoning. Mechanical Systems and Signal Processing, COST Action Special Issue, 17(1), January 2003, 39-46.
- C Mares, MI Friswell & JE Mottershead, Model Updating using Robust Estimation. Mechanical Systems and Signal Processing, 16(1), January 2002, 169-183.
- JK Sinha & MI Friswell, Model Updating: A Tool for Reliable Modelling, Design Modification and Diagnosis. Shock and Vibration Digest, 34(1), January 2002, 25-33.
- H Ahmadian, JE Mottershead & MI Friswell, Boundary Condition Identification by Solving Characteristic Equations. Journal of Sound and Vibration, 247(5), November 2001, 755-763.
- U Prells & MI Friswell, Application of the Variable Projection Method for Updating Models of Mechanical Systems. Journal of Sound and Vibration, 225(2), August 1999, 307-325.
- MI Friswell, DJ Inman & DF Pilkey, The Direct Updating of Damping and Stiffness Matrices. AIAA Journal, 36(3), March 1998, 491-493.
- JE Mottershead & MI Friswell (Guest Eds.), Model Updating, Special Issue of Mechanical Systems and Signal Processing, 12(1), January 1998.
- MI Friswell, Candidate Reduced Order Models for Structural Parameter Estimation. ASME Journal of Vibration and Acoustics, 112(1), January 1990, 93-97.
- MI Friswell & JET Penny, Updating Model Parameters from Frequency Domain Data via Reduced Order Models. Mechanical Systems and Signal Processing, 4(5), September 1990, 377-391.
- MI Friswell, The Adjustment of Structural Parameters using a Minimum Variance Estimator. Mechanical Systems and Signal Processing, 3(2), April 1989, 143-155.
- MI Friswell, JE Mottershead & H Ahmadian, Finite Element Model Updating using Experimental Test Data: Parameterization and Regularization. Transactions of the Royal Society of London, Series A, Special Issue on Experimental Modal Analysis, 359(1778), January 2001, 169-186.
- MJ Terrell, MI Friswell & NAJ Lieven, Constrained Generic Substructure Transformations. Journal of Sound and Vibration, 300(1-2), February 2007, 265-279.
- H Ahmadian, JE Mottershead, S James, MI Friswell & CA Reece, Modelling and Updating of Large Surface-to-Surface Joints in the AWE MACE Structure. Mechanical Systems and Signal Processing, 20(4), May 2006, 868-880.
- M Palmonella, MI Friswell, JE Mottershead & AW Lees, Finite Element Models of Spot Welds in Structural Dynamics: Review and Updating. Computers & Structures, 83(8-9), March 2005, 648-661.
- M Palmonella, MI Friswell, JE Mottershead & AW Lees, Guidelines for the Implementation of the CWELD and ACM2 Spot Weld Models in Structural Dynamics. Finite Elements in Analysis and Design, 41(2), November 2004, 193-210.
- JL Zapico, MP Gonzalez, MI Friswell, CA Taylor & AJ Crewe, Finite Element Model Updating of a Small Scale Bridge. Journal of Sound and Vibration, 268(5), December 2003, 993-1012.
- H Ahmadian, JE Mottershead & MI Friswell, Physical Realisation of Generic Element Parameters in Model Updating. Journal of Vibration and Acoustics, 124(4), October 2002, 628-633.
- JE Mottershead, C Mares, MI Friswell & S James, Selection and Updating of Parameters for an Aluminium Space-Frame Model. Mechanical Systems and Signal Processing, 14(6), November 2000, 923-944.
- JK Sinha and MI Friswell, The Use of Model Updating for Reliable Finite Element Modelling and Fault Diagnosis of Structural Components Used in Nuclear Plants. Nuclear Engineering and Design, 223(1), July 2003, 11-23.
- JE Mottershead, MI Friswell & C Mares, A Method for Determining Model-Structure Errors and for Locating Damage in Vibrating Systems. Meccanica, 34(3), August 1999, 153-166.
- JE Mottershead, MI Friswell, GHT Ng & JA Brandon, Geometric Parameters for Finite Element Model Updating of Joints and Constraints. Mechanical Systems and Signal Processing, 10(2), March 1996, 171-182.
- B Titurus & MI Friswell, Regularization in Model Updating. International Journal for Numerical Methods in Engineering, 75(4), July 2008, 440-478.
- H Ahmadian, JE Mottershead & MI Friswell, Regularisation Methods for Finite Element Model Updating. Mechanical Systems and Signal Processing, 12(1), Januray 1998, 47-64.
- MI Friswell, JE Mottershead & H Ahmadian, Combining Subset Selection and Parameter Constraints in Model Updating. Journal of Vibration and Acoustics, 120(4), October 1998, 854-859.
- U Prells, AW Lees, MI Friswell & MG Smart, Minimisation of the Effect of Uncertainty on Model Estimation. Mechanical Systems and Signal Processing, 12(2), March 1998, 333-355.
- NG Nalitolela, JET Penny & MI Friswell, Updating Model Parameters by Adding an Imagined Stiffness to the Structure. Mechanical Systems and Signal Processing, 7(2), March 1993, 161-172.
- NG Nalitolela, JET Penny & MI Friswell, A Mass or Stiffness Addition Technique for Structural Parameter Updating. International Journal of Analytical and Experimental Modal Analysis, 7(3), July 1992, 157-168.
- S Adhikari, MI Friswell, K Lonkar & A Sarkar, Experimental Case Studies for Uncertainty Quantification in Structural Dynamics. Probabilistic Engineering Mechanics. to appear.
- HH Khodaparast, JE Mottershead & MI Friswell, Perturbation Methods for the Estimation of Parameter Variability in Stochastic Model Updating. Mechanical Systems and Signal Processing, 22(8), November 2008, 1751-1773.
- JE Mottershead, C Mares, S James & MI Friswell, Stochastic Model Updating: Part 2 - Application to a Set of Physical Structures. Mechanical Systems and Signal Processing, 20(8), November 2006, 2171-2185.
- C Mares, JE Mottershead & MI Friswell, Stochastic Model Updating: Part 1 - Theory and Simulated Example. Mechanical Systems and Signal Processing, 20(7), October 2006, 1674-1695.
- JR Fonseca, MI Friswell, JE Mottershead & AW Lees, Uncertainty Identification by the Maximum Likelihood Method. Special Issue of the Journal of Sound and Vibration on Uncertainty, 288(3), December 2005, 587-599.
Last updated February 2009 by MI Friswell