Parameter selection and covariance updating

A simple expression is developed for covariance-matrix correction in stochastic model updating. The need for expensive forward propagation of uncertainty through the model is obviated by application of a formula based only on the sensitivity of the outputs at the end of a deterministic updating process carried out on the means of the parameters. Two previously published techniques are show to reduce to the same simple formula within the assumption of small perturbation about the mean. It is shown, using a simple numerical example, that deterministic updating of the parameter means can result in correct reconstruction of the output means even when the updating parameters are wrongly chosen. If the parameters are correctly chosen, then the covariance matrix of the outputs is correctly reconstructed, but when the parameters are wrongly chosen is found that the output covariance is generally not reconstructed accurately. Therefore, the selection of updating parameters on the basis of reconstructing the output means is not sufficient to ensure that the output covariances will be well reconstructed. Further theory is then developed by assessing the contribution of each candidate parameter to the output covariance matrix, thereby enabling the selection of updating parameters to ensure that both the output means and covariances are reconstructed by the updated model. This latter theory is supported by further numerical examples.

[1]  Jérôme Antoni,et al.  A comprehensive Bayesian approach for model updating and quantification of modeling errors , 2011 .

[2]  Jm M. Ko,et al.  An improved perturbation method for stochastic finite element model updating , 2008 .

[3]  J. Beck,et al.  Updating Models and Their Uncertainties. I: Bayesian Statistical Framework , 1998 .

[4]  Michael Link,et al.  Stochastic model updating—Covariance matrix adjustment from uncertain experimental modal data , 2010 .

[5]  M. Friswell,et al.  Perturbation methods for the estimation of parameter variability in stochastic model updating , 2008 .

[6]  Sondipon Adhikari,et al.  Distributed parameter model updating using the Karhunen–Loève expansion , 2010 .

[7]  Michael Link,et al.  Using stochastic experimental modal data for identifying stochastic finite element parameters of the AIRMOD benchmark structure , 2012 .

[8]  J. Mottershead,et al.  Interval model updating with irreducible uncertainty using the Kriging predictor , 2011 .

[9]  John E. Mottershead,et al.  A comparison of two stochastic model updating methods using the DLR AIRMOD test structure , 2015 .

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

[11]  Ricardo Perera,et al.  A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation , 2012 .

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

[13]  John E. Mottershead,et al.  The sensitivity method in finite element model updating: A tutorial (vol 25, pg 2275, 2010) , 2011 .

[14]  J. Beck,et al.  UPDATING MODELS AND THEIR UNCERTAINTIES. II: MODEL IDENTIFIABILITY. TECHNICAL NOTE , 1998 .

[15]  Ricardo Perera,et al.  Damage identification by response surface based model updating using D-optimal design , 2011 .

[16]  Gerhart I. Schuëller,et al.  A stochastic model updating technique for complex aerospace structures , 2011 .

[17]  Sondipon Adhikari,et al.  A second-moment approach for direct probabilistic model updating in structural dynamics , 2012 .

[18]  Helmut J. Pradlwarter,et al.  Robust model updating with insufficient data , 2009 .

[19]  J.E. Mottershead,et al.  Stochastic model updating: Part 2—application to a set of physical structures , 2006 .

[20]  John E. Mottershead,et al.  Stochastic model updating: Part 1—theory and simulated example , 2006 .

[21]  Tshilidzi Marwala,et al.  Model selection in finite element model updating using the Bayesian evidence statistic , 2011 .

[22]  J. D. Collins,et al.  Statistical Identification of Structures , 1973 .