Model updating

Initially, the FE model of a structure is developed during design stages and will be used to predict the dynamic behaviour of the structure before fabrication of the structure. Once the structure is fabricated, then modal testing can be performed and the measured data are compared with its finite element model counterparts.

Understandably, finite element prediction is not always in good agreement with the experimental results because of limitation in the method which is merely based on assumption such as approximation of boundary condition, physical properties of the structure and meshing process. Therefore, the finite element prediction is not always reconciled with the experimental results.

In modal testing, the measurement of the modal properties such as natural frequencies, mode shapes and modal damping are obtained directly from a real structure. Therefore the experimental results are considered to be more reliable than those obtained from finite element model. Model updating is normally used to improve the correlation between finite element model and physical model by correcting the uncertainties in the model properties and boundary conditions of the finite element model. The basic principles of correlation that are applied to finite element model updating are to utilise advantages of the experimental data to correct the modal properties of the finite element model.

Model updating methods have been developed by a number of researchers over past 25 years (Zang et al., 2006b). Understandably, finite element model updating methods can be classified into two categories, namely one step methods and iterative methods (Brownjohn and Xia, 2000). Historically, the one step procedure of model updating is mainly based on a trial and error approach where the adjustments of physical parameters of the finite element model are done manually. Even though one step procedure offers less computational effort, however it highly depends on the individual’s engineering judgement and experience. On the other hand it must be ensured that the most sensitive parameters are selected in the updating process.

In one step procedure, the updated mass and stiffness matrices that are regenerated from the response data are often not guaranteed to preserve the attributes of the finite element model. The values of the updated parameters used in the procedure cannot be controlled systematically and sometimes they may lose their physical meaning (Mottershead et al., 2011). However, one step procedure for model updating has become more difficult to be implemented, and more systematic approaches are required due to the increasing of complexity of the structures.

Alternatively, the iterative methods based on response sensitivity has appeared to be more popular due to its flexibility by allowing a wide choice of updating parameters and at the same time the physical meaning of updated finite element model are well preserved. In the iterative methods, the choice of algorithms with respect to the updating process is essential. This approach generally depends on minimising errors between the finite element model and experimental data as an objective function by making changes to the pre-selected set of the parameters of the finite element model (Modak et al., 2002a).

Most optimisation problems have constraints. For example, in the gradient based method, the constraints are defined through upper and lower bounds. A number of iterations of the respective system have to be computed to find an optimum value which has important influence on the produced result and the solution or set of solutions which are obtained as the final result of an evolutionary search must necessarily be feasible to satisfy all constraints. However, problems may occur if the objective function has several local minimums, which may cause not only intensive computation but also difficulty to converge due to ill conditioning (Khoo and Chen, 2001). The potential of probabilistic search algorithms such as genetic algorithm (GA), response surface method (RSM) etc, has been explored for model updating Levin and Lieven (1998) and Marwala (2004).

The RSM is modelling method that looks at various design variables and their response and identify the combination of design variables that give the best response. RSM attempts to replace implicit functions of the original design optimisation problem with an approximation model, which traditionally is polynomial and therefore is less expensive to evaluate (Pula and Bauer, 2007). This makes RSM useful in finite element model updating because to match measured data based on the traditional optimisation methods such as gradient methods is computationally expensive and often encounters numerical problems such as ill conditioning in the search of global minimum (Zabel and Brehm, 2009). RSM tends to be immune from such problems. This is largely because RSM is a crude approximation of the FE model rather than the full FE model which is of high dimensional order.

The GA works on the principle of genetic and natural selection based on Darwin’s survival fitness strategy where the dominant members of population will compete with each other to survive and reproduce successfully. As a result, the combination of genes that confers this advantage is likely to breed successfully. Therefore GA has a higher probability of identifying a global optimum solution than gradient based approach However the main drawback with the GA is slow convergence speed at which solution is arrived at, making difficult to implement for a large–scale structure and furthermore, and it contains many choice and parameters that need to be selected Brian and Mark (1999) and Marwala (2010).