FEMtools Model Updating

FEMtools Model Updating contains tools for:

• Sensitivity Analysis – Analyses how changes of parameters influences the structural responses. This in formation can be used for different applications including model updating.

• Model Updating – Iteratively changes updating parameters to make the structure better match the target responses.

• Harmonic Force Identification – Identifies harmonic loads from operational shapes.

• Probabilistic Analysis – Applies uncertainty to parameters to obtain probability distribution on output responses.

• What-If analysis - Study the effect of modeling assumptions on the modal parameters or on other response types.

• Variational Analysis - Find the relation between design variables and responses in the entire design space.

• Pretest analysis - Sensitivity analysis can be used in pretest planning applications like studying the effect of transducer mass loading on the modal parameters.

• Identify sensitive and insensitive areas of the structure for given response and parameter combinations - This will help the analyst to decide which parameters and responses to include in the selection for model updating.

• Model updating - The sensitivity matrix is inverted to find a gain matrix. This gain matrix is multiplied with the difference between predicted and reference response values to find the required parameter change to compensate for this error.

• Design optimization - Find the optimal locations to modify the structure in order to shift modal parameter values or other response types.

• Acoustic sensitivities - Structural sensitivities computed with FEMtools can be exported to acoustic analysis packages where they are used for the calculation of acoustic sensitivities.

How Model Updating Works

Discrepancies between FEA results and reference data like test data may be due to uncertainty in the governing physical relations (for example, modeling non-linear behavior with the linear FEM theory), the use of inappropriate boundary conditions or element material and geometrical property assumptions and modeling using a too coarse mesh. These 'errors' are in practice rather due to lack of information than plain modeling errors. Their effects on the FEA results should be analyzed and improvements must usually be made to reduce the errors associated with the FE model. Model updating has become the popular name for using measured structural data to correct the errors in FE models.

Model updating works by modifying the mass, stiffness, and damping parameters of the FE model until an improved agreement between FEA data and test data is achieved. Unlike direct methods, producing a mathematical model capable of reproducing a given state, the goal of FE model updating is to achieve an improved match between model and test data by making physically meaningful changes to model parameters which correct inaccurate modeling assumptions. Theoretically, an updated FE model can be used to model other loadings, boundary conditions, or configurations (such as damaged configurations) without any additional experimental testing. Such models can be used to predict operational displacements and stresses due to simulated loads.

There are many different methods of finite element model updating. FEMtools uses well-proven iterative, parametric, modal and FRF-based updating algorithms using sensitivity coefficients and weighting values (Bayesian estimation). The process begins with the formulation of an initial FE model using initial values for the update parameters. The FEA results that will be used to check correlation with test are computed using the FE model with the current update parameter values. The model updating method uses the discrepancy between FEA results and test, and sensitivities to determine a change in the update parameters that will reduce the discrepancy. The FE model is then reformed using the new values of the update parameters, and the process repeats until some convergence criteria, analyzed by means of correlation functions, is met.

Force Identification

In some situations, excitation forces are not known and can not directly be measured. A solution is to measure response values (e.g. displacement, surface velocity etc.) and apply inverse methods to identify the excitation force. FEMtools Model Updating was used in an application to identify pressure forces in a muffler cavity from surface velocities measured using a laser-scanning device

Probabilistic Analysis

All physical properties are subject to scatter and uncertainty. It is important to assess how this variability of properties propagates in a structure and results in also variability on the output responses. This has applications in robust design (for example Design for Six Sigma - DfSS) but can be used for statistical correlation and probabilistic model updating.