FEMtools Model Updating
An Integrated Solution for Structural Dynamics Simulation, Model Verification, Validation and Updating
FEMtools Model Updating contains modules for:
Sensitivity analysis is a technique that allows an analyst to get a feeling on how structural responses of a model are influenced by modifications of parameters like spring stiffness, material stiffness, geometry etc. Sensitivity analysis can be used for the following purposes:
Sensitivity coefficients quantify the variation of a response value (e.g. resonance frequency or mass) as a result of modifying a parameter value. The coefficients obtained for all combinations of responses and parameters are stored in a sensitivity matrix. Analyzing this matrix yields information on the sensitive and insensitive zones of the structure. Color graphics are available to visualize these different zones and enable a fast optimization of the parameter selection.
Sensitivity analysis and model updating require that the user selects reference responses and parameters.
Sensitivity coefficients are computed internally by FEMtools using a differential or finite difference method. The possibilities depend on the parameter type and on the element formulation. Alternatively, externally computed sensitivity coefficients can be imported. For example, sensitivities computed using SOL 200 in MSC.Nastran can be imported in FEMtools for model updating.
The following reference response types can be selected for sensitivity analysis:
The following parameter types can be selected for sensitivity analysis:
Parameter can be selected at either the local or the global level:
FEMtools Model Updating includes utilities and methods to update finite element models to better match reference targets like test data. The updating methods are based on the use of sensitivity coefficients that iteratively update selected physical element properties (like for example material properties, and joint stiffness) so that correlation between simulated responses and target values improves. Response types can be static displacements, mass, modal data, FRFs, operational data or correlation values like MAC. Parameters that can be updated are all mass, stiffness and damping properties used in the definition of the FE model. The resulting FE model can be used for further structural analysis with much more confidence.
Example applications are FE model validation and refinement, material identification from vibration testing, FE model reduction, damage detection, ...
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.
Model Updating in FEMtools
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.
Superelement-Based Model Updating
When working with large FE models, a bottom-up modeling, testing and assembly approach should be considered. This is most efficient if superelements are used to model the parts that do not change. If updating parameters are selected in the residual part (= elements that are not included in any superelement), then only the residual part is updated and combined with the superelements with every iteration.
Simultaneous Updating of Multiple Models (MMU)
Multi-Model Updating (MMU) is simultaneous updating of different versions of a finite model corresponding with different structural configurations. For each configuration there is a modal test. For example, solar panels for satellites can be tested during different stages of deployment and for each stage there is a FE model. This provides a richer set of test data to serve as reference for updating element properties that are common in all configurations. Such properties can be, for example, the joint stiffness or material properties. Other examples are a launcher tested with different levels of fuel, or differently shaped test specimens made of a composite material that needs to be identified.
From measured harmonic operational shapes, and an updated finite element model, a system of equations can be solved to obtain the excitation forces.
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 is also used for statistical correlation and probabilistic model updating in case multiple tests have been performed.
Statistical correlation is the graphical and numerical analysis of similarities and differences between point clouds and their statistical derivatives (center of gravity, mean, standard deviation, ...).
Test procedures and results extraction methods are also subject to scatter and uncertainty. Test data should therefore be considered as point clouds that can be compared with similar point clouds obtained from stochastic simulation.
Comparing the position, size and shape of point clouds provides additional insight in the quality of the simulation model and it capacity to represent the true physics of the structure being tested.
Probabilistic Model Updating
Probabilistic model updating is about modifying design parameters and their random properties to improve statistical correlation between simulation and test point clouds and their statistical derivatives.
Design Improvement and Robust Design
When a validated, and thus realistic, simulation model is available, the design can be improved in terms of product performance and robustness. Using a procedure that is similar to probabilistic model updating, design parameters and their random properties are used to modify position, shape and size of simulation point clouds to satisfy design goals and constraints. In most cases these goals are the translation of specifications related to quality, durability and manufacturing tolerance, and thus overall cost.
Design of experiment (DOE) offers a number of techniques to sample the design space of a problem in an efficient way.
In model updating, DOE techniques can be used to find a set of starting values that result in a better correlation with the reference data as the current starting values. DOE is particularly interesting if the correlation between the initial FE-model and the reference data is too poor to perform a sensitivity-based updating.
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