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Finite element model updating and optimization of mechanical systems making use of regressive techniques

Wednesday, 28 May, 2008 - 17:00
Campus: Brussels Humanities, Sciences & Engineering campus
Gunther Steenackers
phd defence

This doctoral thesis is concerned with the finite element updating and optimization of structures based on measured frequency response or modal data. The aim of the thesis is to identify the unknown physical parameters of structures by fitting its initial finite element model to the experimental data and performing optimization runs in an efficient way in order to reduce calculation times. The FE model updating procedure can be regarded as a minimization process in which the discrepancies between the numerical and experimental modal data are minimized by adjusting the unknown model parameters. On the other hand, optimization of finite element models seeks the optimal parameter values (inverse modelling) in order to minimize a pre-defined objective function describing targets to be reached and constraints to be satisfied. In order to fulfill the thesis' goals of performing optimization and updating of FE models in an efficient manner, a regressive optimization technique is and applied to tackle extensive FE calculation time issues in different application fields. The regressive optimization technique is adapted and elaborated, in combination with other properties of the system, for model updating as well as structural design optimization. This regressive optimization technique forms the core of the thesis.

Model updating can be divided into deterministic and stochastic updating problems. As already mentioned, the regressive approach can be used in FE updating problems. To illustrate the efficiency of the proposed technique with respect to its application to in the field of FE model updating, a modal updating is investigated and FRF updating is applied. In order to extend the existing FE updating techniques based on experimental modal data, an operational FE updating and optimization approach is elaborated, based on transmissibility functions. A transmissibility function is defined as the ratio between two measured or calculated responses. As a consequence, this function consists of an amplitude and phase, similar to frequency response functions and thus can be used for operational (output-only) updating and optimization purposes in a same manner as FRFs, taking into account the additional advantages. When using transmissibilities, it is not necessary that the force is measurable and the force can be any persistent excitation. Another benefit when using transmissibilities is the fact that the quality of the transmissibility data generally is less noisy compared to measured crosspower spectra. Moreover using this approach it is proven that the transmissibility poles determine the structural modes of the structure when it is constrained at the excitation point. As a consequence, the poles of the measured transmissibilities can be used directly for updating and optimization purposes when constraining the excitation degree-of-freedom in the accompanied FE model. Based on these theoretical results, a new FE updating and optimization procedure is presented in order to update a finite element model by making use of output-only transmissibility measurements. The regressive updating technique is illustrated on updating a finite element model from output-only transmissibility measurements. The output-only results is compared with the results of a traditional input-output modal analysis procedure. A comparison between the classical EMA, OMA and transmissibility OMA is made on the structure.

A way of applying stochastic updating is done by taking into account the uncertainty on the measurements. If various sets of measurement data are available, weighting of the modal data can be applied, based on the mean value and standard deviation of the estimated resonance frequencies. This information can be taken into account whereby relatively higher weights are assigned to the measured resonance frequencies that are more reliable. This effect on the updating results is examined in. Until now, the subject of regressive model updating is introduced. On the other hand, the regressive technique also be used for generalized optimization cases concerning multiple parameters. Similar to model updating, structural design optimization can be divided into deterministic and stochastic optimization. Deterministic optimization considers the situation where optimal (or desired) target values need to be achieved for certain (FE) output properties by optimizing the input parameter values.

Two application cases on deterministic and topology design optimization is considered, making use of the regressive technique to minimize the process bias between the actual and optimal value to be achieved. A computationally efficient strategy for optimization of structures, described by a finite element model, is presented. The method makes use of transmissibility functions and takes into consideration realistic external loading types that are often defined statistically by means of their power spectral density. The transmissibility optimization is performed by making use of the regressive technique and the updating results and calculation time will be compared with respect to the results when making use of existing optimization techniques.

Complementary to the research performed in the field of deterministic optimization, an indication is given to quantify the uncertainty on the FE model output with respect to the uncertainty on the input design parameters. An important part of this thesis aims to characterize the variability in structural response due to system uncertainties in combination with mean and variance response surface modelling techniques. Modelling these uncertainties provides a format for the efficient description of the randomness in a system and forms the basis for the prediction of the structural response. The suggested robust optimization approach is extended and applied on an application case considering parameter uncertainty. A comparison of different optimal, robust and generalized optimization approaches is investigated and applied on a slat track finite element model, making use of mean and variance response functions to model the uncertainty on the finite element displacement values. Different response surface modelling techniques will be applied and compared on the level of accuracy and calculation time. On the other hand, robust design optimization is considered, suggesting a generalized mean squared error approach in order to minimize variance as well as considering target objectives on the FE output.