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- Larsson, Andreas, 1968-, et al.
(author)
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On the Parameter Identifiability and Test Data Informativeness in Finite Element Model Error Localization
- 2000
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In: Proceedings of IMAC XVIII. - San Antonio, TX. ; , s. 1520-1527, s. 1520-1527
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Conference paper (peer-reviewed)abstract
- Two fundamental questions that arise in finite ele- ment model updating and error localization prob- lems are addressed. These are whether available test data are informative enough with respect to the quantification of possible model errors and whether sufficient identifiability of such errors is at hand for a given test data set. We advocate the use of informativeness and identifiability based indices in a preparatory process to increase the likelihood of a successful error localization. Based on model properties, such informativeness and identifiability indices may be used in the pre-test planning for the determination of frequency, time and spatial resolution to be used in a vibratory test. First, the test data informativeness with respect to model parameters which might be in error is quan- tified. Here a dual assumption is made such that if model parameter perturbations could be detected by data from the planned test, then the test data could be used to detect such perturbations, i.e. the test is informative. A Data Information Richness (DIR) index has been developed to assess the level od Data Informativeness with respect to model parameters. Secondly, the identifiability of the model parame- ters are studied. The dynamic properties of a struc- ture, as recorded by a measurement system, may under certain conditions change similarly by changing one parameter or a set of other parameters. Should that be the case, there is no identifi- ability and before a meaningful error localization may take place, either complementary test data have to be added or a re-parameterization of the model has to be made. To assess the identifiability, identifiability based criteria are further developed, based on earlier work by the authors. A newly developed orthogonality/co-linearity index ocI assist in the re-parameterization of systems with low identifiability. The methods of preparatory error localisation are applied to a six-degree-of-freedom system in a numerical example in which the analytical results of a finite element analysis are taken as substitute for measured data.
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| 2. |
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| 3. |
- Linderholt, Andreas, 1968-, et al.
(author)
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Information in Data Used for Finite Element Model Updating : Theory and Experiment
- 2001
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In: Proceedings of SEM Annual Conference on Experimental Mechanics. - Portland, Oregon.
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Conference paper (peer-reviewed)abstract
- To discriminate bad parameter settings from good, in finite element modelling, experimental data is usually required. Such experimental data should be informative with respect to the parameters in ques- tion. The demand for informativeness put require- ments on the experiment with regards to spatial resolution of sensors, bandwidth of shaker excita- tion, ambient noise levels, etc. In this paper, in- formativeness is studied by means of the Fisher information matrix and parameter accuracy is relat- ed to the adjoint statistical Cramer-Rao lower bound. The evaluation of information content in data used for model updating is discussed. Deter- ministic state-space models and stochastic noise models are used for informativeness evaluation. A numerical study together with Scanning laser vi- brometer measurements, on a system with well known mass perturbations, are used to substantiate the theory.
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| 4. |
- Linderholt, Andreas, 1968-, et al.
(author)
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Informative Data for Model Parameter Updating
- 2001
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In: Proceedings of IMAC XIX. - Orlando, Florida. ; , s. 581-586
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Conference paper (peer-reviewed)abstract
- Before an error localization is to be carried out a preparatory error localization, using only data from an FE-analysis, is justified. The purpose of such preparatory work is both to decide what parameters to use to quantify model errors and to design opti- mal tests for the error localization. A reasonable re- quirement on the parameterization is that the test data are informative with respect to the parameters. That implies that a change of a certain parameter should give a detectable change in the model’s dy- namic behaviour. The aim of this study is to examine data informa- tivity with respect to physical parameters, used in error localization and model updating. The data in- formativity is here quantified by the use of the Fisher information matrix. It is shown that the in- formativity depends on both excitation and meas- urements. It is reasonable to believe that parameters of which test data have low informativ- ity, are of no use for error localization and should not be used for model updating purposes. Such pa- rameters should be excluded from the parameters set or the test aimed for its determination should be re-designed.
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| 5. |
- Linderholt, Andreas, 1968-, et al.
(author)
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On the Requirements of Physical Parameters to be used in Model Updating
- 2001
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In: Proceedings of International Conference on Structural System Identification. - Kassel, Germany.
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Conference paper (peer-reviewed)abstract
- A fundamental question that arises in finite element model updating and error localization problems is which requirements that have to be fulfilled by the physical parameters to be used in the procedures. One requirement is that the test data are informative with respect to the chosen parameters. That implies that a change of a certain parameter should give a detectable change in the model’s dynamic behaviour. Another requirement is that the chosen parameters should be identifiable. The dynamic properties of a structure, as recorded by a measurement system, may under certain conditions change similarly by changing one parameter or a set of other parameters. Should that be the case, there is no identifiability. This article shows that parameters of which test data have low informativeness and parame- ters that are lacking identifiability, are of no use for error localization or model updating and should therefore not be used for these purposes. Thus, before a meaningful error localization may take place either complementary test data have to be added or a re-parameterization of the model has to be made. Before an error localization is to be carried out a preparatory error localization, using only data from an FE-analysis, is justified. The purpose of such preparatory work is both to decide which parameters to use to quantify model errors and to design the tests for the error localiza- tion in order to meet the parameter requirements.
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| 6. |
- Linderholt, Andreas, 1968-, et al.
(author)
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Parameter Identifiability in Finite Element Model Error Localization
- 2003
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In: Mechanical systems and signal processing. - : Elsevier. - 0888-3270 .- 1096-1216. ; 17:3, s. 579-588
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Journal article (peer-reviewed)abstract
- A fundamental question in finite element model updating and error localisation is whether sufficient identifiability of model parameters is at hand for a given set of test data. Under certain conditions, the dynamic properties (to be compared with test data) of a structural model, may change similarly when a certain model parameter or a combination of other parameters are modified. Since low confidence in identified parameters can also be expected for marginally identifiable systems, due to the omnipresent noise when real test data are used, one should seek such states so as to avoid them. Should the problem lack identifiability, then before a meaningful error localisation can be made; either complementary test data have to be added or new parameters chosen for the model. The latter is studied in this paper. An index, the orthogonality/colinearity index, was developed to facilitate finding the best way to reduce the number of parameters when there is low identifiability The use of the index is demonstrated on a six-degree-of-freedom system in a numerical example. The example shows that error localisation or model updating using a parameterisation which has insufficient parameter identifiability is pointless.
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| 7. |
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| 8. |
- Linderholt, Andreas, 1968-, et al.
(author)
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Test Data Informativeness Assessment for Finite Element Model Updating
- 2002
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Reports (other academic/artistic)abstract
- Before a computational model updating or an error localization is to be carried out, a prepara tory error localization using only analytical data is justified. The purpose of such preparation should be to select the parameters for quantifying model errors and also to design optimal tests for determining the correct parameter setting. For a successful error localization, it is required that the test data should be informative with respect to the parameters chosen. The demand for test data informativeness limits the experiment with regard to the spatial resolution of sensors, bandwidth of excitation, signal-to-noise ratios, etc. On the other hand, for a given test condition and test data, the omnipresent noise may make parameter estimates useless because of estima tion covariances that are too large. This is often caused by over parameterized models; these should be identified by the preparatory error localization and remedied by are-parameterization before model updating take place. The aim of this study is to quantify data informativeness with respect to physical parameters that are used in error localization and model updating. The data informativeness is shown to relate to the Fisher information matrix. Deterministic finite-element related state-space models in combination with stochastic noise models are used for evaluating data informativeness. A nu merical study utilizing a finite-element model validated by test data from a scanning laser vi brometer is used to substantiate the theory.
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| 9. |
- Linderholt, Andreas, 1968-, et al.
(author)
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Test Data Informativeness Assessment for Finite Element Model Updating
- 2003
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In: Proceedings of IMAC XXI. - Orlando, Florida.
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Conference paper (peer-reviewed)abstract
- In advance of a computational model updating or an er- ror localization, it can be advantageous to make a pre- paratory error localization using a nominal analytical model. The purpose is then to select parameters for quantifying model errors and also to design effective tests for determining the best parameter setting. For suc- cessful error localization, the test data must be informa- tive with respect to the model parameters chosen. For dynamic computational models, the demand for test data informativeness puts limitations on the experiment with regard to spatial resolution of sensors, bandwidth of excitation, signal-to-noise ratios, etc. Solving a full test design optimization problem is a huge task, sometimes impossible in practice, due to its com- binatorial nature. The number of possible sensor/actua- tor placement combinations grows rapidly as the number of sensor and actuator candidates increases. For industrial sized problems, finding a sub-optimal solu- tion may be a more realistic target. The aim of this study is to quantify data informative- ness, shown to relate to the Fisher information matrix, with respect to physical parameters that are used in error localization and model updating. Deterministic finite- element models in combination with stochastic noise models are used for evaluating data informativeness, and a procedure for test design optimization with re- spect to this is devised.
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| 10. |
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| 11. |
- Linderholt, Andreas, 1968-
(author)
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Test Design for Finite Element Model Updating - Identifiable Parameters and Informative Test Data
- 2003
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Doctoral thesis (other academic/artistic)abstract
- It is important to predict structural phenomena, such as noise and fatigue, stemming from vibrations. To do this, reliable structural dynamic models are needed. To be useful the models have to compare well with reality in the validation against test data; if not, the models should be modified. The thesis research is in the field of computational model updating, which is, more often than not, the updating of uncertain parameters of a finite element model to better correlate to test data. This is a specialization that started to grow in the 1970s, and since then much research has been done. The work presented here concerns the design of tests for model updating, which is one of several model updating sub-tasks. For a test to be useful for model updating, the test data set must be such that the model parameters are sufficiently well identifiable. The dynamic properties of a structure to be compared with test data may under certain conditions change similarly when one parameter or a set of other parameters is changed. When this happens, there is lack of identifiability and, before a meaningful model updating can take place, either complementary test data have to be added or a re-parameterization of the model must be made. An index was developed, the Orthogonality-Co-linearity Index (OCI), that helps to find the best way to reduce the number of parameters when there is low identifiability. For the model updating, test data also need to be informative with respect to the parameters to be tuned. The data informativeness depends on the test design, i.e. the choice of stimuli and the placement of the actuators and sensors. A data informativeness index that supports the design of an informative test is proposed. Procedures were also worked out to make the test design robust with respect to parameter uncertainties. The study is limited to linear and time-invariant systems.
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