| 1. |
- Abrahamsson, Thomas, 1956, et al.
(författare)
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Calibration and cross-validation of a car component using frequency response functions and a damping equalization technique
- 2014
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Ingår i: 26th International Conference on Noise and Vibration Engineering, ISMA 2014, Including the 5th International Conference on Uncertainty in Structural Dynamics, USD 2014. - 9789073802919 ; , s. 2625-2640
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Konferensbidrag (refereegranskat)abstract
- The calibration of an FE model of a car subframe is reported. In this calibration the minimum deviation between finite element model data and experimental data is searched for. The outcome of the calibrated model and cross-validation results are compared with results of testing being made on an ensemble of seemingly identical subframes. The subframe model has 250,440 degrees-of-freedom and the calibration is made for 16 uncertain model parameters. The efficiency of the calibration procedure under these conditions is reported. With model calibration being a cornerstone of the finite element validation procedure, the calibration problem is normally characterized as being a large scale optimization problem with many model parameters to solve for and with deviation metric that are nonlinear in these parameters. The calibrated parameters need to be found by iterative procedures, starting from initial estimates of parameter values. Sometimes these procedures get trapped in local deviation function minima and do not converge to the globally optimal calibration solution that is searched for. Here, a calibration formulation which gives a smooth deviation metric with a large radius of convergence to the global minimum is used. A method that utilizes damping equalization is used to avoid the mode correlation and mode pairing problem that need to be solved in various other model updating procedures. The method is combined with model reduction for increased speed and employs the Levenberg-Marquardt minimizer with randomized starts to achieve the calibration solution. The MATLAB-based open-domain software tool FEMcali has been used for calibration, validation and cross-validation.
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| 2. |
- Abrahamsson, Thomas, 1956, et al.
(författare)
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Calibration and Validation of a Car Subframe Finite Element Model Using Frequency Responses
- 2015
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Ingår i: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319152516 ; 10, s. 9-22
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Konferensbidrag (refereegranskat)abstract
- A finite element model of a car front subframe has been calibrated against test data. Stepped-sine testing has been used to give frequency response function estimates on an ensemble of seemingly identical subframes. Therefore, the deviation between test data and simulation results can be compared in a meaningful way by the outcome of model calibration and cross-validation. Emphasis has been put on the preparation of the test pieces for high fidelity testing and on bettering the chances of getting a calibration outcome that provides insight into the physical processes that govern the subframe dynamics. The front subframe model has more than 200,000 degrees-of-freedom and 17 model calibration parameters. The efficiency of the calibration procedure under these conditions is reported. To achieve efficiency, a calibration with a smooth deviation metric is used together with a damping equalization method that eliminates the need for matching of experimental and analytical eigenmodes. The method is combined with surrogate model frequency response evaluation based on model reduction for increased speed. The Matlab based open-domain software tool FEMcali that employs the Levenberg-Marquardt minimizer with randomized starts has been used for calibration and an unregularized Gauss-Newton minimizer has been used in the cross-validation.
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| 3. |
- Abrahamsson, Thomas, 1956, et al.
(författare)
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FEM calibration with FRF damping equalization
- 2014
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Ingår i: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. - 9783319007670 ; 3, s. 265-278
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Konferensbidrag (refereegranskat)abstract
- A finite element model calibration procedure that uses frequency response function data and relies on damping equalization is presented. In this, the dampings of the finite element model and the corresponding experimental model are set equal before calibration. The damping equalization is made to avoid the mode pairing problem that normally needs to be solved in other model updating procedures. It is demonstrated that one particular use of frequency response data gives a calibration deviation metric that is smooth in the variation of model parameters and give a large radius of convergence to the calibration minimum. The method is combined with model reduction for increased speed and employs a minimizing procedure that employs randomized multiple starting points in the parameter space to get to the calibration solution. The performance of the calibration procedure is demonstrated by two numerical examples. © The Society for Experimental Mechanics, Inc. 2014.
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| 4. |
- Abrahamsson, Thomas, 1956, et al.
(författare)
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Finite element model calibration using frequency responses with damping equalization
- 2015
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Ingår i: Mechanical Systems and Signal Processing. - : Elsevier BV. - 0888-3270 .- 1096-1216. ; 62-63, s. 218-234
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Tidskriftsartikel (refereegranskat)abstract
- Model calibration is a cornerstone of the finite element verification and validation procedure, in which the credibility of the model is substantiated by positive comparison with test data. The calibration problem, in which the minimum deviation between finite element model data and experimental data is searched for, is normally characterized as being a large scale optimization problem with many model parameters to solve for and with deviation metrics that are nonlinear in these parameters. The calibrated parameters need to be found by iterative procedures, starting from initial estimates. Sometimes these procedures get trapped in local deviation function minima and do not converge to the globally optimal calibration solution that is searched for. The reason for such traps is often the multi-modality of the problem which causes eigenmode crossover problems in the iterative variation of parameter settings. This work presents a calibration formulation which gives a smooth deviation metric with a large radius of convergence to the global minimum. A damping equalization method is suggested to avoid the mode correlation and mode pairing problems that need to be solved in many other model updating procedures. By this method, the modal damping of a test data model and the finite element model is set to be the same fraction of critical modal damping. Mode pairing for mapping of experimentally found damping to the finite element model is thus not needed. The method is combined with model reduction for efficiency and employs the Levenberg-Marquardt minimizer with randomized starts to achieve the calibration solution. The performance of the calibration procedure, including a study of parameter bias and variance under noisy data conditions, is demonstrated by two numerical examples.
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| 5. |
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| 6. |
- Abrahamsson, Thomas, 1956, et al.
(författare)
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What Is Normal About Normal Modes?
- 2016
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Ingår i: Conference Proceedings of the Society for Experimental Mechanics Series. - Cham : Springer International Publishing. - 2191-5644 .- 2191-5652. ; 10, s. 97-110
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Konferensbidrag (refereegranskat)abstract
- A normal mode of a vibrating system is a mode that is orthogonal to all other normal modes of that system. The orthogonality is in a weighted sense. For an undamped discretized linear mechanical system, the orthogonality is defined with respect to stiffness and mass such that normal modes are mutually stiffness and mass orthogonal. Another commonly used definition of an oscillating normal mode is that it is a pattern of motion in which all parts of the system vibrate harmonically with the same frequency and therefore with fixed relative phase relations between parts. The normality of a mode is thus not in a statistical sense. For lightly damped linear systems, a normal observation, i.e. one very common observation in the statistical sense, is that the phase relation between the motion of different parts of the system deviates very little from zero or pi. However, this normally occurring behavior should not lead us to think that that always has to be the case. Here it is shown by example that the normal modes of an undamped system may have arbitrary phase relations. One such mode of vibrationmay then possess the property of moving nodal lines, which is often attributed to non-proportionally damped or nonself-adjoint systems. The proper normalization of such modes is discussed and their relation to the well-known modal mass and MAC concepts and also to state-space based normalizations that are usually being used for complex-valued eigenmodes.
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| 7. |
- Allen, Matthew S., et al.
(författare)
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Experimental substructuring
- 2020
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Ingår i: CISM International Centre for Mechanical Sciences, Courses and Lectures. - Cham : Springer International Publishing. - 2309-3706 .- 0254-1971. ; 594, s. 75-181
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this chapter, we outline techniques to use measured dynamic characteristics of components to build an assembled model. Although the basic theory is pretty straightforward, the difficulty in experimental substructuring lies in the limitations in what can be measured and the special techniques needed to alleviate errors in the measured signals.—(Chapter Authors: Daniel Rixen, Maarten van der Seijs, Randall Mayes, Matt Allen & Thomas Abrahamsson).
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| 8. |
- Allen, Matthew S., et al.
(författare)
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Industrial applications & related concepts
- 2020
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Ingår i: CISM International Centre for Mechanical Sciences, Courses and Lectures. - Cham : Springer International Publishing. - 2309-3706 .- 0254-1971. ; 594, s. 183-231
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This section highlights some specialized substructuring methods, such as methods for estimating the fixed-interface modes of a substructure from measurements of the free–free structure with a fixture attached at the interface, and also highlights some industrial examples. Transfer path analysis is reviewed, elaborating some of the similarities in the theoretical foundations. Most information about TPA has been obtained from van der Seijs et al. (2016), please refer to the original paper for a more elaborate discussion.
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| 9. |
- Allen, Matthew S., et al.
(författare)
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Introduction and Motivation
- 2020
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Ingår i: CISM International Centre for Mechanical Sciences, Courses and Lectures. - Cham : Springer International Publishing. - 2309-3706 .- 0254-1971. ; 594, s. 1-4
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- “Divide and Conquer” is a paradigm that helped Julius Cesar to dominate on the wide Roman Empire. The power of dividing systems, then analyze them as parts before combining them in an assembly, is also an approach often followed in science and engineering. In this introductory chapter, we shortly discuss the main idea behind domain decomposition and substructuring applied to mechanical systems.
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| 10. |
- Allen, Matthew S., et al.
(författare)
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Model reduction concepts and substructuring approaches for linear systems
- 2020
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Ingår i: CISM International Centre for Mechanical Sciences, Courses and Lectures. - Cham : Springer International Publishing. - 2309-3706 .- 0254-1971. ; 594, s. 25-73
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this chapter, we give an overview of some of the most common reduction techniques based on substructuring. Although all techniques follow a similar approach, the main difference between the methods lies into the basis vectors used in the approximation subspace to represent the dynamics of each substructure and the manner in which the substructures are a couple.
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