| 1. |
- Chen, Yousheng, 1985-, et al.
(författare)
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Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multi-Harmonic Frequency Responses
- 2016
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Ingår i: Journal of Computational and Nonlinear Dynamics. - : ASME Press. - 1555-1415 .- 1555-1423. ; 11:5
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Tidskriftsartikel (refereegranskat)abstract
- In industry, linear FE-models commonly serve as baseline models to represent the global structural dynamics behavior. However, available test data may show evidence of significant nonlinear dynamic characteristics. In such a case, the baseline linear model may be insufficient to represent the dynamics of the structure. The causes of the nonlinear characteristics may be local in nature and the remaining parts of the structure may be satisfactorily represented by linear descriptions. Although the baseline model can then serve as a good foundation, the physical phenomena needed to substantially increase the model's capability of representing the real structure are most likely not modelled in it. Therefore, a set of candidate nonlinear property parameters to control the nonlinear effects have to be added and subjected to calibration to form a credible model. The selection of the calibration parameters and the choice of data for a calibration metric form a coupled problem. An over-parameterized model for calibration may result in parameter value estimates that do not survive a validation test. The parameterization is coupled to the test data and should be chosen so that the expected co-variances of the chosen parameter's estimates are made small. Accurate test data, suitable for calibration, is often obtained from sinusoidal testing. Because a pure mono-sinusoidal excitation is difficult to achieve during a test of a nonlinear structure, the excitation is here designed to contain sub and super harmonics besides the fundamental harmonic. The steady-state responses at the side frequencies are shown to contain valuable information for the calibration process that can improve the accuracy of the parameter estimates. The nonlinear steady-state solutions can be found efficiently using the multi-harmonic balance method. In this paper, synthetic test data from a model of a nonlinear benchmark structure are used for illustration. The model calibration and an associated K-fold cross-validation are based on the Levenberg-Marquardt and the undamped Gauss-Newton algorithm, respectively. Starting seed candidates for calibration are found by the Latin hypercube sampling method. The realization that gives the smallest deviation to test data is selected as a starting point for the iterative search for a calibration solution. The calibration result shows good agreement with the true parameter setting, and the K-fold cross validation result shows that the variance of the estimated parameters shrinks when adding sub and super harmonics to the nonlinear frequency response functions.
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| 2. |
- Chen, Yousheng, 1985-, et al.
(författare)
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Model Calibration of a Locally Non-linear Structure Utilizing Multi Harmonic Response Data
- 2014
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Ingår i: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 2191-5644 .- 2191-5652. - 9783319045221 - 9783319045214 ; , s. 97-109
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Konferensbidrag (refereegranskat)abstract
- Model correlation and model calibration using test data are natural ingredients in the process of validating computational models. Here, model calibration for the important sub-class of non-linear systems consisting of structures dominated by linear behavior having presence of local non-linear effects is studied. The focus is on the selection of uncertain model parameters together with the forming of the objective function to be used for calibration. To give precise estimation of parameters in the presence of measurement noise, the objective function data have to be informative with respect to the parameters chosen. Also, to get useful data the excitation force is here designed to be multi-harmonic since steady-state responses at the side frequencies are shown to contain valuable information for the calibration process. In this paper, test data from a replica of the Ecole Centrale de Lyon (ECL) nonlinear benchmark together with steady-state solutions stemming from calculations using the Multi-Harmonic Balancing method are used for illustration of the proposed model calibration procedure.
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| 3. |
- Chen, Yousheng, 1985-, et al.
(författare)
-
Model calibration of locally nonlinear structures using information from sub and super harmonic responses
- 2012
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Ingår i: International Conference on Noise and Vibration Engineering 2012 (ISMA 2012). - Leuven : Katholieke Universiteit Leuven, Department of Mechanical Engineering. - 9781622768257 ; , s. 2451-2464
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Large linear finite element models are commonly used in industry to represent global structural behavior and such models are often validated by use of data from vibrational tests. The validated models serve to predict the structural responses due to dynamic loads. Hence, it is important to have models that are able to represent the structural dynamics within the given operating envelope. When test data show proof of non linear behavior, a linear model may not be able to represent the dynamics well enough and thus a modification of the model is required. The main part of the structure may have a linear characteristic whereas localized physical processes can be sources of the observed nonlinearities. Model calibration of such locally nonlinear structures is studied in this paper. Specifically, the calibration process including the selection of appropriate data to be used for calibration of the model parameters chosen is treated. Here, synthetic test data stemming from a model of the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used.
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| 4. |
- Yaghoubi Nasrabadi, Vahid, 1985, et al.
(författare)
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Locally Non-Linear Model Calibration Using Multi Harmonic Responses : Applied on Ecole de Lyon Non-Linear Benchmark Structure
- 2013
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Ingår i: Topics in Nonlinear Dynamics, Volume 1. - New York, NY : Springer. - 9781461465690 ; 1, s. 113-123
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In industry, linear FE-models commonly serve to represent global structural behavior. However, when test data are availa-ble they may show evidence of nonlinear dynamic characteristics. In such a case, an initial linear model may be judged being insufficient in representing the dynamics of the structure. The causes of the non-linear characteristics may be local in nature whereas the major part of the structure is satisfactorily represented by linear descriptions. Although the initial model then can serve as a good foundation, the parameters needed to substantially increase the model’s capability of representing the real structure are most likely not included in the initial model. Therefore, a set of candidate parameters controlling nonlinear effects, opposite to what is used within the vast majority of model calibration exercises, have to be added. The selection of the candidates is a delicate task which must be based on engineering insight into the structure at hand.The focus here is on the selection of the model parameters and the data forming the objective function for calibration. An over parameterized model for calibration render in indefinite parameter value estimates. This is coupled to the test data that should be chosen such that the expected estimate variances of the chosen parameters are made small. Since the amount of information depends on the raw data available and the usage of them, one possibility to increase the estimate precision is to process the test data differently before calibration. A tempting solution may be to simply add more test data but, as shown in this paper, the opposite could be an alternative; disregarding low excessive data may make the remaining data better to dis-criminate between different parameter settings.Since pure mono-harmonic excitation during test is an abnormality, the excitation force is here designed to contain sub and super harmonics besides the fundamental one. Further, the steady-state responses at the side frequencies are here shown to contain most valuable information for the calibration process of models of locally nonlinear structures.Here, synthetic test data stemming from a model representing the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used for illustration. The nonlinear steady state solutions are found using iterative linear reverse path state space calculations. The model calibration is here based on nonlinear programming utilizing several parametric starting points. Candidates for starting points are found by the Latin Hypercube sampling method. The best candidates are selected as starting points for optimization.
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| 5. |
- Chen, Yousheng, 1985-, et al.
(författare)
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A Pretest Planning Method for Model Calibration for Nonlinear Systems
- 2016
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Ingår i: Model Validation and Uncertainty Quantification, Volume 3. - Cham : Springer. - 2191-5644 .- 2191-5652. - 9783319297538 - 9783319297545 ; , s. 371-379
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- With increasing demands on more flexible and lighter engineering structures, it has been more common to take nonlinearity into account. Model calibration is an important procedure for nonlinear analysis in structural dynamics with many industrial applications. Pretest planning plays a key role in the previously proposed calibration method for nonlinear systems, which is based on multi-harmonic excitation and an effective optimization routine. This paper aims to improve the pretest planning strategy for the proposed calibration method. In this study, the Fisher information matrix (FIM), which is calculated from the gradients with respect to the chosen parameters with unknown values, is used for determining the locations, frequency range, and the amplitudes of the excitations as well as the sensor placements. This pretest planning based model calibration method is validated by a structure with clearance nonlinearity. Synthetic test data is used to simulate the test procedure. Model calibration and K-fold cross validation are conducted for the optimum configurations selected from the pretest planning as well as three other configurations. The calibration and cross validation results show that a more accurate estimation of parameters can be obtained by using test data from the optimum configuration.
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| 6. |
- Chen, Yousheng, 1985-, et al.
(författare)
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An Efficient Simulation Method for Large-Scale Systems with Local Nonlinearities
- 2016
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Ingår i: Special topics in structural dynamics, 34th IMAC. - Cham : Springer. - 2191-5644 .- 2191-5652. - 9783319299105 - 9783319299099
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In practice, most mechanical systems show nonlinear characteristics within the operational envelope. However, the nonlinearities are often caused by local phenomena and many mechanical systems can be well represented by a linear model enriched with local nonlinearities. Conventional nonlinear response simulations are often computationally intensive; the problem which becomes more severe when large-scale nonlinear systems are concerned. Thus, there is a need to further develop efficient simulation techniques. In this work, an efficient simulation method for large-scale systems with local nonlinearities is proposed. The method is formulated in a state-space form and the simulations are done in the Matlab environment. The nonlinear system is divided into a linearized system and a nonlinear part represented as external nonlinear forces acting on the linear system; thus taking advantage in the computationally superiority in the locally nonlinear system description compared to a generally nonlinear counterpart. The triangular-order hold exponential integrator is used to obtain a discrete state-space form. To shorten the simulation time additionally, auxiliary matrices, similarity transformation and compiled C-codes (mex) to be used for the time integration are studied. Comparisons of the efficiency and accuracy of the proposed method in relation to simulations using the ODE45 solver in Matlab and MSC Nastran are demonstrated on numerical examples of different model sizes.
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| 7. |
- Chen, Yousheng, 1985-, et al.
(författare)
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Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses
- 2017
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Ingår i: Journal of Computational and Nonlinear Dynamics. - : ASME Press. - 1555-1415 .- 1555-1423. ; 12:4
-
Tidskriftsartikel (refereegranskat)abstract
- Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the École Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated model's output corresponds well with the measured responses.
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| 8. |
- Chen, Yousheng, 1985-, et al.
(författare)
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Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
- 2014
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Ingår i: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 9783319045221 - 9783319045221 ; 2, s. 35-44
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Konferensbidrag (refereegranskat)abstract
- Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.
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| 9. |
- Chen, Yousheng, 1985-
(författare)
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Model Calibration of Nonlinear Mechanical Systems Using Multi-Harmonic Frequency Response Functions
- 2014
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In industry, linear finite element models are commonly employed to represent global structural behavior. It is crucial that the computational models are able to accurately represent the structures’ behavior. This cannot always be achieved by the use of linear models.When vibrational test data show significant nonlinear characteristics, an initial linear finite element model may be judged insufficient in representing the structural behavior. Although an initial model can give a good foundation for the understanding of the dynamic behavior of the structure, the parameters that capture the nonlinear effects are most likely not included. Therefore, a set of candidate parameters controlling the nonlinear effect have to be added. The selection of such candidates is a delicate task which solution is preferably supported by engineering insight into the characteristics of the structure.One part of this work is on the selection of parameters, among all possibly uncertain properties, together with the forming of the objective function to be used for calibration. To obtain precise estimates of the parameters, the objective function data have to be informative with respect to the selected parameters. Further the parameters have to be identifiable. To improve these qualities, a multi-harmonic sinusoidal excitation was designed since the corresponding steady-state responses at the sub- and super- harmonics were shown to contain valuable information for the calibration process. Model calibration of nonlinear systems made by minimizing the differences between predicted and measured multi-harmonic frequency response functions.Further, in the calibration, multi-harmonic frequency response functions need to be calculated recurrently in order to reach convergence; therefore a fast simulation scheme was required. The performance of computations of multi-harmonic frequency response functions calculated using time domain as well as frequency domain simulation techniques were studied and compared.Finally, the proposed calibration method was validated by use of experimental testing on a replica of the Ecole de Lyon nonlinear benchmark structure. It was shown in the validation results that the predictions stemming from the calibrated model matched the experimental data well.
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| 10. |
- Linderholt, Andreas, 1968-, et al.
(författare)
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A study of the coupling between test data accuracy and life prediction
- 2014
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Ingår i: Proceedings of ISMA2014 including USD2014. - Leuven : Katholieke Universiteit Leuven, Department of Mechanical Engineering. - 9781634395069 ; , s. 415-428
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Computational models are regularly used to predict responses and the life of structures. Often, the computational models are validated by use of data stemming from vibration testing. However, the damping values are almost always taken from test alone and hence cannot be validated. Experimentally obtained damping values are well known to have relatively high uncertainties. In the present paper we investigate how life time predictions are affected by modal damping uncertainties by simulating responses due to random loads. The simulations are based on experimental modal analysis results of a structure consisting of two steel plates which are joined by bolts, tested under several different experimental support conditions. The results illustrate the importance of careful consideration of experimental test setups, as these can strongly affect the obtained damping estimates. This, in turn, can lead to large differences in predicted life time.
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| 11. |
- Linderholt, Andreas, 1968-, et al.
(författare)
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Time Domain Dynamic Simulations of Locally Nonlinear Large-Scale Systems
- 2016
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Ingår i: Presented at Aerospace technology congress.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In practice, most mechanical systems show nonlinear characteristics within the operational envelope. However, the nonlinearities are often caused by local phenomena and many mechanical systems can be well represented by a linear model enriched with local nonlinearities. Conventional nonlinear response simulations are often computationally intensive; the problem which becomes more severe when large-scale nonlinear systems are concerned. Thus, there is a need to further develop efficient simulation techniques. In this work, an efficient simulation method for large-scale systems with local nonlinearities is proposed. The method is formulated in a state-space form and the simulations are done in the Matlab environment. The nonlinear system is divided into a linearized system and a nonlinear part represented as external nonlinear forces acting on the linear system; thus taking advantage in the computationally superiority in the locally nonlinear system description compared to a generally nonlinear counterpart. The triangular-order hold exponential integrator is used to obtain a discrete state-space form. To shorten the simulation time additionally, auxiliary matrices, similarity transformation and compiled C-codes (mex) to be used for the time integration are studied. Comparisons of the efficiency and accuracy of the proposed method in relation to simulations using the ODE45 solver in Matlab and MSC Nastran are demonstrated on numerical examples of different model sizes.
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