Structural damage detection using nonlinear parameter identification with Tikhonov regularization

Weber, Benedikt; Paultre, Patrick; Proulx, Jean

doi:10.1002/stc.164

Cited by 49 publications

(47 citation statements)

References 27 publications

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“…Specifically, the two measures of fit are given by experimentally identified and estimated mode shapes for the r -th mode. Alternative measures of fit can easily be used and found in literature [18][19][20][21][22].…”

Section: Modal Residualsmentioning

confidence: 99%

Parameter Estimation of Nonlinear Large Scale Systems Through Stochastic Methods and Measurement of Its Dynamic Response

Giagopoulos¹,

Αραϊλόπουλος²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Section: Modal Residualsmentioning

confidence: 99%

Parameter Estimation of Nonlinear Large Scale Systems Through Stochastic Methods and Measurement of Its Dynamic Response

Giagopoulos¹,

Αραϊλόπουλος²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…For the second group, the measure of fit I 2 ðyÞ is selected to represent the difference between the measured and the model predicted mode shape components for all modes. Specifically, the two measures of fit are given by Alternative measures of fit [3,[19][20][21][22] can easily be accommodated in the proposed formulation. In particular, it is straightforward to show that…”

Section: Modal Residualsmentioning

confidence: 99%

Variability of updated finite element models and their predictions consistent with vibration measurements

Papadimitriou¹,

Ntotsios²,

Giagopoulos³

et al. 2011

Struct. Control Health Monit.

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Abstract:A case study on a small-scale laboratory vehicle frame is used to investigate the variability of the updated finite element (FE) models that arises from model and measurement errors and demonstrate the effect of this variability on response predictions. Conventional weighted modal residuals and recently introduced multi-objective identification methods for structural model updating are used to provide the entire spectrum of Pareto optimal FE models consistent with the measured modal data. Similarities and differences between the two model updating methods are explored and the advantages of the multi-objective identification methods are emphasized. A significant variability in Pareto optimal models is observed, which is indicative of the uncertainty in the updated FE models. The dependence of the variability of the Pareto models on the information contained in the measured data and the size of model and measurement errors is explored by varying the number of measured modes, number of sensors, FE mesh discretization sizes, and number of model parameters. The effectiveness of the updated Pareto optimal models and their predictive capabilities are assessed. Frequency response functions and fatigue lifetime predictions are used as example of structural performance variables in order to demonstrate the variability in the response predictions that arises from the variability in the Pareto optimal models. A large variability in the response predictions is observed that cannot be ignored in decisions based on updated FE models. The multi-objective optimization method provides the general framework for properly accounting for model uncertainty in model-based response predictions consistent with measured data.

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“…V. Melicher et al [13] identified the piecewise constant parameter using the standard TR method. In addition, many works are mainly concerned with the identification of load position and load number in nonlinear system using the standard TR method [14][15][16]. However, the standard TR method is not completely perfect; there are some unavoidable limitations and disadvantages: (i) the standard TR method may determine approximate solutions that are too smooth; (ii) the approximate solution may lack many details that the desired exact solution might possess; therefore, it is very necessary to discuss other regularization methods to improve the limitations and disadvantages of the regularization method mentioned above.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

Wang

Ren

Liu

2018

Mathematical Problems in Engineering

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This paper presents a novel inverse technique to provide a stable optimal solution for the ill-posed dynamic force identification problems. Due to ill-posedness of the inverse problems, conventional numerical approach for solutions results in arbitrarily large errors in solution. However, in the field of engineering mathematics, there are famous mathematical algorithms to tackle the illposed problem, which are known as regularization techniques. In the current study, a novel fractional Tikhonov regularization (NFTR) method is proposed to perform an effective inverse identification, then the smoothing functional of the ill-posed problem processed by the proposed method is regarded as an optimization problem, and finally a stable optimal solution is obtained by using an improved super-memory gradient (ISMG) method. The result of the present method is compared with that of the standard TR method and FTR method; new findings can be obtained; that is, the present method can improve accuracy and stability of the inverse identification problem, robustness is stronger, and the rate of convergence is faster. The applicability and efficiency of the present method in this paper are demonstrated through a mathematical example and an engineering example.

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Structural damage detection using nonlinear parameter identification with Tikhonov regularization

Cited by 49 publications

References 27 publications

Parameter Estimation of Nonlinear Large Scale Systems Through Stochastic Methods and Measurement of Its Dynamic Response

Parameter Estimation of Nonlinear Large Scale Systems Through Stochastic Methods and Measurement of Its Dynamic Response

Variability of updated finite element models and their predictions consistent with vibration measurements

A Novel Fractional Tikhonov Regularization Coupled with an Improved Super-Memory Gradient Method and Application to Dynamic Force Identification Problems

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