Fuzzy finite element model updating of the DLR AIRMOD test structure

Khodaparast, Hamed Haddad; Govers, Yves; Dayyani, Iman; Adhikari, Sondipon; Link, Michael; Friswell, Michael I.; Mottershead, John E.; Sienz, Johann

doi:10.1016/j.apm.2017.08.001

Cited by 36 publications

(20 citation statements)

References 38 publications

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“…19 The fuzzy set, 20 evidence variable, 21 and interval theory 22 are the three commonly used methods to characterize the epistemic uncertainty. By using fuzzy arithmetic, the model updating strategy with epistemic uncertainty has been investigated by several scholars [23][24][25][26][27] where the fuzzy variables were usually transformed into a group of interval variables under the cut-level operation. Based on the evidence theory, Deng et al proposed an evidential model validation method where frame of discernment of evidence variable was determined by Bayesian hypothesis testing and Bayes factor.…”

Section: Introductionmentioning

confidence: 99%

Novel interval theory‐based parameter identification method for engineering heat transfer systems with epistemic uncertainty

Wang

Matthies

2018

Numerical Meth Engineering

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Summary The parameter identification problem with epistemic uncertainty, where only a small amount of experimental information is available, is a challenging issue in engineering. To overcome the drawback of traditional probabilistic methods in dealing with limited data, this paper proposes a novel interval theory‐based inverse analysis method. First, the interval variables are introduced to represent the input uncertainties, whose lower and upper bounds are to be identified. Subsequently, an unbiased estimation method is presented to quantify the experimental response interval from limited measurements. Meanwhile, a quantitative metric is defined to characterize the relative errors between computational and experimental response intervals by which the interval parameter identification can be constructed as a nested‐loop optimization procedure. To improve the computational efficiency of response prediction with respect to various interval variables, a universal surrogate model is established in the support box via Legendre polynomial chaos expansion, where the expansion coefficients can be evaluated by a collocation method under Clenshaw‐Curtis points and Smolyak algorithm. Eventually, a heat conduction example is provided to verify the feasibility of proposed method, especially in the case with noise‐contaminated temperature measurements.

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Section: Introductionmentioning

confidence: 99%

Novel interval theory‐based parameter identification method for engineering heat transfer systems with epistemic uncertainty

Wang

Matthies

2018

Numerical Meth Engineering

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“…Describing uncertainties as fuzzy sets was first introduced by Zadeh [14]. In fuzzy finite element model updating (FFEMU) [6,15,16,17], the fuzzy membership functions are used to define the uncertainties associated with the measured outputs (instead of probability density function) while the membership functions of the uncertain parameters are obtained by applying the interval finite element model updating at different membership function levels. Moens and Vandepitte [15] applied FFEMU to compute the uncertain frequency response functions of damped structures.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Finite Element Model Updating Using Metaheuristic Optimization Algorithms

Boulkaibet¹,

Marwala²,

Friswell³

et al. 2017

Special Topics in Structural Dynamics, Volume 6

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In this paper, a non-probabilistic method based on fuzzy logic is used to update finite element models (FEMs). Model updating techniques use the measured data to improve the accuracy of numerical models of structures. However, the measured data are contaminated with experimental noise and the models are inaccurate due to randomness in the parameters. This kind of aleatory uncertainty is irreducible, and may decrease the accuracy of the finite element model updating process. However, uncertainty quantification methods can be used to identify the uncertainty in the updating parameters. In this paper, the uncertainties associated with the modal parameters are defined as fuzzy membership functions, while the model updating procedure is defined as an optimization problem at each α-cut level. To determine the membership functions of the updated parameters, an objective function is defined and minimized using two metaheuristic optimization algorithms: ant colony optimization (ACO) and particle swarm optimization (PSO). A structural example is used to investigate the accuracy of the fuzzy model updating strategy using the PSO and ACO algorithms. Furthermore, the results obtained by the fuzzy finite element model updating are compared with the Bayesian model updating results.

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“…In recent years, the interval approach has also been applied for FE model updating, see e.g. Gabriele and Valente [89], García et al [90] and Khodaparast et al [91,92]. The interval method can be seen as a specific case of the more general convex modeling approach, coined by Ben-Haim and Elishakoff [93], where it is assumed that the uncertain quantities lie within a convex region.…”

Section: Modeling Of Uncertaintiesmentioning

confidence: 99%

Dealing with uncertainty in model updating for damage assessment: A review

Simoen

Roeck

Lombaert

2015

Mechanical Systems and Signal Processing

397

217

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In structural engineering, model updating is often used for non-destructive damage assessment: by calibrating stiffness parameters of finite element models based on experimentally obtained (modal) data, structural damage can be identified, quantified and located. However, the model updating problem is an inverse problem prone to ill-posedness and ill-conditioning. This means the problem is extremely sensitive to small errors, which may potentially detract from the method's robustness and reliability. As many errors or uncertainties are present in model updating, both regarding the measurements as well as the employed numerical model, it is important to take these uncertainties suitably into account. This paper aims to provide an overview of the available approaches to this end, where two methods are treated in detail: a non-probabilistic fuzzy approach and a probabilistic Bayesian approach. These methods are both elaborated for the specific case of vibration-based finite element model updating for damage assessment purposes.

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Fuzzy finite element model updating of the DLR AIRMOD test structure

Cited by 36 publications

References 38 publications

Novel interval theory‐based parameter identification method for engineering heat transfer systems with epistemic uncertainty

Novel interval theory‐based parameter identification method for engineering heat transfer systems with epistemic uncertainty

Fuzzy Finite Element Model Updating Using Metaheuristic Optimization Algorithms

Dealing with uncertainty in model updating for damage assessment: A review

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