Sequential surrogate modeling for efficient finite element model updating
Introduction
Considering that current design and assessment procedures do not have any quantitative linkage to actual existing structures [1], a process to associate physical models with corresponding existing structures is necessary for the condition assessment.
Finite element (FE) model updating is a representative of such a process, and is based on the inverse problem of identifying structural parameters by refining an initial FE model based on experimental data. FE model updating can be categorized into deterministic and non-deterministic approaches. In the deterministic approach [2], [3], [4], [5], a residual between measured and computed reference properties is used as an objective function, and an iterative optimization scheme is employed to minimize the objective function by adjusting the model parameters; whereas, the non-deterministic approach takes into account the uncertainties associated with modeling and incomplete measurement data [6], [7], [8], [9], [10], [11]. This approach involves finding the most probable models based on the measured data, using a Bayesian statistical framework, and interval and gap analysis.
The most important task in FE model updating is to minimize the systematic error in the FE model. Many engineers prefer using simple approaches owing to their computational efficiency, despite the availability of much more sophisticated modeling approaches [1]. Many researchers have noted that such simple modeling approaches are inadequate, because of their inability to accurately simulate the actual behavior of real structures. Such simple modeling approaches may results in the systematic errors due to modeling simplifications [12], the omission of structural components [13], and FE discretization errors [14]. It is obvious that the presence of systematic errors results in bias in the model prediction, and this leads to incorrect estimations of the updating parameter [15]. Depending on the modeling and our experience, a high-fidelity FE model can increase the required computational time from only seconds to minutes for a simple analysis (e.g., modal analysis). For a single run, this would not be demanding. However, if the FE analysis must be iterated many times, the resulting process would be highly computational-resource intensive.
In this context, surrogate models have recently attracted considerable attention as faster alternatives to the iterative FE analyses. Surrogate modeling is a method of emulating a computer simulation model in the form of a mathematical/statistical approximation, using the input and output of an FE analysis. The fundamental concept of applying surrogating model to reliability analysis is not entirely new. However, the use of surrogate models for FE model updating has been investigated recently, especially in the civil engineering community [16]. Some examples of surrogate models that have so far been investigated are Multilayer perception [17], polynomial model [16], [18], [19], [20], moving least square method for a polynomial model [21]; radial basis function [22]; Kriging model [23]. Surrogate models are constructed by training samples in the parameter space; therefore, generating the samples for the construction of a surrogate model is a key task. Consequently, conventional surrogate modeling for FE model updating has been investigated from a design of experiments (DOE) in the previous studies, such as central composite design [16], [18], [21], [22], uniform design [20], D-optimal design [19], and Sobol sequence sampling [23].
The conventional approach generally employs a trial-and-error method based on different designs (i.e., different subsets) of the training samples, because the response-surface is not known beforehand. It is also difficult to represent complicated response-surfaces in the conventional approach under local variations of response behaviors and non-linearity, because the conventional approach generates samples that spread out uniformly across the parameter space. In addition, it is inefficient to apply the identical training samples to all target outputs, if identical updating parameters of the FE model can generate the different response-surfaces of the target outputs due to their relative sensitivity.
To address the abovementioned difficulties, we propose a sequential surrogate (SS) modeling for the efficient FE model updating based on the Kriging model. The proposed method is able to address the abovementioned difficulties of the conventional approach. One crucial advantage of the proposed method is the ability to statistically interpret the uncertainty in the prediction, so that this approach can use the measure of infill criteria and update a surrogate model by adding a new sample.
The rest of this paper is organized as follows. In Section 2, we first describe the mathematical background of the Kriging model, including the statistical interpretation of the Kriging prediction. Next, we present a conventional sequential surrogate modeling originated from the global optimization community [24], [25], and a potential problem in FE model updating is discussed. In order to address the potential problem, we propose a sequential surrogate modeling for FE model updating. In Section 3, FE model updating based on the Kriging model with the proposed method is performed numerically and experimentally, using a lab-scaled five-story shear building structure. In addition, the computational efficiency is discussed. In Section 4, we provide concluding remarks on the study.
Section snippets
Kriging model
The Kriging model is a surrogate model that originated from Geostatistics [26]. The Kriging model is a way of modeling a function as a realization of Gaussian process. Assuming that the function being modeled is continuous, two samples of the true function will tend to have similar values if the distance between the two samples decreases. This spatial correlation can be used to estimate an unknown function value from the known function values. This property can be given the statistical
Kriging model-based FE model updating with sequential surrogate modeling
In this section, we evaluate the performance of the method proposed in Section 2 by using a five-story shear building. There are two reasons to use this shear building: Firstly, this shear building is simple and easy to understand; Secondly, it has a variety of the response-surfaces from simple and smooth to complex (i.e., non-stationary) one, even for identical input parameters. Therefore, it is appropriate to describe our motivation and evaluate the performance of the proposed method.
This
Conclusions
In this study, we have proposed a new method for more robust and flexible surrogate modeling for FE model updating. Based on our existing knowledge and a literature survey, the previous investigations on surrogate modeling for FE model updating have proceeded on the basis of the classical design of experiments. In such methods, the generated training samples are used identically for all target outputs in order to build surrogate models at once. In addition, a trial-and-error approach is
Acknowledgement
This research was partially supported by a grant (13SCIPA01) from Smart Civil Infrastructure Research Program funded by Ministry of Land, Infrastructure and Transport (MOLIT) of Korea government and Korea Agency for Infrastructure Technology Advancement (KAIA) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2011351).
References (41)
- et al.
Civil structure condition assessment by FE model updating: methodology and case studies
Finite Elem Anal Des
(2001) - et al.
The sensitivity method in finite element model updating: a tutorial
Mech Syst Signal Process
(2011) - et al.
A new multi-objective approach to finite element model updating
J Sound Vib
(2014) - et al.
Bayesian identification of a cracked plate using a population-based Markov Chain Monte Carlo method
Comput Struct
(2011) - et al.
Effect of secondary elements on bridge structural system reliability considering moment capacity
Struct Saf
(2004) - et al.
Finite element model updating taking into account the uncertainty on the modal parameters estimates
J Sound Vib
(2006) - et al.
Structural identification with systematic errors and unknown uncertainty dependencies
Comput Struct
(2013) - et al.
Finite element model updating in structural dynamics by using the response surface method
Eng Struct
(2010) - et al.
Damage identification by response surface based model updating using D-optimal design
Mech Syst Signal Process
(2011) - et al.
Adaptive response surface based efficient finite element model updating
Finite Elem Anal Des
(2014)
A residual-based Gaussian process model framework for finite element model updating
Comput Struct
Exploratory designs for computational experiments
J Stat Plan Infer
Surrogate-based analysis and optimization
Prog Aerosp Sci
A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites
Comput Mater Sci
One more experiment on estimating high-dimensional integrals by quasi-Monte Carlo methods
Math Comput Simul.
Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations
Mech Mater
Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs)
Compos Part B-Eng
Characterising performance of environmental models
Environ Modell Softw
Committee on structural identification of constructed systems
Optimization procedure to correct stiffness and flexibility matrices using vibration tests
AIAA J
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