Elsevier

Computers & Structures

Volume 168, May 2016, Pages 30-45
Computers & Structures

Sequential surrogate modeling for efficient finite element model updating

https://doi.org/10.1016/j.compstruc.2016.02.005Get rights and content

Highlights

  • This study propose a sequential surrogate modeling for FE model updating.

  • Identical input parameters can produce simple and highly complex response-surfaces.

  • Accordingly, the use of the identical samples for surrogate modeling is not efficient.

  • The proposed method adds samples automatically based on the Kriging model.

  • The proposed method can be customized for a variety of the response-surfaces.

Abstract

Despite the numerous studies concerning finite element model updating (FEMU), a challenging computational cost issue persists. Therefore, surrogate modeling has recently gained considerable attention in FEMU. Conventionally, surrogate models are constructed by identical samples for all outputs. It is very inefficient and subjective, if various response-surfaces exhibit even for identical parameters. Accordingly, we propose a sequential surrogate modeling for FEMU. It uses infill criteria to guide sampling for updating surrogate models automatically. The proposed method is successful to construct the different response-surfaces and apply FEMU. It is promising for constructing surrogate models with minimal user intervention and tremendous computational efficiency.

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).

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