A comprehensive Bayesian approach for model updating and quantification of modeling errors

2011 ◽  
Vol 26 (4) ◽  
pp. 550-560 ◽  
Author(s):  
E.L. Zhang ◽  
P. Feissel ◽  
J. Antoni
Keyword(s):  
Bayesian Approach ◽  
Model Updating ◽  
Modeling Errors

scholarly journals Vibration-based Bayesian model updating of civil engineering structures applying Gaussian process metamodel

2019 ◽  
Vol 22 (16) ◽  
pp. 3487-3502
Author(s):  
Hossein Moravej ◽  
Tommy HT Chan ◽  
Khac-Duy Nguyen ◽  
Andre Jesus
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Bayesian Approach ◽  
Model Updating ◽  
Numerical Models ◽  
Element Model ◽  
The Body ◽  
Structural Safety ◽  
Discrepancy Function ◽  
The Finite Element Model

Structural health monitoring plays a significant role in providing information regarding the performance of structures throughout their life spans. However, information that is directly extracted from monitored data is usually susceptible to uncertainties and not reliable enough to be used for structural investigations. Finite element model updating is an accredited framework that reliably identifies structural behavior. Recently, the modular Bayesian approach has emerged as a probabilistic technique in calibrating the finite element model of structures and comprehensively addressing uncertainties. However, few studies have investigated its performance on real structures. In this article, modular Bayesian approach is applied to calibrate the finite element model of a lab-scaled concrete box girder bridge. This study is the first to use the modular Bayesian approach to update the initial finite element model of a real structure for two states—undamaged and damaged conditions—in which the damaged state represents changes in structural parameters as a result of aging or overloading. The application of the modular Bayesian approach in the two states provides an opportunity to examine the performance of the approach with observed evidence. A discrepancy function is used to identify the deviation between the outputs of the experimental and numerical models. To alleviate computational burden, the numerical model and the model discrepancy function are replaced by Gaussian processes. Results indicate a significant reduction in the stiffness of concrete in the damaged state, which is identical to cracks observed on the body of the structure. The discrepancy function reaches satisfying ranges in both states, which implies that the properties of the structure are predicted accurately. Consequently, the proposed methodology contributes to a more reliable judgment about structural safety.

Updating Predictive Models: Calibration, Bias Correction and Identifiability

2010 ◽  
Author(s):  
Paul D. Arendt ◽  
Wei Chen ◽  
Daniel W. Apley
Keyword(s):  
Computer Model ◽  
Bayesian Approach ◽  
Bias Correction ◽  
Process Model ◽  
Model Updating ◽  
Future Research ◽  
Model Parameters ◽  
Sources Of Uncertainty ◽  
Uncertain Model ◽  
Many Sources

Model updating, which utilizes mathematical means to combine model simulations with physical observations for improving model predictions, has been viewed as an integral part of a model validation process. While calibration is often used to “tune” uncertain model parameters, bias-correction has been used to capture model inadequacy due to a lack of knowledge of the physics of a problem. While both sources of uncertainty co-exist, these two techniques are often implemented separately in model updating. This paper examines existing approaches to model updating and presents a modular Bayesian approach as a comprehensive framework that accounts for many sources of uncertainty in a typical model updating process and provides stochastic predictions for the purpose of design. In addition to the uncertainty in the computer model parameters and the computer model itself, this framework accounts for the experimental uncertainty and the uncertainty due to the lack of data in both computer simulations and physical experiments using the Gaussian process model. Several challenges are apparent in the implementation of the modular Bayesian approach. We argue that distinguishing between uncertain model parameters (calibration) and systematic inadequacies (bias correction) is often quite challenging due to an identifiability issue. We present several explanations and examples of this issue and bring up the needs of future research in distinguishing between the two sources of uncertainty.

Experimental validation of a FRF-based model updating method

2016 ◽  
Vol 24 (8) ◽  
pp. 1570-1583 ◽  
Author(s):  
Fariba Shadan ◽  
Faramarz Khoshnoudian ◽  
Daniel J Inman ◽  
Akbar Esfandiari
Keyword(s):  
Measurement Errors ◽  
Model Updating ◽  
Structural Parameters ◽  
Element Model ◽  
Lumped Mass ◽  
Sensitivity Equation ◽  
Modeling Errors ◽  
Incomplete Measurement ◽  
Aluminum Beam

In this paper, a finite element model updating method using frequency response functions is experimentally validated. The method is a sensitivity-based model updating approach which utilizes a pseudo-linear sensitivity equation. The method is robust against the adverse effects of incomplete measurement, measurement errors and modeling errors. The experimental setup consists of a free-free aluminum beam, where changes are introduced by reducing the stiffness and attaching lumped mass at certain parts of the beam. The method is applied to identify the location and amount of the changes in structural parameters. The results indicate that the location and the size of different level of changes in the structure can be properly identified by the method. In addition, a study is done on the influence of the number of impacts and sensors on the quality of the identified parameters.

Use of Measured Vibration of In-Situ Sleeper for Detecting Underlying Railway Ballast Damage

2015 ◽  
Vol 15 (08) ◽  
pp. 1540026 ◽  
Author(s):  
Q. Hu ◽  
H. F. Lam ◽  
S. A. Alabi
Keyword(s):  
Damage Detection ◽  
Bayesian Approach ◽  
Model Updating ◽  
Probabilistic Approach ◽  
Modeling Method ◽  
Detection Methods ◽  
Model Parameters ◽  
Railway Ballast ◽  
Continuous Modeling ◽  
The Bayesian Approach

The identification of railway ballast damage under a concrete sleeper is investigated by following the Bayesian approach. The use of a discrete modeling method to capture the distribution of ballast stiffness under the sleeper introduces artificial stiffness discontinuities between different ballast regions. This increases the effects of modeling errors and reduces the accuracy of the ballast damage detection results. In this paper, a continuous modeling method was developed to overcome this difficulty. The uncertainties induced by modeling error and measurement noise are the major difficulties of vibration-based damage detection methods. In the proposed methodology, Bayesian probabilistic approach is adopted to explicitly address the uncertainties associated with the identified model parameters. In the model updating process, the stiffness of the ballast foundation is assumed to be continuous along the sleeper by using a polynomial of order N. One of the contributions of this paper is to calculate the order N conditional on a given set of measurement utilizing the Bayesian model class selection method. The proposed ballast damage detection methodology was verified with vibration data obtained from a segment of full-scale ballasted track under laboratory conditions, and the experimental verification results are very encouraging showing that it is possible to use the Bayesian approach along with the newly developed continuous modeling method for the purpose of ballast damage detection.

scholarly journals Bayesian model updating with consideration of modeling error

2010 ◽  
pp. 255-266
Author(s):  
Erliang Zhang ◽  
Pierre Feissel ◽  
Jérôme Antoni
Keyword(s):  
Posterior Probability ◽  
Model Updating ◽  
Linear Structure ◽  
Modeling Error ◽  
Posterior Probability Distribution ◽  
Statistical Framework ◽  
Modal Model ◽  
Modeling Errors ◽  
Complete Process

On account of measurement and modeling errors, structural identification is better tackled within the statistical framework. In this work, a complete process of Bayesian inference for the characterization of the dynamic behavior of a linear structure is presented in the frequency domain. The polynomial chaos expansion is adopted as a surrogate model to propagate the parameter uncertainty and thus accelerate the evaluation of their posterior probability distribution. Moreover, one hybrid modal model is proposed by introducing some additional variables so as to deal with the modeling errors. Bayesian updating is validated experimentally on a steel square plate and the proposed hybrid modal model is illustrated numerically on a cantilever beam.

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