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.

scholarly journals Bayesian Probabilistic Framework for Damage Identification of Steel Truss Bridges under Joint Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Wei Zheng ◽  
Yi Yu
Keyword(s):  
Damage Identification ◽  
Model Updating ◽  
Element Model ◽  
Truss Structures ◽  
Future Research ◽  
Model Parameters ◽  
Probabilistic Framework ◽  
Parameter Uncertainties ◽  
Truss Bridges ◽  
Uncertain Model

The vibration-based structural health monitoring has been traditionally implemented through the deterministic approach that relies on a single model to identify model parameters that represent damages. When such approach is applied for truss bridges, truss joints are usually modeled as either simple hinges or rigid connections. The former could lead to model uncertainties due to the discrepancy between physical configurations and their mathematical models, while the latter could induce model parameter uncertainties due to difficulty in obtaining accurate model parameters of complex joint details. This paper is to present a new perspective for addressing uncertainties associated with truss joint configurations in damage identification based on Bayesian probabilistic model updating and model class selection. A new sampling method of the transitional Markov chain Monte Carlo is incorporated with the structure’s finite element model for implementing the approach to damage identification of truss structures. This method can not only draw samples which approximate the updated probability distributions of uncertain model parameters but also provide model evidence that quantify probabilities of uncertain model classes. The proposed probabilistic framework and its applicability for addressing joint uncertainties are illustrated and examined with an application example. Future research directions in this field are discussed.

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.

A Sequential Calibration and Validation Framework for Model Parameter Updating and Bias Correction

2020 ◽  
Author(s):  
Chen Jiang ◽  
Yixuan Liu ◽  
Zhen Hu ◽  
Zissimos P. Mourelatos ◽  
David Gorsich ◽  
...  
Keyword(s):  
Model Validation ◽  
Bias Correction ◽  
Model Parameters ◽  
Model Bias ◽  
Bayesian Calibration ◽  
Prior Distributions ◽  
Model Parameter ◽  
Calibration And Validation ◽  
Validation Framework ◽  
Uncertain Model

Abstract Model parameter updating and bias correction plays an essential role in improving the validity of Modeling and Simulation (M&S) in engineering design and analysis. However, it is observed that the existing methods may either be misled by potentially wrong information if the computer model cannot adequately capture the underlying true physics, or be affected by the prior distributions of the unknown model parameters. In this paper, a sequential model calibration and validation (SeCAV) framework is proposed to improve the efficacy of both model parameter updating and model bias correction, where the model validation and Bayesian calibration are implemented in a sequential manner. In each iteration, the model validation assessment is employed as a filter to select the best experimental data for Bayesian calibration, and to update the prior distributions of uncertain model parameters for the next iteration. The calibrated parameters are then integrated with model bias correction to improve the prediction accuracy of the M&S. A mathematical example is employed to demonstrate the advantages of the SeCAV method.

scholarly journals Uncertainty in design flood profiles derived by hydraulic modelling

2012 ◽  
Vol 43 (6) ◽  
pp. 753-761 ◽  
Author(s):  
Luigia Brandimarte ◽  
Giuliano Di Baldassarre
Keyword(s):  
Traditional Approach ◽  
Model Parameters ◽  
Hydraulic Modelling ◽  
Design Flood ◽  
Po River ◽  
Sources Of Uncertainty ◽  
Explicit Analysis ◽  
Flood Estimation ◽  
River Reach ◽  
Many Sources

The scientific literature has widely shown that hydraulic modelling is affected by many sources of uncertainty (e.g. model structure, input data, model parameters). However, when hydraulic models are used for engineering purposes (e.g. flood defense design), there is still a tendency to make a deterministic use of them. More specifically, the prediction of flood design profiles is often based on the outcomes of a calibrated hydraulic model. Despite the good results in model calibration, this prediction is affected by significant uncertainty, which is commonly considered by adding a freeboard to the simulated flood profile. A more accurate approach would require an explicit analysis of the sources of uncertainty affecting hydraulic modelling and design flood estimation. This paper proposes an alternative approach, which is based on the use of uncertain flood profiles, where the most significant sources of uncertainty are explicitly analyzed. An application to the Po river reach between Cremona and Borgoforte (Italy) is used to illustrate the proposed framework and compare it to the traditional approach. This paper shows that the deterministic approach underestimates the design flood profile and questions whether the freeboard, often arbitrarily defined, might lead to a false perception of additional safety levels.

Integrating Bayesian Calibration, Bias Correction, and Machine Learning for the 2014 Sandia Verification and Validation Challenge Problem

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Wei Li ◽  
Shishi Chen ◽  
Zhen Jiang ◽  
Daniel W. Apley ◽  
Zhenzhou Lu ◽  
...  
Keyword(s):  
Machine Learning ◽  
Predictive Model ◽  
Bias Correction ◽  
Verification And Validation ◽  
Model Parameters ◽  
Loading Conditions ◽  
Multiple Sources ◽  
Bayesian Calibration ◽  
Sources Of Uncertainty ◽  
Machine Learning Model

This paper describes an integrated Bayesian calibration, bias correction, and machine learning approach to the validation challenge problem posed at the Sandia Verification and Validation Challenge Workshop, May 7–9, 2014. Three main challenges are recognized as: I—identification of unknown model parameters; II—quantification of multiple sources of uncertainty; and III—validation assessment when there are no direct experimental measurements associated with one of the quantities of interest (QoIs), i.e., the von Mises stress. This paper addresses these challenges as follows. For challenge I, sensitivity analysis is conducted to select model parameters that have significant impact on the model predictions for the displacement, and then a modular Bayesian approach is performed to calibrate the selected model parameters using experimental displacement data from lab tests under the “pressure only” loading conditions. Challenge II is addressed using a Bayesian model calibration and bias correction approach. For improving predictions of displacement under “pressure plus liquid” loading conditions, a spatial random process (SRP) based model bias correction approach is applied to develop a refined predictive model using experimental displacement data from field tests. For challenge III, the underlying relationship between stress and displacement is identified by training a machine learning model on the simulation data generated from the supplied tank model. Final predictions of stress are made via the machine learning model and using predictions of displacements from the bias-corrected predictive model. The proposed approach not only allows the quantification of multiple sources of uncertainty and errors in the given computer models, but also is able to combine multiple sources of information to improve model performance predictions in untested domains.

Time-domain Markov chain Monte Carlo–based Bayesian damage detection of ballasted tracks using nonlinear ballast stiffness model

2020 ◽  
pp. 147592172096695
Author(s):  
Heung-Fai Lam ◽  
Mujib Olamide Adeagbo ◽  
Yeong-Bin Yang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Damage Detection ◽  
Probability Density ◽  
Time Domain ◽  
Model Updating ◽  
Model Parameters ◽  
Uncertain Model ◽  
Nonlinear Stress

This article reports the development of a methodology for detecting ballast damage under a sleeper based on measured sleeper vibration following the Bayesian statistical system identification framework. To ensure the methodology is applicable under large amplitude vibration of the sleeper (e.g. under trainload), the nonlinear stress–strain behavior of railway ballast is considered. This, on one hand, significantly reduces the problem of modeling error, but, on the other hand, increases the number of uncertain model parameters. The uncertainty associated with the identified model parameters of the rail–sleeper–ballast system may be very high. To overcome this difficulty, the Markov chain Monte Carlo–based Bayesian model updating is adopted in the proposed methodology for the approximation of the posterior probability density function of uncertain model parameters. Owing to the nonlinear behavior of the system, the model updating is performed in the time domain instead of the modal domain. The applicability of the proposed damage detection methodology was first verified numerically using simulated impact hammer test data in two damaged cases perturbed with Gaussian white noise. Second, impact hammer tests of in situ sleepers in the full-scale in-door ballasted track test panel were carried out to collect data for the experimental verification of the proposed methodology. Artificial ballast damage was simulated under the target concrete sleeper by replacing normal-sized ballast particles (∼60 mm) by small-sized ballast particles (∼15 mm). The proposed methodology successfully identified the location and severity of ballast damage under the sleeper. From the calculated posterior marginal probability density functions of model parameters, one can quantify the uncertainties associated with the damage detection results. The proposed methodology is an essential step in the development of a long-term railway track health monitoring system utilizing train-induced vibration.

Bayesian Approach to Non-ignorable Missingness in Latent Growth Models

2021 ◽  
Vol 1 (2) ◽  
pp. 1-30
Author(s):  
Zhenqiu Lu ◽  
Zhiyong Zhang
Keyword(s):  
Bayesian Approach ◽  
Data Augmentation ◽  
Longitudinal Research ◽  
Growth Models ◽  
Sampling Procedure ◽  
Future Research ◽  
Model Parameters ◽  
Model Estimation ◽  
Latent Growth ◽  
Growth Curve Models

Latent growth curve models (LGCMs) are becoming increasingly important among growth models because they can effectively capture individuals' latent growth trajectories and also explain the factors that influence such growth by analyzing the repeatedly measured manifest variables. However, with the increase in complexity of LGCMs, there is an increase in issues on model estimation. This research proposes a Bayesian approach to LGCMs to address the perennial problem of almost all longitudinal research, namely, missing data. First, different missingness models are formulated. We focus on non-ignorable missingness in this article. Specifically, these models include the latent intercept dependent missingness, the latent slope dependent missingness, and the potential outcome dependent missingness. To implement the model estimation, this study proposes a full Bayesian approach through data augmentation algorithm and Gibbs sampling procedure. Simulation studies are conducted and results show that the proposed method accurately recover model parameters and the mis-specified missingness may result in severely misleading conclusions. Finally, the implications of the approach and future research directions are discussed.

An Interval Uncertainty Based Method for Damage Identification

2007 ◽  
Vol 347 ◽  
pp. 551-556 ◽  
Author(s):  
S. Gabriele ◽  
C. Valente ◽  
F. Brancaleoni
Keyword(s):  
Interval Analysis ◽  
Damage Identification ◽  
Model Updating ◽  
Interval Uncertainty ◽  
Model Parameters ◽  
Dynamic Problems ◽  
Framed Structures ◽  
Sources Of Uncertainty ◽  
Inclusion Property ◽  
Interval Approach

The problem of damage identification in presence of uncertainties is faced up in the framework of interval analysis. A method previously developed by the authors in the context of model updating and global minimization for dynamic problems is applied to identify the damage in framed structures. The inclusion property of the interval analysis is exploited to find the bounds of the physical solutions. Model parameters, experimental measures and modelling errors are considered as possible sources of uncertainty. The advantages of the interval approach are discussed through numerical simulations involving the different kind of uncertainties.

Representation of bolted joints in a structure using finite element modelling and model updating

2020 ◽  
Vol 14 (3) ◽  
pp. 7141-7151 ◽  
Author(s):  
R. Omar ◽  
M. N. Abdul Rani ◽  
M. A. Yunus
Keyword(s):  
Finite Element ◽  
Dynamic Behaviour ◽  
Model Updating ◽  
Complex Structure ◽  
Bolted Joints ◽  
Model Parameters ◽  
Fe Model ◽  
Bolted Joint ◽  
Fe Modelling ◽  
Joint Structure

Efficient and accurate finite element (FE) modelling of bolted joints is essential for increasing confidence in the investigation of structural vibrations. However, modelling of bolted joints for the investigation is often found to be very challenging. This paper proposes an appropriate FE representation of bolted joints for the prediction of the dynamic behaviour of a bolted joint structure. Two different FE models of the bolted joint structure with two different FE element connectors, which are CBEAM and CBUSH, representing the bolted joints are developed. Modal updating is used to correlate the two FE models with the experimental model. The dynamic behaviour of the two FE models is compared with experimental modal analysis to evaluate and determine the most appropriate FE model of the bolted joint structure. The comparison reveals that the CBUSH element connectors based FE model has a greater capability in representing the bolted joints with 86 percent accuracy and greater efficiency in updating the model parameters. The proposed modelling technique will be useful in the modelling of a complex structure with a large number of bolted joints.

Sign in / Sign up

Export Citation Format

Share Document