Bayesian inference of random fields represented with the Karhunen–Loève expansion

Uribe, Felipe; Papaioannou, Iason; Betz, Wolfgang; Straub, Daniel

doi:10.1016/j.cma.2019.112632

Cited by 37 publications

(32 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The choice of prior distribution for BMU is one of the first steps (see Traditional Bayesian Model Updating). Appropriate quantification of prior distributions of parameters in a model class can significantly influence results obtained with BMU (Freni and Mannina 2010;Efron 2013;Uribe et al, 2020). In the context of civil infrastructure, model parameters related to aspects such as boundary conditions are specific to each case and cannot be generalized.…”

Section: Suitability For Use In Practicementioning

confidence: 99%

Methodology Maps for Model-Based Sensor-Data Interpretation to Support Civil-Infrastructure Management

Pai¹,

Smith

2022

Front. Built Environ.

View full text Add to dashboard Cite

With increasing urbanization and depleting reserves of raw materials for construction, sustainable management of existing infrastructure will be an important challenge in this century. Structural sensing has the potential to increase knowledge of infrastructure behavior and improve engineering decision making for asset management. Model-based methodologies such as residual minimization (RM), Bayesian model updating (BMU) and error-domain model falsification (EDMF) have been proposed to interpret monitoring data and support asset management. Application of these methodologies requires approximations and assumptions related to model class, model complexity and uncertainty estimations, which ultimately affect the accuracy of data interpretation and subsequent decision making. This paper introduces methodology maps in order to provide guidance for appropriate use of these methodologies. The development of these maps is supported by in-house evaluations of nineteen full-scale cases since 2016 and a two-decade assessment of applications of model-based methodologies. Nineteen full-scale studies include structural identification, fatigue-life assessment, post-seismic risk assessment and geotechnical-excavation risk quantification. In some cases, much, previously unknown, reserve capacity has been quantified. RM and BMU may be useful for model-based data interpretation when uncertainty assumptions and computational constraints are satisfied. EDMF is a special implementation of BMU. It is more compatible with usual uncertainty characteristics, the nature of typically available engineering knowledge and infrastructure evaluation concepts than other methodologies. EDMF is most applicable to contexts of high magnitudes of uncertainties, including significant levels of model bias and other sources of systematic uncertainty. EDMF also provides additional practical advantages due to its ease of use and flexibility when information changes. In this paper, such observations have been leveraged to develop methodology maps. These maps guide users when selecting appropriate methodologies to interpret monitoring information through reference to uncertainty conditions and computational constraints. This improves asset-management decision making. These maps are thus expected to lead to lower maintenance costs and more sustainable infrastructure compared with current practice.

show abstract

Section: Suitability For Use In Practicementioning

confidence: 99%

Methodology Maps for Model-Based Sensor-Data Interpretation to Support Civil-Infrastructure Management

Pai¹,

Smith

2022

Front. Built Environ.

View full text Add to dashboard Cite

show abstract

“…In this case, the solution of the Bayesian inverse problem can be derived analytically. 29 The physical domain is the interval D = [0, L], where L = 5 m is the length of the beam. The beam is subjected to a deterministic point load P = 20 kN at its free right end.…”

Section: D Cantilever Beammentioning

confidence: 99%

“…In the inversion case, the optimal number of terms in the series expansion is unknown and it is controlled by the data. 28,29 In this article, we propose a sequential methodology that is able to perform inference in parameter spaces of different dimension. The method is an extension of the classical BUS (Bayesian updating with structural reliability methods) framework, which expresses a Bayesian inverse problem as an equivalent rare event simulation task.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian inference with subset simulation in varying dimensions applied to the Karhunen–Loève expansion

Uribe

Papaioannou

Latz

et al. 2021

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Uncertainties associated with spatially varying parameters are modeled through random fields discretized into a finite number of random variables. Standard discretization methods, such as the Karhunen-Loève expansion, use series representations for which the truncation order is specified a priori. However, when data is used to update random fields through Bayesian inference, a different truncation order might be necessary to adequately represent the posterior random field. This is an inference problem that not only requires the determination of the often high-dimensional set of coefficients, but also their dimension. In this article, we develop a sequential algorithm to handle such inference settings and propose a penalizing prior distribution for the dimension parameter.The method is a variable-dimensional extension of BUS (Bayesian Updating with Structural reliability methods), combined with subset simulation (SuS). The key idea is to replace the standard Markov Chain Monte Carlo (MCMC) algorithm within SuS by a trans-dimensional MCMC sampler that is able to populate the discrete-continuous parameter space. To address this task, we consider two types of MCMC algorithms that operate in a fixed-dimensional saturated space. The performance of the proposed method with both MCMC variants is assessed numerically for two examples: a 1D cantilever beam with spatially varying flexibility and a 2D groundwater flow problem with uncertain permeability field.

show abstract

“…Further several works on theoretical error analysis in the forward problem are mentioned. The effects of the truncated KLE on the Bayesian inverse problem solution is investigated in [53].…”

Section: Hierarchical Estimationmentioning

confidence: 99%

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

John¹,

Livia²,

Schillings³

et al. 2021

Preprint

View full text Add to dashboard Cite

Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods provide a promising alternative. In this work both methods are first applied to artificially generated data and second on a real world problem, by using data of an electric motor test bench. We show that both methods are able to infer the distribution of varying parameters with a Bayesian hierarchical approach. But the proposed ABC method is computationally much more efficient in order to achieve results with similar accuracy. We suggest to use summary statistics in order to reduce the dimension of the data which significantly increases the efficiency of the algorithm. Further the simulation model is replaced by a Polynomial Chaos Expansion (PCE) surrogate to speed up model evaluations. We proof consistency for the proposed surrogate-based ABC method with summary statistics under mild conditions on the (approximated) forward model.

show abstract

Bayesian inference of random fields represented with the Karhunen–Loève expansion

Cited by 37 publications

References 44 publications

Methodology Maps for Model-Based Sensor-Data Interpretation to Support Civil-Infrastructure Management

Methodology Maps for Model-Based Sensor-Data Interpretation to Support Civil-Infrastructure Management

Bayesian inference with subset simulation in varying dimensions applied to the Karhunen–Loève expansion

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

Contact Info

Product

Resources

About