A Bayesian finite element model updating with combined normal and lognormal probability distributions using modal measurements

Das, Ayan; Debnath, Nirmalendu

doi:10.1016/j.apm.2018.05.004

Cited by 28 publications

(5 citation statements)

References 56 publications

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“…Bayesian FEMU methods combine prior information and test data, the posterior pdf of the parameters is inferred by the MCMC algorithm. This process can be explained as [10][11]:…”

Section: Femu Theory Based On Bayesian Inferencementioning

confidence: 99%

Bayesian Model Updating Based on Kriging Surrogate Model and Simulated Annealing Algorithm

Wang

Yin

Peng

2022

J. Phys.: Conf. Ser.

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Aiming at the problem of difficulty in selecting the proposal distribution and low computational efficiency in the traditional Markov chain Monte Carlo algorithm, a Bayesian model updating method using surrogate model technology and simulated annealing algorithm is proposed. Firstly, the Kriging surrogate model is used to mine the implicit relationship between the structural parameters to be updated and the corresponding dynamic responses, and the Kriging model that meets the accuracy requirement is used to replace the complex finite element model to participate in the iterative calculation to improve the model updating efficiency. Then, the simulated annealing algorithm is introduced to reorganize the Markov chains from different proposal distributions to obtain high-quality posterior samples, which are used to estimate the parameters posterior distributions. Finally, a space truss structure is used to verify the effectiveness of the proposed method.

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“…Bayesian FEMU methods combine prior information and test data, the posterior pdf of the parameters is inferred by the MCMC algorithm. This process can be explained as [10][11]:…”

Section: Femu Theory Based On Bayesian Inferencementioning

confidence: 99%

Bayesian Model Updating Based on Kriging Surrogate Model and Simulated Annealing Algorithm

Wang

Yin

Peng

2022

J. Phys.: Conf. Ser.

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“…Few authors like Bansal 36 and Yin et al 37 utilized similar Bayesian framework for model updating by utilizing reduced order models. In a relatively recent work, strictly positive nature of structural parameters is well‐handled by Das and Debnath 38 in Bayesian framework for model updating by using combined normal and lognormal distributions. Besides, Behmanesh and Moaveni 39 and Lam et al 40 applied advanced Markov chain Monte Carlo (MCMC) techniques for probabilistic damage detection in contribution to structural health monitoring (SHM).…”

Section: Introductionmentioning

confidence: 99%

A multi‐objective framework for finite element model updating using incomplete modal measurements

Debnath

Das

2021

Struct Control Health Monit

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Summary Finite element (FE) model updating in multi‐objective framework helps for better understanding of overall performance in updating (under various variations of weightages assigned to basic components of the objective function) along with providing scope for better judgmental selection. A FE model updating in multi‐objective framework is proposed with no requirement of repeated eigen‐solution along with avoiding repeated possibilities of incurring mode‐pairing error (by adopting an existing framework of system mode shape). Two multi‐objective optimization techniques are adopted: (a) weighted sum and (b) adaptive weighted sum methods. Moreover, a possible single best solution out of the Pareto front is identified based on minimum modal distance value and compared with Gibbs sampling technique (without mode‐matching). Two examples with multiple damage cases utilized in validating the proposed approach are as follows: (a) simulated example (ASCE benchmark structure) and (b) experimental example (four storied shear frame laboratory structure). It is observed that the proposed multi‐objective framework has performed well in FE model updating in case of both simulated and experimental cases. Additionally, a connection (directly relating the multi‐objective weights and error variances) is established between the proposed updating methodology and an existing Bayesian updating methodology to facilitate the probabilistic damage detection in Bayesian framework. Moreover, selection of an appropriate solution (out of the Pareto front) having suitable values of multi‐objective weights facilitates to estimate the suitable values of error variances (based on the proposed connection), consequently enabling an efficient Bayesian FE model updating without requirement of any assumption of error variances.

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“…Beck et al [32,33] are pioneers in establishing the BMUA's fundamental theory. Later, the derivations and improvements to promote the Bayesian approach's capability were only developed for stiffness updating [31,[34][35][36]. However, all aforementioned BMUA work (herein, traditional BMUA) generally only focuses on stiffness updating and is performed based on the classical eigenequation, (K − λM)φ = 0…”

Section: Introductionmentioning

confidence: 99%

Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

Zeng

Kim

2021

Applied Sciences

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The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.

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A Bayesian finite element model updating with combined normal and lognormal probability distributions using modal measurements

Cited by 28 publications

References 56 publications

Bayesian Model Updating Based on Kriging Surrogate Model and Simulated Annealing Algorithm

Bayesian Model Updating Based on Kriging Surrogate Model and Simulated Annealing Algorithm

A multi‐objective framework for finite element model updating using incomplete modal measurements

Stiffness Modification-Based Bayesian Finite Element Model Updating to Solve Coupling Effect of Structural Parameters: Formulations

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