Identification of Structural Stiffness and Mass using Bayesian Model Updating Approach with Known Added Mass: Numerical Investigation

2020 ◽  
Vol 20 (11) ◽  
pp. 2050123
Author(s):  
Jice Zeng ◽  
Young Hoon Kim
Keyword(s):  
Bayesian Approach ◽  
Bayesian Model ◽  
Prior Probability ◽  
Model Updating ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Original System ◽  
New Approach ◽  
Vibration Data ◽  
Structural Mass

The Bayesian model updating approach (BMUA) has been widely used to update structural parameters using modal measurements because of its powerful ability to handle uncertainties and incomplete data. However, a conventional BMUA is mainly used to update stiffness with the assumption that structural mass is known. Because simultaneously updating stiffness and mass leads to unidentifiable case or coupling effect of stiffness and mass, this assumption in conventional BMUA is questionable to update stiffness when the mass has significantly changed. This study proposes a new updating framework based on two structural systems: original and modified systems. A modified system is created by adding known mass to the original system. Different from the conventional Bayesian approach, two sets of measured vibration data in the proposed Bayesian approach are obtainable to address the coupling effect existing in the conventional Bayesian approach. To this end, a new approach reformulates the prior probability distribution function and the objective function. Two numerical simulations are considered to demonstrate the performance of the proposed approach, including (1) parameter identification, (2) posterior uncertainties, (3) probabilistic damage detections. The proposed BMUA outperforms a conventional BMUA in identifying both stiffness and mass.

scholarly journals Probabilistic Damage Detection and Identification of Coupled Structural Parameters using Bayesian Model Updating with Added Mass

2021 ◽  
Author(s):  
jice zeng ◽  
Young Hoon Kim
Keyword(s):  
Convergence Rate ◽  
Damage Detection ◽  
Bayesian Model ◽  
Model Updating ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Added Mass ◽  
Distribution Functions ◽  
Single Chain ◽  
Characteristic Equations

Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to identify structural parameters (e.g., mass and stiffness) as probability distribution functions (PDF) and uncertainties. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single-chain based Markov Chain Monte Carlo (MCMC), leading to a low convergence rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) Algorithm are adopted to draw samples by running multiple Markov chains parallelly to enhance convergence rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.

Bayesian model updating of a large-span steel tied arch bridge: an experimental study

2021 ◽  
Author(s):  
Lanxin Luo ◽  
Huaqiang Zhong ◽  
Ye Xia ◽  
Limin Sun
Keyword(s):  
Experimental Study ◽  
Sensitivity Analysis ◽  
Bayesian Model ◽  
Model Updating ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Fe Model ◽  
Large Span ◽  
Vibration Data ◽  
Tied Arch Bridge

<p>In this paper, a large-span steel tied arch bridge's Bayesian FEMU is carried out based on the ambient vibration data. Firstly, the ERA method is used for modal identification. Then, the benchmark FE model of this bridge is established. Based on the sensitivity analysis, six updating parameters significantly affecting the natural frequency are selected. Subsequently, the objective function of the FEMU is established, and the DRAM algorithm is utilized to simulate the parameter samples conforming to the posterior distribution. Finally, the uncertainty analysis of the updated items is carried out. After FEMU, the results show that the model's frequency uncertainty is reduced, and the theoretical frequencies are highly consistent with the identified frequencies.</p>

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

2021 ◽  
Vol 11 (22) ◽  
pp. 10615
Author(s):  
Jice Zeng ◽  
Young Hoon Kim
Keyword(s):  
Model Updating ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Linear Optimization ◽  
Hessian Matrix ◽  
Element Model ◽  
Optimization Method ◽  
Finite Element Model Updating ◽  
Damage Estimation ◽  
Objective Functions

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.

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

2022 ◽  
Vol 2148 (1) ◽  
pp. 012008
Author(s):  
Zenghui Wang ◽  
Hong Yin ◽  
Zhenrui Peng
Keyword(s):  
Simulated Annealing ◽  
Surrogate Model ◽  
Bayesian Model ◽  
Simulated Annealing Algorithm ◽  
Model Updating ◽  
Structural Parameters ◽  
Dynamic Responses ◽  
Monte Carlo Algorithm ◽  
Kriging Surrogate Model ◽  
Annealing Algorithm

Abstract 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.

Ambient Vibration Test, Modal Identification and Structural Model Updating Following Bayesian Framework

2015 ◽  
Vol 15 (07) ◽  
pp. 1540024 ◽  
Author(s):  
J. Yang ◽  
H. F. Lam ◽  
J. Hu
Keyword(s):  
Bayesian Model ◽  
Structural Model ◽  
Model Updating ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Modal Parameters ◽  
Vibration Test ◽  
Engineering Structures ◽  
Ambient Vibration Test ◽  
Vibration Data

Structural health monitoring (SHM) of civil engineering structures based on vibration data includes three main components: ambient vibration test, modal identification and model updating. This paper discussed these three components in detail and proposes a general framework of SHM for practical application. First, a fast Bayesian modal identification method based on Fast Fourier Transform (FFT) is introduced for efficiently extracting modal parameters together with the corresponding uncertainties from ambient vibration data. A recently developed Bayesian model updating method using Markov chain Monte Carlo simulation (MCMCS) is then discussed. To illustrate the performance of the proposed modal identification and model updating methods, a scale-down transmission tower is investigated. Ambient vibration test is conducted on the target structure to obtain modal parameters. By using the measured modal parameters, model updating is carried out. The MCMC-based Bayesian model updating method can efficiently evaluate the posterior marginal PDFs of the uncertain parameters without calculating high-dimension numerical integration, which provides posterior uncertainties for the target systems.

scholarly journals Vision-Based Structural FE Model Updating Using Genetic Algorithm

2021 ◽  
Vol 11 (4) ◽  
pp. 1622
Author(s):  
Gun Park ◽  
Ki-Nam Hong ◽  
Hyungchul Yoon
Keyword(s):  
Genetic Algorithm ◽  
Model Updating ◽  
Structural Parameters ◽  
Fe Model ◽  
Structural Members ◽  
Stiffness Reduction ◽  
Before And After ◽  
Scale Test ◽  
Fe Model Updating ◽  
Story Building

Structural members can be damaged from earthquakes or deterioration. The finite element (FE) model of a structure should be updated to reflect the damage conditions. If the stiffness reduction is ignored, the analysis results will be unreliable. Conventional FE model updating techniques measure the structure response with accelerometers to update the FE model. However, accelerometers can measure the response only where the sensor is installed. This paper introduces a new computer-vision based method for structural FE model updating using genetic algorithm. The system measures the displacement of the structure using seven different object tracking algorithms, and optimizes the structural parameters using genetic algorithm. To validate the performance, a lab-scale test with a three-story building was conducted. The displacement of each story of the building was measured before and after reducing the stiffness of one column. Genetic algorithm automatically optimized the non-damaged state of the FE model to the damaged state. The proposed method successfully updated the FE model to the damaged state. The proposed method is expected to reduce the time and cost of FE model updating.

scholarly journals Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
B. Asgari ◽  
S. A. Osman ◽  
A. Adnan
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Structural Parameters ◽  
Element Model ◽  
Structural Behavior ◽  
Model Tuning ◽  
The Finite Element Model ◽  
Cable Stayed Bridges

The model tuning through sensitivity analysis is a prominent procedure to assess the structural behavior and dynamic characteristics of cable-stayed bridges. Most of the previous sensitivity-based model tuning methods are automatic iterative processes; however, the results of recent studies show that the most reasonable results are achievable by applying the manual methods to update the analytical model of cable-stayed bridges. This paper presents a model updating algorithm for highly redundant cable-stayed bridges that can be used as an iterative manual procedure. The updating parameters are selected through the sensitivity analysis which helps to better understand the structural behavior of the bridge. The finite element model of Tatara Bridge is considered for the numerical studies. The results of the simulations indicate the efficiency and applicability of the presented manual tuning method for updating the finite element model of cable-stayed bridges. The new aspects regarding effective material and structural parameters and model tuning procedure presented in this paper will be useful for analyzing and model updating of cable-stayed bridges.

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