Algorithms for Bayesian Model Class Selection of Higher-Dimensional Dynamic Systems

2007 ◽  
Author(s):  
Sai Hung Cheung ◽  
James L. Beck
Keyword(s):  
Bayesian Model ◽  
Model Updating ◽  
Structural Dynamic ◽  
Higher Dimensional ◽  
Significant Probability ◽  
Model Class ◽  
Updating Procedure ◽  
Model Class Selection ◽  
Dimensional Integral ◽  
Selection Of

In recent years, Bayesian model updating techniques based on measured data have been applied in structural health monitoring. Often we are faced with the problem of how to select the ‘best’ model from a set of competing candidate model classes for the system based on data. To tackle this problem, Bayesian model class selection is used, which provides a rigorous Bayesian updating procedure to give the probability of different candidate classes for a system, based on the data from the system. There may be cases where more than one model class has significant probability and each of these will give different predictions. Bayesian model class averaging provides a coherent mechanism to incorporate all the considered model classes in the probabilistic predictions for the system. However, both Bayesian model class selection and Bayesian model class averaging require the calculation of the evidence of the model class which requires the nontrivial computation of a multi-dimensional integral. In this paper, several methods for solving this computationally challenging problem of model class selection are presented, proposed and compared. The efficiency of the proposed methods is illustrated by an example involving a structural dynamic system.

Hydrostatic-season-time model updating using Bayesian model class selection

2018 ◽  
Vol 169 ◽  
pp. 40-50 ◽  
Author(s):  
Sonja Gamse ◽  
Wan-Huan Zhou ◽  
Fang Tan ◽  
Ka-Veng Yuen ◽  
Michael Oberguggenberger
Keyword(s):  
Bayesian Model ◽  
Model Updating ◽  
Time Model ◽  
Model Class ◽  
Model Class Selection

Probabilistic identification of underground soil stratification using cone penetration tests

2013 ◽  
Vol 50 (7) ◽  
pp. 766-776 ◽  
Author(s):  
Yu Wang ◽  
Kai Huang ◽  
Zijun Cao
Keyword(s):  
Bayesian Model ◽  
Soil Classification ◽  
Cone Penetration ◽  
Bayesian Approaches ◽  
Soil Layers ◽  
Cone Penetration Tests ◽  
Selection Approach ◽  
Model Class ◽  
Model Class Selection ◽  
Penetration Tests

This paper develops Bayesian approaches for underground soil stratum identification and soil classification using cone penetration tests (CPTs). The uncertainty in the CPT-based soil classification using the Robertson chart is modeled explicitly in the Bayesian approaches, and the probability that the soil belongs to one of the nine soil types in the Robertson chart based on a set of CPT data is formulated using the maximum entropy principle. The proposed Bayesian approaches contain two major components: a Bayesian model class selection approach to identify the most probable number of underground soil layers and a Bayesian system identification approach to simultaneously estimate the most probable layer thicknesses and classify the soil types. Equations are derived for the Bayesian approaches, and the proposed approaches are illustrated using a real-life CPT performed at the National Geotechnical Experimentation Site (NGES) at Texas A&M University, USA. It has been shown that the proposed approaches properly identify the underground soil stratification and classify the soil type of each layer. In addition, as the number of model classes increases, the Bayesian model class selection approach identifies the soil layers progressively, starting from the statistically most significant boundary and gradually zooming into less significant ones with improved resolution. Furthermore, it is found that the evolution of the identified soil strata as the model class increases provides additional valuable information for assisting in the interpretation of CPT data in a rational and transparent manner.

A Comparison Between the Use of Physical Parameters and Correction Factors in Dynamic Model Updating

1995 ◽  
Author(s):  
Walter D’Ambrogio ◽  
Annalisa Fregolent
Keyword(s):  
Elasticity Modulus ◽  
Model Updating ◽  
Mass Density ◽  
Physical Parameters ◽  
Test Case ◽  
Correction Factors ◽  
Scale Factors ◽  
Updating Procedure ◽  
Geometrical Dimensions ◽  
Selection Of

Abstract The selection of quantities and/or variables that have to be corrected during the updating process is addressed in this paper. Among quantities, the major alternative is the choice between correction factors and physical parameters. The former represent scale factors used to adjust mass and stiffness submatrices of the analytical model, while the latter include parameters such as the elasticity modulus, mass density, geometrical dimensions, etc. Advantages and limitations in the process of updating physical parameters instead of correction factors are highlighted: it can be shown that only a limited number of physical parameters can be simultaneously updated for each element. The two approaches are compared using a previously developed updating procedure to solve an experimental test case.

Multiple crack identification in frame structures using a hybrid Bayesian model class selection and swarm-based optimization methods

2017 ◽  
Vol 17 (1) ◽  
pp. 39-58 ◽  
Author(s):  
Laleh Fatahi ◽  
Shapour Moradi
Keyword(s):  
Bayesian Model ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Natural Frequencies ◽  
Optimization Methods ◽  
Crack Identification ◽  
Multiple Crack ◽  
Bee Colony ◽  
Model Class ◽  
Model Class Selection

Crack identification in engineering structures has been widely investigated by researchers. Most of the literature on multiple crack identification, however, has focused on rather simple structures like beams and it is often assumed that the number of cracks is known while this is not a practical assumption. In this article, multiple crack identification in frame structures is investigated based on experimental vibration data using the Bayesian model class selection and swarm-based optimization methods to identify both the number of cracks and their characteristics. To this end, first, the numerical model of the intact frame is updated based on the natural frequencies of the intact state using the particle swarm inspired multi-elitist artificial bee colony algorithm. After updating the intact model of the structure, a set of numerical models of the cracked frame with different numbers of cracks is constructed. Since the number of cracks is not known a priori, the Bayesian model class selection is employed to find the most plausible model class in order to predict the number of cracks. Then, the parameters of the cracks are identified using the particle swarm inspired multi-elitist artificial bee colony algorithm. Instead of pinpointing to one optimal solution obtained after a large number of function evaluations, a set of best solutions whose objective values are less than 10−5 are recorded and the regions where the best solutions are concentrated are identified to see how the solution would differ if less number of function evaluations is employed. To fully assess the effectiveness of this approach, both numerical and experimental examples are utilized. The results confirm the effectiveness of the proposed method for identifying multiple cracks in the frames using a few experimental natural frequencies of the structure. The effect of using more natural frequencies on the accuracy of the location and depth of the cracks is also studied.

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