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1. Accounting for Modeling Errors and Inherent Structural Variability through a Hierarchical Bayesian Model Updating Approach: An Overview

   https://doi.org/10.3390/s20143874  

   Song, Mingming; Behmanesh, Iman; Moaveni, Babak; Papadimitriou, Costas (July 2020, Sensors)

   null (Ed.)

   Mechanics-based dynamic models are commonly used in the design and performance assessment of structural systems, and their accuracy can be improved by integrating models with measured data. This paper provides an overview of hierarchical Bayesian model updating which has been recently developed for probabilistic integration of models with measured data, while accounting for different sources of uncertainties and modeling errors. The proposed hierarchical Bayesian framework allows one to explicitly account for pertinent sources of variability such as ambient temperatures and/or excitation amplitudes, as well as modeling errors, and therefore yields more realistic predictions. The paper reports observations from applications of hierarchical approach to three full-scale civil structural systems, namely (1) a footbridge, (2) a 10-story reinforced concrete (RC) building, and (3) a damaged 2-story RC building. The first application highlights the capability of accounting for temperature effects within the hierarchical framework, while the second application underlines the effects of considering bias for prediction error. Finally, the third application considers the effects of excitation amplitude on structural response. The findings underline the importance and capabilities of the hierarchical Bayesian framework for structural identification. Discussions of its advantages and performance over classical deterministic and Bayesian model updating methods are provided. 

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2. Probabilistic Calibration and Prediction of Seismic Soil Liquefaction using quoFEM

   Satish, AB; Yi, S; Nair, AS; Arduino, P (September 2022, Springer, Cham)

   Wang, L; Zhang, JM; Wang, R (Ed.)

   Liquefaction under cyclic loads can be predicted through advanced (liquefaction-capable) material constitutive models. However, such constitutive models have several input parameters whose values are often unknown or imprecisely known, requiring calibration via lab/in-situ test data. This study proposes a Bayesian updating framework that integrates probabilistic calibration of the soil model and probabilistic prediction of lateral spreading due to seismic liquefaction. In particular, the framework consists of three main parts: (1) Parametric study based on global sensitivity analysis, (2) Bayesian calibration of the primary input parameters of the constitutive model, and (3) Forward uncertainty propagation through a computational model simulating the response of a soil column under earthquake loading. For demonstration, the PM4Sand model is adopted, and cyclic strength data of Ottawa F-65 sand from cyclic direct simple shear tests are utilized to calibrate the model. The three main uncertainty analyses are performed using quoFEM, a SimCenter open-source software application for uncertainty quantification and optimization in the field of natural hazard engineering. The results demonstrate the potential of the framework linked with quoFEM to perform calibration and uncertainty propagation using sophisticated simulation models that can be part of a performance-based design workflow. 

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3. Probabilistic Calibration and Prediction of Seismic Soil Liquefaction Using quoFEM

   Bangalore Satish, A.; Yi, S.-ri; Nair, A.S.; Arduino, P. (September 2022, Proceedings of the 4th International Conference on Performance Based Design in Earthquake Geotechnical Engineering (Beijing 2022))

   Liquefaction under cyclic loads can be predicted through advanced (liquefaction-capable) material constitutive models. However, such constitutive models have several input parameters whose values are often unknown or imprecisely known, requiring calibration via lab/in-situ test data. This study proposes a Bayesian updating framework that integrates probabilistic calibration of the soil model and probabilistic prediction of lateral spreading due to seismic liquefaction. In particular, the framework consists of three main parts: (1) Parametric study based on global sensitivity analysis, (2) Bayesian calibration of the primary input parameters of the constitutive model, and (3) Forward uncertainty propagation through a computational model simulating the response of a soil column under earthquake loading. For demonstration, the PM4Sand model is adopted, and cyclic strength data of Ottawa F-65 sand from cyclic direct simple shear tests are utilized to calibrate the model. The three main uncertainty analyses are performed using quoFEM, a SimCenter open-source software application for uncertainty quantification and optimization in the field of natural hazard engineering. The results demonstrate the potential of the framework linked with quoFEM to perform calibration and uncertainty propagation using sophisticated simulation models that can be part of a performance-based design workflow. 

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4. Frequency Response-Based Uncertainty Analysis of Vibration System Utilizing Multiple Response Gaussian Process

   https://doi.org/10.1115/1.4043609  

   Pan, Wangbai; Tang, Guoan; Tang, Jiong (October 2019, Journal of Vibration and Acoustics)

   This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification. 

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5. Surrogate modeling of structural seismic response using probabilistic learning on manifolds

   https://doi.org/10.1002/eqe.3839  

   Zhong, Kuanshi; Navarro, Javier G.; Govindjee, Sanjay; Deierlein, Gregory G. (February 2023, Earthquake Engineering & Structural Dynamics)

   Abstract Nonlinear response history analysis (NLRHA) is generally considered to be a reliable and robust method to assess the seismic performance of buildings under strong ground motions. While NLRHA is fairly straightforward to evaluate individual structures for a select set of ground motions at a specific building site, it becomes less practical for performing large numbers of analyses to evaluate either (1) multiple models of alternative design realizations with a site‐specific set of ground motions, or (2) individual archetype building models at multiple sites with multiple sets of ground motions. In this regard, surrogate models offer an alternative to running repeated NLRHAs for variable design realizations or ground motions. In this paper, a recently developed surrogate modeling technique, called probabilistic learning on manifolds (PLoM), is presented to estimate structural seismic response. Essentially, the PLoM method provides an efficient stochastic model to develop mappings between random variables, which can then be used to efficiently estimate the structural responses for systems with variations in design/modeling parameters or ground motion characteristics. The PLoM algorithm is introduced and then used in two case studies of 12‐story buildings for estimating probability distributions of structural responses. The first example focuses on the mapping between variable design parameters of a multidegree‐of‐freedom analysis model and its peak story drift and acceleration responses. The second example applies the PLoM technique to estimate structural responses for variations in site‐specific ground motion characteristics. In both examples, training data sets are generated for orthogonal input parameter grids, and test data sets are developed for input parameters with prescribed statistical distributions. Validation studies are performed to examine the accuracy and efficiency of the PLoM models. Overall, both examples show good agreement between the PLoM model estimates and verification data sets. Moreover, in contrast to other common surrogate modeling techniques, the PLoM model is able to preserve correlation structure between peak responses. Parametric studies are conducted to understand the influence of different PLoM tuning parameters on its prediction accuracy. 

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