Modeling Error Estimation and Response Prediction of a 10-Story Building Model Through a Hierarchical Bayesian Model Updating Framework

In this paper a hierarchical Bayesian model updating approach is proposed for calibration of model parameters, estimation of modeling error, and response prediction of dynamic structural systems. The approach is especially suitable for civil structural systems where modeling errors are usually significant. The proposed framework is demonstrated through a numerical case study, namely a 10-story building model. The “measured data” include the numerically simulated modal parameters of a frame model which represents the true structure. A simplified shear building model with significant modeling errors is then considered for model updating with stiffness of different structural components (substructures) chosen as updating parameters. In the proposed hierarchical Bayesian framework, updating parameters are assumed to follow a known distribution model (normal distribution is considered here) and are characterized by the distribution parameters (mean vector and covariance matrix). The error function, which is defined as the misfit between model-predicted and identified modal parameters, is also assumed to follow a normal distribution with unknown parameters. The hierarchical Bayesian approach is applied to estimate the stiffness parameter distributions with mean and covariance matrix referred to as hyperparameters, as well as the modeling error which is quantified by the mean and covariance of error function. Joint posterior probability distribution of all updating parameters is derived from the likelihood function and the prior distributions. A Metropolis-Hastings within Gibbs sampler is implemented to evaluate the joint posterior distribution numerically. Two cases of model updating are studied with first case assuming a zero mean for the error function, and the second case considering a non-zero error mean. The response time history of the building to a ground motion is predicted using the calibrated shear building model for both cases and compared with the exact response (simulated). Good agreements between predictions and measurements are observed for both cases with better accuracy in the second case. This verifies the proposed hierarchical Bayesian approach for model calibration and response prediction and underlines the importance of considering and propagating the uncertainties of structural parameters and more importantly modeling errors

Semi-Supervised Learning Method for the Augmentation of an Incomplete Image-Based Inventory of Earthquake-Induced Soil Liquefaction Surface Effects

Soil liquefaction often occurs as a secondary hazard during earthquakes and can lead to significant structural and infrastructure damage. Liquefaction is most often documented through field reconnaissance and recorded as point locations. Complete liquefaction inventories across the impacted area are rare but valuable for developing empirical liquefaction prediction models. Remote sensing analysis can be used to rapidly produce the full spatial extent of liquefaction ejecta after an event to inform and supplement field investigations. Visually labeling liquefaction ejecta from remotely sensed imagery is time-consuming and prone to human error and inconsistency. This study uses a partially labeled liquefaction inventory created from visual annotations by experts and proposes a pixel-based approach to detecting unlabeled liquefaction using advanced machine learning and image processing techniques, and to generating an augmented inventory of liquefaction ejecta with high spatial completeness. The proposed methodology is applied to aerial imagery taken from the 2011 Christchurch earthquake and considers the available partial liquefaction labels as high-certainty liquefaction features. This study consists of two specific comparative analyses. (1) To tackle the limited availability of labeled data and their spatial incompleteness, a semi-supervised self-training classification via Linear Discriminant Analysis is presented, and the performance of the semi-supervised learning approach is compared with supervised learning classification. (2) A post-event aerial image with RGB (red-green-blue) channels is used to extract color transformation bands, statistical indices, texture components, and dimensionality reduction outputs, and performances of the classification model with different combinations of selected features from these four groups are compared. Building footprints are also used as the only non-imagery geospatial information to improve classification accuracy by masking out building roofs from the classification process. To prepare the multi-class labeled data, regions of interest (ROIs) were drawn to collect samples of seven land cover and land use classes. The labeled samples of liquefaction were also clustered into two groups (dark and light) using the Fuzzy C-Means clustering algorithm to split the liquefaction pixels into two classes. A comparison of the generated maps with fully and manually labeled liquefaction data showed that the proposed semi-supervised method performs best when selected high-ranked features of the two groups of statistical indices (gradient weight and sum of the band squares) and dimensionality reduction outputs (first and second principal components) are used. It also outperforms supervised learning and can better augment the liquefaction labels across the image in terms of spatial completeness

A variational Bayesian inference technique for model updating of structural systems with unknown noise statistics

Dynamic models of structural and mechanical systems can be updated to match the measured data through a Bayesian inference process. However, the performance of classical (non-adaptive) Bayesian model updating approaches decreases significantly when the pre-assumed statistical characteristics of the model prediction error are violated. To overcome this issue, this paper presents an adaptive recursive variational Bayesian approach to estimate the statistical characteristics of the prediction error jointly with the unknown model parameters. This approach improves the accuracy and robustness of model updating by including the estimation of model prediction error. The performance of this approach is demonstrated using numerically simulated data obtained from a structural frame with material non-linearity under earthquake excitation. Results show that in the presence of non-stationary noise/error, the non-adaptive approach fails to estimate unknown model parameters, whereas the proposed approach can accurately estimate them

Detecting demolished buildings after a natural hazard using high resolution RGB satellite imagery and modified U-Net convolutional neural networks

Collapsed buildings are usually linked with the highest number of human casualties reported after a natural disaster; therefore, quickly finding collapsed buildings can expedite rescue operations and save human lives. Recently, many researchers and agencies have tried to integrate satellite imagery into rapid response. The U.S. Defense Innovation Unit Experimental (DIUx) and National Geospatial Intelligence Agency (NGA) have recently released a ready-to-use dataset known as xView that contains thousands of labeled VHR RGB satellite imagery scenes with 30-cm spatial and 8-bit radiometric resolutions, respectively. Two of the labeled classes represent demolished buildings with 1067 instances and intact buildings with more than 300,000 instances, and both classes are associated with building footprints. In this study, we are using the xView imagery, with building labels (demolished and intact) to create a deep learning framework for classifying buildings as demolished or intact after a natural hazard event. We have used a modified U-Net style fully convolutional neural network (CNN). The results show that the proposed framework has 78% and 95% sensitivity in detecting the demolished and intact buildings, respectively, within the xView dataset. We have also tested the transferability and performance of the trained network on an independent dataset from the 19 September 2017 M 7.1 Pueblo earthquake in central Mexico using Google Earth imagery. To this end, we tested the network on 97 buildings including 10 demolished ones by feeding imagery and building footprints into the trained algorithm. The sensitivity for intact and demolished buildings was 89% and 60%, respectively.Published versio

Bayesian model updating of nonlinear systems using nonlinear normal modes

This paper presents a Bayesian model updating methodology for dynamical systems with geometric nonlinearities based on their nonlinear normal modes (NNMs) extracted from broadband vibration data. Model parameters are calibrated by minimizing selected metrics between identified and model-predicted NNMs. In the first approach, a deterministic formulation is adopted, and parameters are updated by minimizing a nonlinear least-squares objective function. A probabilistic approach based on Bayesian inference is next investigated, where a Transitional Markov Chain Monte Carlo is implemented to sample the joint posterior probability distribution of the nonlinear model parameters. Bayesian model calibration has the advantage to quantify parameter uncertainty and to provide an estimation of model evidence for model class selection. The two formulations are evaluated when applied to a numerical cantilever beam with geometrical nonlinearity. The NNMs of the beam are derived from simulated broadband data through nonlinear subspace identification and numerical continuation. Accuracy of model updating results is studied with respect to the level of measurement noise, the number of available datasets, and modeling errors

Structural Identification of an 18-Story RC Building in Nepal Using Post-Earthquake Ambient Vibration and Lidar Data

Few studies have been conducted to systematically assess post-earthquake condition of structures using vibration measurements. This paper presents system identification and finite element (FE) modeling of an 18-story apartment building that was damaged during the 2015 Gorkha earthquake and its aftershocks in Nepal. In June 2015, a few months after the earthquake, the authors visited the building and recorded the building’s ambient acceleration response. The recorded data are analyzed, and the modal parameters of the structure are identified using an output-only system identification method. A linear FE model of the building is also developed to estimate numerically its dynamic properties. The identified modal parameters are compared to those of the model to identify possible shortcomings of the modeling and identification approaches. The identified natural frequencies and mode shapes for two of the three closely spaced vibration modes in the lower frequency range of interest (0.2–1.0 Hz) are in good agreement with the numerical model. The model is used to estimate the response of the building to the nearby recorded ground motion due to earthquake and the main aftershock. The maximum drift ratios are compared to the observed damage in the building and surface defects detected and quantified by the lidar scans as the research team performed a series of light detection and ranging (lidar) scans from interior of selected floors to document the damage patterns along the height of the building

Structural instrumentation and monitoring of the Block Island Offshore Wind Farm

publishedVersio

System and damage identification of civil structures

In recent years, structural health monitoring has received increasing attention in the civil engineering research community with the objective to identify structural damage at the earliest possible stage and evaluate the remaining useful life (damage prognosis) of structures. Vibration- based, non-destructive damage identification is based on changes in dynamic characteristics (e.g., modal parameters) of a structure for identifying structural damage. Experimental modal analysis (EMA) has been used as a technology for identifying modal parameters of a structure based on its measured vibration data. It should be emphasized that the success of damage identification based on EMA depends strongly on the accuracy and completeness of the identified structural dynamic properties. The objective of the research work presented in this thesis is to develop new, and improve/extend existing system identification and damage identification methods for vibration based structural health monitoring. In the first part of the thesis, a new system identification method is developed to identify modal parameters of linear dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. In addition, a comparative study is performed to investigate the performance of several state-of-the-art input-output and output-only system identification methods when applied to actual large structural components and systems. In the second part of the thesis, a finite element model updating strategy, a sophisticated damage identification method, is formulated and computer implemented. This method is then successfully applied for damage identification of two large test structures, namely a full-scale sub-component composite beam and a full-scale seven-story R/C building slice, at various damage levels. The final part of the thesis investigates, based on numerical response simulation of the seven-story building slice, the effects of the variability/uncertainty of several input factors on the variability/uncertainty of system identification and damage identification results. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size

System and damage identification of civil structures

In recent years, structural health monitoring has received increasing attention in the civil engineering research community with the objective to identify structural damage at the earliest possible stage and evaluate the remaining useful life (damage prognosis) of structures. Vibration- based, non-destructive damage identification is based on changes in dynamic characteristics (e.g., modal parameters) of a structure for identifying structural damage. Experimental modal analysis (EMA) has been used as a technology for identifying modal parameters of a structure based on its measured vibration data. It should be emphasized that the success of damage identification based on EMA depends strongly on the accuracy and completeness of the identified structural dynamic properties. The objective of the research work presented in this thesis is to develop new, and improve/extend existing system identification and damage identification methods for vibration based structural health monitoring. In the first part of the thesis, a new system identification method is developed to identify modal parameters of linear dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. In addition, a comparative study is performed to investigate the performance of several state-of-the-art input-output and output-only system identification methods when applied to actual large structural components and systems. In the second part of the thesis, a finite element model updating strategy, a sophisticated damage identification method, is formulated and computer implemented. This method is then successfully applied for damage identification of two large test structures, namely a full-scale sub-component composite beam and a full-scale seven-story R/C building slice, at various damage levels. The final part of the thesis investigates, based on numerical response simulation of the seven-story building slice, the effects of the variability/uncertainty of several input factors on the variability/uncertainty of system identification and damage identification results. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size