Content uploaded by Xiao Liang
Author content
All content in this area was uploaded by Xiao Liang on Jan 29, 2018
Content may be subject to copyright.
A preview of the PDF is not available
Performance-Based Robust Nonlinear Seismic Analysis with Application to Reinforced Concrete Highway Bridge Systems
Figures
Figures - uploaded by Xiao Liang
Author content
All figure content in this area was uploaded by Xiao Liang
Content may be subject to copyright.
... To generate the testing data, 100 NTHA simulations involving bi-directional earthquake excitations are performed followed by 10-min white noise excitations. The earthquake records are selected from PEER NGA2-West database (Pacific Earthquake Engineering Research Center, 2013) following criteria set forward for ground motion (Liang & Mosalam, 2016) selection based on magnitude, source-to-site distance, and soil classification as follows: ...
Structural health monitoring (SHM) is developing rapidly to fulfill the world's need for resilient and sustainable communities. Due to the current advancements in machine learning and data science, data‐driven SHM is an attractive solution for real‐time damage detection compared to the traditional nondestructive evaluation techniques. However, most widely available data‐driven SHM methods rely on fully or partially simulated data to train the statistical model, and thus require a number of predefined assumptions and parameters, or are not adapted for post‐extreme events damage diagnosis. In this study, we propose a density‐based unsupervised learning approach for structural damage detection and localization. This approach leverages cumulative intensity measures for damage‐sensitive feature extraction for the first time in an unsupervised learning approach. Furthermore, a statistical model construction process is proposed based on kernel density maximum entropy (KDME) and Bayesian optimization. The framework is evaluated in three case studies. The first two involve a numerical three‐story building and a numerical nine‐story asymmetrical building that are both subjected to 100 ground motion excitations while considering environmental variations. The proposed framework is able to detect and localize damage in those case studies with an average accuracy of 92%. The third case study, which contains 44 shake‐table tests of a three‐story frame structure with masonry infill, is used to experimentally validate the proposed framework in damage detection. The three case studies demonstrate the potential and robustness of the proposed Bayesian‐optimized, multivariate KDME novelty detection framework for detecting and localizing structural damage, especially after extreme events.
... It is a bin of 10,800 nonlinear response history analyses (NRHA) based on 360 ground motion records with 30 different intensities. Scale factors are selected based on peak ground velocity, which is shown to have a good correlation with global nonlinear seismic demand (Liang & Mosalam, 2016. Each NRHA simulation will be a single realization in this dataset. ...
Automation in structural health monitoring (SHM) has greatly benefited from computer science's recent advances. Unlike images, the existing datasets for other types of input, such as vibration‐based damage data, are relatively smaller, less diverse, and highly imbalanced. Therefore, the reliability of data‐driven models developed for safety‐critical assessments can be questionable. This paper proposes a dual Bayesian inference where damage predictions are accompanied by measuring the model's confidence in predictions. First, it is shown how dual classification is integrated with Bayesian inference. Later, we introduce a surrogate deep learning module to transform the raw uncertainty output into an easily interpretable prediction uncertainty index (PUI). The PUI metric can be used to alarm a decision‐maker of the potential mistakes. The proposed dual Bayesian models are investigated on a 2D structure with seven different sensor layouts. Our approach yields increased robustness for different metrics compared with the benchmark. In addition to the performance boost, PUI information paves the way for a risk‐informed implementation of deep learning models in vibration‐based damage diagnosis.
... In this section, a numerical case study is presented to investigate the performance and robustness of Bayesian U-Nets for damage segmentation. The dataset used in this regard is a 10-story-10-bay reinforced concrete moment frame as in [24], where the structure is simulated with 10,800 nonlinear response history analysis [29][30][31]. The same data splits of 0.8, 0.1, and 0.1 are respectively considered for training, validation, and testing of the models. ...
Post-disaster inspections are critical to emergency management after earthquakes. The availability of data on the condition of civil infrastructure immediately after an earthquake is of great importance for emergency management. Stakeholders require this information to take effective actions and to better recover from the disaster. The data-driven SHM has shown great promises to achieve this goal in near real-time. There have been several proposals to automate the inspection process from different sources of input using deep learning. The existing models in the literature only provide a final prediction output, while the risks of utilizing such models for safety-critical assessments should not be ignored. This paper is dedicated to developing deep Bayesian U-Nets where the uncertainty of predictions is a second output of the model, which is made possible through Monte Carlo dropout sampling in test time. Based on a grid-like data structure, the concept of semantic damage segmentation (SDS) is revisited. Compared to image segmentation, it is shown that a much higher level of precision is necessary for damage diagnosis. To validate and test the proposed framework, a benchmark dataset, 10,800 nonlinear response history analyses on a 10-story-10-bay 2D reinforced concrete moment frame, is utilized. Compared to the benchmark SDS model, Bayesian models exhibit superior robustness with enhanced global and mean class accuracies. Finally, the model's uncertainty output is studied by monitoring the softmax class variance of different predictions. It is shown that class variance correlates well with locations where the model makes mistakes. This output can be used in combination with the prediction results to increase the reliability of this data-driven framework in structural inspections.
... They are scaled on the basis of the peak ground velocity with a similar approach mentioned in Liang and Mosalam. 49 The probability distribution of peak ground velocity values is obtained using CB-14 attenuation model. 50 Thirty scale factors are selected to represent the probability distribution to calculate P r as in Equation (14). ...
Rapid condition monitoring of structural health is essential for post‐earthquake safety assessment. Therefore, information about damage after extreme events could be of great value in resilient communities. This paper proposes a robust framework for the identification of the existence, probable location, and severity of damage using cumulative intensity‐based damage features. Taken into account the seismic hazard uncertainties and the undesirable consequences of misclassification in data‐driven methods, an objective function based on the confusion score matrix is optimized. This process can enhance the reliability of the prediction model in terms of two conflicting criteria, namely, the general accuracy and conservativeness. Support vector machines are utilized for the task of damage classification where Bayesian optimization is used to select the proper damage‐sensitive input features and hyperparameters. A three‐story reinforced concrete (RC) moment frame is designed and modeled in OpenSees to examine the performance of the proposed framework. For this purpose, 5,400 incrementally scaled nonlinear time history analyses are conducted considering 180 ground motions. Two different approaches are introduced to distort signals to simulate measurement noise. The robustness of models is also investigated with respect to different objective functions. Furthermore, in an independent experimental case study, the framework is evaluated on a dataset obtained from 44 shake table trials on a three‐story RC frame with masonry infill. Given the results obtained from the two case studies, it is shown that the proposed framework is capable of robust and reliable identification of damage in near real‐time whereas the concepts of hazard uncertainty and misclassification consequences are properly considered.
... This yields to 180 recorded events that are used to generate the data set in this study. Incremental dynamic analyses are performed based on peak ground velocity (PGV) where scale factors are found in a similar fashion to Liang and Mosalam (2016). The probability distribution for seismic hazard has been obtained from the CB-2014 attenuation model (Campbell & Bozorgnia, 2014) where 30 target PGV values are sampled. ...
Toward reduced recovery time after extreme events, near real-time damage diagnosis of structures is critical to provide reliable information. For this task, a fully convolutional encoder–decoder neural network is developed, which considers the spatial correlation of sensors in the automatic feature extraction process through a grid environment. A cost-sensitive score function is designed to include the consequences of misclassification in the framework while considering the ground motion uncertainty in training. A 10-story-10-bay reinforced concrete (RC) moment frame is modeled to present the design process of the deep learning architecture. The proposed models achieve global testing accuracies of 96.3% to locate damage and 93.2% to classify 16 damage mechanisms. Moreover, to handle class imbalance, three strategies are investigated enabling an increase of 16.2% regarding the mean damage class accuracy. To evaluate the generalization capacities of the framework, the classifiers are tested on 1,080 different RC frames by varying model properties. With less than a 2% reduction in global accuracy, the data-driven model is shown to be reliable for the damage diagnosis of different frames. Given the robustness and capabilities of the grid environment, the proposed framework is applicable to different domains of structural health monitoring research and practice to obtain reliable information.
... Various studies have shown that peak ground velocity (PGV) provides a good correlation (better than e.g., peak ground acceleration) with the global nonlinear seismic demands (e.g., Refs. [45][46][47][48][49][50]. Therefore, in this study, PGV is selected as the intensity measure and the selected 99 pairs of GM records are scaled based on the distribution of PGV [39] from the selected GM scenario. ...
... To model damage, an M7 earthquake scenario is selected which yields 208 GMs [12]. The uncertainty of seismic events for 30 different scale factors is obtained from the CB-14 attenuation model [13]. ...
Near real-time damage diagnosis of building structures after extreme events (e.g., earthquakes) is of great importance in structural health monitoring. Unlike conventional methods that are usually time-consuming and require human expertise, pattern recognition algorithms have the potential to interpret sensor recordings as soon as this information is available. This paper proposes a robust framework to build a damage prediction model for building structures. Support vector machines are used to predict the existence as well as the probable location of the damage. The model is designed to consider probabilistic approaches in determining hazard intensity given the existing attenuation models in performance-based earthquake engineering. Performance of the model regarding accurate and safe predictions is enhanced using Bayesian optimization. The proposed framework is evaluated on a reinforced concrete moment frame. Targeting a selected large earthquake scenario, 6,240 nonlinear time history analyses are performed using OpenSees. Simulation results are engineered to extract low-dimensional intensity-based features that can be used as damage indicators. For the given case study, the proposed model achieves a promising accuracy of 83.1% to identify damage location, demonstrating the great potential of model capabilities.
... To model damage, an M7 earthquake scenario is selected which yields 208 GMs [12]. The uncertainty of seismic events for 30 different scale factors is obtained from the CB-14 attenuation model [13]. ...
Near real-time damage diagnosis of building structures after extreme events (e.g., earthquakes) is of great importance in structural health monitoring. Unlike conventional methods that are usually time-consuming and require human expertise, pattern recognition algorithms have the potential to interpret sensor recordings as soon as this information is available. This paper proposes a robust framework to build a damage prediction model for building structures. Support vector machines are used to predict the existence as well as the probable location of the damage. The model is designed to consider probabilistic approaches in determining hazard intensity given the existing attenuation models in performance-based earthquake engineering. Performance of the model regarding accurate and safe predictions is enhanced using Bayesian optimization. The proposed framework is evaluated on a reinforced concrete moment frame. Targeting a selected large earthquake scenario, 6,240 nonlinear time history analyses are performed using OpenSees. Simulation results are engineered to extract low-dimensional intensity-based features that can be used as damage indicators. For the given case study, the proposed model achieves a promising accuracy of 83.1% to identify damage location, demonstrating the great potential of model capabilities.
... Therefore, the NR with line search algorithm is reused for the simulation until another convergence difficulty is encountered. Such switching [16][17][18] is readily available in OpenSees [19], which is the target scriptable finite element analysis software platform where this proposed algorithm is planned to be implemented to investigate more complex structural systems. ...
This paper proposes a solution algorithm for nonlinear structural analysis problems involving static and/or dynamic loads based on the Lyapunov stability theory. The main idea is to reformulate the equations of motion into a hypothetical dynamical system characterized by a set of ordinary differential equations, whose equilibrium points represent the solutions of the nonlinear structural problems. Starting from the Lyapunov stability theory, it is theoretically demonstrated that this hypothetical dynamical system is characterized by a global convergence to the equilibrium points for structural dynamics, i.e., the convergence is guaranteed independently of the selection of the initial guess. This feature overcomes the inherent limitations of the traditional iterative minimization algorithms and relaxes the restriction on the selection of the initial guess for various structural nonlinear behaviors. Moreover, comparisons between the proposed algorithm and regular Newton-Raphson algorithm are presented using several numerical examples from structural dynamics. Finally, the scalability of the proposed Lyapunov-based algorithm is discussed via adaptive switching of nonlinear solution algorithms at the problematic time steps. ABSTRACT This paper proposes a solution algorithm for nonlinear structural analysis problems involving static and/or dynamic loads based on the Lyapunov stability theory. The main idea is to reformulate the equations of motion into a hypothetical dynamical system characterized by a set of ordinary differential equations, whose equilibrium points represent the solutions of the nonlinear structural problems. Starting from the Lyapunov stability theory, it is theoretically demonstrated that this hypothetical dynamical system is characterized by a global convergence to the equilibrium points for structural dynamics, i.e., the convergence is guaranteed independently of the selection of the initial guess. This feature overcomes the inherent limitations of the traditional iterative minimization algorithms and relaxes the restriction on the selection of the initial guess for various structural nonlinear behaviors. Moreover, comparisons between the proposed algorithm and regular Newton-Raphson algorithm are presented using several numerical examples from structural dynamics. Finally, the scalability of the proposed Lyapunov-based algorithm is discussed via adaptive switching of nonlinear solution algorithms at the problematic time steps.
The demand for resilient and smart structures has been rapidly increasing in recent decades. With the occurrence of the big data revolution, research on data‐driven structural health monitoring (SHM) has gained traction in the civil engineering community. Unsupervised learning, in particular, can be directly employed solely using field‐acquired data. However, the majority of unsupervised learning SHM research focuses on detecting damage in simple structures or components and possibly low‐resolution damage localization. In this study, an unsupervised learning, novelty detection framework for detecting and localizing damage in large‐scale structures is proposed. The framework relies on a 5D, time‐dependent grid environment and a novel spatiotemporal composite autoencoder network. This network is a hybrid of autoencoder convolutional neural networks and long short‐term memory networks. A 10‐story, 10‐bay, numerical structure is used to evaluate the proposed framework damage diagnosis capabilities. The framework was successful in diagnosing the structure health state with average accuracies of 93% and 85% for damage detection and localization, respectively.
A solution algorithm is proposed for nonlinear structural analysis problems involving static and/or dynamic loads based on the Lyapunov stability theory. The main idea is to reformulate the equations of motion into a hypothetical dynamical system characterized by a set of ordinary differential equations, whose equilibrium points represent the solutions of the nonlinear structural problems. Starting from the Lyapunov stability theory, it is demonstrated theoretically that this hypothetical dynamical system is characterized by a global convergence to the equilibrium points for structural dynamics, i.e., the convergence is guaranteed independently of the selection of the initial guess. This feature overcomes the inherent limitations of the traditional iterative minimization algorithms and relaxes the restriction on the selection of the initial guess for various structural nonlinear behaviors. The validation of implementing the algorithm is demonstrated using a geometrically nonlinear pendulum problem with a closed-form exact solution. Moreover, comparisons between the proposed algorithm and Newton-Raphson type algorithms are presented using several numerical examples from structural statics and dynamics. Finally, the scalability of the proposed Lyapunov-based algorithm is discussed via adaptive switching of nonlinear solution algorithms at the problematic time steps.
Reinforced concrete (RC) highway bridges are primary lifeline infrastructures, especially where earthquakes commonly occur. Accurate seismic structural analysis is essential to ensure the safety of bridges. The nonlinear seismic behavior of bridge structures generally exhibits distinct difference in the longitudinal and transverse directions, and thus is sensitive to the selection and modification of the input ground motion records. Performance-based earthquake engineering (PBEE) methodology explicitly takes into account uncertainties in hazard, structural response, damage, and loss estimation. Therefore, PBEE enables a comprehensive understanding of the structural performance in a probabilistic manner. For a given large earthquake scenario, this study takes advantage of the PBEE methodology to develop a reference benchmark probability distribution of seismic demands (PDSD) for a given bridge structure considering different intercept angles of the input ground motions. The accuracy and reliability of all PDSD estimates from various ground motion selection and modification (GMSM) procedures are evaluated against this reference benchmark PDSD. Such evaluation is conducted for several engineering demand parameters (EDPs) of three representative RC highway bridges.
In structural dynamics, direct explicit and implicit integration algorithms are commonly used to solve the temporally discretized differential equations of motion for linear and nonlinear structures. The stability of different integration algorithms for linear elastic structures has been extensively studied for several decades. However, investigations of the stability applied to nonlinear structures are relatively limited and rather challenging. Recently, the authors proposed two systematic approaches using Lyapunov stability theory to investigate the stability property of direct integration algorithms of nonlinear dynamical systems. The first approach is a numerical one that transforms the stability analysis to a problem of convex optimization. The second approach investigates the Lyapunov stability of explicit algorithms considering the strictly positive real lemma. This paper reviews and compares these two Lyapunov-based approaches in terms of their merits and limitations.
In structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion. Integration algorithms are categorized into either implicit or explicit. Implicit algorithms require iterations and may face numerical convergence problems when applied to nonlinear structural systems. On the other hand, explicit algorithms do not need iterations by making use of certain approximations, making them appealing for nonlinear dynamic problems. In this paper, a generic explicit integration algorithm is formulated for a nonlinear system governed by a nonlinear function of the restoring force. Based on this formulation, an approach is proposed to investigate the Lyapunov stability of explicit algorithms by means of the strictly positive real lemma. In this approach, the stability analysis is equivalent to investigating the strictly positive realness of the transfer function for the formulated system. Subsequently, a Nyquist plot is used to determine the range of the system stiffness where the explicit algorithm is stable in the sense of Lyapunov. This approach is applied to two commonly used types of explicit integration algorithms applied to single-degree-of-freedom systems with softening or stiffening behavior.
In structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion. Numerous research efforts focused on the stability and accuracy of different integration algorithms for linear elastic structures. However, investigations of those properties applied to nonlinear structures are limited. Systematic Lyapunov stability and accuracy analyses of several direct integration algorithms for nonlinear structural dynamics are presented. These integration algorithms include the implicit methods of the Newmark family of integration algorithm and the TRBDF2 algorithm, and the explicit methods of operator-splitting (OS) algorithms. Two versions of the OS algorithms, using initial and tangent stiffness formulations, are investigated. The latter one is shown to possess similar stability properties to the implicit Newmark integration. Some arguments of stability regarding these direct integration algorithms from past studies are found to be groundless. An approach that enables performing the stability analysis numerically is proposed. It transforms the stability analysis to a problem of convex optimization. In addition, accuracy of the previously discussed five integration algorithms is investigated using a geometrically nonlinear test problem, in which acceptable amounts of period elongation and amplitude decay were evident.
Preliminary outcome of the comprehensive nonlinear analysis guidelines developed for Caltrans ordinary standard bridges are presented in this report. These new guidelines are intended to improve upon the first generation nonlinear analysis guidelines previously developed through a project funded through the Pacific Earthquake Engineering Research (PEER) Lifelines program [Aviram et al. 2008]. In the present study, the previous guidelines are extended by providing a comprehensive treatment of soil- structure interaction effects, improved modeling of various bridge components (e.g., shear keys), ground motion hazard modeling, and nonlinear dynamic analysis methodologies for Caltrans ordinary standard bridges. Special attention is given to development of methodologies and component models that will enable Caltrans engineers to develop sophisticated bridge models at multiple tiers of complexity. Detailed sensitivity analyses are also provided to assist Caltrans engineers in making informed decisions regarding the appropriate level of bridge model complexity for different design and assessment tasks.
In nonlinear structural dynamics, direct integration algorithms are used to solve the differential equations of motion after they are temporally discretized. Explicit algorithms do not require iterations and thus avoid numerical problems of convergence by making use of certain approximations. Thus, they are appealing for multi-degree-of-freedom (MDOF) nonlinear dynamic problems. In this paper, the study previously conducted by the authors for nonlinear single-degree-of-freedom systems is extended to MDOF ones to investigate the Lyapunov stability of explicit algorithms. For this purpose, a generic-explicit integration algorithm is formulated for generic MDOF nonlinear systems with softening or stiffening behavior governed by nonlinear functions of the restoring forces. This approach transforms the stability analysis of the formulated nonlinear system to investigating the strictly positive realness of its corresponding transfer function matrix. Furthermore, this is equivalent to a problem of convex optimization that can be solved numerically. Using this approach, a sufficient condition that the bounds where the explicit algorithm is stable in the sense of Lyapunov for the MDOF nonlinear system can be obtained. This approach is applied to two commonly used explicit integration algorithms for a bridge structure and also demonstrated by a generic nonlinear multistory shear building.
Reinforced concrete (RC) highway bridges are essential lifeline structures, especially in California, which has numerous active faults at which earthquakes are common occurrences. Accurate seismic structural analysis is important to ensure their safety. The most suitable analytical simulation method for this purpose is nonlinear time-history analysis (NTHA). However, one of the main challenges for NTHA is related to the convergence of the numerical solution, which usually arises at high levels of nonlinearity. Inherent lack of high degrees of redundancy of the bridge systems and the need for their continuous functioning in the aftermath of an earthquake require accurate modeling and robust numerical solutions for the response investigation of these important structures. This paper presents solutions to the problems of convergence encountered in NTHA of RC highway bridges during the use of direct integration algorithms. The considered numerical integration algorithms include two that are explicit, namely, the Newmark and operator-splitting algorithms, and one that is implicit, namely, the TRBDF2 algorithm. Applicability of these integration algorithms, instead of the commonly used implicit Newmark, is explored for three representative RC highway bridges in California. Furthermore, the suitability of an adaptive switching among these integration algorithms during the NTHA is investigated. Finally, the efficacy of the solutions is demonstrated for a challenging performance-based earthquake engineering-related subject that involves a large number of NTHAs to identify the predominantly first-mode engineering demand parameters.