skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

Title: Seismic fragility analysis using nonlinear autoregressive neural networks with exogenous input
Rapidly growing societal needs in urban areas are increasing the demand for tall buildings with complex structural systems. Many of these buildings are located in areas characterized by high seismicity. Quantifying the seismic resilience of these buildings requires comprehensive fragility assessment that integrates iterative nonlinear dynamic analysis (NDA). Under these circumstances, traditional finite element (FE) analysis may become impractical due to its high computational cost. Soft-computing methods can be applied in the domain of NDA to reduce the computational cost of seismic fragility analysis. This study presents a framework that employs nonlinear autoregressive neural networks with exogenous input (NARX) in fragility analysis of multi-story buildings. The framework uses structural health monitoring data to calibrate a nonlinear FE model. The model is employed to generate the training dataset for NARX neural networks with ground acceleration and displacement time histories as the input and output of the network, respectively. The trained NARX networks are then used to perform incremental dynamic analysis (IDA) for a suite of ground motions. Fragility analysis is next conducted based on the results of the IDA obtained from the trained NARX network. The framework is illustrated on a twelve-story reinforced concrete building located at Oklahoma State University, Stillwater campus.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Structure and Infrastructure Engineering
Page Range / eLocation ID:
1 to 15
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. : In order to evaluate urban earthquake resilience, reliable structural modeling is needed. However, detailed modeling of a large number of structures and carrying out time history analyses for sets of ground motions are not practical at an urban scale. Reduced-order surrogate models can expedite numerical simulations while maintaining necessary engineering accuracy. Neural networks have been shown to be a powerful tool for developing surrogate models, which often outperform classical surrogate models in terms of scalability of complex models. Training a reliable deep learning model, however, requires an immense amount of data that contain a rich input-output relationship, which typically cannot be satisfied in practical applications. In this paper, we propose model-informed symbolic neural networks (MiSNN) that can discover the underlying closed-form formulations (differential equations) for a reduced-order surrogate model. The MiSNN will be trained on datasets obtained from dynamic analyses of detailed reinforced concrete special moment frames designed for San Francisco, California, subject to a series of selected ground motions. Training the MiSNN is equivalent to finding the solution to a sparse optimization problem, which is solved by the Adam optimizer. The earthquake ground acceleration and story displacement, velocity, and acceleration time histories will be used to train 1) an integrated SNN, which takes displacement and velocity states and outputs the absolute acceleration response of the structure; and 2) a distributed SNN, which distills the underlying equation of motion for each story. The results show that the MiSNN can reduce computational cost while maintaining high prediction accuracy of building responses. 
    more » « less
  2. Summary

    The objective of this paper is to present incremental dynamic analysis (IDA) and seismic performance evaluation results for a two‐story cold‐formed steel (CFS)–framed building. The archetype building was designed to current U.S. standards and then subjected to full‐scale shake table tests under the U.S. National Science Foundation Network for Earthquake Engineering Simulation (NEES) program. Test results showed that the building's stiffness and capacity were considerably higher than expected and the building suffered only nonstructural damage even at excitations in excess of Maximum Considered Earthquake levels for a high seismic zone. For the archetype building, three‐dimensional finite element models at different modeling fidelity levels were created using OpenSees. The models are subjected to IDA using the far‐field ground motion records prescribed in Federal Emergency Management Agency (FEMA) P695. Seismic performance quantification following the FEMA P695 procedure shows that if the modeling fidelity only follows the state‐of‐the‐practice, ie, only includes shear walls, unsafe collapse margin ratios are predicted. State‐of‐the‐art models that account for participation from CFS gravity walls and architectural sheathing have overall performance that are consistent with testing, and IDA results indicate acceptable collapse margin ratios, predicated primarily on large system overstrength. Neglecting the lateral force resistance of the gravity system and nonstructural components, as done in current design, renders a safe design in the studied archetype, but largely divorced from actual system behavior. The modeling protocols established here provide a means to analyze a future suite of CFS‐framed archetype buildings for developing further insight on the seismic response modification coefficients for CFS‐framed buildings.

    more » « less
  3. 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.

    more » « less
  4. null (Ed.)
    In recent years, several locations in the United States have been experiencing a significant increase in seismicity that has been attributed to oil and gas production. As oil and natural gas production in the United States continues to increase, it is expected that the seismic hazard in these locations will continue to experience a corresponding upsurge. However, many urban structures in these locations are not designed to withstand these increasing levels of seismicity. Accordingly, it is crucial to develop methodologies that can help us quantify the seismic performance of these structures, establish their risk levels, and identify optimal retrofit strategies that will enhance the seismic resilience of these structures. In this context, structural health monitoring (SHM) plays an important role in understanding the seismic performance of structures. SHM can be used, in conjunction with finite element modelling, to provide a realistic representation of the structural performance during a seismic event. In this paper, a framework for seismic risk assessment of reinforced concrete buildings based on SHM is presented. The framework combines nonlinear finite element modeling and SHM data to establish the seismic fragility profile of the structure. The approach is illustrated on a multi- story reinforced concrete structure located on the Oklahoma State University Campus. 
    more » « less
  5. null (Ed.)
    Loss of operation or devastating damage to buildings and industrial structures, as well as equipment housed in them, has been observed due to earthquake-induced vibrations. A common source of operational downtime is due to the performance reduction of vital equipment, which are sensitive to the total transmitted acceleration. A well-known method of protecting such equipment is seismic isolation of the equipment itself (or a group of equipment), as opposed to the entire structure due to the lower cost of implementation. The first objective of this dissertation is assessing a rolling isolation system (RIS) based on existing design guidelines for telecommunications equipment. A discrepancy is observed between the required response spectrum (RRS) and the one and only accelerogram recommended in the guideline. Several filters are developed to generate synthetic accelerograms that are compatible with the RRS. The generated accelerograms are used for probabilistic assessment of a RIS that is acceptable per the guideline. This assessment reveals large failure probability due to displacement demands in excess of the displacement capacity of the RIS. When the displacement demands on an isolation system are in excess of its capacity, impacts result in spikes in transmitted acceleration. Therefore, the second objective of this dissertation is to design impact prevention/mitigation mechanisms. A dual-mode system is proposed where the behavior changes when the displacement exceeds a predefined threshold. A new piecewise optimal control approach is developed and applied to find the best possible mechanism for the region beyond the threshold. By utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin-Voigt device is tuned for illustrative purposes. On the other hand, the preference for protecting equipment decreases as the earthquake intensity increases. In extreme seismic loading, the response mitigation of the primary structure (i.e., life safety and collapse prevention) is of greater concern than protecting isolated equipment. Therefore, the third objective of this dissertation is to develop an innovative dual-mode system that can behave as equipment isolation under low to moderate seismic loading and passively transition to behave as a vibration absorber for the primary structure under extreme seismic loading. To reduce the computational cost of simulating a large linear elastic structure with nonlinear attachments (i.e., equipment isolation with cubic hardening nonlinearity), a reduced order modeling method is introduced that can capture the behavior of such nonlinear coupled systems. The method is applied to study the feasibility of dual-mode vibration isolation/absorber. To this end, nonlinear transmissibility curves for the roof displacement and isolated mass total acceleration are developed from the steady-state responses of dual-mode systems using the harmonic balanced method. The final objective of this dissertation is to extend the reduced order modeling method developed for linear elastic structure with nonlinear attachment to inelastic structures (without attachments). The new inelastic model condensation (IMC) method uses the modal properties of the full structural model (in the elastic range) to construct a linear reduced order model in conjunction with a hysteresis model to capture the hysteretic inter-story restoring forces. The parameters of these hysteretic forces are easily tuned, in order to fit the inelastic behavior of the condensed structure to that of the full model under a variety of simple loading scenarios. The fidelity of structural models condensed in this way is demonstrated via simulation for different ground motion intensities on three different building structures with various heights. The simplicity, accuracy, and efficiency of this approach could significantly alleviate the computational burden of performance-based earthquake engineering. 
    more » « less