Probabilistic Model Updating of Steel Frame Structures Using Strain and Acceleration Measurements: A Multitask Learning Framework

This paper proposes a multitask learning framework for probabilistic model updating by jointly using strain and acceleration measurements. This framework can enhance the structural damage assessment and response prediction of existing steel frame structures with quantified uncertainty. Multitask learning may be used to address multiple similar inference tasks simultaneously to achieve a more robust prediction performance by transferring useful knowledge from one task to another, even in situations of data scarcity. In the proposed model-updating procedure, a spatial frame is decomposed into multiple planar frames that are viewed as multiple tasks and jointly analyzed based on the hierarchical Bayesian model, leading to robust estimation results. The procedure uses a displacement-stress relationship in the modal space because it directly reflects the elemental stiffness and requires no prior knowledge concerning the mass, unlike most existing model-updating techniques. Validation of the proposed framework by using a full-scale vibration test on a one-story, one-bay by one-bay moment resisting steel frame, wherein structural damage to the column bases is simulated by loosening the anchor bolts, is presented. The experimental results suggest that the displacement-stress relationship has sufficient sensitivity toward localized damage, and the Bayesian multitask learning approach may result in the efficient use of measurements such that the uncertainty involved in model parameter estimation is reduced. The proposed framework facilitates more robust and informative model updating

On the hierarchical Bayesian modelling of frequency response functions

Structural health monitoring (SHM) strategies seek to evaluate, predict, and maintain structural integrity, to improve the safety and design service life of structures in operation. Many of these strategies involve monitoring changes in structural dynamics, as damage can affect modal properties and present as changes in the characteristics of the resonance peaks of the frequency response function (FRF). While recent advances have improved the safety and reliability of structures, a number of challenges remain, impeding the practical implementation and generalisation of these systems. Like damage, benign variations, such as those caused by changes in temperature or other environmental fluctuations, can affect dynamic properties, making it difficult to distinguish between damage and normal operating conditions. In addition, newly-deployed structures can have insufficient data to describe the normal operating conditions (i.e., data scarcity), which can impair the development of data-based prediction models. Another common challenge is data loss (i.e., data sparsity), which may result from transmission issues, sensor failure, a sample-rate mismatch between sensors, and other causes. Missing data in the time domain will result in decreased resolution in the frequency domain, which can impair dynamic characterisation. For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn statistical distributions at the population (or parent) and the domain levels simultaneously, to bolster statistical strength among the parameters. As a result, variance is reduced among the parameter estimates, particularly when data are limited. In this paper, a combined probabilistic FRF model is developed for a small population of nominally-identical helicopter blades, using a hierarchical Bayesian structure, to support information transfer in the context of sparse data. The modelling approach is also demonstrated in a traditional SHM context, for a single helicopter blade exposed to varying temperatures, to show how the inclusion of physics-based knowledge can improve generalisation beyond the training data, in the context of scarce data. These models address critical challenges in SHM, by accommodating benign variations that present as differences in the underlying dynamics, while also considering (and utilising), the similarities among the domains

Multitask Sparse Bayesian Learning with Applications in Structural Health Monitoring

We focus on a Bayesian approach to learn sparse models by simultaneously utilizing multiple groups of measurements that are marked by a similar sparseness profile. Joint learning of sparse representations for multiple models has been mostly overlooked, although it is a useful tool for exploiting data redundancy by modeling informative relationships within groups of measurements. To this end, two hierarchical Bayesian models are introduced and associated algorithms are proposed for multitask sparse Bayesian learning (SBL). It is shown that the data correlations for different tasks are taken into account more effectively by using the hierarchical model with a common prediction‐error precision parameter across all related tasks, which leads to a better learning performance. Numerical experiments verify that exploiting common information among multiple related tasks leads to better performance, for both models that are highly and approximately sparse. Then, we examine two applications of multitask SBL in structural health monitoring: identifying structural stiffness losses and recovering missing data occurring during wireless transmission, which exploit information about relationships in the temporal and spatial domains, respectively. These illustrative examples demonstrate the potential of multitask SBL for solving a wide range of sparse approximation problems in science and technology

Identification of Structural Damage, Ground Motion Response, and the Benefits of Dense Seismic Instrumentation

This study explores the problems of identifying structural damage in steel frame buildings, through the use of dense instrumentation over the height of the building, and of characterizing the ground motion response in urban Los Angeles following the 2019 Ridgecrest earthquakes, through the use of dense instrumentation from available seismic networks, including the very dense Community Seismic Network. First we explore the possibility of tracing possible nonlinear behavior of a structure by updating an equivalent linear system model in short time segments of the earthquake-induced excitation and response time histories, using a moving time window approach. The stiffness and damping related parameters of the equivalent linear model are estimated by minimizing a measure of fit between the measured and model predicted response time histories for each time window. We explore the effectiveness of the methodology for two example applications, a single-story and a six-story steel moment frame building. For the single-story building, the methodology is shown to be very effective in tracing the nonlinearities, while the six-story building is designed to also reveal the limitations of the methodology, mainly arising from the different types of model errors manifested in the formulation. Next, we investigate the problem of structural damage identification through the use of sparse Bayesian learning (SBL) techniques. This is based on the premise that damage in a structure appears only in a limited number of locations. SBL methods that had been previously applied for structural damage identification used measurements related to modal properties and were thus limited to linear models. Here we present a methodology that allows for the application of SBL in non-linear models, using time history measurements recorded from a dense network of sensors installed along the building height. We develop a two-step optimization algorithm in which the most probable values of the structural model parameters and the hyper-parameters are iteratively obtained. An equivalent single-objective minimization problem that results in the most probable model parameter values is also derived. We consider the example problem of identifying damage in the form of weld fractures in a 15-story moment resisting steel frame building, using a nonlinear finite element model and simulated acceleration data. Fiber elements and a bilinear material model are used in order to account for the change of local stiffness when cracks at the welds are subjected to tension and the model parameters characterize the loss of stiffness as the crack opens under tension. The damage identification results demonstrate the effectiveness and robustness of the proposed methodology in identifying the existence, location, and severity of damage for a variety of different damage scenarios, and degrees of model and measurement errors. The results show the great promise of the SBL methodology for damage identification by integrating nonlinear finite element models and response time history measurements. The final part of the thesis involves studying the ground motion response in urban Los Angeles during the two largest events (M7.1 and M6.4) of the 2019 Ridgecrest earthquake sequence using recordings from multiple regional seismic networks as well as a subset of 350 stations from the much denser Community Seismic Network. The response spectral (pseudo) accelerations for a selection of periods of engineering significance are calculated. Significant spectral acceleration amplification is present and reproducible between the two events. For the longer periods, coherent spectral acceleration patterns are visible throughout the Los Angeles Basin, while for the shorter periods, the motions are less spatially coherent. The dense Community Seismic Network instrumentation allows us to observe smaller-scale coherence even for these shorter periods. Examining possible correlations of the computed response spectral accelerations with basement depth and Vs30, we find the correlations to be stronger for the longer periods. Furthermore, we study the performance of two state-of-the-art methods for estimating ground motions for the largest event of the Ridgecrest earthquake sequence, namely 3D finite difference simulations and ground motion prediction equations. For the simulations, we are interested in the performance of the two Southern California Earthquake Center 3D Community Velocity Models (CVM-S and CVM-H). For the ground motion prediction equations, we consider four of the 2014 Next Generation Attenuation-West2 Project equations. For some cases, the methods match the observations reasonably well; however, neither approach is able to reproduce the specific locations of the maximum response spectral accelerations, or match the details of the observed amplification patterns.</p