Bayesian dynamic linear models for structural health monitoring

In several countries, infrastructure is in poor condition, and this situation is bound to remain prevalent for the years to come. A promising solution for mitigating the risks posed by ageing infrastructure is to have arrays of sensors for performing, in real time, structural health monitoring across populations of structures. This paper presents a Bayesian dynamic linear model framework for modeling the time-dependent responses of structures and external effects by breaking it into components. The specific contributions of this paper are to provide (a) a formulation for simultaneously estimating the hidden states of structural responses as well as the external effects it depends on, for example, temperature and loading, (b) a state estimation formulation that is robust toward the errors caused by numerical inaccuracies, (c) an efficient way for learning the model parameters, and (d) a formulation for handling nonuniform time steps

Assemblage rigide boulonné pour les charpentes de bâtiments multiétagés en béton préfabriqué

Les bâtiments actuels faits de pièces en béton préfabriqué utilisent généralement des assemblages qui n’offrent que peu ou pas de continuité à la structure. Il en résulte une sous utilisation importante des matériaux par rapport à une même structure se comportant de façon monolithique. Plusieurs études portant sur des assemblages rigides, soudés ou assemblés par post-tension, ont déjà été réalisées. Bien que structuralement viable, aucun de ces modèles ne s'est avéré capable de répondre pleinement aux besoins de l'industrie. Les tolérances de construction trop serrées et la complexité de réalisation ont souvent posé problème. Les travaux présentés ici portent donc sur le développement d'un assemblage rigide boulonné, utilisable à grande échelle, destiné à l'industrie du bâtiment multiétagé en béton préfabriqué. L'étude entreprise comporte deux phases, soit la conception du système structural et la détermination de la rigidité des assemblages. Les résultats obtenus sont utilisés afin de comparer le nouveau concept aux charpentes actuelles. La démarche d’analyse s’appuie sur le logiciel VisualDesign pour élaborer la structure du bâtiment, et sur le logiciel d’analyse par éléments finis ANSYS pour la caractérisation du comportement des assemblages. Les efforts de recherche ont été orientés de manière à établir la faisabilité du modèle, afin de permettre le développement futur de projets de recherche en partenariat avec l’industrie.To this day, the connections of precast concrete buildings offer little or no continuity to the structure. Consequently, when compared to monolithic structures, the material is clearly not used to its full capacity. Studies on rigid connections, welded or assembled by post tension, have been carried out by a few investigators. Although structurally valid, none of the proposed connections proved able to meet the needs of the construction industry, due to stringent erection tolerances and complexity of assembly. The work presented here concerns the development of a bolted rigid connection system likely to be used on a large scale by the precast concrete construction industry. The study is separated in two parts. The first is concerned with the development and tuning of the new structural system while the second one deals with the determination of the rigidity of the proposed connection. The connection behaviour is then used to compare the amount of material used in the new system and the actual precast system. The software Visual Design was used to analyse the building structure, and the finite element software ANSYS to determine the characteristic behaviour of the new connection. The intent of the research is to establish the feasibility of the proposed model, so that future research and development efforts can be carried out in partnership with the precast industry

Hierarchical Bayes for the Explicit Estimation of Model Prediction Errors

An extensive research effort is dedicated to Bayesian estimation methods for analyzing the empirical behaviour of structures. State-of-the-art structural identification methods currently quantify model uncertainties by estimating hyper-parameters for the prediction-error prior. This paper exposes that this uncertainty quantification procedure does not fully recognize the epistemic nature of model prediction errors, because their posterior probability density function (PDF) is not explicitly estimated and their interaction with model parameters are not considered. This paper presents a Hierarchical Bayes formulation for estimating the joint posterior PDF of model parameters and prediction errors. This Hierarchical Bayes approach allows capturing the dependencies between unknown model parameters and unknown prediction errorsit offers a more accurate picture of the structural behaviour than when estimating the prior hyper-parameters alone. The application of this method to large-scale structures requires an adequate model the for the prediction-error prior, which remains a case-specific challenge

Multimodel structural performance monitoring

Journal ArticleMeasurements from load tests may lead to numerical models that better reflect structural behavior. This kind of system identification is not straightforward due to important uncertainties in measurement and models. Moreover, since system identification is an inverse engineering task, many models may fit measured behavior. Traditional model updating methods may not provide the correct behavioral model due to uncertainty and parameter compensation. In this paper, a multimodel approach that explicitly incorporates uncertainties and modeling assumptions is described. The approach samples thousands of models starting from a general parametrized finite-element model. The population of selected candidate models may be used to understand and predict behavior, thereby improving structural management decision making. This approach is applied to measurements from structural performance monitoring of the Langensand Bridge in Lucerne, Switzerland. Predictions from the set of candidate models are homogenous and show an average discrepancy of 4-7% from the displacement measurements. The tests demonstrate the applicability of the multimodel approach for the structural identification and performance monitoring of real structures. The multimodel approach reveals that the Langensand Bridge has a reserve capacity of 30% with respect to serviceability requirements.Swiss National Science Foundatio

Empirical validation of bayesian dynamic linear models in the context of structural health monitoring

Bayesian Dynamic Linear Models (BDLM) are traditionally employed in the fields of applied statistics and Machine Learning. This paper performs an empirical validation of BDLM in the context of Structural Health Monitoring (SHM) for separating the observed response of a structure into subcomponents. These sub-components describe the baseline response of the structure, the effect of traffic, and the effect of temperature. This utilization of BDLM for SHM is validated with data recorded on the Tamar Bridge (UK). This study is performed in the context of large-scale civil structures where missing data, outliers and non-uniform time steps are present. The study shows that the BDLM is able to separate observations into generic sub-components allowing to isolate the baseline behavior of the structure

An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building

This report describes a state-of-the-art performance-based earthquake engineering methodology that is used to assess the seismic performance of a four-story reinforced concrete (RC) office building that is generally representative of low-rise office buildings constructed in highly seismic regions of California. This “benchmark” building is considered to be located at a site in the Los Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its seismic lateral system that was designed according to modern building codes and standards. The building’s performance is quantified in terms of structural behavior up to collapse, structural and nonstructural damage and associated repair costs, and the risk of fatalities and their associated economic costs. To account for different building configurations that may be designed in practice to meet requirements of building size and use, eight structural design alternatives are used in the performance assessments. Our performance assessments account for important sources of uncertainty in the ground motion hazard, the structural response, structural and nonstructural damage, repair costs, and life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic seismic hazard analysis and the evaluation of controlling seismic sources (through disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to 2475 years). Innovative procedures for ground motion selection and scaling are used to develop acceleration time history suites corresponding to each of the seven ground motion levels. Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural modeling uncertainties are investigated through comparison of these two modeling approaches, and through variations in structural component modeling parameters (stiffness, deformation capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on a combination of test data, observations from post-earthquake reconnaissance, and expert opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural building components, including wallboard partitions, interior paint, exterior glazing, ceilings, sprinkler systems, and elevators. The risk of casualties and the associated economic costs are evaluated based on the risk of structural collapse, combined with recent models on earthquake fatalities in collapsed buildings and accepted economic modeling guidelines for the value of human life in loss and cost-benefit studies. The principal results of this work pertain to the building collapse risk, damage and repair cost, and life-safety risk. These are discussed successively as follows. When accounting for uncertainties in structural modeling and record-to-record variability (i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of the various designs range from 2% to 7% for earthquake ground motions that have a 2% probability of exceedance in 50 years (2475 years return period). When integrated with the ground motion hazard for the southern California site, the collapse probabilities result in mean annual frequencies of collapse in the range of [0.4 to 1.4]x10 -4 for the various benchmark building designs. In the development of these results, we made the following observations that are expected to be broadly applicable: (1) The ground motions selected for performance simulations must consider spectral shape (e.g., through use of the epsilon parameter) and should appropriately account for correlations between motions in both horizontal directions; (2) Lower-bound component models, which are commonly used in performance-based assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is more appropriate to use median component behavior, including all aspects of the component model (strength, stiffness, deformation capacity, cyclic deterioration, etc.); (3) Structural modeling uncertainties related to component deformation capacity and post-peak degrading stiffness can impact the variability of calculated collapse probabilities and mean annual rates to a similar degree as record-to-record variability of ground motions. Therefore, including the effects of such structural modeling uncertainties significantly increases the mean annual collapse rates. We found this increase to be roughly four to eight times relative to rates evaluated for the median structural model; (4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the most common of which was a story mechanism in the third story (differing from the multi-story mechanism predicted by nonlinear static pushover analysis); (5) Soil-foundation-structure interaction effects did not significantly affect the structural response, which was expected given the relatively flexible superstructure and stiff soils. The potential for financial loss is considerable. Overall, the calculated expected annual losses (EAL) are in the range of $52,000 to$97,000 for the various code-conforming benchmark building designs, or roughly 1% of the replacement cost of the building ($8.8M). These losses are dominated by the expected repair costs of the wallboard partitions (including interior paint) and by the structural members. Loss estimates are sensitive to details of the structural models, especially the initial stiffness of the structural elements. Losses are also found to be sensitive to structural modeling choices, such as ignoring the tensile strength of the concrete (40 EAL) or the contribution of the gravity frames to overall building stiffness and strength (15 change in EAL). Although there are a number of factors identified in the literature as likely to affect the risk of human injury during seismic events, the casualty modeling in this study focuses on those factors (building collapse, building occupancy, and spatial location of building occupants) that directly inform the building design process. The expected annual number of fatalities is calculated for the benchmark building, assuming that an earthquake can occur at any time of any day with equal probability and using fatality probabilities conditioned on structural collapse and based on empirical data. The expected annual number of fatalities for the code-conforming buildings ranges between 0.05*10 -2 and 0.21*10 -2 , and is equal to 2.30*10 -2 for a non-code conforming design. The expected loss of life during a seismic event is perhaps the decision variable that owners and policy makers will be most interested in mitigating. The fatality estimation carried out for the benchmark building provides a methodology for comparing this important value for various building designs, and enables informed decision making during the design process. The expected annual loss associated with fatalities caused by building earthquake damage is estimated by converting the expected annual number of fatalities into economic terms. Assuming the value of a human life is$3.5M, the fatality rate translates to an EAL due to fatalities of $3,500 to$5,600 for the code-conforming designs, and $79,800 for the non-code conforming design. Compared to the EAL due to repair costs of the code-conforming designs, which are on the order of$66,000, the monetary value associated with life loss is small, suggesting that the governing factor in this respect will be the maximum permissible life-safety risk deemed by the public (or its representative government) to be appropriate for buildings. Although the focus of this report is on one specific building, it can be used as a reference for other types of structures. This report is organized in such a way that the individual core chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the implementation of the PBEE methodology of the PEER framework, as applied to the benchmark building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis (Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained, readers interested in additional details can find them in the appendices

Anomaly detection with the Switching Kalman Filter for structural health monitoring

Detecting changes in structural behaviour, i.e. anomalies over time is an important aspect in structural safety analysis. The amount of data collected from civil structures keeps expanding over years while there is a lack of data-interpretation methodology capable of reliably detecting anomalies without being adversely affected by false alarms. This paper proposes an anomaly detection method that combines the existing Bayesian Dynamic Linear Models framework with the Switching Kalman Filter theory. The potential of the new method is illustrated on the displacement data recorded on a dam in Canada. The results show that the approach succeeded in capturing the anomalies caused by refection work without triggering any false alarms. It also provided the specific information about the dam's health and conditions. This anomaly detection method offers an effective data-analysis tool for Structural Health Monitoring