•A Kalman filtering approach for SHM under changing environmental conditions.•Statistical properties of the residual are used to discriminate damage.•A Bayesian test and a damage measure are proposed ...for practical considerations.•The approach is assessed under uniform and non-uniform temperature fields.
A Kalman filtering based framework for structural damage assessment under changing environmental conditions is presented. The approach is based on the well-known property that the filtering residual is a realization of a white stochastic process when the filter is operating under optimal conditions. To decouple structural damage and environmental effects two additional properties of the filtering residual are employed: i) under global changes in the structure caused by environmental variations the residual remains a white process, and thus its spectral density is approximately constant; ii) local changes caused by structural damage induce peaks in the residual spectral density at the affected vibration frequencies, and thus the residual is a colored process. A Bayesian whiteness test is employed to discriminate between the two situations under finite length data conditions (damage detection), while a normalized damage measure based on the spectral moments of the residual spectral density is proposed as a quantitative damage-sensitive feature (damage quantification). The proposed approach is numerically verified in a continuous beam model of a bridge under different operating conditions, including a robustness assessment for non-uniform temperature fields. It is shown that the approach has the capability to decouple physical changes caused by structural damage and varying environmental conditions, providing robust damage measures for structural health monitoring applications.
This paper examines the effect of structural damage on the practical/computational identifiability of the parameters that define nonlinear models of building structures subjected to ...earthquake‐induced base motions. The objective is to determine the level of physical damage expected to successfully estimate the nonlinear parameters of restoring force models. For this purpose, the analyses aim to determine if the parameters that define a hysteretic (Bouc‐Wen type) model can be identified within a predefined level of accuracy from accelerations measured during seismic events that cause minor damage. The identified model is then interrogated to determine if it can provide accurate predictions of the response and damage level experienced during strong ground motions that cause moderate‐to‐severe damage. The damage model adopted is a Park–Ang type model and the unscented Kalman filter is used for parameter estimation. The results are verified using simulated two‐dimensional building models and validated using experimental data from a large‐scale shake table test.
An accurate and reliable identification of structural damage is of prime importance to evaluate the structural integrity of civil infrastructure systems. However, the adverse effect of normal ...fluctuations in the environment on the effectiveness of damage detection techniques remains a continuing challenge in structural health monitoring applications. In this paper, we present the application of principal component analysis (PCA) to temporal damage detection in continuous beam bridge structures subjected to changing environmental effects. For this purpose, we show that sudden discontinuities in the principal components occur at the onset of damage, and that these discontinuities are observed in the projections of the vibration data on the principal components space. The magnitude of the discontinuity is used to define a damage index for damage quantification. A comprehensive numerical study is used to validate the approach on a continuous beam model of highway bridge structures. In particular a sensitivity analysis is conducted to study the effect of both temperature-dependent boundary conditions and material properties on the principal components for multiple damage scenarios. The numerical results show that the approach is robust to mild nonlinearities caused by the effect of temperature on material properties of composite steel-concrete sections and boundary conditions. Furthermore, the approach is experimentally validated using data of the Z24 bridge in Switzerland measured during a period of one year. It is shown that the approach has the capability of tracking the temporal evolution of various damage states induced on the bridge during the testing program.
Summary
The application of Bayesian system identification in the context of a hysteretic negative stiffness system for seismic protection of structures is presented. The negative stiffness system ...employs the concept of apparent weakening to decrease the effective lateral stiffness of structures subjected to strong earthquakes, resulting in a significant reduction of the base shear and other seismic demands. In this paper, results from large‐scale experimental testing performed by Rice University and the University at Buffalo ‐ SUNY are used to estimate the parameters that define the nonlinear models of structures equipped with negative stiffness systems. For this purpose, an unscented Kalman filter for augmented‐state nonlinear estimation is employed for structural identification. It is shown that the identified models have the capability to accurately predict the nonlinear hysteretic behavior of the modified structure. The predicted response quantities include lateral drifts and accelerations, base shear, restoring forces, and internal forces in structural members. The identified models provide benchmark parameters that can be used to predict the performance of negative stiffness systems, which is useful for the future design of structures equipped with this type of earthquake protection devices.
This article presents updated seismic hazard curves, spectra, and maps of ground motion intensity measures for the northern region of the Dominican Republic (DR) obtained using a probabilistic ...seismic hazard analysis (PSHA). The analysis performed uses as input data an earthquake recurrence model based on fault slip rates derived from GPS measurements published in the aftermath of the 2010 Haiti earthquake. The seismicity rate data are used to calibrate a composite characteristic earthquake model, which is combined with a Poisson process to provide a temporal characterization of earthquake occurrence. The seismic hazard curves and maps presented include parameters such as (horizontal) peak ground acceleration and pseudo-spectral response accelerations at 0.2s and 1.0s periods for 5% damping at firm rock sites. The results show that the ground motion parameters with a 2% probability of exceedance (PE) in 50 years determined in this study are up to 46% larger than the corresponding parameters specified in the current DR building code seismic hazard maps for the northern DR. Moreover, the design response spectra for a site in the city of Santiago specified in the code is significantly lower than the 2% PE in 50 years uniform hazard spectra determined in this study for vibration periods smaller than 0.5s, a range that includes the majority of the structures that define the built environment of the DR.
In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior ...distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.
•There have been very few researches on unscented Kalman filter with unknown input.•A novel UKF-UI is proposed for recursive state-input-system identification of nonlinear systems.•The proposed UKF ...is derived analogously to the procedures of the conventional UKF.•Data fusion of partially measured accelerations and displacements is used to prevent the drifts in identification.•Such a presented analytical solution of UKF-UI is not available in previous literatures.
The unscented Kalman filter (UKF) has proven to be an effective approach for the identification of nonlinear systems from limited output measurements. However, the conventional UKF requires that measurements of the input excitations are available to successfully perform nonlinear system identification, which limits its application in cases where it is difficult or impractical to measure the inputs. In this paper a novel unscented Kalman filter with unknown input (UKF-UI) is proposed for the simultaneous identification of nonlinear structural systems and external excitations. Based on the estimation-based procedures of the conventional UKF, the analytical recursive solutions of the proposed UKF-UI are derived in an analogous fashion resulting in a recursive nonlinear least-squares problem for the unknown input. Moreover, data fusion of partially measured acceleration and displacement responses is used to alleviate the drifts typically observed in the estimated inputs and displacements. Numerical and experimental validation examples are used to demonstrate the effectiveness of the proposed UKF-UI algorithm for the simultaneous identification of nonlinear parameters and unknown external excitations using data fusion of partially measured system responses.
•A Bayesian framework for structural integrity assessment of structures is presented.•The approach employs of a Bayesian filter to estimate the response at unmeasured locations.•The estimated ...response is used as input to mechanics-based damage measures.•The approach is experimentally validated in the context of a full-scale seven story structure.
In this paper a Bayesian framework is employed to estimate the seismic strong-motion response and the state of structural integrity of a full-scale structure. The approach is applied in the context of a full-scale section of a seven-story shear wall building designed for southern California and tested at the George E. Brown Jr. Network for Earthquake Engineering Simulation shake table site at the University of California San Diego. The test structure was subjected to earthquake records of increasing amplitude until severe damage was observed, and the dynamic response was measured during the experimental program using an array of sensors. The proposed approach provides an estimate of the nonlinear dynamic response at unmeasured degrees of freedom by combining a potentially inaccurate structural model with sparse acceleration measurements using an unscented Kalman filter. Although the method also provides an optimal estimate of the parameters that define the mathematical models, joint state-parameter estimation is not the main purpose of this study. To assess the modeling robustness of the approach two model classes are considered: a linear time-varying cantilever beam model that accounts only for flexural deformations, and a coupled nonlinear chain-cantilever model that accounts for both flexural and shear deformations. It is shown that the approach has the capability to accurately estimate the time-history response and engineering demands of interest, such as floor displacements and accelerations, inter-story drifts, base shear, and overturning moment induced by strong base excitations where the structure experienced considerable nonlinear excursions. The estimated demands are subsequently used to compute damage measures to perform a quantitative assessment of the state of structural integrity.
In this paper we present the results from a validation study of a recently proposed model-based state observer for structural and mechanical systems. The observer uses a finite element model of the ...structure and noise contaminated measurements to estimate the state and stress time histories at arbitrary locations in the structure of interest. The initial conditions and unknown excitations are described by random vectors and random processes with known covariance and power spectral density. A laboratory model consisting of an aluminum cantilever beam was used to perform the experiment. Two types of loading conditions were tested: an impact hammer test and a band limited excitation delivered through a shaker. The results obtained with the proposed observer are compared to the measured stress at the locations of interest, and to estimates obtained using well-established estimation methods such as Luenberger observers and the Kalman filter. The main finding is that for all experiments conducted the proposed model-based observer yielded estimates with higher or comparable accuracy to all other methods considered, with the advantage of requiring significantly less computational effort and with a more direct and transparent implementation.
•Estimation of stress and strain time histories based on acceleration measurements.•The proposed observer can be implemented using high-fidelity finite element models.•Reduced computational cost with respect to Kalman filter, without loss of accuracy.•Experimental validation of state observers in structural dynamics.•Robustness against measurement noise and model errors.
