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A full-scale seven-story reinforced concrete building slice was tested on the unidirectional UCSD-NEES shake table during the period October 2005 - January 2006. A rectangular wall acted as the main lateral force resisting system of the building slice. The shake table tests were designed to damage the building progressively through four historical earthquake records. The objective of the seismic tests was to validate a new displacement-based design methodology for reinforced concrete shear wall building structures. At several levels of damage, ambient vibration tests and low amplitude white noise base excitations tests were applied to the building which responded as a quasi-linear system with dynamic parameters evolving as a function of structural damage. Six different state-of-the-art system identification algorithms including three output-only and three input-output methods were used to estimate the modal parameters (natural frequencies, damping ratios, and mode shapes) at different damage levels based on the response of the building to ambient as well as white noise base excitations, measured using DC-coupled accelerometers. The modal parameters estimated at various damage levels using different system identification methods are compared in order to: (1) validate/cross-check the modal identification results and study the performance of each of these system identification methods, and (2) investigate the sensitivity of the identified modal parameters to actual structural damage. For a given damage level, the modal parameters identified using different methods are found to be in good agreement indicating that these estimated modal parameters are likely to be close to the actual modal parameters of the building specimen.

A full-scale seven-story reinforced concrete building section was tested on the UCSD-NEES shake table during the period October 2005 - January 2006. The shake table tests were designed to damage the building progressively through four historical earthquake records. At various levels of damage, ambient vibration tests and low amplitude white noise base excitations with root-mean-square accelerations of 0.03g and 0.05g were applied to the building, which responded as a quasi-linear system with parameters evolving as a function of structural damage. Modal parameters (natural frequencies, damping ratios and mode shapes) of the building were identified at different damage levels based on the response of the building to ambient as well as low amplitude white noise base excitations, measured using DC coupled accelerometers. This paper focuses on damage identification of this building based on changes in identified modal parameters. A sensitivity-based finite element model updating strategy is used to detect, localize and quantify damage at each damage state considered. Three sets of damage identification results are obtained using modal parameters identified based on ambient, 0.03g, and 0.05g RMS white noise test data, respectively. The damage identification results obtained in all three cases do not exactly coincide, but they are consistent with the concentration of structural damage observed at the bottom two stories of the building. The difference in the identified damage results is mainly due to the significant difference in the identified modal parameters used in the three cases. The assumption of a quasi-linear dynamic system is progressively violated with increasing level of excitation. Therefore, application of nonlinear FE model updating strategies is recommended in future studies to resolve the errors caused by structural response nonlinearity.

A full-scale seven-story reinforced concrete shear wall building structure was tested on the UCSD-NEES shake table in the period October 2005 - January 2006. The shake table tests were designed so as to damage the building progressively through several his¬torical seismic motions reproduced on the shake table. A sensitivity-based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis-of-variance (ANOVA) and meta-modeling. These five input factors are: (1-3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (modeling error). A full factorial design of experiments is considered for these five input factors. In addition to ANOVA and meta-modeling, this study investigates the one-at-a-time sensitivity analysis of the identified damage to the level of uncertainty in the identified modal parameters of the first three longitudinal modes. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Therefore, the experiments can be designed so that the more influential input factors (to the total uncertainty/variability of the damage identification results) are set at optimum levels so as to yield more accurate damage identification results.

The Alfred Zampa Memorial Bridge (AZMB), a newly built long-span suspension bridge, is located 32km northeast of San Francisco on interstate Highway I-80. A set of dynamic field tests were conducted on the AZMB in November 2003, just before the bridge opening to traffic. These tests provided a unique opportunity to identify the modal properties of the bridge in its as-built condition with no previous traffic loads or seismic excitation. A benchmark study on modal identification of the AZMB is performed using three different state-of-the-art system identification algorithms based on ambient as well as forced vibration measurements. These system identification methods consist of: (1) the multiple-reference natural excitation technique combined with the eigensystem realization algorithm, (2) the data-driven stochastic subspace identification method, and (3) the enhanced frequency domain decomposition method. Overall, the modal parameters identified using these system identification methods are found to be in very good agreement for each type of tests (ambient and forced vibration tests). For most vibration modes, the natural frequencies and mode shapes identified using the two different types of test data also match very well. However, the modal damping ratios identified from forced vibration test data are in general higher than those estimated from ambient vibration data. The identified natural frequencies and mode shapes are finally compared with their analytical counterparts from a three-dimensional finite element model of the AZMB. The modal properties of the AZMB presented in this paper can be used as baseline in future health monitoring studies of this bridge.

The General Realization Algorithm (GRA) is developed to identify modal parameters of linear multi-degree-of-freedom dynamic systems subjected to measured (known) arbitrary dynamic loading from known initial conditions. The GRA extends the well known Eigensystem Realization Algorithm (ERA) based on Hankel matrix decomposition by allowing an arbitrary input signal in the realization algorithm. This generalization is obtained by performing a weighted Hankel matrix decomposition, where the weighting is determined by the loading. The state-space matrices are identified in a two-step procedure that includes a state reconstruction followed by a least squares optimization to get the minimum prediction error for the response. The statistical properties (i.e., bias, variance, and robustness to added output noise introduced to model measurement noise and modeling errors) of the modal parameter estimators provided by the GRA are investigated through numerical simulation based on a benchmark problem with non-classical damping.

The damage identification study presented in this paper leveraged a full-scale sub-component experiment conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego. As payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set of low-amplitude vibration response data was acquired from the beam at various damage levels. The Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse responses recorded in its undamaged and various damaged states using accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage in the beam through a finite element model updating procedure. The identified damage is consistent with the observed damage in the composite beam.

In this paper, wind-induced vibration response of Vincent Thomas Bridge, a suspension bridge located in San Pedro near Los Angeles, California, is simulated using a detailed three-dimensional finite element model of the bridge and a state-of-the-art stochastic wind excitation model. Based on the simulated wind-induced vibration data, the modal parameters (natural frequencies, damping ratios, and mode shapes) of the bridge are identified using the data-driven stochastic subspace identification method. The identified modal parameters are verified by the computed eigenproperties of the bridge model. Finally, effects of measurement noise on the system identification results are studied by adding zero-mean Gaussian white noise processes to the simulated response data. Statistical properties of the identified modal parameters are investigated under increasing level of measurement noise. The framework presented in this paper will allow to investigate the effects of various realistic damage scenarios in long-span cable-supported (suspension and cable-stayed) bridges on changes in modal identification results. Such studies are required in order to develop robust and reliable vibration-based structural health monitoring methods for this type of bridges, which is a long-term research objective of the authors.

This paper describes a set of dynamic field tests performed on the Alfred Zampa Memorial Bridge (AZMB), also known as the New Carquinez Bridge, which is located 32km northeast of San Francisco on interstate Highway I-80. The AZMB, opened to traffic in November 2003, is the first suspension bridge in the United States with an orthotropic steel deck, reinforced concrete towers and large-diameter drilled shaft foundations. The dynamic field tests described herein were conducted just before the bridge opening to traffic. They included ambient vibration tests, mainly wind-induced, and forced vibration tests based on controlled traffic loads and vehicle-induced impact loads. Four different controlled traffic load patterns and seven different vehicle-induced impact load configurations were used in the forced vibration tests. The dynamic response of the bridge was measured through an array of 34 uni-axial and 10 tri-axial force-balanced accelerometers deployed along the whole length of the bridge. These dynamic field tests provided a unique opportunity to determine the dynamic (modal) properties of the bridge in its as-built (baseline) condition with no previous traffic loads or seismic excitation. Such properties could be used to validate and/or update the finite element models used in the design phase of this bridge. They could also be used as baseline for future health monitoring studies of this bridge. At the end of the paper, the ambient vibration test data were used to identify the bridge modal parameters (natural frequencies, damping ratios and mode shapes) using the data-driven stochastic subspace identification method.

This paper presents a method to compute response sensitivities of finite element models of structures based on a three-field mixed formulation. The methodology is based on the direct differentiation method (DDM), and produces the response sensitivities consistent with the numerical finite element response. The general formulation is specialized to frame finite elements and details related to a newly developed steel-concrete composite frame element are provided. DDM sensitivity results are validated through the forward finite difference method (FDM) using a finite element model of a realistic steel-concrete composite frame subjected to quasi-static and dynamic loading. The finite element model of the structure considered is constructed using both monolithic frame elements and composite frame elements with deformable shear connection based on the three-field mixed formulation. The addition of the analytical sensitivity computation algorithm presented in this paper extends the use of finite elements based on a three-field mixed formulation to applications that require finite element response sensitivities. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating.

This paper focuses on the effects upon the design point search of gradient discontinuities caused by non-smoothness of material constitutive models in the context of finite element reliability analysis. The response computation algorithm for the Menegotto-Pinto smooth material constitutive model is extended to response sensitivity analysis using the Direct Differentiation Method. Response sensitivity and reliability analysis results are compared for a structural system modelled using smooth and non-smooth material constitutive laws, respectively. Both material and discrete loading sensitivity parameters are considered. Structural reliability analyses are performed using the First-Order Reliability Method. Implications of using smooth versus non-smooth material constitutive models in finite element response, response sensitivity and reliability analyses are discussed. A sufficient condition on the smoothness of uni-axial material constitutive models for obtaining continuous finite element response sensitivities is stated and proved for the quasi-static case. The issue of continuity/discontinuity of response sensitivities for the dynamic case is discussed within the application examples.

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross-section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the Direct Differentiation Method (DDM). The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a non-symmetric, two-span continuous beam subjected to monotonic loading, and a frame sub-assemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through Forward Finite Difference (FFD) analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.

This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in the number of elements required for a given level of accuracy in the computed response of the finite element model. This advantage of force-based elements is of even more interest in structural reliability analysis, which requires accurate and efficient computation of structural response and structural response sensitivities. This paper focuses on material non-linearities in the context of both static and dynamic response analysis. The formulation presented herein assumes the use of a general-purpose non-linear finite element analysis program based on the direct stiffness method. It is based on the general so-called direct differentiation method (DDM) for computing response sensitivities. The complete analytical formulation is presented at the element level and details are provided about its implementation in a general-purpose finite element analysis program. The new formulation and its implementation are validated through some application examples, in which analytical response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The force-based finite element methodology augmented with the developed procedure for analytical response sensitivity computation offers a powerful general tool for structural response sensitivity analysis.

Strong motion recordings from four seismically isolated buildings are used in time-invariant and time-variant modal identification analyses. The buildings are identified as equivalent, time-varying, linear dynamic systems characterized by their time-varying modal parameters (including fundamental-mode natural frequencies, damping ratios, and mode shapes). The identification analyses for each site are repeated using multiple earthquake recordings. In the case of one building, the inferred isolator stiffness and damping during several earthquakes is compared with experimental results. Spectral displacements of the ground motion at the effective fundamental period of the seismically isolated building are found to correlate well with two measures of isolator behavior—the maximum reduction in fundamental mode frequency during strong shaking, and the fraction of the peak total building deformation occurring within the isolators. While the recorded ground motions have much smaller amplitudes than the design basis motions, extrapolation of the observed trends in frequency reduction and relative isolator deflection to larger levels of shaking indicates performance estimates consistent with those assumed in design (which were based on laboratory testing of the isolators).