Sara Wadia-Fascetti

Significance of Modeling Error in Structural Parameter Estimation

Structural health monitoring systems rely on algorithms to detect potential changes in structural parameters that may be indicative of damage. Parameter estimation algorithms seek to identify changes in structural parameters by adjusting parameters of an a priori finite-element model of a structure to reconcile its response with a set of measured test data. Modeling error, represented as uncertainty in the parameters of a finite-element model of the structure, curtails capability of parameter estimation to capture the physical behavior of the structure. The performance of four error functions, two stiffness-based and two flexibility-based, is compared in the presence of modeling error in terms of the propagation rate of the modeling error and the quality of the final parameter estimates. Three different types of parameters are used in the parameter estimation procedure: (1) unknown parameters that are to be estimated, (2) known parameters assumed to be accurate, and (3) uncertain parameters that manifest the modeling error and are assumed known and not to be estimated. The significance of modeling error is investigated with respect to excitation and measurement type and locations, the type of error function, location of the uncertain parameter, and the selection of unknown parameters to be estimated. It is illustrated in two examples that the stiffness-based error functions perform significantly better than the corresponding flexibility-based error functions in the presence of modeling error. Additionally, the topology of the structure, excitation and measurement type and locations, and location of the uncertain parameters with respect to the unknown parameters can have a significant impact on the quality of the parameter estimates. Insight into the significance of modeling error and its potential impact on the resulting parameter estimates is presented through analytical and numerical examples using static and modal data.

Effectiveness of 2-D and 2.5-D FDTD Ground-Penetrating Radar Modeling for Bridge-Deck Deterioration Evaluated by 3-D FDTD

Computational modeling effectively analyzes the wave propagation and associated interaction within heterogeneous reinforced concrete bridge decks, providing valuable information for sensor selection and placement. It provides a good basis for the implementation of the inverse problem in defect detection and the reconstruction of subsurface properties, which is beneficial for defect diagnosis. The objective of this study is to evaluate the effectiveness of lower order models in the evaluation of bridge-deck subsurfaces modeled as layered media. The two lower order models considered are a 2-D model and a 2.5-D model that uses the 2-D geometry with a compressed coordinate system to capture wave behavior outside the cross-sectional plane. Both the 2- and 2.5-D models are compared to the results obtained from a full 3-D model. A filter that maps the 3-D excitation signal appropriately for 2- and 2.5-D simulations is presented. The 2.5-D model differs from the 2-D model in that it is capable of capturing 3-D wave behavior interacting with a 2-D geometry. The 2.5-D matches results from the corresponding 3-D model when there is no variation in the third dimension. Computational models for air-launched ground-penetrating radar with 1-GHz central frequency and bandwidth for the detection of bridge-deck delamination are implemented in 2-, 2.5-, and 3-D using FDTD simulations. In all cases, the defect is identifiable in the results. Thus, it is found that in layered media (such as bridge decks) 2- and 2.5-D models are good approximations for modeling bridge-deck deterioration, each with an order of magnitude reduction in computational time.

Earthquake Response Spectra Models Incorporating Fuzzy Logic with Statistics

The ground motion at a site depends on the rupture mechanism, source-to-site distance, local geologic conditions, and energy released by an earthquake. However, design spectra represent expected responses that do not explicitly include the influence of the uncertainties associated with these fundamental features. The aim of this article is to present a viable methodology that can be used to develop a response spectra using fuzzy logic and statistical analysis and to demonstrate how fuzzy-statistical response spectra can be used to evaluate potential structural response. Site-specific response spectra from the Northridge (California, U.S.) earthquake are used to develop response spectra models that quantify uncertainties inherent to the ground motion. The uncertainty in these computational models is quantified using fuzzy-set logic, statistics, and random vibrations. The local geologic conditions are characterized as rock or alluvium, and fuzzy sets are used to represent near, intermediate, and far epicentral distances. Proposed ground-motion models are used to define uncertain input motion for use in dynamic analyses of an example structure. The resulting structural responses are compared with those obtained from time-dependent accelerations. Comparisons are made with the current design codes, and suggested implementation strategies for the proposed models are discussed.

Practical Issues in the Application of Structural Identification

ABSTRACT The stiffness parameters of a structural system can be adjusted to match the analytical models response in order to reproduce the measured test data. There are a number of practical issues that must be considered for the successful application of parameter estimation to full-scale structures. These include the design and implementation of the experiment; errors in the mathematical model used for parameter estimation; and errors in the parameter estimation procedure itself. Modeling error, the uncertainty in the parameters of a finite element model, can have a significant impact on the quality of the resulting parameter estimates. The impact of modeling error on the resulting parameter estimates is investigated with two scenarios: deterioration and damage. Deterioration error is modeled as uncertainty in a single parameter distributed across the structure. Damage error is modeled as localized undetected change in a single parameter and a single element. Three types of parameters are used in an existing parameter estimation procedure: (1) unknown parameters which are to be estimated, (2) known parameters assumed to be accurate, and (3) uncertain parameters that are assumed known and not to be estimated. The third group introduces the modeling error into the parameter estimation. Modeling error is investigated with respect to load and measurement locations, the type of error function used (stiffness-based or flexibility-based), and the selection of unknown parameters to be estimated. In the example presented, the stiffness-based error function performed much better than the flexibility-based error function. However, topology of the structure, load and measurement locations, and location of the uncertain parameters with respect to the unknown parameters can have a significant impact on the quality of the parameter estimates.

Comparison of the Accuracy of 2D vs. 3D FDTD Air-Coupled GPR Modeling of Bridge Deck Deterioration

Computational modeling is beneficial in the preparation for nondestructive wave-based sensing. Forward models, which can be implemented through a variety of computational modeling techniques, enable parametric evaluations to assess the functionality of a sensor under different conditions, and are integral to the solution of the inverse problem. The focus of this article is on the comparison of two-dimensional (2D) and three-dimensional (3D) Finite Difference Time Domain (FDTD) models. This article gives a presentation of the accuracy of 2D modeling by comparing FDTD simulations of reinforced bridge deck deterioration in 2D and 3D. Simulations for a healthy and delaminated bridge deck are examined. It is shown that the difference in propaga-tion between the 3D and 2D point sources must be considered and is more pronounced at greater distances from the source location. The effect of scattering from the delamination is visible and, while there is variation in amplitude between the 3D and 2D models, the shapes of the resulting waveforms (including the peak arrival times) are well matched.

Integrated Sensor and Media Modeling Environment Developed and Applied to Ground-Penetrating Radar Investigation of Bridge Decks

Integrated sensor and media modeling environment has been developed to simulate subsurface sensing systems and environmental parameters relevant to the subsurface sensing modalities. The modeling environment is designed to represent complexity in subsurface features, sensor models, and the integration of the sensors with the subsurface environment. The ability to model complex subsurface environments and any potential random distribution of subsurface properties allows for realistic modeling of heterogeneous subsurface environments such as bridged deck/pavement systems. Many applications can benefit from the modeling, simulation, and interpretation capabilities in the new modeling environment that supports improved understanding of system behavior through simulations to evaluate the ability of a particular modality to detect defects. While numerous modeling packages exist to simulate different wave-based modalities, the integrated sensor and media modeling environment is developed to, in a straightforward manner, physically represent the complex subsurface civil infrastructure environment. Physical modeling capabilities enable the object-oriented programming environment facility portability to other application domains as a generic volume serves as the boundaries for internal elements modeled to represent realistic changes in material properties and buried objects. Model development is demonstrated on a realistic bridge deck example.

A Time Domain Equivalent Source Model of an Impulse GPR Antenna Based on Measured Radiation Fields

Ground Penetrating Radar (GPR) is a valuable tool for determining bridge deck health. The ability to simulate scattering from bridge deck elements and the complex interactions between them, as well as from changes due to the presence and relative location of defects is important for understanding observed responses. These simulations can be performed using electromagnetic computational modeling techniques such as Finite-Difference Time Domain (FDTD). In order to accurately model the GPR investigation, it is necessary to have a time domain equivalent source model that can launch and receive electromagnetic waves into the computational space that replicates the signals transmitted and received by the physical GPR antenna. However, due to complexity of design and proprietary information, the GPR unit is typically very difficult, or even impossible, to fully model with sufficient detail. For bridge deck applications, simulation in two-dimensions adequately captures much of the three-dimensional scattering. Two-dimensional simulations have significant computational savings over three-dimensions, and are more feasible to be iteratively implemented to solve inverse problems. The work presented here uses experimental results and presents a computational approach to determine the characteristics suitable for excitation of a two-dimensional FDTD model.

Predictive and Diagnostic Load Rating Model of a Prestressed Concrete Bridge

This paper presents a probabilistic model of the load rating process incorporated with field inspection observations applied to a prestressed concrete bridge to capture deterioration characteristics. The main computational tool used is a Bayesian network. The model is developed around the main load-carrying member, an interior beam, and the effects of corrosion of its interior steel. Bridge load ratings are calculated as variables based on the following design methodologies: allowable stress; load factor; and load and resistance factor design. Two investigations on an actual bridge are conducted that demonstrate the predictive and diagnostic capabilities of the model. The results show the usefulness of this model in bridge management.

Forward Time Domain Ground Penetrating Radar Modeling of Scattering from Anomalies in the Presence of Steel Reinforcements

Ground penetrating radar (GPR) for nondestructive testing is applied to civil infrastructure such as bridges and roadways. Conventional methods of processing and analyzing GPR data for civil infrastructure are often qualitative, using relative reflection amplitude from subsurface boundaries or reinforcing steel (rebars) as an indicator of health. A Finite Difference Time Domain (FDTD) simulation of GPR is used to generate a bridge deck response of a heterogeneous model of a healthy bridge deck. The result is a healthy deck background that can be removed from measured data to bring anomalies to attention. For the purpose of this article, the measured data is also simulated. In lieu of modeling the identified rebars as perfect electrical conductors (PECs), they are modeled as hard point source excitations to allow for examination of the effect that the scattered waves from the rebar can have on an anomaly. This is an important consideration for application of many inversion methods.

Investigation of born approximation applied to non-destructive evaluation of concrete media

The accuracy of the Born Approximation as a forward model of elastic wave scattering in the context of simulating Impact Echo tests of reinforced of concrete is investigated in this paper. The ability of a forward model to realistically simulate the physics of a system can be important when such a model is used as part of an inverse solution. Synthetic data of scattering by air void defects that are typically present in damaged civil engineering structures is generated by a two-dimensional Finite Difference in Time Domain (FDTD) model for elastic wave propagation in an infinite, homogeneous and isotropic concrete medium. Horizontal elongated cracks and air voids with compact shapes are considered in this study for comparison between the synthetic and the Born approximated data. It is observed that the Born Approximation simulates a compact air void better than a horizontal elongated one. This knowledge provides insight on Born Approximation as part of an inverse solution towards imaging of air voids of various shapes in a damaged civil engineering structure.