Model Updating of UCF Benchmark Model Using PARIS

This paper presents a structural parameter estimation technique for finite element model updating for the bridge benchmark model at the University of Central Florida (UCF) and the anticipated nondestructive tests. The purpose of the benchmark problem is to evaluate the reliability of damage assessment methodologies commonly used in structural health monitoring of the highway bridges. Simulations using both static and modal data of healthy and damaged models will be evaluated to fine tune and compare parameter estimation methodologies. The benchmark grid has two clear spans with the beams remaining continuous across the middle supports, 18 ft beams in the longitudinal direction that transfer the loads to the supports. Six feet long transverse beams provide lateral stability and load transfer at three foot intervals. In preparations for the future benchmark tests at the UCF, simulated measurements for various model cases are used for damage assessments using PARameter Identification System (PARIS) software packages developed at Tufts University. Element stiffness and mass properties of finite element models will be updated to match the predicted analytical response with UCF benchmark measured data. Estimates of structural properties will be used to determine damage in terms of significant differences between the parameters of the initial analytical model and those of the updated benchmark laboratory bridge deck model. Introduction Highway bridges are a key component of the transportation infrastructure system. Of the approximately 590,000 highway bridges in the US, 27% are considered structurally deficient or functionally obsolete [1]. One major challenge is to find a cost effective maintenance system that provides useful information about the infrastructure in an efficient and effective manner [2]. Damage can accumulate during the life of a structure and reach a level such that the structure becomes deficient. Also, some forms of damage may remain unidentified to visual inspection and can lead to component failure or catastrophic failure in the absence of a structural healthIMAX-XXV 2007 by Sanayei, Bell & Rao 1 monitoring program. These issues as well as others, complicate the current managerial focus for bridge systems requiring the ability to plan and forecast levels of structural deterioration and to predict the need for maintenance or rehabilitation procedures. Structural parameter estimation has a great potential for the purpose of finite element model updating for structural health monitoring of in-service structures, specifically as part of a bridge management system. Structural parameter estimation is the art of reconciling an a priori finite element model (FEM) with nondestructive test (NDT) data. The difference between the initial (or design) parameters and the estimated parameters reveal the condition change in the structure, including damage location and severity. Sanayei et al. [3] developed a two stage damage assessment method for damage localization and damage quantification using combined static and modal data for simultaneous estimation of stiffness and mass parameters at the component level. Farrar et al. [4] summarize the current, state of the art, including damage identification methods using measured modal responses. Jang et al. [5] offer a comprehensive study of the integration of the analytical and the experimental sides of parameter estimation. Doebling et al. [6] uses vibration test data to identify a structure’s local stiffness through the disassembly of the flexibility matrix. UCF Physical Model The benchmark problem by Catbas [7] is used to evaluate the reliability of structural health monitoring methodologies, Figure 1(a). It is similar in relative geometry to the overpasses along typical interstate highways; the grid has two clear spans with the beams remaining continuous across the middle supports. It has two 18 ft. beams in the longitudinal direction that transfer the applied loads to three the supports. Lateral stability and load transfer is provided by transverse beams at 3 ft. intervals from end to end of the grid. Each member of the test structure has the same constant cross-section. S3x5.7 were used for the grid members as they were found to be the most desirable structural steel cross section in terms of modal frequencies, deflections, rotations, stresses, and strains that are representative for typical short to medium span highway bridges. (Courtesy of UCF) (a) Laboratory Bridge Model (left) (b) Typical Bolted Connection (right) Figure 1. University of Central Florida Benchmark Problem on Health Monitoring of Highway Bridges Each cross member is connected to the girders by two clip angles and two plates, using a total of 30 bolts for each typical connection, as shown in Figure 1(b). The clip angles provide a “shear connection” while the plates on top and bottom form a “moment connection.” The advantage to this connection is that there are many bolts to loosen and even removed to analyze various scenarios such as zero moment transfer and “semi-rigid” connections with different levels of stiffness. The supports of the structure were designed such that almost any boundary condition can be modeled. Examples include pin supports, rollers, fixed support, semi-rigid support using any type of elastic material like neoprene pads, Catbas [8]. IMAX-XXV 2007 by Sanayei, Bell & Rao 2 Parameter Estimation Formulation A structure considered for NDT for parameter estimation can be excited either statically with applied loads cases, F, measuring displacements, U, and rotations, θ, or dynamically measuring frequency response functions of lightly damped systems and extracting natural resonance frequencies, ω and associated mode shapes, φ, for linear parameter estimation. A selected number of measurements gathered sparsely at certain strategically selected degrees of freedom (DOF) is used for parameter estimation. Four distinct error functions are used for parameter estimation in this paper. A brief formulation of each error function used in this paper is presented here. Static Error Functions The “static stiffness-based error function”, [Ess(p)], as shown in equation (1), was developed by Sanayei and Nelson [9]. It is based on the residual forces at a subset of DOF. It is essentially the difference between the predicted and measured forces. The complete formulation using a subset of measurements is presented by Sanayei and Onipede [10]. ( ) [ ] ( ) [ ][ ] [ ] ] [ ] [ measured predicted ss F F F U p K p E − = − = (1) ( ) [ ] ( ) [ ] [ ] [ ] ] [ ] [ 1 measured predicted sf U U U F p K p E − = − = − (2) The “static flexibility-based error function”, [Esf(p)], as shown in equation (2) was developed by Sanayei et al. [11]. [Esf(p)] is based on the residual displacements at a subset of DOF. The unknown structural stiffness parameters are represented by {p}. Modal Error Functions Using the basic modal analysis theory, Sanayei et al. [12] developed the “modal stiffness-based error function”, [Ems(p)], as shown in equation (3). The “modal flexibility-based error function”, [Emf(p)] was also developed by Sanayei et al. [13], as shown in equation (4). ( ) { } ( ) [ ]{ } ( ) [ ]{ }j j j j ms p M p K p E Φ − Φ = 2 ω (3) ( ) { } ( ) [ ] ( ) [ ]{ } { }j j j j mf p M p K p E Φ − Φ = −1 2 ω (4) These error functions are based on the residual modal elastic and inertia forces estimated at a subset of DOF. It uses the mode shapes, {Φ}j, and natural frequencies, ωj, extracted from an NDT data set for mode j. [K(p)] and [M(p)] are the analytical stiffness and mass matrices, respectively. All four of the above error functions are capable of performing parameter estimation using a subset of measurements. Minimization of any [E(p)] with respect to the vector of unknown parameters, {p}, leads the search for parameter estimation of the objective function, J(p), that is the Frobenius Norm of any error function [10]. ( ) ( ) vibration of e or case load measured j and DOF measured i where p E p J i j ij mod 2