Finite Element Model Updating of Scale Bridge Model Using Measured Modal Response Data AUTHORS

One of the most promising fields of finite element model updating involves using data obtained from the modal response of a structure to update a finite element model. The University of Central Florida (UCF) has constructed a scale model of a two span bridge. Using an impact hammer and accelerometers mounted on the structure, the first 17 natural frequencies and mode shapes were identified. Using two different residual error functions, a subset of the measured modal data was used to verify and update a finite element model of the structure so that it better reflects the behavior of the system. The results of the updating process are presented. INTRODUCTION The transportation infrastructure of the United States is deteriorating quickly. Of the nearly 600,000 bridges in the US, more than 150,000 of them are either structurally deficient or functionally obsolete (FWHA, 2007). Many of these bridges were built during the interstate highway initiative which started in 1956 and with the typical bridge design lifespan of about 50 years, many more bridges are expected to join the structurally deficient ranks in the coming years. Finite element model updating can be a useful tool in structural health monitoring. It gives inspectors another tool to aid in rating structures. Parameter estimation does not rely on visual inspection so inaccessible structural components such as steel imbedded in concrete can be observed. Parameter estimation can give an objective evaluation of the structure in question. As technology advances, the sensors and data acquisition systems (DAQ) used to collect nondestructive test (NDT) data are becoming more affordable. This work uses modal data collected from a scale model of a bridge deck at the University of Central Florida. The data includes mode shapes and corresponding natural frequencies. It is used to update a finite element model so that the model more closely reflects the observed behavior. This work makes use of a research computer program called PARIS (posted at http://engineering.tufts.edu/cee/people/sanayei/PARIS/home.html). PARIS was developed at Tufts University for finite element model updating (Sanayei, 1998). Structural Health Monitoring is a wide field of research that employs many different methods of evaluation. The context of this work includes monitoring of structures through the use of measured NDT data. Schulz and Commander (1995) present an efficient method for instrumenting and load testing a bridge. They use strain gauges which can be attached to a structure quickly with C-clamps. For railroad bridges the loading consists of driving a locomotive with known axle weights across the structure at “crawl speed” while sensors monitor the response continuously. The result is a series of static load tests. With continuous monitoring 98 Structures 2009: Don't Mess with Structural Engineers © 2009 ASCE Downloaded 01 Aug 2011 to 130.64.82.105. Redistribution subject to ASCE license or copyright. Visithttp://www.ascelibrary.org it is easy to identify non-linearities and other anomalies in the response of the structure. They can typically instrument, test and remove their sensors in five to eight hours, proving that this procedure does not need to be time intensive or costly. The modal response of a structure can be a useful indicator for damage detection. Catbas, Brown and Aktan (2006) use mode shapes to calculate a modal flexibility matrix. If enough modes are used, this flexibility matrix behaves like the static flexibility matrix. Multiplying this matrix by a uniform load vector results in a deflected shape that is characteristic of the structure in question. It is shown through field tests of a steel girder bridge that this method can identify a damaged section of a structure. Catbas, Gul and Burkett (2008) expand on this method by calculating the curvature of the deflected shape. They show that the curvature vectors amplify differences in the structural response making damage easier to identify. Olund and DeWolf (2007) present a passive health monitoring system employed on several highway bridges in Connecticut. Passive monitoring has the advantage of many data points over a long period of time, but the structural excitation is unknown. They mainly focus on natural frequencies because it is fairly independent of the loading. They use an innovative trigger method that only records data during significant loadings of the structure to reduce the amount of data recorded. Using the data collected, they can create a benchmark model of the structure in its healthy state. Using the benchmark model they can compare it to any new data to determine if there is any change in the behavior of the structure. Maalej et. al (2002) also use the benchmark approach with continuous monitoring. The use of multiple types of data or “data fusion” in parameter estimation is an area of active research. Bell et. al (2007) use dynamic mode shapes and frequencies as well as static data including displacements, tilts and strains to update a finite element model of a scale bridge deck located at the University of Cincinnati Infrastructure Institute. Because the different types of measurements vary over several orders of magnitude, there is a need for normalization that gives each measurement a reasonable weight in the estimation process. They choose to normalize everything with respect to the initial values of the error function. This solution produces reasonable results, but the final estimates vary depending on the initial assumptions of the unknown parameters. In this research measured modal data such as natural frequencies and mode shapes are used for finite element model updating. Two residual error functions are used to estimate the structural parameters. Structural parameters are stiffness and mass properties at the element level. ERROR FUNCTIONS The generalized Eigenvalue problem that represents the dynamic behavior of elastic structures can be expressed as, 2 ω = K M φ φ . (1) In this formulation φ denotes the mode shape of the structure and ω is the corresponding natural frequency. Equation (1) can also be partitioned as,