Effects of changing ambient temperature on finite element model updating of the Dowling Hall Footbridge
Highlights
► Effects of changing ambient temperatures on FE model updating of a footbridge are studied. ► Two sets of FE models are updated based on 17 weeks of data, before and after removing temperature effects. ► The variations of updating parameters are quantified after the temperature effects are removed. ► More accurate damage identification results are obtained when accounting for temperature effects.
Introduction
Major structural failures in recent years have focused public attention on the need for improved infrastructure monitoring and maintenance [1]. In January 2009, the American Society of Civil Engineers (ASCE) issued its latest Report Card for America’s Infrastructure [2], the fourth since 1998. This report asserts that our current infrastructure is poorly maintained, is unable to meet current and future demands, and is in some cases, unsafe. Deteriorating conditions and inflation have added hundreds of billions to the total cost of repairs, needed upgrades and replacements. In this report, bridges receive a grade of C. More than 26% of the nation’s bridges are either structurally deficient or functionally obsolete. An estimated $17 billion annual investment is needed to substantially improve current bridge conditions. As part of the solution, ASCE proposes that owners of the infrastructure should be required to perform ongoing evaluations and maintenance to keep them functioning at a safe and satisfactory level. To manage the nation’s infrastructure system, it is essential to understand the true state of structural health and rate of degradation of each significant bridge structure. This often cannot be determined from visual inspections alone. Vibration-based structural health monitoring (SHM) provides information that is complementary to visual inspections.
The basis for vibration-based SHM is that the dynamic parameters of a structure are functions of its physical properties (mass, damping, and stiffness). Therefore, changes in these physical properties due to “structural damage” will be reflected by changes in dynamic parameters such as natural frequencies, damping ratios and mode shapes. Numerous methods for vibration-based damage assessment of structures have been proposed in the literature. Extensive reviews on vibration-based damage identification have been provided in [3], [4], [5]. Sensitivity-based FE model updating is among these methods [6], [7]. In this method, the physical parameters of a FE model of the structure are updated to match the measured modal properties of the structure as damage evolves, and the updated modeling parameters are used to detect, locate, and quantify damage. In some recent studies, FE model updating methods have been successfully applied for damage identification of real-world, large-scale structures [8], [9], [10], [11]. However, the accuracy and spatial resolution of the damage identification results depend significantly on the accuracy and completeness of the identified modal parameters [12]. The estimation variability/uncertainty of the modal parameters can be influenced by several factors. One of the most important factors (and one of the few that can be measured) is changing environmental conditions, such as ambient air temperature [13], [14], [15], [16], [17]. Therefore, separation methods are needed to remove the effects of changing ambient temperatures from system identification (e.g., natural frequencies) and damage identification (e.g., model calibration factors) results. Even though researchers have underlined the importance of environmental effects in structural identification, little work has been done to quantify these effects on damage identification results.
The focus of this study is (1) to quantify the variation of FE model updating results for the Dowling Hall Footbridge induced by the measured ambient temperatures, and (2) to reduce this variation through removing the temperature effects from identified natural frequencies. The paper is organized in the following order. In Section 2, the Dowling Hall Footbridge and its continuous monitoring system are introduced. A brief review of the automated system identification process and modeling of the identified natural frequencies versus measured temperatures are provided in Section 3. In Section 4, the initial and reference FE models of the footbridge as well as the sensitivity based FE model updating process used in this study are reviewed. Two series of FE model updating are performed using the hourly-identified natural frequencies before and after removing the temperature effects. Variation in the FE model updating results before and after removing the temperature effects and a discussion of the observations are presented in Section 5. Finally, some concluding remarks are offered in Section 6.
Section snippets
Footbridge structure
The Dowling Hall Footbridge is located on the Medford campus of Tufts University. Fig. 1 shows the south view of the footbridge. The bridge consists of two 22 m spans and it is 3.9 m wide. It connects Dowling Hall on its eastern end to Tufts main campus on its western end. The footbridge is supported by an abutment on the west side and by two piers, one in the mid-span and one on the east side near Dowling Hall. The pier heights are 3.8 m and 11.4 m in the mid-span and eastern side, respectively.
Automated operational modal analysis
The data-driven stochastic subspace identification (SSI-Data) method is applied to the cleaned ambient vibration data for modal identification of the footbridge [20]. The data cleansing process consists of: (1) down-sampling from 2048 Hz to 128 Hz for computational efficiency, (2) filtering between 2 and 55 Hz using a Finite Impulse Response (FIR) filter, (3) removing voltage spikes in the time domain, and (4) re-filtering to remove any high frequency components introduced by cleaning the voltage
Initial and reference finite element models, and the finite element model updating process
This section briefly reviews modeling of an initial FE model of the Dowling Hall Footbridge, the sensitivity-based FE model updating process used, and calibration of a reference FE model for the footbridge. FE model updating is a nonlinear least-squares optimization problem in which selected parameters of the FE model (e.g., element stiffness values) will be updated/calibrated to minimize the discrepancies between experimentally measured and FE computed response features such as modal
Before removing the temperature effects
Vibration response of the footbridge is recorded once every hour, which should provide 24 × 7 = 168 sets of modal parameters per week or 168 × 17 = 2856 sets of modal parameters over the 17-week monitoring period considered in this study. However, the number of model updating runs during this period is only 2088. The missed updating runs can be mostly attributed to technical problems with the monitoring system and system identification errors. The technical problems include network connection failure,
Summary and conclusions
A prototype continuous monitoring system was installed on the Dowling Hall Footbridge in November 2009. The monitoring system consists of eight accelerometers to monitor vibrations and ten thermocouples to measure temperatures. A set of data is recorded once an hour or when triggered by large vibrations. The monitoring system has been running continuously since January of 2010 and is still providing data. In this study, the measured data during the first 17 weeks of monitoring (January 5–May 1)
Acknowledgments
The authors would like to acknowledge partial support of this project by the National Science Foundation Grant No. 1125624 which was awarded under the Broadening Participation Research Initiation Grants in Engineering (BRIGE) program. The authors also acknowledge Mr. Peter Moser, former graduate student of Tufts University, for his contributions to the design and deployment of the continuous monitoring system on the Dowling Hall Footbridge.
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