30 Structural Stiffness Identification of Skewed Slab Bridges with Limited Information for Load Rating Purpose 247 Fig. 30.4 The ANN estimated versus the actual 30.3 Experimental Study 30.3.1 Test Description The structure tested in this study was the War Branch Bridge located in the Staunton District in the state of Virginia. The superstructure is comprised of two 9.75-m long, simply-supported reinforced concrete slabs that are 0.53 m thick and have a 45ı skew angle (see Fig. 30.5). The deck has 0.3 m diameter voids oriented in the direction of traffic and spaced 0.45 m apart. Built in 1976, the 2014 inspection report described the bridge to be in “fair” condition, with a deck/superstructure condition rating of 7. The bridge was selected from amongst the Virginia Department of Transportation (VDOT) population of reinforced concrete slab bridges with plans, with special consideration given to geometry similarity to the population of this major category of bridges without plans. For the vibration testing experiments, one of the two spans in the bridge was instrumented with accelerometers. All instrumentation and acquisition comprised of Bridge Diagnostics, Inc. (BDI) equipment, where individual sensors physically connected to four-channel nodes, which in turn interfaced wirelessly with a base station/data acquisition unit. Vibration testing consisted of a series of experiments with excitation provided separately by ambient loading (wind and normal traffic), impact hammer, and electro-magnetic shaker. 30.3.2 Modal Data Identification In this paper, an algorithm based on the VMD is employed for identifying the modal properties of the bridge. In this method, the measured acceleration signals are decomposed into the modal responses by means of the VMD algorithm, and each obtained modal response has a center frequency which represents the natural frequency of the structure. Then, damping ratios are estimated by doing a fitting process on decaying amplitude of modal response. This method is capable of identifying all natural frequencies and damping ratios using only a single measurement of acceleration response at one suitable location. Mode shapes are then identified from the results of modal responses at all sensing location of the structure. The VMD is first used to decompose an acceleration signal S(t) into a set of sub-signals (modes), Sk(t), k D1, 2, : : : , K, which have a compact bandwidth in spectral domain. It can be assumed each sub-signal to be compacted around a center vibration!k which is determined using the decomposition algorithm. Therefore, each sub-signal represents the modal response of structure. In this process, the constrained variational problem is formed by means of Hilbert transform and frequency mixing based on minimizing the bandwidth of sub-signals. In order to render the problem unconstrained, the quadratic penalty and Lagrangian multipliers are employed. More information about the VMD algorithm can be found in [9].
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