## 2 Operational Modal Analysis of a Skewed Highway Bridge
### Operational Modal Analysis  
In order to identify the experimental modes of the bridge, vibration measurements were performed on the structure under operational conditions. During the tests, one of the traffic lanes was closed to allow the sensor placement, while the other was still open (see Figure 1b). The excitation of the structure was mainly ambient, due to mild wind and traffic on both the tested and the adjacent spans. The tests were performed during the day time. The traffic was not very busy, but there was generally at least one vehicle passing over the tested bridge for each measurement duration. The passing vehicles included cars and even some heavy trucks, as shown in Figure 1b. As shown in Figure 3, there were thirty-four measurement points in total, mostly on one of the traffic lanes. The points were aligned along the skew direction of the bridge in agreement to the bending direction, as suggested by the a priori finite element model built before the testing. Vertical accelerations of the bridge deck were recorded. Since the width of the bridge deck is of a similar magnitude as the span length, the dynamic behavior of the deck is expected to be close to that of a plate instead of a beam. In order to catch the torsion modes and the bending modes in the transversal cross-section, a node, labeled as No. 34, was placed on the other side of the bridge close to the side barrier where the traffics were open. The measurements had to be divided into several setups since the number of the points exceeded the number of the acquisition system channels. Three reference nodes, indicated by R1, R2, and R3, common to all the setups, served as the basis for combining the mode shapes identified from each individual setup. The adopted measurement system was the wireless sensing system developed in the aforementioned project. Figure 4a shows one of the wireless units deployed during the measurements, to which four external piezoelectric (PCB) accelerometers were connected. In total, there were four wireless units, also known as the clients, installed in the experimental campaign. A self-developed graphical user interface of the wireless measuring system was operated from a laptop, which also acted as the acquisition server (see Figure 4b). All the functions of the system could be easily managed through the user interface, including data acquisition, wireless communication, and time synchronization among all the client units. System identification was carried out by the stochastic subspace identification (SSI) algorithm, as implemented in the MACEC software package [37]. Data processing included the following steps: (1) reduction of the sampling rate of the wireless data from 3906 Hz to 100 Hz; (2) removal of the drift of the signal due to its DC components; (3) removal of the low-frequency noise through a high-pass filter with a cut-off frequency of 2 Hz. For the covariance-driven SSI algorithm, the algorithmic parameter i--half the number of block rows--is set to 180. The system identification is performed for the state-space systems sequentially in orders from 2 to 250. In the corresponding stabilization diagram, the stabilization criteria are: 1% for frequencies, 5% for damping ratios and 1% for Modal assurance criterion (MAC) of the mode shapes. Figure 4: The wireless sensing system: (**a**) One of the client units; (**b**) server. Two ambient vibration measurement campaigns were conducted on the bridge on 25-26 November 2009 and 2 February 2011, respectively. During the first test, a traditional wired acquisition system was used in order to obtain the operational modal results as the reference. The measurement periods were both ten minutes for the wired and the wireless systems. During the second test, the measurements were repeated with a ten-min and a fifteen-min period, respectively, for each setup of the wireless system. The corresponding experimental results were denoted by Wired, WL1, WL2, and WL3 in turn, as shown in Table 1. Seven modes were identified below 40 Hz by all the tests.