# Development and Field Validation of Wireless Sensors for Railway Bridge Modal Identification
## 4 Wireless Sensor Node Measurement Performance Assessment  
The main scope of the field test was to verify if acceleration data acquired by sensor nodes were suitable to be used for modal identification of a typical railway bridge. The identification of modal characteristics is significant for SHM techniques since a change of these structural features in time can be attributed to the presence of an extensive damage in the structure [10]. In this framework, frequency domain algorithms have been the most popular, thanks to their simplicity and processing speed [39]. The goal of this analysis is to understand if acceleration data collected are significant and can be used to compute the main bridge natural frequencies. One of the simplest methods for the identification of modal parameters found in the literature is the basic frequency domain (BFD) method. This approach is also known as peak-picking method since modes are identified by picking the peaks in power spectral density (PSD) plots [40]. Since usually not all the natural frequencies are represented in an averaged PSD of a single measurement location, it is necessary to consider all measured locations to ensure the identification of the structural natural frequencies of interest. An interesting method to avoid the analysis of several PSD plots through the introduction of a new frequency indicator function based on a group of PSDs is explained in [41]. This newly defined natural frequency indicator is the function named averaged normalized power spectral densities (\(ANPD\)), which can be computed through Equation (1). \[ANSPD_{i}(f_{k})=\frac{1}{l}\sum_{i=1}^{i=l}NPSD_{i}(f_{k}), \tag{1}\]  
\(NPSD_{i}(f_{k})\) is defined by Equation (2). \[NSPD_{i}(f_{k})=\frac{PSD_{i}(f_{k})}{\sum\limits_{k=0}^{k=n}PSD_{i}(f_{k})}, \tag{2}\]  
Figure 10: Exemplary acceleration time histories acquired by the wireless sensors possibly triggered by a heavy vehicle transiting on the upper deck. where \(f_{k}\) represents the discrete frequency and \(n\) is the number of discrete frequencies. The peaks of the _ANPSDs_, obtained through the elaboration of the data collected by wireless sensor nodes, were then used to estimate the natural frequencies of the bridge and the results of this procedure are visible for lateral and vertical axes in Figure 11.  
In order to assess the accuracy in the frequency estimation obtained with acceleration data collected by the wireless sensors, reference values of natural frequencies of the different modes were obtained thanks to the processing of data acquired by the wired system. The time interval in which the signals used to estimate the reference frequencies were acquired corresponds to the nighttime hours, during which there are no train passages. Thus, the input to the system was solely natural excitation from the environment and, to a very limited if non-zero extent, from road traffic. For this application, road traffic was considered a source of random noise as well. Then, these signals were filtered and cleansed to remove anomalies, and PSDs were derived for each acquisition channel. These PSDs, coming from relatively long signals (in the order of hours) had a clear enough spectral content to estimate the natural frequencies, corresponding to the frequency value at the resonance peaks. In particular, regarding the vertical modes, the natural frequencies of the first three bending and torsional modes are successfully estimated. For the lateral modes instead, the natural frequencies of the first three bending modes are estimated. The results are summarized in Table 4 where the second column reports the reference values obtained by the conventional wired system, while in the third column, estimations obtained from data collected by wireless sensor nodes are reported. The reference values were computed, as explained previously, by taking advantage of a large database obtained with the permanent installation of the conventional wired system on the structure for several months.