## 2 A Cochlea-Inspired Artificial Filter Bank (CAFB) for Structural Health Monitoring  
### Principle of the CAFB  
A previous study has developed the CAFB using n number of band-pass filters to obtain and compress the dynamic response for structures which is required in SHM on civil structures. As shown in Figure 1, CAFB is performed the signal processing (Input of signal (Step 1); Decomposition (Step 2); Reconstruction (Step 3); Compression (Step 4)) using a raw signal obtained from the structure. Figure 1: Principle of the cochlea-inspired artificial filter bank (CAFB). As shown in Figure 1, CAFB is using two kinds of algorithms; one is BOA (band-pass optimizing algorithm) to selectively obtain the interested frequency band, and the other is PPA (peak picking algorithm) to compress the selected signals. First, the BOA was used to design multiple band-pass filters in parallel such that they could be suitably used to determine the target mode required to evaluate the dynamic behavior of the civil structure and additionally calculate the reconstruction signal by altering the design conditions, such as the number, bandwidth, and interval of the band-pass filters. Finally, the reconstruction signal was evaluated through a comparison with the raw data acquired from the target structure. To evaluate the reconstruction signal compared to the raw data, the reconstruction error (RE) is the comparative difference between the composition of filtered signals and the original (raw) signal as expressed in Equation (1) and Figure 2. The RE defined in Equation (1) is represented by the relative difference of absolute values between the original and reconstruction signals. Here, \(u(t)\) is the raw data as a function of the response time, \(y(t)\) is the reconstruction signal as a function of the response time, and \(T\) is the total length of the response time, i.e., the total length of the input signal. The closer to 0 the reconstruction error is, the better the reconstruction effect. \[\text{RE}=\frac{\int_{0}^{T}\lvert u(t)-y(t)\rvert/\lvert u(t)\rvert}{T}=\frac {\int_{0}^{T}\lvert\delta_{1}\rvert/\lvert u(t)\rvert}{T} \tag{1}\]  
Next, a peak-picking algorithm (PPA) was developed for compression, which determines the peak value based on only the reconstruction signal determined through Equation (1). The PPA's calculation process can be summarized as follows: First, the calculated reconstruction signal is read from the optimized filter bank. Second, the reconstruction signal is classified into three (3) data groups. Third, each group's derived function is calculated based on three data points in each group. Fourth, peak values (time and measuring data) are derived by assessing the slope (sign) of each group's derived function. In this study, a central difference method is used as a way to extract peak values while the PPA is calculating. Figure 3 below reveals the central difference method's conceptual diagram, and a derived function can be calculated through Equation (2):  
\[f^{\prime}(x(i))=\frac{f(x(i+1))-f(x(i-1))}{x(i+1)-x(i-1)} \tag{2}\]  
Based on the size of the reconstruction data determined through Equation (1) above, the effects of data compression through PPA can be defined by comparing a relative data size with the extracted peak value. For this, this study defines the data CR (compressive ratio) as stated in Equation (3) below:  
\[\text{CR}=\frac{NS_{0}-NS_{C}}{NS_{0}} \tag{3}\]  
Figure 2: Principle of reconstruction error (RE). Here, \(NS_{C}\) is the number of the compressive signal and \(NS_{O}\) is the number of the reconstruction signal. The closer to 0 the compressive ratio is, the better the compression effect is. The compressed signal is transmitted to the host through the WSNs. The reconstruction error (RE) shown in Equation (1) signifies an index for the precision of reconstruction signals which were first filtered through the CAFB.