# Data Driven Leakage Detection and Classification of a Boiler Tube
## 2 Methods and Procedures for Leakage Classification of the Boiler Tube
### Wavelet Packet Decomposition  
The acoustic emission (AE) signals acquired from the boiler tube are used to record information about the health state of the tube in the time domain. The signal waveform represents the signal amplitude values (voltage) recorded at specific time intervals. During the signal acquisition process, the signal amplitude values vary randomly. There is no clear pattern in the time domain waveform of the signals. Moreover, the inclusion of unwanted signals from the surrounding environment in the form of noise makes leak detection and classification more difficult just by observing the time domain values of the signals. To thoroughly analyze the signals for the extraction of descriptive features associated with different health states of the boiler tube, a sophisticated signal processing technique is required. There are several signal analysis techniques in the literature, like, traditional fast Fourier transform (FFT), short-time Fourier transform (STFT), empirical mode decomposition (EMD). All of these techniques have been implemented in the literature for different types of signal analysis in the fault diagnosis domain, but these techniques either have limited signal analysis capacity or have hectic computation procedures. For instance, the Fourier transform cannot provide time information of the analyzed signals. Similarly, STFT has the problem of fixed resolution [18]. Choosing an appropriate windowing function is a challenge in the STFT calculation. A narrow window provides good time resolution, whereas a wider window yields better frequency resolution. Always there will be a tradeoff while selecting the window size. In EMD, intrinsic mode functions (IMFs) are calculated and cannot be predicted before they are observed empirically. Moreover, the number of IMFs cannot be predicted before the decomposition. In EMD, oscillations in a signal are considered at the very local level. Their calculation involves detailed signal processing techniques like extrema identification, interpolation and residual calculation of a signal. Thus, EMD calculation depends on a number of options which need signal processing expertise from the user. Moreover, in EMD, the iterative calculation of the IMFs increases the latency of the algorithm. Therefore, it is not recommended to provide online solutions [19]. Therefore, in this study, a wavelet packet transform (WPT) based AE signal analysis was performed, which provided better time-frequency resolution and lower latency of the algorithm. WPT provides better time-frequency resolution compared to short-time Fourier transform (STFT). This turns out to be a promising tool to extract health state features from complex AE signals. WPT is a variant of a basic wavelet transform that divides the input signals into different subbands based on the high pass and low pass filters. In WPT, a signal is decomposed according to the criteria that at each level \(j\) the number of nodes is \(2^{j}\). In WPT, both detailed and approximated coefficients are decomposed to form a binary tree contrary to the discrete wavelet transform (DWT). In this way, WPT provides a more detailed time-frequency, on both lower and higher frequencies of the signals, than conventional DWT analysis. Each node in a specific level in DWT provides half the frequency resolution width of the preceding level and twice that of the next level. In this study, fourth-level decomposition of acoustic emission signals was carried out. Level 4 decomposition of the signals resulted in \(2^{4}=16\) nodes. Figure 2 shows the adopted 4-level WP tree structure. Figure 1: The proposed boiler tube leakage detection model. After decomposition of the AE signals, the relative energy and entropy of each node were calculated. The wavelet values were used as input features to the subsequent DNN.