# Preprocessing Acoustic Emission Signal of Broken Wires in Bridge Cables
## 2 Materials and Methods
### Basic Theory of Acoustic Emission Technology
#### 2.1.3 Acoustic Emission Signal Analysis Methods  
The AE analysis methods applied in this paper include characteristic parameter correlation analysis, spectral analysis and wavelet analysis, respectively.  
The purpose of the characteristic parameter correlation analysis method is to correlate two or more characteristic parameters to find out the influence of the correlation between the parameters [24]. Then, it further determines the nature of the AE signal through the influence relationship.  
The AE signal is transient and random, and belongs to the category of non-smooth random signal. It consists of a series of frequency and mode rich signals. However, the signal characteristics in the time domain are rather one-sided for describing AE signal, since the transient signal is also accompanied by frequency and phase information. This requires further analysis of the signal in the frequency domain, i.e., spectral analysis. The spectral analysis method is to transfer the AE signal from the time domain to the frequency domain, and obtain the AE signal characteristics, as well as the state of the AE source through the time domain expression [25]. The most commonly used spectral analysis method for AE signals is the fast Fourier transform (FFT) spectral analysis method. The FFT method is a fast algorithm of discrete Fourier transform (DFT), which makes up for the shortcomings of the Fourier transform method in terms of operational efficiency. It has an important role in AE signal processing.  
Wavelet transform (WT) is an effective mathematical tool [26]. The wavelet refers to its attenuation and fluctuation characteristics, respectively. It can show good local characteristics, since wavelets can have high resolution in time and frequency domains. The wavelet transform is also called a \"mathematical microscope\" by researchers because of its high resolution and the ability to focus on arbitrary details of the signal through the telescoping transform. The wavelet transform has been widely used in many fields, and has made outstanding contributions to the further characterization of AE signals.  
The expressions of wavelet transform are shown in Equations (1) and (2).  
\[W_{f}(a,b)=\int\limits_{-\infty}^{\infty}f(t)\overline{\varphi_{a,b}(t)dt} \tag{1}\]  
\[\varphi_{a,b}(t)=\frac{1}{\sqrt{a}}\varphi(\frac{t-b}{a}) \tag{2}\]  
In the above equation, \(a\) is the scale factor, \(b\) is the translation parameter and \(\varphi(t)\) is the wavelet. According to the mathematical expression of the wavelet transform, it transforms the time function to the time-scale plane and focuses on the details of the time-domain function by the scale factor and the translation parameter. This makes it possible to extract certain features of the mutated signal.  
The choice of wavelet basis is also an important issue of the wavelet transform. The wavelet basis functions include Harr wavelets, symlets, Daubechies wavelets, Meyer wavelets, and Coifman wavelets, etc. The selection of wavelet basis functions is related to the correctness and validity of the analysis results. The Daubechies (db) wavelet is a finite tightly-branched orthogonal wavelet with a long enough support width, and the vanishing moment and regularity are also superior. According to the wavelet analysis of the AE signal, the number of decomposition layers should not exceed five layers [27].