## 3 Signal Analysis  
### Conventional Time-Frequency Analysis  
High frequency signals were discovered during numerous arc fault experiments. They could reflect the dynamic arc discharge process and be acquired using high frequency transducers [14]. At first, air molecules in the wire gap are ionized in the initiation of arc discharge, and the motion of plasma is then intensified further. According to electromagnetic theory, great quantities of high frequency signals are initially released. The signals are then gradually reduced during the remainder of the current cycle [14]. As a result, high frequency signals are produced periodically when arc faults exist in circuits. However, these signals are uncertain as a result of the unknown external conditions including the effects of electrode materials, surface states, oxide layers, adsorbed gases, arc currents, arc gaps of dielectric materials, _etc._  
Figure 1: Experimental platform of arc faults. Figure 2: Detected high frequency signals of different load states. (**a**) Halogen lamp normal; (**b**) Halogen lamp arc fault; (**c**) Vacuum cleaner normal; (**d**) Vacuum cleaner arc fault; (**e**) Electrical drill normal; (**f**) Electrical drill arc fault. In order to find the features of arc faults, some typical load signals are selected for analysis. The high frequency signals of different loads in arc faults and normal states are shown in Figure 2. There are many high frequency signals and short pulses generated during the arcing process when the loads work in arc fault states as shown in Figure 2b,d and f. The high frequency signals with big amplitudes are densely distributed. However, high frequency signals can be also acquired during the normal states as shown in Figure 2a,c and e.  
As a result of the switch transformers alternating between on/off state, there are many high frequency signals generated in current cycles when the halogen lamps work in the normal state as shown in Figure 2a. Similarly, when the vacuum cleaner and the electrical drill work in normal states, some random interference pulses appear in the circuits as shown in Figure 2c,e. Due to electric brush motors in the vacuum cleaner and electrical drill, electrical discharge occurs and produces many high frequency signals when the electric brush changes the current phase. Electric sparks can be seen from the electrical drill windows even when working in the normal states. The electric sparks are caused by load arcs which are not dangerous but are similar to fault arcs. It is usually very difficult to discriminate load arcs directly from measured frequency signals. The analysis above indicates that it is difficult to find a reasonable numerical threshold to classify arc faults and the normal states in all loads by simply inspecting the constant amplitude of the high frequency signals. This is because that arc fault signals are usually mixed with much interference consisting of circuit noise, quantization noise from the acquisition process, random noise from electric parts, _etc._ They are both close to the Gaussian distribution. As a result of their existence, the SNR decreases considerably. The frequency aliasing is hard to overcome. In frequency domain, the power spectra of vacuum cleaner are shown in Figure 3. The frequency distributions of arc faults and normal states in power spectra are similar. As we know, the power spectrum is based on second-order statistics. Signals are only analyzed by the amplitude (_e.g._ Figures 2c,e, 3a and b) but lack phase coupling information. So the power spectrum may fail in providing a satisfactory description in a non-Gaussian or nonlinear process. In addition, there are many high frequency signals generated in current cycles when the vacuum cleaner works in normal state. The power spectrum applies the Fourier transform to all signals and is sensitive to the Gaussian noise. Hence it is difficult to distinguish the effective components from the mixed signals of arc faults through the power spectrum.