## 1 Introduction  
Statistical data from fire services show that over 90% of electrical fires are caused by arc faults, over currents, short circuits and leakages [1; 2; 3; 4]. Leakage protectors and over current breakers are respectively used to protect electrical circuits from leakages and over currents presently, but they cannot be used to protect circuits from arc faults. There are three types of arc faults: ground arc fault, parallel arc fault and series arc fault. Parallel and ground arc faults respectively share similar features to ground fault and over current and are thus easy to be detected [5]. However, fault features from series arc faults are usually submerged by load currents and background noise, thus making accurate recognition difficult. To accurately describe an arc fault in mathematics, some arc fault models were proposed. [PERSON] and [PERSON] developed an instantaneous arc model for a resistive-inductive system [6]. This model could predict arc fault currents because arc voltage was a current-dependent function. Another similar arc fault model for alternating current (AC) systems was derived by the probability method [7]. [PERSON] provided a simplified model which could be used to analyze and determine basic parameters such as arc resistance and ignition voltage [8]. To fit with the arc fault scenarios described in UL1699 which was a standard for arc fault circuit interrupter (AFCI), a meta-model based on Mayr and [PERSON] models was built [9]. Arc fault models usually provide theoretical bases for arc fault detection. When arc faults occur in circuits, some abnormal behaviors are found on arc light, arc sounds, arc radiation signals, arc voltages and arc currents. Arc light and arc sounds usually change obviously and they can be used for arc fault detection [10; 11]. The study in [12] estimated the amplitude of arc voltage by least error squares method. The voltage was compared with a given threshold value to identify arc faults. Another similar approach for arc fault detection by the amplitude comparison of arc voltage was proposed in [13]. The simulation of the approach was successfully done using a square wave arc model. [PERSON] obtained the radiated electromagnetic energy from arc source using a stick and a loop antenna [14]. He then concluded that the radiation signals could be used for arc fault detection. Although arc fault behaviors of arc light, arc sounds, arc radiation signals and arc voltages are obvious, they appear on stationary sites. Hence, there are some limitations in arc fault detection methods based on these behaviors since the sites, time and intensities of series arc faults are random. The study in [15] briefly summarized the frequency features of currents. Researchers in the study believed that the high frequency components (greater than 20 kHz) existed in arc fault currents. In the frequency domain, the spectrum energy variations of line currents can be used to detect series arc faults [16]. In many studies, a large quantity of load currents in arc faults and normal states were first acquired. Arc fault features were then found by advanced signal processing approaches, and arc faults were finally discriminated from the load states based on these features. Those advanced approaches are: using the absolute sum value of coefficients in multiresolution signal decomposition [17], combining discrete wavelet transform and wavelet networks [18], using discrete wavelet transform andan artificial neural network [19, 20], using Gabor Transform and artificial neural network [21], reconstructing the information entropy of signals in different frequency bands [22], _etc._  
For this paper, in order to improve the accuracy of arc fault detection, a large number of arc fault high frequency signals will be collected by a transducer to find any common features among arc faults. High frequency signals are usually mixed with Gaussian noise, such as circuit noise and quantization noise from the acquisition process [23].