## 1 Introduction
Indicator diagram: The indicator diagram reflects the change curve of the piston position and the corresponding pressure in the cylinder in a working cycle of the reciprocating compressor. The piston position can be expressed by the cylinder gas volume, crank angle, piston stroke, etc. For reciprocating compressors, the thermal performance can reflect various types of faults and the indicator diagram can reflect many changes in thermal performance. Therefore, once the gas valve fails, the shape of the indicator diagram will change accordingly. This is the reason why many scholars have used indicator diagrams to perform fault diagnosis as well as carrying out a lot of research. [PERSON] et al. [8] used backpropagation neural network(BPNN) to identify the fault type based on extracting the features of the geometric properties of the indicator diagram. He effectively diagnosed four common faults of the gas valve. [PERSON] et al. [9] proposed curvelet transform to extract the typical features in the indicator diagram and reduced the dimensions of the high-dimensional features through principal component analysis. Next, he input features to support vector machines (SVM) for failure pattern recognition. This was effective in discriminating clogged exhaust valves, clogged intake valves, and leaked exhaust valves, etc. However, the indicator diagram converts 1-D signal into 2-D signal, which increases the complexity of feature extraction. The extracted features are difficult to fully cover all the information of the indicator diagram. The information on the pressure in the cylinder and the position of the piston is difficult to collect. As a result, diagnosis by the indicator diagram has great limitations. [PERSON] et al. [10] established a dynamic model of coupling translation joints with subsidence for time-varying load in a planar mechanical system. He discussed 42 kinds of coupling rub-impact scenarios of double translational joints with subsidence. Finally, [PERSON] et al. [11] employed the Poincare cross-section method and the maximum Lyapunov exponent method to prove the chaotic behavior of the reciprocating compressor system. [PERSON] et al. [12] explored the causes of self-excited oscillation caused by the bearing by establishing a mathematical model of the rotor system and proves the instability of the system. The chaotic behavior and the instability of system is often one of the reasons that make the signal more complex. Therefore, the fault signal of a reciprocating compressor has complex nonlinear and non-stationary characteristics. In addition, the signal contains a lot of noise, and some traditional signal processing methods are not applicable. For instance, fast Fourier transform (FFT) can be effectively applied to rotating machinery, but it cannot achieve good results when processing reciprocating compressor signals. Hence, alternative methods are used for processing nonlinear or transient signals, such as wavelet transform (WT) and empirical mode decomposition (EMD). They decompose the signal into different frequency bands and extract steady-state and linear features from different frequency bands. [PERSON] et al. [13] used the wavelet transform with the basis function of Bior3.5 wavelet to decompose the original vibration signal into various frequency bands. Then, he utilized energy spectrum analysis and used the energy spectrum features as the input of the support vector machine for diagnosis. The experimental results show that the accuracy of fault identification exceeds 90%. [PERSON] [14] employed ensemble empirical mode decomposition (EEMD) to decompose the vibration signal into intrinsic modal functions (IMFs) of different frequencies and used the Hilbert spectrum to extract the fault characteristics of the natural gas compressor. However, it is difficult to select the basis function of the wavelet transforms and there is no standard to select the basis function for different signals. EMD also has many problems, such as modal aliasing.