## 1 Introduction  
Reciprocating compressors generally work continuously at full load and many times without a backup, then maintenance management must guarantee maximum efficiency, avoid unscheduled stops, and decrease maintenance times. All this is a challenge because the compressors are elements that work in extreme working conditions such as high temperatures, variable pressures, and alternative movements. As consequence, its critical elements such as valves and roller bearings are more likely to failure [1; 2; 3; 4]. In this context, the application of Prognostics and Health Management (PHM) technologies is important to develop intelligent fault diagnosis systems to guarantee high reliability in the operation and avoid catastrophic damages [5]. Several types of signals are useful for fault diagnosis in reciprocating compressors, such as vibration, acoustic emission, electric current, pressure and temperature [6]. Vibration signals have been studied, for both signal analysis to detect faults [4; 7] and for fault classification [8]. Compressor are reciprocating machines that works with different mechanical multi-component coupling elements, and the vibration signals have non-linear and non-stationary characteristics [9]. Several research works applying PHM technologies in reciprocating compressors have been reported. A research concerning the condition monitoring of the valves by using analytical and data-driven technologies is reported in [10]. The research analyzes different valve failure modes, and also investigates the type of sensors useful for detecting such faults. The fault diagnosis of reciprocating compressor valves using information entropy and Support Vector Machines (SVM) is reported in [11]. The extraction of information entropy features was performed on vibration signals for classifying three types of valve conditions: normal, slightly damaged and severe damaged. An approach for detecting cracked or broken valves under varying load conditions is reported in [4]. The approach is based on time-frequency analysis of the vibration signal. The fault detection is based on the comparison between the spectrogram of the vibration signal and a reference spectrogram representing a healthy valve. The method provides high classification accuracy considering different load conditions. A method for fault detection in reciprocating compressor valves using basic pursuit, wave matching and SVM is reported in [12]. The features used for classification are extracted by wave matching of the vibration signal, regarding a parameterized waveform that is optimized by using a differential evolution algorithm. This approach is used for classifying three valve conditions including the normal condition, spring deterioration and valve plate deformation. The algorithm attains classification accuracies up to 100%. Research concerning the modeling of reciprocating compressors uses phase space trajectories, Poincare maps, and large Lyapunov exponents for identifying the chaotic behavior of a reciprocating compressor system with a subsidence rub-impact fault [13; 14]. Non-linear and chaotic dynamical systems can be analyzed by using tools like the phase space diagram and the Poincare plot [15]. The phase space diagram is used for visualizing the behavior of dynamical systems by representing the trajectories such as a 3D trajectory for a chaotic system [16]. The Poincare map is obtained from the phase space diagram by sampling points in the phase space. For instance, for the case of a 3D phase space, the Poincare section is obtained from the interception of the phase space trajectories with a plane. The Poincare map (also known as Poincare section) has been used for visualizing non-linear, chaotic behavior of faults in gears and bearing elements [17]. Estimation of features extracted from Poincare maps aiming at fault characterization has been reported in [18]. In that research, authors proposed a damage index that is calculated based on the length of the phase space represented by the Poincare map.