# Transmission Condition Monitoring of 3D Printers Based on the Echo State Network
## 1 Introduction  
As a rapid prototyping technology, 3D printing is based on a digital model and can be sticky with powdered metal or plastic. Materials are used to construct objects via layer-by-layer printing [1]. The application domain of 3D printing is expanding rapidly. In the electronics, aviation, automobile manufacturing, and medical industries, 3D printing can produce small batches of customized components with low cost and high efficiency [2]. The quality of 3D printing products are greatly reduced when transmission faults occur [3]. Under these circumstances, a novel cable-driven parallel 3D printer was developed to fine tune the transmission of 3D printers [4], and a spring-assisted mechanism was investigated to identify the transmission performance of 3D printers by comparison with a conventional tilting mechanism [5]. However, even if the transmission mechanism of the 3D printer is well designed, it will encounter faults during its life time. In summary, it is necessary to develop low-cost transmission condition monitoring techniques for 3D printers, which will monitor the quality of 3D printing. Over the past few decades, many methods for monitoring mechanical systems have been developed, such as vibration monitoring, temperature-based diagnosis, spectrum analysis, etc. [6; 7]. For instance, condition monitoring of machine-bearing housing using the measured experimental values of the acceleration amplitude of mechanical vibrations was studied in Reference [8], a new switching unscented Kalman filter algorithm was proposed in Reference [9] to predict the remaininguseful life of bearings, and a method based on a generalized synchro-squeezing transform with vibration data was proposed to detect gearbox faults in Reference [10]. In addition, work in condition monitoring for machinery includes an approach using moment and rotor angle sensors that was proposed to monitor wind turbines [11] and the use of multiple sparse auto-encoders reported for dynamic state monitoring of 3D printers [12]. At present, new intelligent classification methods such as artificial neural networks (ANNs) [13], SVM [14], fuzzy logic [15], and neighborhood preserving embedding (NPE) [16] have been gradually employed for condition monitoring. An ANN is an information processing system designed to imitate the way human brain's work [17]. This model has the capabilities of associative memory, pattern matching, and similarity induction. This is why the model has the ability to accomplish nonlinear mapping the relationship between system states and fault causes [18]. However, ANN tends to fall into local minimum and over-fitting problems when applied to condition monitoring [19]. In Reference [20], it was confirmed that a back propagation neural network (BPNN), a kind of ANN, is not an effective technique for condition monitoring of 3D printers, while SVMs can effectively diagnose 3D printers when using high-cost attitude sensors. However, data noise increases when low-cost attitude sensors are employed for data collection. Thus, the condition monitoring accuracy of SVMs will decrease dramatically. For this reason, it is necessary to propose a more effective monitoring method for 3D printers. The echo state network (ESN), proposed by [PERSON] in 2001 [21], is a type of recurrent neural network, which includes a large, sparse, and randomly connected set of neurons, known as the reservoir. After initialization, the reservoir remains fixed and the learning effort is only necessary for the output (readout) connections. The ESN can be viewed as a type of reservoir computing (RC) and is particularly suitable for time-series processing [22]. In this paper, the monitoring data of the 3D printer was time-series data. Moreover, the ESN is still an effective method in dealing with time-series data with high noise [21; 22; 23]. Hence, ESN is employed for transmission condition monitoring of 3D printers in this paper. However, due to the high dimension of the attitude data, it is better to extract some features as the input data for ESN.