###### Abstract
Numerous researchers have attempted to find the best feature that presents the condition of welding electrode tips. Several handcrafted features--including half-cycle peak, maximum, slope, mean, and standard deviation--have been proposed in prior work [1; 13; 14]. However, it is challenging to develop a single feature that represents the whole process. To address this challenge, a combination of various handcrafted features that use principal component analysis [15] and neural networks [16] have been developed. Nonetheless, there is not yet a universal feature (or health indicator) for monitoring welding electrode tips in a spot welding system. The type of waveforms can be generally divided into stationary and non-stationary as shown in Figure 1. The stationary waveforms can be further categorized into random, periodic, and quasi-periodic. Periodic and quasi-periodic waveforms are deterministic and made up of discrete sinusoidal components. The non-stationary waveforms can be grouped into transient, cyclostationary, and continuously varying. Cyclostationary waveforms are an amplitude modulated white noise. To understand the characteristic of the waveforms, appropriate signal processing techniques should be used. For example, periodic and quasi-periodic waveforms can be visualized in one-dimensional (1D) space (i.e., the frequency domain) using Fourier transform (FT), while nonstationary waveforms can be plotted in two-dimensional (2D) space using wavelet transform (WT) and Wigner-Ville distribution (WVD). If nonstationary waveforms are analyzed using FT, the changes in frequency with time will be ignored as FT integrates the waveform over all time. Therefore, a proper technique should be selected by the user depending on the type of waveforms. However, it is challenging to select the most relevant signal technique since the dynamics of an engineered system are often complex and multiple waveform types exist in data collected from the system. The state of engineered systems usually changes in time. The study of complex dynamics can help describe, forecasting such changes. A dynamical system can be described by (1) a phase space, (2) a continuous or discrete time and (3) a time-evolution law [18]. Suppose that the state \(x\) of a system at a fixed time \(t\) can be defined by \(d\) components. \[\overrightarrow{x}(t)=(x_{1}(t),x_{2}(t),\ldots,x_{d}(t))^{T} \tag{1}\]  
where \(\overrightarrow{x}(t)\) is the vector in the \(d\)-dimensional phase space of the system. As an example, \(\overrightarrow{x}(t)\) for the dynamic resistance waveform reduces to the scalar in a single dimensional phase space. For time-continuous systems, the time evolution is described by a set of differential equations:  
\[\dot{\overrightarrow{x}}(t)=\frac{d\overrightarrow{x}(t)}{dt} \tag{2}\]  
In general, a system returns to former states. A recurrence is a fundamental characteristic of dynamical systems. The method of recurrence plots (RPs) [19] received significant attentions in the fields of engineering [20], biology [21], and neuroscience [22]. RPs that visualize trajectories in the phase space are especially advantageous in the case of high dimensional systems. Other signal processing techniques (e.g., FT, WT, and WVD) mentioned above can visualize only the state of a single dimensional system, not the state of high dimensional systems. Recently, convolutional neural networks (CNNs), such as VGG-16 [23] and ResNet [24], have shown excellent performance for classifying hundreds and thousands of images. Unlike traditional feature engineering, CNNs can be used to extract features in an unsupervised manner (i.e., unsupervised feature engineering) that does not require human experience. An objective interpretation regarding images of RP structures can be made. Therefore, it is worth examining a combination of RP imaging technique and CNN for monitoring welding electrode tips in a spot welding system.