## 1 Introduction  
With the development of the fields of aerospace and aeronautics, more and more superalloys, such as nickel-based material [1], have been adopted due to their excellent high-temperature performance, superior mechanical strength, and corrosion resistance [2]. Meanwhile, the high hardness, low thermal conductivity, and high-temperature stability of superalloys also make them extremely difficult to be machined using traditional machining methods [3]. Therefore, in recent years, non-traditional machining methods have been explored and investigated further for the precision machining of superalloys, and electrical discharge machining (EDM) is an important part due to its low cost and high flexibility [4]. In the EDM process, when an open circuit voltage is applied between two electrodes, the discharge does not occur immediately but after a certain discharge delay time, resulting in the gap phenomenon. Then, at the discharge spot, the workpiece is melted and vaporized due to the heat generated by the plasma channel, thus achieving the purpose of material removal. During the discharge process, machining parameters play an important role and affect the machining quality and efficiency [5]. To improve the machining result, several research works have been completed by researchers. In the work of [PERSON] et al. [6], they proposed an optimization method for improving the corner accuracy of WEDM, taking into account parameters such as pulse-on time, voltage, wire tension, and flushing pressure. By integrating response surface methods and algorithms, they achieved the prediction of corner errors while simultaneously recommending the optimal parameters. In addition, with the wide adoption of machine learning, it has also been considered in the WEDM field. Through the combination of machining parameters and the corresponding machining results, [PERSON] et al. [7] used deep learning to monitor the machining process of the fir-tree slot that appears on turbine disks. Moreover, as material removal in EDM is achieved through the accumulation of numerous discharges, the preceding discharge also has a crucial influence on the gap phenomenon, thus affecting subsequent discharges [8]. Since the EDM process involves immersing the electrodes in a dielectric liquid such as oil or water [9], the melting material is cooled to become debris particles. With the flushing flow, the debris particles are ejected from the discharge position and the material removal process is completed. During this process, bubbles generated by the discharges always exist in the gap between the tool electrode and the workpiece. This kind of gap phenomenon is tough to observe due to the narrow gap width being filled with dielectric liquid. [PERSON] and [PERSON] [10] investigated the debris particles generated by EDM through the study of a single discharge in gelatin. These authors found that the debris particles generated by discharge always accumulate at the boundary of the bubble. Then, in recent years, [PERSON] et al. [11] used a high-speed video camera and transparent electrodes to observe the Sinking Electrical Discharge Machining (SEDM) gap, finding that the probability of the next discharge occurring at the boundary of the bubble was the highest because of the debris which concentrates at the boundary of the bubble. A recent study by [PERSON] et al. [12] shows that while debris affects bubble production, it does not alter the bubble distribution model. Accumulated conductive debris increases discharge frequency, reducing bubble production efficiency and disrupting oscillation. Similarly, [PERSON] et al. [13] introduced a new experimental setup for generating single discharge craters in WEDM, concluding that bubbles significantly influence material removal. They observed that ineffective pulses can be caused by either short circuits or bubbles, with bubbles being inhibited axially along the wire. Future research will use acoustic emission signals to distinguish between effective and bubble-related discharges.