## 1 Introduction  
China is rich in shale gas resources, which are an important area of increased production for natural gas in the future. The geological resources of shale gas range from 80.45 to 144.5 \(\times\) 10\({}^{12}\) m\({}^{3}\), and the deep (>3500 m) resources account for more than 65%. As the main production area of shale gas in China, the Sichuan Basin has 11.2 \(\times\) 10\({}^{12}\) m\({}^{3}\) reserves, accounting for more than 69% of China's shale gas [1, 2, 3, 4]. Deep and ultra-deep shale gas resources have great potential, but well drilling faces many challenges, such as complex geological conditions, low drilling efficiency, severe bit wear, and long drilling cycle [5, 6, 7, 8]. Since its introduction into the oil and gas drilling business in the 1970s, the Polycrystalline Diamond Compact (PDC) bit has quickly grabbed the attention of the worldwide oil and gas bit market due to its benefits of high rate of penetration and extended footage. Accordingto the data, PDC bit footage currently accounts for more than 90% of the total footage of oil and gas bits in the world, with a growing market share of 75-80% [9]. In terms of material assurance, the structural design of a PDC bit has a direct impact on its overall performance, including the rate of penetration (ROP), wear rate, single footage, drilling stability, and so on [10]. Excessive tripping and bit loss will affect 15-20% of the total drilling cost when the structural design of the bit is unreasonable [11]. Scientific and reasonable bit structure design is beneficial for removing cuttings, reducing the mechanical specific energy (MSE), improving the rock-breaking efficiency, and ensuring excellent bit performance. The ROP and footage are strongly related to the mining time and drilling cost as important indexes for evaluating the use effect of drill bits. An accurate forecast of the ROP and footage of a drill bit can improve resource allocation and aid in the creation of operation plans, boosting drill bit use efficiency and accomplish the goal of speeding up and decreasing expenses [12]. In recent years, there has been a relative dearth of research on bit footage prediction, whereas many experts and scholars have conducted considerable research on ROP prediction. The traditional theoretical derivation prediction method obtains the mathematical derivation formula through a large number of experiments. [PERSON]'s ROP model lays the groundwork for subsequent prediction research [13]; [PERSON] et al. established the relationship between the WOB (weight on bit) index, rotational speed index, hydraulic index, and other parameters, proposed the ROP coefficient K, and established a ROP prediction model combined with a logging sound wave [14]. [PERSON] et al. solved the coefficient of ROP equation using multiple regression analysis and obtained distinct regression coefficients for different forms [15]. Drilling is a difficult process, and the formation conditions, tool structure, and operating settings all play a role in the rock-breaking ability of the drill bit [16]. It is hard to obtain the geological conditions and coefficients of drilling parameters, and it is difficult to effectively represent the ROP as a mathematical function of some critical variables. As a result, some studies in recent years have recommended using a data-driven model in the field of artificial intelligence to forecast and optimize the ROP, and the neural network method has been widely adopted [17; 18]. [PERSON] [19] and [PERSON] et al. [20] used integrated algorithms to build ROP prediction models based on K nearest neighbor and decision tree methods, with goodness of fit serving as the ROP prediction evaluation metric. To establish the ROP prediction model of directional wells, [PERSON] [21] and [PERSON] et al. [22] used an artificial neural network algorithm; [PERSON] [23] and [PERSON] et al.