# A Hybrid Neural Network Model for Predicting Bottomhole Pressure in Managed Pressure Drilling
## 1 Introduction  
Real-time monitoring of BHP is an important reference for the drilling program design, optimization of drilling parameters, and the dynamic regulation of production programs, which can provide a basic guarantee for safe, efficient drilling and the development of oil and gas [1]. For deep high-temperature and high-pressure drilling, accurate and efficient calculation of BHP is more critical to ensure drilling safety. The traditional methods of estimating BHP mainly include mechanistic model-based calculation and using gauge or well testing, but there are major economic and technical limitations in this method; although the mechanistic model calculation method [2, 3, 4, 5, 6, 7, 8] is less costly, it is difficult to consider all complex environmental conditions simultaneously. Therefore, most of the methods can hardly process a large variety of datasets and only perform well under certain conditions. Recently, the introduction of intelligence technology has realized accurate and efficient prediction of BHP based on surface monitoring data and provides scientific basisand technical support for safe drilling and efficient production. Many researchers have conducted exploratory research on intelligent prediction methods of BHP. One of the most representative is the use of Artificial Neural Network (ANN) techniques. As early as 1995, [PERSON] et al. [9] established a prediction model of BHP based on ANN according to the three-phase flow law of oil, gas and water, and compared the field data to verify the feasibility of the neural network model of BHP. Subsequently, several scholars have used machine learning methods and built different types of ANN models to predict BHP, such as [PERSON] et al. [10], [PERSON] et al. [11], [PERSON] et al. [12], [PERSON] et al. [13], [PERSON] et al. [14], [PERSON] and [PERSON] [1], and [PERSON] et al. [15]. The prediction results from these studies all indicate the following similarities:  
* The ANN models have significantly improved the accuracy and efficiency of BHP compared with traditional calculation modeling, overcome the limitations of empirical and mechanistic models, and even replaced the function of downhole sensors. * These models scarcely considered the temporal properties of datasets and variation mechanism of BHP. Furthermore, some researchers highlighted that the optimization algorithms also played a significant role in improving the performance of the intelligent prediction model of drilling BHP. Several studies on BHP prediction using optimization algorithms, for instance, particle swarm optimization algorithm [16], gray wolves optimization algorithm [17], ant swarm algorithm [18], and genetic algorithm [19; 20; 21], have revealed that optimization algorithms combined with the traditional neural network models have higher precision and stronger robustness. Compared with a single solvable model, this model combined with the optimization algorithm can solve issues globally and is independent of the initial conditions. In fact, with the development of artificial intelligence, more and more researchers have begun to explore the integration of intelligence and mechanisms to further improve the performance of intelligent models such as data fusion, a combination of data and mechanism, etc. In terms of BHP prediction, the following research has been conducted. [PERSON] et al. [22] integrated multiple flow parameters into comprehensive parameters such as wellbore Reynolds number or dimensionless diameter, which also improved the generalization ability of the model. [PERSON] et al. [23] presented a principal component analysis to reduce the number of input parameters, simplify the model structure, and weaken the overfitting of the model. [PERSON] et al. [24] considered the mechanism relations among input parameters, constructed neural network sub-modules, and integrated all sub-modules into a functional neural network system, which improved the model's mechanism description.