# Turbofan Engine Health Prediction Model Based on ESO-BP Neural Network
## 1 Introduction  
Turbofan engines are one of the core components of an aircraft [1]. Predicting the remaining useful life (RUL) of the engine and implementing prognostics and health management (PHM) are critical for formulating a targeted maintenance strategy [2]. The turbofan engine health prediction model helps to reduce the risk of unplanned downtime and maximize the operational lifespan [3].  
The prediction model for the RUL of turbofan engines is developed based on either their physical structure model or the degradation trends among various monitoring sensors. There are two types of existing methods for estimating RUL: those based on physical models [4, 5] and data-driven approaches [6, 7, 8, 9]. Data-driven methods analyze data and identify complex data relationships, achieving accurate predictions of changes in the turbofan engine's state [10]. Data-driven predictions for the RUL of turbofan engines are influenced by various factors, including the number of operating cycles, operating parameters, and sensor data.  
The back-propagation (BP) neural network, which was proposed by [PERSON] et al. [11] in 1986, is a feed-forward neural network trained with the error back-propagation algorithm. It is currently acknowledged as one of the most extensively employed neural network models, celebrated for its simple principles, high computational speed, and robust regression prediction capabilities [12]. However, BP neural networks frequently experienceslow convergence and a tendency to become stuck in local optima due to the random selection of initial weights and thresholds [13]. Currently, there is a surge in the use of neural networks coupled with intelligent optimization algorithms. In 2022, [PERSON] et al. [14] introduced a chaotic krill herd algorithm optimized BP neural network, achieving a 3.65% reduction in prediction error for kidney bean yield. [PERSON] and [PERSON] [12] enhanced BP neural networks by utilizing the improved Sparrow Search Algorithm, resulting in an R\({}^{2}\) value of 0.99 for sea surface temperature retrieval. [PERSON] et al. [15] introduced the IA-PSO-BP model, which achieved an R\({}^{2}\) value of 0.97 for ground pressure prediction.  
In the field of intelligent optimization algorithms, [PERSON] et al. [16] presented a novel algorithm named SO in 2022. However, this algorithm has persistent drawbacks, such as the random movement of individual positions, which may lead to local optima and poor stability. In 2023, [PERSON] and [PERSON] [17] introduced the snow ablation optimizer (SAO), which incorporates elite sets, demonstrating both rapid convergence and a high convergence accuracy.  
This study presents an ESO-BP model for predicting the health of turbofan engines. The goal is to enhance the prediction accuracy and stability of the BP neural network in the context of predicting turbofan engine health. The subsequent sections are organized as follows: Section 2 introduces the elite snake optimizer (ESO). Section 3 elaborates on the proposed model architecture. Section 4 covers the experimental specifics, results, and analysis. Section 5 discusses the findings. Finally, Section 6 concludes the study.