# Prediction of Truck Fuel Consumption Based on Crossformer-LSTM Characteristic Distillation
## 2 Related Work
### Research on Fuel Consumption Models  
Existing truck fuel consumption prediction methods can be divided into two main types: (1) physical models based on vehicle dynamics principles, and (2) data-driven models [9].  
The first type of model primarily employs mathematical formulas based on the internal structure of vehicles and the operating principles of their components, such as the physical or chemical processes within the engine, to provide accurate predictions [10]. For instance, [PERSON] et al. [11] utilized sensors installed along specific road sections to capture vehicle state parameters at designated locations as inputs for their model. Similarly, [PERSON] et al. [12] used traditional microscopic models to predict vehicle fuel consumption. These models are characterized by a highly deterministic mathematical framework, requiring a profound understanding of the system and its critical sub-processes. However, they are often constrained to specific regions and predefined routes, neglecting the impact of varying road conditions and weather, which limits their applicability in real-world scenarios.  
The second category of models primarily depends on sensors and onboard equipment to gather comprehensive operational data related to fuel usage. By analyzing extracted features from the data, these models establish nonlinear correlations with fuel consumption, enabling accurate predictions. Data-driven approaches for predicting fuel consumption often incorporate machine learning methods like random forests and SVMs, alongside deep learning techniques such as BP neural networks, RNNs, and LSTMs. For instance, [PERSON] et al. [13] utilized SVM to build a regression model for predicting fuel consumption, considering factors like driving distance, and achieved results using extensive datasets. Nevertheless, SVM struggles with nonlinear regression problems, leading to reduced accuracy when the connection between variables and fuel consumption lacks linearity. [PERSON] et al. [14] applied a BP neural network to develop a model for predicting fuel consumption, which examines temporal and spatial dimensions to better understand the influencing factors. The findings showed that the BP neural network was effective and appropriate for predicting fuel consumption. Additionally, [PERSON] et al. [15] suggested using an RNN for instantaneous fuel consumption predictions; however, conventional RNNs face challenges like gradient explosion and vanishing, which may reduce efficiency. [PERSON] et al. [16] proposed an LSTM-based energy management strategy for electric vehicles, achieving a 24.03%.  
Despite significant advancements in fuel consumption prediction, challenges remain, particularly in addressing missing data and enhancing model practicality. Traditional physics-based models have limitations in accounting for the impact of various road and weather conditions on fuel consumption. Simultaneously, some data-driven models may perform suboptimally when handling nonlinear relationships and complex spatiotemporal patterns.  
In this study, distillation techniques have been introduced to improve the practicality of our model, address prediction issues with missing data, optimize processing speed, and reduce parameters. By transferring knowledge from the teacher model to the student model, we enhanced computational efficiency while maintaining predictive performance. This innovative approach provides a viable solution for effective fuel consumption prediction in real-world applications. The CLMFD model not only excels in prediction performance but also improves practical usability, particularly in addressing missing data. This research presents a more innovative and practical method for future fuel consumption prediction tasks.