Research on Train Energy Optimization Based on Dynamic Adaptive Hybrid Algorithms
Abstract
:1. Introduction
2. Mathematical Model for Train Optimization
2.1. A Dynamics Model of the Uniform Rod for Trains
- g: gravitational acceleration (unit: );
- : gradient at position l;
- R: curve radius at position l (unit: m);
- L: tunnel length (unit: m).
2.2. Energy Consumption–Time Model Based on Discretization of Grade Resistance of Track
- (1)
- Under traction mode, assuming constant acceleration within the operational step length Δs, the acceleration, running time, and energy consumption within the interval can be expressed as follows:
- (2)
- Under cruising mode, where the traction force equals resistance, the energy consumption within a unit step length Δs corresponds to the work performed against resistance. Consequently, the acceleration, running time, and energy consumption within the interval are defined as follows:
- (3)
- Under coasting mode, the speed begins to decrease, and both the traction force and energy consumption are reduced to 0. Within the interval, the acceleration and running time are defined as follows:
- (4)
- Under braking mode, the train generates regenerative braking energy. Let the feedback efficiency of regenerative braking energy be denoted as . The regenerative braking energy is defined as
2.3. Energy Consumption Model
3. Dynamic Adaptive PSO-SA Algorithm for Train Energy Consumption Optimization
- (1)
- The dynamic adjustment method for the inertia weight is defined as follows:
- (2)
- Learning factors c1 and c2 regulate the flight of population particles towards the personal optimum and the global optimum. Their adjustment methods are as follows:
4. Case Analysis
4.1. Railway Line Information
4.2. Evaluation of Dynamic Adaptive PSO-SA Algorithm
4.3. Comparison of Dynamic Modeling
5. Conclusions
- (1)
- The proposed uniform bar dynamics model resolves the accuracy–efficiency trade-off between single-mass and multi-mass models. By incorporating equivalent slope resistance discretization, it enhances track model precision and, when combined with the uniform bar model, improves the applicability and accuracy of energy consumption models under complex track conditions.
- (2)
- To solve the optimization model, an adaptive PSO-SA algorithm was developed. Building upon the hybrid PSO-SA framework, it improves inertia weights and learning factors, demonstrating excellent optimization performance, a fast convergence speed, and superior solution distribution characteristics—making it particularly suitable for train traction energy optimization.
- (3)
- Validation using the Xinzhun Line showed that the proposed method achieves 19% energy savings compared to conventional approaches, demonstrating strong practical applicability and confirming its correctness and effectiveness.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Category | Parameter |
---|---|
Maximum operating speed (km/h) | 160 |
Full-load weight (t) | 6000 |
Maximum tractive force (kN) | 580 |
Maximum braking force (kN) | 400 |
Electric braking power (kW) | 7200 |
Total locomotive efficiency | ≥0.85 |
Basic resistance (kN) | 1.20 + 0.0065v + 0.000279v2 |
Evaluation Indicators | Improved Adaptive PSO-SA Algorithm | PSO-SA | PSO | SA |
---|---|---|---|---|
Average optimal energy consumption (kW·h) | 2139.05 | 2349.48 | 2595.62 | 2606.35 |
Punctuality error (s) | 8.22 | 20.86 | 31.15 | 33.48 |
Average number of iterations | 805 | 836 | 906 | 915 |
Average convergence time (s) | 3.09 | 3.89 | 4.59 | 4.46 |
Evaluation Indicators | Single Particle Model | Uniform Rod Model | Multi-Particle Model |
---|---|---|---|
Energy consumption (kWh) | 2348.24 | 2125.65 | 2103.86 |
Calculation time (t) | 2.89 | 3.13 | 4.05 |
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Li, J.; Shi, Y.; Zhang, T.; Li, X.; Wang, X. Research on Train Energy Optimization Based on Dynamic Adaptive Hybrid Algorithms. Electronics 2025, 14, 1588. https://doi.org/10.3390/electronics14081588
Li J, Shi Y, Zhang T, Li X, Wang X. Research on Train Energy Optimization Based on Dynamic Adaptive Hybrid Algorithms. Electronics. 2025; 14(8):1588. https://doi.org/10.3390/electronics14081588
Chicago/Turabian StyleLi, Jiawei, Yong Shi, Tengya Zhang, Xin Li, and Xiaoxin Wang. 2025. "Research on Train Energy Optimization Based on Dynamic Adaptive Hybrid Algorithms" Electronics 14, no. 8: 1588. https://doi.org/10.3390/electronics14081588
APA StyleLi, J., Shi, Y., Zhang, T., Li, X., & Wang, X. (2025). Research on Train Energy Optimization Based on Dynamic Adaptive Hybrid Algorithms. Electronics, 14(8), 1588. https://doi.org/10.3390/electronics14081588