Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning
Abstract
:1. Introduction
2. Materials and Methods
- A Simulink [24] model of the rocket: Engineered from experimental data obtained from the Icarus Team at Politecnico di Torino, this model aims to compute the trajectory of a maneuverable rocket. It provides validated data related to path dynamics.
- Optimization algorithm: built upon the Simulink model, the proposed genetic algorithm (GA) was designed to identify the optimal maneuver to achieve a target point with the desired accuracy.
- Artificial neural network: trained using data derived from the preceding GA simulations, this neural network (NN) improves decision-making and predictive capabilities in trajectory design, minimizing the computational cost to reach an optimum setup.
2.1. Simulink Model
- The atmosphere was modelled using the International Standard Atmosphere (ISA) model [25].
- The assumed rockets are non-spinning and stabilized with fixed wings.
- The flat earth reference frame is assumed to be inertial, which is acceptable for low-range rockets.
- Gravity is considered constant throughout the flight.
- The rocket operates under subsonic conditions, according to numerically and experimentally simulated design data.
- High-order aerodynamic effects, arising from unsteady aerodynamics, are considered negligible. While these reduce accuracy, particularly under conditions of high maneuvering angles, the resulting error from this assumption remains comparable in magnitude to other errors associated with other modeling assumptions and adopted simplifications.
- Erosive burning effects were not considered.
- The rocket was modelled as a rigid body.
2.2. Optimization Script
- The ramp zenith: This is defined as the angle between the earth’s vertical-to-surface axis and the ramp axis. This integer variable can adopt discrete values equal to 0°, 15°, 30°, or 45° sexagesimal degrees, representing a classified discrete ramp movement’s range.
- The thrust deflection angle: this represents the output of the thrust vector and is treated as a continuous variable bounded between 0° and 5°.
2.3. Neural Network
- Classification Algorithm: initially, the solution space is partitioned through a classification strategy, with the zenith angle serving as the clustering criterion.
- Regression: following the classification stage, a regression is adopted to forecast the continuous deflection angle based on the target coordinates, tailoring, for each cluster, the maneuverer’s deflection angle.
2.4. Workflow
3. Results
- The time elapsed until the target is reached.
- The zenith angle of the launch ramp.
- The deflection angle of the thrust required for implementing maneuvers.
- Accuracy, quantified as a percentage, where 100% signifies exact alignment with the target’s center of gravity, and 0% indicates a failure to meet the target.
3.1. GA Results
3.2. Classification
3.3. Regression
3.4. Testing the Neural Network on a New Batch
3.5. Computational Cost Comparison
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
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Description | Value |
---|---|
Population size | 50 |
Maximum number of generations | 200 |
Constraint tolerance | 1 × 10−3 |
Creation function rate | 0.8 |
Crossover function | Arithmetic crossover |
Mutation function | Adaptive feasible mutation |
Selection function | Roulette wheel selection |
Distance measurement function | Crowding distance |
Nonlinear constraint algorithm | Augmented Lagrangian |
Elite count | 2 |
Fitness limit | 1 |
Fitness scaling function | Rank scaling |
Function tolerance | 1 × 10−6 |
Description | Value |
---|---|
Loss function | Categorical Crossentropy |
Accuracy metric | Accuracy |
Batch size | 512 |
Hidden layers | 10, with a predetermined neuron distribution |
Activation function | ReLU for hidden layers and Softmax for the output layer |
Number of epochs | 10,000 |
Description | Value |
---|---|
Loss function | Mean Square Error |
Accuracy metric | Mean Absolute Error |
Batch size | 512 |
Hidden layers | 10, with a specific distribution of neurons per layer |
Activation function | ReLU for hidden layers and linear for the output layer |
Number of epochs | 10,000 |
Zenith Angle [°] | Minimum Loss |
---|---|
0° | 1.3869 × 10−6 |
15° | 3.0502 × 10−6 |
30° | 5.4031 × 10−6 |
45° | 1.8426 × 10−8 |
Thrust Deflection [deg] | Zenith [deg] | Accuracy [%] | Elapsed Time [s] | |
---|---|---|---|---|
GA | 2.35 | 0 | 95% | 58.98 |
NN | 2.29 | 0 | 89% | 1.05 |
COMPARATION | 2.55% | 0% | −6.32% | 98.22% |
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Ferro, C.; Cafaro, M.; Maggiore, P. Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning. Aerospace 2024, 11, 912. https://doi.org/10.3390/aerospace11110912
Ferro C, Cafaro M, Maggiore P. Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning. Aerospace. 2024; 11(11):912. https://doi.org/10.3390/aerospace11110912
Chicago/Turabian StyleFerro, Carlo, Matteo Cafaro, and Paolo Maggiore. 2024. "Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning" Aerospace 11, no. 11: 912. https://doi.org/10.3390/aerospace11110912
APA StyleFerro, C., Cafaro, M., & Maggiore, P. (2024). Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning. Aerospace, 11(11), 912. https://doi.org/10.3390/aerospace11110912