Surrogate-Assisted Optimisation of an Aircraft-Wing Maintenance Panel

Multi-objective shape optimisation of an aluminium maintenance panel with an oval-shaped port under biaxial loading. Two regression surrogates — a Gaussian Process (GPR) and a neural network (NN) — are trained on FEA stress data, then driven by NSGA-II to approximate the mass / max-von-Mises-stress Pareto front.

Problem

Variable	Description	Bounds (m)
W1	Plate half-width	0.30 – 0.70
W2	Port half-width	0.10 – 0.15
R	Port fillet radius	0.03 – 0.07
t	Plate thickness	0.01 – 0.02

Objectives (both minimised):

• Mass m = ρ · t · (4·W1² − 4·W2² + (4−π)·R²), with ρ = 2700 kg/m³.
• Maximum von Mises stress σ_max, predicted by the trained surrogate.

Training data comes from 256 quarter-symmetric Abaqus FEA simulations (data/TrainingData_256.csv), split 80/20 into train/test.

Repository layout

plane-wing/
├── data/        Raw FEA training data (CSV) and Abaqus stress-extract scripts
├── notebooks/   Model-development notebooks
│   ├── sampling_test.ipynb   LHS / Sobol / uniform sampling comparison
│   ├── test_gpr.ipynb        GPR kernel selection & training
│   └── test_nn.ipynb         NN architecture search, training, Pareto comparison
├── src/         Runnable Python entry points
│   ├── MaintenancePlate_Optimisation.py      NSGA-II driven by the GPR surrogate
│   ├── MaintenancePlate_Optimisation_NN.py   NSGA-II driven by the NN surrogate
│   └── MaintenancePlate_StressExtract.py     Abaqus-side FEA automation
├── models/      Trained surrogates (gpr_best_pipeline.pkl, nn_surrogate.pt, nn_scalers.joblib)
├── results/     All CSV outputs (experiment sweeps, Pareto fronts, metrics)
└── figures/     All PNG figures generated for the report

Approach

Surrogates

• GPR (test_gpr.ipynb) — scikit-learn pipeline with StandardScaler and an ARD-Matern kernel, selected by 5-fold CV on RMSE.
• NN (test_nn.ipynb) — a 4-layer × 128-unit MLP with SiLU activations (architecture chosen from an 8-experiment CV sweep over activation, depth, width, regularisation, optimiser, learning rate, batch size and training-set size). Trained with Adam + early stopping.

Optimisation

NSGA-II (pymoo) with population 100, 100 generations, LHS initialisation, SBX crossover, polynomial mutation, seed 1. The surrogate replaces the FEA call inside Problem._evaluate, giving millisecond-scale evaluations.

Key results (held-out test set, N = 52)

Metric	GPR	NN
RMSE (MPa)	see results/final_metrics.csv and comparison-code cell	0.307
MAE (MPa)	-	0.203
MAPE (%)	-	0.418
R²	-	0.9994

(Run the final cell in test_nn.ipynb to reproduce the full side-by-side table.)

Final Pareto fronts are in results/pareto_front_{gpr,nn}.csv and figures/fig_pareto_comparison.png.

Reproducing

pip install numpy pandas scikit-learn torch pymoo joblib matplotlib

# 1. (Re)train the GPR surrogate
jupyter notebook notebooks/test_gpr.ipynb

# 2. (Re)train the NN surrogate and run all hyperparameter experiments
jupyter notebook notebooks/test_nn.ipynb

# 3. Run NSGA-II with each surrogate
python src/MaintenancePlate_Optimisation.py      # GPR-driven
python src/MaintenancePlate_Optimisation_NN.py   # NN-driven

All random seeds are fixed (SEED = 42 for training, seed = 1 for NSGA-II), so numbers in the tables should reproduce exactly.

Notes

• The original Abaqus .cae file and the UCL coursework brief are excluded from version control (see .gitignore) — they are not mine to redistribute.
• FEA in src/MaintenancePlate_StressExtract.py requires Abaqus on the UCL Winion cluster; the surrogate pipeline here is fully standalone.
• The scripts were developed on macOS / Python 3.11. No GPU is required — the NN has ~50 k parameters and trains in ~1.5 s on CPU.

Context

Originally submitted as Coursework 2 for MECH0107 — Data-Driven Methods for Engineers (UCL).