Case Study: Predicting Automotive Rim Energy Absorption Using Multimodal Deep Learning

Context

In the field of vehicle safety, one of the most critical development steps is the execution of crash tests and crash test simulations. These activities allow engineers to understand, qualify, and quantify forces, accelerations, and material deformations — variables that directly influence survival rates and injury severity.

To gain deeper insight into automotive rim deformation behavior and energy absorption, manufacturers perform pressing-force experiments and corresponding simulations. In these tests, an automotive rim is subjected to a controlled pressing load until structural failure, while force and displacement are recorded. The resulting force-displacement curve is later integrated to compute absorbed energy. This metric is essential for passenger safety: the more energy the rim absorbs, the less energy is transferred to the occupants.

Opportunity

Pressing experiments provide high-value information but are destructive — each tested rim or prototype must be discarded. They also involve significant costs, including prototype manufacturing, test preparation, operations, and engineering time.

Simulations are non-destructive but not cost-free. They require simulation clusters, specialized engineers, and considerable computation time.

The increasing adoption of machine learning in engineering creates an opportunity to estimate structural behavior before physical or simulated testing. A predictive model capable of estimating force-displacement curves from rim geometry and material parameters can reduce the need for destructive tests, accelerate early design decisions, lower simulation and prototyping costs, and provide rapid insight into design performance.

Approach

A multimodal deep learning model was developed to predict force-displacement curves from two types of input. The first input consists of automotive rim design images processed through a CNN backbone (VGG16 or ResNet50). The second input consists of material and geometric parameters processed through a fully connected MLP.

The architecture follows a dual-branch design in which visual and numerical information are processed in parallel before being combined. The image branch leverages a pretrained CNN to extract high-level geometric features from rim design images, while the numerical branch employs a lightweight MLP to encode material and geometric parameters. The resulting representations are concatenated and passed through a final dense prediction head, which maps the fused latent space to the target force-displacement curve.

Pre-processing steps included Z-score normalization for numerical inputs and min-max normalization for the output curve. To ensure scalability and reproducibility, a standardized data pipeline was developed to automate these transformations, enabling consistent preprocessing across datasets of different sizes and configurations. The pipeline was implemented in Python using PyTorch.

To assess model robustness, a 5-fold cross-validation was performed across the full dataset. Additionally, a gradient-based sensitivity analysis was conducted to evaluate the influence of each input parameter on model output. By feeding random input tensors through the trained model and computing the output-input Jacobian matrix via backpropagation, it was possible to rank parameters by the magnitude of their gradients — with larger gradients indicating stronger influence on the predicted curve. This approach enables the model to learn relationships between visual geometry, material properties, and structural response while providing interpretable insights into which parameters drive the prediction.

One important limitation of this work is the size of the available dataset. The original dataset comprised 146 samples, which was expanded to 370 through data augmentation techniques. While augmentation partially mitigates the constraint, the dataset remains relatively small for a deep learning application, which may limit the model's ability to generalize across highly diverse rim geometries or material configurations not well represented in the training distribution. Further validation on larger datasets would strengthen the robustness of the findings.

Impact

The model demonstrated that force-displacement curves can be estimated without destructive testing or full simulation cycles. To evaluate predictive accuracy, the RMSE between the predicted and ground-truth force-displacement curves was computed individually for each sample in the held-out test set, capturing point-wise error across the full curve. Averaging these per-sample errors yielded a mean RMSE of 2.5% on the normalized scale. Furthermore, the interquartile range of 1.3% indicates that the majority of predictions fell well within this error margin, confirming that strong performance was consistent across varying rim geometries and material configurations rather than driven by a small subset of easy cases. Model stability was further validated through 5-fold cross-validation, while the gradient-based sensitivity analysis provided interpretable evidence of which design and material parameters most strongly influence structural response.

This work demonstrates how data-driven predictive engineering can complement traditional development workflows, enabling faster iteration and more informed decision-making in early design phases.