# Probabilistic Risk Assessment of an Obstacle Detection System for GoA 4 Freight Trains

arXiv: https://arxiv.org/abs/2306.14814 · HTML: https://mlsanity.com/paper/2306.14814/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 5 of 5)

- [Concolic Testing for Deep Neural Networks](https://mlsanity.com/paper/1805.00089/) (2018)
- [Quantitative Projection Coverage for Testing ML-enabled Autonomous Systems](https://mlsanity.com/paper/1805.04333/) (2018)
- [A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations](https://mlsanity.com/paper/2201.09656/) (2021)
- [A singular Riemannian geometry approach to Deep Neural Networks II. Reconstruction of 1-D equivalence classes](https://mlsanity.com/paper/2112.10583/) (2021)
- [An Automotive Case Study on the Limits of Approximation for Object Detection](https://mlsanity.com/paper/2304.06327/) (2023)

## Built on by (most cited first, 3 of 3)

- [A Stochastic Approach to Classification Error Estimates in Convolutional Neural Networks](https://mlsanity.com/paper/2401.06156/) (2023)
- [A singular Riemannian Geometry Approach to Deep Neural Networks III. Piecewise Differentiable Layers and Random Walks on n-dimensional Classes](https://mlsanity.com/paper/2404.06104/) (2024)
- [FPGA-Based Neural Network Accelerators for Space Applications: A Survey](https://mlsanity.com/paper/2504.16173/) (2025)

## Abstract (arXiv)

In this paper, a quantitative risk assessment approach is discussed for the design of an obstacle detection function for low-speed freight trains with grade of automation (GoA)~4. In this 5-step approach, starting with single detection channels and ending with a three-out-of-three (3oo3) model constructed of three independent dual-channel modules and a voter, a probabilistic assessment is exemplified, using a combination of statistical methods and parametric stochastic model checking. It is illustrated that, under certain not unreasonable assumptions, the resulting hazard rate becomes acceptable for specific application settings. The statistical approach for assessing the residual risk of misclassifications in convolutional neural networks and conventional image processing software suggests that high confidence can be placed into the safety-critical obstacle detection function, even though its implementation involves realistic machine learning uncertainties.