# Object-Size-Driven Design of Convolutional Neural Networks: Virtual Axle Detection based on Raw Data

arXiv: https://arxiv.org/abs/2309.01574 · HTML: https://mlsanity.com/paper/2309.01574/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 78 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [U-Net and its variants for medical image segmentation: theory and applications](https://mlsanity.com/paper/2011.01118/) (2020)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Neural Architecture Search: Insights from 1000 Papers](https://mlsanity.com/paper/2301.08727/) (2023)
- [Deep Learning for Audio Signal Processing](https://mlsanity.com/paper/1905.00078/) (2019)
- [Sound Event Detection: A Tutorial](https://mlsanity.com/paper/2107.05463/) (2021)
- [Deep Representation Learning in Speech Processing: Challenges, Recent Advances, and Future Trends](https://mlsanity.com/paper/2001.00378/) (2020)
- [A Unified Framework for U-Net Design and Analysis](https://mlsanity.com/paper/2305.19638/) (2023)
- [Receptive Field Regularization Techniques for Audio Classification and Tagging with Deep Convolutional Neural Networks](https://mlsanity.com/paper/2105.12395/) (2021)
- [Audio representations for deep learning in sound synthesis: A review](https://mlsanity.com/paper/2201.02490/) (2022)
- [Virtual Axle Detector based on Analysis of Bridge Acceleration Measurements by Fully Convolutional Network](https://mlsanity.com/paper/2207.03758/) (2022)

## Abstract (arXiv)

As infrastructure ages, the need for efficient monitoring methods becomes increasingly critical. Bridge Weigh-In-Motion (BWIM) systems are crucial for cost-effective determination of loads and, consequently, the residual service life of road and railway infrastructure. However, conventional BWIM systems require additional sensors for axle detection, which must be installed in potentially inaccessible locations or places that interfere with bridge operation. This study presents a novel approach for real-time detection of train axles using sensors arbitrarily placed on bridges, providing an alternative to dedicated axle detectors. The developed Virtual Axle Detector with Enhanced Receptive Field (VADER) has been validated on a single-track railway bridge using only acceleration measurements, detecting 99.9% of axles with a spatial error of 3.69cm. Using raw data as input outperformed the state-of-the-art spectrogram-based method in both speed and memory usage by 99%, thereby making real-time application feasible for the first time. Additionally, we introduce the Maximum Receptive Field (MRF) rule, a novel approach to optimise hyperparameters of Convolutional Neural Networks (CNNs) based on the size of objects. In this context, the object size relates to the fundamental frequency of a bridge. The MRF rule effectively narrows the hyperparameter search space, overcoming the need for extensive hyperparameter tuning. Since the MRF rule can theoretically be applied to all unstructured data, it could have implications for a wide range of deep learning problems, from earthquake prediction to object recognition.