Neural Network Virtual Sensors for Fuel Injection Quantities with Provable Performance Specifications

TL;DR

This paper applies provable neural network robustness techniques to develop virtual sensors for fuel injection measurement, significantly reducing error under sensor noise compared to standard models.

Contribution

It demonstrates the adaptation of provable robustness methods to real-world sensor data, achieving guaranteed error bounds for fuel injection virtual sensors.

Findings

Standard neural networks have high susceptibility to sensor noise.

Robust models can guarantee at most 16.5% mean relative error under noise.

Targeted robustness improves accuracy within specific fuel injection ranges.

Abstract

Recent work has shown that it is possible to learn neural networks with provable guarantees on the output of the model when subject to input perturbations, however these works have focused primarily on defending against adversarial examples for image classifiers. In this paper, we study how these provable guarantees can be naturally applied to other real world settings, namely getting performance specifications for robust virtual sensors measuring fuel injection quantities within an engine. We first demonstrate that, in this setting, even simple neural network models are highly susceptible to reasonable levels of adversarial sensor noise, which are capable of increasing the mean relative error of a standard neural network from 6.6% to 43.8%. We then leverage methods for learning provably robust networks and verifying robustness properties, resulting in a robust model which we can provably guarantee has at most 16.5% mean relative error under any sensor noise. Additionally, we show how specific intervals of fuel injection quantities can be targeted to maximize robustness for certain ranges, allowing us to train a virtual sensor for fuel injection which is provably guaranteed to have at most 10.69% relative error under noise while maintaining 3% relative error on non-adversarial data within normalized fuel injection ranges of 0.6 to 1.0.