GDFlow: Anomaly Detection with NCDE-based Normalizing Flow for Advanced Driver Assistance System

TL;DR

GDFlow tackles anomaly detection in ADAS braking data by learning the normal driving distribution with a novel combination of Neural Controlled Differential Equations and Normalizing Flow, enabling continuous, spatio-temporal modeling of multivariate time series. The model introduces a graph-aware, NCDE-based encoding pipeline and a quantile-based maximum likelihood objective to sharpen boundary decisions between normal and anomalous patterns. Across real-world Hyundai datasets and standard time-series benchmarks, GDFlow achieves state-of-the-art performance with strong generalization and reduced hyperparameter sensitivity, while maintaining efficient inference suitable for deployment in production ADAS systems. This work advances robust, scalable anomaly detection for adaptive braking by capturing complex temporal dynamics and sensor interdependencies in electric vehicle driving behavior.

Abstract

For electric vehicles, the Adaptive Cruise Control (ACC) in Advanced Driver Assistance Systems (ADAS) is designed to assist braking based on driving conditions, road inclines, predefined deceleration strengths, and user braking patterns. However, the driving data collected during the development of ADAS are generally limited and lack diversity. This deficiency leads to late or aggressive braking for different users. Crucially, it is necessary to effectively identify anomalies, such as unexpected or inconsistent braking patterns in ADAS, especially given the challenge of working with unlabelled, limited, and noisy datasets from real-world electric vehicles. In order to tackle the aforementioned challenges in ADAS, we propose Graph Neural Controlled Differential Equation Normalizing Flow (GDFlow), a model that leverages Normalizing Flow (NF) with Neural Controlled Differential Equations (NCDE) to learn the distribution of normal driving patterns continuously. Compared to the traditional clustering or anomaly detection algorithms, our approach effectively captures the spatio-temporal information from different sensor data and more accurately models continuous changes in driving patterns. Additionally, we introduce a quantile-based maximum likelihood objective to improve the likelihood estimate of the normal data near the boundary of the distribution, enhancing the model's ability to distinguish between normal and anomalous patterns. We validate GDFlow using real-world electric vehicle driving data that we collected from Hyundai IONIQ5 and GV80EV, achieving state-of-the-art performance compared to six baselines across four dataset configurations of different vehicle types and drivers. Furthermore, our model outperforms the latest anomaly detection methods across four time series benchmark datasets. Our approach demonstrates superior efficiency in inference time compared to existing methods.

Figures (2)

• Figure 1: Data preprocessing for deceleration profile generation, where the X-axis is the time, and the Y-axis represents the acceleration, speed, and distance, respectively.
• Figure 2: The overall architecture of GDFlow. The preprocessed input data $\mathbf{W}_p^{(i)}$ is first converted into a continuous path $X(T)$ through cubic spline interpolation. This path passes through two CDE functions to encode spatio-temporal information, resulting in $H(T)$ and $Y(T)$, respectively. These are then combined through matrix multiplication to form $S(T)$, which is used for density estimation in the NF. The log-likelihoods obtained from this process are further processed with a quantile function to produce $\mathcal{L}_{Q-NLL}$, which is used to detect normal or anomalies based on the threshold $\tau$.