# Real-Time Vibration Energy Prediction for Semi-Active Suspensions Using Inertial Sensors: A Physics-Guided Deep Learning Approach

## TL;DR

A new deep learning model predicts vehicle vibrations in real-time, enabling proactive suspension control.

## Contribution

A physics-guided deep learning framework with wavelet features and a novel physics loss for vibration prediction.

## Key findings

- The model achieves a predictive phase lead of 100–200 ms for road impact shocks.
- It has low inference latency (0.20 ms) and compact parameter size (0.10 M) for real-time deployment.

## Abstract

What are the main findings?
A Physics-Informed Gated CNN (PI-GCNN) framework is proposed that integrates continuous wavelet transform (CWT) features with an asymmetric sparse physics loss to accurately predict multi-modal vibration energy.Experimental validation on the PVS 9 real-vehicle dataset demonstrates that the model achieves a significant predictive phase lead of 100–200 ms and a low inference latency of 0.20 ms.

A Physics-Informed Gated CNN (PI-GCNN) framework is proposed that integrates continuous wavelet transform (CWT) features with an asymmetric sparse physics loss to accurately predict multi-modal vibration energy.

Experimental validation on the PVS 9 real-vehicle dataset demonstrates that the model achieves a significant predictive phase lead of 100–200 ms and a low inference latency of 0.20 ms.

What are the implications of the main findings?
The achieved phase lead creates a critical actuation window for semi-active suspensions, enabling a shift from reactive feedback to proactive feedforward control to effectively mitigate road impact shocks.With a compact parameter size of 0.10 M, the proposed algorithm offers a computationally efficient solution feasible for real-time deployment on resource-constrained automotive embedded chips.

The achieved phase lead creates a critical actuation window for semi-active suspensions, enabling a shift from reactive feedback to proactive feedforward control to effectively mitigate road impact shocks.

With a compact parameter size of 0.10 M, the proposed algorithm offers a computationally efficient solution feasible for real-time deployment on resource-constrained automotive embedded chips.

Response latency and sensor noise are universal challenges in closed-loop control systems. In the context of semi-active suspensions, these issues also exist and manifest as critical bottlenecks. Due to the highly transient nature of road shocks, the inherent physical actuation delays of the hardware, combined with the phase lag introduced by traditional signal filtering, often cause the control response to significantly lag behind the physical excitation. To address this issue from a predictive perspective, this study proposes a Physics-Informed Gated Convolutional Neural Network (PI-GCNN) designed to predict future multi-modal energy evolution, thereby enabling feedforward control. Unlike traditional feedback mechanisms, the proposed framework employs the Continuous Wavelet Transform (CWT) to convert short-horizon inertial data into time–frequency scalograms, effectively isolating transient shock features from background vibrations. A novel physics-guided gating mechanism is embedded within the network architecture to regulate feature activation. This mechanism is trained using an asymmetric sparse physics loss, which combines L1 regularization with adaptive spectral consistency constraints to enforce noise suppression on flat roads while ensuring sensitivity to impacts. Extensive validation was conducted using high-fidelity heavy truck simulations and the public PVS 9 real-world dataset. The results confirm that the PI-GCNN achieves a predictive phase lead of approximately 100–200 ms over real-time baselines, creating a valuable actuation window for suspension dampers. Furthermore, the model demonstrates exceptional computational efficiency, with a parameter count of 0.10 M and a single-frame inference latency of 0.25 ms, making it highly suitable for deployment on resource-constrained automotive edge computing platforms.