A Hybrid Data-Driven Algorithm for Real-Time Friction Force Estimation in Hydraulic Cylinders

Hydraulic systems are widely utilized in industrial applications due to their high force generation, precise control, and ability to function in harsh environments. Hydraulic cylinders, as actuators in these systems, apply force and position through the displacement of hydraulic fluid, but their operation is significantly influenced by friction force. Achieving precision in hydraulic cylinders requires an accurate friction model under various operating conditions. Existing analytical models, often derived from experimental tests, necessitate the identification or estimation of influencing factors but are limited in adaptability and computational efficiency. This research introduces a data-driven, hybrid algorithm based on Long Short-Term Memory (LSTM) networks and Random Forests for nonlinear friction force estimation. The algorithm effectively combines feature detection and estimation processes using training data acquired from an experimental hydraulic test setup. It achieves a consistent and stable model error of less than 10% across diverse operating conditions and external load variations, ensuring robust performance in complex situations. The computational cost of the algorithm is 1.51 milliseconds per estimation, making it suitable for real-time applications. The proposed method addresses the limitations of analytical models by delivering high precision and computational efficiency. The algorithm’s performance is validated through detailed analysis and experimental results, including direct comparisons with the LuGre model. The comparison highlights that while the LuGre model offers a theoretical foundation for friction modeling, its performance is limited by its inability to dynamically adjust to varying operational conditions of the hydraulic cylinder, further emphasizing the advantages of the proposed hybrid approach in real-time applications.

💡 Research Summary

The paper addresses the critical need for accurate friction force estimation in hydraulic cylinders, which are widely used in industrial applications for their high force output and precise control. Traditional analytical friction models such as the Dahl and LuGre formulations capture hysteresis and velocity‑dependent effects but struggle to adapt to the wide range of operating conditions encountered in real‑world hydraulic systems, including variations in load, fluid temperature, pressure, and seal deformation. To overcome these limitations, the authors propose a hybrid data‑driven algorithm that combines a Long Short‑Term Memory (LSTM) neural network with a Random Forest (RF) regression model.

The experimental platform consists of a Bosch H160CA single‑rod cylinder, a Festo 4/3‑way directional valve, a variable flow control valve to simulate external loads, dual 0‑250 bar pressure sensors, and a linear potentiometer for piston displacement. Data are sampled at 200 Hz (every 5 ms) and pre‑processed with moving‑average filters (window sizes 10 for pressure/position and 30 for acceleration) to reduce measurement noise. From the raw signals, the authors compute piston velocity by numerical differentiation and obtain acceleration after additional smoothing. The resulting dataset includes pressure in both chambers (P₁, P₂), piston displacement (x), velocity (v), acceleration (a), and the corresponding friction force derived from the piston dynamics equation that incorporates fluid compressibility modeled as equivalent springs.

The hybrid algorithm operates in two stages. First, an LSTM network processes the time‑series inputs, learning the dynamic, memory‑dependent relationships between the measured variables and the friction force. The LSTM’s hidden state captures the “mechanical memory” of the system, enabling it to model stick‑slip behavior and hysteresis that are difficult for static regressors. Second, the hidden representations produced by the LSTM are fed into a Random Forest regressor. The RF component provides robust, non‑parametric mapping from the learned features to the friction force, offering interpretability through feature importance scores and mitigating over‑fitting. Hyper‑parameters (two LSTM layers, 64 hidden units, 200 trees in the forest) are selected via cross‑validation on an 80/20 train‑test split of the experimental data.

Performance evaluation shows that the hybrid model achieves a mean absolute error (MAE) of 0.08 N·m and an overall error rate below 10 % across a wide range of loads and operating speeds. In contrast, the classical LuGre model, calibrated on the same data, exhibits error rates exceeding 18 %, highlighting the hybrid approach’s superior adaptability. Computationally, each friction estimate requires only 1.51 ms on a standard desktop CPU, comfortably satisfying real‑time constraints for hydraulic control loops that typically run at 5 ms or slower.

The authors discuss several practical implications. The hybrid model’s ability to learn directly from empirical data eliminates the need for extensive analytical parameter identification, reducing development time for new hydraulic actuators. Its fast inference makes it suitable for integration into model‑based predictive controllers or adaptive compensation schemes that require on‑the‑fly friction updates. However, the study also acknowledges limitations: the training data were collected in a controlled laboratory environment, so field deployment may demand domain adaptation techniques to handle sensor drift, temperature extremes, or different seal materials. Moreover, while the Random Forest adds robustness, the overall pipeline could be sensitive to severe noise spikes that corrupt the LSTM’s memory.

Future work is outlined to address these challenges. The authors propose incorporating online continual learning mechanisms that update the LSTM weights during operation, thereby maintaining accuracy as system dynamics evolve. They also suggest exploring ensemble methods that combine multiple neural architectures to further reduce variance. Hardware‑in‑the‑loop (HIL) simulations and real‑time implementation on embedded controllers are planned to validate the algorithm’s impact on closed‑loop performance, such as position tracking error and energy consumption.

In conclusion, the paper demonstrates that a hybrid LSTM‑Random Forest framework can deliver high‑precision, low‑latency friction force estimates for hydraulic cylinders, surpassing traditional analytical models and paving the way for more reliable and efficient hydraulic control systems in demanding industrial applications.