# Machine learning regression approach for predicting continuous GRF components

Taysir Rezgui, Mayssa Salem

► To cite this version:

Taysir Rezgui, Mayssa Salem. Machine learning regression approach for predicting continuous GRF components. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16172. hal-05191724v2

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Submitted on 23 Oct 2025

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# Machine learning regression approach for predicting GRF components from 3D Heel Acceleration

Taysir Rezgui*, Mayssa Salem

Systems and Applied Mechanics Laboratory (LASMAP),
Carthage University, Tunisia Polytechnic School (EPT), La Marsa, Tunisia

* Corresponding author: taysir.rezgui@ept.ucar.tn

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** GRF prediction, regression models, machine learning, walking

© 2025 The Authors
Licence CC-BY 4.0
Published by Société de Biomécanique

## 1. Introduction

Assessing ground reaction forces (GRF) is a fundamental tool of human movement analysis in medical diagnosis, rehabilitation, and sports performance evaluation. It permits analyzing joint dynamics and gait stability and detect potential weaknesses or imbalances. These measurements, in three directions, are obtained using force plates as a gold standard, but they are costly and restricted to laboratory settings. For outdoor monitoring, wearable sensors have been attractive. However, IMU measurements were limited to kinematics, and load insoles only measure normal forces. As a result, researchers have explored alternative methods for GRF estimation using information from wearable sensors combined with multi-segment, musculoskeletal models and machine learning approaches. These last approaches have been recently widely explored (Girka et al., 2022; Kiernan et al., 2023; Martínez-Pascual et al. 2023). The use of artificial neural networks to predict GRF, particularly long short-term memory (LSTM), represents a promising approach in real-world environments (Martínez-Pascual et al., 2023).

However, some limitations have been detected: the use of a high number of inputs defined as statistical features of temporal signals from a single IMU placed in the sacrum or 7 IMUs placed in the lower limbs and for specific gait conditions. Also, prior studies have mainly focused on predicting the vertical ground reaction forces (vGRF). Despite their importance for a complete dynamic

motion analysis, the prediction of anteroposterior (AP) and mediolateral (ML) forces remains underexplored.

Our study aims to evaluate the performance of traditional (non-deep learning) machine learning methods, in estimating GRF components using 3D Heel Acceleration which represents a minimalistic, practical, and commonly adopted location for IMU placement in ambulatory and real-world gait monitoring contexts.

## 2. Methods

In this study, we focused on walking in different conditions using an instrumented treadmill, and we have used two public datasets: (1) Zee et al. (2022) dataset contains gait measurements of 10 healthy subjects under different speed, step length, and width conditions; (2) Fukuchi et al. (2018) dataset contains 42 volunteers walking at 8 different speeds.

We have selected a total of 9870 gait cycles. For each cycle, we extracted GRF and trajectories from heel-mounted markers. Then, accelerations were derived by computing the second derivatives of trajectories. All signals were then normalized to 0-100% of the stance phase and segmented into 101 points. GRFs were also normalized by the subject's body weight. We have tested three regression models using default hyperparameters as provided by Python libraries: Random Forest (with 100 individual trees), XGBoost (with 100 individual trees) and LSTM (with 2 layers and 50 units each). We fixed a batch size of 32 and a learning rate of 0.001.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Example of predicted GRF signals during stance phase using ML Regression Models: the orange line represent the predicted values, the bleu lines represent the actual "true" values.</figcaption></figure>

The dataset was randomly divided into 80% for training and 20% for testing and validation. For our regression models, the input data were the temporal series of heel accelerations in three directions, combined with a single feature representing the side. The output data are the signals of GRF components. To evaluate the accuracy of regression methods, the root mean square error (RMSE), mean absolute error (MAE), and cross-correlation coefficient (R²) were calculated. Regression models were built using Python libraries, including Scikit-learn (RF), TensorFlow Keras (LSTM), and XGBoost and implemented through Google Colab.

## 3. Results and discussion

Results presented in Table 1 indicate that the random forest regressor outperformed both XGBoost and LSTM models in predicting the three GRF components from vertical heel acceleration throughout the gait cycle. RF achieved the lowest MAE and RMSE, and the highest R² values for vGRF (RMSE = 0.0760, R² = 97.77%) and ML forces (RMSE = 0.0116, R² = 91.99%), as illustrated in Figure 1 (a–c). However, prediction performance for ML forces remains lower compared to AP and vertical components. In addition, XGBoost slightly exceeds other regressors in prediction AP forces (R²=99.52%), but signals were clearly noisy (fig. 1(e-f)). In other hand, LSTM provides acceptable performance for 3 GRF components (R²=82.51-96.80%) but is the weakest among tested algorithms (figure 1.d).

This suggests that, when using a few number of inputs, traditional machine learning models may be more effective than the neural network approach. The

variability of walking conditions in the database represents a primary factor contributing to prediction inaccuracies in GRF estimation. In fact, the increase in walking speed reduces the heel strike peak in vGRF, which may justify the fact that it was not accurately predicted using LSTM. Moreover, modifications in step length, width, and speed may cause alterations in ML component to ensure stability during walking. This variability may justify the lowest performances of regression models in prediction ML signals.

<table><caption>**Table 1.** Performance metrics analysis of ML regression models in predicting GRF Components.</caption><thead><tr><th>Input</th><th></th><th>MAE (N/kg)</th><th>RMSE(N/ kg)</th><th>R<sup>2</sup> (%)</th></tr></thead><tbody><tr><td rowspan="3">RF</td><td>vGRF</td><td>0.0514</td><td>0.0760</td><td>97.77</td></tr><tr><td>AP</td><td>0.0114</td><td>0.0154</td><td>99.43</td></tr><tr><td>ML</td><td>0.0087</td><td>0.0116</td><td>91.99</td></tr><tr><td rowspan="3">XGBoost</td><td>vGRF</td><td>0.0918</td><td>0.1253</td><td>92.58</td></tr><tr><td>AP</td><td>0.0105</td><td>0.0141</td><td>99.52</td></tr><tr><td>ML</td><td>0.0093</td><td>0.0123</td><td>90.79</td></tr><tr><td rowspan="3">LSTM</td><td>vGRF</td><td>0.0795</td><td>0.0985</td><td>96.80</td></tr><tr><td>AP</td><td>0.0149</td><td>0.0197</td><td>99.12</td></tr><tr><td>ML</td><td>0.0127</td><td>0.0167</td><td>82.51</td></tr></tbody></table>

To improve prediction accuracy, future research may focuses on smoothing signal to enhance continuity and improve temporal consistency in the predicted force profiles, and also, incorporating hyperparameter tuning could help improve model performance, rather than default hyperparameters as provided by Python libraries. In addition, to overcome the challenge of heterogeneity in walking conditions within the dataset, exploring two-stages approach can be fruitful and more accurate: identifying, in first step, the walking conditions using classification, followed a prediction of GRF using specific data subset.

## 4. Conclusions

The main objective was to enable accurate prediction of continuous GRF waveforms to enhance accessibility of dynamic analysis for clinical and sports applications. By using temporal acceleration signals of heels during gait, traditional regression methods, typically Random Forest regressor, excels in predicting the 3 components
of the GRF, regardless of the walking conditions. This
demonstrate the potential of using minimal sensor data
(accelerations for only the heel marker) for gait moni-
toring using high fidelity reference dataset (MOCAP).
Further study will focus on evaluating the performances
of these algorithms when using raw acceleration for
IMU sensor placed at the heel for use in real-world
environments. Moreover, the present framework will be
expanded to include the prediction of GR moments and
CoP, which are critical for accurate inverse dynamics.
For generalizability assessment, future work will also
focus on validating the model across pathological gait
patterns and reducing computational costs for cost-ef-
fective solution for clinical and sports applications in
real-world settings.

Conflict of Interest Statement

None

Contributor Roles

MS: Conceptualization, Methodology, Software, Writing
original draft; TR: Conceptualization, Methodology,
Validation, Writing- review & editing; Supervision.

Data, software, code availability

Dataset 1: Fukuchi et al. (2018). A public data set of overground and treadmill walking kinematics and kinetics of healthy individuals. figshare. Dataset. https://doi.org/10.6084/m9 figshare.5722711.v5

Dataset 2: Van Der Zee et al. (2021), Mundinger, Emily; van der Zee, Tim (2021). Biomechanics dataset of healthy human walking at various conditions. figshare. Dataset. https://doi.org/10.6084/m9 figshare.16530939.v4

References

Girka, A., Kulmala, J. P., & Äyrämö, S. (2022). Deep learning approach for prediction of impact peak appearance at ground reaction force signal of running activity. *Computer Methods in Biomechanics and Biomedical Engineering, 23*(14), 1052-1059. https://doi.org/10.1080/10255842.2020.1786072

Kiernan, D., Ng, B., & Hawkins, D.A. (2023). Acceleration-based estimation of vertical ground reaction forces during running: A comparison of methods across running speeds, surfaces, and

foot strike patterns. *Sensors*, 23, 8719. https://doi.org/10.3390/s23218719

Martínez-Pascual, D., Catalán, J. M., Blanco-Ivorra, A., Sanchís, M., Arán-Ais, F., & García-Aracil, N. (2023). Estimating vertical ground reaction forces during gait from lower limb kinematics and vertical acceleration using wearable inertial sensors. *Front. Bioeng. Biotechnol.*, 11, 1199459. https://doi.org/10.3389/fbioe.2023.1199459

Van der Zee, T. J., Mundinger, E. M., & Kuo, A.D. (2022). A biomechanics dataset of healthy human walking at various speeds, step lengths and step widths. *Sci Data*, 9, 704. https://doi.org/10.1038/s41597-022-01817-1

Fukuchi, C. A., Fukuchi, R. K., & Duarte, M. (2018). A public dataset of overground and treadmill walking kinematics and kinetics in healthy individuals. *PeerJ*, 6, e4640. https://doi.org/10.7717/peerj.4640