Predicting stride time variability from waist-mounted IMU data using machine learning: toward non-invasive gait stability monitoring in endurance running

Abstract

Background

Stride time variability (STV) is an important indicator of gait stability and motor control during running, yet its assessment typically depends on laboratory-based systems or distal sensor placement. This study evaluated whether a single waist-mounted inertial measurement unit (IMU) can estimate STV during prolonged treadmill running using machine learning.

Method

Eighteen healthy young adults completed 30 min of treadmill running at self-selected speeds while IMUs were placed on the right dorsal foot and low back. Stride times were identified from the foot-mounted IMU and used to calculate STV as the coefficient of variation of 50 consecutive strides, which served as the reference outcome. From the waist-mounted IMU, time- and frequency-domain features were extracted from tri-axial acceleration and angular velocity signals. Four regression models, including artificial neural network (ANN), random forest (RF), decision tree (DT), and XGBoost, were developed to estimate STV. Model performance was evaluated using leave-one-subject-out cross-validation with root mean squared error (RMSE), mean absolute error (MAE), and coefficient of determination (R²).

Results

All models demonstrated good subject-independent predictive ability, with XGBoost achieving the best overall performance (R² =0.942, MAE = 0.005, RMSE = 0.009). Features related to forward acceleration, particularly mean and dominant frequency in the X direction, were consistently among the most influential predictors.

Conclusion

These findings suggest that trunk kinematics recorded from a single waist-mounted IMU contain sufficient information to estimate running STV, supporting the feasibility of unobtrusive gait stability monitoring during endurance running with implications for assessing fall risk and rehabilitation progress.

Introduction

Running is a fundamental individual activity that is essential for various athletics and health-related pursuits [1]. Dynamic stability during running is crucial for both performance optimization and injury prevention, especially for endurance running [2]. It refers to the ability of a runner to maintain controlled motion and trajectory in response to internal physiological changes or external perturbations [3]. Stride time variability (STV), as one essential indicator for gait stability, is the variation of the temporal distances between subsequent strides [4]. STV directly characterizes temporal consistency of gait cycles and has been frequently linked to stability and variability in locomotion [5]. The stride time (ST) is the temporal distance from one heel strike to the subsequent heel strike of the same foot. Traditional methods for measuring ST in running have relied heavily on laboratory-based equipment, such as force plates and motion capture systems [6–9], which do not lend themselves to in-situ monitoring. Understanding the complexities of human gait dynamics necessitates monitoring STV in natural and uncontrolled settings, significantly benefiting athletic populations and recreational enthusiasts [10].

The advent of wearable technology has revolutionized the monitoring of physical activities by allowing continuous data collection during various activities [11–13]. Body-worn sensors, such as inertial measurement units (IMUs), can provide a wealth of information, such as acceleration and angular velocities, which are critical and sufficient for assessing gait kinematics [14]. These sensors are not only cost-effective but also unobtrusive, thus preserving the natural gait of the runner [15]. The placement of IMU sensors significantly affects the accuracy and utility of the collected data [16, 17]. Due to the specific dynamics of foot movement, sensors placed on the foot can provide required and substantial information on ground contact, foot strike, and the micro-movements that are crucial for evaluating STV [18]. Despite these advantages, the placement configuration of IMU on foot presents challenges, primarily due to the high impact and accelerated movement at this location, leading to sensor displacement or drop during dynamic endurance movement [19]. Moreover, sensors on the foot may interfere with natural gait patterns and cause discomfort at the sensor fixation position, potentially altering the normal gait patterns. These practical considerations necessitate a balance between the detailed data and the stable sensor placement. The sensor placement on the lower back has been favored due to its stability and ability to capture the body’s central dynamics. The lower back serves as a central point of mass and offers a comprehensive view of overall body motion, making it an ideal location for assessing STV. Sensors at this location are less prone to displacement and typically do not interfere with natural running movements, thereby providing reliable and consistent data over extended periods. While placing sensors on the lower back provides several advantages for monitoring gait dynamics, they might miss specific movements that are crucial for a more detailed analysis of gait dynamics since data captured from the lower back might be smoothed out or less pronounced due to low-pass effects of the lower limb joints and superimposing movements of the upper body [4]. Storm et al. [17] indicated that the waist IMU-based gait event detection method failed in some of the steps in walking, which could be even worse for running due to the fast speed. Similarly, a systematic review [20] also pointed out that foot-based gait event detection possesses higher accuracy and repeatability than lower trunk-based ones.

Given these considerations, machine learning methods can be leveraged to enhance the analysis and interpretation of waist-based IMU data through processing and extracting complex features from the raw data that may not be immediately apparent through basic observational techniques. Caramia et al. [21] extracted multiple gait features from IMUs to train machine learning models with high classification accuracy on grading the severity level of Parkinson’s disease, implying the clinical application of IMU data-driven models. Zhang et al. [22] developed support vector regression models with the input of IMU information to estimate gait parameters for ambulatory running tasks. With the assistance of single-IMU data, multiple machine learning models exhibit reliable predictions on continuous monitoring of fallers [23]. The integration of wearable sensors and machine learning algorithms exhibits powerful abilities in the accurate interpretation of sensor data to biomechanical parameters.

This study evaluates whether a single waist-mounted IMU can estimate stride time variability during prolonged treadmill running, using machine-learning models trained on trunk kinematic features and reference stride timing derived from distal foot sensing. We aim to develop predictive machine learning models that leverage waist-based IMU data to predict STV and discern instability in gait. This study could significantly contribute to the application of wearable technology for dynamic stability analysis. By advancing our understanding of how machine learning can be applied to biomechanical data, the research may help improve preventative strategies and performance optimization techniques in dynamic activities.

Methods

Data acquisition

Eighteen participants aged 20–30 (10 males and 8 females) were recruited in this study. All participants were free of lower limb musculoskeletal injuries in the preceding 12 months. The ethical approval was obtained from the Human Subjects Ethics Sub-Committee of the Hong Kong Polytechnic University (Number: HSEARS20150121003) Written informed consents were obtained from all participants prior to formal tests. This study was carried out in accordance with the Declaration of Helsinki.

All participants were provided fitted footwear and tight clothes for the experiments. As shown in Fig. 1, two 9-degree-of-freedom IMUs (Xsens, MTw), each containing a 3-axis accelerometer, a 3-axis gyroscope, and a 3-axis magnetometer, were attached to each participant, with one placed on the right dorsal foot and the other placed on the lower trunk at the level of the fifth lumbar vertebra (L5) [17]. The sensing axes of the waist-mounted IMU were aligned with the X, Y, and Z axes, which pointed to the upward, left, and backward directions, respectively. Before the treadmill running, participants were required to warm up for 5 min and get accustomed to the footwear. During the formal tests, participants performed 30-minute running tasks with self-selected speeds. The running speeds for male and female participants were 10.06 ± 0.87 km/h and 7.78 ± 0.85 km/h, respectively. IMU data from the foot and the lower back were obtained during the whole run with a sampling frequency of 120 Hz.

Fig. 1.

Workflow of the data collection and model configuration

Data preprocessing

STV was defined as the coefficient of variation (CV) of stride time (ST), as expressed in Eq. (1), and was used as the reference indicator of running gait [24]. The STV evaluation could identify subtle alternations in gait patterns that may not be reflected from individual strides, providing valuable information during continuous dynamic activities. In the current study, STV was calculated from the ST based on the right foot-based IMU data for the whole running [14]. The IMU data were pre-processed using a low-pass Butterworth filter with a cutoff frequency of 6 Hz to eliminate noise and smooth the signal prior to segmentation and feature extraction. Gait cycles were segmented using acceleration peaks of the foot-mounted IMU data to detect each heel strike event [20, 25]. Raw acceleration signals for the right foot shown in Fig. 1 were used to extract heel strike events. To ensure accurate and robust calculation, the initial 30 s of data were removed for each task due to a brief adaptation period, minimizing start-up instability effects on the calculation of ST [9]. The calculated ST for continuous strides was displayed in Fig. 2. A total of 30,270 strides were extracted. Model evaluation was performed using leave-one-subject-out cross-validation, whereby data from one participant were reserved as the test set in each iteration and data from the remaining participants were used for training. This subject-independent strategy was adopted to reduce data leakage and better assess model generalizability across runners.

1

Fig. 2.

The ST of continuous strides

The input for machine learning models predicting STV contained multiple significant features extracted from the waist-based IMU data as listed in Table 1. These features were derived from the acceleration and gyroscope data recorded during running tests. The primary input variables include the mean, standard deviation (SD), range, root mean square (RMS), dominant frequency (DF), and peak values of these signals from waist-mounted IMU in the three spatial axes (X, Y, and Z). DF (defined as Eq. 2) refers to the frequency component with the highest amplitude in the Fourier-transformed acceleration and gyroscope signals, representing the primary oscillatory behavior in the signal and identifying rhythmic gait consistency. Additionally, derived parameters, including the roll, pitch, and yaw angles, could provide important context for detailed body orientation and the dynamic stability of each stride, which were also regarded as input. These features, which represent various aspects of the runner’s dynamic state, were then used to train the machine learning models to predict STV. By utilizing these features, the models can effectively track changes in gait stability over time, offering a non-invasive tool for monitoring running performance and identifying early signs of fatigue or motor control impairments.

2

Table 1.

Description of IMU-derived features used for STV prediction

Feature Name	Description	Unit	Interpretation
Acc X/Y/Z (max)	Maximum acceleration along the X, Y, and Z axes	m/s²	Represents the highest instantaneous acceleration during a stride; indicates impact intensity.
Acc X/Y/Z (min)	Minimum acceleration along the X, Y, and Z axes	m/s²	Lowest acceleration within a stride; corresponds to deceleration or heel-strike phase.
Acc X/Y/Z (range)	Difference between maximum and minimum acceleration per axis	m/s²	Reflects the total variation in acceleration; larger range implies greater dynamic movement amplitude.
Acc X/Y/Z (rms)	Root mean square of acceleration signals	m/s²	Represents overall acceleration magnitude, incorporating both positive and negative fluctuations.
Acc X/Y/Z (DF)	Dominant frequency of acceleration signal (from FFT)	Hz	Indicates stride or cadence frequency, quantifying rhythmic consistency in running gait.
Acc X/Y/Z (SD)	Standard deviation of acceleration	m/s²	Measures variability in acceleration, related to dynamic stability and movement smoothness.
Gyro X/Y/Z (max)	Maximum angular velocity along each axis	rad/s	Represents peak rotational velocity, linked to trunk or pelvis rotation during gait cycles.
Gyro X/Y/Z (min)	Minimum angular velocity along each axis	rad/s	Lowest angular velocity; indicates reversal or deceleration of segment rotation.
Gyro X/Y/Z (range)	Difference between maximum and minimum angular velocity	rad/s	Describes total angular movement amplitude; higher range reflects larger torso rotations.
Gyro X/Y/Z (rms)	Root mean square of angular velocity	rad/s	Quantifies average rotational activity; higher values indicate more dynamic torso motion.
Gyro X/Y/Z (DF)	Dominant frequency of angular velocity signal	Hz	Captures rhythmic rotation frequency; reflects stride regularity and coordination.
Gyro X/Y/Z (SD)	Standard deviation of angular velocity	rad/s	Reflects rotational variability, related to balance control and dynamic stability.

where is the time-domain signal (acceleration or angular velocity), and FFT denotes the Fast Fourier Transform.

Model configuration and evaluation

In the study, four machine learning models including artificial neural networks (ANN), random forest (RF), decision trees (DT), and XGBoost were selected to perform the STV prediction tasks, capturing relationships between the extracted features derived from waist-mounted IMU data only and STV calculated from foot-mounted IMU data. Cross-validation was used during hyperparameter tuning for machine learning models to ensure the robustness of each model [23, 26]. Hyperparameters including the number of hidden layers and their units, dropout rates, and learning rates were optimized to obtain better predictive performance of ANN. The rectified linear unit (ReLU) activation function was employed in the hidden layers, while the output layer used a linear activation function due to the regression nature of the task. RF regressor with tuned estimators and the maximum depth is an ensemble learning method that constructs multiple decision trees and averages their outputs. The DT model was built with the optimized parameters, including maximum depth and minimum samples split, to provide a powerful predicting ability of the STV. The XGBoost model was selected due to its ability to handle large datasets and complex relationships [27]. Hyperparameters for the learning rate, number of estimators, and maximum depth were optimized to improve performance by reducing bias and variance. GridSearchCV algorithm was employed to optimize hyperparameters for the selective models, ensuring the best-performing configurations for models [28].

To assess the performance of each model, evaluation metrics were calculated to quantify and compare the performance of these models. R-squared (R²) quantifies the proportion of variance in the dependent variable (STV) that is explained by the independent variables [29, 30]. Higher R² values indicate a better fit of the model to the data. Mean absolute error (MAE) measures the average magnitude of errors between predicted and actual values, of which lower values indicate better predictive accuracy [31, 32]. Root mean squared error (RMSE) provides an error metric that is in the same units as the target variable, making it more interpretable [33]. Lower RMSE indicates better model performance [34]. Additionally, the study also identified influential features that contribute to the higher prediction power for these models, providing more insights into the dynamic stability during continuous running.

Results

Figure 3 presents the Pearson correlation coefficients between selected IMU-derived features and STV, providing insights into the linear relationships between sensor-based biomechanical indicators and gait stability. Among the top features, forward acceleration metrics (Acc X (max), Acc X (mean), and Acc X (min)) exhibited strong positive correlations with STV, while, conversely, several rotational features, particularly from the gyroscope’s pitch axis (X), demonstrated moderate to strong negative correlations with STV. The performance of the optimized predictive models was thoroughly evaluated by comparing their accuracy and consistency under leave-one-subject-out cross-validation, ensuring the models’ robustness and generalizability. Various metrics including RMSE, MAE, and R² were used to assess the models’ capability to predict STV. As shown in Table 2, all predictive models exhibited good performance in the prediction of STV during continuous running tasks. DT revealed the worst performance with a slightly lower R² of 0.916, the highest RMSE of 0.011, and an MAE of 0.006. XGBoost yielded the highest R² of 0.942, the lowest RMSE of 0.009, and MAE of 0.005. The other two predictive models (ANN and RF) also revealed high accuracy in the STV prediction. The Bland-Altman diagram in Fig. 4 was used to show the agreement between the predicted STV from XGBoost, which has the best prediction performance and the actual observed STV. For this best-performing model, the Bland-Altman plot showed that the predicted STV values closely aligned with the true STV values, with most points lying within the 95% limits of agreement, suggesting that the model provides reliable and consistent estimates for STV.

Fig. 3.

Top predictive IMU-derived features associated with stride time variability (STV). Acc = acceleration; Gyr = gyroscope angular velocity; DF = dominant frequency; X = anterior-posterior direction; Y = mediolateral direction

Table 2.

Evaluation matrix for all models

Models	RMSE	MAE	R 2
ANN	0.010	0.006	0.933
RF	0.010	0.006	0.929
DT	0.011	0.006	0.916
XGBoost	0.009	0.005	0.942

Fig. 4.

Left: Relationship between predicted and reference stride time variability (STV). The solid line represents the line of identity (y = x). Right: Bland–Altman plot of agreement between predicted and reference STV. The dashed line represents the mean difference, while the solid lines indicate the upper and lower limits of agreement (95% confidence interval)

Regarding the feature importance, acceleration-related parameters consistently emerged as the most important feature for predicting STV across all models (shown in Table 3). Notably, the mean and DF of the acceleration in the X direction ranked among the top two important features in most models. Additionally, gyroscopic-derived parameters were also frequently highlighted as key predictors. XGBoost showed the best performance in predicting STV, and the top influential feature was the DF of acceleration in the X direction.

Table 3.

The ranking of feature importances for all models

Feature ranking	ANN	RF	DT	XGBoost
1	Acc X (mean)	Acc X(DF)	Acc X(mean)	Acc X(DF)
2	Acc X(DF)	Acc X(mean)	Gyro X(peak)	Acc X(mean)
3	Gyro Y(DF)	Gyro X (min)	Acc Z(DF)	Gyro X(DF)
4	Gyro Y(mean)	Acc X (max)	Gyro X(max)	Gyro Y(DF)
5	Acc Z(mean)	Acc Y(mean)	Gyro Y(DF)	Gyro X(max)

ANN Artificial neural networks, RF Random forest, DT Decision trees, Acc Acceleration, Gyro Gyroscope, DF Dominant frequency

Discussion

The study configured several machine learning models with the derived parameters from waist-mounted IMU only to continuously monitor STV which is one key indicator for dynamic stability. These models exhibited high accuracy and good generalizability. Additionally, some significant features were highlighted to imply their substantial contribution to the STV prediction. The results indicate the potential applications of a combination of wearable sensors and machine learning models on the monitoring of biomechanics during dynamic activities.

The use of waist-mounted IMU data for predicting STV possesses advantages over regular methods. The study leveraged machine learning algorithms to predict STV based on one waist-mounted IMU, obtaining excellent performance on the assessment of dynamic stability in endurance running. Especially, the predictive model XGBoost emerged as the best-performing model with an R² of 0.942, the lowest RMSE of 0.009 and MAE of 0.005, suggesting that the model was able to capture the complex relationships between the IMU-derived features and STV and explain over 94% of the variance in STV. XGBoost could handle non-linear relationships and complex feature interactions [35], making it more suitable for the complex relationship between the derived features from acceleration and gyroscope and STV in dynamic movement patterns. The other three machine learning models also achieved relatively high R² values, such as ANN (0.933) and RF (0.929), further demonstrating the robustness of machine learning algorithms in predicting STV, regardless of the different models. These findings are particularly noteworthy since they highlight the capability of machine learning algorithms to extract meaningful variables from IMU data and enable continuous monitoring in gait analysis.

Waist-mounted IMUs also offer a simplified and practical sensing configuration for capturing global body motion during running. Unlike distal sensors, trunk-mounted measurements reflect the integrated effects of lower-limb movements and whole-body coordination, which are closely related to stride regulation. In this context, the ability of the models to accurately predict STV from waist-derived features suggests that variability in trunk dynamics contains meaningful information about stride-to-stride timing control, highlighting the potential of using central body kinematics as a surrogate representation of gait variability. Such an approach may facilitate more accessible monitoring of running stability in field-based or long-duration conditions where complex sensor setups are not feasible [36].

To evaluate the linear association between sensor-derived parameters and gait stability, the correlation between selected IMU features and STV was assessed. Interestingly, certain features, such as Acc X(DF), demonstrated low Pearson correlation with STV, yet were consistently ranked as highly influential in the predictive models, particularly in XGBoost. This discrepancy underscores the limitation of simple linear correlation metrics in capturing complex relationships. Unlike correlation, machine learning models like XGBoost can detect nonlinear dependencies and feature interactions, where the predictive value of a feature emerges only in specific contexts. Thus, even features with weak linear associations can substantially enhance model accuracy when embedded in a multivariate, nonlinear predictive framework. To further interpret models, influential features for each configured model were identified using the permutation importance approach, indicating the significant contribution of the top features to STV prediction. Among all the features, acceleration in the X direction holds the strongest predictive power in the prediction of STV for most models. The prominence of x-axis acceleration as a predictive feature in STV regression underscores the importance of horizontal motion in understanding stride dynamics during running. The x-axis acceleration, typically aligned with the direction of forward movement, provides crucial information on the runner’s temporal gait characteristics. Temporal changes in this acceleration directly correlate with the rhythmic consistency of each stride cycle, making it essential for predicting STV. As runners vary in speed, the fluctuations in x-axis acceleration reflect the forces involved in maintaining forward propulsion. This relationship can reveal subtle changes in stride length, frequency, and pace adjustments over time. Even minor variations in acceleration might signify irregularities in stride time or propulsion inefficiencies, reflecting how well runners manage the cyclic loading and unloading phases within each stride. Moreover, the strong predictive capability of acceleration DF in the x-direction highlights the relationship between cadence consistency and stride duration, which is closely associated with STV. During natural movement, stride frequency is critical information for body coordination that maintains balance and facilitates movement during periodic motions [37]. DF provides insights into how consistently a runner can maintain their rhythm [38]. Changes in this frequency may suggest irregularities in gait control, leading to greater STV. Additionally, features related to the gyroscope, such as the peak values of angular velocities, also played important roles in the prediction of STV, underscoring the importance of rotational dynamics in maintaining stability during movement. The significant features highlight the key aspects derived from the waist-mounted IMU data that are most relevant to the dynamic stability.

The study investigated the application of machine learning models to the prediction of STV which is one key parameter for assessing gait stability and dynamic motor control. The machine learning models incorporated into waist-based IMU data offer a practical and effective alternative for monitoring gait dynamics in both clinical and real-world settings without the limitation of wearability. This investigation provides further support for non-invasive, continuous gait monitoring and shows promise for future personalized training and rehabilitation applications.

While the use of waist-mounted IMU sensors combined with machine learning models to predict STV shows great performance in monitoring dynamic gait stability, the study has some limitations. The participants recruited in the study were all young and healthy, which may not be fully representative of the broader population. The predictive performance of the models may vary across different populations, such as older adults. Therefore, the generalizability of the results may be limited. The performance of models may require further validation across a wider range of populations. Moreover, the dataset over 30,000 strides used in this study was relatively small and homogeneous, which may introduce bias and limit the model’s ability to generalize effectively. The findings may not fully generalize to outdoor running conditions, where environmental variability could influence IMU signals and potentially affect model performance. Further studies should focus on larger and more diverse datasets that include various age groups and physical conditions. By addressing these limitations, future research can refine the predictive models and ensure their applicability in a broader clinical context.

Conclusion

The study investigated the combination of waist-based IMU data and machine learning models to predict STV in endurance runs. It provides a non-intrusive, cost-effective, and reliable approach for continuous monitoring of gait stability. The feature importance analysis was also performed across all machine learning models, revealing that the most predictive features were those related to the acceleration in the x-direction, such as the mean and DF of the x-axis acceleration. By demonstrating that STV can be accurately predicted from waist-mounted IMU data, this study suggests the potential for more user-friendly and portable solutions in gait stability monitoring. These findings support the growing evidence that wearable technologies such as IMUs, combined with machine learning techniques, may offer effective means of monitoring these factors. The predictive power of these models may also have potential to be extended to personalized gait training and injury prevention programs in-situ monitoring in daily life.

Authors’ contributions

Shane Fei Chen and Ming Zhang conceived and designed research. Shane Fei Chen performed experiments. Shane Fei Chen and Xianglin Zhao analyzed data and interpreted results of experiments. Shane Fei Chen drafted the manuscript. Jason Tak-Man Cheung and Ming Zhang edited and revised the manuscript.

Funding

Not applicable.

Data availability

The data from the current study are available from the corresponding author on reasonable request.

Declarations

Ethics approval and consent to participate

The study was granted by the Human Subjects Ethics Sub-Committee of the Hong Kong Polytechnic University (Number: HSEARS20150121003). Written informed consents were obtained from all participants prior to formal tests.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.