Design and implementation of a countermovement jump performance estimation system using a wearable device with IMUs based on machine learning algorithms

The vertical jump is a specific action often utilized in sports science to assess the general physical condition of an athlete. CMJ is one of the most common types of exercise used for general physical assessment. To measure the physical condition of a subject, a researcher first asks the subject to perform a vertical jump (e.g., CMJ) while standing on a force plate. From this, a stream of force-time data is captured and converted into a series of variables (usually 7), which reflect the subject’s jumping performance and the overall physical condition. Swinton et al. [31] described how to apply the force-time curve of a CMJ and squat jump (SJ) to resistance training. They established a connection between resistance training activity, SJ, and CMJ, demonstrating a way of improving training efficiency. Rice et al. [29] examined the power-time and force-time curves for male and female basketball players to determine whether there was a significant difference between the genders. Pupo et al. [28] measured the CMJ and SJ performance of volleyball players and sprint runners, and then discussed the relation between the jump performance variables. They showed that the maximum force and the peak velocity were the main determinants of jump height and power, and that the sprint runners’ jump performance was superior to volleyball players. Kirby et al. [19] discussed the relationship between jump performance variables, including net impulse, peak force, peak power, peak velocity, and jump height. The result showed that relative net vertical impulse has a significant correlation to jump height, and peak force is negatively correlated with jump height. Lake et al. [21] used push press and loaded CMJ to quantify load and its effect on resistance training, by evaluating peak and mean power. McMahon et al. [26] researched senior and academy rugby league players as they performed CMJs. They found that senior players had superior jump height and impulse performance. McLellan et al. [25] discussed how RFD affects vertical jump performance. They studied the relationship between RFD and other vertical jump variables such as peak force and peak power in the eccentric phase. The result showed that RFD has a significant association with some of those variables.

Some studies have already applied machine learning to vertical jump data. Zhou et al. [34] used machine learning methods to predict football players’ CMJ jump height. Their models utilized LR, random forest, and decision-tree regression. The result showed that the Pearson product-moment correlation coefficient of all their models was >0.85. Kipp et al. [18] used a machine learning approach to predict the CMJ performance of track and field athletes after resistance training. Chiang et al. [11] proposed using wearable IMU devices instead of a force plate, to evaluate CMJ performance. They collected CMJ data from the IMU device and the force plate, then converted the acceleration data into features, and finally used the force plate data as the ground truth to train the machine learning models so that they could predict the CMJ performance. The models they utilized were decision-tree regression, LSVR, and LR. The experiment results showed that the machine learning models made good predictions for CMJ peak force, net impulse, and flight time.

Recently, there have been many research projects relating to the cooperation of sensors and machine learning. These research papers cover a wide variety of fields, and most researchers hope to replace expensive instruments or complex measurement systems with simple, low-cost sensors and machine learning. Bauman et al. [5] did a preliminary investigation of predicting time-to-next heel strike with acceleration data and machine learning. They used two accelerometers, and used their x- and y-axis data as the raw data. The acceleration data was first processed through a second-order 10 Hz cutoff Butterworth filter. They used the sliding window to process the acceleration data to obtain its primary features. These features were subsequently fed into artificial neural networks (ANN) and a teacher forcing ANN for training, and a grid search could then be used to find optimal model hyperparameters. Chaaban et al. [7] proposed a predictive method based on one or multiple IMU sensors to predict vertical ground force and knee biomechanics. They tied various numbers of sensors to a test subject’s leg to collect the gyro and acceleration data measured by the IMUs as their model training data. In their experiments, they compared the performance difference between single and various multi-sensor setups. They determined that their setup was a valid way to replace expensive and complex laboratory force plate measurement systems.

Johnson et al. [15] proposed a method of collecting acceleration data via five sensors tied to different physical locations on a test subject’s body, then using deep learning to assess the predictive quality of these data concerning multidimensional ground reaction forces while running, and sidestepping. Lim et al. [24] proposed the sacrum as the key measurement point for single IMU setups. Being near the center of mass (CoM), the sacrum can be used to effectively capture and predict dynamic data (e.g., torque of the knee, ground reaction force of the knee) of the lower limbs, by an ANN. They also showed that the CoM is a dynamic determinant of walking. Through biomechanical analysis, it is possible to approximate the subject’s ground reaction force, and even the segment-angle of their lower limbs, by the weighted sum of CoM dynamics. Acceleration data were converted to velocity and displacement, and this was used to create features that can be used to predict lower limb kinetics and kinematics.

The test subject performs several CMJs, as shown in Figure 1A. The raw acceleration-time data from the wearable IMU are logged, and Figure 4A is a plot of that data. Figure 4B shows the same data after a sixth order 30 Hz Butterworth filter has been applied to reduce noise. It is also necessary to subtract gravity (1 g) from the acceleration-time data to bring the y-axis steady-state to 0 g (Figure 4C). Finally, the normalized acceleration-time data can be divided into individual jumps (Figure 4D).

Figure 4:

Data preprocessing of CMJ acceleration data. (A) Raw IMU acceleration data (B) Raw IMU data post-Butterworth filter. (C) Post-Butterworth filter data, after elimination of the gravity component. (D) Acceleration data after jump segmentation. CMJ, countermovement jump; IMU, inertial measurement unit.

a.i

Feature extraction from the processed acceleration data

Feature extraction from the preprocessed acceleration-time data for each CMJ is possible following the method proposed in references [10, 11]. This study extracts statistical features, time intervals, and critical point values, and then computes averages. The critical values from the raw acceleration-time data look like those presented in Figure 5, where point A represents the peak acceleration value, before the jumper leaves the ground, points B and D are where the acceleration value in the original acceleration-time series is zero, before normalization (i.e., 1 g in the normalized acceleration-time data), and point C is the lowest acceleration value before landing. Point E is the maximum acceleration value during the contact phase, and Point F is the second-highest acceleration value, also occurring in the contact phase, but after Point E. All of the 31 extracted features and their descriptions are listed in Table 1.

Figure 5:

Critical point extraction from post-processed IMU acceleration-time data. IMU, inertial measurement unit.

Table 1:

Feature	Description
Mean	The mean of the acceleration data
SD	The standard deviation of the acceleration data
IQR	The interquartile range of the acceleration data
Skewness	The skewness of the acceleration data
Kurtosis	The kurtosis of the acceleration data
Frequency	The dominant frequency of the acceleration data
Entropy	The sample entropy of the acceleration data
value_A	The value of point A
value_C	The value of point C
value_E	The value of point E
value_F	The value of point F
duration_AC	The time interval from point A to point C
duration_BD	The time interval from point B to point D
duration_CE	The time interval from point C to point E
duration_EF	The time interval from point E to point F
slope_AL	The slope from (point A − 20 ms) to point A
slope_AR	The slope from point A to (point A + 20 ms)
slope_CL	The slope from (point C − 20 ms) to point C
slope_CR	The slope from point C to (point C + 20 ms)
slope_EL	The slope from (point E − 10 ms) to point E.
slope_ER	The slope from point E to (point E + 10 ms).
slope_FL	The slope from (point F − 10 ms) to point F
slope_FR	The slope from point F to (point F + 10 ms)
slope_AC	The slope from point A to point C
slope_CE	The slope from point C to point E
slope_DE	The slope from point D to point E
slope_EF	The slope from point E to point F.
Integration	The integration value before point C
average_A	The average value between (point A − 80 ms) and (point A + 20 ms)
average_C	The average value between (point C − 20 ms) and (point C + 180 ms).
average_E	The average value between (point E − 20 ms) and (point E + 180 ms)

IQR, Interquartile range.

Next, it is necessary to compute the seven performance variables to derive ground truth values for training the machine learning models. Six of the performance variables are derived from the normalized force-time data, as shown in Figure 2. These variables include net impulse, rate of force development (RFD), peak force, flight time, average loading rate, and second peak force; only the peak power variable is derived from the power-time data.

The lack of power-time data means that it is necessary to derive the power-time data from the raw force-time data by the use of Eqs (1)–(3); where t represents time, a(t) represents acceleration at time t, F(t) represents force at time t, m is mass, v(t) is the velocity at time t, and P(t) represents power at time t, measured in Watts. Since the subject weight affects the power value, the machine learning system has to take the maximal peak power value, divided by the subject weight to create a Watt/kg value. This is used to eliminate the effect of subject weight on peak power, and Figure 7 shows the power-time data before and after division by the subject weight. (1) at=Ftm a\left( t \right) = {{F\left( t \right)} \over m} (2) vt=∫atdt v\left( t \right) = \int {a\left( t \right)dt} (3) Pt=Ft⋅vt P\left( t \right) = F\left( t \right) \cdot v\left( t \right)

Figure 7:

Data preprocessing of CMJ power data. (A) Raw power data. (B) Power data, divided by the subject weight. CMJ, countermovement jump.

This study simultaneously collects acceleration-time and force-time data. The acceleration-time data are collected using a NAXSEN IMU sensor, produced by SIPPLink Technology. ⁽⁴⁾ The size (50 mm × 46 mm × 9 mm) and appearance of the device are shown in Figure 8A. The small dimensions of the device mean that it is easily worn by the test subject, close to their sacrum, as shown in Figure 8B. The force-time data are collected by a 3D portable force plate produced by Kistler (model 9260AA6), and the appearance and dimensions (600 mm × 500 mm × 50 mm) of the device are shown in Figure 8C. The sample rate of both the IMU sensor and force plate is set at 1,000 Hz.

Figure 8:

A NAXSEN IMU tied on a jumper and a Kistler 9260AA6 force plate. (A) Appearance of the SIPPLink Technology. (B) Placement of the IMU on the test subject. (C) Kistler 9260AA6 force plate used during this study. IMU, inertial measurement unit.

A total of 19 healthy test subjects aged 20–40 years provided a total of 870 CMJ observations. This placement is closer to the subject’s CoM and consequently captures the body dynamics more effectively. Specifically, it provides a lower error rate than when attached to the subject’s ankle, according to Lee et al. [22]. The IMU is attached to the test subject’s clothing as shown in Figure 8B.

Previous studies [3] report that different types of shoes create a sufficiently large margin of error in the results, which requires compensation, especially affecting the average loading rate and the second peak force when landing. Therefore, each subject performs 10 CMJs barefoot on the force plate, with a short interval between jumps.

The application is configured to capture and log data from the devices at 1,000 Hz, which directly corresponds to the devices’ sampling rates. To obtain a data resolution of 1,000 Hz from the IMU, the device must be directly wired to a computer. In this system, a standard universal serial bus (USB) cable is used; however, it should be noted that using a wired connection would be impractical for real-life applications. The only wireless communications protocol offered by the IMU is Bluetooth, which limits the maximum streaming sample rate to 50 Hz. This is inconsistent with the native sampling rate of the force plate, which is 1,000 Hz. To address this issue, the acceleration-time data are up-sampled from 50 Hz to 1,000 Hz, by both duplication and linear interpolation. The features extracted from the original acceleration-time data (at 1,000 Hz) and the two sets of up-sampled acceleration-time data (now at 1,000 Hz) are used to train the regression models and determine the model fit. Each of the CMJ performance variables is obtained from the force-time data. In total, 80% of the observations are used for model training and 20% are used for testing.

The performance metric used to determine model performance is the mean absolute percentage error (MAPE) model, shown in Eq. (4), where y_k is the actual value of a performance variable, derived from the force-time data; y^k {{\hat y}_k} is the predicted value of the performance variable, derived by the machine learning method, using the available acceleration-time data; and n is the number of CMJs. Each experiment is repeated five times to ensure the robustness of the model. This study uses the default parameter values for the five regression models in scikit-learn, which are documented in Table 2. (4) MAPE=100n∑k=1nyk−y^kyk MAPE = {{100} \over n}\sum\limits_{k = 1}^n {\left| {{{{y_k} - {{\hat y}_k}} \over {{y_k}}}} \right|}

Since using unsuitable features may significantly affect the predictive performance of the selected models, a feature selection task is performed to validate and, where necessary, remedy the model(s). Since there are at most 2³¹ – 1 non-empty subsets of the 31 extracted features in the worst case, it is time-consuming to exhaustively train different regression models using each of these subsets to obtain the model with the lowest prediction error (e.g. MAPE). Therefore, a feature selection analysis is performed using the scikit-learn Select k Best tool [1] to reduce the exhaustive training effort. For each of the seven performance variables, k is varied from 1 to 31, to select the k most significant features of the related performance variable. The predictive performance for each variable under MAPE is examined using each of the five regression models, with a different k value. The experimental results of each of the seven performance variables are shown in Figures 9A–9G. Figures 9A–9G show that the performance of most regression models improves as the number of k increases, in terms of MAPE. This indicates that most of the 31 extracted features are relevant to the predictive ability of the variables.

Figure 9:

Prediction results from varying the number (k) of selected features for each performance variable, under each of the five regression models. (A) Peak force. (B) Second peak force. (C) Flight time. (D) Average loading rate. (E) Net impulse. (F). Peak power. (G) RFD. DTR, decision tree regression; LGBMR, light gradient boosting machine regression; LR, linear regression; LSVR, linear support vector regression; MAPE, mean absolute percentage error; RFD, rate of force development; XGBR, eXtreme gradient boosting regression.

The experimental results in this section show the comparative success of the five regressions, assessed by MAPE, when estimating the seven CMJ performance variables. These data are tested on the three types of acceleration data: (1) the original 1,000 Hz data, (2) the 50 Hz data up-sampled by duplication, and (3) the 50 Hz data up-sampled by interpolation. These results are shown in Tables 3A–3C, respectively. We can see that LGBMR is the best among all compared regression models to predict almost all of seven performance variables on all three types of datasets in terms of MAPE. Even though LGBMR is not the best in the task of predicting the average loading rate on the original 1,000 Hz among all models, the MAPE of LGBMR is only slightly inferior to XGBR. Therefore, we still select LGBMR as our final prediction model for its excellent ability to predict almost all of the performance variables of a CMJ. Interestingly, the MAPE in the second peak force is higher than the MAPE in other variables. After consulting with domain experts, we believe that the errors in the second peak force originate from the contact phase, as different subjects may employ varying landing strategies. For each performance variable of a CMJ, the selected features achieving the best prediction results of LGBMR are listed in Table 4.

So far, in this study, LGBMR has proven to be the superior machine learning-based method for predicting flight time. However, there are alternate conventional ways of collecting acceleration data to estimate the vertical jump variable. To compare the predictive performance of the LGBMR model being examined here, it is now compared to the performance of the integration-based method proposed in reference [27]. As shown in Table 5, in terms of MAPE, LGBMR outperforms the integration-based method, when predicting CMJ flight time.

Despite the progress made in this study, there is considerable scope for further research. For example, rather than up-sampling the acceleration-time observations, it is likely possible to derive more findings from the available data; however, this will take time as it involves hunting for patterns and features.

Furthermore, obtaining a larger sample of test subjects would be beneficial, as this would provide a more comprehensive evaluation of the system across a broader range of body weights, fitness levels, and demographic groups. In particular, it will be necessary to collaborate with athletes and coaches to assess key aspects, such as latency, accuracy, usability, and overall applicability in real-world settings. Such collaboration is also essential to deepen our understanding of the precise relationships among the variables investigated in this study.