Nineteen elite swimmers took part in this study, whose attributes are shown in Table 1. They were informed of the procedure and gave their written consent prior to participation. This study was approved by the EPFL human research ethics committee (HREC, No: 050/2018). One IMU (Physilog^® IV, GaitUp, CH.) was attached to swimmer’s sacrum, using waterproof band (Tegaderm, 3M Co., USA). The sensor contained a 3D gyroscope (±2000 °/s) and 3D accelerometer (±16 g), with a sampling rate of 500 Hz (Figure 1). A functional calibration was performed after sensor installation with simple movements in land (upright standing and squats) before the measurement to make the data independent of sensor placement on swimmer’s body (Dadashi et al., 2013). During the measurements, the swimmers were asked to perform four one-way trials in each swimming technique (i.e. front crawl, breaststroke, butterfly, backstroke) with a progressive velocity (70–100%) in a 25 m indoor pool, starting with wall push-off inside water. The trials were separated with 1-min rests, and the total duration of the measurement was around 1 hour per swimmer.

Two systems were used as references in our study to validate the goal metrics estimated by the IMU. The first one was a set of four 2-D cameras (GoPro Hero 7 Black, GoPro Inc., US) used for detecting the swimming phases. The cameras synchronized with the IMU, using the LED light of a push-button (Hamidi Rad et al., 2021) were attached to the pool wall (distributed along the length of the pool) to videotape all the lap from wall to wall underwater with a 60 Hz rate (Figure 1). The second reference system was a tethered speedometer (SpeedRT^®, ApLab, Rome, Italy), attached with a belt to the waist of the swimmer. The speedometer calculated the displacement and velocity of the swimmer at a rate of 100 Hz and was used for finding the reference values of goal metrics in different swimming phases. As the speedometer was installed on the starting block above the swimmer’s level, it caused a parallax problem (Le Sage et al., 2011). Since the device level difference with respect to the still pool water was known (62 ± 1 cm), the velocity projection along the swimming direction was separated as the forward velocity of the swimmer.

The general flowchart for performance evaluation is outlined in Figure 2. The algorithm includes three parts: 1) IMU data preparation 2) phase detection and phase-based micro variables extraction, 3) kinematic variable selection and goal metrics estimation. IMU data preparation aims to transfer the data to the global frame to achieve the true motion data of swimmer’s sacrum. Then we divided each lap into four phases of Push, Glid, StPr and Swim by camera or IMU (Hamidi Rad et al., 2021). In order to observe the error induced by IMU-based phase detection, the rest of the analysis was done once with swimming phases detected by cameras and once by the IMU for comparison, the results of which are illustrated in supplementary materials. Using the data in global frame (acceleration ( A c c X , A c c Y , A c c Z ), angular velocity ( G y r X , G y r Y , G y r Z ) and orientation (Roll, Pitch, Yaw)) within the detected phases, we extracted the micro variables of each phase.

In the third part of this approach, we used the extracted phase-based micro variables to estimate the goal metrics. First, LASSO (least absolute shrinkage and selection operator) variable selection is used to rank and select the micro variables with higher importance (Fonti and Belitser, 2017). Using the speedometer and camera data, several goal metrics are extracted on the velocity and displacement of the swimmer in different swimming phases. These goal metrics are representatives of how well the swimmer performed in the corresponding phase. Finally, we used the selected micro variables to estimate the goal metrics. The principal outputs of this analysis are the selected variables and the error of using them for goal metrics estimation.

The cross-validated values (R², RMSE and the relative RMSE in percent) of LASSO regression model used for estimating the corresponding goal metric are reported in Table 3 for each goal metric. Table 3 shows that LASSO regression model fits the data with an R² value more than 0.75 for most goal metrics in all swimming techniques. The RMSE of the regression are less than 0.15 m s (11%) for all goal metrics defined over velocity and less than 0.21 s (7%) and 0.52 s (5%) for T 5 m and T 15 m respectively. The highest value of relative RMSE belongs to Glid end velocity with 11.1%, while the relative error is less than 10% in all other cases. The results are also calculated with swimming phases found by cameras for comparison in supplementary materials (Supplementary Table SA1).

The selected variables for each goal metric estimation during front crawl technique are listed in Table 4. Same tables for other swimming techniques are brought in supplementary materials (Supplementary Tables A2–A4). Among acceleration axes, A c c Y and its related variables [e.g. Mean ( A c c Y ), Max ( A c c Y ), Int ( A c c Y )] are more selected for different goal metrics. G y r Z and φ related variables seem to be more associated with the defined goal metrics than other axes of orientation in front crawl technique. For T 5 m _, T 15 m and lap average velocity, a mixture of variables from corresponding phases are selected, some of which were already selected for the specific goal metric of these phases.

The overall contribution of each category in estimating the goal metrics is illustrated in Figure 4 for all four swimming techniques. It is observable that propulsion category plays an important role in Push phase, while posture-related variables are more selected in Glid phase. StPr phase is less affected by efficiency compared to other categories. Efficiency and propulsion categories are both significant in determining the average velocity per cycle in Swim phase. Duration/rate category is dominant in estimating average velocity of Swim phase and lap average velocity. T 5 m and T 15 m are affected mainly by a mixture of propulsion, posture and duration/rate categories depending on the swimming technique.

The selected kinematic variables within each swimming phase were used for estimating the corresponding goal metrics (Table 3). Estimating the Push maximum velocity and Glid end velocity showed similar results in different swimming techniques, as the two initial phases are the same for them (only for backstroke, the swimmer has a supine posture). The relative RMSE is the highest for Glid end velocity estimation (11%) because this goal metric has the lowest value in the whole lap. In the StPr phase, the average velocity shows a high amount of variability among the swimmers, and determination coefficient (i.e. the proportion of the variance of the true goal metric value explained by the regression model) is relatively lower for it (less than 0.8 in all techniques) compared to other goal metrics in all techniques, because a linear model is not efficient enough in reflecting the variation of this goal metric, and a non-linear model might estimate it better.

Average velocity per cycle is estimated in all techniques with a determination coefficient more than 0.84 and an RMSE less than 0.076 m/s and relative error less than 6%. However, estimating the average velocity of the whole Swim phase achieved poorer results (R² of 0.71–0.90 in different techniques). As estimating each cycle average velocity is more accurate in all techniques, the average value of all cycles in Swim phase can also be used for estimating Swim phase average velocity. The regression models for estimating T 5 m show less accuracy (R² less than 0.80 in different techniques), making it difficult to trust the estimation results. Depending on swimming technique and swimmers’ pace, they might start StPr phase earlier than 5 m from the wall. So T 5 m   is partly affected by StPr phase and using only Push and Glid phases might not be enough for estimation. On the contrary, the first three phases (Push, Glid and StPr) finish before 15 m from the wall and using them for estimating the T 15 m results in more accurate regression models (R² more than 0.75 in different techniques). Finally, the lap average velocity is estimated using a selection of the kinematic variables from all phases with a relatively small error (RMSE less than 0.063 m/s for all techniques). The results have been only slightly improved when using cameras for phase detection (section 1 of Supplementary Materials).

As shown in Table 4 and Figure 4 during the Push phase, the kinematic variables related to φ and A c c Y are ranked as more important, which shows the significance of keeping the right posture and generating high propulsion in Push phase. The Mean ( G y r Z ) and Eff ( A c c Y ) are selected at last. The weight contribution of Push kinematic variables can be categorized more in propulsion and posture groups, which is the same for all techniques (Figures 4A–D), as the Push movement is the same. During Glid phase, phase duration is chosen the first, since the longer the Glid phase is, the more velocity will be lost. Momentum ( A c c Y ) and Int ( A c c Y ) are also considered important since they represent the effect of water drag on swimmer’s body. High Range ( φ ) and Mean ( φ ) during Glid are a sign of bad posture, which causes more drag. In terms of categories, none of the micro variables can be categorized in propulsion because Glid phase does not include any propulsive motion. As a result, the categories of posture and duration/rate are the dominant groups in this phase, regardless of the technique.

StPr phase has the highest amount of velocity variation on speedometer data and the average velocity during this phase is related to a combination of forward acceleration, accelerating efficiency, number of kicks and phase duration. Two types of efficiency-related variables are selected for this phase. Eff ( A c c Y ) represents the ratio of positive to all forward acceleration and Eff_dir ( A c c Y ) is the ratio of forward acceleration to the acceleration norm. Since this phase includes strong kicking, generating the highest amount of acceleration in forward direction ( A c c Y ) with respect to other axes is selected as an important variable. StPr phase is the same for front crawl, butterfly and backstroke as it includes butterfly kicks in all of them. Figures 4A,C,D also shows similar categories of propulsion, efficiency and duration/rate for the variables selected in this phase. For breaststroke technique, StPr phase includes one upper limbs cycle followed by a lower limb action and the posture related variables are also important compared to other categories (Figure 4B).

For Swim phase goal metrics, the average velocity per stroke is mainly associated with the duration of each cycle and the DPS. The Mean ( φ ) is also selected which relates to the swimmer’s posture. This selection is the same in all swimming techniques (Figures 4B–D) as the average velocity per stroke can be estimated by dividing the DPS by the cycle duration. The second goal metric of Swim phase is the average velocity of the whole phase. The variables related to the rate and number of strokes are more dominant as the swimmers increase the stroke rate for fast swimming. The SD ( A c c Y ), Mean ( φ ) and Range ( θ ) are other kinematic variables selected for estimating this goal metric, highlighting the significance of consistent propulsion and body posture in Swim phase. As a result, the three categories of duration/rate, posture and propulsion are more pronounced for estimating Swim phase average velocity in all techniques.

T 5 m , T 15 m and lap average velocity are dependent on more than one phase, and the variable selection algorithm picks a number of variables from each phase. Most of the selected variables for these goal metrics were already selected for relevant phases such as selecting Momentum ( A c c Y ) of Glid for T 5 m , Glid duration for T 15 m or stroke rate for lap average velocity, proving the significance of such variables even in a larger scale. Moreover, this shows the dependence of overall swimmer’s performance on their local performance in each phase. Among the techniques, T 5 m and T 15 m are estimated with a mixture of propulsion, posture and duration/rate categories in front crawl, breaststroke and butterfly, whereas during backstroke, the propulsion is dominant for both goal metrics. This emphasises on the tendency of the swimmers to longer underwater phases in backstroke (De Jesus et al., 2011), that asks for highly propulsive butterfly kicks.

With an overall observation on Figure 4, it is noted that the dominant categories in swimming phases are in line with the swimming phase biomechanics. Push phase asks for high propulsion, and Glid phase is more about keeping the right posture to avoid the drag. StPr phase is a combination of propulsion, posture and efficiency. Since the variable selection algorithm chooses the best variables for goal metric estimation, the variables which have the strongest relationship with the goal metrics are selected. As a result, we cannot assert that the rest of the variables are of no importance in swimming. For example, the DPS and cycle duration were dominant in estimating the average velocity per cycle in Swim phase, while no one can ignore the importance of orientation-related variables (e.g. θ angle) (Psycharakis and Sanders, 2010) or propulsion (Toussaint, 2002) in this phase. However, having a longer DPS in a shorter cycle duration is the result of correct orientation and high propulsion so the selected variables include other variable categories implicitly.

This study shows that a single sacrum IMU can provide kinematic variables relevant to the performance of the swimmer, in different techniques and phases for performance evaluation without using complex instrumentation such as speedometers or cameras. This offers new tools for training, where for example output of the IMU can be transferred to a mobile application for coaches and swimmers to easily follow the progress of the swimmers. Although using wearables induces more drag on swimmer body (Magalhaes et al., 2015), it needs extremely less effort than cameras for preparation and use, and it overcomes many of the limits of video-based systems (Callaway et al., 2010). The kinematic variables that were found dominant in our study were already analyzed using IMU of video-based methods but their relationship with the goal metrics were not studied. Swimmer’s posture during Push and Glid (Pereira et al., 2015), Glid duration (Guimaraes and Hay, 1985), StPr kicking rate (Shimojo et al., 2014), Swim stroke rate (Beanland et al., 2014) or DPS (Bächlin et al., 2008) are examples of the micro variables that were found relevant to performance, and we also found them significant in this study.

Both male and female swimmers were included for generating the results of this study to have a larger, more variant dataset. Comparing the swimmers due to their individual differences is out of the scope of our study. The estimations are done over all swimming velocities so the results are valid for 70–100 percent of swimmers’ paces. The synchronization error between the three systems of IMU, cameras and speedometer is a source of error in this study. Since tethered speedometer was used as reference in this study, the measurements were done over one-way trials without turn and turn motion is not evaluated. In this study, we used linear regression to have interpretable models highlighting the main variables correlated to the goal metrics. More complex non-linear models could be used if the goal is more accurate prediction of goal metrics.