## 4 Evaluation
### Experiment Procedure  
To evaluate the machine learning models for estimating knee flexion and knee valgus angles, participants wore the supporter device on both knees and performed various movements. The participants performed movements that changed knee flexion and valgus angles while wearing the supporter device shown in Figure 3, and the stretch sensor values during these changes were collected. The movements conducted in the experiment were chosen in consultation with experts in rehabilitation and sports medicine, referencing ACL injury screening tests [8; 15] and rehabilitation tests [17; 30]. The following 13 movements were selected, with examples shown in Figure 4:1. Flexion movement (Squat);
2. Maximizing knee valgus at 30\({}^{\circ}\) flexion;
3. Maximizing knee valgus at 60\({}^{\circ}\) flexion;
4. Maximizing knee valgus at 90\({}^{\circ}\) flexion;
5. Walking;
6. Running;
7. Drop jump from a 30 cm platform;
8. Single-leg hop;
9. Three single-leg hops;
10. Three consecutive jumps;
11. Three single-leg cross jumps;
12. Cutting to the right;
13. Cutting to the left. Movements involving a single leg were performed on both legs, and each movement was repeated three times consecutively. The device was not removed between movements. The sampling frequency of the stretch sensors used in this experiment was 100 Hz. The experimental environment is shown in Figure 5. To obtain ground truth data, a VICON NEXUS 2 3D motion analysis system (Vicon Motion Systems, Oxford, UK) consisting of 16 infrared cameras was used to measure at a sampling frequency of 100 Hz. Infrared reflective markers were attached to 43 landmarks on the body. The ground truth knee joint angles were obtained by creating segments for the left and right feet, lower legs, thighs, and pelvis from 24 markers on the lower body, as shown in Figure 6, and the Euler angles between the thigh and lower leg segments were calculated. Figure 4: Movement examples. White arrows indicate the direction of movement. Figure 5: Experimental environment. The calibration procedure was as follows: Mask all unnecessary reflections from the infrared cameras. In the capture volume, wave an active LED want to ensure that the markers are visible to the cameras throughout the entire area where 3D data will be captured. The system continues calibration until sufficient calibration information is acquired, with the mean calibration residuals for trials remaining under 1.00 mm. The laboratory coordinate system was defined using a right-handed coordinate system. Marker coordinates were filtered using a low-pass Butterworth filter of the fourth order with a cut-off frequency of 6 Hz to remove noise. Gaps in the marker data were interpolated using the Pattern Fill or Rigid Body Fill methods [31,32]. Infrared-reflecting markers, 14 mm in diameter, were attached based on anatomical landmarks by two physical therapists, each with over ten years of clinical experience and expertise in motion analysis. The marker set was referenced from our previous study [33]. The local coordinate system for the femur was established with the origin at the midpoint between the lateral and medial epicondyles. The hip joint center was calculated based on a previous study [34], using the anterior superior iliac spine and the greater trochanter. The Z-axis was defined as the line connecting the hip joint center to the origin. The X-axis was defined as the line connecting the lateral and medial epicondyles. The Y-axis was orthogonal to both the X and Z axes. For the tibia, the local coordinate system was established with the origin at the midpoint between the lateral and medial condyles. The Z-axis was defined as the line connecting the midpoint of the medial and lateral malleoli to the origin. The X-axis was defined as the line connecting the lateral and medial condyles. The Y-axis was orthogonal to both the X and Z axes. Using these local coordinate systems, the knee joint angles were calculated based on Euler angles with an XYZ rotation sequence.