# Potential of IMU Sensors in Performance Analysis of Professional Alpine Skiers

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## Abstract

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## 1. Introduction

- What is the best location on the body to attach an IMU sensor to capture the key characteristic of the turns in alpine skiing?
- From the selected location, how should data be analyzed to evaluate the skier’s performance, particularly the lateral-asymmetric test and the adaptation effect of training?

## 2. Literature

#### 2.1. Motion Analysis Using Different Experimental Devices

#### 2.2. Performance Analysis Using Different Experimental Devices

## 3. Description of the Experiment

## 4. IMU Location Analysis

- Pattern correlation analysis;
- Clustering analysis;
- Turn detection analysis.

#### 4.1. Pattern Correlation Analysis

#### 4.2. Clustering Analysis

#### 4.3. Turn Detection Analysis

## 5. Skiing Performance Analysis and Validation

- Lateral-asymmetric performance test;
- Test for the adaptation effect of training.

#### 5.1. Lateral-Asymmetric Performance Test

- Hypothesis test for the time duration:In the hypothesis test from Equation (6), the null hypothesis, ${H}_{0}$, is that there is no significant difference in the time duration between left and right turns $({\mu}_{L}^{*}={\mu}_{R}^{*})$. The alternative, ${H}_{1}$, is that there is a significant difference in the time duration between left and right turns $({\mu}_{L}^{*}\ne {\mu}_{R}^{*})$. Because the population variances of the time duration data for left and right turns are equal, the test statistic, ${T}_{0}^{*}$, is defined as the following Equation (8). In this equation, ${{\widehat{\mu}}_{L}}^{*}$ and ${{\widehat{\mu}}_{R}}^{*}$ indicate the sample means of the time duration in left and right turns, whereas ${{s}_{L}^{*}}^{2}$ and ${{s}_{R}^{*}}^{2}$ indicate the sample variances of the time duration in left and right turns. ${n}_{L}^{*}$ and ${n}_{R}^{*}$ are the number of samples for each dataset.$${T}_{0}^{*}=\frac{{{\widehat{\mu}}_{L}}^{*}-{{\widehat{\mu}}_{R}}^{*}}{{S}_{p}\sqrt{\frac{1}{{n}_{L}^{*}}+\frac{1}{{n}_{R}^{*}}}}\phantom{\rule{4pt}{0ex}}\mathrm{where}\phantom{\rule{4pt}{0ex}}{S}_{p}=\sqrt{\frac{({n}_{L}^{*}-1){{s}_{L}^{*}}^{2}+({n}_{R}^{*}-1){{s}_{R}^{*}}^{2}}{{n}_{L}^{*}+{n}_{R}^{*}-2}}$$Finally, the calculated test statistic is 4.27, and its absolute value, $|{T}_{0}^{*}|$, is larger than ${t}_{0.025}({n}_{L}^{*}+{n}_{R}^{*}-2=46)\cong 2.01$, such that it falls into the rejection region. Thus, the null hypothesis that there is a significant difference in the time duration between left and right turns is rejected.
- Hypothesis test for the maximum foot pressure ratio:Following the hypothesis test of Equation (7), the null hypothesis, ${H}_{0}$, is that there is no significant difference in the maximum foot pressure ratio between left and right turns $({\mu}_{L}^{+}={\mu}_{R}^{+})$. The alternative, ${H}_{1}$, is that there is a significant difference in the maximum foot pressure ratio between left and right turns $({\mu}_{L}^{+}\ne {\mu}_{R}^{+})$. Because the population variances of the maximum foot pressure ratio data for left and right turns are not equal, the test statistic, ${T}_{0}^{+}$, is defined as Equation (9). In this equation, ${{\widehat{\mu}}_{L}}^{+}$ and ${{\widehat{\mu}}_{R}}^{+}$ indicate the sample means of the maximum foot pressure ratio in left and right turns, whereas ${{s}_{L}^{+}}^{2}$ and ${{s}_{R}^{+}}^{2}$ indicate the sample variances of the maximum foot pressure ratio in left and right turns. ${n}_{L}^{+}$ and ${n}_{R}^{+}$ are the number of samples for each dataset.$${T}_{0}^{+}=\frac{{{\widehat{\mu}}_{L}}^{+}-{{\widehat{\mu}}_{R}}^{+}}{\sqrt{\frac{{{s}_{L}^{+}}^{2}}{{n}_{L}^{+}}+\frac{{{s}_{R}^{+}}^{2}}{{n}_{R}^{+}}}},\mathrm{where}\mathrm{the}\mathrm{degree}\mathrm{of}\mathrm{freedom}\phantom{\rule{4pt}{0ex}}{v}^{+}=\frac{{\left(\frac{{{s}_{L}^{+}}^{2}}{{n}_{L}^{+}}+\frac{{{s}_{R}^{+}}^{2}}{{n}_{R}^{+}}\right)}^{2}}{\frac{{\left(\frac{{{s}_{L}^{+}}^{2}}{{n}_{L}^{+}}\right)}^{2}}{{n}_{L}^{+}-1}+\frac{{\left(\frac{{{s}_{R}^{+}}^{2}}{{n}_{R}^{+}}\right)}^{2}}{{n}_{R}^{+}-1}}$$Finally, the calculated test statistic is 2.62, and its absolute value, $|{T}_{0}^{+}|$, is larger than ${t}_{0.025}({v}^{+}=35)\cong 2.03$, such that it falls into the rejection region. Thus, the null hypothesis that there is a significant difference in the maximum foot pressure ratio or the balance in weight shifts between left and right turns is rejected.

#### 5.2. Test for the Adaptation Effect of Training

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

IMU | Inertial measurement unit |

FIS | FÉDÉRATION INTERNATIONALE DE SKI |

3-D | 3-dimensional |

IoT | Internet of Things |

KNSU | Korea National Sports University |

K-S test | Kolmogorov–Smirnov test |

CV | Critical value |

## Appendix A: Hypothesis Tests for Lateral-Asymmetry Analysis

#### A.1. K-S Test

K-S Test | K-S Statistics | CV (α = 0.05) |
---|---|---|

Time duration (R) | 0.146 | 0.269 |

Time duration (L) | 0.231 | 0.269 |

Foot pressure ratio (R) | 0.106 | 0.269 |

Foot pressure ratio (L) | 0.186 | 0.269 |

**Figure A1.**Plot of the empirical cumulative distribution function (cdf) and the standard normal cdf for a visual comparison of the K-S test result.

#### A.2. Checking the Variance of Population Data

- Hypothesis test for the variances of the time duration data:Following Equation (A2), the null hypothesis, ${H}_{0}$, is that there is no significant difference in the population variances of the time durations between left and right turns ${{\sigma}_{L}^{*}}^{2}={{\sigma}_{R}^{*}}^{2}$. The alternative, ${H}_{1}$, is that there is a significant difference in the population variances of the time durations between left and right turns ${{\sigma}_{L}^{*}}^{2}\ne {{\sigma}_{R}^{*}}^{2}$. Finally, the calculated test statistic, ${F}_{0}^{*}$, is 0.743, that the null hypothesis cannot be rejected because ${F}_{0.975}(23,23)=0.43<{F}_{0}^{*}=0.743<{F}_{0.025}(23,23)=2.31$.Thus, there is no significant difference in the population variances of the time duration between left and right turns.
- Hypothesis test for the variances of the maximum foot pressure ratio:Following Equation (A2), the null hypothesis, ${H}_{0}$, is that there is no significant difference in the population variance of the maximum foot pressure ratio between left and right turns ${{\sigma}_{L}^{+}}^{2}={{\sigma}_{R}^{+}}^{2}$. The alternative, ${H}_{1}$, is that there is a significant difference in the population variance of the maximum foot pressure ratio between left and right turns (${{\sigma}_{L}^{+}}^{2}\ne {{\sigma}_{R}^{+}}^{2}$). Finally, the calculated test statistic, ${F}_{0}^{+}$, is 3.40 that the null hypothesis is rejected because ${F}_{0.025}(23,23)=2.31<{F}_{0}^{+}=3.40$.Thus, there is a significant difference in the population variances of the maximum foot pressure ratio between left and right turns.

## Appendix B: Adaptation Effect of Training

- Hypothesis test for the number of trials vs. time duration:In the hypothesis test from Equation (B1), the null hypothesis, ${H}_{0}$, is that there is no significant correlation between the number of trials and the time duration. The alternative, ${H}_{1}$, is that there is a significant correlation between the number of trials and the time duration.Finally, the calculated t-statistics is $|-2.373|=2.373$ with ${r}^{*}=-0.696$ and the degree of freedom ${n}^{*}-2=6$; with a significance level (α) of 0.10, ${T}_{0.05}=1.943$. Because ${T}_{0.05}=1.943<{T}^{*}=2.373$, the null hypothesis is rejected. By this analysis, the causal relationship between the number of trials and the time duration is confirmed.

## Appendix C: Summary of the Survey

Question 1: Are there any personal characteristics that might affect the performance? |

• It is quite demanding to maintain against the forces acting on the left foot or leg, because of the aftereffects of inveteratedisc surgery on the left lumbar. |

• For the best performance, some period of adaptation to the experimental equipment and the course would be required. |

• Thorough inspection of the snow surface is mandatory for the best performance (i.e., distribution and quality of snow on the surface). |

• Because I could not thoroughly inspect the experimental course, I expected that this would have a negative effect on performance. |

Question 2: Are there any comments for the experiments? |

• Because the experimental course was short and enough time was given for rest after each trial, there was less effect of fatigue when performing the turns during the whole experiment. Rather, I felt that my performances improved as I gradually adapted to the experimental devices and factors, such as snow quality and snow distribution. |

• I believe that the performance was greatly affected by the quality of the snow among many other factors that might affect performance. |

• In my point of view, there was more snow on the surface than ice, which is not a favorable environment to perform carving turns. |

• The pressure sensors in the boots did not influence significantly the performance during the experiments. However, I do not want to use them for daily training. |

• The IMU sensors attached to the feet distracted from the control of skis while performing the turns. |

Question 3: Evaluate yourself in a range from one to 10 (10 for the best) for each trial. |

• Please refer to Table 6 in Section 5 |

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**Figure 5.**Example of the normalized IMU data (Trial 8) for the roll motion; the x-axis is the time, and the y-axis indicates the normalized roll angle, ${M}_{l}^{t}$.

**Figure 8.**The roll angle pattern from the IMU at the pelvis: x- and y-axes represent the time and angle of the roll motion, respectively.

Specification (IMU) | |

Channel | Up to 18 sensors |

Static accuracy | $\pm 0.{4}^{\circ}$ |

Dynamic accuracy | $\pm 1.{2}^{\circ}$ |

Sampling frequency | 100 Hz |

Data output | Joint angles, acceleration, quaternions |

Specification (Foot Pressure) | |

Channel | 13 sensors per insole |

Sensitivity | 0.25 N/cm${}^{2}$ |

Coverage | Up to 50% |

Range | 0.0∼40.0 N/cm${}^{2}$ |

Sampling frequency | 50 Hz |

Principle | Capacitive |

Category | Trial 1 | Trial 2 | Trial 3 | Trial 4 | Trial 5 | Trial 6 | Trial 7 | Trial 8 | Mean | Median |
---|---|---|---|---|---|---|---|---|---|---|

Head | 0.76 | 0.85 | 0.79 | 0.75 | 0.78 | 0.76 | 0.84 | 0.75 | 0.78 | 0.77 |

Upper Spine | 0.71 | 0.89 | 0.88 | 0.88 | 0.88 | 0.88 | 0.93 | 0.85 | 0.86 | 0.88 |

Lower Spine | 0.72 | 0.43 | 0.88 | 0.88 | 0.88 | 0.32 | 0.93 | 0.85 | 0.74 | 0.87 |

Pelvis | 0.74 | 0.91 | 0.88 | 0.88 | 0.89 | 0.89 | 0.92 | 0.85 | 0.87 | 0.88 |

Upper Arm (L) | 0.70 | 0.71 | 0.68 | 0.69 | 0.72 | 0.70 | 0.74 | 0.70 | 0.71 | 0.70 |

Upper Arm (R) | 0.48 | 0.69 | 0.73 | 0.43 | 0.60 | 0.44 | 0.79 | 0.63 | 0.60 | 0.61 |

Forearm (L) | 0.72 | 0.74 | 0.72 | 0.74 | 0.55 | 0.73 | 0.75 | 0.69 | 0.70 | 0.73 |

Forearm (R) | 0.50 | 0.66 | 0.70 | 0.43 | 0.53 | 0.42 | 0.78 | 0.58 | 0.58 | 0.56 |

Hand (L) | 0.40 | -0.13 | 0.51 | 0.61 | 0.52 | 0.21 | 0.14 | 0.16 | 0.30 | 0.31 |

Hand (R) | 0.49 | 0.64 | 0.53 | 0.50 | 0.61 | 0.67 | 0.48 | 0.48 | 0.55 | 0.52 |

Thigh (L) | 0.69 | 0.91 | 0.88 | 0.88 | 0.90 | 0.89 | 0.92 | 0.87 | 0.87 | 0.89 |

Thigh (R) | 0.74 | 0.84 | 0.84 | 0.80 | 0.83 | 0.79 | 0.89 | 0.85 | 0.82 | 0.84 |

Shank (L) | 0.78 | 0.89 | 0.84 | 0.82 | 0.84 | 0.87 | 0.89 | 0.85 | 0.85 | 0.84 |

Shank (R) | 0.71 | 0.89 | 0.87 | 0.87 | 0.86 | 0.88 | 0.89 | 0.85 | 0.85 | 0.87 |

Foot (L) | 0.73 | 0.87 | 0.86 | 0.82 | 0.85 | 0.86 | 0.88 | 0.84 | 0.84 | 0.86 |

Foot (R) | 0.73 | 0.90 | 0.88 | 0.84 | 0.86 | 0.89 | 0.90 | 0.85 | 0.86 | 0.87 |

Average | 0.66 | 0.72 | 0.78 | 0.74 | 0.75 | 0.70 | 0.79 | 0.72 | 0.73 | 0.75 |

Location | Trial 1 | Trial 2 | Trial 3 | Trial 4 | Trial 5 | Trial 6 | Trial 7 | Trial 8 | Total (Avg.) |
---|---|---|---|---|---|---|---|---|---|

Upper Spine | 100% | 100% | 100% | 129% | 100% | 100% | 100% | 100% | 104% |

Lower Spine | 100% | 0% | 100% | 100% | 100% | 0% | 100% | 100% | 75% |

Pelvis | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

Thigh (L) | 129% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 104% |

Thigh (R) | 200% | 129% | 114% | 100% | 171% | 114% | 286% | 171% | 161% |

Shank (L) | 86% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 98% |

Shank (R) | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

Foot (L) | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

Foot (R) | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |

Turns | Turn 1 (R) | Turn 3 (R) | Turn 5 (R) | |||

Attributes | Time Duration (s) | Max Pressure Ratio | Time Duration (s) | Max Pressure Ratio | Time Duration (s) | Max Pressure Ratio |

Trial 1 | 2.32 | 0.89 | 2.07 | 0.85 | 2.69 | 0.85 |

Trial 2 | 2.25 | 0.94 | 1.71 | 0.88 | 1.86 | 0.78 |

Trial 3 | 2.49 | 0.80 | 2.02 | 0.72 | 1.94 | 0.72 |

Trial 4 | 2.62 | 0.93 | 1.79 | 0.78 | 2.14 | 0.77 |

Trial 5 | 2.34 | 0.93 | 1.81 | 0.77 | 1.74 | 0.76 |

Trial 6 | 2.30 | 0.92 | 1.80 | 0.83 | 2.05 | 0.70 |

Trial 7 | 2.28 | 0.83 | 1.85 | 0.82 | 1.74 | 0.67 |

Trial 8 | 2.39 | 0.89 | 1.97 | 0.69 | 1.75 | 0.66 |

Turns | Turn 2 (L) | Turn 4 (L) | Turn 6 (L) | |||

Attributes | Time Duration (s) | Max Pressure Ratio | Time Duration (s) | Max Pressure Ratio | Time Duration (s) | Max Pressure Ratio |

Trial 1 | 2.05 | 0.81 | 1.62 | 0.92 | 3.10 | 0.97 |

Trial 2 | 1.82 | 0.88 | 1.57 | 0.83 | 1.50 | 0.89 |

Trial 3 | 1.80 | 0.88 | 1.62 | 0.83 | 1.55 | 0.87 |

Trial 4 | 1.72 | 0.87 | 1.57 | 0.87 | 1.39 | 0.89 |

Trial 5 | 1.61 | 0.81 | 1.52 | 0.76 | 1.46 | 0.87 |

Trial 6 | 1.85 | 0.76 | 1.39 | 0.85 | 1.74 | 0.84 |

Trial 7 | 1.80 | 0.87 | 1.51 | 0.88 | 1.53 | 0.88 |

Trial 8 | 1.77 | 0.86 | 1.42 | 0.89 | 1.50 | 0.90 |

IMU Sensor | Foot Pressure Sensors | ||
---|---|---|---|

Null (${H}_{0}$) | ${\mu}_{L}^{*}={\mu}_{R}^{*}$ | Null (${H}_{0}$) | ${\mu}_{L}^{+}={\mu}_{R}^{+}$ |

Alternative (${H}_{1}$) | ${\mu}_{L}^{*}\ne {\mu}_{R}^{*}$ | Alternative (${H}_{1}$) | ${\mu}_{L}^{+}\ne {\mu}_{R}^{+}$ |

Critical points ($\alpha =0.05$) | 2.01 | Critical points ($\alpha =0.05$) | 2.03 |

t-statistics | 4.27 | t-statistics | 2.62 |

Results | ${H}_{0}$ rejected | Results | ${H}_{0}$ rejected |

Trial | Trial 1 | * | Trial 2 | Trial 3 | Trial 4 | Trial 5 | Trial 6 | Trial 7 | Trial 8 |
---|---|---|---|---|---|---|---|---|---|

Self-assessment (out of 10) | 2.5 | 3.5 | 3.5 | 4.5 | 5 | 5 | 5 | 5 | 6 |

Time duration | 13.85 | N/A | 10.71 | 11.42 | 11.23 | 10.48 | 11.13 | 10.71 | 10.80 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yu, G.; Jang, Y.J.; Kim, J.; Kim, J.H.; Kim, H.Y.; Kim, K.; Panday, S.B.
Potential of IMU Sensors in Performance Analysis of Professional Alpine Skiers. *Sensors* **2016**, *16*, 463.
https://doi.org/10.3390/s16040463

**AMA Style**

Yu G, Jang YJ, Kim J, Kim JH, Kim HY, Kim K, Panday SB.
Potential of IMU Sensors in Performance Analysis of Professional Alpine Skiers. *Sensors*. 2016; 16(4):463.
https://doi.org/10.3390/s16040463

**Chicago/Turabian Style**

Yu, Gwangjae, Young Jae Jang, Jinhyeok Kim, Jin Hae Kim, Hye Young Kim, Kitae Kim, and Siddhartha Bikram Panday.
2016. "Potential of IMU Sensors in Performance Analysis of Professional Alpine Skiers" *Sensors* 16, no. 4: 463.
https://doi.org/10.3390/s16040463