步態分析應用於多種領域之中，如人物辨識、臨床醫學、運動科學等。而其資訊的取得，在現有系統中主要透過攝影機、光學捕捉、壓力感測等的方式來進行蒐集，此些方法雖然能夠提供極為準確的步態資訊，卻也有著場地限制、穿戴麻煩、設備成本昂貴的缺點，使其在應用層面上會受到限制。

在本研究中，我們嘗試使用價格低廉的慣性感測元件(IMU)，希望藉由其非接觸型且可攜帶的特性，使其應用範圍能夠廣泛至日常生活中。實驗中我們配戴1個IMU於左腳上，蒐集其測量所得的左腳加速度和角速度等6軸資訊，以此來估計與人體動作、足部狀態、運動傷害等有重大關聯的足底壓力二大資訊：垂直地面反作用力 (vGRF)和步態壓力中心(COP)。

本研究中，我們蒐集6位健康受試者行走時的左腳IMU資訊，並經由我們設計的演算法處理以及不同的機器學習模型訓練，來預測vGRF和COP的特性，並以F-scan壓力感測系統所蒐集的vGRF和COP作為真實情況來進行比對。為考量未來實時監測、需採edge computing的使用情境，其資料量與運算複雜度是主要考量。在vGRF預測上，我們使用長短期記憶模型進行預測，其預測之方均根誤差為0.14倍的體重重量、正規化方均根誤差為8.68%；而在COP偏移量預測上，使用長短期記憶模型進行預測，其左右偏移量的正規化方均根誤差為16.35%；使用卷積神經網路進行預測，其左右偏移量的正規化方均根誤差為17.29%；而使用類神經網路模型預測COP偏移量之軌跡多項式係數的情況下，其左右偏移量的正規化方均根誤差為19.79%。

Gait analysis is widely applied for different applications such as human detection, clinical medicine, and sport science. Commonly the video, optical, and pressure sensing techniques, are used for these purposes. However, for long-term monitoring, these systems are limited with equipment setup, operation condition, and cost.

We select the inertial measurement unit (IMU) as the sensing device in this research. With IC technologies today IMU can be low power and wearable. Many works have applied this sensing method for kinetics based on the acceleration and angular velocity. We plan to use IMU extensively to estimate the pressure information like vertical ground reaction force (vGRF) and center of pressure (COP) those were commonly detected by pressure sensors.

In this research, we collect left foot IMU data during walking from 6 healthy participants, apply different machine learning models to predict vGRF and COP, and compare the results with ground truth collected from the pressure sensors. For vGRF estimation, by long short-term memory (LSTM) model, the normalized root mean square error (NRMSE) is equal to 8.68%. For COP estimation, the long short-term memory (LSTM), convolutional neural network (CNN) model, and trajectory polynomial with artificial neural network (ANN) model, NRMSE in medial-lateral (ML) direction are 16.35%, 17.29%, and 19.79% respectively.

Abstract............................ii
目錄................................iv
圖目錄.............................vii
表目錄...............................x

第一章 緒論.....................2
1.1 研究動機.....................2
1.2 研究目的.....................3
1.3 研究架構.....................3

第二章 文獻回顧與討論..........................................4
2.1 步態運動之步態週期..........................................4
2.2 步態運動的特徵..............................................6
2.3 慣性感測元件(Inertial Measurement Unit，IMU)與步態預測......8
2.4 多感測元件同步整合.........................................10
2.5 章節總結...................................................10

第三章 實驗設計與資料蒐集..............12
3.1 實驗設備與受測者....................12
3.1.1 IMU...............................12
3.1.2 F-scan壓力感測鞋墊................13
3.1.3 受測者............................14
3.2 前置實驗............................15
3.3 實驗裝置佩戴及實驗流程..............16
3.3.1 實驗裝置佩戴......................16
3.3.2 F-scan系統個人化校準..............17
3.3.3 系統資料同步訊號..................18
3.3.4 實驗行走流程......................18
3.3.5 實驗資料蒐集結果..................18

第四章 機器學習演算法設計與訓練流程...........20
4.1 vGRF以機器學習訓練流程.....................22
4.1.1 事件偵測.................................23
4.1.2 資料重組.................................24
4.1.3 特徵提取.................................25
4.1.4 長短期記憶(LSTM)模型預測.................26
4.2 COP偏移量機器學習訓練流程..................30
4.2.1 事件偵測.................................31
4.2.2 資料重組.................................31
4.2.3 特徵提取.................................32
4.2.4 模型預測.................................32
4.3 COP軌跡曲線係數機器學習訓練流程............35
4.3.1 事件偵測.................................35
4.3.2 資料重組.................................36
4.3.3 特徵提取.................................36
4.3.4 模型預測.................................37
4.4 COP機器學習模型使用之損失函數設計..........39

第五章 驗證及測試結果與分析....................................42
5.1 vGRF預測....................................................42
5.1.1 vGRF預測之訓練集、驗證集和測試集分配......................42
5.1.2 vGRF預測之驗證集表現......................................43
5.1.3 vGRF預測之測試集流程改變..................................46
5.1.4 vGRF預測之測試結果........................................47
5.1.5 vGRF預測指標與分析........................................54
5.1.6 Impact force與預測........................................57
5.2 COP偏移量預測...............................................58
5.2.1 COP偏移量預測之訓練集、驗證集和測試集分配.................58
5.2.2 COP偏移量預測之驗證集表現.................................59
5.2.3 COP偏移量預測及COP偏移量軌跡多項式預測之測試集流程改變....62
5.2.4 COP偏移量預測之測試結果...................................65
5.2.5 COP偏移量預測指標與分析...................................68
5.2.6 特殊步伐加入後之測試結果..................................70
5.3 研究結果之比較..............................................72

第六章 結論與未來工作..........74
6.1 結論........................74
6.2 研究限制與改善方法..........75
6.3 未來工作....................76

參考文獻........................78

[1] J. Taborri, E. Palermo, S. Rossi, and P. Cappa, “Gait Partitioning Methods: A Systematic Review,” Sensors, vol. 16, no. 1, p. 66, Jan. 2016.
[2] J. Perry and J. M Burnfield, "Gait analysis: normal and pathological function. 2nd," 2010.
[3] R. Headon and R. Curwen, “Recognizing movements from the ground reaction force,” Proceedings of the 2001 workshop on Percetive user interfaces, 2001.
[4] T. Keller, A. Weisberger, J. Ray, S. Hasan, R. Shiavi, and D. Spengler, “Relationship between vertical ground reaction force and speed during walking, slow jogging, and running,” Clinical Biomechanics, vol. 11, no. 5, pp. 253–259, Jul. 1996.
[5] S. P. Messier, C. Legault, C. R. Schoenlank, J. J. Newman, D. F. Martin, and P. Devita, “Risk Factors and Mechanisms of Knee Injury in Runners,” Medicine & Science in Sports & Exercise, vol. 40, no. 11, pp. 1873–1879, Nov. 2008.
[6] L. Wong, A. Hunt, J. Burns, and J. Crosbie, “Effect of Foot Morphology on Center-of-Pressure Excursion During Barefoot Walking,” Journal of the American Podiatric Medical Association, vol. 98, no. 2, pp. 112–117, Mar. 01, 2008.
[7] A. Ruhe, R. Fejer, and B. Walker, “Center of pressure excursion as a measure of balance performance in patients with non-specific low back pain compared to healthy controls: a systematic review of the literature,” European Spine Journal, vol. 20, no. 3, pp. 358–368, Aug. 19, 2010.
[8] C. J. Hass, D. E. Waddell, R. P. Fleming, J. L. Juncos, and R. J. Gregor, “Gait Initiation and Dynamic Balance Control in Parkinson’s Disease,” Archives of Physical Medicine and Rehabilitation, vol. 86, no. 11, pp. 2172–2176, Nov. 2005.
[9] A. H. Abdul Razak, A. Zayegh, R. K. Begg, and Y. Wahab, “Foot Plantar Pressure Measurement System: A Review,” Sensors, vol. 12, no. 7, pp. 9884–9912, Jul. 2012.
[10] A. Hollinger, “Evaluation of Commercial Force-Sensing Resistors,” 2006.
[11] C. Ahmadizadeh and C. Menon, “Investigation of Regression Methods for Reduction of Errors Caused by Bending of FSR-Based Pressure Sensing Systems Used for Prosthetic Applications,” Sensors, vol. 19, no. 24, p. 5519, Dec. 2019.
[12] A. Ancillao, S. Tedesco, J. Barton, and B. O’Flynn, “Indirect Measurement of Ground Reaction Forces and Moments by Means of Wearable Inertial Sensors: A Systematic Review,” Sensors, vol. 18, no. 8, p. 2564, Aug. 05, 2018.
[13] A. Karatsidis, G. Bellusci, H. Schepers, M. de Zee, M. Andersen, and P. Veltink, “Estimation of Ground Reaction Forces and Moments During Gait Using Only Inertial Motion Capture,” Sensors, vol. 17, no. 12, p. 75, Dec. 31, 2016.
[14] M. Aurbach, K. Wagner, F. Süß, and S. Dendorfer, “Implementation and Validation of Human Kinematics Measured Using IMUs for Musculoskeletal Simulations by the Evaluation of Joint Reaction Forces,” IFMBE Proceedings, pp. 205–211, 2017.
[15] K. J.-H. Ngoh, D. Gouwanda, A. A. Gopalai, and Y. Z. Chong, “Estimation of vertical ground reaction force during running using neural network model and uniaxial accelerometer,” Journal of Biomechanics, vol. 76, pp. 269–273, Jul. 2018.
[16] M. Lee and S. Park, “Estimation of Three-Dimensional Lower Limb Kinetics Data during Walking Using Machine Learning from a Single IMU Attached to the Sacrum,” Sensors, vol. 20, no. 21, p. 6277, Nov. 04, 2020.
[17] F. J. Wouda et al., “Estimation of Vertical Ground Reaction Forces and Sagittal Knee Kinematics During Running Using Three Inertial Sensors,” Frontiers in Physiology, vol. 9, Mar. 22, 2018.
[18] X. Jiang, C. Napier, B. Hannigan, J. J. Eng, and C. Menon, “Estimating Vertical Ground Reaction Force during Walking Using a Single Inertial Sensor,” Sensors, vol. 20, no. 15, p. 4345, Aug. 04, 2020.
[19] J. Podobnik, D. Kraljić, M. Zadravec, and M. Munih, “Centre of Pressure Estimation during Walking Using Only Inertial-Measurement Units and End-To-End Statistical Modelling,” Sensors, vol. 20, no. 21, p. 6136, Oct. 28, 2020.
[20] S. Blum, D. Hölle, M. G. Bleichner, and S. Debener, “Pocketable Labs for Everyone: Synchronized Multi-Sensor Data Streaming and Recording on Smartphones with the Lab Streaming Layer,” Sensors, vol. 21, no. 23, p. 8135, Dec. 05, 2021.
[21] A. G. Herbert-Copley, E. H. Sinitski, E. D. Lemaire, and N. Baddour, “Temperature and measurement changes over time for F-Scan sensors,” 2013 IEEE International Symposium on Medical Measurements and Applications (MeMeA). IEEE, May 2013.
[22] E. Morin, S. Reid, J. M. Eklund, H. Lay, Y. Lu, J. Stevenson, and J. T. Bryant, “Comparison of ground reaction forces measured with a force plate, FScan and multiple individual force sensors,” Ergonomics Research Group, Queen’s University, Kingston, 2002.
[23] A. R. Anwary, H. Yu and M. Vassallo, "Optimal Foot Location for Placing Wearable IMU Sensors and Automatic Feature Extraction for Gait Analysis," IEEE Sensors Journal, vol. 18, no. 6, pp. 2555-2567, March. 15, 2018
[24] C. Tjhai and K. O’Keefe, “Step-size estimation using fusion of multiple wearable inertial sensors,” 2017 International Conference on Indoor Positioning and Indoor Navigation (IPIN). IEEE, Sep. 2017.
[25] J. Rueterbories, E. G. Spaich, B. Larsen, and O. K. Andersen, “Methods for gait event detection and analysis in ambulatory systems,” Medical Engineering & Physics, vol. 32, no. 6, pp. 545–552, Jul. 2010.
[26] A. Choi, H. Jung, and J. H. Mun, “Single Inertial Sensor-Based Neural Networks to Estimate COM-COP Inclination Angle During Walking,” Sensors, vol. 19, no. 13, p. 2974, Jul. 05, 2019.
[27] C. Tudor-Locke, S. M. Camhi, C. Leonardi, W. D. Johnson, P. T. Katzmarzyk, C. P. Earnest, T. S. Church, “Patterns of adult stepping cadence in the 2005–2006 NHANES,” Preventive Medicine, vol. 53, no. 3, pp. 178–181, Sep. 2011.
[28] S. Hochreiter and J. Schmidhuber, “Long Short-Term Memory,” Neural Computation, vol. 9, no. 8, pp. 1735–1780, Nov. 01, 1997.
[29] N. Weber, (2017). Why LSTMs Stop Your Gradients From Vanishing: A View from the Backwards Pass. Retrieved from:
https://weberna.github.io/blog/2017/11/15/LSTM-Vanishing-Gradients.html#fn:3
[30] H. Ismail Fawaz, G. Forestier, J. Weber, L. Idoumghar, and P.-A. Muller, “Deep learning for time series classification: a review,” Data Mining and Knowledge Discovery, vol. 33, no. 4, pp. 917– 963, Mar. 02, 2019.
[31] V. Racic, A. Pavic, and J. M. W. Brownjohn, “Experimental identification and analytical modelling of human walking forces: Literature review,” Journal of Sound and Vibration, vol. 326, no. 1–2, pp. 1–49, Sep. 2009.
[32] D. H. K. Chow, A. D. Holmes, C. K. L. Lee, and S. W. Sin, “The Effect of Prosthesis Alignment on the Symmetry of Gait in Subjects with Unilateral Transtibial Amputation,” Prosthetics & Orthotics International, vol. 30, no. 2, pp. 114–128, Aug. 2006.
[33] P. Senin, “Dynamic Time Warping Algorithm Review,” Information and ComputerScience Department University of Hawaii, USA 855(1-23), 40, Dec. 2008.
[34] P. Pathak and J. Ahn, “A Pressure-Pad-Embedded Treadmill Yields Time-Dependent Errors in Estimating Ground Reaction Force during Walking,” Sensors, vol. 21, no. 16, p. 5511, Aug. 17, 2021.
[35] L. Yung-Hui and H. Wei-Hsien, “Effects of shoe inserts and heel height on foot pressure, impact force, and perceived comfort during walking,” Applied Ergonomics, vol. 36, no. 3, pp. 355–362, May 2005.
[36] M. W. Whittle, “Generation and attenuation of transient impulsive forces beneath the foot: a review,” Gait and Posture, vol. 10, no. 3, pp. 264–275, Dec. 1999.
[37] C. D. Samaan, M. J. Rainbow, and I. S. Davis, “Reduction in ground reaction force variables with instructed barefoot running,” Journal of Sport and Health Science, vol. 3, no. 2, pp. 143–151, Jun. 2014.
[38] C. D. Pollard, J. A. Ter Har, J. J. Hannigan, and M. F. Norcross, “Influence of Maximal Running Shoes on Biomechanics Before and After a 5K Run,” Orthopaedic Journal of Sports Medicine, vol. 6, no. 6, Jun. 01, 2018.