反向跳躍中肌肉力分布之最佳化估算：階段性分析與局部肌電圖驗證

Abstract

本論文針對人體生物力學領域中，無法直接量測之肌肉力問題，提出一套結合穿戴式感測技術與最佳化演算法的肌肉力估算架構，並以反向跳(Countermovement Jump)動作為研究對象，發展可應用於非實驗室環境下的動作分析方法。傳統肌肉力分析多仰賴實驗室設備與固定目標函數，難以反映動作階段變化與實際應用需求。本研究突破此侷限，設計具階段性調整能力的多目標函數模型，並結合慣性測量單元(IMU)感測資料，建立一套適用於遠距復健及日常運動場域的分析流程。

本研究首先建立簡化人體肌肉骨骼模型，並利用希爾式肌肉模型模擬肌肉力學行為，將反向跳動作分為下蹲與推蹬兩階段分別進行最佳化計算。分析過程中，針對目標函數中各子目標(如力矩誤差、肌肉應力、功與功率)進行權重設計與測試，以提升模擬結果的生理合理性與動力學精度。最終透過肌電圖(EMG)驗證模擬結果之啟動時機與趨勢，確保模型具備生理一致性。

研究結果顯示，所提出之方法能合理分配各肌肉於不同動作階段的施力，並展現良好的生理解釋力。多層次分析證實參數設置與目標函數彈性有助於提升模型可信度與應用潛力。

綜合而言，本論文建立了一套具生理一致性與動作分析能力的肌肉力模擬架構，為下肢肌群功能分析提供重要基礎，並具備高度擴充性與遠距應用潛力，對運動科學與復健領域具有實質貢獻。

This thesis addresses the challenge of estimating muscle forces, which cannot be directly measured in the field of human biomechanics, by proposing a framework that integrates wearable sensing technology with optimization algorithms. Focusing on the countermovement jump (CMJ) as the research subject, the study develops a motion analysis method applicable outside laboratory environments. Traditional muscle force analysis often relies on laboratory equipment and fixed objective functions, which limits its ability to reflect changes across movement phases and meet practical application needs. To overcome these limitations, this research designs a multi-objective function model with phase-specific adjustment capabilities and incorporates IMU sensor data to establish an analysis process suitable for remote rehabilitation and everyday sports scenarios. The methodology involves constructing a simplified human musculoskeletal model and using the Hill-type muscle model to simulate muscle mechanics, dividing the countermovement jump into squatting and push-off phases for separate optimization calculations. During analysis, weights for each sub-objective—such as moment error, muscle stress, work, and power—are designed and tested to enhance the physiological plausibility and dynamic accuracy of the simulation results. Electromyography (EMG) is used to verify the timing and trends of simulated muscle activation, ensuring physiological consistency of the model. The results demonstrate that the proposed method can reasonably allocate muscle forces across different movement phases and exhibits strong physiological interpretability. Multi-level analysis confirms that flexible parameter settings and objective functions improve the model’s credibility and application potential. In conclusion, this thesis establishes a muscle force simulation framework with physiological consistency and motion analysis capabilities, providing a significant foundation for lower limb muscle function analysis and offering high extensibility and potential for remote applications, thereby making a substantial contribution to sports science and rehabilitation.