Article(id=1244321221911883983, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, articleNumber=null, orderNo=null, doi=10.16156/j.1004-7220.2025.05.028, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1740844800000, receivedDateStr=2025-03-02, revisedDate=1742832000000, revisedDateStr=2025-03-25, acceptedDate=null, acceptedDateStr=null, onlineDate=1774598897673, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774598897673, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774598897673, creator=13701087609, updateTime=1774598897673, updator=13701087609, issue=Issue{id=1244321215637209904, tenantId=1146029695717560320, journalId=1244284848500682798, year='2025', volume='40', issue='5', pageStart='1079', pageEnd='1366', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774598896178, creator=13701087609, updateTime=1774599509568, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244323788452639476, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244323788452639477, tenantId=1146029695717560320, journalId=1244284848500682798, issueId=1244321215637209904, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1295, endPage=1302, ext={EN=ArticleExt(id=1244321222226456788, articleId=1244321221911883983, tenantId=1146029695717560320, journalId=1244284848500682798, language=EN, title=Estimating Running Ground Reaction Force Curves Using Long Short-Term Memory Neural Network and Markerless Motion Capture System, columnId=1244321216404767539, journalTitle=Journal of Medical Biomechanics, columnName=Original Articles, runingTitle=null, highlight=null, articleAbstract=
Objective

By applying the long short-term memory (LSTM) neural network model and using lower body landmark coordinates obtained from a markerless motion capture system as inputs, to estimate ground reaction force (GRF) curves during running.

Methods

The video images and GRF data of 59 amateur runners during running were collected by the markerless motion capture system and three-dimensional (3D) force plates. The LSTM model was established, and the 3D coordinates of 11 lower body landmarks, obtained via the Theia3D markerless system, were used as inputs to estimate the 3D GRF curves during the stance of running. The estimation performance was evaluated using correlation coefficients r, root mean square error (RMSE), and normalized root mean square error (nRMSE) by comparing LSTM model estimation and force plate measurement. Statistical parametric mapping was used to analyze differences in GRF curves estimated by the LSTM model and measured by the force plate, while paired t-tests were used to assess differences in GRF characteristics between model estimation and actual measurement.

Results

A strong correlation (r>0.85, P<0.001) and lower error (RMSE<0.3 body weight, nRMSE<15%) was found between the LSTM model estimation and actual measurements. No significant difference was found in GRF curve intervals between LSTM model estimation and actual measurements. There was no significant difference in GRF characteristics between LSTM model estimation and actual measurements (P>0.05).

Conclusions

Based on the LSTM model, the 3D GRF curves can be effectively estimated by lower body landmark coordinates obtained from the makerless motion capture system, thereby acquiring the highly accurate GRF characteristics. The LSTM model developed in this study can be used to monitor injury risks during running in outdoor environments.

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目的

应用长短时记忆神经网络(long short-term memory,LSTM)模型,以无标记动作捕捉系统所得下肢关节点坐标作为输入变量,估算跑步过程中的地面反作用力(ground reaction forces,GRF)曲线。

方法

采用无标记动作捕捉系统和三维测力台同步采集59名业余跑者跑步动作下的视频图像和动力学数据。建立LSTM模型,以Theia3D无标记动作捕捉系统获取的11个下肢关节点三维坐标作为输入变量估算跑步支撑阶段三维GRF曲线。使用相关系数、均方根误差(root mean square error,RMSE)和标准化均方根误差(normalized root mean square error,nRMSE)评估LSTM模型的估算效果,采用统计参数映射分析LSTM模型估算和测力台实测曲线的差异,采用配对样本t检验分析模型估算与实测GRF特征差异。

结果

LSTM模型估算所得GRF与实测值之间高度相关(r>0.85,P<0.001)且误差较小(RMSE<0.3倍体重,nRMSE<15%)。LSTM模型估算所得GRF曲线与实测曲线之间不存在显著差异区间。基于LSTM估算曲线计算所得GRF特征与实测值不存在显著差异(P>0.05)。

结论

基于LSTM模型,可从无标记动作捕捉系统获取的下肢关节点三维坐标有效估算人体跑步时GRF曲线,并获得准确性较高的GRF特征。本研究建立的LSTM模型可以用于户外环境下监控跑步过程中的损伤风险。

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刘卉,教授,E-mail:
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作者贡献声明:

周玉林负责研究设计、数据采集、数据分析及撰写论文;赵峻辰协助研究实施及数据采集;李翰君、时会娟、刘卉负责研究设计、研究指导和论文修改。

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articleId=1244321221911883983, language=EN, label=Tab. 1, caption=

Results of LSTM model for estimating GRF during running (n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
方向 rRMSE/BWnRMSE/%
前后0.992±0.0080.038±0.0185.78±2.81
左右0.951±0.0480.019±0.00710.68±3.83
垂直0.993±0.0120.110±0.0594.36±2.28
), ArticleFig(id=1244321231353262782, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321221911883983, language=CN, label=表1, caption=

LSTM模型估算跑步动作GRF结果(n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
方向 rRMSE/BWnRMSE/%
前后0.992±0.0080.038±0.0185.78±2.81
左右0.951±0.0480.019±0.00710.68±3.83
垂直0.993±0.0120.110±0.0594.36±2.28
), ArticleFig(id=1244321231479091913, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321221911883983, language=EN, label=Tab. 2, caption=

Comparison of GRF characteristics between LSTM model estimation and force plate measurement (n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
指标LSTM测力台 P
推进力峰值/BW0.296±0.0530.297±0.0620.789
制动力峰值/BW0.360±0.0680.362±0.0740.403
垂直冲击峰值/BW1.524±0.2961.540±0.3060.372
垂直主动峰值/BW2.513±0.2272.528±0.2240.277
VLR/(BW·s-150.84±7.9251.60±8.800.380
), ArticleFig(id=1244321231562978005, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321221911883983, language=CN, label=表2, caption=

LSTM模型估算和测力台实测GRF特征结果比较(n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
指标LSTM测力台 P
推进力峰值/BW0.296±0.0530.297±0.0620.789
制动力峰值/BW0.360±0.0680.362±0.0740.403
垂直冲击峰值/BW1.524±0.2961.540±0.3060.372
垂直主动峰值/BW2.513±0.2272.528±0.2240.277
VLR/(BW·s-150.84±7.9251.60±8.800.380
), ArticleFig(id=1244321231672029921, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321221911883983, language=EN, label=Tab. 3, caption=

Estimation error of LSTM model for estimating GRF characteristics (n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
指标绝对误差相对误差/%
推进力峰值/BW0.02±0.016.85±5.22
制动力峰值/BW0.02±0.014.78±3.84
垂直冲击峰值/BW0.11±0.087.29±5.86
垂直主动峰值/BW0.09±0.063.51±2.44
VLR/(BW·s-15.30±4.0210.39±3.75
), ArticleFig(id=1244321231772693228, tenantId=1146029695717560320, journalId=1244284848500682798, articleId=1244321221911883983, language=CN, label=表3, caption=

LSTM模型估算GRF特征误差(n=72)

, figureFileSmall=null, figureFileBig=null, tableContent=
指标绝对误差相对误差/%
推进力峰值/BW0.02±0.016.85±5.22
制动力峰值/BW0.02±0.014.78±3.84
垂直冲击峰值/BW0.11±0.087.29±5.86
垂直主动峰值/BW0.09±0.063.51±2.44
VLR/(BW·s-15.30±4.0210.39±3.75
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基于长短时记忆模型与无标记动作捕捉系统估算跑步地面反作用力曲线
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周玉林 1 , 赵峻辰 1 , 李翰君 1, 2 , 时会娟 1, 2 , 刘卉 1, 2
医用生物力学 | 论著 2025,40(5): 1295-1302
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医用生物力学 | 论著 2025, 40(5): 1295-1302
基于长短时记忆模型与无标记动作捕捉系统估算跑步地面反作用力曲线
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周玉林1, 赵峻辰1, 李翰君1, 2, 时会娟1, 2, 刘卉1, 2
作者信息
  • 1.北京体育大学 运动人体科学学院,北京 100084
  • 2.北京体育大学 国家体育总局体能训练与身体机能恢复实验室,北京 100084

通讯作者:

刘卉,教授,E-mail:
Estimating Running Ground Reaction Force Curves Using Long Short-Term Memory Neural Network and Markerless Motion Capture System
Yulin ZHOU1, Junchen ZHAO1, Hanjun LI1, 2, Huijuan SHI1, 2, Hui LIU1, 2
Affiliations
  • 1.School of Sport Science, Beijing Sport University, Beijing 100084, China
  • 2.Key Laboratory for Performance Training & Recovery of General Administration of Sport, Beijing Sport University, Beijing 100084, China
出版时间: 2025-10-01 doi: 10.16156/j.1004-7220.2025.05.028
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目的

应用长短时记忆神经网络(long short-term memory,LSTM)模型,以无标记动作捕捉系统所得下肢关节点坐标作为输入变量,估算跑步过程中的地面反作用力(ground reaction forces,GRF)曲线。

方法

采用无标记动作捕捉系统和三维测力台同步采集59名业余跑者跑步动作下的视频图像和动力学数据。建立LSTM模型,以Theia3D无标记动作捕捉系统获取的11个下肢关节点三维坐标作为输入变量估算跑步支撑阶段三维GRF曲线。使用相关系数、均方根误差(root mean square error,RMSE)和标准化均方根误差(normalized root mean square error,nRMSE)评估LSTM模型的估算效果,采用统计参数映射分析LSTM模型估算和测力台实测曲线的差异,采用配对样本t检验分析模型估算与实测GRF特征差异。

结果

LSTM模型估算所得GRF与实测值之间高度相关(r>0.85,P<0.001)且误差较小(RMSE<0.3倍体重,nRMSE<15%)。LSTM模型估算所得GRF曲线与实测曲线之间不存在显著差异区间。基于LSTM估算曲线计算所得GRF特征与实测值不存在显著差异(P>0.05)。

结论

基于LSTM模型,可从无标记动作捕捉系统获取的下肢关节点三维坐标有效估算人体跑步时GRF曲线,并获得准确性较高的GRF特征。本研究建立的LSTM模型可以用于户外环境下监控跑步过程中的损伤风险。

长短时记忆模型  /  地面反作用力  /  无标记动作捕捉  /  跑步损伤
Objective

By applying the long short-term memory (LSTM) neural network model and using lower body landmark coordinates obtained from a markerless motion capture system as inputs, to estimate ground reaction force (GRF) curves during running.

Methods

The video images and GRF data of 59 amateur runners during running were collected by the markerless motion capture system and three-dimensional (3D) force plates. The LSTM model was established, and the 3D coordinates of 11 lower body landmarks, obtained via the Theia3D markerless system, were used as inputs to estimate the 3D GRF curves during the stance of running. The estimation performance was evaluated using correlation coefficients r, root mean square error (RMSE), and normalized root mean square error (nRMSE) by comparing LSTM model estimation and force plate measurement. Statistical parametric mapping was used to analyze differences in GRF curves estimated by the LSTM model and measured by the force plate, while paired t-tests were used to assess differences in GRF characteristics between model estimation and actual measurement.

Results

A strong correlation (r>0.85, P<0.001) and lower error (RMSE<0.3 body weight, nRMSE<15%) was found between the LSTM model estimation and actual measurements. No significant difference was found in GRF curve intervals between LSTM model estimation and actual measurements. There was no significant difference in GRF characteristics between LSTM model estimation and actual measurements (P>0.05).

Conclusions

Based on the LSTM model, the 3D GRF curves can be effectively estimated by lower body landmark coordinates obtained from the makerless motion capture system, thereby acquiring the highly accurate GRF characteristics. The LSTM model developed in this study can be used to monitor injury risks during running in outdoor environments.

long short-term memory model  /  ground reaction forces  /  markerless motion capture  /  running injury
周玉林, 赵峻辰, 李翰君, 时会娟, 刘卉. 基于长短时记忆模型与无标记动作捕捉系统估算跑步地面反作用力曲线. 医用生物力学, 2025 , 40 (5) : 1295 -1302 . DOI: 10.16156/j.1004-7220.2025.05.028
Yulin ZHOU, Junchen ZHAO, Hanjun LI, Huijuan SHI, Hui LIU. Estimating Running Ground Reaction Force Curves Using Long Short-Term Memory Neural Network and Markerless Motion Capture System[J]. Journal of Medical Biomechanics, 2025 , 40 (5) : 1295 -1302 . DOI: 10.16156/j.1004-7220.2025.05.028
采集分析跑步过程中所受地面反作用力(ground reaction force,GRF)对防治跑步相关损伤(running related injury,RRI)具有重要意义,但目前在实验室之外很难准确获得跑步时的三维GRF。跑步是群众参与最广泛的运动之一,但RRI发生率高达71.3%[1]。此类损伤轻则制约人体运动,严重时会影响正常生活质量。已有研究表明,跑步支撑阶段GRF峰值[2]和垂直加载率(vertical loading rate,VLR)[3]与RRI的发生有关。目前,三维测力台是准确采集三维GRF相关数据的主要方法,但在户外环境下由于安装和信号传输问题,测力台使用受限[4];而压力鞋垫等可穿戴设备只能测量垂直压力,且设备易损坏[5-6]。因此,在非实验室环境下多通过模型估算的方式获取GRF。
以神经网络为代表的数据驱动模型在估算动力学方面效果较好,但其输入变量的实用性较低。神经网络模型具备深入挖掘数据的能力,进而构建出输入与输出变量之间的复杂映射关系,最终进行数据估算。其中,长短时记忆(long short-term memory,LSTM)模型能够处理不同输入长度的数据,特别适合时间序列数据分析[7]。目前,该模型已经成功应用于走路[8]、跑步[9]和侧切变向[10]等动作下的GRF估算中。此外,现有动力学估算研究中的输入变量主要为基于惯性传感器获得的环节加速度[11-12]和红外动作捕捉系统获得的体表反光点坐标[10,13-14]等参数。户外环境下,红外动作捕捉系统几乎无法使用。惯性传感器易受磁场干扰,长时间佩戴会产生较大的累积偏移误差,且对人体自然运动模式产生一定影响[15]。因此,现有研究成果很难直接应用到户外实践中。
无标记动作捕捉系统可在户外环境下获得人体关节坐标等运动学参数,然而该参数能否有效估算跑步过程中的GRF尚不明确。拍摄运动员动作视频并进行解析是户外环境下获取运动学数据最常用的方式[16],能够克服红外动作捕捉系统和惯性测量单元(inertial measurement unit,IMU)的缺陷。目前,智能识别算法已经能够快速准确地从视频图像中获取人体运动过程中的关节点坐标[17],甚至估算环节姿态[18-19]。上述算法提升了视频解析的效率。因此,以智能识别算法所获运动学参数作为神经网络模型的输入变量对GRF进行估算,具有极大的应用潜力。Theia3D能够从多视角图像中估算人体17个环节的运动学数据,并以4×4矩阵的形式给出环节坐标系原点和三维姿态角度,目前已经成功应用在步行[20]、跑步[21]以及侧切变向[18]等多种运动的数据采集中。然而,基于该系统获取的关节点坐标作为输入变量估算跑步过程中的GRF,效果尚不明确。
本文旨在建立以无标记动作捕捉系统获取的下肢关节点坐标作为输入变量的LSTM模型,估算跑步过程中三维GRF曲线,并验证其有效性。本研究假设如下:①LSTM模型估算与实测的GRF曲线之间高度相关;②LSTM模型估算与实测GRF曲线之间不存在显著差异区间;③基于LSTM模型估算所得GRF特征与实测值之间无显著差异。
选取59名以健身休闲为目的且不具备专业训练背景的业余跑者(男性24名,女性35名),身高(170±7.8)cm,体重(63.7±10.5)kg,周跑量(12±8.9)km。所有受试者半年内均无下肢手术史,且实验前24 h内没有进行剧烈运动。经1名专业康复师筛查发现,28名受试者(男性10名,女性18名)存在髌股关节疼痛综合征。本研究获得北京体育大学伦理委员会批准(2024499H)。
受试者签署知情同意书并充分热身后,换上紧身衣物并穿着测试跑鞋进行跑步测试。为充分模拟跑者日常跑步训练以及采集更多的数据建立数据库,要求受试者围绕数据采集区域进行5 km场地跑,并分别在跑步前以及跑步1、2、3、4和5 km时共6次进入采集区域进行数据采集。受试者每次进采集区域需要进行3次有效测试,1次有效测试定义为:①跑步动作流程自然无任何调整;②跑步速度在(13±0.65)km/h范围内;③左右腿各有1次完整的支撑期;④支撑腿足部与测力台完整接触。上述测试结束24 h之后,为扩大数据库中的数据量,受试者再次来到采集区域穿着另一双测试跑鞋进行同样的5 km跑步测试。两次测试结束之后,受试者所有测试工作完成。
采用12个视频镜头(采样频率100 Hz,Qualisys公司,瑞典)和3块9287C三维测力台(采样频率1 kHz,Kistler公司,瑞士)同步采集跑步过程中的影像学和动力学数据,采用Smartspeed分段计时实时反馈系统(Fusion Sport Pty公司,澳大利亚)监控受试者跑速(见图1)。
使用Qualisys Track Manager编写好的PAF文件[22]进行以下操作:①调用Theia3D 2022(Theia Markerless公司,加拿大)对视频数据进行处理,基于逆向运动学估算获得人体全身环节运动学数据,其下肢运动链中骨盆和髋、膝、踝关节的自由度分别为6、3、3和6[20];②调用Theia3D将处理好的运动学数据联合测力台信号导出为C3D格式文件;③调用Visual 3D软件(Preview v2022.06.02,C-Motion公司,美国)导入C3D文件,自动生成骨盆、大腿、小腿、前足和后足环节坐标系,其中将骨盆、大腿、小腿和后足坐标系的原点分别定义为骨盆、髋/膝/踝关节中心点。虚拟生成足跟点和足尖点[22]。由此获取骨盆中心、双侧髋/膝/踝中心、足跟点和足尖点共11个关节点的三维坐标。随后,将GRF通过体重(body weight,BW)进行标准化。仅对双侧下肢的支撑阶段进行分析,其定义为垂直GRF>10 N阶段,并将垂直GRF>10 N的第1帧定义为着地时刻。
数据库的单个数据样本中只包含单侧腿的支撑阶段前后10 ms内所有下肢关节点坐标和GRF曲线。因此,1次有效测试数据中包含左、右腿共2个有效数据样本。数据样本包含支撑阶段前后10 ms内11个关节点坐标和3个方向GRF。建立着地坐标系,以避免大地坐标系原点设置对估算结果的影响。着地坐标系原点为着地时刻骨盆中心点在水平面的投影,坐标轴方向和大地坐标系一致。将计算获取的11个关节点均转换到着地坐标系中。转换完成的关节点坐标通过3次样条插值为GRF相同的数据长度。跑步腾空阶段的GRF数据设置为0。
将59名受试者随机划分到训练集(55名)和测试集(4名)。部分视频数据目标识别错误(识别到镜头内受试者之外的人)导致运动学数据无效,且测试集受试者间数据缺失状况差异大,为保证测试集中数据的均衡性,对数据进行分层随机抽样,选取了其中1双鞋下人物识别正确的任意3圈下的数据用于模型测试。最终,训练集中和测试集的样本数量分别为3 924、72例。为增加模型的适用性,将左右腿样本一并放入模型进行训练,且各子集中比例相同。本文建立的LSTM估算模型的输入变量特征为33(11个关节点×3维坐标)×动作时间长度,输出特征为3(1个GRF×3个方向)×动作时间长度。模型训练前使用MinMaxScaler将各类数据缩放到0~1,以确保GRF各方向均能被有效训练。训练过程中,将训练集中的数据随机划分为5份,每份数据依次作为验证集进行超参数验证,其余数据进行模型训练,因此每组超参数进行了5次验证。使用Optuna[23]进行最优超参数搜索,其搜索范围和最优超参数如图2所示。当最优超参数确定后,基于最初的训练集训练模型,并基于测试集评估模型效果。神经网络模型的训练过程在Python Pytorch 2.4.1中进行,使用Cuda 12.1加速,其硬件设备为台式机,处理器为Core i7-7800X,内存为16GB,显卡为GeForce RTX 2080 Ti,内存为12GB(NVIDIA公司,美国)。
使用均方根误差(root mean square error,RMSE)和标准化均方根误差(normalized root mean square error,nRMSE)评价LSTM模型估算误差[8,13,24-26],仅对支撑阶段内估算所得数据进行分析。此外,将支撑阶段的GRF数据标准化为100个时间节点用于曲线间差异分析。为了进一步探究本文建立的LSTM估算模型在RRI相关研究中的实用性,还从估算的GRF数据中提取冲击峰值、主动峰值和VLR等垂直方向特征[11,27-28]以及制动力和推进力峰值等前后方向特征[29]进行分析(见图3)。由于部分跑者不存在明显的冲击峰值,故采用支撑期13%的垂直GRF作为冲击峰值[30]
针对研究假设①,使用Pearson相关分析LSTM模型估算与实测GRF曲线间相关性;针对研究假设②,使用统计参数映射(statistical parametric mapping,SPM)对两种方法获得GRF曲线区间差异进行分析;针对研究假设③,使用配对样本t检验分析两种方法所得GRF特征的差异。上述所有检验中统计显著性定为一类误差概率不大于0.05,所有分析使用Matlab 2020a(MathWorks公司,美国)完成。
相关分析结果显示,LSTM模型估算的GRF曲线与实测值均高度相关,其72个样本中均呈现高度相关(前后方向:r>0.947;左右方向:r>0.851;垂直方向:r>0.961),且P<0.001。估算误差方面,3个方向上表现出较小的绝对误差(前后方向:RMSE<0.060BW;左右方向:RMSE<0.033BW;垂直方向:RMSE<0.360BW)和相对误差(前后方向:nRMSE<12.82%;左右方向:nRMSE<15.26%;垂直方向:nRMSE<11.32%),见表1
SPM分析结果显示,LSTM模型估算跑步动作支撑阶段3个方向的GRF曲线与测力台实测曲线之间均不存在具有显著差异区域(见图4)。
配对样本t检验结果显示,基于LSTM估算所得GRF曲线提取的推进力峰值、制动力峰值、垂直冲击峰值、垂直主动峰值和VLR与测力台实测值之间差异没有统计学意义(见表2)。
本文还发现,基于模型所得GRF特征的绝对误差均较小,且所有GRF峰值特征的相对误差均小于10%,VLR的相对误差小于15%(见表3)。
本文发现,基于LSTM模型,从无标记动作捕捉系统获取的关节点坐标估算所获GRF与实测值之间高度相关,且两种方法获取的曲线之间不存在统计学上的显著差异区间。此外,基于LSTM模型估算所获GRF曲线计算的特征值与实测值也无统计学显著差异。上述结果证明,LSTM模型结合无标记动作捕捉系统可作为在非实验室环境下获取动力学参数的一种有效手段,并可应用于RRI风险监控。
本文结果支持研究假设①,即LSTM模型估算获得与实测的GRF曲线之间高度相关。本研究估算所得GRF与实测值之间的相关系数r在0.85~0.99之间,与前人基于IMU[11-12,24,31-32]和体表反光点[27-28]的相应结果接近,表明基于无标记动作捕捉系统获取的运动学数据可有效估算跑步动作下GRF。此外,本文相关系数r还明显优于以图像二维关节点作为输入变量的研究[25,33-34],提示三维关节点坐标含有的信息更丰富且对于模型估算效果更重要。左右方向上相关系数r低于其他方向,这与文献[13243133-34]结果类似。机器学习模型在处理变化幅度较大的数据时,具有更强的分类和预测效果。跑步动作下左右方向GRF变化幅度较小,故该方向的估算效果较差。在侧切变向等左右方向GRF幅度和变化较大的活动中[26],模型在学习这些变化时更加有效,故估算结果具有更高的相似性。
本文基于LSTM模型,通过无标记动作捕捉系统所获关节点坐标估算得到的GRF误差较小。垂直GRF是跑步相关研究中的重要参数,本文估算误差(RMSE=0.11BW,nRMSE=4.36%)优于前人研究中基于IMU[9,11,24,31]、体表反光点[27-29]和二维图像关节点坐标[25,33-35]的相应结果。在前后和左右GRF的估算误差方面,本文结果同样低于文献[253133-35]研究结果。本文认为,以无标记动作捕捉系统获取的关节点坐标作为输入变量时,其估算的跑步三维GRF误差更低。然而,垂直GRF估算误差要略大于Ngoh等[12]结果,推测与本文测试速度要大于该研究有关。左右GRF具有较小的估算绝对误差和较大相对误差,该结果与前人研究结果一致[25,31,35]。由于跑步过程中左右GRF的幅度较小,尽管绝对误差较低,但相对误差较大。目前,尚无明确证据表明左右方向GRF与RRI存在直接关联,因此该方向较差的估算效果对实际应用影响较小。
本文结果支持研究假设②,即LSTM模型估算获得与实测的GRF曲线之间不存在显著差异区间。相关系数r和RMSE等参数反映了模型的整个数据曲线估算效果,SPM可以检测多组曲线间具有显著差异的部分,可以弥补上述参数的不足。LSTM模型估算所获3个方向的GRF曲线与实测曲线之间均不存在显著差异区间,表明基于无标记动作捕捉系统获取的关节点坐标可准确估算跑步动作三维GRF曲线。Mundt等[25]研究发现,以图像二维关节点坐标估算所获跑步支撑阶段GRF曲线中,在前后和垂直方向上均与实测曲线具有显著差异的区间。此外,Ripic等[36]基于Kinect结合肌骨模型估算步行动作GRF,其估算结果与实测曲线在3个方向上均存在显著差异区间。上述结果提示,关节点三维坐标结合LSTM模型是获取人体运动过程中准确GRF曲线的有效手段。
本文结果支持检验假设③,基于LSTM模型估算所得的GRF特征与实测值之间不存在显著差异。垂直冲击峰值、垂直主动峰值和VLR等指标已被证明与RRI的发生密切相关[2,37]。为确保本文模型的应用效果,对上述指标的有效性进行分析。结果显示,垂直冲击峰值、垂直主动峰值和VLR的估算误差均小于文献[911-1227-2931]研究结果。此外,推进力峰值和制动力峰值估算误差同样小于文献[29]研究结果。上述结果表明,下肢关节点三维坐标含有的信息足够用于LSTM模型准确估算跑步动作下GRF特征。然而,垂直主动峰值误差要大于Bogaert等[38]基于TSFresh算法从骶骨加速度提取的特征作为输入的结果,从三维关节点坐标曲线中进一步提取特征作为输入变量可能会提升模型的估算性能。
本文基于LSTM模型,利用无标记动作捕捉系统获取的三维关节点坐标,实现了跑步动作下三维GRF的准确估算。该方法具有以下优势:①LSTM模型不需要对输入变量进行时间标准化,可实时进行数据估算,方便后期进行VLR和冲量等时间相关指标的计算;②输入变量来自视频拍摄,其受环境限制较小,适用于训练比赛等户外环境。此外,本文提出的方法还可用于估算压力中心,并结合Theia获取的人体模型,进行关节动力学分析。
①只选取了1种跑步速度进行训练和估算,在未来研究中应探究模型在其他跑步速度下的GRF估算效果。②只选取了Theia这1种人体姿态识别算法获取的关节点坐标进行估算,然而,当使用如Openpose等其他常用的姿态识别算法获取的关节坐标作为输入变量时,其GRF的估算效果尚不明确,需在后续研究中加以验证。
基于LSTM模型,可从Theia3D无标记动作捕捉系统获取的关节点坐标有效估算人体跑步的GRF曲线,并基于估算曲线可获得准确性较高的GRF特征。本研究建立的模型可用于户外环境下监控跑步过程中的损伤风险。
  • 国家自然科学基金项目(12132009)
  • 中央高校基本科研业务费专项资金(2024TNJN009)
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doi: 10.16156/j.1004-7220.2025.05.028
  • 接收时间:2025-03-02
  • 首发时间:2026-03-27
  • 出版时间:2025-10-01
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  • 收稿日期:2025-03-02
  • 修回日期:2025-03-25
基金
国家自然科学基金项目(12132009)
中央高校基本科研业务费专项资金(2024TNJN009)
作者信息
    1.北京体育大学 运动人体科学学院,北京 100084
    2.北京体育大学 国家体育总局体能训练与身体机能恢复实验室,北京 100084

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刘卉,教授,E-mail:
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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

Genus
种数
Number of
species
占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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