AI-Enabled Piezoelectric Wearable for Joint Torque Monitoring
Corresponding Author: Hubin Zhao
Nano-Micro Letters,
Vol. 17 (2025), Article Number: 247
Abstract
Joint health is critical for musculoskeletal (MSK) conditions that are affecting approximately one-third of the global population. Monitoring of joint torque can offer an important pathway for the evaluation of joint health and guided intervention. However, there is no technology that can provide the precision, effectiveness, low-resource setting, and long-term wearability to simultaneously achieve both rapid and accurate joint torque measurement to enable risk assessment of joint injury and long-term monitoring of joint rehabilitation in wider environments. Herein, we propose a piezoelectric boron nitride nanotubes (BNNTs)-based, AI-enabled wearable device for regular monitoring of joint torque. We first adopted an iterative inverse design to fabricate the wearable materials with a Poisson’s ratio precisely matched to knee biomechanics. A highly sensitive piezoelectric film was constructed based on BNNTs and polydimethylsiloxane and applied to precisely capture the knee motion, while concurrently realizing self-sufficient energy harvesting. With the help of a lightweight on-device artificial neural network, the proposed wearable device was capable of accurately extracting targeted signals from the complex piezoelectric outputs and then effectively mapping these signals to their corresponding physical characteristics, including torque, angle, and loading. A real-time platform was constructed to demonstrate the capability of fine real-time torque estimation. This work offers a relatively low-cost wearable solution for effective, regular joint torque monitoring that can be made accessible to diverse populations in countries and regions with heterogeneous development levels, potentially producing wide-reaching global implications for joint health, MSK conditions, ageing, rehabilitation, personal health, and beyond.
Highlights:
1 Artificial intelligence-enabled wearable device with boron nitride nanotubes (BNNTs)-based piezoelectric film for accurate joint torque sensing.
2 Inverse-designed structure optimizes biomechanical compatibility for enhanced knee motion tracking.
3 High-sensitivity BNNTs/polydimethylsiloxane composite enables precise and dynamic knee motion signal detection.
4 Lightweight neural network processes complex signals for accurate torque, angle, and load estimation.
5 Real-time monitoring system provides instant knee torque assessment for daily use.
Keywords
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- E. Sebbag, R. Felten, F. Sagez, J. Sibilia, H. Devilliers et al., The world-wide burden of musculoskeletal diseases: a systematic analysis of the world health organization burden of diseases database. Ann. Rheum. Dis. 78(6), 844–848 (2019). https://doi.org/10.1136/annrheumdis-2019-215142
- A. Cieza, K. Causey, K. Kamenov, S.W. Hanson, S. Chatterji et al., Global estimates of the need for rehabilitation based on the global burden of disease study 2019: a systematic analysis for the global burden of disease study 2019. Lancet 396(10267), 2006–2017 (2021). https://doi.org/10.1016/S0140-6736(20)32340-0
- M.D. National Academies of Sciences, Selected Health Conditions and Likelihood of Improvement with Treatment. Selected Health Conditions and Likelihood of Improvement with Treatment (National Academies Press, Washington, D.C., 2020).
- A. Braybrooke, K. Baraks, R. Burgess, A. Banerjee, J.C. Hill, Quality indicators for the primary and community care of musculoskeletal conditions: a systematic review. Arch. Phys. Med. Rehabil. 106(3), 459–472 (2025). https://doi.org/10.1016/j.apmr.2024.08.022
- Musculoskeletal health. (2024). https://www.england.nhs.uk/elective-care-transformation/best-practice-solutions/musculoskeletal/
- H. Pang, S. Chen, D.M. Klyne, D. Harrich, W. Ding et al., Low back pain and osteoarthritis pain: a perspective of estrogen. Bone Res. 11(1), 42 (2023). https://doi.org/10.1038/s41413-023-00280-x
- Versus Arthritis, The State of Musculoskeletal Health 2024. The State of Musculoskeletal Health 2024 (Chesterfield, 2024).
- Office for Health Improvement and Disparities (OHID), Guidance Musculoskeletal health: applying All Our Health. (2022). https://www.gov.uk/government/publications/musculoskeletal-health-applying-all-our-health/musculoskeletal-health-applying-all-our-health
- J. Adamson, S. Ebrahim, P. Dieppe, K. Hunt, Prevalence and risk factors for joint pain among men and women in the West of Scotland twenty-07 study. Ann. Rheum. Dis. 65(4), 520–524 (2006). https://doi.org/10.1136/ard.2005.037317
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- A.E. Engin, M.S. Korde, Biomechanics of normal and abnormal knee joint. J. Biomech. 7(4), 325–334 (1974). https://doi.org/10.1016/0021-9290(74)90027-X
- E.G. Meyer, R.C. Haut, Excessive compression of the human tibio-femoral joint causes ACL rupture. J. Biomech. 38, 2311–2316 (2005). https://doi.org/10.1016/j.jbiomech.2004.10.003
- J. Verheul, N.J. Nedergaard, J. Vanrenterghem, M.A. Robinson, Measuring biomechanical loads in team sports–from lab to field. Sci. Med. Footb. 4(3), 246–252 (2020). https://doi.org/10.1080/24733938.2019.1709654
- D.S. Logerstedt, J.R. Ebert, T.D. MacLeod, B.C. Heiderscheit, T.J. Gabbett et al., Effects of and response to mechanical loading on the knee. Phys. Med. 52(2), 201–235 (2022). https://doi.org/10.1007/s40279-021-01579-7
- B. Innocenti, Biomechanics of the knee joint, in Human Orthopaedic Biomechanics. (Elsevier, Netherland, 2022), pp.239–263
- L. Zhang, G. Liu, B. Han, Z. Wang, Y. Yan et al., Knee joint biomechanics in physiological conditions and how pathologies can affect it: a systematic review. Appl. Bionics Biomech. 2020, 7451683 (2020). https://doi.org/10.1155/2020/7451683
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- J. Holder, U. Trinler, A. Meurer, F. Stief, A systematic review of the associations between inverse dynamics and musculoskeletal modeling to investigate joint loading in a clinical environment. Front. Bioeng. Biotechnol. 8, 603907 (2020). https://doi.org/10.3389/fbioe.2020.603907
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- C. Jacq, T. Maeder, S. Emery, M. Simoncini, E. Meurville et al., Investigation of polymer thick-film piezoresistors for medical wrist rehabilitation and artificial knee load sensors. Procedia Eng. 87, 1194–1197 (2014). https://doi.org/10.1016/j.proeng.2014.11.380
- M. Arvanitidis, D. Jiménez-Grande, N. Haouidji-Javaux, D. Falla, E. Martinez-Valdes, People with chronic low back pain display spatial alterations in high-density surface EMG-torque oscillations. Sci. Rep. 12(1), 15178 (2022). https://doi.org/10.1038/s41598-022-19516-7
- S. Yang, J. Cheng, J. Shang, C. Hang, J. Qi et al., Stretchable surface electromyography electrode array patch for tendon location and muscle injury prevention. Nat. Commun. 14(1), 6494 (2023). https://doi.org/10.1038/s41467-023-42149-x
- J. Chapman, A. Dwivedi, M. Liarokapis, A wearable, open-source, lightweight forcemyography armband: on intuitive, robust muscle-machine interfaces. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). September 27-October 1, 2021. Prague, Czech Republic. IEEE, (2021). pp. 4138–4143. https://doi.org/10.1109/iros51168.2021.9636345
- Z.G. Xiao, C. Menon, Performance of forearm FMG and sEMG for estimating elbow, forearm and wrist positions. J. Bionic Eng. 14(2), 284–295 (2017). https://doi.org/10.1016/S1672-6529(16)60398-0
- Z. Qing, Z. Lu, Z. Liu, Y. Cai, S. Cai et al., A simultaneous gesture classification and force estimation strategy based on wearable A-mode ultrasound and cascade model. IEEE Trans. Neural Syst. Rehabil. Eng. 30, 2301–2311 (2022). https://doi.org/10.1109/TNSRE.2022.3196926
- D. Kim, J. Ko, Y.-K. Kim, S.S. Lee, S. Ahn et al., Spontaneous alignment of boron nitride nanotubes into polycrystalline film arrays for enhanced piezoelectric nanogeneration. Small Struct. 5(11), 2400259 (2024). https://doi.org/10.1002/sstr.202400259
- A. Niguès, A. Siria, P. Vincent, P. Poncharal, L. Bocquet, Ultrahigh interlayer friction in multiwalled boron nitride nanotubes. Nat. Mater. 13(7), 688–693 (2014). https://doi.org/10.1038/nmat3985
- Y. Huang, J. Lin, J. Zou, M.-S. Wang, K. Faerstein et al., Thin boron nitride nanotubes with exceptionally high strength and toughness. Nanoscale 5(11), 4840–4846 (2013). https://doi.org/10.1039/c3nr00651d
- X. Zeng, J. Sun, Y. Yao, R. Sun, J.-B. Xu et al., A combination of boron nitride nanotubes and cellulose nanofibers for the preparation of a nanocomposite with high thermal conductivity. ACS Nano 11(5), 5167–5178 (2017). https://doi.org/10.1021/acsnano.7b02359
- J.H. Kang, G. Sauti, C. Park, V.I. Yamakov, K.E. Wise et al., Multifunctional electroactive nanocomposites based on piezoelectric boron nitride nanotubes. ACS Nano 9(12), 11942–11950 (2015). https://doi.org/10.1021/acsnano.5b04526
- J. Zhang, S. Ye, H. Liu, X. Chen, X. Chen et al., 3D printed piezoelectric BNNTs nanocomposites with tunable interface and microarchitectures for self-powered conformal sensors. Nano Energy 77, 105300 (2020). https://doi.org/10.1016/j.nanoen.2020.105300
- P. Snapp, C. Cho, D. Lee, M.F. Haque, S. Nam et al., Tunable piezoelectricity of multifunctional boron nitride nanotube/poly(dimethylsiloxane) stretchable composites. Adv. Mater. 32, 2004607 (2020). https://doi.org/10.1002/adma.202004607
- B.J. Stetter, T. Stein, Machine learning in biomechanics: enhancing human movement analysis, in Artificial Intelligence in Sports, Movement, and Health. (Springer Nature Switzerland, Cham, 2024), pp.139–160
- Y. Guo, H. Zhang, L. Fang, Z. Wang, W. He et al., A self-powered flexible piezoelectric sensor patch for deep learning-assisted motion identification and rehabilitation training system. Nano Energy 123, 109427 (2024). https://doi.org/10.1016/j.nanoen.2024.109427
- Y. Chen, X. Zhang, C. Lu, Flexible piezoelectric materials and strain sensors for wearable electronics and artificial intelligence applications. Chem. Sci. 15(40), 16436–16466 (2024). https://doi.org/10.1039/d4sc05166a
- Y. Luo, Y. Li, P. Sharma, W. Shou, K. Wu et al., Learning human–environment interactions using conformal tactile textiles. Nat. Electron. 4(3), 193–201 (2021). https://doi.org/10.1038/s41928-021-00558-0
- U.D. Larsen, O. Signund, S. Bouwsta, Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. J. Microelectromech. Syst. 6(2), 99–106 (1997). https://doi.org/10.1109/84.585787
- L. Mizzi, E. Salvati, A. Spaggiari, J.-C. Tan, A.M. Korsunsky, 2D auxetic metamaterials with tuneable micro-/nanoscale apertures. Appl. Mater. Today 20, 100780 (2020). https://doi.org/10.1016/j.apmt.2020.100780
- L. Mizzi, E. Salvati, A. Spaggiari, J.-C. Tan, A.M. Korsunsky, Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting. Int. J. Mech. Sci. 167, 105242 (2020). https://doi.org/10.1016/j.ijmecsci.2019.105242
- J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the nelder: mead simplex method in low dimensions. SIAM J. Optim. 9(1), 112–147 (1998). https://doi.org/10.1137/s1052623496303470
- A.F. Möslein, M. Gutiérrez, B. Cohen, J.-C. Tan, Near-field infrared nanospectroscopy reveals guest confinement in metal-organic framework single crystals. Nano Lett. 20(10), 7446–7454 (2020). https://doi.org/10.1021/acs.nanolett.0c02839
- D. Griffin, J. Lim, Signal estimation from modified short-time Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 32(2), 236–243 (1984). https://doi.org/10.1109/TASSP.1984.1164317
- A.C. Belkina, C.O. Ciccolella, R. Anno, R. Halpert, J. Spidlen et al., Automated optimized parameters for T-distributed stochastic neighbor embedding improve visualization and analysis of large datasets. Nat. Commun. 10(1), 5415 (2019). https://doi.org/10.1038/s41467-019-13055-y
- Dina Zhabinskaya, University of California Davis: Physics 7B General Physics. University of California Davis: Physics 7B General Physics (University of California Davis, n.d.).
- R. Riemer, E.T. Hsiao-Wecksler, Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors. J. Biomech. 41(7), 1503–1509 (2008). https://doi.org/10.1016/j.jbiomech.2008.02.011
References
E. Sebbag, R. Felten, F. Sagez, J. Sibilia, H. Devilliers et al., The world-wide burden of musculoskeletal diseases: a systematic analysis of the world health organization burden of diseases database. Ann. Rheum. Dis. 78(6), 844–848 (2019). https://doi.org/10.1136/annrheumdis-2019-215142
A. Cieza, K. Causey, K. Kamenov, S.W. Hanson, S. Chatterji et al., Global estimates of the need for rehabilitation based on the global burden of disease study 2019: a systematic analysis for the global burden of disease study 2019. Lancet 396(10267), 2006–2017 (2021). https://doi.org/10.1016/S0140-6736(20)32340-0
M.D. National Academies of Sciences, Selected Health Conditions and Likelihood of Improvement with Treatment. Selected Health Conditions and Likelihood of Improvement with Treatment (National Academies Press, Washington, D.C., 2020).
A. Braybrooke, K. Baraks, R. Burgess, A. Banerjee, J.C. Hill, Quality indicators for the primary and community care of musculoskeletal conditions: a systematic review. Arch. Phys. Med. Rehabil. 106(3), 459–472 (2025). https://doi.org/10.1016/j.apmr.2024.08.022
Musculoskeletal health. (2024). https://www.england.nhs.uk/elective-care-transformation/best-practice-solutions/musculoskeletal/
H. Pang, S. Chen, D.M. Klyne, D. Harrich, W. Ding et al., Low back pain and osteoarthritis pain: a perspective of estrogen. Bone Res. 11(1), 42 (2023). https://doi.org/10.1038/s41413-023-00280-x
Versus Arthritis, The State of Musculoskeletal Health 2024. The State of Musculoskeletal Health 2024 (Chesterfield, 2024).
Office for Health Improvement and Disparities (OHID), Guidance Musculoskeletal health: applying All Our Health. (2022). https://www.gov.uk/government/publications/musculoskeletal-health-applying-all-our-health/musculoskeletal-health-applying-all-our-health
J. Adamson, S. Ebrahim, P. Dieppe, K. Hunt, Prevalence and risk factors for joint pain among men and women in the West of Scotland twenty-07 study. Ann. Rheum. Dis. 65(4), 520–524 (2006). https://doi.org/10.1136/ard.2005.037317
R.W. Nuckols, S. Lee, K. Swaminathan, D. Orzel, R.D. Howe et al., Individualization of exosuit assistance based on measured muscle dynamics during versatile walking. Sci. Robot. 6(60), eabj1362 (2021). https://doi.org/10.1126/scirobotics.abj1362
Y. Jin, J.T. Alvarez, E.L. Suitor, K. Swaminathan, A. Chin et al., Estimation of joint torque in dynamic activities using wearable A-mode ultrasound. Nat. Commun. 15(1), 5756 (2024). https://doi.org/10.1038/s41467-024-50038-0
A.E. Engin, M.S. Korde, Biomechanics of normal and abnormal knee joint. J. Biomech. 7(4), 325–334 (1974). https://doi.org/10.1016/0021-9290(74)90027-X
E.G. Meyer, R.C. Haut, Excessive compression of the human tibio-femoral joint causes ACL rupture. J. Biomech. 38, 2311–2316 (2005). https://doi.org/10.1016/j.jbiomech.2004.10.003
J. Verheul, N.J. Nedergaard, J. Vanrenterghem, M.A. Robinson, Measuring biomechanical loads in team sports–from lab to field. Sci. Med. Footb. 4(3), 246–252 (2020). https://doi.org/10.1080/24733938.2019.1709654
D.S. Logerstedt, J.R. Ebert, T.D. MacLeod, B.C. Heiderscheit, T.J. Gabbett et al., Effects of and response to mechanical loading on the knee. Phys. Med. 52(2), 201–235 (2022). https://doi.org/10.1007/s40279-021-01579-7
B. Innocenti, Biomechanics of the knee joint, in Human Orthopaedic Biomechanics. (Elsevier, Netherland, 2022), pp.239–263
L. Zhang, G. Liu, B. Han, Z. Wang, Y. Yan et al., Knee joint biomechanics in physiological conditions and how pathologies can affect it: a systematic review. Appl. Bionics Biomech. 2020, 7451683 (2020). https://doi.org/10.1155/2020/7451683
S.E. Forrester, M.R. Yeadon, M.A. King, M.G. Pain, Comparing different approaches for determining joint torque parameters from isovelocity dynamometer measurements. J. Biomech. 44(5), 955–961 (2011). https://doi.org/10.1016/j.jbiomech.2010.11.024
J. Holder, U. Trinler, A. Meurer, F. Stief, A systematic review of the associations between inverse dynamics and musculoskeletal modeling to investigate joint loading in a clinical environment. Front. Bioeng. Biotechnol. 8, 603907 (2020). https://doi.org/10.3389/fbioe.2020.603907
M. Safaei, R. Michael Meneghini, S.R. Anton, Force detection, center of pressure tracking, and energy harvesting from a piezoelectric knee implant. Smart Mater. Struct. 27(11), 114007 (2018). https://doi.org/10.1088/1361-665X/aad755
C. Jacq, T. Maeder, S. Emery, M. Simoncini, E. Meurville et al., Investigation of polymer thick-film piezoresistors for medical wrist rehabilitation and artificial knee load sensors. Procedia Eng. 87, 1194–1197 (2014). https://doi.org/10.1016/j.proeng.2014.11.380
M. Arvanitidis, D. Jiménez-Grande, N. Haouidji-Javaux, D. Falla, E. Martinez-Valdes, People with chronic low back pain display spatial alterations in high-density surface EMG-torque oscillations. Sci. Rep. 12(1), 15178 (2022). https://doi.org/10.1038/s41598-022-19516-7
S. Yang, J. Cheng, J. Shang, C. Hang, J. Qi et al., Stretchable surface electromyography electrode array patch for tendon location and muscle injury prevention. Nat. Commun. 14(1), 6494 (2023). https://doi.org/10.1038/s41467-023-42149-x
J. Chapman, A. Dwivedi, M. Liarokapis, A wearable, open-source, lightweight forcemyography armband: on intuitive, robust muscle-machine interfaces. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). September 27-October 1, 2021. Prague, Czech Republic. IEEE, (2021). pp. 4138–4143. https://doi.org/10.1109/iros51168.2021.9636345
Z.G. Xiao, C. Menon, Performance of forearm FMG and sEMG for estimating elbow, forearm and wrist positions. J. Bionic Eng. 14(2), 284–295 (2017). https://doi.org/10.1016/S1672-6529(16)60398-0
Z. Qing, Z. Lu, Z. Liu, Y. Cai, S. Cai et al., A simultaneous gesture classification and force estimation strategy based on wearable A-mode ultrasound and cascade model. IEEE Trans. Neural Syst. Rehabil. Eng. 30, 2301–2311 (2022). https://doi.org/10.1109/TNSRE.2022.3196926
D. Kim, J. Ko, Y.-K. Kim, S.S. Lee, S. Ahn et al., Spontaneous alignment of boron nitride nanotubes into polycrystalline film arrays for enhanced piezoelectric nanogeneration. Small Struct. 5(11), 2400259 (2024). https://doi.org/10.1002/sstr.202400259
A. Niguès, A. Siria, P. Vincent, P. Poncharal, L. Bocquet, Ultrahigh interlayer friction in multiwalled boron nitride nanotubes. Nat. Mater. 13(7), 688–693 (2014). https://doi.org/10.1038/nmat3985
Y. Huang, J. Lin, J. Zou, M.-S. Wang, K. Faerstein et al., Thin boron nitride nanotubes with exceptionally high strength and toughness. Nanoscale 5(11), 4840–4846 (2013). https://doi.org/10.1039/c3nr00651d
X. Zeng, J. Sun, Y. Yao, R. Sun, J.-B. Xu et al., A combination of boron nitride nanotubes and cellulose nanofibers for the preparation of a nanocomposite with high thermal conductivity. ACS Nano 11(5), 5167–5178 (2017). https://doi.org/10.1021/acsnano.7b02359
J.H. Kang, G. Sauti, C. Park, V.I. Yamakov, K.E. Wise et al., Multifunctional electroactive nanocomposites based on piezoelectric boron nitride nanotubes. ACS Nano 9(12), 11942–11950 (2015). https://doi.org/10.1021/acsnano.5b04526
J. Zhang, S. Ye, H. Liu, X. Chen, X. Chen et al., 3D printed piezoelectric BNNTs nanocomposites with tunable interface and microarchitectures for self-powered conformal sensors. Nano Energy 77, 105300 (2020). https://doi.org/10.1016/j.nanoen.2020.105300
P. Snapp, C. Cho, D. Lee, M.F. Haque, S. Nam et al., Tunable piezoelectricity of multifunctional boron nitride nanotube/poly(dimethylsiloxane) stretchable composites. Adv. Mater. 32, 2004607 (2020). https://doi.org/10.1002/adma.202004607
B.J. Stetter, T. Stein, Machine learning in biomechanics: enhancing human movement analysis, in Artificial Intelligence in Sports, Movement, and Health. (Springer Nature Switzerland, Cham, 2024), pp.139–160
Y. Guo, H. Zhang, L. Fang, Z. Wang, W. He et al., A self-powered flexible piezoelectric sensor patch for deep learning-assisted motion identification and rehabilitation training system. Nano Energy 123, 109427 (2024). https://doi.org/10.1016/j.nanoen.2024.109427
Y. Chen, X. Zhang, C. Lu, Flexible piezoelectric materials and strain sensors for wearable electronics and artificial intelligence applications. Chem. Sci. 15(40), 16436–16466 (2024). https://doi.org/10.1039/d4sc05166a
Y. Luo, Y. Li, P. Sharma, W. Shou, K. Wu et al., Learning human–environment interactions using conformal tactile textiles. Nat. Electron. 4(3), 193–201 (2021). https://doi.org/10.1038/s41928-021-00558-0
U.D. Larsen, O. Signund, S. Bouwsta, Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. J. Microelectromech. Syst. 6(2), 99–106 (1997). https://doi.org/10.1109/84.585787
L. Mizzi, E. Salvati, A. Spaggiari, J.-C. Tan, A.M. Korsunsky, 2D auxetic metamaterials with tuneable micro-/nanoscale apertures. Appl. Mater. Today 20, 100780 (2020). https://doi.org/10.1016/j.apmt.2020.100780
L. Mizzi, E. Salvati, A. Spaggiari, J.-C. Tan, A.M. Korsunsky, Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting. Int. J. Mech. Sci. 167, 105242 (2020). https://doi.org/10.1016/j.ijmecsci.2019.105242
J.C. Lagarias, J.A. Reeds, M.H. Wright, P.E. Wright, Convergence properties of the nelder: mead simplex method in low dimensions. SIAM J. Optim. 9(1), 112–147 (1998). https://doi.org/10.1137/s1052623496303470
A.F. Möslein, M. Gutiérrez, B. Cohen, J.-C. Tan, Near-field infrared nanospectroscopy reveals guest confinement in metal-organic framework single crystals. Nano Lett. 20(10), 7446–7454 (2020). https://doi.org/10.1021/acs.nanolett.0c02839
D. Griffin, J. Lim, Signal estimation from modified short-time Fourier transform. IEEE Trans. Acoust. Speech Signal Process. 32(2), 236–243 (1984). https://doi.org/10.1109/TASSP.1984.1164317
A.C. Belkina, C.O. Ciccolella, R. Anno, R. Halpert, J. Spidlen et al., Automated optimized parameters for T-distributed stochastic neighbor embedding improve visualization and analysis of large datasets. Nat. Commun. 10(1), 5415 (2019). https://doi.org/10.1038/s41467-019-13055-y
Dina Zhabinskaya, University of California Davis: Physics 7B General Physics. University of California Davis: Physics 7B General Physics (University of California Davis, n.d.).
R. Riemer, E.T. Hsiao-Wecksler, Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors. J. Biomech. 41(7), 1503–1509 (2008). https://doi.org/10.1016/j.jbiomech.2008.02.011