# A New Time–Frequency Feature Extraction Method for Action Detection on Artificial Knee by Fractional Fourier Transform

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## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Fractional Fourier Transform (FRFT)

#### 2.1.1. Definition

#### 2.1.2. Discrete FRFT

#### 2.1.3. Transform Effect

#### 2.2. Feature

#### 2.3. Classifier

## 3. Experiment

#### 3.1. Experiment Design

#### 3.2. Results and Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Liu, N.; Diao, X. Summary of knee prosthesis. Orthop. J. China
**2006**, 14, 225–226. [Google Scholar] - Tan, G.Z.; Xiao, H.F.; Wang, Y.C. Optimal Fuzzy PID Controller with Incomplete Derivation and Its Simulation Research on Application of Intelligent Artificial Legs. Control Theory Appl.
**2002**, 190, 462–466. [Google Scholar] - Ma, S.; Wang, R.; Shen, Q.; Zhang, T.; Liu, Q. The Research Advance of Active Artificial Knee-joint Prosthesis. In Proceedings of the 6th Beijing International Forum on Rehabilitation, Beijing China, 21 October 2011; pp. 259–264. [Google Scholar]
- Lisha, H.; Wang, S.; Chen, Y. Fall detection algorithms based on wearable device: A review. J. Zhejiang Univ. Eng.
**2018**, 52, 1717–1728. [Google Scholar] - Chen, M. Research on the Method of Falling Detection Based on Doppler Radar; Taiyuan Technology University: Tai Yuan, China, 2018. [Google Scholar]
- Yuan, J. The Design and Research of Visual Fall Detection System for Elderly People; Jiangxi Science and Technology University: Gan Zhou, China, 2018. [Google Scholar]
- Ren, L.; Shi, W.; Yu, Z.; Cao, Y. ALARM: A novel fall detection algorithm based on personalized threshold. In Proceedings of the International Conference on E-health Networking, Application & Services, Boston, MA, USA, 14–17 October 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 410–415. [Google Scholar]
- De Cillis, F.; de Simio, F.; Guido, F.; Incalzi, A.R.; Setola, R. Fall-detection solution for mobile platforms using accelerometer and gyroscope data. In Proceedings of the International Conference on Engineering in Medicine and Biology Society, Milan, Italy, 25–29 August 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 3727–3730. [Google Scholar]
- Cheng, S.H. An intelligent fall detection system using triaxial accelerometer integrated by active RFID. In Proceedings of the International Conference on Machine Learning and Cybernetics, Lanzhou, China, 13–16 June 2014; IEEE: Piscataway, NJ, USA, 2014; pp. 517–522. [Google Scholar]
- Ha, K.H.; Varol, H.A.; Goldfarb, M. Volitional Control of a Prosthetic Knee Using Surface Electromyography. IEEE Trans. Biomed. Eng.
**2018**, 58, 144–151. [Google Scholar] [CrossRef] [PubMed] - Aziz, O.; Russell, C.M.; Park, E.J.; Robinovitch, S.N. The effect of window size and lead time on pre-impact fall detection accuracy using support vector machine analysis of waist mounted inertial sensor data. Conf. Proc. IEEE Eng. Med. Biol. Sci.
**2014**, 2014, 30–33. [Google Scholar] - Pierleoni, P.; Belli, A.; Palma, L.; Pellegrini, M.; Pernini, L.; Valenti, S. A high reliability wearable device for elderly fall detection. Sens. J.
**2015**, 15, 4544–4553. [Google Scholar] [CrossRef] - Cheng, J.; Chen, X.; Shen, M. A framework for daily activity monitoring and fall detection based on surface electromyography and accelerometer signals. IEEE J. Biomed. Health Inf.
**2013**, 17, 38–45. [Google Scholar] [CrossRef] [PubMed] - Zhou, C.C.; Tu, C.L.; Gao, Y.; Wang, F.-X.; Gong, H.-W.; Lian, P.; He, C.; Ye, X.-S. A low-power, wireless, wrist-worn device for long time heart rate monitoring and fall detection. In Proceedings of the International Conference on Orange Technologies, Xi’an, China, 20–23 September 2014; IEEE: Piscataway, NJ, USA, 2014; pp. 33–36. [Google Scholar]
- Park, S.Y.; Ju, H.; Park, C.G. Stance Phase Detection of Multiple Actions for Military Drill Using Foot-mounted IMU. Sensors
**2016**, 14, 16. [Google Scholar] - Chou, Y.H.; Cheng, H.C.; Cheng, C.H.; Su, K.H.; Yang, C.Y. Dynamic time warping for IMU based activity detection. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Budapest, Hungary, 9–12 October 2016; IEEE: Piscataway, NJ, USA, 2016; pp. 3107–3112. [Google Scholar]
- Zhang, Z.; Lo, B. A Multi-sensor Fusion Approach for Intention Detection. In Converging Clinical and Engineering Research on Neuro-Rehabilitation III: Proceedings of the 4th International Conference on Neuro-Rehabilitation, Pisa, Italy, 16–20 October 2008; Springer: Cham, Switzerland, 2008; Volume 21, pp. 454–458. [Google Scholar]
- Mohammadian, R.N.; van Laarhoven, T.; Furlanello, C.; Marchiori, E. Novelty Detection using Deep Normative Modeling for IMU-Based Abnormal Movement Monitoring in Parkinson’s Disease and Autism Spectrum Disorders. Sensors
**2018**, 18, 3533. [Google Scholar] [CrossRef] [PubMed] - Nukala, B.T.; Shibuya, N.; Rodriguez, A.I.; Tsay, J.; Nguyen, T.Q.; Zupancic, S.; Lie, D.Y.C. A real-time robust fall detection system using a wireless gait analysis sensor and an Artificial Neural Network. In Proceedings of the International Conference on Healthcare Innovation, Seattle, WA, USA, 8–10 October 2014; IEEE: Piscataway, NJ, USA, 2014; pp. 219–222. [Google Scholar]
- Jian, H.; Chen, H. A portable fall detection and alerting system based on k-NN algorithm and remote medicine. Communications
**2015**, 12, 23–31. [Google Scholar] [CrossRef] - Lisowska, A.; Wheeler, G.; Inza, V.; Poole, I. An evaluation of supervised, novelty-based and hybrid approaches to fall detection using silmee accelerometer data. In Proceedings of the International Conference on Computer Vision Workshops, Santiago, Chile, 7–13 December 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 10–16. [Google Scholar]
- Wang, J.; Chen, R.; Sun, X.; She, M.; Kong, L. Generative models for automatic recognition of human daily activities from a single triaxial accelerometer. In Proceedings of the International Joint Conference on Neural Networks, Brisbane, Australia, 10–15 June 2012; IEEE: Piscataway, NJ, USA, 2012; pp. 1–6. [Google Scholar]
- Li, C.; Lin, M.; Yang, L.T.; Ding, C. Integrating the enriched feature with machine learning algorithms for human movement and fall detection. J. Supercomput.
**2014**, 67, 854–865. [Google Scholar] [CrossRef] - Jiang, Z. Fractional Fourier Transform. Chin. J. Quantum Electron.
**1996**, 4, 289–300. [Google Scholar] - Tao, R.; Qi, L.; Wang, Y. Theory and Applications of the Fractional Fourier Transform; Tsinghua University Press: Beijing, China, 2004. [Google Scholar]
- Liang, W. Fractional Fourier Transform and Application; Chongqing University: Chong Qing, China, 2008. [Google Scholar]
- Namias, V. The fractional order Fourier transform and its applications in the quantum mechanics. Inst. Math. Appl.
**1980**, 25, 241–265. [Google Scholar] [CrossRef] - Li, C.; Su, Z.; Li, Q.; Zhao, H. An Indoor Positioning Error Correction Method of Pedestrian Multi-Motions Recognized by Hybrid-Orders Fraction Domain Transformation. IEEE Access.
**2019**, 7, 11360–11377. [Google Scholar] [CrossRef] - Zhao, J.; Tao, R.; Li, Y.L.; Wang, Y. Uncertainty principles for linear canonical transform. IEEE Trans. Signal Process.
**2009**, 57, 2856–2858. [Google Scholar] [CrossRef] - Shinde, S.; Gadre, V.M. An uncertainty principle for real signals in the fractional Fourier transform domain. IEEE Trans. Signal Process.
**2001**, 49, 2545–2548. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Results of Multiorder fractional Fourier transform (FRFT) with single action (order: 0–1).

**Figure 3.**(

**a**) The results of FRFT of walking in 0.7 order. (

**b**) The results of FRFT of different actions in 0.7 order.

**Figure 4.**The Order–Amplitude figures of different features of 40 groups for the walk action. (

**a**) $range$, (

**b**) $std$, (

**c**) $var$, (

**d**) $rms$, (

**e**) $IQR$, (

**f**) $mean$, (

**g**) $pksMean$ and (

**h**) $pksNum$.

**Figure 5.**Standard deviation and mean of eight features of the walk action. (

**a**) The standard deviation of each feature, (

**b**) The mean of each feature.

**Figure 6.**The Order–Amplitude figures of different features of 40 groups for the upstairs action. (

**a**) $range$, (

**b**) $std$, (

**c**) $var$, (

**d**) $rms$, (

**e**) $IQR$, (

**f**) $mean$, (

**g**) $pksMean$ and (

**h**) $pksNum$.

**Figure 7.**Standard deviation and mean of eight features of the upstairs action. (

**a**) The standard deviation of each feature, (

**b**) The mean of each feature.

**Figure 8.**The Order–Amplitude figures of different features of 40 groups for the dwstairs action. (

**a**) $range$, (

**b**) $std$, (

**c**) $var$, (

**d**) $rms$, (

**e**) $IQR$, (

**f**) $mean$, (

**g**) $pksMean$ and (

**h**) $pksNum$.

**Figure 9.**Standard deviation and mean of eight features of the dwstairs action. (

**a**) The standard deviation of each feature, (

**b**) The mean of each feature.

**Figure 10.**The Order–Amplitude figure of different features of 40 groups for the run action. (

**a**) $range$, (

**b**) $std$, (

**c**) $var$, (

**d**) $rms$, (

**e**) $IQR$, (

**f**) $mean$, (

**g**) $pksMean$ and (

**h**) $pksNum$.

**Figure 11.**Standard deviation and mean of eight features of the run action. (

**a**) The standard deviation of each feature, (

**b**) The mean of each feature.

**Figure 12.**The effect of classification. (

**a**) walk and dwstairs with the features $std$ and $pksNum$ when Order = 0.67; (

**b**) walk and dwstairs with the features $std$ and $pksNum$ when Order = 0.20; (

**c**) walk and dwstairs with the features $range$ and $pksMean$ when Order = 0.67; (

**d**) dwstairs and upstairs with the features $range$ and $pksNum$ when Order = 0.64; (

**e**) dwstairs and upstairs with the features $range$ and $pksNum$ when Order = 0.20; (

**f**) dwstairs and upstairs with the features $rms$ and $IQR$ when Order = 0.64; (

**g**) walk and upstairs with the features $rms$ and $mean$ when Order = 0.71; (

**h**) walk and upstairs with the features $rms$ and $mean$ when Order = 0.20; (

**i**) walk and upstairs with the features $std$ and $IQR$ when Order = 0.71; (

**j**) all the actions with the features $rms$ and $mean$ when Order = 0.75; (

**k**) all the actions with the features $range$ and $IQR$ when Order = 0.75; (

**l**) all the actions with the features $pksMean$ and $pksNum$ when Order = 0.75.

**Figure 13.**The effect of classification with two features extracted directly in the time domain without FRFT. (

**a**) walk and dwstairs with the features $std$ and $pksNum$; (

**b**) dwstairs and upstairs with the features $range$ and $pksNum$; (

**c**) walk and upstairs with the features $rms$ and $mean$; (

**d**) all the actions with the features $var$ and $IQR$.

**Figure 14.**The structure and process of the classifier. As different orders and feature vectors are needed to classify walk, upstairs and dwstairs, one can distinguish walk and dwstairs first, and then separate upstairs from walk and dwstairs, respectively, then separate upstairs from walk and dwstairs, respectively.

**Figure 15.**The artificial knee. The position of the pneumatic cylinder, servo motor and control circuit with inertial measurement unit (IMU) have been pointed out.

**Figure 16.**MEMS (microelectromechanical systems)-IMU, the position of IMU and barometer have been pointed out.

**Figure 17.**The results of each sub-classifier. (

**a**) run and other actions with the features $rms$ and $pksNum$; (

**b**) walk and dwstairs with the features $std$ and $pksNum$; (

**c**) walk and upstairs with the features $rms$ and $mean$; (

**d**) dwstairs and upstairs with the features $range$ and $pksNum$.

Features | Calculation Method |
---|---|

Maximum | $max(A)$ |

Minimum | $min(A)$ |

Mean | $mean(A)={\displaystyle \sum _{i}\frac{{A}_{i}}{n}}$ |

Extreme Difference | $range(A)=max(A)-min(A)$ |

Variance | $var(A)=\frac{{\displaystyle \sum _{i}{({A}_{i}-mean(A))}^{2}}}{n}$ |

Standard Deviation | $std(A)=\sqrt{var(A)}$ |

Root Mean Square | $rms(A)=\sqrt{\frac{{\displaystyle \sum _{i}{A}_{i}^{2}}}{n}}$ |

Absolute Value | $abs({A}_{i})=\left|{A}_{i}\right|$ |

Signal Amplitude Area | $sma(A)=\frac{1}{t}({\displaystyle {\int}_{0}^{t}\left|{A}_{x}\right|dt+}{\displaystyle {\int}_{0}^{t}\left|{A}_{y}\right|dt+}{\displaystyle {\int}_{0}^{t}\left|{A}_{z}\right|dt})$ |

Correlation Coefficient | $cc(A)=\frac{cov({A}_{x},{A}_{y})}{var({A}_{x},{A}_{y})}$ |

Interquartile Range | $IQR={Q}_{3}-{Q}_{1}$ |

Number of Peaks | The number of peaks in signal ($pksNum$) |

Mean of Peaks | $pksMean=\frac{{\displaystyle \sum _{\mathrm{i}}pk{s}_{i}}}{n}$ |

Feature | STD | ||
---|---|---|---|

Min | Mean | ||

Value | Order | ||

Range | 0.6996 | 0.390 | 1.1189 |

Standard Deviation (Std) | 0.1494 | 0.453 | 0.1854 |

Variance (Var) | 0.4785 | 0.453 | 0.6612 |

Root Mean Square (RMS) | 0.0382 | 0.635 | 0.0387 |

Interquartile Range (IQR) | 0.2171 | 0.310 | 0.3105 |

Mean | 0.2799 | 1 | 0.3076 |

Mean of Peaks (pksMean) | 0.6857 | 0.043 | 1.1725 |

Number of Peaks (pksNum) | 0.5430 | 0.992 | 2.6806 |

Feature | STD | ||
---|---|---|---|

Min | Mean | ||

Value | Order | ||

Range | 1.9913 | 0.981 | 3.0821 |

Std | 0.4898 | 0.997 | 0.5659 |

Var | 2.4833 | 0.428 | 3.1291 |

RMS | 0.0527 | 0.607 | 0.0535 |

IQR | 0.3743 | 0.130 | 0.7365 |

Mean | 0.3249 | 1 | 0.7060 |

pksMean | 1.9208 | 0.701 | 2.8684 |

pksNum | 0.5633 | 1 | 2.7401 |

Feature | STD | ||
---|---|---|---|

Min | Mean | ||

Value | Order | ||

Range | 0.6453 | 0.400 | 1.2644 |

Std | 0.1589 | 0.281 | 0.1978 |

Var | 0.4816 | 0.308 | 0.7028 |

RMS | 0.0209 | 0.624 | 0.0213 |

IQR | 0.2369 | 0.212 | 0.3018 |

Mean | 0.1681 | 1 | 0.2500 |

pksMean | 0.6681 | 0.194 | 1.3048 |

pksNum | 0.6485 | 0.997 | 2.9343 |

Feature | STD | ||
---|---|---|---|

Min | Mean | ||

Value | Order | ||

Range | 2.3835 | 0.803 | 3.3444 |

Std | 0.4612 | 0.168 | 0.5488 |

Var | 3.6646 | 0.169 | 4.9012 |

RMS | 0.0783 | 0.663 | 0.0803 |

IQR | 0.6780 | 0.318 | 0.8944 |

Mean | 0.6471 | 0.020 | 0.8000 |

pksMean | 0.9936 | 0.031 | 1.2464 |

pksNum | 2.8274 | 0.991 | 4.4601 |

Project | Value |
---|---|

Age | 24 |

Weight | 65 kg |

Position of prosthesis | Left |

High | 174 cm |

Gender | M |

Parameters | Main Specifications | |||
---|---|---|---|---|

Sustainable Working Hours | ≥ 24 h | |||

Operating Voltage | 3.3 to 30 V | |||

Sustainable Working Temperature | −40 °C to 85 °C | |||

Power Consumption | 550 mW@5.0 V | |||

Core Circuit Board Dimensions | 33 mm × 20 mm × 22 mm | |||

Weight | <100 g | |||

Sensing Range | 0° to 360° | |||

Static Accuracy | ±0.5° (roll, pitch); ±1° (yaw) | |||

Dynamic Accuracy | ±1° RMS | |||

Resolution | 0.05° | |||

Output Frequency | 0.01 to 100 Hz | |||

Sensor | Accelerometer | Gyroscope | Parameters | Barometer |

Measure range | ±10 g | ±1000°/s | Measure range | 10 to 1200 mbar |

Nonlinear | <0.2% of FS | <0.1% of FS | Resolution | 10 cm |

Bias stability | ±4 mg | 9.2°/h | Bias stability | ±1 mbar/year |

Sub-Classifier | b | c | d | e |
---|---|---|---|---|

Accuracy | 0.9505 | 0.9538 | 0.9143 | 0.8939 |

Precision | 0.7843 | 0.9836 | 0.9836 | 0.9341 |

Recall | 1 | 0.9326 | 0.8696 | 0.8667 |

F1–Score | 0.3053 | 0.7018 | 0.7157 | 0.6753 |

Sub-Classifier | Fractional Domain | Time Domain |
---|---|---|

b | 0.9505 | 0.9011 |

c | 0.9538 | 0.8259 |

d | 0.9143 | 0.7424 |

e | 0.8939 | 0.7629 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, T.; Liu, N.; Su, Z.; Li, C.
A New Time–Frequency Feature Extraction Method for Action Detection on Artificial Knee by Fractional Fourier Transform. *Micromachines* **2019**, *10*, 333.
https://doi.org/10.3390/mi10050333

**AMA Style**

Wang T, Liu N, Su Z, Li C.
A New Time–Frequency Feature Extraction Method for Action Detection on Artificial Knee by Fractional Fourier Transform. *Micromachines*. 2019; 10(5):333.
https://doi.org/10.3390/mi10050333

**Chicago/Turabian Style**

Wang, Tianrun, Ning Liu, Zhong Su, and Chao Li.
2019. "A New Time–Frequency Feature Extraction Method for Action Detection on Artificial Knee by Fractional Fourier Transform" *Micromachines* 10, no. 5: 333.
https://doi.org/10.3390/mi10050333