# Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating

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## Abstract

**:**

## 1. Introduction

- (1)
- We attempt to apply nonlinear dynamics and chaotic theory to built-in sensor signal analysis.
- (2)
- We calculate the optimal delay time and proper correlation dimension, and then we reveal the nonlinear properties of built-in accelerometer in the smart device by reconstructing the attractors.

## 2. Feasibility of Built-in Accelerometer

## 3. Nonlinear Characteristics Analysis

## 4. Experiments and Results Analysis

## 5. Nonlinear Mapping between Microphone and Accelerometer

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zhang, L.; Pathak, P.H.; Wu, M.; Zhao, Y.; Mohapatra, P. Accelword: Energy efficient hotword detection through accelerometer. In Proceedings of the 13th Annual International Conference on Mobile Systems, Applications, and Services, Florence, Italy, 18–22 May 2015; pp. 301–315. [Google Scholar]
- Michalevsky, Y.; Boneh, D.; Nakibly, G. Gyrophone: Recognizing Speech from Gyroscope Signals. In Proceedings of the 23rd Security Symposium, San Diego, CA, USA, 20–22 August 2014; pp. 1053–1067. [Google Scholar]
- Trippel, T.; Weisse, O.; Xu, W.; Honeyman, P.; Fu, K. WALNUT: Waging Doubt on the Integrity of MEMS Accelerometers with Acoustic Injection Attacks. In Proceedings of the 2017 IEEE European Symposium on Security and Privacy (EuroS&P), Paris, France, 26–28 April 2017; pp. 3–18. [Google Scholar]
- Young, P.J.; Jin, J.H.; Woo, S.; Lee, D.H. BadVoice: Soundless voice-control replay attack on modern smartphones. In Proceedings of the 28th International Conference on Ubiquitous and Future Networks (ICUFN), Vienna, Austria, 5–8 July 2016; pp. 882–887. [Google Scholar]
- Yuri, M.M.; Kasim, S.; Hassan, R.; Abdullah, Z.; Ruslan, H.; Jahidin, K.; Arshad, M.S. Smart mirror for smart life. In Proceedings of the 2017 6th ICT International Student Project Conference (ICT-ISPC), Johor, Malaysia, 23–24 May 2017; pp. 1–5. [Google Scholar]
- Mehta, D.D.; Zañartu, M.; Van Stan, J.H.; Feng, S.W.; Cheyne, H.A.; Hillman, R.E. Smartphone-based detection of voice disorders by long-term monitoring of neck acceleration features. In Proceedings of the 2013 IEEE International Conference on Body Sensor Networks, Cambridge, MA, USA, 6–9 May 2013; pp. 1–6. [Google Scholar]
- Mourcou, Q.; Fleury, A.; Diot, B.; Vuillerme, N. Proprio: A smartphone-based system to measure and improve proprioceptive function. In Proceedings of the 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Orlando, FL, USA, 16–20 August 2016; pp. 2622–2625. [Google Scholar]
- Pipanmaekaporn, L.; Wichinawakul, P.; Kamolsantiroj, S. Mining Acceleration Data for Smartphone-based Fall Detection. In Proceedings of the 10th International Conference on Knowledge and Smart Technology (KST), Chiang Mai, Thailand, 31 January–3 February 2018; pp. 74–79. [Google Scholar]
- Masulli, F.; Parenti, R.; Studer, L. Neural Modeling of Non-Linear Processes: The Relevance of the Takens-Mane Theorem. Int. J. Chaos Theory Appl.
**1999**, 4, 59–74. [Google Scholar] - Van der Schaaf, J.; Van Ommen, J.R.; Takens, F.; Schouten, J.C.; Van den Bleek, C.M. Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds. Chem. Eng. Sci.
**2004**, 59, 1829–1840. [Google Scholar] [CrossRef] - Algaba, A.; Domínguez-Moreno, M.C.; Merino, M.; Rodríguez-Luis, A.J. Takens–Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. Commun. Nonlinear Sci. Numer. Simul.
**2016**, 30, 25–30. [Google Scholar] [CrossRef] - Xu, Y.; Mabonzo, V.D. Analysis of Takens–Bogdanov points for delay differential equations. Appl. Math. Comput.
**2012**, 218, 49–53. [Google Scholar] [CrossRef] - Box, G.E.; Jenkins, G.M.; Reinsel, G.C.; Ljung, G.M. Time Series Analysis: Forecasting and Control; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Gu, J.; Chen, S.; Sivasundaram, S. Nonlinear Analysis on Traffic Flow Based on Catastrophe and Chaos Theory. Discret. Dyn. Nat. Soc.
**2014**, 2014, 535167. [Google Scholar] [CrossRef] - Kugiumtzis, D. State space reconstruction parameters in the analysis of chaotic time series—The role of the time window length. Physica D
**1996**, 95, 13–28. [Google Scholar] [CrossRef] - Kim, H.S.; Eykholt, R.; Salas, J.D. Nonlinear dynamics, delay times, and embedding windows. Physica D
**1999**, 127, 48–60. [Google Scholar] [CrossRef] - Guariglia, E. Entropy and Fractal Antennas. Entropy
**2016**, 18, 84. [Google Scholar] [CrossRef] - Guido, R.C. Practical and useful tips on discrete wavelet transforms. IEEE Signal Process. Mag.
**2015**, 32, 162–166. [Google Scholar] [CrossRef] - Guariglia, E. Harmonic Sierpinski Gasket and Applications. Entropy
**2018**, 20, 714. [Google Scholar] [CrossRef] - Guido, R.C.; Addison, P.S.; Walker, J. Introducing wavelets and time-frequency analysis. IEEE Eng. Biol. Med. Mag.
**2009**, 28, 13–18. [Google Scholar] [CrossRef] [PubMed]

**Figure 3.**Time-frequency diagram of response signals to chirp signal. (

**a**) Microphone (

**b**) Built-in accelerometer.

**Figure 6.**An instance of $\overline{{S}_{2}}(t)$, $\Delta \overline{{S}_{2}}(t)$ and ${S}_{c}(t)$ from the measured signal.

**Figure 8.**The output signal of the accelerometer at different distances. (

**a**) The output signal of the accelerometer at distance of 5 cm; (

**b**) The output signal of the accelerometer at distance of 10 cm; (

**c**) The output signal of the accelerometer at distance of 15 cm.

**Figure 9.**The recorded voice at 5 cm and 30 cm, respectively for comparison. (

**a**) The recorded voice at 5 cm; (

**b**) The recorded voice at 30 cm.

**Figure 10.**The attractors of $\tau $ = 3,4,5,6 at X-axis when saying “oh”. (

**a**) The attractor of $\tau $ = 3; (

**b**) The attractor of $\tau $ = 4; (

**c**) The attractor of $\tau $ = 5; (

**d**) The attractor of $\tau $ = 6.

**Figure 11.**The attractors of $\tau $ = 3,4,5,6 at Y-axis when saying “two”. (

**a**) The attractor of $\tau $ = 3; (

**b**) The attractor of $\tau $ = 4; (

**c**) The attractor of $\tau $ = 5; (

**d**) The attractor of $\tau $ = 6.

**Figure 12.**The attractors of $\tau $ = 3,4,5,6 at Z-axis when saying “zero”. (

**a**) The attractor of $\tau $ = 3; (

**b**) The attractor of $\tau $ = 4; (

**c**) The attractor of $\tau $ = 5; (

**d**) The attractor of $\tau $ = 6.

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**MDPI and ACS Style**

Zhao, N.; Liu, Y.; Shen, J.
Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating. *Future Internet* **2019**, *11*, 81.
https://doi.org/10.3390/fi11030081

**AMA Style**

Zhao N, Liu Y, Shen J.
Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating. *Future Internet*. 2019; 11(3):81.
https://doi.org/10.3390/fi11030081

**Chicago/Turabian Style**

Zhao, Ning, Yuhe Liu, and Junjie Shen.
2019. "Nonlinear Analysis of Built-in Sensor in Smart Device under the Condition of Voice Actuating" *Future Internet* 11, no. 3: 81.
https://doi.org/10.3390/fi11030081