# Dynamic Stress Measurement with Sensor Data Compensation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Sensor Data Compensation

#### 2.2. Heuristic Algorithms for BP Neural Network

#### 2.3. Stress Measurements of Parachutes

## 3. The Dynamic Measurement with Compensation System of Airdropped WSN

#### 3.1. Network Structure and Deployment

#### 3.2. DC-BPNN Model Establishment

#### 3.3. Voltage-Stress Conversion Model

## 4. Adaptive Artificial Bee Colony Algorithm IN DC-BPNN Model

#### 4.1. Adaptive ABC--Improvement of Path Search

#### 4.2. Stability of AABC Algorithm in DC-BPNN Model

## 5. Experiments

#### 5.1. Model Training in THMTT Machine

#### 5.2. Airdropped Experiment

#### 5.3. Effectiveness of AABC

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wu, S.; Niu, J.; Chou, W.; Guizani, M. Delay-Aware Energy Optimization for Flooding in Duty-Cycled Wireless Sensor Networks. IEEE Trans. Wirel. Commun.
**2016**, 15, 8449–8462. [Google Scholar] [CrossRef] - Xiao, Y.; Rayi, V.; Sun, B.; Du, X.; Hu, F.; Galloway, M. A Survey of Key Management Schemes in Wireless Sensor Networks. J. Comput. Commun.
**2007**, 30, 2314–2341. [Google Scholar] [CrossRef] - Liu, G.J.; Tan, R.; Zhou, R.; Xing, G.L.; Song, W.Z.; Lees, J.M. Volcanic Earthquake Timing using Wireless Sensor Networks. In Proceedings of the 12th ACM/IEEE Conference on Information Processing in Sensor Networks (IPSN), Philadelphia, PA, USA, 8–11 April 2013; pp. 91–102. [Google Scholar]
- Du, X.; Xiao, Y.; Guizani, M.; Chen, H.H. An Effective Key Management Scheme for Heterogeneous Sensor Networks. Ad Hoc Netw.
**2007**, 5, 24–34. [Google Scholar] [CrossRef] - Giggenbach, D.; Epple, B.; Horwath, J.; Moll, F. Optical Satellite Downlinks to Optical Ground Stations and High-Altitude Platforms. Lect. Notes Electr. Eng.
**2008**, 16, 331–349. [Google Scholar] [CrossRef] - Zhao, J.; Zhuang, Y.; Gu, J.; Xu, Y.; Sun, J. Sensor Module Based on the Wireless Sensor Network for the Dynamic Stress on the Flexible Object with Large Deformation. J. Sens.
**2016**, 2016, 1–11. [Google Scholar] [CrossRef] - Motz, M.; Ausserlechner, U.; Holliber, M. Compensation of Mechanical Stress-Induced Drift of Bandgap References with On-Chip Stress Sensor. IEEE Sens. J.
**2015**, 15, 5115–5121. [Google Scholar] [CrossRef] - Deng, C.; Mao, Y.; Ren, G. MEMS Inertial Sensors-Based Multi-Loop Control Enhanced by Disturbance Observation and Compensation for Fast Steering Mirror System. Sensors
**2016**, 16, 1920. [Google Scholar] [CrossRef] [PubMed] - Xie, F.; Weiss, R.; Weigel, R. Hysteresis Compensation Method for Magnetoresistive Sensors Based on Single Polar Controlled Magnetic Field Pulses. IEEE Trans. Ind. Electron.
**2017**, 64, 710–716. [Google Scholar] [CrossRef] - Matko, V.; Milanović, M. High-Precision Hysteresis Sensing of the Quartz Crystal Inductance-to-Frequency Converter. Sensors
**2016**, 16, 995. [Google Scholar] [CrossRef] - Matko, V. Next Generation AT-Cut Quartz Crystal Sensing Devices. Sensors
**2011**, 11, 4474–4482. [Google Scholar] [CrossRef][Green Version] - Xu, M.; Han, T.; Lin, Z. Energy-Efficient Time Synchronization in Wireless Sensor Networks via Temperature-Aware Compensation. ACM Trans. Sens. Netw.
**2016**, 12, 1–29. [Google Scholar] [CrossRef] - Verma, M.; Asmita, S.; Shukla, K. A Regularized Ensemble of Classifiers for Sensor Drift Compensation. IEEE Sens. J.
**2016**, 16, 1310–1318. [Google Scholar] [CrossRef] - Li, Z.; Zhao, X. BP artificial neural network based wave front correction for sensor-less free space optics communication. Opt. Commun.
**2017**, 385, 219–228. [Google Scholar] [CrossRef] - Liu, S.; Hou, Z.; Yin, C. Data-Driven Modeling for UGI Gasification Processes via an Enhanced Genetic BP Neural Network with Link Switches. IEEE Trans. Neural Netw. Learn. Syst.
**2016**, 27, 1–12. [Google Scholar] [CrossRef] [PubMed] - Karaboga, D.; Basturk, B. A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. J. Glob. Optim.
**2007**, 39, 459–471. [Google Scholar] [CrossRef] - Xu, Y.; Gao, F.; Ren, H.; Zhang, Z.; Jiang, X. An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target. Sensors
**2017**, 17, 1188. [Google Scholar] [CrossRef] [PubMed] - Zheng, Y.; Wu, J.; Yang, Y. Temperature compensation of eddy current sensor based on temperature-voltage model. In Proceedings of the 12th World Congress on Intelligent Control. and Automation (WCICA), Guilin, China, 12 June 2016; pp. 438–441. [Google Scholar]
- Bu, X.; Wu, X.; Wei, D.; Huang, J. Neural-approximation-based robust adaptive control of flexible air-breathing hypersonic vehicles with parametric uncertainties and control input constraints. Inf. Sci.
**2016**, 346, 29–43. [Google Scholar] [CrossRef] - Wei, P.; Cheng, C.; Liu, T. A Photonic Transducer based Optical Current Sensor using Back-Propagation Neural Network. IEEE Photon. Technol. Lett.
**2016**, 28, 1513–1516. [Google Scholar] [CrossRef] - Chen, X.; Zhang, M.; Ruan, K. A Ranging Model Based on BP Neural Network. Intell. Autom. Soft Comput.
**2016**, 22, 325–329. [Google Scholar] [CrossRef] - Kirkpatrick, S.; Gelatt, C.; Vecchi, M. Optimization by Simulated Annealing. Read. Comput. Vis.
**1987**, 220, 606–615. [Google Scholar] - Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] [CrossRef][Green Version] - Dorigo, M.; Birattrai, M.; Stutzle, T. Ant colony optimization. IEEE Comput. Intell. Mag.
**2006**, 1, 28–39. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle Swarm Optimization. In Encyclopedia of Machine Learning; Springer: Boston, MA, USA, 2011; Volume 4, pp. 760–766. [Google Scholar]
- Chakrabarti, A. Mass-Spring-Damper System as the Mathematical Model for the Pattern of Sand Movement for an Eroding Beach Around Digha, West Bengal, India. J. Sediment. Res.
**1977**, 47, 311–330. [Google Scholar] [CrossRef] - Meng, J.C.S.; Thomson, J.A.L. Numerical studies of some non-linear hydrodynamic problems by discrete vortex element methods. J. Fluid Mech.
**1978**, 84, 433–453. [Google Scholar] [CrossRef] - Du, X.; Guizani, M.; Xiao, Y.; Chen, H.H. Transactions papers, A Routing-Driven Elliptic Curve Cryptography based Key Management Scheme for Heterogeneous Sensor Networks. IEEE Trans. Wirel. Commun.
**2009**, 8, 1223–1229. [Google Scholar] [CrossRef] - Jalalifar, M.; Byun, G. A Wide Range CMOS Temperature Sensor with Process Variation Compensation for On-Chip Monitoring. IEEE Sens. J.
**2016**, 16, 5536–5542. [Google Scholar] [CrossRef] - Gibbs, M.N.; Mackay, D.C. Variational Gaussian process classifiers. IEEE Trans. Neural Netw.
**2002**, 11, 1458–1464. [Google Scholar] - Bousquet, O.; Elisseeff, A. Stability and generalization. J. Mach. Learn. Res.
**2002**, 2, 499–526. [Google Scholar] - Hardt, M.; Recht, B.; Singer, Y. Train faster, generalize better: Stability of stochastic gradient descent. Int. Conf. Mach. Learn.
**2016**, Jun 11, 1225–1234. [Google Scholar] - Shalev-Shwartz, S.; Shamir, O.; Srebro, N.; Sridharan, K. Learnability, stability and uniform convergence. J. Mach. Learn. Res.
**2010**, 11, 2635–2670. [Google Scholar] - Budil, D.E.; Lee, S.; Saxena, S.; Freed, J.H. Nonlinear-Least-Squares Analysis of Slow-Motion EPR Spectra in One and Two Dimensions Using a Modified Levenberg–Marquardt Algorithm. J. Magn. Reson. Ser. A
**1996**, 120, 155–189. [Google Scholar] [CrossRef]

**Figure 1.**Structure of dynamic measurement system based on airdropped WSN. (

**a**) Overall system structure. (

**b**) Deployment detail on a parachute.

**Figure 4.**Experiments in THMTT machine. (

**a**) Overall structure of the machine. (

**b**) Core part of the testing machine.

Methods of Compensation | Main Idea | Disadvantages | Speed | Accuracy | |
---|---|---|---|---|---|

Hardware [5,6,7,8,9] | Use different complex circuits. | Costly, complex circuit, difficult to debug. | Fast | High | |

Software | Interpolation [17] | The ranges are segmented into pieces, and each segment is expressed by a polynomial. | The higher the accuracy is, the more storage space it needs. | Low | Depend on number of segments. |

LSPCF [18] | Find a matching function by minimizing the square of the error. | Ill-conditioned equations and long time-consumption caused by high order of fitted linear curves. | Medium | Medium | |

BP-NN [19,20] | Minimize network error sum squares by feedback learning, with simpler implementation process. | Easy to fall into local optimal. | Fast | High |

AABC | DC-BPNN |
---|---|

Colony size | Solution quantity |

Food source quality (Fitness) | MSE |

Speed of searching the best food source | Speed of optimization |

Best food source | Global optimal solution |

Food source dimension | Neural network dimension |

Methods | MSE | Time | |||
---|---|---|---|---|---|

Optimal Solution | Average Value | Variance | Average (s) | Variance | |

LM | 2.13 × 10^{−9} | 2.31 × 10^{−8} | 2.56 × 10^{−8} | 2.49 | 0.0224 |

ABC | 2.23 × 10^{−10} | 2.91 × 10^{−9} | 2.87 × 10^{−9} | 2.29 | 0.0337 |

AABC | 4.79 × 10^{−13} | 4.17 × 10^{−12} | 2.35 × 10^{−12} | 2.11 | 0.0646 |

© 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**

Gu, J.; Dong, Z.; Zhang, C.; Du, X.; Guizani, M. Dynamic Stress Measurement with Sensor Data Compensation. *Electronics* **2019**, *8*, 859.
https://doi.org/10.3390/electronics8080859

**AMA Style**

Gu J, Dong Z, Zhang C, Du X, Guizani M. Dynamic Stress Measurement with Sensor Data Compensation. *Electronics*. 2019; 8(8):859.
https://doi.org/10.3390/electronics8080859

**Chicago/Turabian Style**

Gu, Jingjing, Zhiteng Dong, Cai Zhang, Xiaojiang Du, and Mohsen Guizani. 2019. "Dynamic Stress Measurement with Sensor Data Compensation" *Electronics* 8, no. 8: 859.
https://doi.org/10.3390/electronics8080859