# Application of PZT Ceramic Sensors for Composite Structure Monitoring Using Harmonic Excitation Signals and Bayesian Classification Approach

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## Abstract

**:**

## 1. Introduction

- malignant tumor detection [33];

## 2. Structural Health Monitoring Based on Harmonic Excitation of PZT Sensors and Voltage Transfer Ratio

- the configuration of PZT transducers;
- the type of excitation voltage applied to PZT actuators.

## 3. Definition of Data Classification Method

#### 3.1. General Bayesian Setup

#### 3.2. Maximum Likelihood Method

#### 3.3. Principal Component Analysis Representation Space of Signal Features

- 0.01 s for integration of 1-d normal distribution;
- 1.2 s for integration of 2-d normal distribution;
- 79.5 s for integration of 3-d normal distribution;

#### 3.4. Definition of Bayesian Setup for Voltage Transfer Ratio Approach to SHM

## 4. Experiment Results and Discussion

#### 4.1. Application of Voltage Transfer Ratio Approach to Artificial Damage Detection

- Type I sensing paths which runs transversally through artificial damage and are sensitive to transmission mode of elastic waves interaction with damage;
- Type II sensing paths which are tangential to artificial damage or runs it its proximity and can be affected by transmission mode (to some extent) and reflection mode of wave interaction with damage;
- Type III sensing paths which are separated from artificial damage but are affected by waves reflected from damage;
- Type IV sensing paths which are well separated from damage and are not influenced by its presence.

- Type I sensing paths are defined by the following pair of PZT transducers:
- -
- for location no. 1: 3–5, 1–7, 2–8, 4–6;

- -
- for location no. 3: 2–8, 3–6.

- Type II sensing paths are defined by the following pair of PZT transducers:
- -
- for location no. 1: 1–6, 4–7;

- -
- for location no. 3: 3–7, 2–5.

- Type III sensing paths are defined by the following pair of PZT transducers:
- -
- for location no. 1: 3–7, 1–5;

- -
- for location no. 3: 2–7, 3–5.

#### 4.2. Application of Voltage Transfer Ratio Approach to Impact Damage Detection

- Type I sensing paths which runs transversally through BVID;
- Type II sensing paths which runs in close proximity of impact damage;
- Type III sensing paths which are separated from impact damage and are barely influenced by its presence.

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BVID | Barely Visible Impact Damage |

DI (DIs) | Damage Index (Damage Indices) |

EMI | Electromechanical Impedance |

GFRP | Glass Fiber Reinforced Polymer |

ML | Maximum Likelihood |

PCA | Principal Component Analysis |

SHM | Structural Health Monitoring |

## References

- Fraden, J. Handbook of Modern Sensors; Springer-Verlag: New York, NY, USA, 2010. [Google Scholar]
- Boller, C.; Chang, F.K.; Fujino, Y. (Eds.) Encyclopedia of Structural Health Monitoring; John Wiley & Sons, Ltd.: Chichester, UK, 2009. [Google Scholar]
- Staszewski, W.; Boller, C.; Tomlinson, G. Health Monitoring of Aerospace Structures; John Wiley & Sons, Ltd.: Chichester, UK, 2004. [Google Scholar]
- Mukhopadhyay, S.C. New Developments in Sensing Technology for Structural Health Monitoring; Springer-Verlag: Berlin/Heidelberg, Germany, 2011; Volume 96. [Google Scholar]
- Adams, D. Health Monitoring of Structural Materials and Components: Methods with Applications; John Wiley & Sons, Ltd.: Chichester, UK, 2007. [Google Scholar]
- Heywang, W.; Lubitz, K.; Wersing, W. Piezoelectricity: Evolution and Future of a Technology; Springer-Verlag: Berlin/Heidelberg, Germany, 2008; Volume 114. [Google Scholar]
- Giurgiutiu, V. Structural Health Monitoring: With Piezoelectric Wafer Active Sensors, 2nd ed.; Elsevier Academic Press: Amsterdam, The Netherlands, 2014. [Google Scholar]
- Su, Z.; Ye, L. Identification of Damage Using Lamb Waves: From Fundamentals to Applications; Springer-Verlag: Berlin/Heidelberg, Germany, 2009; Volume 48. [Google Scholar]
- Stepinski, T.; Uhl, T.; Staszewski, W. Advanced Structural Damage Detection: From Theory to Engineering Applications; John Wiley & Sons, Ltd.: Chichester, UK, 2013. [Google Scholar]
- Yang, J. An Introduction to the Theory of Piezoelectricity; Springer Science & Business Media: Boston, MA, USA, 2005; Volume 9. [Google Scholar]
- Mei, H.; Haider, M.F.; Joseph, R.; Migot, A.; Giurgiutiu, V. Recent advances in piezoelectric wafer active sensors for structural health monitoring applications. Sensors
**2019**, 19, 383. [Google Scholar] [CrossRef] [Green Version] - Dragan, K.; Dziendzikowski, M. A method to compensate non-damage-related influences on Damage Indices used for pitch-catch scheme of piezoelectric transducer based Structural Health Monitoring. Struct. Health Monit.
**2016**, 15, 423–437. [Google Scholar] [CrossRef] - Janapati, V.; Kopsaftopoulos, F.; Li, F.; Lee, S.J.; Chang, F.K. Damage detection sensitivity characterization of acousto-ultrasound-based structural health monitoring techniques. Struct. Health Monit.
**2016**, 15, 143–161. [Google Scholar] [CrossRef] - Yadav, S.K.; Mishra, S.; Kopsaftopoulos, F.; Chang, F.K. Reliability of crack quantification via acousto-ultrasound active-sensing structural health monitoring using surface-mounted PZT actuators/sensors. Struct. Health Monit.
**2021**, 20, 219–239. [Google Scholar] [CrossRef] - Amerini, F.; Meo, M. Structural health monitoring of bolted joints using linear and nonlinear acoustic/ultrasound methods. Struct. Health Monit.
**2011**, 10, 659–672. [Google Scholar] [CrossRef] - Rucka, M. Monitoring steel bolted joints during a monotonic tensile test using linear and nonlinear Lamb wave methods: A feasibility study. Metals
**2018**, 8, 683. [Google Scholar] [CrossRef] [Green Version] - Li, N.; Wang, F.; Song, G. Monitoring of bolt looseness using piezoelectric transducers: Three-dimensional numerical modeling with experimental verification. J. Intell. Mater. Syst. Struct.
**2020**, 31, 911–918. [Google Scholar] [CrossRef] - Demetgul, M.; Senyurek, V.Y.; Uyandik, R.; Tansel, I.; Yazicioglu, O. Evaluation of the health of riveted joints with active and passive structural health monitoring techniques. Measurement
**2015**, 69, 42–51. [Google Scholar] [CrossRef] - Mickens, T.; Schulz, M.; Sundaresan, M.; Ghoshal, A.; Naser, A.; Reichmeider, R. Structural health monitoring of an aircraft joint. Mech. Syst. Signal Process.
**2003**, 17, 285–303. [Google Scholar] [CrossRef] - Li, W.; Liu, T.; Gao, S.; Luo, M.; Wang, J.; Wu, J. An electromechanical impedance-instrumented corrosion-measuring probe. J. Intell. Mater. Syst. Struct.
**2019**, 30, 2135–2146. [Google Scholar] [CrossRef] - Li, W.; Liu, T.; Zou, D.; Wang, J.; Yi, T.H. PZT based smart corrosion coupon using electromechanical impedance. Mech. Syst. Signal Process.
**2019**, 129, 455–469. [Google Scholar] [CrossRef] - Dai, W.; Wang, X.; Zhang, M.; Zhang, W.; Wang, R. Corrosion monitoring method of porous aluminum alloy plate hole edges based on piezoelectric sensors. Sensors
**2019**, 19, 1106. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lim, Y.Y.; Kwong, K.Z.; Liew, W.Y.H.; Soh, C.K. Non-destructive concrete strength evaluation using smart piezoelectric transducer—A comparative study. Smart Mater. Struct.
**2016**, 25, 085021. [Google Scholar] [CrossRef] - Lim, Y.Y.; Smith, S.T.; Padilla, R.V.; Soh, C.K. Monitoring of concrete curing using the electromechanical impedance technique: Review and path forward. Struct. Health Monit.
**2021**, 20, 604–636. [Google Scholar] [CrossRef] - Zhang, J.; Zhang, C.; Xiao, J.; Jiang, J. A PZT-based electromechanical impedance method for monitoring the soil freeze–thaw process. Sensors
**2019**, 19, 1107. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, C.; Wang, X.; Yan, Q.; Vipulanandan, C.; Song, G. A novel method to monitor soft soil strength development in artificial ground freezing projects based on electromechanical impedance technique: Theoretical modeling and experimental validation. J. Intell. Mater. Syst. Struct.
**2020**, 31, 1477–1494. [Google Scholar] [CrossRef] - Tua, P.; Quek, S.; Wang, Q. Detection of cracks in cylindrical pipes and plates using piezo-actuated Lamb waves. Smart Mater. Struct.
**2005**, 14, 1325. [Google Scholar] [CrossRef] - Yan, S.; Li, Y.; Zhang, S.; Song, G.; Zhao, P. Pipeline damage detection using piezoceramic transducers: Numerical analyses with experimental validation. Sensors
**2018**, 18, 2106. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Song, H.; Lim, H.J.; Sohn, H. Electromechanical impedance measurement from large structures using a dual piezoelectric transducer. J. Sound Vib.
**2013**, 332, 6580–6595. [Google Scholar] [CrossRef] - Abbas, M.; Shafiee, M. Structural health monitoring (SHM) and determination of surface defects in large metallic structures using ultrasonic guided waves. Sensors
**2018**, 18, 3958. [Google Scholar] [CrossRef] [Green Version] - Hameed, M.S.; Li, Z.; Chen, J.; Qi, J. Lamb-wave-based multistage damage detection method using an active PZT sensor network for large structures. Sensors
**2019**, 19, 2010. [Google Scholar] [CrossRef] [Green Version] - Marzani, A.; Testoni, N.; De Marchi, L.; Messina, M.; Monaco, E.; Apicella, A. An open database for benchmarking guided waves structural health monitoring algorithms on a composite full-scale outer wing demonstrator. Struct. Health Monit.
**2020**, 19, 1524–1541. [Google Scholar] [CrossRef] - Menegaz, G.L.; Tsuruta, K.M.; Finzi Neto, R.M.; Steffen, V., Jr.; Araujo, C.A.; Guimarães, G. Use of the electromechanical impedance method in the detection of inclusions: Application to mammary tumors. Struct. Health Monit.
**2021**, 20, 818–833. [Google Scholar] [CrossRef] - Junior, P.; D’addona, D.M.; Aguiar, P.R.; Teti, R. Dressing tool condition monitoring through impedance-based sensors: Part 1—PZT diaphragm transducer response and EMI sensing technique. Sensors
**2018**, 18, 4455. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Junior, P.; D’Addona, D.M.; Aguiar, P.R.; Teti, R. Dressing tool condition monitoring through impedance-based sensors: Part 2—Neural networks and k-nearest neighbor classifier approach. Sensors
**2018**, 18, 4453. [Google Scholar] [CrossRef] [Green Version] - Roach, D.P.; Neidigk, S. Does the Maturity of Structural Health Monitoring Technology Match User Readiness; Technical Report; Sandia National Lab. (SNL-NM): Albuquerque, NM, USA, 2011. [Google Scholar]
- Giurgiutiu, V. Structural Health Monitoring of Aerospace Composites; Elsevier Academic Press: Atlanta, GA, USA, 2015. [Google Scholar]
- Hale, J. 787 From The Ground Up. Aero Mag.
**2006**, 4, 17–23. [Google Scholar] - Gay, D. Composite Materials: Design and Applications; CRC Press: Boca Raton, FL, USA, 2015. [Google Scholar]
- Bielawski, R. Composite materials in military aviation and selected problems with implementation. Rev. Air Force Acad.
**2017**, 15, 11. [Google Scholar] [CrossRef] - Talreja, R. Fatigue of composite materials. In Modern Trends in Composite Laminates Mechanics; Springer-Verlag: Wien, Austria, 2003; pp. 281–294. [Google Scholar]
- Poon, C.; Benak, T.; Gould, R. Assessment of impact damage in toughened resin composites. Theor. Appl. Fract. Mech.
**1990**, 13, 81–97. [Google Scholar] [CrossRef] - Li, C.; Hu, N.; Yin, Y.; Sekine, H.; Fukunaga, H. Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model. Compos. Part A Appl. Sci. Manuf.
**2002**, 33, 1055–1062. [Google Scholar] [CrossRef] - Bieniaś, J.; Jakubczak, P.; Surowska, B.; Dragan, K. Low-energy impact behaviour and damage characterization of carbon fibre reinforced polymer and aluminium hybrid laminates. Arch. Civ. Mech. Eng.
**2015**, 15, 925–932. [Google Scholar] [CrossRef] - Tie, Y.; Zhang, Q.; Hou, Y.; Li, C. Impact damage assessment in orthotropic CFRP laminates using nonlinear Lamb wave: Experimental and numerical investigations. Compos. Struct.
**2020**, 236, 111869. [Google Scholar] [CrossRef] - Smith, R.; Jones, L.; Zeqiri, B.; Hodnett, M. Ultrasonic C-scan standardisation for fibre-reinforced polymer composites: Minimising the uncertainties in attenuation measurements. Insight
**1998**, 40, 34–43. [Google Scholar] - Tuloup, C.; Harizi, W.; Aboura, Z.; Meyer, Y.; Khellil, K.; Lachat, R. On the use of in-situ piezoelectric sensors for the manufacturing and structural health monitoring of polymer-matrix composites: A literature review. Compos. Struct.
**2019**, 215, 127–149. [Google Scholar] [CrossRef] - Diamanti, K.; Hodgkinson, J.M.; Soutis, C. Detection of Low-velocity Impact Damage in Composite Plates using Lamb Waves. Struct. Health Monit.
**2004**, 3, 33–41. [Google Scholar] [CrossRef] - Ochôa, P.; Infante, V.; Silva, J.M.; Groves, R.M. Detection of multiple low-energy impact damage in composite plates using Lamb wave techniques. Compos. Part B Eng.
**2015**, 80, 291–298. [Google Scholar] [CrossRef] - Dziendzikowski, M.; Kurnyta, A.; Dragan, K.; Klysz, S.; Leski, A. In situ Barely Visible Impact Damage detection and localization for composite structures using surface mounted and embedded PZT transducers: A comparative study. Mech. Syst. Signal Process.
**2016**, 78, 91–106. [Google Scholar] [CrossRef] - De Luca, A.; Caputo, F.; Khodaei, Z.S.; Aliabadi, M. Damage characterization of composite plates under low velocity impact using ultrasonic guided waves. Compos. Part B Eng.
**2018**, 138, 168–180. [Google Scholar] [CrossRef] - Dziendzikowski, M.; Niedbala, P.; Kurnyta, A.; Kowalczyk, K.; Dragan, K. Structural health monitoring of a composite panel based on PZT sensors and a transfer impedance framework. Sensors
**2018**, 18, 1521. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Taboga, M.; Maximum likelihood. In Lectures on Probability Theory and Mathematical Statistics, 3rd ed.; Kindle Direct Publishing: 2017; Volume Online appendix. Available online: https://www.statlect.com/fundamentals-of-statistics/maximum-likelihood (accessed on 3 September 2021).
- Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer-Verlag: New York, NY, USA, 2009. [Google Scholar]
- Mori, N.; Biwa, S.; Hayashi, T. Reflection and transmission of Lamb waves at an imperfect joint of plates. J. Appl. Phys.
**2013**, 113, 074901. [Google Scholar] [CrossRef] [Green Version] - Annamdas, V.G.; Radhika, M.A. Electromechanical impedance of piezoelectric transducers for monitoring metallic and non-metallic structures: A review of wired, wireless and energy-harvesting methods. J. Intell. Mater. Syst. Struct.
**2013**, 24, 1021–1042. [Google Scholar] [CrossRef] - Na, W.S.; Baek, J. A review of the piezoelectric electromechanical impedance based structural health monitoring technique for engineering structures. Sensors
**2018**, 18, 1307. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lee, J.W. An Experimental Study on Bolt Looseness Monitoring Using Low-Cost Transfer Impedance Technique. Int. J. Steel Struct.
**2021**, 21, 349–359. [Google Scholar] [CrossRef] - Chiu, W.K.; Koh, Y.; Galea, S.C.; Rajic, N. Smart structure application in bonded repairs. Compos. Struct.
**2000**, 50, 433–444. [Google Scholar] [CrossRef] - Bhalla, S.; Gupta, A.; Bansal, S.; Garg, T. Ultra low-cost adaptations of electro-mechanical impedance technique for structural health monitoring. J. Intell. Mater. Syst. Struct.
**2009**, 20, 991–999. [Google Scholar] [CrossRef] - Tenreiro, A.F.G.; Lopes, A.M.; da Silva, L.F. A review of structural health monitoring of bonded structures using electromechanical impedance spectroscopy. Struct. Health Monit.
**2021**, 1475921721993419. [Google Scholar] [CrossRef] - Flynn, E.B.; Todd, M.D. A Bayesian approach to optimal sensor placement for structural health monitoring with application to active sensing. Mech. Syst. Signal Process.
**2010**, 24, 891–903. [Google Scholar] [CrossRef] - Rogers, T.; Worden, K.; Fuentes, R.; Dervilis, N.; Tygesen, U.; Cross, E. A Bayesian non-parametric clustering approach for semi-supervised structural health monitoring. Mech. Syst. Signal Process.
**2019**, 119, 100–119. [Google Scholar] [CrossRef] - Huo, H.; He, J.; Guan, X. A Bayesian fusion method for composite damage identification using Lamb wave. Struct. Health Monit.
**2020**. [Google Scholar] [CrossRef] - Zhang, Y.M.; Wang, H.; Wan, H.P.; Mao, J.X.; Xu, Y.C. Anomaly detection of structural health monitoring data using the maximum likelihood estimation-based Bayesian dynamic linear model. Struct. Health Monit.
**2020**. [Google Scholar] [CrossRef] - Yang, Y.; Chadha, M.; Hu, Z.; Vega, M.A.; Parno, M.D.; Todd, M.D. A probabilistic optimal sensor design approach for structural health monitoring using risk-weighted f-divergence. Mech. Syst. Signal Process.
**2021**, 161, 107920. [Google Scholar] [CrossRef] - Taboga, M.; Bayesian inference. In Lectures on Probability Theory and Mathematical Statistics, 3rd ed.; Kindle Direct Publishing: 2017; Volume Online appendix. Available online: https://www.statlect.com/fundamentals-of-statistics/Bayesian-inference (accessed on 3 September 2021).
- Mujica, L.; Rodellar, J.; Fernandez, A.; Güemes, A. Q-statistic and T2-statistic PCA-based measures for damage assessment in structures. Struct. Health Monit.
**2011**, 10, 539–553. [Google Scholar] [CrossRef] - Taboga, M.; Normal distribution—Maximum Likelihood Estimation. In Lectures on Probability Theory and Mathematical Statistics, 3rd ed.; Kindle Direct Publishing: 2017; Volume Online appendix. Available online: https://www.statlect.com/fundamentals-of-statistics/normal-distribution-maximum-likelihood (accessed on 3 September 2021).
- Statsmodels. Available online: https://www.statsmodels.org/stable/examples/notebooks/generated/generic_mle.html (accessed on 3 September 2021).
- Steminc. Available online: https://www.steminc.com/PZT/en/piezo-disc-transducer-450-khz (accessed on 4 August 2021).
- Digilent. Available online: https://store.digilentinc.com (accessed on 4 August 2021).
- A.A. Lab Systems Ltd. Available online: https://www.lab-systems.com/products/amplifier/a303.html (accessed on 4 August 2021).
- R Project. Available online: https://cran.r-project.org/ (accessed on 3 September 2021).
- Yang, C.; Liang, K.; Zhang, X.; Geng, X. Sensor placement algorithm for structural health monitoring with redundancy elimination model based on sub-clustering strategy. Mech. Syst. Signal Process.
**2019**, 124, 369–387. [Google Scholar] [CrossRef] - Liu, Z.; Zhong, X.; Dong, T.; He, C.; Wu, B. Delamination detection in composite plates by synthesizing time-reversed Lamb waves and a modified damage imaging algorithm based on RAPID. Struct. Control Health Monit.
**2017**, 24, e1919. [Google Scholar] [CrossRef] - Dziendzikowski, M.; Dragan, K.; Katunin, A. Localizing impact damage of composite structures with modified RAPID algorithm and non-circular PZT arrays. Arch. Civ. Mech. Eng.
**2017**, 17, 178–187. [Google Scholar] [CrossRef] - Wang, S.; Wu, W.; Shen, Y.; Liu, Y.; Jiang, S. Influence of the PZT sensor array configuration on Lamb wave tomography imaging with the RAPID algorithm for hole and crack detection. Sensors
**2020**, 20, 860. [Google Scholar] [CrossRef] [Green Version] - Yang, C. A novel uncertainty-oriented regularization method for load identification. Mech. Syst. Signal Process.
**2021**, 158, 107774. [Google Scholar] [CrossRef] - Shao, J.; Tu, D. The Jackknife and Bootstrap; Springer-Verlag: New York, NY, USA, 2012. [Google Scholar]

**Figure 1.**Cross section visualization of an impact damage of composite structure obtained with use of computer tomography.

**Figure 2.**Example of a sinusoidal steady–state excitation of PZT sensors [52]: (

**a**) PZT sensors configuration; (

**b**) output voltages acquired on PZT sensors.

**Figure 3.**Example of the DIs obtained for the pristine state of the structure and when a damage is present [52].

**Figure 4.**Example of the DIs in two dimensions obtained for two simulated structural states with indication of PCA transformed DIs spaces and vectors corresponding to new data point in both coordinate systems.

**Figure 6.**View of the selected specimen used in the experiment with indication of PZT sensors and artificial damage localization.

**Figure 7.**Examples of Damage Indices obtained for the first PZT network: (

**a**) for damage in location no. 1; (

**b**) for damage in location no. 3.

**Figure 8.**Aggregated Damage Indices obtained for different sensor networks: (

**a**) network 1; (

**b**) network 2.

**Figure 12.**Aggregated Damage Indices obtained for different type of damage: (

**a**) artificial damage (network 1); (

**b**) BVID damage (network 2).

True Class | |||||
---|---|---|---|---|---|

Type I | Type II | Type III | Type IV | ||

result class | Type I | 0.93 | 0.04 | 0 | 0 |

Type II | 0.02 | 0.89 | 0.11 | 0 | |

Type III | 0.05 | 0 | 0.02 | 0 | |

Type IV | 0 | 0.07 | 0.87 | 1 |

True Class | |||||
---|---|---|---|---|---|

Type I | Type II | Type III | Type IV | ||

result class | Type I | 0.99 | 0.12 | 0.00 | 0 |

Type II | 0.01 | 0.87 | 0.19 | 0 | |

Type III | 0 | 0 | 0.26 | 0.20 | |

Type IV | 0 | 0.01 | 0.55 | 0.80 |

True Class | |||||
---|---|---|---|---|---|

Type I | Type II | Type III | Type IV | ||

result class | Type I | 0.97 | 0.17 | 0 | 0 |

Type II | 0.03 | 0.70 | 0.12 | 0 | |

Type III | 0 | 0.01 | 0.23 | 0.03 | |

Type IV | 0 | 0.12 | 0.65 | 0.97 |

True Class | |||||
---|---|---|---|---|---|

Type I | Type II | Type III | Type IV | ||

result class | Type I | 0.99 | 0.24 | 0 | 0 |

Type II | 0.01 | 0.58 | 0.20 | 0 | |

Type III | 0 | 0.04 | 0.33 | 0.18 | |

Type IV | 0 | 0.14 | 0.47 | 0.82 |

**Table 5.**Rate of classification of Bayesian classifier for BVID data (network 2) based on training data obtained for artificial damage (network 1).

True Class | ||||
---|---|---|---|---|

Type I | Type II | Type III | ||

result class | Type I | 0.66 | 0.78 | 0 |

Type II | 0 | 0.06 | 0 | |

Type III | 0 | 0.11 | 0.04 | |

Type IV | 0.34 | 0.05 | 0.96 |

**Table 6.**Rate of classification of nearest-neighbor classifier for BVID data (network 2) based on training data obtained for artificial damage (network 1).

True Class | ||||
---|---|---|---|---|

Type I | Type II | Type III | ||

result class | Type I | 0.71 | 0.54 | 0 |

Type II | 0 | 0.42 | 0.15 | |

Type III | 0 | 0.04 | 0.01 | |

Type IV | 0.29 | 0 | 0.84 |

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**MDPI and ACS Style**

Dziendzikowski, M.; Heesch, M.; Gorski, J.; Dragan, K.; Dworakowski, Z.
Application of PZT Ceramic Sensors for Composite Structure Monitoring Using Harmonic Excitation Signals and Bayesian Classification Approach. *Materials* **2021**, *14*, 5468.
https://doi.org/10.3390/ma14195468

**AMA Style**

Dziendzikowski M, Heesch M, Gorski J, Dragan K, Dworakowski Z.
Application of PZT Ceramic Sensors for Composite Structure Monitoring Using Harmonic Excitation Signals and Bayesian Classification Approach. *Materials*. 2021; 14(19):5468.
https://doi.org/10.3390/ma14195468

**Chicago/Turabian Style**

Dziendzikowski, Michal, Mateusz Heesch, Jakub Gorski, Krzysztof Dragan, and Ziemowit Dworakowski.
2021. "Application of PZT Ceramic Sensors for Composite Structure Monitoring Using Harmonic Excitation Signals and Bayesian Classification Approach" *Materials* 14, no. 19: 5468.
https://doi.org/10.3390/ma14195468