Distributed Piezoelectric Sensor System for Damage Identification in Structures Subjected to Temperature Changes
Abstract
:1. Introduction
2. Theoretical Background
2.1. Principal Component Analysis
2.1.1. PCA Modeling
2.1.2. Normalization: Group Scaling
2.1.3. Projection of New Data onto the PCA Model
2.2. Machine Learning
2.2.1. Nearest Neighbor Pattern Classification
- Fine k-NN: a nearest neighbor classifier that makes finely-detailed distinctions between classes with the number of neighbors set to one.
- Medium k-NN: a nearest neighbor classifier with fewer distinctions than a fine k-NN with the number of neighbors set to 10.
- Coarse k-NN: a nearest neighbor between classes, with the number of neighbors set to 100.
- Cosine k-NN: a nearest neighbor classifier that uses the cosine distance metric. The cosine distance between two vectors u and v is defined as:
- Cubic k-NN: a nearest neighbor classifier that uses the cubic distance metric. The cubic distance between two n-dimensional vectors u and v is defined as:
- Weighted k-NN: a nearest neighbor classifier that uses distance weighting. The weighted Euclidean distance between two n-dimensional vectors u and v is defined as:
2.2.2. Decision Trees
- Compared with other machine learning methods, trees are simple and easy to understand.
- Decision trees use different methods and can be combined to obtain a single prediction.
- The combination of different trees usually produces better results.
- Because of its simplicity, more elaborated methods can produce better results in classification and regression tasks.
2.2.3. Support Vector Machines
3. Damage Classification Methodology
Data Acquisition System
4. Experimental Setup and Results
- (i)
- an aluminum plate with four piezoelectric transducers; and
- (ii)
- a composite plate of carbon fiber polymer with six piezoelectric transducers.
4.1. First Specimen: Aluminum Plate
- and
- .
- no damage (healthy or pristine structure);
- Damage 1;
- Damage 2; and
- Damage 3.
4.2. Second Specimen: Carbon Fiber Plate
- and
- .
- no damage (healthy or pristine structure);
- Damage 1;
- Damage 2; and
- Damage 3.
5. Concluding Remarks
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Machine Name | Healthy | Damage 1 | Damage 2 | Damage 3 |
---|---|---|---|---|
Medium Tree | 66% | 76% | 70% | 56% |
Simple Tree | 64% | 60% | 30% | 58% |
Complex Tree | 72% | 76% | 58% | 56% |
Linear SMV | 70% | 60% | 26% | 60% |
Quadratic SVM | 78% | 70% | 56% | 70% |
Cubic SVM | 86% | 68% | 66% | 72% |
Fine Gaussian SVM | 90% | 80% | 66% | 78% |
Medium Gaussian SVM | 76% | 80% | 56% | 74% |
Coarse Gaussian SVM | 94% | 64% | 14% | 38% |
Fine k-NN | 94% | 78% | 74% | 80% |
Medium k-NN | 80% | 62% | 64% | 74% |
Coarse k-NN | 94% | 42% | 2% | 24% |
Cosine k-NN | 84% | 58% | 78% | 72% |
Cubic k-NN | 80% | 64% | 62% | 76% |
Weighted k-NN | 94% | 66% | 68% | 80% |
Boosted Trees | 96% | 0% | 42% | 42% |
Bagged Trees | 84% | 70% | 66% | 78% |
Subspace Discriminant | 56% | 44% | 32% | 46% |
Subspace k-NN | 94% | 78% | 72% | 80% |
Rusboosted Trees | 98% | 0% | 42% | 0% |
Machine Name | Healthy | Damage 1 | Damage 2 | Damage 3 |
---|---|---|---|---|
Medium Tree | 55.00% | 63.33% | 60.83% | 52.50% |
Simple Tree | 40.00% | 60.00% | 63.33% | 42.50% |
Complex Tree | 57.50% | 64.17% | 75.83% | 65.83% |
Linear SVM | 41.67% | 59.17% | 45.00% | 47.50% |
Quadratic SVM | 65.83% | 73.33% | 85.00% | 75.50% |
Cubic SVM | 70.83% | 75.00% | 86.67% | 74.17% |
Fine Gaussian SVM | 59.17% | 64.17% | 83.33% | 78.33% |
Medium Gaussian SVM | 55.83% | 60.00% | 82.50% | 63.33% |
Coarse Gaussian SVM | 52.50% | 10.83% | 33.33% | 56.67% |
Fine k-NN | 63.33% | 61.67% | 80.00% | 70.00% |
Medium k-NN | 65.00% | 46.67% | 75.00% | 63.33% |
Coarse k-NN | 52.50% | 37.50% | 60.83% | 35.83% |
Cosine k-NN | 65.00% | 43.33% | 79.17% | 60.83% |
Cubic k-NN | 59.17% | 47.50% | 72.50% | 60.00% |
Weighted k-NN | 61.67% | 58.33% | 83.33% | 74.17% |
Boosted Trees | 16.67% | 62.50% | 60.83% | 71.67% |
Bagged Trees | 71.67% | 72.50% | 90.00% | 84.17% |
Subspace Discriminant | 33.33% | 45.83% | 45.00% | 55.83% |
Subspace k-NN | 70.83% | 72.50% | 89.17% | 82.50% |
Rusboosted Trees | 0.00% | 62.50% | 0.00% | 93.33% |
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Vitola, J.; Pozo, F.; Tibaduiza, D.A.; Anaya, M. Distributed Piezoelectric Sensor System for Damage Identification in Structures Subjected to Temperature Changes. Sensors 2017, 17, 1252. https://doi.org/10.3390/s17061252
Vitola J, Pozo F, Tibaduiza DA, Anaya M. Distributed Piezoelectric Sensor System for Damage Identification in Structures Subjected to Temperature Changes. Sensors. 2017; 17(6):1252. https://doi.org/10.3390/s17061252
Chicago/Turabian StyleVitola, Jaime, Francesc Pozo, Diego A. Tibaduiza, and Maribel Anaya. 2017. "Distributed Piezoelectric Sensor System for Damage Identification in Structures Subjected to Temperature Changes" Sensors 17, no. 6: 1252. https://doi.org/10.3390/s17061252
APA StyleVitola, J., Pozo, F., Tibaduiza, D. A., & Anaya, M. (2017). Distributed Piezoelectric Sensor System for Damage Identification in Structures Subjected to Temperature Changes. Sensors, 17(6), 1252. https://doi.org/10.3390/s17061252