Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability
Abstract
:1. Introduction
2. State–Space Model and P-Type IL Method
3. Dynamic Linearization and MFA Controller Design
4. The Stopping Criteria Design
4.1. Preliminary Notion of Imprecise Probability
4.2. The Diagnosis Method Design
4.2.1. Fault Reliability
4.2.2. Establish Fault Probability Interval
4.2.3. Diagnosis Cost Functions and Decision-Making
5. The Summary of the Proposed Method
6. Numerical Simulations
6.1. FE Modeling and Setting of Controller Parameters
6.2. Harmonic Excitation
6.3. Random Excitation
7. Experiments
7.1. ExperimentSetup
7.2. Modal Analysis
7.3. ExperimentResults
8. Conclusions and Outlooks
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Graphite-Epoxy (GE) | Piezoelectric Material |
---|---|
Yong’s modulus () | Elastic stiffness () |
Shear modulus () | |
Piezoelectric stain () | |
Poisson’s ratio | |
Permittivity () | |
Density () | |
Density () | |
Mode | Numerical (Hz) | Experimental (Hz) | Error Percentage |
---|---|---|---|
1 | 5.4377 | 5.326 | 2.1% |
2 | 24.217 | 21.259 | 13.9% |
3 | 28.683 | 31.593 | −9.2% |
Algorithm | Case 1 | Case 2 | Experiment | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Point A | Point B | Sensor a/b | Sensor c | Point A | Point B | Sensor a/b | Sensor c | Sensor a/b | Sensor c | |
Uncontrolled | 2.262 × 10−3 | 8.805 × 10−3 | 7.420 | 4.314 | 3.430 × 10−3 | 12.793 × 10−3 | 9.934 | 5.249 | 3.764 | 2.167 |
P-type IL | 1.526 × 10−3 | 5.909 × 10−3 | 4.590 | 2.706 | 2.238 × 10−3 | 8.169 × 10−3 | 6.323 | 3.356 | 2.563 | 1.488 |
Robust MFA-IL | 1.479 × 10−3 | 5.719 × 10−3 | 4.348 | 2.561 | - | - | - | - | - | - |
Proposed method | 1.488 × 10−3 | 5.763 × 10−3 | 4.413 | 2.598 | 2.080 × 10−3 | 7.590 × 10−3 | 5.800 | 3.065 | 2.480 | 1.444 |
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Bai, L.; Feng, Y.-W.; Li, N.; Xue, X.-F.; Cao, Y. Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability. Symmetry 2019, 11, 746. https://doi.org/10.3390/sym11060746
Bai L, Feng Y-W, Li N, Xue X-F, Cao Y. Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability. Symmetry. 2019; 11(6):746. https://doi.org/10.3390/sym11060746
Chicago/Turabian StyleBai, Liang, Yun-Wen Feng, Ning Li, Xiao-Feng Xue, and Yong Cao. 2019. "Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability" Symmetry 11, no. 6: 746. https://doi.org/10.3390/sym11060746