Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation
Abstract
:1. Introduction
2. Virtual Impulse Response Function
3. Regularized ARMA Time Series Model
3.1. Introduction of ARMA Time Series Model
3.2. Regularization of ARMA Time Series
3.3. Derivation of Regularized ARMA Time Series
3.4. The Selection of Regularization Coefficient α
3.5. Regularized ARMA Time Series Modeling
- Determine the sample Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) of the signal to be simulated.
- Choose the appropriate model based on the sample autocorrelation coefficient and partial autocorrelation coefficient properties.
- Determine the model order using AIC or other criteria.
- Validate the model. If the geometric model does not pass the test, go to Step 2, reselect the model, and fit again.
- Optimize the model. If the fitted model passes the test, then it still moves to Step 3, taking full consideration of the possibilities, creating a number of quasi-models, and selecting the optimal model from all the tested fitted models.
- Calculate regularization coefficients and regularization time series models based on optimal model parametric.
- Extract the AR coefficients as feature vectors from the regularized time-series fitting optimal model.
4. Damage Identification Procedure
- For a structured health monitoring system in which the sensors have been placed, the virtual impulse response function is obtained by comparing a large vibration response with another response where the damage may occur.
- Use the regularized ARMA time series model to fit the obtained virtual impulse response and extract the AR coefficient of the best-fit model as the damage feature vector.
- Compare the AR coefficient extracted from the undamaged working condition and damage condition and calculate the damage index.
5. Numerical Simulation
5.1. Three-Degrees-of-Freedom Chain Structure
5.2. Damage Identification Process
6. Verification Using the Data of the Alamos Three-Floor Shear Structure
6.1. Test Structure Description
6.2. Damage Identification Process
7. Discussion
8. Conclusions
- It has strong robustness to environmental excitation and can effectively identify damage based on environmental excitation.
- The direct use of structural vibration response for non-parametric damage identification has strong practicality and allows for real-time damage monitoring.
- The results of numerical simulations show that the method is sensitive to slight damage to the structure. Even a 5% reduction in stiffness can be identified.
Author Contributions
Funding
Conflicts of Interest
References
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Cases | Top Floor Stiffness Reduction Percentage |
---|---|
Case 1 | 0% |
Case 2 | 5% |
Case 3 | 10% |
Case 4 | 15% |
Case 5 | 20% |
Case 6 | 25% |
Case 7 | 30% |
Label | State Condition | Description |
---|---|---|
State #1 | Undamaged | Baseline condition |
State #2 | Damaged | 87.5% Stiffness reduction in column 1BD |
State #3 | Damaged | 87.5% Stiffness reduction in columns 1AD and 1BD |
State #4 | Damaged | 87.5% Stiffness reduction in column 2BD |
State #5 | Damaged | 87.5% Stiffness reduction in columns 2AD and 2BD |
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Zhang, X.; Li, D.; Song, G. Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation. Vibration 2018, 1, 138-156. https://doi.org/10.3390/vibration1010011
Zhang X, Li D, Song G. Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation. Vibration. 2018; 1(1):138-156. https://doi.org/10.3390/vibration1010011
Chicago/Turabian StyleZhang, Xuan, Dongsheng Li, and Gangbing Song. 2018. "Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation" Vibration 1, no. 1: 138-156. https://doi.org/10.3390/vibration1010011