Numerical and Experimental Verification of a Multiple-Variable Spatiotemporal Regression Model for Grout Defect Identification in a Precast Structure
Abstract
:1. Introduction
2. Methodology
2.1. Theory Background
2.1.1. Linear Regression Model
2.1.2. Accuracy Verification
2.1.3. Damage Indicator
2.2. Proposed Methodology
- When investigating both the non-defective and defective structures, the acceleration responses of nodes near sleeves in both structures were obtained using an accelerometer network.
- A reasonable linear regression model (SVR model, TVSR model, TVSTR model, or the proposed multiple-variable model proposed in Section 3.3.4) was adopted to analyze the obtained acceleration responses.
- The coefficient of determination (CoD) r2 or the adjusted CoD r2adj was calculated to verify the accuracy of the linear regression model.
- Every damage indicator was calculated based on the two linear regression models of the non-defective and defective states. Generally, the damage indicators of nodes near defects were larger than those of other nodes, and the locations of the defects could be identified.
3. Numerical Simulation on Grout Defect Identification in Precast Beam-Column Connection
3.1. Finite Element Model (FEM)
3.2. Working Cases
3.3. Results and Discussion
3.3.1. Acceleration Responses
3.3.2. Results Based on the SVR, TVSR, and TVSTR Models
3.3.3. Comparison of the SVR, TVSR, and TVSTR Models
3.3.4. Multiple-Variable Regression Model
3.3.5. Robustness Analysis of Damage Indicator
4. Experimental Verification of Grout Defect Identification in a Precast Concrete Frame Structure
4.1. Experimental Model
4.2. Experimental Setup
4.3. Experimental Steps
- The vibration exciter was arranged at the excitation point in the middle of the beam, whose location is shown in Figure 17. At the same time, the annunciator, power amplifier, and acquisition system were arranged as well.
- Once the external force was applied, the acceleration time history curves of each measuring point were recorded by the acquisition system.
- Using the proposed multiple-variable regression model, the damage indicators were calculated based on the acceleration responses to identify the defects.
4.4. Results and Discussion
4.4.1. Acceleration Responses
4.4.2. Results Based on Multiple-Variable Regression Model
5. Conclusions
- 1
- Comparing the SVR, TVSR, and TVSTR model algorithms, the TVSTR model could most accurately identify the defective components, the SVR was the second best, and the TVSR was the worst, in which the defect of case 8_9 in the numerical simulation could not be identified well. A flowchart of the regression model recognition algorithm was proposed based on multiple spatiotemporal variables.
- 2
- Grout defects in the precast concrete frame structure were successfully identified based on the proposed multiple-variable regression model, with results showing that the total damage indicators of nodes near defects were greater than those of other nodes.
- 3
- The total damage indicator displayed robustness against different levels of noise with SNRs of 1 dB, 5 dB, and 10 dB inputted, but attention still needs to paid to avoid the significant environmental noise that was present during the experiment to obtain good identification results.
- 4
- The proposed method has the limitations that the damage indicator was calculated based on two working conditions, where the structural design and boundary conditions were the same. At the same time, the result could only show the damage difference between the two conditions and one control working case needed to be chosen.
Author Contributions
Funding
Conflicts of Interest
References
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Boundary | Case | Sleeve Location | Degree of Defects | Excitation Location |
---|---|---|---|---|
Fixed supports for the bottom column end, incomplete fixed supports for the other three ends, with no horizontal constraints in the plane | 1 | Upper column | None | Horizontal rightward on top column end |
2 | Upper column | 20% stiffness reduction | Horizontal rightward on top column end | |
3 | Upper column | 30% stiffness reduction | Horizontal rightward on top column end | |
4 | Bottom column | None | Horizontal rightward on top column end | |
5 | Bottom column | 20% stiffness reduction | Horizontal rightward on top column end | |
6 | Upper column | None | Vertical downward on right beam end | |
7 | Upper column | 20% stiffness reduction | Vertical downward on right beam end | |
Fixed supports for the four ends | 8 | Upper column | None | Horizontal rightward on top column end |
9 | Upper column | 20% stiffness reduction | Horizontal rightward on top column end |
r2 | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Measure Node | 1 | - | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 0.81 | 0.96 |
2 | 1.00 | - | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 0.81 | 0.96 | |
3 | 1.00 | 1.00 | - | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.81 | 0.96 | |
4 | 1.00 | 1.00 | 1.00 | - | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 0.82 | 0.96 | |
5 | 1.00 | 1.00 | 1.00 | 1.00 | - | 1.00 | 0.99 | 0.99 | 0.99 | 1.00 | 0.82 | 0.96 | |
6 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | - | 0.99 | 0.99 | 0.99 | 0.99 | 0.83 | 0.96 | |
7 | 0.99 | 0.99 | 1.00 | 0.99 | 0.99 | 0.99 | - | 0.99 | 0.99 | 0.99 | 0.84 | 0.97 | |
8 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 0.99 | - | 1.00 | 1.00 | 0.80 | 0.95 | |
9 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 0.99 | 1.00 | - | 1.00 | 0.80 | 0.95 | |
10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 1.00 | 1.00 | - | 0.81 | 0.95 | |
11 | 0.81 | 0.81 | 0.81 | 0.82 | 0.82 | 0.83 | 0.84 | 0.80 | 0.80 | 0.81 | - | 0.89 | |
12 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 | 0.97 | 0.95 | 0.95 | 0.95 | 0.89 | - |
Damage Indicator (°) | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Measure Node | 1 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 |
2 | 0.00 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
3 | 0.00 | 0.00 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
4 | 0.00 | 0.00 | 0.00 | - | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
5 | 0.00 | 0.00 | 0.00 | 0.00 | - | 0.00 | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | - | 0.00 | 0.00 | 0.01 | 0.00 | 0.00 | 0.00 | |
7 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | - | 0.03 | 0.07 | 0.00 | 0.00 | 0.00 | |
8 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | - | 0.03 | 0.04 | 0.03 | 0.03 | |
9 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.07 | 0.03 | - | 0.06 | 0.06 | 0.04 | |
10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.06 | - | 0.00 | 0.00 | |
11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.06 | 0.00 | - | 0.00 | |
12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.04 | 0.00 | 0.00 | - |
Total Damage Indicator | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Case | 1_2 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.20 | 0.32 | 0.64 | 0.20 | 0.18 | 0.14 |
1_3 | 0.08 | 0.08 | 0.10 | 0.10 | 0.08 | 0.08 | 0.34 | 0.60 | 0.96 | 0.32 | 0.28 | 0.22 | |
4_5 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.06 | 0.11 | 0.24 | |
6_7 | 0.02 | 0.02 | 0.02 | 0.03 | 0.04 | 0.06 | 0.22 | 0.12 | 0.10 | 0.19 | 0.09 | 0.09 | |
8_9 | 0.55 | 0.58 | 0.61 | 0.47 | 0.49 | 0.49 | 1.09 | 1.24 | 0.90 | 1.24 | 0.94 | 0.84 |
Total Damage Indicator | Measure Node | ||||
---|---|---|---|---|---|
1–3 | 4–6 | 7–9 | 10–12 | ||
Case | 1_2 | 0.030 | 0.0091 | 0.049 | 0.0027 |
1_3 | 0.047 | 0.014 | 0.078 | 0.0044 | |
4_5 | 0.0021 | 0.0022 | 0 | 0.12 | |
6_7 | 0.011 | 0.0077 | 0.061 | 0.0019 | |
8_9 | 0.044 | 0.027 | 0.13 | 0.23 |
r2adj | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Measure Node | 1 | - | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.84 | 0.98 |
2 | 1.00 | - | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.84 | 0.98 | |
3 | 1.00 | 1.00 | - | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.84 | 0.98 | |
4 | 1.00 | 1.00 | 1.00 | - | 1.00 | 1.00 | 0.99 | 1.00 | 1.00 | 1.00 | 0.85 | 0.98 | |
5 | 1.00 | 1.00 | 1.00 | 1.00 | - | 1.00 | 0.99 | 0.99 | 0.99 | 1.00 | 0.85 | 0.98 | |
6 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | - | 0.99 | 0.99 | 0.99 | 0.99 | 0.86 | 0.98 | |
7 | 0.99 | 0.99 | 1.00 | 0.99 | 0.99 | 0.99 | - | 0.99 | 0.99 | 0.99 | 0.86 | 0.99 | |
8 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 0.99 | - | 1.00 | 1.00 | 0.83 | 0.97 | |
9 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 0.99 | 1.00 | - | 1.00 | 0.83 | 0.97 | |
10 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.99 | 0.99 | 1.00 | 1.00 | - | 0.83 | 0.97 | |
11 | 0.87 | 0.87 | 0.87 | 0.87 | 0.88 | 0.88 | 0.89 | 0.85 | 0.85 | 0.85 | - | 0.93 | |
12 | 0.98 | 0.98 | 0.98 | 0.98 | 0.98 | 0.98 | 0.99 | 0.97 | 0.97 | 0.97 | 0.91 | - |
Total Damage Indicator | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Case | 1_2 | 0.038 | 0.043 | 0.054 | 0.058 | 0.042 | 0.039 | 0.22 | 0.37 | 0.60 | 0.21 | 0.19 | 0.16 |
1_3 | 0.060 | 0.069 | 0.088 | 0.093 | 0.068 | 0.063 | 0.35 | 0.59 | 0.97 | 0.34 | 0.31 | 0.25 | |
4_5 | 0.060 | 0.060 | 0.060 | 0.060 | 0.060 | 0.060 | 0.021 | 0.018 | 0.016 | 0.045 | 0.16 | 0.31 | |
6_7 | 0.047 | 0.052 | 0.064 | 0.054 | 0.066 | 0.085 | 0.24 | 0.19 | 0.15 | 0.17 | 0.12 | 0.075 | |
8_9 | 0.54 | 0.57 | 0.61 | 0.47 | 0.50 | 0.46 | 1.15 | 1.23 | 0.86 | 1.17 | 0.86 | 0.76 |
Total Damage Indicator | Measure Node | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Signal-to-Noise Ratio | 0 dB | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.02 | 0.20 | 0.32 | 0.64 | 0.20 | 0.18 | 0.14 |
1 dB | 0.02 | 0.021 | 0.03 | 0.025 | 0.03 | 0.03 | 0.20 | 0.31 | 0.64 | 0.19 | 0.18 | 0.15 | |
5 dB | 0.03 | 0.04 | 0.042 | 0.044 | 0.043 | 0.046 | 0.19 | 0.29 | 0.60 | 0.19 | 0.17 | 0.15 | |
10 dB | 0.042 | 0.06 | 0.058 | 0.064 | 0.065 | 0.064 | 0.18 | 0.25 | 0.58 | 0.18 | 0.17 | 0.16 |
Instrument | Model | Overview | Features |
---|---|---|---|
Signal source | KD5602 | Output mode: Sinusoidal, logarithmic, linear Frequency range: 10 Hz–20 kHz | |
Power amplifier | KD5702 | Rated output power: 200 W Rated output voltage: 14 V Rated output current: 15 A Frequency range: 20 Hz–10 kHz | |
Vibration exciter | KDJ-20 | Maximum force: 200 N Maximum amplitude: ±5 mm Frequency range: DC ≈2 kHz | |
Acceleration sensor | KD8-LP16D | Calibration value: about 60 mV/g | |
Data acquisition system | INV3060 | Corresponding acquisition software: DASP-V10 produced by China Orient Institute of Noise & Vibration |
r2adj | Measure Node | |||||||
---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
Measure Node | 1 | 1.00 | 0.95 | 0.88 | 0.83 | 0.80 | 0.81 | 0.82 |
2 | 0.95 | 1.00 | 0.92 | 0.87 | 0.82 | 0.97 | 0.83 | |
3 | 0.87 | 0.91 | 1.00 | 0.84 | 0.86 | 0.91 | 0.89 | |
4 | 0.83 | 0.86 | 0.83 | 1.00 | 0.84 | 0.80 | 0.83 | |
5 | 0.80 | 0.82 | 0.86 | 0.85 | 1.00 | 0.88 | 0.95 | |
6 | 0.80 | 0.96 | 0.91 | 0.81 | 0.87 | 1.00 | 0.89 | |
7 | 0.82 | 0.83 | 0.89 | 0.84 | 0.95 | 0.90 | 1.00 |
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Zhang, X.; Tang, H.; Zhou, D.; Chen, S.; Zhao, T.; Xue, S. Numerical and Experimental Verification of a Multiple-Variable Spatiotemporal Regression Model for Grout Defect Identification in a Precast Structure. Sensors 2020, 20, 3264. https://doi.org/10.3390/s20113264
Zhang X, Tang H, Zhou D, Chen S, Zhao T, Xue S. Numerical and Experimental Verification of a Multiple-Variable Spatiotemporal Regression Model for Grout Defect Identification in a Precast Structure. Sensors. 2020; 20(11):3264. https://doi.org/10.3390/s20113264
Chicago/Turabian StyleZhang, Xuan, Hesheng Tang, Deyuan Zhou, Shanshan Chen, Taotao Zhao, and Songtao Xue. 2020. "Numerical and Experimental Verification of a Multiple-Variable Spatiotemporal Regression Model for Grout Defect Identification in a Precast Structure" Sensors 20, no. 11: 3264. https://doi.org/10.3390/s20113264