Outlier-Detection Methodology for Structural Identification Using Sparse Static Measurements
<p>The general framework for the structural identification using error-domain model falsification (EDMF). The contributions of this paper are highlighted by the shaded boxes.</p> "> Figure 2
<p>The model–class validation methodology. The model classes for which the prediction intervals of the initial population do not include measured values at several locations may reveal flaws in the model class definition, rather than the outliers in the measurement dataset.</p> "> Figure 3
<p>The outlier-detection steps.</p> "> Figure 4
<p>The outlier-detection procedure in step 2.</p> "> Figure 5
<p>The Exeter Bascule Bridge: (<b>a</b>) side elevation; (<b>b</b>) static load test.</p> "> Figure 6
<p>The Exeter Bascule Bridge: (<b>a</b>) the plan view including the sensor locations and the truck position; (<b>b</b>) the locations of the strain gauges on the main girders and the elevation of the instrumented secondary beam.</p> "> Figure 7
<p>The model–class definitions: (<b>a</b>) the initial model class; (<b>b</b>) the updated model class.</p> "> Figure 8
<p>The outlier-detection methodology showing: Step 1—for three sensors (<math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, the deflection camera, and <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>2</mn> </msub> </mrow> </semantics></math>), the cumulative density function (CDF) of #CMs, obtained using simulated measurements (solid lines). The values of CMS population (<math display="inline"><semantics> <mrow> <mo>#</mo> <mi>C</mi> <mi>M</mi> <mi>s</mi> </mrow> </semantics></math>) using real measurements are indicated by the dashed lines and the corresponding probability values from the simulated measurements are determined.</p> "> Figure 9
<p>The outlier detection: step 2. (<b>a</b>) CDFs of the expected #CMs using all sensors and the network without <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>1</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> is computed as the maximum distance between the two CDFs in the <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> area. (<b>c</b>) The detail of the two CDFs and the outlier check.</p> "> Figure 10
<p>The outlier detection: step 2. (<b>a</b>) CDFs of the expected #CMs using all sensors and the network without the deflection measurement. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> is computed as the maximum distance between the two CDFs in the <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> area. (<b>c</b>) The detail of the two CDFs and the outlier check.</p> "> Figure 11
<p>The outlier detection: step 2. (<b>a</b>) CDFs of the expected #CMs using all sensors and the network without <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> is computed as the maximum distance between the two CDFs in the <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> area. (<b>c</b>) The detail of the two CDFs and the outlier check.</p> "> Figure 12
<p>The updated sensor network—without the suspicious sensor <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>2</mn> </msub> </mrow> </semantics></math>—is checked. (<b>a</b>) CDFs of the expected #CMs using the updated network without <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>G</mi> <mn>2</mn> </msub> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> is computed as the maximum distance between the two CDFs in the <math display="inline"><semantics> <mo>Δ</mo> </semantics></math> area. (<b>c</b>) The detail of the two CDFs and the outlier check.</p> "> Figure 13
<p>The variation of <math display="inline"><semantics> <mrow> <mo>#</mo> <mi>C</mi> <mi>M</mi> <mi>s</mi> </mrow> </semantics></math> when one sensor at a time is removed and falsification is carried out iteratively. High variations reveal suspicious measurements, according to Reference [<a href="#B32-sensors-18-01702" class="html-bibr">32</a>].</p> "> Figure 14
<p>The variation of <math display="inline"><semantics> <mrow> <mo>#</mo> <mi>C</mi> <mi>M</mi> <mi>s</mi> </mrow> </semantics></math> when one sensor at a time is removed and falsification is carried out iteratively. The dark bar refers to the sensor where the outliers are simulated as described in <a href="#sensors-18-01702-t006" class="html-table">Table 6</a>.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Background—EDMF
2.2. Methodology
2.2.1. Model–Class Validation
2.2.2. Outlier Detection
3. Results
3.1. Exeter Bridge Description
3.2. Parameters and Modelling Uncertainties
3.3. Sensor Configuration
3.4. Results for Model–Class Validation
3.5. Results for Outlier Detection
3.6. Detection of Simulated Outliers
4. Discussion
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Parameters | Initial Intervals |
---|---|
—Equivalent Young’s modulus of aluminium deck (GPa) | [60; 80] |
—Rotational stiffness of bearing devices (log(Nmm/rad)) | [8; 12] |
—Axial stiffness of hydraulic jacks (log(Nmm)) | [3; 5] |
Uncertainty Source | Uncertainty Form | Uncertainty Magnitude |
---|---|---|
FE model simplification (%) | Uniform | −5%; +20% |
Mesh refinement (%) | Uniform | −1%; +1% |
Additional (%) | Uniform | −2%; +2% |
Uncertainty Source | Uncertainty Form | Uncertainty Magnitude |
---|---|---|
Sensor accuracy | ||
Camera (mm) | Uniform | −0.1; +0.1 |
Strain gauges () | Uniform | −2; +2 |
Measurement repeatability | ||
Camera (%) | Gaussian | ; |
Strain gauges (%) | Gaussian | ; |
Sensor installation | ||
Strain gauges (%) | Uniform | −2%; +2% |
Prediction Intervals | Deflection (mm) | ||||||
---|---|---|---|---|---|---|---|
Minimum | 7.7 | 23.2 | 111.5 | 0.8 | 12.1 | 48.5 | 227.9 |
Maximum | 9.9 | 28.6 | 119.7 | 20.8 | 16.4 | 78.1 | 255.7 |
Measurement | 6.8 | 4.3 | 1.8 | 21.7 | 17.7 | 73.8 | 83.5 |
Validation | ✗ | ✗ | ✗ | ✗ | ✗ | ✓ | ✗ |
Prediction Intervals | Deflection (mm) | ||||||
---|---|---|---|---|---|---|---|
Minimum | 1.0 | −2.4 | −2.7 | 0.5 | 12.2 | 48.8 | −20.8 |
Maximum | 13.2 | 71.3 | 107.0 | 23.5 | 18.0 | 80.5 | 267.9 |
Measurement | 6.8 | 4.3 | 1.8 | 21.7 | 17.7 | 73.8 | 83.5 |
Validation | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Scenario | Sensor | True Measurement | Simulated Outlier | Detection | |
---|---|---|---|---|---|
1 | Deflection | +25% | 56 | ✓ | |
2 | Deflection | −20% | 0 | ✓ | |
3 | −20% | 28 | ✓ | ||
4 | 4 | ✓ | |||
5 | 8 | ✓ |
Parameter | Scenario: No Outlier | Scenario: 3 | Scenario: 5 |
---|---|---|---|
(60.2; 79.8) | (71.5; 79.8) | (63.8; 74.8) | |
(8.08; 11.94) | (8.29; 11.91) | (9.01; 10.16) | |
(4.28; 4.35) | (4.29; 4.34) | (4.46; 4.47) |
Scenario | SLS Reserve Capacity |
---|---|
No outlier | 2.09 |
Scenario 3 | 2.07 |
Scenario 5 | 2.31 |
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Proverbio, M.; Bertola, N.J.; Smith, I.F.C. Outlier-Detection Methodology for Structural Identification Using Sparse Static Measurements. Sensors 2018, 18, 1702. https://doi.org/10.3390/s18061702
Proverbio M, Bertola NJ, Smith IFC. Outlier-Detection Methodology for Structural Identification Using Sparse Static Measurements. Sensors. 2018; 18(6):1702. https://doi.org/10.3390/s18061702
Chicago/Turabian StyleProverbio, Marco, Numa J. Bertola, and Ian F. C. Smith. 2018. "Outlier-Detection Methodology for Structural Identification Using Sparse Static Measurements" Sensors 18, no. 6: 1702. https://doi.org/10.3390/s18061702
APA StyleProverbio, M., Bertola, N. J., & Smith, I. F. C. (2018). Outlier-Detection Methodology for Structural Identification Using Sparse Static Measurements. Sensors, 18(6), 1702. https://doi.org/10.3390/s18061702