2. Data Description
- Laboratory data: Concrete cylinders of 3in diameter and 6in height as per ASTM testing standards, and beams (15 × 15 cm × 90 cm) made of various industrial mixes and cured under different conditions were fabricated and tested. Direct tests were used to obtain values for density, porosity, and compressive strength and the corresponding beams were scanned using a 900-MHz GSSI antenna. The direct test values and calculated attributes from scans were used to develop machine learning models to predict the material properties on Streicker bridge in Section 4. The details of data collection can be found in the previous work by the authors ; the lab data and connection with the modeling pipeline (Section 3) are summarized in Figure 1.
- Streicker bridge: Streicker bridge at Princeton University is the real-life application structure for this paper. The pedestrian bridge provides strategic connection between the east and west ends of the campus. It is a post-tensioned prestressed bridge in the shape of a chromosome. It is 105 m long and consists of a 35 m deck-stiffened arch (the main span) and four approach legs. The approach legs are continuous curved concrete girders. The front view of the bridge is shown in Figure 2. The main span and all legs except the southeast leg were constructed in August 2009. The southeast leg was constructed in October of that year using the same specified concrete mix (Class A HPC with design strength of 41 MPa at 28 days).Streicker bridge was instrumented with long-gage fiber optic sensors at the time of construction for research and teaching purposes. A schematic of Fiber Bragg Grating (FBG) sensor used for temperature monitoring is shown in Figure 3. A brief description of the working is as follows: When a light is sent from the reading unit, specific wavelengths of the light are reflected back by the Bragg gratings in the fiber. Depending on the strain in the fiber, the reflected wavelength changes. The fiber optic sensors installed in Streicker bridge measure both the temperature and strain.The sensor locations along the main span and southeast leg are shown in Figure 4 by black boxes. The sensors have been continuously monitoring strain and temperature with periodic interruptions for maintenance since their installation in 2009. These sensors are installed at various locations on the bridge which provide the temperature data that are required for the maturity index calculations. The temperature readings have an uncertainty of 0.14 C. These sensors are used for compressive strength calculations based on the maturity method. Two typical locations are also highlighted in Figure 4. The GPR attributes collected on Streicker bridge in 2016 and 2020 are used to identify the spatial and temporal variation in concrete in a structure. There are two types of data sets used from previous studies for validation of those predicted values:
- Temperature measurements: Streicker bridge is instrumented with Fiber Bragg Grating (FBG) fiber-optic sensors which have been regularly collecting temperature and strain data from the time of construction in 2009. The sensor locations along the main span and southeast leg are shown in Figure 4 by black boxes. The sensors have been continuously monitoring strain and temperature with periodic interruptions for maintenance since their installation in 2009. These sensors are installed at various locations on the bridge which provide the temperature data that are used for the maturity index estimates of compressive strength. The temperature readings have an uncertainty of 0.14 C. The location of the typical sensors in the main span (P8h9) and southeast leg (P10h11) are highlighted in Figure 4.
- Core reserves: Class A HPC concrete with a design strength of 41 MPa (at 28 days) was used for the construction of the bridge. The bridge was constructed in two phases; one in August 2009 (main span and northeast leg included) and the other in October 2009 (southeast leg). Even though the design strengths were the same for the two construction phases, the measured compressive strength on the reserved cores indicate a nominal compressive strength of 51 MPa for the main span (MS) and northeast (NE) leg and 59 MPa for southeast (SE) leg at 28 days . Figure 5 shows the compressive strengths of the reserved cores based on the strength tests performed at US Laboratories Inc. (Broomall, PA, USA). Six samples were tested for the concrete poured in August (MS and NE leg) at 2, 3, 7, and 28 days and four samples were tested for the October pour (SE leg) at 3, 4, 7, 14, and 28 days. In this work, we try to identify the spatial variation using GPR attributes.
2.1. GPR Survey of Streicker Bridge
2.2. Data Processing
3.1. Machine Learning Pipeline
- Data imputation: The total samples tested directly in the laboratory for density, compressive strength, and porosity were 219, 146, and 73, respectively. Since the number of samples tested for compressive strength and porosity were small, a data imputation was performed. Mean substitution was chosen as it is a standard practice in data science even if it sometimes results in statistically correlated samples .
- Stratified split of train-validation data: For a small sample set such as ours, stratified splitting of training and validation sets avoids overfitting. The stratified approach further guarantees that a sample in the validation set would have the same mix of concrete in the training set while preserving the distribution of properties .
- Feature selection: Since many of the attributes had more than 500 features, feature selection was adopted to improve the computational efficiency of the machine learning models. The feature selection was performed using the score. The top “n” features were chosen heuristically based on the scores.
- Model tuning approach: All the machine learning models were first trained using a baseline set of hyper-parameters. These hyper-parameters were then fine-tuned to improve the predictions using randomized search and grid search . The cross-validation score was used to determine the best parameters in all these cases.
3.2. Maturity Index Model
4.1. GPR Attributes: Qualitative Spatial and Temporal Variation
4.1.1. Spatial Variation
4.1.2. Temporal Variation
4.2. Quantitative Differences between Legs
4.2.1. In Situ Property Estimation Using GPR Attributes
4.2.2. Compressive Strength Calculation Using Maturity Method
5. Conclusions and Discussion
- Instantaneous amplitude and summary attributes can statistically distinguish between the concrete in Streicker bridge on the basis of relative material properties.
- Spatial variation in the physical properties of the two phases of concrete is identified with amplitude-based attributes such as raw means, total energy, and two different measures of attenuation.
- Temporal variation in the physical properties over a four-year period is difficult to determine due to the use of different antennas and seasonal differences, but the comparison does identify how sensitive attributes are to the antenna relative to the different concrete.
- The GPR attributes predict a 5.01 MPa difference in the mean compressive strength, a 13.6 kg/m difference in density, and a 0.23% difference in porosity between the southeast and northeast legs of the bridge.
- The quantitative strength predictions from the GPR attributes are reasonable and fall between the lower bound of the 28-day reserved concrete core strength and the upper bound from the maturity method and temperature history of the concrete.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|Main Attribute||Equation||Derived Attribute||Equation|
|Instantaneous Amplitude||Total energy|
|Intensity||Raw average amplitude||Average(A)|
|Dielectric Constant ()|
|Attribute||Range SE Leg||Range NE Leg|
|Raw Means||[−542.13, 196.38]||[−464.25, 60.93]|
|Attenuation DW constant||[−0.73, 6.16]||[−0.47, 6.23]|
|Attenuation DW ratio||[0.58, 101.32]||[0.70, 107.22]|
|SNR||[−16.797, 12.224]||[−16.899, 14.009]|
|Attenuation constant||[−6.51, 15.00]||[−6.18, 20.17]|
|Dielectric constant||[3.01, 78.74]||[3.10, 93.71]|
|Attribute||Welch’s t-Score||p-Value||Mann–Whitney U-Score||p-Value|
|Attenuation DW constant||86.57||0.0||0.0|
|Attenuation DW ratio||−67.88||0.0||0.0|
|Attribute||Southeast Leg||Northeast Leg||Ratio SE/NE|
|Attenuation constant (DW)||−0.60||1.17||−1.29||1.63||0.46||0.72|
|Attenuation ratio (DW)||3.41||2.70||1.84||4.48||1.85||0.60|
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