Figure 1.
Visual representation of the data analysis and modeling process. Key steps include Data Processing, Formulation of Measurements, Statistical Analysis and Modeling, and Evaluation.
Figure 1.
Visual representation of the data analysis and modeling process. Key steps include Data Processing, Formulation of Measurements, Statistical Analysis and Modeling, and Evaluation.
Figure 2.
Percentage distribution of bridge deck’s wearing surface types before data processing: Wood or Timber, Gravel, Monolithic Concrete, Bituminous, Not applicable, Other, Integral Concrete, Latex Concrete, Epoxy Overlay, and Low Slump Concrete.
Figure 2.
Percentage distribution of bridge deck’s wearing surface types before data processing: Wood or Timber, Gravel, Monolithic Concrete, Bituminous, Not applicable, Other, Integral Concrete, Latex Concrete, Epoxy Overlay, and Low Slump Concrete.
Figure 3.
Distribution of computed Deterioration Scores (based on computation of slope) across different types of bridge wearing surfaces: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 3.
Distribution of computed Deterioration Scores (based on computation of slope) across different types of bridge wearing surfaces: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 4.
Distribution of maintenance interventions (categorized as zero, one, and two) across various bridge wearing surface types.
Figure 4.
Distribution of maintenance interventions (categorized as zero, one, and two) across various bridge wearing surface types.
Figure 5.
Baseline Difference Score (BDS) across various types of bridge wearing surfaces: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 5.
Baseline Difference Score (BDS) across various types of bridge wearing surfaces: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 6.
Comparison of the baseline characteristics and performance of various bridge wearing surfaces including Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 6.
Comparison of the baseline characteristics and performance of various bridge wearing surfaces including Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Figure 7.
Influential variables in predicting bridge deck maintenance with various wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Others. Influential sorted by the sum of SHAP feature importance value.
Figure 7.
Influential variables in predicting bridge deck maintenance with various wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Others. Influential sorted by the sum of SHAP feature importance value.
Figure 8.
Distribution of influential variables with respect to intervention and non-intervention groups in predicting bridge deck maintenance with Monolithic Concrete wearing surface. Deck age, Deterioration, and Performance are the most influential variables.
Figure 8.
Distribution of influential variables with respect to intervention and non-intervention groups in predicting bridge deck maintenance with Monolithic Concrete wearing surface. Deck age, Deterioration, and Performance are the most influential variables.
Figure 9.
Two-way Partial Dependency Plot (PDP) showing interactions between Deck age (x-axis) and Deterioration (y-axis) for a bridge deck with Monolithic Concrete surface. The left side illustrates the grid format, and the right side presents contours. Lighter shades depict interactions related to bridge deck intervention, while darker shades represent non-intervened conditions.
Figure 9.
Two-way Partial Dependency Plot (PDP) showing interactions between Deck age (x-axis) and Deterioration (y-axis) for a bridge deck with Monolithic Concrete surface. The left side illustrates the grid format, and the right side presents contours. Lighter shades depict interactions related to bridge deck intervention, while darker shades represent non-intervened conditions.
Figure 10.
Distribution of influential variables with respect to repair and non-repair groups in predicting bridge deck maintenance with Gravel wearing surface. Deterioration, Longitude, and Deck Area are the most influential variables.
Figure 10.
Distribution of influential variables with respect to repair and non-repair groups in predicting bridge deck maintenance with Gravel wearing surface. Deterioration, Longitude, and Deck Area are the most influential variables.
Figure 11.
A two-way partial dependency plot (PDP) that shows the interaction between top influential factors for bridge deck with Gravel wearing surface. X-axis Deterioration Score and y-axis Deck Area. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non−intervened bridge deck.
Figure 11.
A two-way partial dependency plot (PDP) that shows the interaction between top influential factors for bridge deck with Gravel wearing surface. X-axis Deterioration Score and y-axis Deck Area. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non−intervened bridge deck.
Figure 12.
Distribution of influential variables with respect to repair and non-repair groups in predicting bridge deck maintenance with Wood wearing surface. Deterioration, Latitude, and Longitude are the most influential variables.
Figure 12.
Distribution of influential variables with respect to repair and non-repair groups in predicting bridge deck maintenance with Wood wearing surface. Deterioration, Latitude, and Longitude are the most influential variables.
Figure 13.
A two-way partial dependency plot (PDP) that shows the interaction between top influential factors for bridge deck with Wood wearing surface. X-axis Deterioration Score and y-axis Latitude. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Figure 13.
A two-way partial dependency plot (PDP) that shows the interaction between top influential factors for bridge deck with Wood wearing surface. X-axis Deterioration Score and y-axis Latitude. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Figure 14.
Distribution of influential variables with respect to intervened and non−intervened groups in predicting bridge deck maintenance with Bituminous wearing surface. Deck Area, Deterioration, and Membrane Type are the most influential variables.
Figure 14.
Distribution of influential variables with respect to intervened and non−intervened groups in predicting bridge deck maintenance with Bituminous wearing surface. Deck Area, Deterioration, and Membrane Type are the most influential variables.
Figure 15.
A two-way PDP shows interaction between top influential factors for bridge deck with Bituminous wearing surface. X-axis Deck Area and y-axis Deterioration Score. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Figure 15.
A two-way PDP shows interaction between top influential factors for bridge deck with Bituminous wearing surface. X-axis Deck Area and y-axis Deterioration Score. The left side illustrates the grid format, and the right side presents contours. The lighter shades in PDP plot are interactions between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Figure 16.
Distribution of influential variables with respect to intervention and non−intervention in predicting bridge deck maintenance with Low Slump Concrete wearing surface. Deck Age, Average Daily Traffic, and Deck Protection are the most influential variables.
Figure 16.
Distribution of influential variables with respect to intervention and non−intervention in predicting bridge deck maintenance with Low Slump Concrete wearing surface. Deck Age, Average Daily Traffic, and Deck Protection are the most influential variables.
Figure 17.
A two-way PDP shows the interaction between top influential factors for bridge deck with Low Slump Concrete wearing surface. X-axis (Deck Age) and y-axis (Average Daily Traffic). The left side illustrates the grid format, and the right side presents contours. The lighter shaded regions in the PDP plot are interaction between influential variables regarding intervention of bridge deck and darker shades are related to non−intervened bridge deck.
Figure 17.
A two-way PDP shows the interaction between top influential factors for bridge deck with Low Slump Concrete wearing surface. X-axis (Deck Age) and y-axis (Average Daily Traffic). The left side illustrates the grid format, and the right side presents contours. The lighter shaded regions in the PDP plot are interaction between influential variables regarding intervention of bridge deck and darker shades are related to non−intervened bridge deck.
Figure 18.
Distribution of influential variables with respect to intervention and non-intervention in predicting bridge deck maintenance with Other wearing surface. Deterioration, Longitude, and Average Daily Traffic type are the most influential variables.
Figure 18.
Distribution of influential variables with respect to intervention and non-intervention in predicting bridge deck maintenance with Other wearing surface. Deterioration, Longitude, and Average Daily Traffic type are the most influential variables.
Figure 19.
A two-way PDP shows the interaction between top influential factors for bridge deck with Other wearing surface. X-axis Deterioration Score and y-axis Average Daily Traffic. The left side illustrates the grid format, and the right side presents contours. The lighter shaded regions in the PDP plot are interaction between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Figure 19.
A two-way PDP shows the interaction between top influential factors for bridge deck with Other wearing surface. X-axis Deterioration Score and y-axis Average Daily Traffic. The left side illustrates the grid format, and the right side presents contours. The lighter shaded regions in the PDP plot are interaction between influential variables regarding intervention of bridge deck and darker shades are related to non-intervened bridge deck.
Table 1.
Categorization and description of variables.
Table 1.
Categorization and description of variables.
Category | Factor | Description |
---|
Physical | Age/year-built | Year of construction |
Structure length | Length of the structure |
Width | Width of deck |
Number of spans | Number of spans in main unit |
Deck | Condition ratings of the bridge component |
Region | Longitude | Longitude |
Latitude | Latitude |
Structural Type | Material type | Kind of material used such as Concrete, Steel, Wood or Timber |
Deck protection | Protective system on bridge deck |
Membrane type | Membrane used as a part of protective system on bridge deck |
Environmental | Precipitation | Annual mean precipitation in inches or millimeters |
Snowfall | Annual mean snowfall |
Freeze-thaw | Annual mean freeze-thaw |
Service | Owner | Maintenance responsibility of bridges |
Table 2.
Descriptive summary of numerical variables.
Table 2.
Descriptive summary of numerical variables.
Factor | Mean | Median | Std. Dev | Min | Q1 | Q3 | Max |
---|
Traffic | 1820.28 | 50 | 7873.3 | 2 | 25.50 | 235 | 165,270 |
Deck-age | 40.52 | 34 | 25.39 | 1 | 19 | 69 | 122 |
Area | 234.65 | 100.5 | 600.18 | 28.81 | 61.25 | 229.99 | 20,659 |
Snowfall | 57.41 | 58 | 7.39 | 41.97 | 51.05 | 62.92 | 73.315 |
Freezethaw | 105.79 | 103.81 | 6.65 | 98.44 | 101.97 | 106.76 | 133 |
Precipitation | 2.03 | 2.08 | 0.265 | 1.05 | 1.94 | 2.18 | 2.5 |
Longitude | −94.40 | −97.35 | 18.241 | −104.95 | −98.58 | −96.56 | 0.0 |
Latitude | 39.74 | 41.125 | 7.68 | 40.0 | 40.53 | 41.75 | 43.16 |
Deterioration | 0.0971 | 0.045 | 0.145 | 0.173 | 0.0002 | 0.103 | 1.5 |
Length | 29.65 | 15.8 | 54.06 | 6.1 | 9.8 | 30.8 | 1644.7 |
Spans | 1.81 | 1.0 | 1.57 | 1 | 1 | 3 | 52 |
Performance | 0.748 | 0.67 | 0.51 | 2.86 | 0.34 | 1.06 | 3.18 |
Table 3.
Frequency and percentage breakdown of categorical variables.
Table 3.
Frequency and percentage breakdown of categorical variables.
Factor | Frequency Count | Percentage |
---|
Material |
Steel | 4684 | 0.511801 |
Concrete Continuous | 987 | 0.107845 |
Wood or Timber | 975 | 0.106534 |
Pres. Concrete | 964 | 0.105332 |
Steel Continuous | 689 | 0.075284 |
Concrete | 662 | 0.072334 |
Pres. Concrete Continuous | 186 | 0.020323 |
Other | 5 | 0.000546 |
Membrane Type |
None | 8744 | 0.955420 |
Preformed Fabric | 151 | 0.016499 |
Built-up | 135 | 0.014751 |
Unknown | 77 | 0.008413 |
Not Applicable | 22 | 0.002404 |
Other | 15 | 0.001639 |
Epoxy | 8 | 0.000874 |
Deck Protection |
None | 7473 | 0.816543 |
Epoxy Coated Reinforcing | 1429 | 0.156141 |
Unknown | 120 | 0.013112 |
Galvanized Reinforcing | 87 | 0.009506 |
Not Applicable | 25 | 0.002732 |
Other | 8 | 0.000874 |
Other Coated Reinforcing | 4 | 0.000437 |
Cathodic Protection | 2 | 0.000219 |
Internally Sealed | 2 | 0.000219 |
Polymer Impregnated | 2 | 0.000219 |
Owner |
County Highway | 7072 | 0.772727 |
State Highway | 1664 | 0.181818 |
City Highway | 294 | 0.032124 |
Other Local | 62 | 0.006774 |
Other State | 25 | 0.002732 |
Railroad | 12 | 0.001311 |
Private | 10 | 0.001093 |
Bureau of Indian Affairs | 8 | 0.000874 |
Corps of Engineers (Civil) | 2 | 0.000219 |
Bureau of Reclamation | 2 | 0.000219 |
National Park Services | 1 | 0.000109 |
Maintenance |
Intervention | 3739 | 0.408 |
No Intervention | 5413 | 0.591 |
Table 4.
Bridge deck condition ratings as described in NBI Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges [
17].
Table 4.
Bridge deck condition ratings as described in NBI Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges [
17].
Rating | Description |
---|
N | Not Applicable |
9 | Excellent Condition |
8 | Very Good Condition |
7 | Good Condition |
6 | Satisfactory Condition |
5 | Fair Condition |
4 | Poor Condition |
3 | Serious Condition |
2 | Critical Condition |
1 | Imminent Failure Condition |
0 | Failed Condition |
Table 5.
Description of maintenance intervention and abbreviation.
Table 5.
Description of maintenance intervention and abbreviation.
Type | Abbreviation | Criteria |
---|
Repair | Rep | If deck transition within 4 condition ratings |
Rehab | Rab | If deck goes from 4 or 5 (or less) to 8 or 9 |
Replace | Rec | If deck all goes from 4, 5, or 6 to 8 or 9 |
Not applicable | NA | These bridges do not exist |
Inspection variance | Var | Allowable inspection tolerance is 1 NBI condition code |
None | N | No change in deck condition ratings |
Table 6.
Bridge Intervention Matrix (BIM) maps the improvement in bridge condition ratings to the possible bridge intervention. The abbreviations used in this table are explained in
Table 5 above.
Table 6.
Bridge Intervention Matrix (BIM) maps the improvement in bridge condition ratings to the possible bridge intervention. The abbreviations used in this table are explained in
Table 5 above.
To Condition |
---|
From Condition | | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
9 | N | | | | | | | | |
8 | Var | N | | | | | | | |
7 | Rep | Var | N | | | | | | |
6 | Rep | Rep | Var | N | | | | | |
5 | Rab | Rep | Rep | Var | N | | | | |
4 | Rec | Rec | Rab | Rep | Var | N | | | |
3 | Rec | Rec | Rab | Rep | Rep | Var | N | | |
2 | Rec | Rec | Rab | Rab | Rep | Rep | Rep | N | |
1 | NA | NA | NA | NA | NA | NA | NA | NA | N |
Table 7.
Distribution of Bridge Deck Surface Wearing Type by Count and Percentage in the state of Nebraska.
Table 7.
Distribution of Bridge Deck Surface Wearing Type by Count and Percentage in the state of Nebraska.
Type | Count | Percent |
---|
Wood or Timber | 2262 | 17.12 |
Gravel | 1331 | 10.07 |
Monolithic Concrete | 7582 | 57.40 |
Bituminous | 864 | 6.54 |
Not applicable | 76 | 0.48 |
Other | 377 | 2.85 |
None | 76 | 0.57 |
Integral Concrete | 225 | 1.70 |
Latex Concrete | 34 | 0.25 |
Epoxy Overlay | 72 | 0.54 |
Low Slump Concrete | 321 | 2.43 |
Table 8.
Correlation analysis between Performance (P), Deterioration (D), and Maintenance (M) by Surface Wearing Type of Bridge Deck in the state of Nebraska.
Table 8.
Correlation analysis between Performance (P), Deterioration (D), and Maintenance (M) by Surface Wearing Type of Bridge Deck in the state of Nebraska.
Attribute | P-M | P-D | D-M |
---|
All | −0.155 | 0.172 | −0.259 |
Monolithic Concrete | −0.316 | −0.270 | −0.260 |
Gravel | −0.075 | 0.023 | −0.239 |
Wood or Timber | 0.080 | −0.068 | −0.321 |
Bituminous | 0.131 | 0.050 | 0.171 |
Other | 0.008 | 0.128 | −0.203 |
Low Slump Concrete | −0.034 | 0.371 | 0.010 |
Table 9.
Comparative analysis of model performance for Logistic Regression (LR), Decision Tree (DT), XGBoost (XGB), and LightBoost (LB), across different bridge wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Table 9.
Comparative analysis of model performance for Logistic Regression (LR), Decision Tree (DT), XGBoost (XGB), and LightBoost (LB), across different bridge wearing surface types: Monolithic Concrete, Gravel, Wood or Timber, Bituminous, Low Slump Concrete, and Other.
Model | Accuracy | Precision | F1 Score | AUC | Kappa |
---|
Monolithic Concrete |
LR | 0.767 | 0.725 | 0.735 | 0.841 | 0.735 |
DT | 0.884 | 0.870 | 0.865 | 0.881 | 0.747 |
XGB | 0.911 | 0.881 | 0.897 | 0.963 | 0.819 |
LB | 0.905 | 0.872 | 0.893 | 0.964 | 0.808 |
Gravel |
LR | 0.779 | 0.565 | 0.568 | 0.768 | 0.413 |
DT | 0.859 | 0.712 | 0.724 | 0.818 | 0.630 |
XGB | 0.881 | 0.747 | 0.778 | 0.939 | 0.694 |
LB | 0.873 | 0.737 | 0.768 | 0.936 | 0.669 |
Wood or Timber |
LR | 0.673 | 0.572 | 0.562 | 0.696 | 0.302 |
DT | 0.714 | 0.616 | 0.633 | 0.702 | 0.399 |
XGB | 0.761 | 0.675 | 0.700 | 0.839 | 0.501 |
LB | 0.760 | 0.681 | 0.689 | 0.832 | 0.492 |
Bituminous |
LR | 0.647 | 0.172 | 0.256 | 0.565 | 0.089 |
DR | 0.741 | 0.227 | 0.312 | 0.179 | 0.179 |
XGB | 0.811 | 0.375 | 0.461 | 0.745 | 0.326 |
LB | 0.750 | 0.684 | 0.456 | 0.811 | 0.445 |
Low Slump Concrete |
LR | 0.743 | 0.666 | 0.603 | 0.779 | 0.435 |
DT | 0.820 | 0.727 | 0.774 | 0.821 | 0.626 |
XGB | 0.884 | 0.851 | 0.821 | 0.862 | 0.747 |
LB | 0.871 | 0.851 | 0.821 | 0.840 | 0.721 |
Other |
LR | 0.718 | 0.437 | 0.341 | 0.581 | 0.136 |
DT | 0.700 | 0.357 | 0.594 | 0.180 | 0.180 |
XGB | 0.772 | 0.500 | 0.390 | 0.831 | 0.258 |
LB | 0.772 | 0.571 | 0.410 | 0.776 | 0.207 |