Development and Utilization of Bridge Data of the United States for Predicting Deck Condition Rating Using Random Forest, XGBoost, and Artificial Neural Network

Abstract

Accurately predicting the condition rating of a bridge deck is crucial for effective maintenance and repair planning. Despite significant research efforts to develop deterioration models, the efficacy of Random Forest, eXtreme Gradient Boosting (XGBoost), and Artificial Neural Network (ANN) in predicting the condition rating of the nation’s bridge decks has remained unexplored. This study aims to assess the effectiveness of these algorithms for deck condition rating prediction at the national level. To achieve this, the study collected bridge data, which includes National Bridge Inventory (NBI), traffic, and climate regions gathered using Geospatial Information Science (GIS) and remote sensing techniques. Two datasets were collected: bridge data for a single year of 2020 and historical bridge data covering a five-year period from 2016 to 2020. Three models were trained using 319,404 and 1,246,261 bridge decks in the single-year bridge data and the five-year historical bridge data, respectively. Results show that the use of historical bridge data significantly improves the performance of the models compared to the single-year bridge data. Specifically, the Random Forest model achieved an overall accuracy of 83.4% and an average F1 score of 79.7%. In contrast, the XGBoost model achieved an overall accuracy of 79.4% and an average F1 score of 77.5%, while the ANN model obtained an overall accuracy of 79.7% and an average F1 score of 78.4%. Permutation-based variable importance reveals that NBI, traffic, and climate regions significantly contribute to model development. In conclusion, the Random Forest, XGBoost, and ANN models, trained using updated historical bridge data, provide useful tools for accurately predicting the condition rating of bridge decks in the United States, allowing infrastructure managers to efficiently schedule inspections and allocate maintenance resources.

1. Introduction

Bridges are critical infrastructures in the U.S. transportation system that make movement possible between different geographical areas [1], and their performance affects the operating capacity of the system in terms of safety, efficiency, and economy [2]. According to the annual analysis by the American Road and Transportation Builders Association (ARTBA), 36% or nearly 224,000 of the nation’s bridges, encompassing deck, superstructure, and substructure components, need structural repair, rehabilitation, or replacement [3]. However, they still serve more than 167.5 million daily trips across the country. If placed end-to-end, these bridges stretch over 6100 miles, long enough to cross the country from Los Angeles to Portland, Maine and back again. A study by the American Society of Civil Engineers (ASCE) found that the average age of the nation’s bridges increased to 44 years. Most of the country’s bridges were designed for a life span of 50 years, so an increasing number of bridges will soon need major rehabilitation or retirement. Therefore, continuous planning of maintenance, repair, and rehabilitation is required to ensure public safety [4].

Typically, bridges located on public roads with lengths more than 6.1 m (20 feet) are visually inspected at least once every 2 years to monitor their deterioration, resulting in a very costly process of more than $2.7 billion per year [5]. However, the availability of historical bridge data and environmental data has presented unprecedented opportunities to develop deterioration models that accurately predict the future condition rating of a bridge. These models can assist infrastructure managers in scheduling inspections and making informed decisions regarding repair strategies [6,7]. There are various types of deterioration models such as deterministic, probabilistic, and artificial intelligence (AI) and machine learning (ML) models [7,8,9,10].

Deterministic models assume that the deterioration process is certain and do not account for random errors or uncertainty in their predictions [11,12]. In contrast, probabilistic models are used to capture the stochastic nature of bridge deterioration and are commonly applied when uncertain deterioration occurs due to random factors such as traffic loads, climate conditions, structural attributes, and material properties [13,14,15]. Markovian methods, which are widely used probabilistic models for the analysis of bridge deterioration [7,16,17], have been criticized for their memoryless nature. This assumption implies that the prediction of the future condition rating solely depends on the current condition rating and ignores its history [18]. In contrast, AI and ML models have been increasingly utilized to predict the future condition rating of bridges, surpassing the restrictions of deterministic and probabilistic models [19,20,21,22,23,24,25,26]. Deterioration models can be developed for either the entire bridge or its various components, such as deck, superstructure, and substructure. Nevertheless, researchers have paid more attention to the deck compared to other components due to its exposure to heavy traffic, varying temperatures, deicing salts, and abrasive forces [27,28].

To this end, Kong, Li, Zhang, and Das [22] demonstrated the ability of eXtreme Gradient Boosting (XGBoost) in binary classification of 152,714 bridge decks into young bridges with poor condition ratings and old bridges with good condition ratings, that achieved 91% overall accuracy. Similar overall accuracy was achieved by the XGBoost model when trained using 152,714 bridge decks. In a separate study, the historical National Bridge Inventory (NBI) and traffic data of Michigan bridges were utilized to develop ML models for predicting deck condition rating, and the k-nearest neighbors (KNN) model was the second optimal model, after Artificial Neural Network (ANN), with an overall accuracy of 89% [20]. Assaad and El-adaway [29] developed ANN and KNN models by studying 19,269 bridges in Missouri. The authors identified the best subset of ten predictor variables that affect the classification of deck condition rating and reported 91.44% accuracy obtained by the ANN model.

In 2021, a non-linear regression model was developed on Michigan bridge deck condition rating data over 25 years [30]. Deck age or the number of years since the last major reconstruction was the only parameter incorporated into the model. Then, the impact of Average Daily Traffic (ADT), age, and deck area on concrete bridge deck deterioration was evaluated using deterioration curves. Liu, Nehme, and Lu [31] employed deep learning models to estimate parameters within a Markov chain using maximum likelihood training. The likelihood function is based on observed transitions between different condition ratings. The authors applied this approach to historical NBI data spanning from 1993 to 2019. They utilized a Convolutional Neural Network (CNN) as the deep learning model and showcased its performance by achieving a low prediction error, with a maximum mean-squared-error near 0.5 in a 26-year forecast.

The impact of climate data on prediction performance of deterioration models was evaluated by Liu and El-Gohary [32]. To this end, 1078 bridge instances in nine states were incorporated to develop different ANN models, trained with and without climate data. The experimental results indicate the marginal positive effect of climate data on the prediction performance of deterioration models. In another study, Nguyen and Dinh [33] utilized Forward Neural Network (FNN) to predict the future deck condition rating of highway bridges in Alabama using eight predictor variables. Among the predictor variables, age had a significant effect on the ANN’s performance, followed by design load and main structure design. The results indicate that the obtained ANN model trained by 2572 bridges achieved an accuracy of 73.6%. Manafpour, Guler, Radlińska, Rajabipour, and Warn [34] analyzed 30 years of 22,000 bridges in Pennsylvania using a Semi-Markov time-based model and estimated the transition probabilities of those bridges for the deterioration of concrete bridge decks. The study found that the following predictor variables significantly influence the deck condition rating: type of rebar protection, continuous versus supported spans, deck length, number of spans, bridge location, and whether the bridge is part of the interstate system or not.

Radovic, Ghonima, and Schumacher [35] removed the effect of climate data by analyzing the 9809 concrete highway bridge decks located in the Northeast climate region using the clustering technique. In another study conducted for the Michigan Department of Transportation (MDOT), Winn and Burgueno [36] developed ANN models for predicting the deck condition rating of bridge decks using 1956 bridges in Michigan. By utilizing bridge condition data spanning from 2006 to 2010 from three transportation agencies, Bektas, Carriquiry, and Smadi [27] developed classification and regression trees (CARTs) to predict deck, substructure, and superstructure condition ratings. Deterioration curves of Nebraska bridges were developed using NBI condition ratings, spanning from 1998 to 2010, by Hatami and Morcous [37]. The authors placed 15,568 bridges in families based on predictor variables including structure type, deck type, wearing surface, deck protection, ADT, ADTT, functional classification, type of service, and highway agency district, and modeled the condition rating as a function of age only. One year earlier, Huang [9] developed an ANN model on 1241 bridges in Wisconsin to predict the condition rating of bridge decks. The model not only learns from NBI and traffic data such as design load, deck length, skew angle, maximum span length, and the number of spans, but also learns from climate data by introducing region divisions.

The regression methodology was adopted by Hong, Chung, Han, and Lee [38], which presented a model based on the deterioration rate for predicting the end of service life of concrete bridge decks. Individual regression models for 30 departments of transportation, containing 23,404 concrete bridge decks, were developed using age as the most correlated predictor variable with condition rating as the response variable. NBI and traffic data of concrete bridge decks in Quebec, Canada, and their associated regions were utilized to develop decision trees for modeling deck deterioration and evaluating their performance [39]. In another study, 18 predictor variables of a subset of 222 bridges in Kansas were used to examine the extent to which wrapper methods could improve the prediction accuracy of the decision tree algorithm for the application of bridge decks [40]. The experiments revealed that the bagged decision tree yielded a better accuracy of 73.4% compared to 67.7% obtained from the decision tree. The evaluation indicates a slight increment in the prediction accuracy over the Markov chain developed using the same dataset. Morcous, Rivard, and Hanna [11] applied an AI technique to the real-world data from 521 bridges obtained from the Canadian Province of Quebec. The developed case-based reasoning (CBR) application in considering the effects of NBI and traffic data along with regions yielded 70% correctness.

Despite extensive research efforts to develop accurate predictive models for bridge deck deterioration, the effectiveness of Random Forest, XGBoost, and ANN in predicting the condition rating of the nation’s bridge decks has remained unexplored. This gap in exploration is primarily attributed to the fact that existing models have been trained using a relatively small sample of bridge decks, mainly from one state, which may not be representative of the entire population of over 460,000 bridge decks in the United States. Therefore, this study contributes to the body of knowledge by assessing how well the Random Forest, XGBoost, and ANN algorithms perform in classifying the condition rating of the nation’s bridge decks. Conducting a nationwide investigation is crucial due to significant variations of bridge deck characteristics, climate, and traffic across the United States. This investigation enables the study to effectively identify influential variables essential for developing national predictive models. The subsequent sections of this study outline the research methodology, including data preparation, model development and evaluation, as well as the results obtained from the training and evaluation of models. This study reports outcomes from two experiments, each involving the development of three models using two distinct datasets: the bridge data of 2020 and the five-year historical bridge data (2016–2020). Subsequently, the models are compared, and the findings are discussed. Finally, this study provides concluding remarks, and offers recommendations for further research.

2. Research Methodology

This study employed a three-step research methodology:

• Data preparation: This study developed two sets of national bridge data by incorporating NBI, traffic, and climate regions. One dataset is for the year 2020 and another encompasses five years (2016–2020) of historical bridge data.
• Model development and evaluation: Each dataset was preprocessed and divided into an 80% training set and a 20% test set. Subsequently, three models including Random Forest, XGBoost, and ANN were trained and evaluated based on overall accuracy and average F1 score on the test set. To address the imbalance in bridge deck condition rating across ten categories, separate F1 scores were computed for each condition rating to comprehensively assess models’ performance. Meanwhile, a permutation-based approach was employed to identify important features, among NBI, traffic, and climate regions, for development of the ML models.
• Model selection and discussion: The effectiveness of the developed models was examined using training time, overall accuracy, and average F1 score.

3. Data Preparation

The bridge data in the United States were developed through several essential steps. First, NBI, including traffic data, was collected and only the potential predictor variables influencing deterioration were retained. Second, bridges were spatially located using latitude and longitude information provided in the NBI data, and their locations were verified using remote sensing technology. Finally, the appropriate climate region was assigned to each bridge using its location by Geospatial Information Science (GIS) technology. The following subsections provide a detailed description of bridge data development. By following the same procedure, bridge data in one year can be established and by including multiple bridge data, historical bridge data can be developed.

3.1. NBI and Traffic Data Collection

The annually submitted NBI data comprises a considerable amount of information about the United States’ bridge network. It contains 116 coded items to describe each bridge, including basic design information, current service, condition ratings, etc. [41].

Table 1. The description of a bridge deck in different condition ratings.

Condition 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

represents the description of a bridge deck in different condition ratings.

Out of 35 potential predictor variables of NBI data, which were initially selected based on existing studies [29,32,33,34,36,39,42], only 19 variables were retained using engineering judgments.

Table 2. The identified NBI predictor variables.

No.	NBI Variable	Type	Item	Description
1	Age	Numeric	Computed using 27, 90, 106	Bridge age
2	ADT	Numeric	Computed using 29, 30, 90, 114, 115	Average daily traffic
3	ADTT	Numeric	109	Percent of daily truck traffic
4	Lanes_On	Numeric	28A	Lanes on the structure
5	Number_Spans_Main	Numeric	45	Number of main spans
6	Length_Max_Span	Numeric	48	Length of maximum span
7	Curb_Width	Numeric	Computed using 50A, 50B	Width of curb
8	Deck_Area	Numeric	Computed using 49, 52	Deck area
9	Operating_Rating	Numeric	64	Operating rating
10	Highway_District	Categorical	2	Highway agency district
11	Design_Load	Categorical	31	Designed live load
12	Reconstructed	Categorical	Computed using 106	Reconstruction status
13	Main_Material	Categorical	43A	Main structure material
14	Main_Design	Categorical	43B	Main structure design
15	Spans_Material	Categorical	44A	Span structure material
16	Spans_Design	Categorical	44B	Span structure design
17	Deck_Geometry	Categorical	68	Rating for deck geometry
18	Deck_Type	Categorical	107	Type of deck system
19	Wearing_Surface	Categorical	108A	Wearing surface

lists the identified NBI predictor variables. It is worth noting that the NBI and traffic data were collected from the U.S. Department of Transportation website [43].

As can be seen in Table 2, the five following predictor variables were calculated by integrating several items in the NBI data.

• “Reconstructed”: zero, if “year reconstructed” (item 106) is zero, otherwise one.
• “Age”: subtraction of “year built” (item 27) from “year of inspection” (two last digits of item 90), if “Reconstructed” is zero, otherwise subtraction of “year reconstructed” (item 106) from “year of inspection” (two last digits of item 90). Note that for a reconstructed bridge “Age” would be equivalent to the number of years since the last major reconstruction.
• ADT: is computed using Equation (1).

$$\mathrm{A}\mathrm{D}\mathrm{T}=\left(\frac{\mathrm{F}\mathrm{A}\mathrm{D}\mathrm{T}-\mathrm{L}\mathrm{A}\mathrm{D}\mathrm{T}}{\mathrm{Y}\mathrm{F}\mathrm{A}\mathrm{D}\mathrm{T}-\mathrm{Y}\mathrm{A}\mathrm{D}\mathrm{T}}\right)\times \left(\mathrm{Y}\mathrm{I}-\mathrm{Y}\mathrm{A}\mathrm{D}\mathrm{T}\right)+\mathrm{L}\mathrm{A}\mathrm{D}\mathrm{T}$$

(1)

where FADT = Future ADT (item 114); LADT = Latest ADT (item 29); YFADT = Year of Future ADT (item 115); YADT = Year of ADT (item 30); and YI = Year of Inspection (two last digits of item 90).

4.

Curb_Width: sum of the “left curb width” (item 50A) and the “right curb width” (item 50B).

5.

Deck_Area: multiplying the “structure length” (item 49) and the “deck width” (item 52).

3.2. Spatially Locating Bridges

Next, bridges were spatially located using GIS technology and their locations were verified using remote sensing technology. To this end, items 16 and 17 in the NBI data, representing latitude and longitude, were used as location references for bridges. GIS technology incorporated such location references to represent 613,290 bridges as points in a vector space. Note that such points would be leveraged to associate bridges with climate regions. Difficulties in assigning accurate vector space locations were primarily attributed to incorrect latitude and longitude coordinate values of some bridges, mainly originating from typographical errors in the data entry phase. To alleviate such problems, 254 structures with null and zero latitude and longitude were removed. Next, state boundaries were considered as a criterion for validating latitude and longitude locations provided in the NBI data. By doing so, 648 bridges falling out of the boundary of the associated state were removed and the rest remained. Figure 1 shows the bridges inside and outside Alabama, represented using white and red dots, respectively.

It is noteworthy that the administrative borders of states were expanded by an arbitrary buffer, in this case, 2 miles, used as state boundaries. This approach led to retaining bridges beyond and near administrative borders. Figure 2 shows a bridge over the Mississippi River in Arkansas that is located between the administrative border and the 2-mile-extended boundary and hence was retained. Although the present study used administrative borders to assess the validity of the spatial locations of bridges, the designated county in the NBI data, as a smaller division, seems more accurate. However, it is important to acknowledge that employing county-level data may introduce additional complexities and potentially prolong the evaluation process due to the finer granularity of county boundaries.

Locations of bridges were visually verified through overlaying points, representing the spatial location of bridges, on high-resolution satellite images. However, due to the large number of bridges in the United States, this approach may only be applicable to suspicious bridges. Figure 3 illustrates the spatial locations of two bridges, in Connecticut, overlaid on GeoEye satellite imagery. These bridges were removed from further analysis because they were located on farms. Note that assessing the validity of bridge locations is crucial because such locations are leveraged to allocate a climate region to each structure.

Utilizing the previously described approach, we collected data on 612,388 bridges located throughout the United States, encompassing 48 contiguous states and the District of Columbia. Figure 4 portrays the spatial distribution of bridges in the United States collected in the present study. This dataset offers valuable insights into the spatial distribution of bridges across the nation. As depicted in Figure 4, it becomes evident that bridges exhibit varying densities across the United States. Particularly, bridges are much denser in the eastern half of the country compared to the western half. This disparity in distribution is primarily attributed to the prevalence of rivers and streams in the eastern half, necessitating a denser network of bridges to facilitate transportation and connectivity.

Table 3. The initial number of bridges in the NBI data in each state, number of bridges with incorrect spatial locations, percentage of bridges removed, and number of bridges retained.

State	Initial Bridges	Bridges with Incorrect Spatial Locations			Bridges Removed (%)	Bridges Remained
		Missing Longitude or Latitude	Zero Longitude or Latitude	Outside the State
Alabama	16,155	1	5	32	0.24	16,117
Arizona	8428	0	1	3	0.05	8424
Arkansas	12,946	0	32	0	0.25	12,914
California	25,763	0	31	2	0.13	25,730
Colorado	8829	0	14	6	0.23	8809
Connecticut	4357	0	0	105	2.41	4252
Delaware	882	0	0	1	0.11	881
District of Columbia	243	0	0	3	1.23	240
Florida	12,592	0	2	4	0.05	12,586
Georgia	14,964	0	0	1	0.01	14,963
Idaho	4522	0	6	3	0.2	4513
Illinois	26,848	0	0	0	0	26,848
Indiana	19,327	0	0	0	0	19,327
Iowa	23,982	0	0	1	0	23,981
Kansas	24,948	0	0	8	0.03	24,940
Kentucky	14,422	0	2	1	0.02	14,419
Louisiana	12,853	0	1	2	0.02	12,850
Maine	2472	0	0	0	0	2472
Maryland	5430	33	6	280	5.87	5111
Massachusetts	5229	0	0	0	0	5229
Michigan	11,271	0	0	2	0.02	11,269
Minnesota	13,471	0	1	0	0.01	13,470
Mississippi	16,878	0	0	9	0.05	16,869
Missouri	24,538	0	0	0	0	24,538
Montana	5271	0	12	9	0.4	5250
Nebraska	15,348	0	0	3	0.02	15,345
Nevada	2056	0	2	56	2.82	1999
New Hampshire	2514	0	0	0	0	2514
New Jersey	6801	0	0	13	0.19	6788
New Mexico	4024	0	1	4	0.12	4019
New York	17,552	0	0	0	0	17,552
North Carolina	18,749	0	1	25	0.14	18,723
North Dakota	4312	0	1	43	1.02	4268
Ohio	27,072	0	0	0	0	27,072
Oklahoma	23,155	0	3	0	0.01	23,152
Oregon	8214	0	24	3	0.33	8187
Pennsylvania	22,965	0	0	3	0.01	22,962
Rhode Island	777	0	0	0	0	777
South Carolina	9455	0	0	3	0.03	9452
South Dakota	5880	1	2	0	0.05	5877
Tennessee	20,235	0	1	0	0	20,234
Texas	54,682	0	2	0	0	54,680
Utah	3062	0	1	0	0.03	3061
Vermont	2827	0	0	3	0.11	2824
Virginia	13,963	0	28	5	0.24	13,930
Washington	8338	0	23	13	0.43	8302
West Virginia	7295	0	9	0	0.12	7286
Wisconsin	14,271	0	1	0	0.01	14,270
Wyoming	3122	0	7	3	0.32	3112
Total	613,290					612,388

lists the initial number of bridges in the NBI data in each state, number of bridges with incorrect spatial locations, percentage of bridges removed, and number of bridges retained. According to Table 3, 5.87%, 2.82%, 2.41%, 1.23%, and 1.02% of bridges in Maryland, Nevada, Connecticut, District of Columbia, and North Dakota were removed, respectively, while less than 0.5% of bridges in other states were removed. Furthermore, Texas leads the nation in the number of bridges; of the 612,388 nation bridges, 54,680 bridges belong to public highways, roads, and streets of Texas, while Rhode Island with 777 bridges comprises the minimum number of bridges.

3.3. Climate Region Collection

Then spatial locations of bridges were utilized to assign a climate region to each bridge structure. Figure 5 shows the nine climatically consistent regions within the United States, defined by NOAA. According to Figure 5, California and Nevada are in the West region, while Florida and Alabama are in the Southeast region.

4. Model Development and Evaluation

4.1. Predictor and Response Variables

To conduct experiments, two distinct datasets were generated: the bridge data of 2020 and the five-year historical bridge data spanning the period from 2016 to 2020. A total of 20 variables, including 9 numerical and 11 categorical, were introduced as predictor variables. It is noteworthy that all 9 numerical and 10 categorical variables represented NBI and traffic data, while climate regions were introduced by only one categorical variable.

Table 4. The list of 20 predictor variables.

No.	Predictor Variable	Type
1	Age	Numeric
2	ADT	Numeric
3	ADTT	Numeric
4	Lanes_On	Numeric
5	Number_Spans_Main	Numeric
6	Length_Max_Span	Numeric
7	Curb_Width	Numeric
8	Deck_Area	Numeric
9	Operating_Rating	Numeric
10	Highway_District	Categorical
11	Design_Load	Categorical
12	Reconstructed	Categorical
13	Main_Material	Categorical
14	Main_Design	Categorical
15	Spans_Material	Categorical
16	Spans_Design	Categorical
17	Deck_Geometry	Categorical
18	Deck_Type	Categorical
19	Wearing_Surface	Categorical
20	NOAA_Climate_Regions	Categorical

represents the list of 20 predictor variables.

A multiclass variable that includes 10 deck condition ratings, from 0 to 9, was introduced as the response variable. Failed condition rating is represented by 0, while excellent condition rating is represented by 10.

Table 5. The multiclass response variable.

Response Variable	Values
Multiclass	0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

represents the multiclass response variable.

4.2. Feature Selection

Feature selection is a technique that helps identify important and relevant features in the dataset while discarding redundant or irrelevant ones, to be used in ML and data mining tasks. The goal of feature selection is to create a small subset of predictor variables that still captures the vital characteristics of the dataset [44]. This approach offers several benefits, including reduced size of dataset, lower storage requirements, improved prediction accuracy, prevention of overfitting, and reduced execution and training time by focusing on easy-to-interpret predictor variables [45]. There are several methods for feature selection, such as filter, embedded, wrapper, and hybrid. In this study, permutation-based variable importance was utilized as a feature selection technique, which falls under the category of filter algorithms, which evaluate the relationship between each predictor variable and the response variable independently [46].

Random Forest uses a permutation-based approach to measure the positive effect of a variable on prediction performance. The importance of a variable is calculated as the average increase in error rate or decrease in model accuracy on out-of-bag (OOB) observations when the values of the respective predictor variable are randomly permuted. The permutation-based variable importance measures the difference between the OOB error rate before and after permuting the values of the predictor variable $\mathrm{j}$ [47]. The variable importance of variable $\mathrm{j}$ is defined by Equation (2):

$${\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}_{\mathrm{j}}=\frac{1}{\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}}{\sum }_{\mathrm{t}=1}^{\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}}\left({\mathrm{E}\mathrm{R}}_{\mathrm{t}\tilde{\mathrm{j}}}{-\mathrm{E}\mathrm{R}}_{\mathrm{t}\mathrm{j}}\right)$$

(2)

where $\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}$ denotes the number of trees in the forest, ${\mathrm{E}\mathrm{R}}_{\mathrm{t}\tilde{\mathrm{j}}}$ and ${\mathrm{E}\mathrm{R}}_{\mathrm{t}\mathrm{j}}$ represent the mean error rate on OOB data in tree $\mathrm{t}$ after and before permuting the predictor variable $\mathrm{j}$, respectively. If the predictor variable is not associated with the response variable, the permutation of its values will have no impact on the error rate. Conversely, if the response and the predictor variable are associated, permuting the values of the predictor variable will disturb this association, resulting in an increased error rate and a decrease in model accuracy. In general, the larger the decrease in model accuracy after permutation, the more informative the corresponding predictor variable is [48,49,50,51]. This insight, obtained from the OOB data, can aid in interpreting the developed model and identifying the predictor variables that offer the most predictive power. Additionally, excluding predictor variables that do not provide any useful information leads to more time-efficient analysis, improving performance, and avoidance of overfitting [52,53].

Sampling with replacement, available in the ranger package, version 0.13.1, was introduced by Wright and Ziegler [54]. This feature has led to the creation of a variable importance plot, which ranks the predictor variables based on the reduction of model accuracy if their associated values are permuted. Figure 6 shows the variable importance plot using the permutation-based variable importance approach. According to Figure 6, the most contributing predictor variable in determining deck condition rating is the age of a deck or the number of years since the last major reconstruction. It is noteworthy that climate regions (NOAA_Climate_Regions) and traffic (e.g., ADT and ADTT) are recognized as influential variables contributing to the deterioration of bridge decks. Additionally, other variables, representing various characteristics of bridge decks, are identified to influence the predictive performance of the deterioration models. These variables include Deck_Area, Operating_Rating, Main_Material, Highway_District, Wearing_Surface, Length_Max_Span, Design_Load, Deck_Geometry, Number_Spans_Main, Main_Design, Curb_Width, Deck_Type, Reconstructed, Lanes_On, Spans_Material, and Spans_design.

4.3. Data Cleaning

Before developing models, the data need to undergo cleaning and transformation to ensure that they are in the appropriate format. Data cleaning involves handling records with either missing or invalid values, which can negatively impact the model performance [55,56], as well as removing duplicate instances [57]. To enable the creation of a wider range of classification models, categorical variables are encoded into numeric values [58] using label encoding or one-hot encoding [59] and numerical variables are centered and scaled [60] using Min-Max scaling, Z-score standardization, logarithmic transformation, Box-Cox transformation, and robust scaling [61].

Statistical analysis of the bridge data of 2020 indicates that 76.71% of the structures in the year 2020 across the United States were bridge decks, while only 23.29% were structures without decks. Figure 7 illustrates the distribution of bridge decks in the United States and in each state. Figure 7 highlights a noteworthy contrast in the year 2020: in Arizona, less than half of the structures were bridge decks, whereas in some states like New Mexico, Texas, Oklahoma, Kansas, North Dakota, Minnesota, Tennessee, Alabama, Georgia, and North Dakota, bridge decks constituted slightly over 75% of the total. It is worth noting that in certain states such as Washington, Oregon, Idaho, and Montana, bridge decks made up more than 10% of the total.

Figure 8 displays the distribution of bridge decks with 10 different condition ratings, from 0 to 9, in the United States and in each state. As depicted in Figure 8, a small fraction of bridge decks (2.41%) in the year 2020 had a condition rating of 9, while those with a condition rating of 8 accounted for 13.72% of the nation’s bridge decks. It is noteworthy that the largest proportion of bridge decks (42.68%) had a condition rating of 7, followed by 25.33% with a condition rating of 6, and 12.37% with a condition rating of 5. Meanwhile, only 2.73% of bridge decks had a condition rating of 4, and 0.76% had condition ratings of 0, 1, 2, and 3. These proportions emphasize the significant imbalance in the distribution of bridge decks across the United States and within each state when considering ten different condition ratings.

Subsequently, both datasets were cleaned by removing structures without decks, instances with missing or invalid values, and duplicate records. In this context, invalid values refer to negative values found in the numerical predictor variables listed in Table 4. Only distinct values were retained by removing duplicate records.

Table 6. The number of instances removed from the bridge data of 2020 and the five-year historical bridge data (2016–2020).

	Number of Bridges in the Bridge Data of 2020	Number of Bridges in the Five-Year Historical Bridge Data
Structures without decks	142,647	731,334
Missing values	63,265	420,915
Invalid values	493	369,451
Duplicate instances	6728	1498
Total	213,133	1,523,198

lists the number of instances removed from the bridge data of 2020 and the five-year historical bridge data (2016–2020). According to Table 6, a total of 213,133 and 1,523,198 bridge decks were removed from the bridge data of 2020 and the five-year historical bridge data (2016–2020), respectively.

4.4. Data Partitioning

After cleaning, 399,255 and 1,557,827 bridge decks were retained for analysis in the bridge data of 2020 and the five-year historical bridge data (2016–2020), respectively. Next, the observations of bridge decks in each bridge dataset were randomly divided into an 80% training set and a 20% test set. The training sets were used to train models, while the test sets were used to evaluate their performance.

Table 7. The number of bridge decks in the bridge data of 2020 and the five-year historical bridge data (2016–2020) that were used to train models and evaluate their performance.

	The Bridge Data of 2020	The Five-Year Historical Bridge Data (2016–2020)
Number of bridges	399,255	1,557,827
Training set (80%)	319,404	1,246,261
Test set (20%)	79,851	311,566

represents the number of bridge decks in the bridge data of 2020 and the five-year historical bridge data (2016–2020) that were used to train models and evaluate their performance. According to Table 7, 319,404 and 1,246,261 bridge decks in the bridge data of 2020 and the five-year historical bridge data (2016–2020) were used to train models, while 79,851 and 311,566 bridge decks in the bridge data of 2020 and the five-year historical bridge data (2016–2020) were used to evaluate their performance.

4.5. Model Performance

The models’ performance was evaluated using two metrics calculated on the test set: namely, overall accuracy and average F1 score. The overall accuracy represents the percentage of correctly classified instances out of the total number of instances. On the other hand, average F1 score is the mean of the F1 scores of all classes, where the F1 score is the harmonic mean of precision and recall [62] for a given class, which is calculated by Equation (3):

$$\mathrm{F}1\mathrm{score}=2\times \frac{{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}_{}\times \mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}$$

(3)

where precision is the proportion of true positive predictions among all positive predictions, and recall is the proportion of true positive predictions to the total number of actual positive cases.

5. Results of Training and Evaluating Models

From the variety of available classification models in the literature, we chose to use two tree-based ensemble models, namely Random Forest and XGBoost, as well as a more complex model, namely ANN. These models were deemed appropriate for the present study due to their common characteristics. Firstly, they have been successful in data-driven structural health-monitoring [63,64,65,66,67] and investigating infrastructure problems in previous studies [28,33,68,69]. Secondly, the existing studies have demonstrated the effectiveness of Random Forest [70,71], XGboost [22,28], and ANN [25,29,33,72,73] in capturing the complex and nonlinear relationships among the variables involved in predicting bridge condition rating. The following is a general overview of the models trained and evaluated in this study.

5.1. Random Forest

According to the original formulation by Breiman [74], Random Forest is a tree-based ensemble that uses bootstrap samples and randomness in the tree-building procedure. The decorrelation between trees achieved this way leads to significant improvement in accuracy estimated either using an OOB or a test set [75,76]. According to Hastie, Tibshirani, Friedman, and Friedman [49], the predictions on OOB data are used to compute OOB error, which is almost identical to that obtained by $\mathrm{N}$-fold cross-validation. Two parameters, including $\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}$ (number of trees) and $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$ (number of predictor variables), need to be tuned for estimating a Random Forest model [77]. The number of trees can be determined experimentally by adding the successive trees until the OOB error stabilizes [78,79,80]. While the Random Forest yields the optimal performance on most datasets with the default value of $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$, e.g., the square root of the total number of predictor variables [81,82,83].

The Random Forest models in this study were implemented in the R programming language, version 4.2.0, using the ranger package, version 0.13.1. The default hyperparameters for the ranger package in classification tasks are $\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}$= 500 and $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}=\sqrt{\mathrm{p}}$, where $\mathrm{p}$ indicates the number of predictor variables. The best hyperparameters were selected based on the lowest and stabilized OOB error. Two Random Forest models were developed using the training sets derived from the bridge data of 2020 and the five-year historical bridge data (2016–2020). The Random Forest models were fine-tuned by optimizing the $\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}$ and $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$ parameters based on the OOB error on the training set. Trees were added incrementally until the OOB error on the training set reached a stabilized state. Additionally, the optimized value of $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$ was selected by finding the minimum OOB error across values ranging from 5 to 11. The OOB error curve became stable after 500 trees, and there was minimal variation (0.1%) in the OOB error for $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$ values ranging from 5 to 11. Consequently, the Random Forest models for the bridge data of 2020 and the five-year historical bridge data (2016–2020) were trained using the default values of $\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{e}$ (e.g., 500) and $\mathrm{m}\mathrm{t}\mathrm{r}\mathrm{y}$ (e.g., 5) in approximately 4 and 73 min, respectively. Then, the test sets were utilized to evaluate the performance of the developed Random Forest classifiers.

Table 8. The confusion matrix of the Random Forest classifier on the test set of the bridge data of 2020.

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		63	2	5	5	9	13	8	0	0	0	60.0	58.3
1		0	1	0	0	0	0	0	0	0	0	100.0	11.8
2		2	0	17	1	1	5	1	1	0	0	60.7	36.2
3		3	0	0	25	13	9	4	3	0	0	43.9	12.0
4		2	0	3	29	169	138	39	14	3	1	42.5	13.2
5		24	8	20	124	821	3439	1759	784	108	14	48.4	39.1
6		10	5	18	140	840	4407	10,544	4847	377	60	49.6	50.7
7		6	0	1	34	303	2405	7761	26,609	4772	305	63.1	69.7
8		1	0	1	1	8	68	196	1841	4655	719	62.1	52.7
9		0	0	1	0	2	9	21	63	276	855	69.7	53.8
Sum		111	16	66	359	2166	10,493	20,333	34,162	10,191	1954
Recall		56.8	6.25	25.8	7.0	7.8	32.8	51.9	77.9	45.7	43.8
										Overall accuracy			58.1%
										Average F1 score			39.7%

presents the confusion matrix of the Random Forest classifier on the test set of the bridge data of 2020. As indicated in Table 8, the Random Forest model achieved an overall accuracy of 58.1% and an average F1 score of 39.7%, indicating a noteworthy difference of 18.4% between the two metrics on the test set. According to Table 8, the Random Forest model could not efficiently learn the underlying pattern when dealing with only 16 bridge decks with a condition rating of 1, resulting in the lowest F1 score of 11.8%. Conversely, when dealing with a substantial number of bridge decks, such as 34,162 with a condition rating of 7, the Random Forest model excelled and achieved the highest F1 score of 69.7% for this condition rating.

Table 9. The confusion matrix of the Random Forest classifier on the test set of the five-year historical bridge data (2016–2020).

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		346	4	3	6	22	43	18	2	1	1	77.6	78.2
1		0	32	0	3	1	0	0	1	1	0	84.2	71.9
2		9	0	258	16	13	2	2	0	1	0	85.7	83.1
3		4	0	12	1226	114	46	9	9	3	6	85.8	77.1
4		11	2	12	151	6614	806	174	117	21	11	83.5	76.2
5		35	8	10	165	1418	31,405	3551	1374	245	54	82.1	80.1
6		25	3	18	109	785	4985	63,955	6709	474	64	82.9	82.2
7		9	1	5	58	415	2643	10,211	116,257	8441	380	84.0	86.9
8		0	1	2	10	40	187	449	4637	33,252	1563	82.8	79.8
9		0	0	0	7	9	26	49	173	717	6499	86.9	80.9
Sum		439	51	320	1751	9431	40,143	78,418	129,279	43,156	8578
Recall		78.8	62.7	80.6	70.0	70.1	78.2	81.6	89.9	77.1	75.8
										Overall accuracy			83.4%
										Average F1 score			79.7%

, on the other hand, exhibits the confusion matrix of the Random Forest classifier on the test set of the five-year historical bridge data (2016–2020). According to Table 9, the Random Forest achieved an overall accuracy of 83.4% and an average F1 score of 79.7%, indicating a lower difference of 3.7% between the two metrics on the test set. The notably improved performance of the Random Forest model, which was trained using the historical bridge data, can be attributed to its utilization of more extensive bridge data, enabling it to capture the underlying pattern effectively. Additionally, the reduced disparity between the overall accuracy and the average F1 score of the Random Forest model, trained using the historical bridge data, suggests that the second model exhibits less performance variation across the ten imbalanced condition ratings and hence is more consistent in its performance.

5.2. XGBoost

XGBoost, developed by Chen and Guestrin [84], iteratively builds an ensemble of decision trees, with each tree trained to correct the errors made by previous tree(s). The predictions from all these weak learners are then combined through a weighted majority vote to produce the final prediction [85]. XGBoost, which utilizes small decision trees with fewer splits, produces a more interpretable model.

The XGBoost models in this study were developed in the R programming language, version 4.2.0, using the xgboost package [86], version 1.6.0.1. The models were built using the default values provided by the package. The “number of boosting iterations” refers to the total number of base learners generated by the algorithm. Each base learner is built to reduce the error of the previous base learner. Overfitting can occur with too many iterations and underfitting can occur with too few, so early stopping is applied to monitor the validation loss and stop training when the model stops improving [87]. The learning rate determines the step size for updating the weights of each feature to optimize the objective function. A trade-off exists between the learning rate and the number of iterations, with a small learning rate requiring a larger number of iterations for sufficient convergence [88]. The log loss, also known as cross-entropy loss, is used to measure the performance of the classification model. A higher log loss indicates a larger discrepancy between the predicted probability and the actual label [89].

Two XGBoost models were developed using training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020).

Table 10. The parameter values used for training the XGBoost models using the training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020).

Parameter	Argument	The Bridge Data of 2020	The Five-Year Historical Bridge Data
Max number of boosting iterations	“nrounds”	1000	10,000
Training stops after 3 rounds	“early_stopping_rounds”	3	3
Maximum depth of a tree	“max_depth”	6	6
Learning rate	“eta”	0.3	0.3

lists the parameter values used for training the XGBoost models using the training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020). The “early_stopping_rounds” parameter was utilized to stop the training process once the model’s performance stabilized. The XGBoost model for the bridge data of 2020 completed training after approximately 4 min at 176 iterations, as the model’s performance did not improve during the final three iterations on the test set. On the other hand, the XGBoost model for the five-year historical bridge data (2016–2020) demonstrated gradual improvement over 10,000 iterations and concluded training after approximately 894 min. Subsequently, the test sets were employed to evaluate the performance of the developed XGBoost classifiers.

Table 11. The confusion matrix of the XGBoost classifier on the test set of the bridge data of 2020.

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		65	3	4	3	12	14	10	2	0	0	57.5	58.0
1		0	1	0	0	0	0	0	0	0	0	100.0	11.8
2		3	0	23	0	1	5	1	1	0	0	67.6	46.0
3		4	1	0	36	27	28	10	1	0	0	33.6	15.5
4		3	2	7	39	123	130	43	16	2	0	33.7	9.7
5		21	7	15	119	789	2964	1611	823	136	25	45.5	34.9
6		11	2	13	130	887	4666	9759	5130	393	50	46.4	47.2
7		3	0	2	31	317	2600	8621	26,208	5108	299	60.7	67.8
8		1	0	0	1	5	79	249	1833	4167	666	59.5	48.5
9		0	0	2	0	5	7	29	148	385	914	61.3	53.1
Sum		111	16	66	359	2166	10,493	20,333	34,162	10,191	1954
Recall		58.6	6.25	34.8	10	5.7	28.2	48.0	76.7	40.9	46.8
										Overall accuracy			55.4%
										Average F1 score			39.2%

presents the confusion matrix of the XGBoost classifier on the test set of the bridge data of 2020. As indicated in Table 11, the XGBoost classifier achieved an overall accuracy of 55.4% and an average F1 score of 39.2%, indicating a noteworthy difference of 16.2% between the two metrics on the test set. Additionally, Table 11 highlights that the XGBoost model exhibits lower recall when classifying bridge decks with condition ratings of 3 and 4 in comparison to classification of bridge decks with higher condition ratings. The tendency of the XGBoost model to classify bridge decks with condition ratings of 3 and 4 as higher condition ratings, such as 5 and 6, might be attributed to the limited number of bridge decks with 3 and 4 condition ratings compared to those with higher condition ratings.

Table 12. The confusion matrix of the XGBoost classifier on the test set of the five-year historical bridge data (2016–2020).

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		330	4	1	4	23	32	18	5	1	2	78.6	76.8
1		2	31	0	1	2	0	0	1	0	0	83.8	70.5
2		6	0	256	11	14	3	5	1	1	0	86.2	83.0
3		4	2	11	1226	112	60	13	9	5	7	84.6	76.6
4		26	1	13	166	6400	814	224	120	33	15	81.9	74.2
5		36	7	11	151	1430	28,933	4044	1858	319	44	78.6	75.2
6		22	3	19	114	901	6323	59,307	9097	661	80	77.5	76.6
7		12	3	8	64	482	3722	14,147	112,570	9706	392	79.8	83.3
8		1	0	1	8	56	233	612	5402	31,583	1287	80.6	76.7
9		0	0	0	6	11	23	48	216	847	6751	85.4	81.9
Sum		439	51	320	1751	9431	40,143	78,418	129,279	43,156	8578
Recall		75.2	60.8	80.0	70.0	67.9	72.1	75.6	87.1	73.2	78.7
										Overall accuracy			79.4%
										Average F1 score			77.5%

, on the other hand, exhibits the confusion matrix of the XGBoost classifier on the test set of the five-year historical bridge data (2016–2020). According to Table 12, the XGBoost classifier achieved an overall accuracy of 79.4% and an average F1 score of 77.5%, indicating a lower difference of 1.9% between the two metrics on the test set. The notably improved performance of the XGBoost model, which was trained using the historical bridge data, can be attributed to utilization of more extensive bridge data, enabling it to capture the underlying pattern effectively. Additionally, the reduced disparity between the overall accuracy and the average F1 score of the XGBoost model, trained using the historical bridge data, suggests that the second model exhibits less performance variation across the ten imbalanced condition ratings and hence is more consistent in its performance.

5.3. ANN

ANN is capable of approximating complexity based on a parallel and layered structure [24]. The information flow in an ANN model happens through communication among three types of layers: input, hidden, and output layers. While a single-hidden-layer ANN can only address linear separable patterns [90], a Deep Neural Network (DNN) with multiple hidden layers can learn more complex nonlinear relationships between inputs and outputs [91].

The key parameters of ANN include the number of hidden layers, number of nodes in each hidden layer, dropout layers, and activation functions. The number of hidden layers can significantly impact the performance of the network; more hidden layers potentially improve accuracy but also increase complexity [92]. The number of nodes in each hidden layer determines the complexity of the network. Too few nodes may result in underfitting, while too many nodes may lead to overfitting [93]. Dropout layers prevent overfitting in neural networks by randomly dropping out a portion of neurons during the training process [94]. The right activation function can improve the performance of the network [95]. The common activation functions are as follow:

• Sigmoid, described in Equation (4), looks like an s-shape and is used to predict the probability that varies between 0 and 1.

$$\mathrm{f}(\mathrm{x})=\frac{1}{1+{\mathrm{e}}^{-\mathrm{x}}}$$

(4)

2.

The Hyperbolic Tangent (TanH), described in Equation (5), is also sigmoidal (s-shaped). The range of TanH is between −1 and 1.

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{2}{1+{\mathrm{e}}^{-2\mathrm{x}}}-1$$

(5)

3.

The Rectified Linear Unit (ReLU), described in Equation (6), is the most common activation function with better performance than other functions [96]. ReLU will output input directly if it is positive, otherwise, it will output zero.

$$\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{c}0\hspace{0.33em}\hspace{0.33em}\mathsf{f}\mathsf{o}\mathsf{r}\hspace{0.33em}\hspace{0.33em}\mathsf{x}<0\\ \mathsf{x}\hspace{0.33em}\hspace{0.33em}\mathsf{f}\mathsf{o}\mathsf{r}\hspace{0.33em}\hspace{0.33em}\mathsf{x}\ge 0\end{array}\right.$$

(6)

4.

The Scaled Exponential Linear Unit (SELU), described in Equation (7), automatically converges to a zero mean and unit variance.

$$\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{c}\mathsf{\lambda }\mathsf{\alpha }\left({\mathrm{e}}^{\mathrm{x}}-1\right)\hspace{0.33em}\hspace{0.33em}\mathsf{f}\mathsf{o}\mathsf{r}\hspace{0.33em}\hspace{0.33em}\mathsf{x}<0\\ \mathsf{\lambda }\mathsf{x}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathsf{f}\mathsf{o}\mathsf{r}\hspace{0.33em}\hspace{0.33em}\mathsf{x}\ge 0\end{array}\right.$$

(7)

where $\mathsf{\lambda }$ and $\mathsf{\alpha }$ are the following approximate values:

$$\mathsf{\lambda }\approx 1.0507009873554804934193349852946$$

$$\mathsf{\alpha }\approx 1.6732632423543772848170429916717$$

5.

The Softmax activation function, described in Equation (8), is a combination of multiple sigmoid functions that can be used as a function in the output layer of an ANN in multiclass classification problems. The function for every data point of all individual classes returns the probability [95]. Then the class of each data point is identified based on the highest probability.

$$\mathrm{f}(\mathrm{x})=\frac{{\mathrm{e}}^{{\mathrm{x}}_{\mathrm{k}}}}{\sum _{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{e}}^{{\mathrm{x}}_{\mathrm{k}}}}$$

(8)

where $\mathrm{k}$ is the number of classes in the multiclass classifier.

The ANN models in this study were implemented in the R programming language, version 4.2.0, using the keras package [97], version 2.9.0. Two ANN models were developed using training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020). The number of nodes in the input layer was equivalent to the number of predictor variables, and the number of nodes in the output layer was equal to the number of classes in the response variable (ten deck condition ratings from 0 to 9). The random grid search along with 10-fold cross-validation were used to determine the key parameters of the ANN model, including number of hidden layers, activation functions, number of nodes in each hidden layer, and dropout layers. The grid search explored various configurations, ranging from 1 to 5 hidden layers, different activation functions (ReLU, SELU, TanH), different number of nodes (ranging from 32 to 512), and various ratios for dropout layers (varying from 0.1 to 0.5). The optimal configuration was determined based on overall accuracy and average F1 score on the test set.

Table 13. The parameter values employed for training the ANN models using the training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020).

Parameter	The Bridge Data of 2020			The Five-Year Historical Bridge Data
	Nodes	Dropout Rate	Activation Function	Nodes	Dropout Rate	Activation Function
Input layer	250	-	-	250	-	-
First hidden layer	128	0.1	ReLU	128	0.1	ReLU
Second hidden layer	64	0.1	ReLU	64	0.1	ReLU
Third hidden layer	-	-	-	32	0.1	ReLU
Output layer	10	-	Softmax	10	-	Softmax

presents the parameter values employed for training the ANN models using the training sets of the bridge data of 2020 and the five-year historical bridge data (2016–2020).

The ANN models, consisting of multiple hidden layers, with input layer consisting of 250 nodes, and output layer consisting of 10 nodes, were developed. The models used ReLU activation functions in the hidden layers, Softmax in the output layer, and dropout layers with predefined ratios to reduce overfitting. The models were trained using the Adam optimization algorithm with categorical_crossentropy loss and 100 epochs. It took approximately 5 and 225 min to train the ANN models using the bridge data of 2020 and the five-year historical bridge data (2016–2020), respectively. Subsequently, the test sets were employed to evaluate the performance of the developed ANN classifiers.

Table 14. The confusion matrix of the ANN classifier on the test set of the bridge data of 2020.

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		67	3	2	13	11	11	25	5	5	0	47.2	53.0
1		9	2	7	10	35	4	4	2	3	2	2.6	4.3
2		5	1	31	73	72	2	2	1	0	2	16.4	24.3
3		13	4	5	60	267	9	7	1	4	1	16.2	16.4
4		10	0	2	34	380	16	2	6	1	2	83.9	29.0
5		1	2	8	79	1020	3360	2186	802	165	8	44.0	37.1
6		3	4	5	54	216	4021	7825	3901	308	22	47.8	42.7
7		3	0	3	27	100	3017	10,049	27,610	5550	115	59.4	68.5
8		0	0	3	7	65	52	197	1749	4035	767	58.7	47.3
9		0	0	0	2	0	1	36	85	120	1035	80.9	64.0
Sum		111	16	66	359	2166	10,493	20,333	34,162	10,191	1954
Recall		60.4	12.5	47.0	16.7	17.5	32.0	38.5	80.8	39.6	53.0
										Overall accuracy			55.6%
										Average F1 score			38.7%

presents the confusion matrix of the ANN classifier on the test set of the bridge data of 2020. As indicated in Table 14, the ANN classifier achieved an overall accuracy of 55.6% and an average F1 score of 38.7%, indicating a noteworthy difference of 16.9% between the two metrics on the test set. Additionally, Table 14 highlights that the ANN model exhibits lower recall when classifying bridge decks with condition ratings of 3 and 4 in comparison to classification of bridge decks with higher condition ratings. The tendency of the ANN model to classify bridge decks with condition ratings of 3 and 4 as higher condition ratings, such as 5 and 6, might be attributed to the limited number of bridge decks with 3 and 4 condition ratings compared to those with higher condition ratings.

Table 15. The confusion matrix of the ANN classifier on the test set of the five-year historical bridge data (2016–2020).

	Manual Inspection	0	1	2	3	4	5	6	7	8	9	Precision	F1 Score
Prediction
0		290	0	12	5	10	55	21	5	0	0	72.9	69.3
1		0	39	2	0	0	2	2	2	3	2	75.0	75.7
2		7	1	250	5	2	25	12	1	0	1	82.2	80.1
3		8	0	7	1350	65	87	35	18	1	7	85.6	81.1
4		10	4	11	207	7010	643	152	126	15	2	85.7	79.6
5		75	1	21	124	1102	31,223	6136	3656	254	54	73.2	75.4
6		36	4	12	43	989	6950	61,921	15,257	508	99	72.2	75.4
7		7	2	5	14	214	1021	9865	103,725	5950	425	85.6	82.8
8		5	0	0	3	38	135	222	5978	36,058	1385	82.3	82.9
9		1	0	0	0	1	2	52	511	367	6603	87.6	81.9
Sum		439	51	320	1751	9431	40,143	78,418	129,279	43,156	8578
Recall		66.1	76.5	78.1	77.1	74.3	77.8	79.0	80.2	83.6	77.0
										Overall accuracy			79.7%
										Average F1 score			78.4%

on the other hand, exhibits the confusion matrix of the ANN classifier on the test set of the five-year historical bridge data (2016–2020). According to Table 15, the ANN classifier achieved an overall accuracy of 79.7% and an average F1 score of 78.4%, indicating a lower difference of 1.3% between the two metrics on the test set. The notably improved performance of the ANN model, which was trained using the historical bridge data, can be attributed to utilization of more extensive bridge data, enabling it to capture the underlying pattern effectively. Additionally, the reduced disparity between the overall accuracy and the average F1 score of the ANN model, trained using the historical bridge data, suggests that the second model exhibits less performance variation across the ten imbalanced condition ratings and hence is more consistent in its performance.

6. Model Selection and Discussion

Given that the three models were trained using identical training sets and were evaluated using the same test sets, it seems reasonable to assess their effectiveness for prediction purposes by examining training time and prediction performance.

Table 16. The training time and prediction performance of the three models that were trained and evaluated using the bridge data of 2020 and the five-year historical bridge data (2016–2020).

	ML Algorithm	Time (min)	Overall Accuracy	Average F1 Score
The bridge data of 2020	Random forest	4	58.1%	39.7%
	XGBoost	4	55.4%	39.2%
	ANN	5	55.6%	38.7%
The five-year historical bridge data (2016–2020)	Random Forest	73	83.4%	79.7%
	XGBoost	894	79.4%	77.5%
	ANN	225	79.7%	78.4%

lists the training time and prediction performance of the three models that were trained and evaluated using the bridge data of 2020 and the five-year historical bridge data (2016–2020). According to Table 16, when the models were trained using the 319,404 bridge decks in the bridge data of 2020, the Random Forest model achieved 58.1% overall accuracy and 39.7% average F1 score in just 4 min. The XGBoost model was also trained in 4 min and obtained 55.4% overall accuracy and 39.2% average F1 score. The ANN model was trained in 5 min and obtained 55.6% overall accuracy and 38.7% average F1 score.

According to Table 16, when the 1,246,261 bridge decks in the five-year historical bridge data (2016–2020) were used to train models, the Random Forest model was trained in 73 min and achieved 83.4% overall accuracy and 79.7% average F1 score. While the XGBoost model was trained in 894 min and obtained 79.4% overall accuracy and 77.5% average F1 score. The ANN model achieved 79.7% overall accuracy and 78.4% average F1 score after being developed in 225 min.

These findings indicate that the inclusion of five years of historical bridge data (2016–2020) significantly enhances the predictive capabilities of the models compared to relying solely on the bridge data of 2020. This underscores that the historical bridge data offers adequate data for the algorithms to learn from, leading to the accurate classification of bridge decks into ten distinct condition ratings. To elaborate, a single year of bridge data includes one record for each bridge deck in the United States, constituting only one feature vector (a numerical representation of a record) within the feature space (a multi-dimensional space representing feature vectors). Conversely, multi-year bridge data involves multiple records for each bridge deck in the United States, contributing to numerous feature vectors within the feature space. Given that the characteristics of a bridge deck may not undergo significant changes within a few years, and its climate region remains constant, the incorporation of data spanning multiple years generates denser feature vectors within the feature space. This denser representation allows the ML models to better discern the underlying patterns within the bridge data, thereby enabling them to draw more accurate decision boundaries to distinguish the ten classes representing ten different deck condition ratings. As a result, this substantial increase in data significantly enhances the models’ performance compared to learning from just one year of bridge data.

Therefore, using historical bridge data, all the three models demonstrate proficiency in predicting the condition rating of the nation’s bridge decks. Notably, the Random Forest model, as can be seen in Table 9, effectively classifies bridge decks with condition ratings of 3 and 4, achieving average F1 scores of 77.1% and 76.2%, respectively. Similarly, the XGBoost model, as illustrated in Table 12, accurately categorizes bridge decks with condition ratings of 3 and 4, achieving average F1 scores of 76.6% and 74.2%, respectively. Moreover, the ANN model, as can be seen in Table 15, effectively classifies bridge decks with condition ratings of 3 and 4, achieving average F1 scores of 81.1% and 79.6%, respectively. These observations underscore the three models’ ability to avoid misclassifying bridge decks with low condition ratings as having high condition ratings, thereby mitigating uncertainty in maintenance decision-making.

Therefore, the Random Forest, XGBoost, and ANN models, trained with historical bridge data, serve as valuable tools to estimate the future condition rating of a bridge deck. With knowledge of the characteristics and climate region of a particular bridge deck in a specific year, infrastructure managers can leverage these models to effectively allocate maintenance resources, particularly focusing on bridge decks anticipated to have a significant need, thereby saving both costs and time in the overall maintenance strategy. Although these models, trained using historical bridge data, appear to be efficient models for the purpose of condition rating prediction of the nation’s bridge decks, there are numerous bridge decks that were misclassified. Sources of errors that cause misclassified bridge decks can be addressed in three categories.

The first source of error can be attributed to the inherent variability in human perception during the assignment of condition rating to a bridge deck. Essentially, an inspector tends to demonstrate a margin of ±1 error when determining a condition rating. Consequently, incorporating bridge decks, whose predicted ratings fall within this ±1 margin of error as correct predicted condition ratings, significantly enhances the overall accuracy of classification models. As an example, this inclusion results in an increase in overall accuracies from 83.4% to 97.3% for the Random Forest model, from 79.4% to 96.6% for the XGBoost model, and from 79.7% to 97.1% for the ANN model, when the five-year historical bridge data (2016–2020) are employed as the dataset. This suggests that considering the errors introduced by human assessment when evaluating the performance of classification models results in models achieving overall accuracies exceeding 90%. Consequently, neglecting the human-induced errors in assessing classification model performance leads to differences between models’ performances.

The second source of error can be attributed to the data quality. In particular, the initial values of the predictor variables corresponding to the misclassified bridge decks, with a margin of ±1 the correct predictions, should be investigated. If possible, erroneous values should be corrected, otherwise the corresponding bridge deck should be removed from the dataset. Subsequently, the models should be retrained using the refined and high-quality dataset. The third source of error can be linked to the lack of incorporating other predictor variables introduced by the big bridge data analytics framework proposed by Liu and El-Gohary [23,98], such as hazard data, National Bridge Element (NBE) data, textual inspection, and maintenance reports.

To investigate whether Random Forest, XGBoost, and ANN models exhibit the same performance when a subset of the bridge data is utilized as the dataset, it is necessary to draw a sample that represents the characteristics of the entire population of over 460,000 of the nation’s bridge decks. This can be accomplished by employing stratified sampling and randomly selecting bridge decks from the population. Subsequently, the models should be trained and assessed using the collected sample. Then, a comparison should be made between the performance of the models on the sample and their performance on the entire population. This comparison serves to determine whether these models demonstrate consistent performance when a sample of bridge decks is utilized as the dataset.

7. Conclusions and Future Work

The objective of this study was to evaluate the effectiveness of the Random Forest, XGBoost, and ANN algorithms in accurately predicting the condition rating of bridge decks in the United States. For doing so, the study employed an approach to develop bridge data in the United States by utilizing remote sensing and GIS technologies to collect NBI, traffic, and climate regions. This approach allowed for the creation of bridge data in a single year, as well as historical bridge data spanning several years. To conduct experimental investigations, datasets for the year 2020 and a historical dataset covering a five-year period from 2016 to 2020 were created and used to develop three models. This study created datasets for the year 2020 and a historical dataset covering a five-year period from 2016 to 2020 by incorporating NBI, traffic, and climate regions to develop three models: Random Forest, XGBoost, and ANN.

Subsequently, 20 variables, identified through literature review and engineering judgments, were employed as predictor variables and 10 different deck condition ratings were introduced as the response variable. The preprocessed bridge datasets were then divided into an 80% training set and a 20% test set to train and evaluate models. The findings demonstrate that using historical bridge data significantly enhances the predictive performance of the models compared to using data from a single year. This implies that the historical bridge data that incorporates multi-year bridge data provides adequate information for the models to learn and hence improves their predictive performance. The experimental results indicate that, when trained using historical bridge data, the Random Forest, XGBoost, and ANN models exhibited overall accuracies of 83.4%, 79.4%, and 79.7%, respectively. Additionally, they achieved average F1 scores of 79.7%, 77.5%, and 78.4%, respectively. This implies that the Random Forest, XGBoost, and ANN models, trained using the five years of bridge data, could effectively predict the condition ratings of bridge decks across the United States.

Notably, the permutation-based variable importance suggests that the age of a deck or the number of years since the last major reconstruction was the most important predictor variable contributing to bridge deck deterioration. In addition, climate regions were identified as the second most critical variable influencing the development of the model. This suggests that the deterioration of bridge decks depends on their locations. Furthermore, traffic was recognized as another critical factor accelerating deterioration of a bridge deck. Additionally, various bridge deck characteristics, like deck type, were also recognized for their influence on the predictive performance of deterioration models. It is evident that the reconstruction of a bridge deck can delay its deterioration, aligning with the recognition of “Reconstructed” as an important factor. Therefore, to develop a bridge deck deterioration model, it seems essential to incorporate NBI, traffic, and climate regions.

In conclusion, this study underscores the efficacy of the Random Forest, XGBoost, and ANN algorithms, trained with historical bridge data that includes NBI, traffic, and climate data. The developed models serve as promising tools for accurately predicting the condition rating of bridge decks in the United States. The predicted condition ratings by these models can be utilized to efficiently monitor the deterioration of the nation’s bridge decks, particularly those located in urban areas experiencing high traffic volumes. By plugging in the age of a particular bridge deck in each year, along with its climate region, traffic details, and other relevant characteristics into the trained model, one can predict the future condition ratings of that bridge deck. These estimated condition ratings over time enable decision makers to proactively plan maintenance, rehabilitation, or reconstruction efforts, ensuring timely preservation of bridge decks that contribute to the safety of public commutes.

Although the Random Forest, XGBoost, and ANN models, trained using the five-year historical bridge data (2016–2020), were recognized as the accurate models for classifying the nation’s bridge decks, further research seems required. The research should incorporate longer historical bridge data spanning multiple years, which has been available since 1992, and evaluate its impact on the performance of the models. Additionally, the development of other ML models using historical bridge data and evaluation of their performance are recommended. Future work should continue to explore the potential of leveraging ML and AI algorithms to enhance the health monitoring of infrastructure.