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United States Department of Transportation United States Department of Transportation

Bridge Deck Condition Rating Forecast—Machine Learning Models

Heng Liu, Ph.D.; Jean A. Nehme, Ph.D., P.E.; and Ping Lu, Ph.D., P.E.

1. Background Information

Machine learning models are developed to forecast bridge conditions using deep learning algorithms. Current model development focuses on bridge decks. In the future, models will be expanded to cover other types of bridge components (e.g., superstructures and substructures). These forecasting models complement the Federal Highway Administration (FHWA) InfoBridge™ (FHWA, 2019a) data visualization tools in depicting future performance trends of highway bridge components.

Historical bridge inspection data from the FHWA National Bridge Inventory (NBI) (FHWA, 1995; FHWA, 2019b) are used in conjunction with climate data to develop machine learning models. The research methodology employed is a data-driven modeling approach using a deep learning algorithm (Liu and Zhang, 2020). This research effort has expanded the training datasets from a single State to the entire Nation.

Deep learning is a machine-learning technique that allows computational models comprised of multiple processing layers to learn “data representations” of a high-dimensional and complex dataset. In the context of condition forecasting, “data representations” is equivalent to the statistical interrelationships or data patterns that describe how various factors influence the bridge-component deterioration process. The current modeling effort considers 28 factors, such as traffic volumes, construction materials, and climate factors. For a complete list of the factors, see Table 1 at the end of this document. The specific deep-learning algorithm employed for data analysis is the convolutional neural network (CNN); Liu and Zhang (2020) introduce the CNN algorithm. Deep Learning in Nature (LeCun et al., 2015) and Deep Learning by Goodfellow et al. (2016) provide additional information about deep learning.  

The following briefly describes the method overview, the description of the data source, and the technical procedure that was used during the implementation. A full-length technical article is under preparation to be published in a peer-reviewed journal (Liu et al., 2020).

2. Method Overview

The data pattern underlying the historical bridge inspection records contains useful information in describing the deterioration trends of highway bridge decks. Therefore, developing an appropriate algorithm that can identify data patterns buried in history can solve the condition-forecasting problem. The data-mining algorithm emphasizes the changing trends of bridge-deck condition ratings, along with other factors that may influence the deck-deterioration process. The current research applies CNN for corresponding data-mining and pattern recognition.

Mathematically, the CNN model computes the conditional probabilities of future condition ratings given the values of current bridge information, as described in Equation (1),

Equation 1. Description of the computation output from trained deep learning models. The term on the left side is a symbolic representation of evaluating the deep learning model with given input. The term on the right side is a bracket contains a vector of probabilities. The probabilities are conditional based on given input. The output represents the computed conditional probabilities of condition ratings. Condition ratings are one digit number describing the overall physical condition of a bridge component, such as deck, superstructure, and substructure.


where X and Y are the input and output of the CNN model, respectively; CR  denotes the condition rating (see definitions in the coding guide by FHWA, 1995). Condition-rating values are assumed to not be lower than 3. In the NBI, condition-rating data of 3 or below are sparse and would not result in a reliable training dataset.

The probability function incorporates all the bridge factors listed in Table 1. The function is evaluated for every future inspection. These are usually performed biennially.

Due to the probabilistic nature of CNN model forecasting, deterioration modeling for long-term forecasting, based on CNN, will be subjected to significant uncertainty that may propagate forward in time. The deterioration model incorporates stochastic process modeling to account for uncertainties. The modeling employs a standard Markov chain (Frangopol et al, 2004; Morcous et al., 2003) procedure that assumes the deterioration process complies with the Markov property.

3. Data Source

The research uses NBI and climatic data from InfoBridge. The climatic data refer to the annual numbers (unit in days) of freeze-thaw cycles and snowfalls. The NASA (National Aeronautics and Space Administration) MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications, Version 2) program provides the original source of climate data.

4. Procedure

The step-by-step process of the modeling approach is briefly described as follows:

Step 1, Data Preparation.

This step aims to restructure original bridge inspection records into the data format that is recognizable to the employed deep learning algorithm. In the current model development, the model input is a data matrix that consists of current values of considered factors. Each input data matrix has an associated data label (i.e., output) to supervise the model training. The data labels are the actual condition ratings that were given by bridge inspectors in the successive inspections to the time of records settled in the data matrices.

Step 2, Deep Learning Model Development.

This step trains and validates the employed deep learning model. The prepared dataset from Step 1 is initially randomly split into three subsets for model training, validation, and testing, respectively. The validation and testing subsets are independent of training and both are used to validate the performance of the trained CNN model. The CNN model is further optimized with Bayesian optimization using the validation data subset (Mockus et al., 1978). The testing data is employed for final model evaluation.

Step 3, Condition Rating Forecasting.

This step computes and stores the forecasting results in a data table format. The data table contains seven columns for the seven possible condition ratings (from 9 to 3, see definitions in the coding guide by FHWA, 1995) and multiple numbers of rows representing the forecasting time in terms of inspection years. The current effort limits forecasting years to 2070. The data entries in the table are probabilities of condition ratings in each inspection year. The computation repeats for each bridge.

Step 4, InfoBridge Implementation.

This step converts the forecasting results from the data table to the curve plots that are accessible in LTBP InfoBridge. The plots contain a pair of upper/lower bounding curves as defined in Equation (2),

Equation 2. Description of rules for drawing a pair of upper/lower bounding curves. The equation has two sub-equations. The first one applies to the lower bound and the second to the upper. The first sub-equation limits the total amount of probabilities lower than the lower bound to a user-specified value alpha. The second sub-equation limits the total amount of probabilities higher than the upper bound to the same alpha. Alpha is set to 25 percent.


where α is a user-specified value that defines the amount of uncertainty below the lower bound or above the upper bound. Currently, the value of α is selected to be 25 percent.

5. References

  1. FHWA. (2019a). Federal Highway Administration, InfoBridge, Washington, DC, obtained from:, last accessed March 18, 2020.
  2. FHWA. (1995). Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges, , Washington, DC, obtained from:, last accessed March 18, 2020.
  3. FHWA. (2019b). Datasets between 1983 and 2018, National Bridge Inventory, Washington, DC, obtained from:, last accessed March 18, 2020.
  4. Frangopol, D. M., Kallen, M. J., and Noortwijk, J. M. V. (2004). Probabilistic Models for Life‐Cycle Performance of Deteriorating Structures: Review and Future Directions, Progress in Structural Engineering and Materials, 6(4), 197‒212.
  5. Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press.
  6. LeCun, Y., Bengio, Y., and Hinton, G. (2015). Deep Learning, , (7553), 436‒444.
  7. Liu, H., and Zhang, Y. (2020). Bridge Condition Rating Data Modeling Using Deep Learning Algorithm, Structure and Infrastructure Engineering,
  8. Liu, H., Nehme, J., Zhang, Y., and Lu, P. (2020). Life-Cycle Condition Rating Forecasting of Highway Bridge Components Using Deep Learning Algorithm (in preparation).
  9. Mockus, J., Tiesis, V., and Zilinskas, A. (1978). The Application of Bayesian Methods for Seeking the Extremum, , (2), 117‒129.
  10. Morcous, G., Lounis, Z., and Mirza, M. S. (2003). Identification of Environmental Categories for Markovian Deterioration Models of Bridge Decks, Journal of Bridge Engineering, 8(6), 353‒361.
  11. Snoek, J., Larochelle, H., and Adams, R. P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms, , pp. 2951‒2959.


Table 1. Description of Considered Factors for Deterioration Modeling of Bridge Decks.


 Influencing Factors

Data Source1



Item 16



Item 17



Item 20


Maintenance Responsibility

Item 21


Functional Class of Inventory Route

Item 26



Items 27, 90, 106


Lanes on Structure

Item 28A


Average Daily Traffic (ADT)

Item 29


Average Daily Truck Traffic (ADTT)

Item 109


Inspection Interval (Months)3

Item 90


Designated Inspection Frequency

Item 91


National Highway System

Item 104


Reconstruction Status

Item 106


Maximum Deck Condition Improvement4

Item 58



Item 34


Kind of Material and/or Design

Item 43A


Type of Design and/or Construction

Item 43B


Number of Spans in Main Unit

Item 45


Length of Maximum Span

Item 48


Structure Length

Item 49


Bridge Roadway Width Curb-To-Curb

Item 51


Deck Structure Type

Item 107


Type of Wearing Surface

Item 108A


Type of Membrane

Item 108B


Deck Protection

Item 108C


Annual Number of Freeze-Thaw Cycles



Annual Number of Snowfalls



Current Deck-Condition Rating

Item 58

1. Items listed in this column refer to the coding item in the NBI.

2. Age is calculated based on the absolute variation of inspection year–year built or year reconstructed–year built, whichever is lower. NBI items 27, 90, and 106 record the year built, inspection date, and year reconstructed, respectively.

3. Inspection interval is calculated based on the time variation between the date of the current and the forecasted inspections.

4. Maximum deck-condition improvement is the maximum increment of deck-condition ratings between two adjacent inspection records until the current inspection year.

5. The NASA MERRA-2 provides the corresponding data source.



Last updated: Wednesday, April 22, 2020