Modeling the Quantitative Assessment of the Condition of Bridge Components Made of Reinforced Concrete Using ANN

Abstract

Bridges in Ukraine are one of the most important components of the infrastructure, requiring attention from government agencies and constant funding. The object of the study was the methodology for quantifying the condition of bridge components. The Artificial Neural Network-based (ANN) tool was developed to quantify the technical condition of bridge components. The literature analysis showed that in most cases the datasets were obtained during the inspection of bridges to solve the problems of assessing the current technical condition. The lack of such a database prompted the creation of a dataset on the basis of the Classification Tables of the Operating Conditions of the Bridge Components (CT). Based on CTs, five datasets were formed to assess the condition of the bridge components: bridge span, bridge deck, pier caps beam, piers and abutments, approaches. The next step of this study was creating, training, validating and testing ANN models. The network with ADAM loss function and softmax activation showed the best results. The optimal values of MAPE and R² were achieved at the 100th epoch with 64 neurons in the hidden layer and were equal to 0.1% and 0.99998, respectively. The practical application of the ANN models was carried out on the most common type of bridge in Ukraine, namely, a road beam bridge of small length, made of precast concrete. The novelty of this study consists of the development of a tool based on the use of ANN model, and the proposal to modify the methodology for quantifying the condition of bridge components. This will allow minimizing the uncertainties associated with the subjective judgments of experts, as well as increasing the accuracy of the assessment.

1. Introduction

In recent years, the traffic intensity and weight of vehicles have increased on the roads of Ukraine, which has a more significant impact on all components of the road infrastructure. Bridges are one of the most important elements of the infrastructure, requiring attention from government agencies and constant funding to maintain their proper operational condition. A large number of bridges were built according to technical standards that do not meet modern traffic conditions in terms of carrying capacity and dimensions of the roadway.

According to the current norms of Ukraine, the service life of bridges, depending on the type of construction, is 70–100 years. The average age of bridges on public roads is 53 years, a number of the bridges are over 80 years old, about 12%, and the residual life of the structures is close to exhaustion. There is increasing concern that road bridges are deteriorating as a result of design and construction errors, initial defects in materials and construction, environmental erosion, increased loads, and natural and man-made hazards [1,2]. In addition, due to the dynamically changing environment and non-linear loading factors, it is quite difficult to assess the structural conditions and establish appropriate maintenance schemes even for a single bridge [3]. An important task is to obtain reliable information about the actual condition of bridges, conduct a rating of bridges, and identify structures that require urgent repair work.

As of 2019, 28,397 bridges with a total length of 818.2 km are in operation on the roads of Ukraine. The largest number are road bridges—19,304 (67.98%), in second place are railway bridges—7647 (26.93%) followed by pedestrian bridges—1446 (5.09%) [4]. Road bridges are divided into bridges located on public roads—79% and on the roads of settlements (so-called communal bridges)—21%. By length, bridges can be divided into small—49.7%, medium—44.2% and large—6.1%. Reinforced concrete bridges are the most common in Ukraine—91.5%, of which about 90% are beam bridges. According to the type of span construction, slab spans are the most common in Ukraine—52% and ribbed ones—43%. The bulk of the bridges are built from precast concrete—65%, monolithic bridges—30%, and prefabricated monolithic—5%. Thus, it can be stated that the most common in Ukraine are road beam bridges of small or medium length, made of precast concrete. As of 2019, about 35% of all bridges on public roads were inspected, of which 13% needed immediate overhaul and reconstruction. There is no reliable information on the number of surveyed communal bridges and data on their technical condition [5].

In our opinion, one of the global and urgent problems of the bridge industry in Ukraine is the lack of a unified management system that would combine the knowledge base regarding the condition and characteristics of all existing bridges. The role of bridge control systems is to monitor, diagnose and predict the technical condition of structures and plan the optimal maintenance of the bridges [6].

Currently, the software complex “Analytical Expert System for Bridge Management” (AESBM) is operating in Ukraine, which functions as a database and contains survey data on the condition of bridges on public roads. The AESBM database contains about 150 technical parameters for each bridge and stores detailed information about individual components of bridges, such as superstructures, piers and foundations. The passport of each bridge contains photographs of the general view, roadway, main components and defects. At the same time, a big problem with the database is the absence of the technical condition of bridges located on the roads of settlements (communal bridges).

Creation, filling and maintenance of the national bridge management system will allow us to:

• carry out certification of bridges, which should contain data on the technical condition of structures, their bearing capacity, information on repairs and defects found;
• carry out regular supervision and assessment of the technical condition of the bridge;
• forecast the technical condition of the bridge and develop recommendations that help extend the life of the structure.

The initial step preceding these stages is the inspection of bridges which requires huge efforts, a great amount of time, and huge financial expenditures. At present, a large amount of information about the technical condition of the bridge components is stored in paper form, which complicates the transformation into data and gaining knowledge necessary for decision-making. In this regard, stakeholders are directing efforts towards the development and implementation of modern digital tools that can be used to quickly and easily quantify the technical condition of bridge components. The data obtained on the basis of a quantitative assessment can be used to make decisions during the operation phase of bridges. Road infrastructure managers are trying to intensify work on the development of methods that will allow to quickly and efficiently assess the condition of a bridge and, depending on its technical condition, plan repair works.

Recently, different Machine Learning (ML) tools in general and neural network in particular have been actively used as a decision-making tool in various areas of bridge management such as condition quantification, damage detection and condition prediction [7,8].

Moradi et al. defined the study purpose to develop a robust and time-saving method based on ML to predict the compressive strength of concrete containing binary SCM [9]. The ML-based model showed high accuracy and was able to predict the compressive strength of concrete containing any arbitrary SCMs. Fan et al. [10] analysed the latest advances in machine learning and its applications in the reinforced concrete bridge control system. The study covers a range of machine learning techniques used in structural design, construction quality management and bridge inspection. Due to the non-linear nature of the relationship between bridge features and wear behaviour, artificial neural networks (ANN) have proven to be the most suitable tool for discovering and modelling such relationships.

An interesting area of research is modelling the life cycle of recycled materials in bridge structures. Zadehmohamad et al. investigated the benefits of adding tire rubber as an inclusion to backfill behind integral bridge abutments [11]. The results show that adding tire rubber to the backfill would be beneficial for both pressure and settlement behind the abutment. Amakye et al. investigated the possibility of using mixtures of brick dust, ground granulated blast furnace slag, recycled plastic and recycled glass for road pavement [12].

Althaqafi and Chou developed three ANN models to improve the prediction accuracy of the deterioration of bridge decks, superstructures, and substructures. A large dataset of historical bridge condition assessment data was applied to train and test the proposed ANN models. The accuracy of these models was 90%, 90%, and 89% on the testing set [13]. Hassan et al. declared the research aim to develop a generalized condition assessment approach to monitor and evaluate existing facility elements [14]. The methodology is reinforced with an ANN model to predict the element deterioration. The ANN model showed reliable results with R² values of 0.99, 0.98, and 0.99 for training, validation and testing sets, respectively.

Thus, the purpose of this article is to create a tool for quantitative assessment of the technical condition of the bridge components using ANN. The object of the study was the methodology for quantifying the condition of bridge components. The practical application of the technique was carried out on the most common type of bridge in Ukraine, namely, a road beam bridge of small/medium length, made of precast concrete. Since short and medium span beam bridges are one of the most common types of bridges worldwide, interest in this study is expected not only in Ukraine, but also in other countries [15].

The article has the following structure: Section 2. analyses the current methodology for inspection and assessment of bridges, and the experience of using machine learning methods in bridge assessment was explored; Section 3. presents a methodology for assessing the technical condition of bridge components using ANN; Section 4. presents the results of using ANN to assess the technical condition of bridge components and describes the application of the trained ANN model on a real road bridge. Section 5. and Section 6. present the discussion and conclusions of the study.

The novelty of this study consists of the development of a tool based on the use of the ANN model and the proposal to modify the methodology for quantifying the condition of bridge components. This will allow minimizing the uncertainties and inaccuracies associated with the subjective judgments of experts, and increasing the accuracy of the assessment.

2. Literature Review

2.1. The Assessment of the Bridge Condition

Bridge management refers to standard decision-making tasks, which are based on the choice of available alternative solutions. As a rule, decision-making is based on an assessment of the technical condition of the bridge components, which in turn is based on inspection data. Estimates are mostly subjective and vary in accuracy, depend on the experience and knowledge of individuals, and are often determined by linguistic and quality values. Methods for assessing the technical condition associated with inspections are often simplified. Due to high cost, more advanced and accurate methods (related to material testing) are applied to single events.

The inspection and assessment of the condition of the bridge is critical to the successful operation of the bridge management system. Since 1972, the National Bridge Inventory (NBI) has been the main data source for bridge management in The United States [16]. According to the National Bridge Inspection Standards, road bridges must be inspected every two years, and condition assessments of bridge components are recorded in the NBI database. The condition assessment of bridges in the US is mainly performed by visual inspection [17]. The contents of a road bridge inspection include visual inspection, interior inspection, mechanical performance evaluation, and geometric parameters inspection. The assessment of structural components of the bridge is based on subjective assessments of the inspectors and is a single-digit number characterizing the general condition of the component being assessed on a scale from 0 to 9 [18,19].

Therefore, monitoring is an important component of the road bridge operating system. To make effective management decisions on the strategy of bridge operation, it is necessary to have effective and most probable models for assessing and predicting the condition of bridges. The frequency of inspection of road bridges in Ukraine is regulated by “DBN V.2.3-6:2009. Bridges and pipes. Examination and testing” [20] and depends on their age. Bridges aged from 1 to 20 years are examined every 5 years, those from 21 to 40 years are examined every 4 years, those from 41 to 60 years are examined every 3 years, and bridges over 60 years old are examined every 2 years.

The monitoring of a bridge can be conditionally divided into two processes: technical inspection and quantitative assessment of the technical condition. Technical inspection consists of carrying out a visual assessment of the condition of the object (components of the object) with fixation of the identified design and standard deviations. The output data of the technical inspection are qualitative and quantitative indicators of the operational properties of the facility, which allow assessing the technical condition of the structure, determining the residual life of the structure, and planning the operation of the bridge.

Assessment of technical conditions of road bridges in Ukraine is carried out on the basis of “DSTU-N B V.2.3-23:2009. Guidelines for assessing and predicting the technical condition of road bridges” [21]. The technical condition is a set of qualitative and quantitative indicators characterizing the operational suitability of a structure. The bridge is considered as a system of seven groups of structural components: superstructure, piers, foundations, scaffold, roadway, approaches, regulatory structures.

After the inspection of the bridge components, the detected defects, damages and other signs of degradation are compared with the data contained in the “Classification table of the operational conditions of the bridge components”. The standard contains 20 classification tables relating to all the most important components of the bridge. According to the results of the comparison, each component of the bridge is assigned a technical condition from 1 to 5 (“Condition 1”—serviceable, “Condition 2”—partially serviceable, “Condition 3”—acceptably serviceable, “Condition 4”—almost unserviceable, “Condition 5”—unserviceable.

After assessing the operational conditions of the group components, the technical condition of a bridge as a whole is assessed:

$$E=\frac{80\times (5-{{\displaystyle \sum }}_{i=1}^7{a}_i{D}_i)}{4}+20$$

(1)

where $a_i$—the coefficient of influence of the condition of the i-th component on the general condition of the structure (approved in DSTU-N V.2.3-23), $D_i—$ assessment of the operational condition of a group of parts.

Depending on the value of the assessment of the technical condition (E), the bridge is assigned the appropriate condition and the need to perform operational measures is determined. “Condition 1” corresponds to the number of points 100-95, “Condition 2”—94-80, “Condition 3”—79-60, “Condition 4”—59-40, “Condition 5”—39-20.

2.2. Using ANN Models to Assess Bridge Condition

An artificial neural network is an adaptive system that uses a collection of neurons to process data and establish a relationship between input and output data. Interest in using ANN is associated with the possibility of simultaneous processing of information, efficient approximation of nonlinear dependencies, network training and subsequent use of the trained network. ANN is suitable for solving big data problems and can directly extract multivariate features and non-linear relationships between data, and minimize uncertainties, imprecision and subjective judgment. The greatest difficulty in the application of ANN is associated with the need to conduct a network training process that requires a large amount of input data.

The area of neural networks application was analysed in bridge control, namely: solving problems of quantitative assessment and prediction of the bridge technical condition [18,22]. Nguyen and Dinh [23] proposed using an ANN model to predict the condition of bridges based on an assessment of the condition of the bridge’s structural components. Data from 2572 bridges were extracted from the NBI database and used to train, validate and evaluate the ANN model. The input layer of the model consisted of eight parameters: the current age of a bridge, average daily traffic, structure, load, main structure design, superstructure design, number of main spans, percentage of daily truck use, and growth rate. Yusuf and Hamid [24] used ANN and multiple regression analysis (MRA) to model a bridge condition score based on a limited number of datasets. Based on the Root Mean Squared Error (RMSE) and R² values, the authors claim that ANN models perform better than MRA. Liu and Zhang [18] presented a deep learning-based bridge condition estimation modelling approach using selected data from the NBI database. The authors have developed an approach that makes it possible to predict the future conditions of road bridge components based on historical inspection data. Huang [25] used statistical analysis to identify significant factors influencing bridge deck wear. After identifying the eleven most important factors, the author proposed an ANN model for predicting the wear. The developed model accurately predicted the condition of the bridge deck and can provide the necessary information for maintenance planning and decision making. Li and Burgueno [26] tested several bridge abutment wall damage prediction models using the NBI database. An ensemble of neural networks with a new data organization scheme turned out to be the most effective model (forecast accuracy of 86%). The results of the study showed that damage prediction models can be useful for the effective management of the restoration of existing bridges, as well as for the design of new ones. Xia et al. [27] proposed a method based on the use of artificial intelligence to assess the condition of bridges and optimize their maintenance. The method includes data integration, condition assessment and maintenance optimization. The neural network models the degradation of bridges and quantifies the impact of the maintenance scheme on the future condition.

The literature analysis shows that ANNs are actively used in various areas of bridge management. The use of artificial neural networks allows solving the tasks of quantitative assessment of the state of bridge elements, identification of factors that have the greatest impact on bridge wear, damage detection, and state forecasting. Currently, various types of neural networks are actively used for the analysis of visual images.

The authors in most cases used sets of historical data obtained during the inspection of bridges to solve the problems of assessing the current and predicting technical condition of the bridge. Unfortunately, as mentioned earlier, in Ukraine there is no database of historical data on the state of bridge components in electronic form. In this regard, the database was created artificially on the basis of the Classification Tables of the Operating Conditions of the Bridge Components. The process of creating and using data is described in more detail in Section 3.1.

3. Methods

3.1. The Creation of Datasets for Quantitative Assessment of the Technical Condition of Bridge Components

As noted earlier, one of the main problems of the bridge industry in Ukraine is the lack of a properly working bridge management system. There are also no digital data on inspections, assessment of the technical condition and rating of communal bridges.

The lack of historical data inspired the creation of a tool for quantitative assessment of the technical condition of bridge components based on the Classification Table of the Operational Conditions of Bridge Components (CT). CTs are 20 annexes to the DSTU, which compare the existing defects/violations with the level of technical condition of the bridge components. Since the road beam bridge of small/medium length, made of precast concrete, was chosen as the object of the study, the following classification tables were applied: “A.1. The operational condition of the bridge deck”, “A.2. The operational condition of span structures made of reinforced concrete”, “A.11. The operational condition of the pier caps beam”, “A.12. The operational condition of the piers and A.13. the operational conditions of the abutments” and “A.17. The operational condition of approaches”. Such a set of CTs allows us to determine the technical condition of important components of this type of bridge.

In fact, CTs are a set of rules for determining the condition of a bridge component, each of which can be written as:

$$if{x}_1=a\wedge x_2=b\wedge \dots x_n=m then y=\left[1;5\right]$$

where $y—$ total numerical assessment of the condition of the bridge component, which can have a value in the range from 1 to 5, $x_1\dots x_n$—the type of defects or inconsistencies, $a\dots m$—the numerical value of the defects or inconsistencies.

The next step was to create a dataset for training and testing the ANN model. The dataset was generated from CT “A.2. The operational condition of span structures made of reinforced concrete”

Table 1. Part of the dataset to assess the condition of the bridge span.

The Level of Aggressive Environment	The Width of a Single Crack, mm	The Width of a Shrinkage Crack, mm	The Level of a Concrete Chipping	The Level of a Rebar Exposure	The Level of a Rebar Leaching	The Level of a Reinforcement Corrosion	The Width of an Oblique Crack, mm	The Width of a Power Crack, mm	The Level of a Concrete Damage	The Level of a Concrete Leaching	The Level of a Structural Deformation	The Level of a Beam Support	The Value of pH	The Assessment of Condition
(1;5)	(0.0;0.5)	(0.0;0.5)	(0;5)	(0;5)	(0;5)	(0;5)	(0.0;0.3)	(0.0;0.3)	(0;2)	(0;2)	(0;1)	(0;1)	(7;11)	(1;5)
x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13	x14	y
1	0	0	0	0	0	0	0	0	0	0	0	0	11	1
…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..
1	0	0	1	0	0	0	0	0	0	0	0	0	11	1
2	0.1	0.1	2	1	0	0	0	0	0	0	0	0	10	2
…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..
2	0.2	0.2	2	1	1	0	0	0	0	0	0	0	10	2
3	0.21	0.21	3	2	2	1	0.1	0.1	0	0	0	0	9	3
…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..
3	0.3	0.3	3	3	3	2	0.1	0.1	0	0	0	0	9	3
4	0.31	0.31	3	3	3	2	0.1	0.1	1	1	0	0	8	4
…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..
4	0.4	0.4	4	4	4	3	0.2	0.2	1	1	0	0	8	4
5	0.41	0.41	4	4	4	4	0.2	0.2	2	2	0	0	7	5
…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..	…..
5	0.5	0.5	5	5	5	5	0.3	0.3	2	2	1	1	7	5

shows a part of the set of input variables (x₁… x₁₄) and the output value (y) assessment the condition of the bridge span.

The input variables are numerical values of defects obtained by “stepping” to increase their value. For example, the defect value x₂ “The width of a single crack” for “Condition 2” can be from 0.1 to 0.2 mm. A stepping increase in x₂ value from 0.1 to 0.2 with a step of 0.01 mm allows the formation of 10 additional records in the dataset. In case of the defects, the condition of which, according to CT, is assessed by linguistic variables, for example, “Presence of corrosion of reinforcement”, the verbal value was replaced by a numerical assessment of “The level of a reinforcement corrosion” with a scale from 0 to 5 (where 0—no defect; 5—the highest level defect is present).

The numerical scale of the level of defects is present in

Table 2. Parameters of ANN models.

	ANN 1				ANN 2				ANN 3
activator	Sigmoid				Sigmoid				ReLU
optimizer	ADAM				SGD				ADAM
hidden neurons	16	32	64	128	16	32	64	128	16	32	64	128
R2	0.99980	0.99990	0.99994	0.99939	0.99952	0.99858	0.99989	0.99979	0.99974	0.99989	0.99968	0.99022
MAPE, %	0.3	0.2	0.1	0.5	0.4	0.7	0.1	0.2	0.3	0.2	0.3	1.70
	ANN 4				ANN 5				ANN 6
activator	ReLU				softmax				softmax
optimizer	SGD				ADAM				SGD
hidden neurons	16	32	64	128	16	32	64	128	16	32	64	128
R2	0.99964	0.99993	0.99977	0.99987	0.99992	0.99961	0.99999	0.99997	0.99973	0.99898	0.99947	0.99875
MAPE, %	0.3	0.1	0.2	0.2	0.1	0.3	0.1	0.1	0.2	0.5	0.3	0.5

. This approach was used for all numerical and verbal indicators of CT “A.2. The operational condition of span structures made of reinforced concrete,” which made it possible to form a dataset of 475 records. Using a similar approach, four more datasets were formed to assess the condition of the bridge components: the bridge deck (14 input variables, 485 records); the pier caps beam (11 input variables, 365 entries); the piers and abutments (13 input variables, 415 records); the approaches (10 input variables, 335 records). Appendix A shows the input variables that were used for the four models. The next step of the study was the creation of five ANN models to assess the technical condition of bridge components.

3.2. The Creation of ANN Model

The ANN architecture usually consists of:

• input layer that receives signals and transmits them to the neurons of the hidden layer,
• one or more hidden layers that receive a set of input data and, after processing by an activation function, produce a result,
• the output layer that receives the output from the hidden layer and calculates the output value [28].

As a rule, the number of hidden layers and the number of neurons that ensure optimal network performance is determined by trial and error [29]. As an example, the procedure for creating the ANN model for assessing the condition of the bridge span will be presented. As a result of the experiments, the network architecture with one hidden layer was adopted as optimal. The number of neurons in the hidden layer was also determined experimentally, gradually increasing the number of neurons from 16 to 128. The input layer consists of 14 neurons and the output layer has 1 neuron (Figure 1).

Neural network models were checked with the activation functions: ReLU, softmax, and sigmoid. The sigmoid function can be used in ANN with many layers, but this can result in the activation of almost all neurons, which will reduce the performance of the neural network. The advantage of using the ReLU activation function is that fewer neurons are activated and network performance is increased. The softmax function transforms a vector of numbers into a vector of probabilities with the interval [0, 1]. This function converts a vector z of dimension K into a vector σ of the same dimension, where each coordinate σ_i of the resulting vector is represented by a number in the interval [0, 1].

The coordinates σ_i are calculated as follows:

$$\sigma {\left(z\right)}_i=\frac{e^{z_i}}{{{\displaystyle \sum }}_{k=1}^K{e}^{z_k}}.$$

(2)

The loss function is a measure of how well the prediction model forecasts the expected value. In the learning process, at each stage, the problem of minimizing the loss function and updating the weight network to improve accuracy is solved. The comparison between the target and actual values for a neuron is in the base of calculation of loss function. The mean square error (MSE) was used as a loss function [30]:

$$MSE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n{\left(Y_i^{\prime }-Y_i\right)}^2.$$

(3)

where $Y_i^{\prime }—$the output calculated by the model, $Y_i—$the target output.

An optimization algorithm is a technique used to slightly change parameters such as weights and biases so that the model performs correctly and quickly. Optimizers determine the optimal set of model parameters so that the model performs the best for a particular problem. The most common optimization technique used by most neural networks is the gradient descent algorithm, and the most popular optimization algorithms are Stochastic Gradient Descent (SGD) [31] and Adaptive Moment Estimation (ADAM) [32]. SGD is an iterative optimization technique that uses randomly selected samples to evaluate gradients. SGD performs a weight update for each x_i input and y_i output. The learning rate in ADAM is maintained per weight and adapted separately as training progresses, while SGD maintains a single learning rate for all weight updates and does not change during training [33,34].

The performance of the ANN was evaluated using the mean absolute error (MAE) quality metric [35]:

$$MAE=\frac{1}{n}{\displaystyle \sum }_{i=1}^n{Y}_i^{\prime }-Y_i\vee .$$

(4)

A comparative analysis of the performance of six neural networks was conducted using the mean absolute percentage error (MAPE) and the coefficient of determination (R²).

The MAPE indicator is determined using [36]:

$$MAPE=\frac{100\%}{n}{\displaystyle \sum }_{i=1}^n\left|\frac{Y_i-Y_i^{\prime }}{Y_i}\right|.$$

(5)

where R²$—$a statistical measure used to predict future outcomes or test hypotheses based on other related information [37]:

$$R^2=1-\frac{\sum {\left(Y_i-Y_i^{\prime }\right)}^2}{\sum {\left(Y_i-\overline{Y_i}\right)}^2}.$$

(6)

where $\overline{Y_i}—$the mean of the target output data.

4. Results

4.1. Training, Validation and Testing ANN Models

The next step of this study was to train, validate, and test six ANN models. The models were tested with 16, 32, 64 and 128 neurons in the hidden layer. The number of epochs was 100, and increasing the number of epochs did not lead to an improvement in model performance. Table 2 shows the parameters of the ANN models.

Comparing the ANN models, one can see that the best performance results (the minimum value of the average absolute error and the maximum value of the coefficient of determination) had the ANN5 model. This model used the softmax activation function and the ADAM optimizer. The optimal values of MAPE and R² were achieved with 64 neurons in the hidden layer and were equal to 0.1% and 0.99998, respectively.

The next description of the results refers to the ANN5 model and allows the evaluation of the possibility prediction of the output value in new datasets. Figure 2 shows the results of the calculation of the mean square error for the training and validation datasets. The maximum value of MSE in the first epoch was: training sample—0.2402; the validation set is 0.0456. The minimum MSE values in the 100th epoch was the training set—0.00018505 and the validation set—0.00013507.

Figure 3 shows the results of the calculation of the mean absolute error (MAE) for the training and validation datasets. The maximum value of MAE in the first epoch was: training sample—0.0145; the validation set is 0.0019. The minimum MAE values in the 100th epoch was the training set—0.00001929 and the validation set—0.00001818.

In general, it can be argued that the values of the mean absolute error (MAE) and the mean square error (MSE) of the training and validation testing samples did not differ much, and the neural network model was able to predict the values of the condition of the bridge components with high accuracy.

After training and testing, the model was saved in an H5 and JSON files, which contains model architecture, model weights, and training configuration (loss function, optimizer algorithm). This saving of the model allows its subsequent use on new datasets to obtain a forecast without need for retraining.

To test the effectiveness of the model and predict the output value, a new random dataset was created. It contained five records, one for each level of technical condition (

Table 3. Random dataset.

x1	x2	x3	x4	x5	x6	x7	x8	x9	x10	x11	x12	x13	x14	Y	Y’	Deviation (∆ Y), %
1	0.0	0.0	0	0	0	0	0	0	0	0	0	0	11	1	0.99074	0.92599
2	0.17	0.2	2	1	1	0	0	0	0	0	0	0	10	2	2.00446	0.22301
3	0.28	0.3	3	2	2	1	0.1	0.1	0	0	0	0	9	3	2.99372	0.20945
4	0.35	0.35	4	4	4	3	0.2	0.2	0	0	0	0	8	4	4.00106	0.02644
5	0.5	0.45	4	5	4	4	0.26	0.29	1	2	0	1	7	5	4.99941	0.01188

).

The last column shows the deviation in % between the target value (Y) and the resulting prediction (Y’). In general, the level of deviations between the target and forecast values was estimated as low, which confirms the quality of the forecast. The largest deviation can be observed for the level of condition 1 (0.92599%), the smallest for “Condition 5” (0.01188%), while the deviation value decreases during moving from “Condition 1” to “Condition 5”. It seems that with the condition level increase, the number of criteria increases as well and, accordingly, the number of records in the dataset. Therefore, “Condition 1” has 15 records, and “Condition 5” has 200 records. The entire process described in Section 4.1. was repeated for the remaining four components of the bridge.

Table 4. Optimal MAPE and R² values obtained for five ANN models.

	A.1. The Operational Condition of the Bridge Deck	A.11. The Operational Condition of the Pier Caps Beam	A.2. The Operational Condition of Span Structures Made of Reinforced Concrete	A.12. The Operational Condition of the Piers and A.13. the Operational Conditions of the Abutments	A.17. The Operational Condition of Approaches
R2	0.99592	0.99998	0.99845	0.99999	0.98970
MAPE, %	1.79	0.1	0.6	0.1	1.80

shows the optimal MAPE and R² values obtained for all five models.

4.2. Verification of the ANN Model for Assessing the Condition of Components on the Example of a Road Bridge

The practical use of the model was made on the basis of the data obtained from the report of the inspection of a beam-type road bridge made of precast concrete. The total length is 42.44 m; height—4.6 m; the width is 25.45 m. The bridge inspection was conducted in September–October 2019. The bridge is located on one of the streets of a city. There are no data on the year of construction of the bridge (approximately 1985). The examination was carried out in accordance with the requirements of “DBN V.2.3-6:2009. Bridges and pipes. Inspection and testing” [20], “DSTU-N B V.2.3-23:2009. Guidelines for assessing and predicting the technical condition of road bridges” [21] and a number of other regulatory documents. There was no technical passport and design documentation for the bridge.

Figure 4 shows the cross-section of the bridge as viewed from the abutment No. 0.

The bridge structure consists of two abutments, no.0 (C0-1...C0-14) and no. 3 (C3-1...C3-14), each has 14 driven piles; two intermediate piers no. 1 (C1-1...C1-34) and no. 2 (C2-1...C2-34), and each has 34 driven piles. The total number of driven piles is 96 pcs. The monolithic pier caps beams (R0-1...R0-5, R1-1...R1-7, R2-1...R2-7, R3-1...R3-5) rest on top of the piers, their total number is 24 pcs. The span structures of the bridge, made of prefabricated reinforced concrete slabs with oval voids (P01-1...P01-20, P12-1...P12-20, P23-1...P23-20), are supported on the pier caps beam, their total number is 60 pcs.

The span structures are covered with a 235–345 mm thick asphalt concrete roadway with bituminous waterproofing. Prefabricated reinforced concrete pavement blocks freely rest on three extreme span slabs on each side along the length of the bridge. Asphalt pavement on paving blocks has a thickness of up to 100 mm. Approaches in the form of cones are arranged in the under-bridge area, the slopes of the cones are covered with monolithic concrete 70–90 mm thick. In sections along the slopes lie cone stops in the form of reinforced concrete beams. In the approaches on the sides of the bridge, the slopes of the cones and part of the coastline below the bridge along the river are protected by prefabricated reinforced concrete slabs and cast-in-situ concrete pavement. The report contains data on the inspection carried out and the defects and inconsistencies found for each of the bridge components: 96 driven piles, 24 monolithic pier caps beams and 60 reinforced concrete slabs. In addition, there is a description of defects in the bridge deck and approaches.

The data from the report on detected defects for each of the components were loaded into the corresponding ANN model and the values of the technical condition of the component were calculated.

Table 5. The results of the calculation of the technical condition of the components of the bridge.

Name of the ANN Model	Name of a Component	Condition Assessment
A.1. Operational condition of the bridge deck	Bridge deck	3.95257
Average value		3.95257
A.2. Operational condition of span structures made of reinforced concrete	Slab P01-1	5.00022
	Slab P12-3	2.00299
	Slab P23-2	2.99845
	Slab P23-20	3.00751
Average value		2.41665
A.11. Operational condition of the pier caps beam	Pier cap beam RO-1	2.98382
	Pier cap beam R1-7	1.99939
	Pier cap beam R3-3	3.94583
Average value		2.57634
A.12. Operational condition of the piers and A.13. the operational conditions of the abutments	Pile C0-1	2.01872
	Pile C1-10	2.00116
	Pile C2-7	2.99596
	Pile C2-19	1.99953
	Pile C3-5	2.00545
	Pile C3-14	2.99833
Average value		2.00922
A.17. Operational condition of approaches	Approach pile	4.00783
Average value		4.00783

shows a part of the obtained results of the calculation of the technical condition of the components of the bridge. The “Condition assessment” column shows the predicted values of the technical condition of the bridge components, which were obtained using the ANN model (Y’).

At the same time, it is important to inform interested parties and pay special attention (red light) to the component in the database, the condition of which is estimated in the range from 4.5 to 5.0. Such actions are due to the fact that the technical condition of this component is classified as “incapacitated”, which indicates the need to stop or limit the operation of the entire structure. Measures must be taken urgently to prevent an accident and the issues of reconstruction or closure of the structure should be resolved.

The next step after quantitative assessment of the technical condition of bridge components is the stage of assessing the groups of components. The calculation is made as an average value of the assessment of the condition of the components of the group. The results of the calculation are shown in Table 5.

The final stage after the assessment of the condition of groups of bridge components is the stage of assessing the condition of the bridge. As noted in Section 3.1., the bridge rating is the weighted average of the determination of the operational condition of the groups of bridge components and is calculated by the Equation (1).

Calculation of the assessment of the technical condition of the bridge is presented in

Table 6. The assessment of the bridge condition.

The Groups of Bridge Components	${\mathit{\alpha }}_{\mathit{i}}$	${\mathit{D}}_{\mathit{i}}$	${\mathit{\alpha }}_{\mathit{i}}{\mathit{D}}_{\mathit{i}}$
The bridge deck	0.06	3.95257	0.23715
The bridge span	0.38	2.41665	0.91833
The pier caps beam	0.22	2.57634	0.56679
The piers and abutments	0.22	2.00922	0.44203
The approaches	0.12	4.00783	0.48094
∑			2.6452

.

Then, E = 80 × (5 − 2.6452)/4 + 20 ≈ 67 points.

According to the approved methodology, which establishes the relationship between the level of the condition of the structure and the number of points, the rating of this bridge is at the level of “Condition 3” (79–60 points)—acceptably serviceable. This level of rating involves scheduled inspections, reducing time between periodic inspections, and performing scheduled repairs.

5. Discussion

Before choosing the type and architecture of a neural network, we analysed a number of studies on the use of neural networks for solving such problems [38,39,40,41]. Fabianowski et al. [6] conducted a comparative study of three network models CNN (Convolutional neural network), MLP (Multilayer perceptron) and RNN (Recurrent neural network). The MLP model showed the highest efficiency—61%, the CNN model showed an efficiency of 43%, and the RNN model a maximum of 31%.

MLP is a type of neural network in which data from an input layer are passed to one or more hidden layers, and a result is obtained at the output layer. This type of neural networks is highly flexible, widely used and can be used to study the existence of relationships between input and output data [42,43]. Since there are no rules for creating networks, the development of the MLP architecture was carried out experimentally using the trial-and-error method. For example, all the ANN models used one hidden layer of neurons. Increasing the number of hidden layers by one or two had no effect on improving the model’s performance. The models were tested with 16, 32, 64 and 128 neurons in the hidden layer. Using the trial and error method, it was found that the best performance results (the minimum value of the average absolute error and the maximum value of the coefficient of determination) had the models with 64 neurons in the hidden layer.

The possibility of using the proposed ANN model to assess the condition of bridge components was analysed and compared with the quality of its work with models from similar studies. The most used method for assessing the performance of ANN models is the comparison of various error indicators (MAE, MAPE, RMSE, MSE, and others), as well as determination and regression coefficients.

Sobanjo [44] used MLP to predict the condition score of the bridge decks using the age of the bridge as the only input. Out of a set of 38 estimates, the network was able to correctly predict 79%. Cattan and Mohammadi [45] developed a neural network approach to predicting the condition of railway bridges. The study showed that successful network training can be achieved if the input dataset contains parameters with a diverse combination of correlation coefficients. Various combinations of input parameters were tested, and the most efficient network had a predictive score of about 73%. Assaad and El-Adaway [46] developed an asset management system to assess and predict bridge deck wear conditions. Two machine learning models were designed to predict the condition of the bridge deck: ANN and k-nearest neighbours (KNN). As a result, they obtained a model that can predict with an accuracy of 91.44%. Nguyen and Dinh [23] used the ANN model to predict the condition of bridges based on the assessment of the condition of the bridge structural components. The results showed that the resulting ANN model can predict the assessment of the condition of the bridge deck with an accuracy of 73.6%.

Comparing the performance of forecasts in similar studies with the value of the MAPE error in this study (the largest value for the ANN “А.17. The operational condition of approaches” is 1.80%), it can be concluded that the level of forecasting is quite high. This finding also confirms the low deviation ∆Y in Table 5 that was calculated for the random dataset.

It should also be noted that the proposed neural network model solves the regression task, which makes it possible to obtain exact values at the output, and not just class labels (integer values), as in solving classification tasks. The use of regression allows obtaining an assessment of the condition of a component with high accuracy, for example, up to five decimal places. Using integer values to evaluate does not always reflect the real condition of the component and can greatly distort the reality. For example, two components’ scores of 2.50 and 3.49 would be rounded to 3.0, but the real difference between those scores is 39.6%.

Unfortunately, this advantage is levelled at the stage of assessing the condition of the entire bridge. Therefore, the development of proposals for changing the methodology for assessing the condition of the entire bridge may be the next stage of the study. In addition, it is necessary to reconsider the approach to determine the frequency of inspection of bridges, which should take into account not only its age, but also the assessment of the condition and place in the rating. Separately, it should be emphasized that when identifying components of the condition, which are estimated in the range of 4.5–5.0, the interested parties should immediately be informed about this fact.

6. Conclusions

The object of the study was the methodology for quantifying condition of bridge components. The literature analysis showed that in most cases were used sets of data obtained during the inspection of bridges to solve the problems of assessing the current technical condition. The lack of such a database prompted the creation of a dataset on the basis of the Classification Tables of the Operating Conditions of the Bridge Components (CT). CTs is a set of rules that compares the existing defects/violations with the level of technical condition of the bridge components. Based on CTs, five datasets were formed, to assess the condition of the bridge components: bridge span, bridge deck, pier caps beam, piers and abutments, approaches. The next step of this study was to create, train, validate and test ANN models that correspond to the bridge components. Thus, datasets were created for training and testing five ANN models: “A.1. The operational condition of the bridge deck”, “A.2. The operational condition of span structures made of reinforced concrete”, “A.11. The operational condition of the pier caps beam”, “A.12. The operational condition of the piers and A.13. The operational conditions of the abutments”, A.17. The operational condition of approaches”. For each of the models, six variants were created that differ in number of neurons in the hidden layer, activation functions and optimization algorithms. The neural network with the softmax activation and optimizer ADAM showed the best results. The minimal value of MAPE and the maximal value of R² were achieved at the 100th epoch with 64 neurons in the hidden layer and were equal to 0.1% and 0.99998, respectively. Comparison of the MAPE and R² indicators of the created ANN models with models in similar studies for quantitative assessment of the condition of the bridge components showed that the level of consistency between the forecast and target data is quite high. The practical application of the technique was conducted on the most common type of bridge in Ukraine, namely, a road beam bridge of small/medium length, made of precast concrete. The condition was assessed: 96 driven piles, 24 pier caps beam and 60 reinforced concrete slabs. At the final stage of the study, the technical condition of groups of components was calculated, and the condition of the bridge was also assessed. Specifically, the changes in the methods for calculating the condition of the whole bridge are the aim of the following studies. Based on the study, an ANN-based tool was developed to quantify the technical condition of bridge components, which can be used by stakeholders to make decisions during the operational phase.