The results indicated the obtained ANN model can predict the condition rating of the bridge deck with an accuracy of 73.6%. If a margin error of ±1 was used, the accuracy of the proposed model reached a much higher value of 98.5%. Besides, a sensitivity analysis was conducted for individual input parameters revealed that Current Bridge Age was the most important predicting parameter of bridge deck rating. It was followed by the Design Load and Main Structure Design.
Journal of Science and Technology in Civil Engineering NUCE 2019 13 (3): 15–25 PREDICTION OF BRIDGE DECK CONDITION RATING BASED ON ARTIFICIAL NEURAL NETWORKS Tu Trung Nguyena,∗, Kien Dinhb a Dept of Civil, Construction, and Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487, USA b CONSEN INC., 5590 Avenue Clanranald, H3X 2S8, Montréal, QC, Canada Article history: Received 16/07/2019, Revised 08/08/2019, Accepted 12/08/2019 Abstract An accurate prediction of the future condition of structural components is essential for planning the maintenance, repair, and rehabilitation of bridges As such, this paper presents an application of Artificial Neural Networks (ANN) to predict future deck condition for highway bridges in the State of Alabama, the United States A library of 2572 bridges was extracted from the National Bridge Inventory (NBI) database and used for training, validation, and testing the ANN model, which had eight input parameters and one output being the deck rating Specifically, the eight input parameters are Current Bridge Age, Average Daily Traffic, Design Load, Main Structure Design, Approach Span Design, Number of main Span, Percent of Daily Truck Traffic, and Average Daily Traffic Growth Rate The results indicated the obtained ANN model can predict the condition rating of the bridge deck with an accuracy of 73.6% If a margin error of ±1 was used, the accuracy of the proposed model reached a much higher value of 98.5% Besides, a sensitivity analysis was conducted for individual input parameters revealed that Current Bridge Age was the most important predicting parameter of bridge deck rating It was followed by the Design Load and Main Structure Design The other input parameters were found to have neglectable effects on the ANN’s performance Finally, it was shown that the obtained ANN can be used to develop the deterioration curve of the bridge deck, which helps visualize the condition rating of a deck, and accordingly the maintenance need, during its remaining service life Keywords: condition rating; bridge deck; deterioration curve; artificial neural networks; sensitivity analysis https://doi.org/10.31814/stce.nuce2019-13(3)-02 c 2019 National University of Civil Engineering Introduction According to the American Society of Civil Engineers’ 2017 Infrastructure Report Card [1], about one in 11(9.1%) of the bridges in the United States were rated to be structurally deficient “Almost four in 10 (39%) are over 50 years or older, and an additional 15% are between the ages of 40 and 49 The average bridge in the U.S is 43 years old Most of the country’s bridges were designed for a lifespan of 50 years, so an increasing number of bridges will soon need major rehabilitation or retirement.” [1] It is known that, in order to have an optimum repair strategy, the future condition rating of the bridges needs to be predicted with a high level of accuracy At present, the visual inspection technique is the most commonly used method to determine the condition rating of a bridge structure in the United States [2] During the examination, the inspectors gather a large amount of information related to operational, geometric, and defects/condition of the ∗ Corresponding author E-mail address: nttu@crimson.ua.edu (Nguyen, T T.) 15 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering bridges Those inspection data are then archived in the NBI database For each bridge structure, such data reflect the condition ratings of superstructure, substructure, and bridge deck More specifically, the deck condition rating is stored in item No 58 of the NBI records The bridge deck is rated as an integer number between and 9, in which means a bridge being in a failed condition while 9, on the other hand, indicates an excellent condition The bridge with a component’s condition rating of or lower will be considered as structurally deficient The deck condition rating is performed for the entire deck, i.e., deck surface, sides and deck bottom Table shows a detailed description of the bridge deck in various ratings, which was taken from the Michigan Department of Transportation’s guidelines [2] Such an overall deck rating will be employed as the prediction output of this study Table Bridge deck condition rating (NBI item 58) Code Description N NOT APPLICABLE Code N for culverts and other structures without decks, e.g., filled arch bridge NEW CONDITION No noticeable or noteworthy deficiencies which affect the condition of the deck GOOD CONDITION Minor cracking less than 0.8 mm wide with no spalling, scaling or delamination on the deck surface or underneath GOOD CONDITION Open cracks less than 1.6 mm wide at a spacing of m or more, light shallow scaling allowed on the deck surface or underneath Deck will function as designed FAIR CONDITION Deterioration of the combined area of the top and bottom surface of the deck is 2% or less of the total area There may be a considerable number of open cracks greater than 1.6 mm wide at a spacing of 1.5 m or less on the deck surface or underneath Medium scaling on the surface is 6.4 mm to 13 mm in depth Deck will function as designed FAIR CONDITION Heavy scaling Excessive cracking and up to 5% of the deck area are spalled; 20–40% is water saturated and/or deteriorated Disintegrating of edges or around scuppers Considerable leaching through deck Some partial depth fractures, i.e., rebar exposed (repairs needed) POOR CONDITION Deterioration of the combined area of the top and bottom surface of the deck is between 10–25% of the total area Deck will function as designed SERIOUS CONDITION The deck is showing advanced deterioration that has seriously affected the primary structural components Deterioration of the combined area of the top and bottom surface of the deck is more than 25% of the total area Structural evaluation and/or load analysis may be necessary to determine if the structure can continue to function without restricted loading or structurally engineered temporary supports There may be a need to increase the frequency of inspections CRITICAL CONDITION Deterioration has progressed to the point where the deck will not support design loads and is therefore posted for reduced loads Emergency deck repairs or shoring with structurally engineered temporary supports may be required by the crews There may be a need to increase the frequency of inspections IMMINENT FAILURE CONDITION Bridge is closed to traffic due to the potential for deck failure, but corrective action may put the bridge back in service FAILED CONDITION Bridge closed In the current practice, the operational and physical characteristics of bridge components (superstructure, substructure, and deck) are evaluated visually by a bridge inspector based on his or her own assessment Such visual inspection requires the inspector to assign a subjective rating for each bridge component The overall rating of a bridge is then calculated through the integration of those component ratings Since for each bridge, the instant rating indicates the immediate level of repair needed for its structure, it is important to predict accurately the future ratings of a bridge, and accordingly, its 16 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering components, so that bridge engineers can develop an effective bridge repair/rehabilitation plan In the literature, several deterioration models of bridge decks based on chemical and physical processes have been proposed [3–6] Other research applied stochastic models such as Markov chains, or reliability-based methodology [7, 8] In recent years, an alternative approach using an Artificial Neural Network has been widely applied to structural condition assessment For example, Cattan and Mohammadi [9] used an ANN model to predict the condition rating of railway bridges in the Chicago metropolitan area Al-Barqawi and Zayed [10] predicted the condition of underground water main pipes with the ANN model The application of ANN model has also been expanded to predict the condition rating of a certain component of a bridge such as abutment [11], bridge deck [12–15] In this study, a supervised learning ANN model was developed and used to predict the condition rating of bridge decks using available information in the NBI database In addition, a similar methodology was also utilized to analyze the sensitivity of the input parameters in predicting the future condition of bridge decks Dataset used for training, validation, and testing the proposed ANN model is the NBI data from the State of Alabama in 2018 This dataset was downloaded from the Federal Highway Administration (FHWA) website [16] Original data were refined before being used to develop the ANN model The subsequent section provides details on the data refinement Database preparation The original NBI data obtained from the FHWA website comprises valuable information about the United States’ bridge network However, based on the initial analysis, the NBI database also contained multiple errors and data outside a normal range, i.e outliners In order to minimize the potential negative effects of such data on the performance of the ANN model, the refinement of original data was carried out Specifically, the original data were filtered with consideration to a number of criteria as discussed in the following paragraphs The initial refinement focused on removing the records containing flawed data The original dataset was checked for errors such as zero or negative Average Daily Traffic, zero Number of main Span, negative Ages The bridges with those errors were removed from the database The refinement also targeted at the bridges with reconstruction and repaired records In this study, the authors used the ANN model to predict the condition rating of bridge decks without previous intervention, i.e., previous repair or replacement Thus, the bridges with repair and reconstruction activities were also removed from the database In another refinement step, the bridges with an overall deck rating of or or no rating were considered not being qualified for the inputs, and therefore they were also removed from the database The next refinement was aimed to remove the input parameters those are likely not important According to the previous study [14], 11 NBI items were considered to have a significant influence on concrete bridge deck performance Those variables were: Age, Year Built, Average Daily Traffic, Percent of Daily Truck Traffic, Average Daily Truck Traffic, Number of main Span, Region, Steel Reinforcement Protection, Structure Design Type, Design Load, and Approach Surface Type [14] However, due to the uncertainty in the NBI data, the number of items used in this study was reduced to seven items as following: (i) Year Built (item 27), (ii) Average Daily Traffic (item 29), (iii) Design Load (item 31), (iv) Main Structure Design (item 43B), (v) Approach Span Design (item 44B), (vi) Number of main Span (item 45), (vii) Percent of Daily Truck Traffic (item 109) The overall condition rating of bridge deck was the output of the ANN model, thus the Deck Condition Rating (item 58) was utilized for a supervised learning of the ANN In addition, the Current Bridge Age item was created to replace the Year Built item from NBI database The age of a bridge 17 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering was equal to the subtraction of 2019 and the year that the bridge was built (Year Built, item 27) Furthermore, a new item, Average Daily Traffic (ADT) Growth Rate, was added to the inputs This parameter and the Current Bridge Age item were used later as the variable parameters for constructing the deterioration curve of bridges The ADT Growth Rate parameter is the annual growth rate of ADT It was calculated by the following equation AGR = FADT − LADT 100% FDT − LDT (1) where AGR = Percent of annual ADT Growth Rate; FADT = Future ADT (item 114); LADT = Latest ADT (item 29); FDT = Future year of ADT (item 115); LDT = Latest year of ADT (item 30) In the last refinement, the old bridges with abnormal ratings were removed from the database This refinement was performed to ensure that the rating records reflect the reasonable typical deterioration for a bridge deck To perform this refinement, the records were removed if they met one of the following conditions: (i) age ≥ 30 and deck rating ≥ 6, (ii) age ≥ 25 and deck rating ≥ 7, (ii) age ≥ 20 and deck rating ≥ 8, and (iv) age ≥ 15 and deck rating ≥ [14] After performing refinement, the final dataset was a matrix that contains 2572 rows and columns The range of the input and output parameters is listed in Table Some bridges were forecast with a reduction in the number of average daily traffic, and as a result, the value of the additional parameter (ARG) was negative, as seen in Table The classification of the deck condition rating is presented in Table This dataset was used for the ANN model with the inputs were the data from column to column and the outputs were the data from column Table Characteristics of input and output No Parameter Item Contraction Unit Min Max Current Bridge Age Average Daily Traffic Design Load Main Structure Design Approach Span Design Number of main Span Percent of Daily Truck Traffic ADT Growth Rate Deck Condition Rating 29 31 43B 44B 45 109 58 CBA ADT DLD MSD ASD NMS PDT AGR DCR year No No % % - 0 1 −2.78 119 157350 22 22 48 75 26.5 Table Number of records in each specific range the bridge deck rating Condition Rating Total Number of records 65 1136 128 602 479 153 2572 Methods As mentioned earlier, the ANN model was used to predict the condition rating for bridge decks Artificial Neural Network is an adaptive system using a number of fully connected neutrons to process the data and then establish the relationship between the inputs and outputs A typical neutron 18 Table Number of records in each specific range the bridge deck rating Condition Rating Total Number of records 65 1136 128 602 479 153 2572 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering Methods often consists of five components as depicted in Fig The input section provides information (trigAs mentioned earlier, the ANN model was used to predict the condition rating for bridge decks Artificial Neural Network gering signals) for theusing neutron information is then going through an evaluation system is an adaptive system a numberThe of fully connected neutrons to process the data and then establish the relationship betweenwhere and outputs A typical neutron often consistson of five as depicted in Fig The input section provides a weighttheisinputs assigned to each input depending thecomponents importance of the inputs After that, a summainformation (triggering signals) for the neutron The information is then going through an evaluation system where a weight tion is performed to obtain a net input that comes to a neuron The net input is then processed in the is assigned to each input depending on the importance of the inputs After that, a summation is performed to obtain a net input determination toThe produce value in the inoutput neuron section [17].to produce value in the output neuron [17] that comessection to a neuron net input is then processed the determination Input x1 x2 w1 x3 w3 xn n Evaluation Summation Determination Output w2 Sum Sigmoid Output wn Components of of aasimple neuron FigureFigure Components simple neuron Neural networks learn to map between input and output through a common learning process called error back-propagation Neural networks learn to map between input and output through a common learning process called It works by using the errors presented in the network output to adjust the weights between two adjacent layers The error backerror back-propagation It works usingin which the errors in theandnetwork to adjust the propagation consists of two different by processes, one is a presented feed-forward process the other isoutput a back-propagation In thetwo feed-forward process, the inputs areerror used to obtain the outputs based onconsists the weightsof initially or obtained weightsprocess between adjacent layers The back-propagation twoassumed different processes, from the previous adjustment The errors are then passed backwards to the input layers through the back-propagation process, in which one is a feed-forward process and the other is a back-propagation process In the feed-forward the weights are adjusted during this process to minimize the network errors to an acceptable level process, the inputs are used to obtain the outputs based on the weights initially assumed or obtained The ANN model often contains multiple neutrons with an input layer, multiple hidden layers, and an output layer, as shown from thein Fig previous adjustment The errors are then passed backwards to the input layers through the In this study, the input layer consisted of eight parameters/neutrons, namely Current Bridge Age (CBA), Average back-propagation process, theLoad weights are adjusted during thisApproach process to Design minimize network Daily Traffic (ADT), Design (DLD), Main Structure Design (MSD), Span (ASD),the Number of main errors Span (NMS),level Percent of Daily Truck (PDT), and ADT Growth Rate (AGR) The output of the ANN model was the Deck to an acceptable Rating (DCR) The dataset was divided arbitrarily into training, validation, and testing data subsets The training TheCondition ANN model often contains multiple neutrons with an input layer, multiple hidden layers, and subset consistedKien of 70%,Dinh/ i.e 1800 bridges, ofof theScience entire database validation subset 15%, i.e 386 instances, of Tu T Nguyen, andThe Technology incontained Civileight Engineering an output layer, as shown in Fig.Journal study, layer consisted the entire database The remaining, i.e.In 386this samples, werethe usedinput for testing the proposed ANNof model Theparameters/neutrons, trained ANN model was then utilized to develop a degradation curve for a specific bridge Input layer CBA ADT DLD MSD ADS NMS PDT AGR hidden layer output layer DCR Figure Structure of ANN Figure Structure of ANN model model In addition, the ANN models were also employed to study the19 importance/effects of each input parameter to the output To perform this task, each ANN model was trained and used to predict the output with a single input parameter The performance of the model with that input was then evaluated and recorded Repeated this task for all the input parameters The results were then ranked to explore the importance of each input to the output of the ANN model Tu T Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering Tu T Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering Input layer hidden layer output layer Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering Input layer hidden layer output layer namely Current Bridge Age (CBA), CBA Average Daily Traffic (ADT), Design Load (DLD), Main Structure Design (MSD), Approach Span Design (ASD), Number of main Span (NMS), Percent of Daily ADT 12 CBA Truck (PDT), and ADT Growth Rate (AGR) The output of the ANN model was the Deck Condition ADT DLD 23 divided Rating (DCR) The dataset was arbitrarily into training, validation, and testing data subsets The training subset consisted 34of DLD 70%, i.e 1800 bridges, of the entire database DCR The validation subMSD set contained 15%, i.e 386 instances, of the entire database The remaining, i.e 386 samples, were DCR MSD ADS used for testing the proposed 5ANN model The trained ANN model was then utilized to develop a ADS 56 bridge degradation curve for a specific NMS In addition, the ANN models were also employed to study the importance/effects of each input 67 NMS PDT parameter to the output To perform this task, each ANN model was trained and used to predict the PDT AGR The performance of the model with that input was then evaluated output with a single input parameter AGR and recorded Repeated this task for all the input parameters The results were then ranked to explore the importance of each input to the output of the ANN model Figure Structure of ANN model Gradient = 0.076679, at epoch 22 Gradient = 0.076679, at epoch 22 -3 Mu = 1e-05, at epoch 22 Mu = 1e-05, at epoch 22 Mean Squared Error (mse) -4 10 -4 10 mu mu 10 -3 10 -5 val fail val fail 10 -5 10 Validation epoch2222 Validation Checks Checks == 6,6,atatepoch 1010 44 66 88 10 12 10 12 22 Epochs Epochs 22 14 14 1616 10 10 10 -1 22 10 10 55 00 00 Train Train Validation ValidationTest Test Best Best 2 10 Mean Squared Error (mse) 10 10 10 10 -5 10 -5 10 gradient gradient Structure of ANN model In addition, the ANN models were also Figure employed to study the importance/effects of each input parameter to the output Results and discussion To perform this the task, each ANNwere model trained to predict the output with a single input parameter In addition, ANN models alsowas employed to and studyused the importance/effects of each input parameter to the output The performance thetask, model with thatmodel input was evaluated andtorecorded Repeated for allinput the input parameters To perform of this each ANN was then trained and used predict the output this withtask a single parameter The The The model this has eightevaluated neutrons inrecorded the input layer, tenANN neurons hidden layer,The performance of the modeltoin with thatstudy input was then Repeated this task for all in thethe input parameters results wereANN then ranked explore the importance of each and input to the output of the model results were then ranked explore layer the importance of each to the activation output of thefunction ANN model and one neuron in thetooutput It employs theinput sigmoid The regression method Results and discussion is used to generate output for the ANN model The output (condition rating) is rounded up or down Results and discussion The ANN model in this study has eight neutrons in the input layer, ten neurons in the hidden layer, and one neuron in the to the nearest valid this rating For instance, if the condition ratingneurons of a bridge obtained from theneuron ANNinisthe ANN model in the study hasactivation eight neutrons in theThe input layer, tenmethod inused the hidden layer, output and onefor outputThe layer It employs sigmoid function regression is to generate the ANN model 6.51, it will be rounded up to Fig shows some information about the training and performance output layer It employs the sigmoid activation regression method is used to generate for the ANN model The output (condition rating) is rounded up orfunction down to The the nearest valid rating For instance, if output the condition rating of a bridge The output (condition rating) is it rounded or downuptoto the valid rating Forinformation instance, condition of aperformance bridge of the proposed ANN model After training was completed, the ANN modelif the was used torating predict the obtained from the ANN is 6.51, will beup rounded 7.nearest Figure shows some about the training and from the ANN is 6.51, it willtraining beItrounded tonoting Figure shows information the and performance ofobtained the proposed ANN model After wasupcompleted, the ANN model was predict the that output withnot the testing output with the testing dataset is worth that the some testing dataused is about atoset oftraining data was of the proposed ANN model After training was completed, the ANN model was used to predict the output with the testing dataset It is in worth noting thatset the A testing data is a set of data that was not included inof thethe training set A detailed discussion included the training detailed discussion about the performance ANN model can be dataset It is worth noting that the testing data is a set of data that was not included in the training set A detailed discussion about the performance of the ANN model can be found in the subsequent sections foundtheinperformance the subsequent sections about of the ANN model can be found in the subsequent sections -1 10 10 0 1818 2020 22 22 (a) Training (a) Training Training 24 46 68 10 10 12 12 14 22 Epochs 22 Epochs 14 16 16 18 2018 2220 22 (b)Validation Validation (b)(b) Validation Figure 3.3.Information thethe proposed ANN model Figure Information of proposed ANN model Figure Information ofofthe proposed ANN model 4.1.Model Modelperformance performance 4.1 4.1 Model performance ordertotoevaluate evaluate the the performance ANN model, a confusion matrix and and a bubble plot were used used The The InInorder performanceof ofthe theproposed proposed ANN model, a confusion matrix a bubble plot were confusionmatrix matrix is is often often applied applied for classification problems to to report numerical results thanks to itstoability to show the the confusion for classification problems report numerical results thanks its ability to show In order to evaluate the performance of the proposed ANN plot model, a confusion matrix and a bubble relationsbetween between classified classified outputs The bubble (scatter plot)plot) provides a visualization of theof the relations outputs and andthe thetrue trueones ones[18] [18] The bubble plot (scatter provides a visualization plot were used The matrix iswere often applied for classification to report numerical confusion matrix with theconfusion number of presented viavia the diameter of the dotproblems [19] The details of those two methods confusion matrix with the number ofinstances instanceswere presented the diameter of the dot [19] The details of those two methods were presented in the following sections results thanks to its ability to show the relations between classified outputs and the true ones [18] were presented in the following sections The bubble plot (scatter plot) provides a visualization of the confusion matrix with the number of 20 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering instances were presented via the diameter of the dot [19] The details of those two methods were presented in the following sections a Confusion matrix The confusion matrices were created for both training and testing data sets The columns of a confusion matrix represent the true rating value from the manual inspection, and the rows show the predicted rating values by the proposed ANN model Two indicators, Correct Rating (CR) and Acceptable Rating (AR), were used to evaluate the performance of the network The CR is the percentage of predicted ratings that accurately matched the visual inspection rating The AR is a ratio of predicted values within a rating margin of error over the actual rating values Table Confusion matrix of bridge deck rating in training Manual Inspection Prediction 5 SUM 0 0 0 0 0 3 40 810 0 854 49 19 0 74 CR (%) AR (%) 100 100 100 100 94.8 99.6 66.2 98.6 SUM 0 37 254 88 380 0 138 222 88 456 0 0 12 19 32 44 816 95 412 322 107 1800 66.8 99.7 48.7 98.2 59.4 96.9 75.4 99.2 Table Confusion matrix of bridge deck rating in the test set Manual Inspection Prediction 5 SUM 1 0 0 1 0 0 10 172 0 0 183 0 0 16 CR (%) AR (%) 50.0 50.0 50.0 100 93.9 99.5 50.0 100 SUM 0 52 25 86 0 30 49 16 96 0 0 0 1 11 177 15 88 74 19 386 60.5 96.5 51.0 98.9 100 100 73.6 98.5 In the confusion matrix, the element j (i is the row, and j is the column) indicates that the proposed ANN model predicted the rating as i while the true rating values as recorded in the database is j The elements in the diagonal of the confusion matrix (aii in the bold gray cells) are the elements correctly classified by the network These elements were used to calculate the CR for each individual rating, and for the overall network As presented in Table 4, the proposed ANN had an overall CR of 75.4% for the training data subset 21 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering The subjective rating of the visual inspection process is well recognized, therefore a margin error of ±1 is selected in this study account for of that subjectivity The light in gray cells in the confusion Tu T Nguyen, Kiento Dinh/ Journal Science and Technology Civil Engineering matrix represent the values of ratings within the margin of error The AR indicator was calculated Tu Tu T T Nguyen, Nguyen, Kien Kien Dinh/ Dinh/ Journal Journal of of Science Science and and Technology Technology in in Civil Civil Engineering Engineering Tu T Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering for the overall network and for the individual ratings Taking into account this margin, the overall prediction for the0 training data significantly1 increased19to ratings of0 the proposed ANN model subset 16 0 0 2 16 16 19 19 99.2%,999as shown in000Table 000 0 16 111 19 SUM 2 183 16 86 96 386 Table a confusion matrix deck 86 condition ratings in 1the The SUM SUM presents 183 183for the bridge 16 16 86 86 96 96 11 test set 386 386 SUM 222 222 183 16 96 386 proposed ANN model the new/unseen the testing data set with CR (%) 50.0 performed 50.0 well for 93.9 50.0 data in 60.5 51.0 100 the overall 73.6 CR CR(%) (%) 50.0 50.0 50.0 50.0 93.9 93.9 50.0 50.0 60.5 60.5 51.0 51.0 100 100 73.6 73.6 CR (%) 50.0 50.0 93.9 50.0 60.5 51.0 100 73.6 CR of 73.6%, When the margin error was applied, AR AR (%) as seen 50.0 in Table100 99.5 100 of ±1 96.5 98.9the overall 100value of98.5 AR(%) (%) 50.0 50.0 100 100 99.5 99.5the great100 100 100 96.5 96.5 98.9 98.9 100 100 98.5 98.5 was AR increased to 98.5% The100 results show potential of the ANN98.9 model at 100 predicting ratings AR (%) 50.0 99.5 96.5 98.5 4.1.2 Bubble plots within a ±1 plots rating 4.1.2 4.1.2.Bubble Bubble plots plots interval 4.1.2 Bubble An alternative technique to present the classification results is a bubble plot Figure shows the bubble plots for the performance of the ANN model in different data sets with an identical scaling factor In those plots, the diameter of the dots performance performance ofofthe the theANN ANN ANN model modelin inindifferent different different data data sets sets with withananidentical identical scaling scalingis factor factor InInthose those those plots, plots, the thediameter diameter of ofthe the the dots dots performance of model sets with scaling factor plots, the dots An alternative technique present the classification results a bubble plot Fig 4diameter shows the bubrepresents for the number of casesto with an data identical ratinganatidentical each point Because theInnumber of samples in the of validation and represents represents for for the the number number of of cases cases with with an an identical identical rating rating at at each each point point Because Because the the number number of of samples samples in in the the validation validation and and represents forsubset the of cases with an of identical rating each point Because theof number of samples in the validation and ble plotsdata for thenumber performance ofhalf the ANN in different data sets with an identical scaling factor testing is approximately the sizemodel of theattraining subset, the size the bubbles in validation and testing plots testing testingdata datasubset subset subsetis isisapproximately approximately approximatelyhalf half halfof ofofthe the thesize size sizeof ofofthe the thetraining trainingsubset, subset, subset,the the thesize size sizeof ofofthe the thebubbles bubbles bubblesin ininvalidation validationand and andtesting testingplots plots plots testing data are smaller Thethe dots on the diagonal linedots indicate the training number ofthe accurate predictions, andwith the validation dots within thetesting limit of upper In those plots, diameter of the represents for number of cases an identical rating at are are smaller smaller The The dots dots on on the the diagonal diagonal line line indicate indicate the the number number of of accurate accurate predictions, predictions, and and the the dots dots within within the the limit limit of of upper upper are smaller The dots on the diagonal line indicate the number of accurate predictions, and the dots within the limit of upper and lower error margin the line number represent the number of in instances within a ±1and rating interval each point Because of samples the validation testing data subset is approximately and andlower lowererror errormargin margin marginline line linerepresent represent representthe the thenumber number numberof ofofinstances instances instanceswithin within withinaaa±1 ±1 ±1rating rating ratinginterval interval interval and lower error b Bubble plots technique An Analternative alternative technique techniqueto totopresent present presentthe the theclassification classification classificationresults results resultsis isisaaabubble bubble bubbleplot plot plot.Figure Figure Figure444shows shows showsthe the thebubble bubble bubbleplots plots plotsfor for forthe the the An alternative 88 88 Prediction Prediction Ratings Ratings Prediction Ratings Prediction Ratings 99 Prediction Ratings Ratings Prediction Prediction PredictionRatings Ratings 99 77 77 66 66 55 55 44 333 33 44 44 Diagonal line Diagonal Diagonalline line line Diagonal Error margin Error Errormargin margin margin 55 66 77 88 99 Manual Inspection Ratings Manual Manual Inspection Inspection Ratings Ratings 33 3 33 Diagonal line Diagonal Diagonal line line Diagonal line Error margin Error Error margin margin Error margin 55 77 44 55Manual 66 77Ratings 88 99 Inspection Manual Manual Inspection Inspection Ratings Ratings Manual Inspection Ratings (a) Training (a) Training (a) Training (a) Training (b) Validation (b) Validation (b) (b) Validation Validation (b) Validation 88 88 8 Prediction Ratings Ratings Prediction Ratings Prediction Ratings 99 9 Ratings Prediction Ratings Prediction Prediction Ratings Ratings 99 77 77 7 66 66 6 55 55 5 44 33 33 44 4 Diagonal line Diagonal Diagonal line line Diagonal line Error margin Error margin margin Error margin 44 55 66 77 Manual Inspection Ratings Manual Inspection Ratings Manual Inspection Ratings 88 33 3 33 3 99 9 (c) Testing (c) Testing (c) Testing (c) Testing Diagonal Diagonal Diagonal line lineline Diagonal line Error margin Error Error margin margin Error margin 44 4 55 5 66 6 77 7 88 8 Manual Inspection Ratings Manual Manual Inspection Inspection Ratings Ratings Manual Inspection Ratings 99 9 (d) Overall (d) Overall (d) (d) Overall Overall (d) Overall Figure 4.4 Bridge deck deck ratings ratings Bubble plots plots Figure Bridge deck ratings –––Bubble plots Figure 4.4.Bridge deck ratings Bubble plots Figure Bridge deck ratings –Bubble Bubble plots 4.2 4.2 Deterioration curves 4.2.Deterioration Deteriorationcurves curves 22 for bridge deck was created using the proposed ANN model This curve can be to the The The deterioration curve for bridge deck was created using using the the proposed proposed ANN ANN model model This This curve curve can can bebeused used used totopredict predict predict the thethe Thedeterioration deteriorationcurve curve for bridge deck was created using the proposed ANN model This curve can be used to predict during itsits service life InInIn the development of deterioration curve for aaaspecific bridge, two performance performance the bridge deck during service life the the development development ofofthe the the deterioration deterioration curve curve for forfor specific specific bridge, bridge, two two performanceofof ofthe thebridge bridgedeck deck during its service life the development of the deterioration curve a specific bridge, two (CBA) and Average Daily Traffic (ADT) were changed in step, other parameters were parameters, parameters, Current Bridge Age (CBA) and Average Daily Traffic Traffic (ADT) (ADT) were were changed changed inineach each step, step, other other parameters parameters were were parameters,Current CurrentBridge BridgeAge Age (CBA) and Average Daily Traffic (ADT) were changed ineach each step, other parameters were ofof bridge age was 1year, the change of daily traffic was calculated by the kept kept constant While the increment bridge age was year, the the change change ofofaverage average average daily daily traffic traffic was was calculated calculated by byusing using using the thethe keptconstant constant.While Whilethe theincrement increment of bridge age was 1year, year, the change of average daily traffic was calculated by using Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering half of the size of the training subset, the size of the bubbles in validation and testing plots are smaller The dots on the diagonal line indicate the number of accurate predictions, and the dots within the limit of upper and lower error margin line represent the number of instances within a ±1 rating interval 4.2 Deterioration curves Tu T Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering The deterioration curve for bridge deck was created using the proposed ANN model This curve can be used to predict the performance of the bridge deck during its service life In the development where is the average daily for traffic of the current year;two 𝐴𝐷𝑇parameters, dailyBridge traffic of the (CBA) next year; ARG is the 1234 is the average of theADT deterioration curve a specific bridge, Current Age and Averannual average daily traffic growth rate To obtain the deterioration curve for the deck of a specific bridge, the following steps age Daily Traffic (ADT) were changed in each step, other parameters were kept constant While the were applied increment of bridge age was year, the change of average daily traffic was calculated by using the Obtain equation the initial value of inputs of the bridge of interest from the database following ADTnext = (1 + ARG) ADT (2) Decide the number of years to be simulated where ADT the to average dailyANN traffic of the current ADTnext is the average daily traffic of the Apply the is inputs the proposed model for the rating year; prediction next year; ARG is the annual average daily traffic growth rate To obtain the deterioration curve for Increase age by bridge, year and the calculate 𝐴𝐷𝑇1234 the4.deck of the a specific following steps were applied Obtain initial of inputs of the bridge of interest from the database Repeat stepsthe and forvalue the entire life of simulation Decide the number of years to be simulated Figure shows an example of the bridge deck rating projection using the proposed ANN model In this figure, a circle dot Apply the inputs to the proposed ANN rating represents the overall deck rating predicted by the ANNmodel model for Thethe square dotsprediction and diamond dots represent the upper limit Increase the age by year and calculate ADT nextbridge was seven years old with a current rating (DCR) of and lower limit of the predicted condition rating, respectively This AGR Repeat stepsThe and for the lifetoofpredict simulation and an of 2.5% simulation wasentire performed the condition rating for the bridge deck over 60 years Details shows an example the can bridge deck rating6 projection using the proposed ANN model In of the Fig initial5input parameters of this of bridge be seen in Table Fig 5, a circle dot represents the overall deck rating predicted by the ANN model The square dots and Table Initial input parameters from the database diamond dots represent the upper limit and lower limit of the predicted condition rating, respectively Inputwas seven CBA years ADT MSD (DCR) ASD ARGsimulation This bridge old with aDLD current rating of andNMS an AGR PDT of 2.5% The was performed condition 60 years Value to 7predict the 17503 rating for the bridge deck over 10 Details 2.5of the initial input parameters of this bridge can be seen in Table +1 error -1 error Rounded Original NBI rating 10 20 30 40 50 60 Deck Age, (Years) Figure 5 Lifetime ratingsprediction prediction Figure Lifetimebridge bridge deck deck ratings 4.3 Input sensitivity analysis To study the influence of a single input parameter to the23 overall deck rating for the bridges, the ANN model was used to run the sensitivity analysis In each case, a single input was used with the ANN model to predict the output The performance of each simulation instance was evaluated using the coefficient of determination (R2) The coefficient of determination measures the correlation between input and output variables using equation (3) Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering Table Initial input parameters from the database Input CBA ADT DLD MSD ASD NMS PDT ARG Value 17503 2 10 2.5 4.3 Input sensitivity analysis To study the influence of a single input parameter to the overall deck rating for the bridges, the ANN model was used to run the sensitivity analysis In each case, a single input was used with the ANN model to predict the output The performance of each simulation instance was evaluated using the coefficient of determination (R2 ) The coefficient of determination measures the correlation between input and output variables using equation (3) R2 = − n ˆ i )2 i=1 (yi − y n ¯ )2 i=1 (yi − y (3) where yi is the ith actual output, y¯ is the mean of the actual outputs, yˆ i is the ith predicted rounded outputs, and n is the total number of samples The results of the input analysis simulation are shown in Table Table Sensitivity analysis for the inputs Input R2 Ranking CBA ADT DLD MSD ASD NMS PDT AGR 0.93 0.18 0.60 0.52 0.23 0.08 0.14 0.05 As can be seen in Table 7, the most influential input parameter for the proposed ANN model was the Current Bridge Age (CBA) with a value of R2 was 0.93 The Design Load (DLD) and Main Structure Design (MSD) came in the second and third place with an R2 of 0.60 and 0.52, respectively The results were reasonable since the performance of a bridge deck was likely linearly dependent on time In addition, the design load was related to the type of load that applied to the bridge decks, thus a strong relationship between the design load parameter and the performance of a bridge deck was comprehensible Other input parameters presented the limited correlation to the output Conclusions In this paper, an ANN model was developed for predicting the condition rating of bridge deck using the available information in the NBI database The bridge data in the State of Alabama were used to train, validate, and test the proposed ANN model The model worked well with the new data 24 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering in the testing data set with the percentage of prediction accuracy of 73.6% Within the margin error of ±1, the prediction accuracy of the model can achieve 98.5% The trained ANN model can be used effectively to develop the deterioration curve for the bridge deck With such a curve, the future condition rating of the bridge deck can be easily predicted In addition, a sensitivity study of the input parameters revealed that the Current Bridge Age (CBA) is the most important predicting factor to the bridge deck condition rating/deterioration Other factors such as Design Load (DLD) and Main Structure Design (MSD) also had some significant effects on the deck deterioration References [1] ASCE (2017) Infrastructure report card American Society of Civil Engineers [2] MDOT (2011) NBI rating guidelines Michigan Department of Transportation [3] Derucher, K., K G., Ezeldin, S (1994) Materials for civil and highway engineers 3rd edition, PrenticeHall., Englewood Cliffs, N.J [4] Enright, M P., Frangopol, D M (1998) Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion Engineering Structures, 20(11):960–971 [5] Bhargava, K., Ghosh, A K., Mori, Y., Ramanujam, S (2006) Analytical model for time to cover cracking in RC structures due to rebar corrosion Nuclear Engineering and Design, 236(11):1123–1139 [6] Isgor, O B., Razaqpur, A G (2006) Modelling steel corrosion in concrete structures Materials and Structures, 39(3):291–302 [7] Markow, M J (2009) Bridge management systems for transportation agency decision making NCHRP Synthesis 397, Washington, DC: The National Academies Press [8] Frangopol, D M., Kong, J S., Gharaibeh, E S (2001) Reliability-based life-cycle management of highway bridges Journal of Computing in Civil Engineering, 15(1):27–34 [9] Cattan, J., Mohammadi, J (1997) Analysis of bridge condition rating data using neural networks Computer-Aided Civil and Infrastructure Engineering, 12(6):419–429 [10] Al-Barqawi, H., Zayed, T (2006) Condition rating model for underground infrastructure sustainable water mains Journal of Performance of Constructed Facilities, 20(2):126–135 [11] Li, Z., Burgue˜no, R (2010) Using soft computing to analyze inspection results for bridge evaluation and management Journal of Bridge Engineering, 15(4):430–438 [12] Morcous, G (2002) Comparing the use of artificial neural networks and case-based reasoning in modeling bridge deterioration In Proc., 30th Annual Conference of Canadian Society for Civil Engineering, Curran Associates, Inc, 2471–2479 [13] Lee, J., Sanmugarasa, K., Blumenstein, M., Loo, Y.-C (2008) Improving the reliability of a Bridge Management System (BMS) using an ANN-based Backward Prediction Model (BPM) Automation in Construction, 17(6):758–772 [14] Emily, W K (2011) Artificial neural network models for the prediction of bridge deck condition ratings Master’s thesis, Michigan State University, USA [15] Huang, Y.-H (2010) Artificial neural network model of bridge deterioration Journal of Performance of Constructed Facilities, 24(6):597–602 [16] FHWA (2019) Federal highway administration National Bridge Inventory [17] Topcu, I B., Sarıdemir, M (2007) Prediction of properties of waste AAC aggregate concrete using artificial neural network Computational Materials Science, 41(1):117–125 [18] Diez, P (2018) Smart wheelchairs and brain-computer interfaces, chapter - Introduction, 1–21 Academic Press [19] Leban, G., Zupan, B., Vidmar, G., Bratko, I (2006) Vizrank: Data visualization guided by machine learning Data Mining and Knowledge Discovery, 13(2):119–136 25 ... the An alternative 88 88 Prediction Prediction Ratings Ratings Prediction Ratings Prediction Ratings 99 Prediction Ratings Ratings Prediction Prediction PredictionRatings Ratings 99 77 77 66 66... Ratings Prediction Ratings Prediction Ratings 99 9 Ratings Prediction Ratings Prediction Prediction Ratings Ratings 99 77 77 7 66 66 6 55 55 5 44 33 33 44 4 Diagonal line Diagonal Diagonal line... failed condition while 9, on the other hand, indicates an excellent condition The bridge with a component’s condition rating of or lower will be considered as structurally deficient The deck condition