Paper ICMPA093 8th International Conference on Managing Pavement Assets
DEVELOPMENT OF PRIORITY INDEX ASSESSMENT MODEL FOR ROAD PAVEMENTS IN NIGERIA Adebayo Owalabi1* and O. S. Abiola2 1 Dept. of Civil Engineering, Federal University of Technology, Nigeria 2 Dept. of Civil Engineering, University of Agriculture, Abeokuta, Nigeria * Corresponding Author´s Email:
[email protected]
ABSTRACT Against the background that regular maintenance is necessary to preserve highway investments, reduce users' cost and cost of goods and services, this paper presents the results of a research aimed at developing a priority assessment index for pavement management system (PMS) in Nigeria using artificial neural network (ANN) and linear regression. As a key component of PMS, priority assessment index plays a crucial role where forecast results provide a basis for prioritizing highway pavement maintenance. Comprehensive investigations were carried out on the expressway linking Lagos (the economic nerve of Nigeria) with Ibadan (the largest city in West Africa)- apparently one of the most heavily trafficked roads in the country. Data relating to traffic characteristics, pavement condition ratings, distress types, pavement thickness and roughness index, were collected. Of these variables, only three were found to be statistically significant namely: traffic volume, pavement condition score and roughness index. These variables were combined into a convenient scale to get a single priority assessment index. The R2 values of 0.95 and 0.98 show that both ANN model and linear regression can be used satisfactorily to prioritize highway pavement maintenance. The results of this research will provide a method of effectively managing road pavements in Nigeria and other developing countries of the world with similar climatic, soil and traffic conditions. KEYWORDS: Prioritize, Pavement, Maintenance, Preserve, Highway, Investment. INTRODUCTION The standard of living of a region reflects a state of its links of communication and in particular that of its road network (1). As a result of aging, overuse, misuse and/or mismanagement, deterioration and catastrophic failure of a road may occur. The cost of restoring such road to the required standard becomes higher, likewise that required to move goods and people along them, with a consequent effect on cost of goods and services. A good pavement management system is therefore necessary to reduce the rate of deterioration, prolong life of pavements, reduce vehicle operating cost, ensure safety of road users and preserve highway investment (2), (3). A pavement management system is a planning tool that is able to model pavement and surface deterioration due to the effects of traffic and environmental ageing, and contains a series of decision units used to determine how and when repair should be done. The prioritization of maintenance activities is commonly applied in pavement maintenance planning. A widely adopted practice is to express maintenance priority in the form of a priority index, computed by means of an empirical mathematical expression (the priority model) which is convenient to use (4) A number of pavement condition prediction models which simulate the deterioration process of road pavements and forecast their condition over time have been developed for use by road maintenance agencies in various countries. They include Defect Rating Index (5), Maintenance
Owalabi and Abiola
Needs Index (6), Present Serviceability Rating (PSR) and Surface Rating (SR) (7). Sometimes, two or more indices are combined and the resulting composite indices are used for ranking road pavements for maintenance operations. For example, the Florida Department of transportation uses three indices (Crack Index, Rut Index and Ride Index) to capture different attributes of pavement condition and a composite index (Pavement Condition Rating) which combines the other three indices to represent the overall pavement condition. Similarly, Physical Distress Score and Ride Score were combined by Oguara (8) to obtain an overall Pavement Condition Index. Traditionally, ranking of highway sections for maintenance operations in Nigeria have been based wholly on the experience and judgement of highway engineers and maintenance personnel. However, due to the randomness and complex interactions of the factors involved in pavement deterioration mechanism, this approach is inefficient, prone to errors and may lead to improperly scheduled maintenance activities. It is sad to note that most of the roads in the country are in various states of disrepair and many of them have become death traps and sources of economic drain in terms of high road users cost, loss of lives and property and loss of highway investment (9). The officials of various transportation departments wait for small potholes to deteriorate into craters and become death traps before they respond. As a road is constructed and opened to traffic, all sort of activities develop around it and the hopes of people in the locality are raised. These hopes and aspirations become dashed as the road deteriorates and its level of service diminishes. Against this backdrop, this paper presents the methodology for developing models for prioritizing road pavement maintenance in Nigeria using multiple linear regression and artificial neural network techniques and putting into consideration the interplay of all possible factors that affect pavement deterioration process, taking Lagos- Ibadan expressway-one of the most heavily trafficked roads in the country as case study. Regression is one of the most widely used and powerful analysis techniques for constructing performance models. Similarly, Artificial Neural Network (ANN), an emerging computational technique, enjoys extensive application in modelling of pavement performance due to its robustness and ability to be used as an arbitrary function approximation mechanism which learns from observed data (10), (11), (12), (13). Similar to a biological brain, provided with exemplar data, neural networks can be trained to learn the relationship underlying the data based on certain learning rules. The developed priority assessment model will serve as a tool for effective management of road pavements in Nigeria and other developing countries of the world with similar climatic, soil and traffic conditions. The Road in Focus Lagos-Ibadan expressway is one of the most heavily trafficked roads in Nigeria, linking Lagos (the economic nerve centre of Nigeria) with Ibadan (the largest city in West Africa). The road lies between longitude 30 30' and 30 48' East of Greenwich Meridian and latitude 60 40' and 60 50' North of the equator, in the south western part of the country. Its pavement is presently characterized by cracks, rutting, depressions and potholes making riding quality poor. There had also been at least three layers of asphalt concrete overlays on the road since inception raising the carriageway up to 125mm above the shoulder. Figure 1 shows the map of the road.
Paper ICMPA093 8th International Conference on Managing Pavement Assets
FIGURE 1 Map of Road under Study
MODEL PARAMETERS In other to determine the model parameters, data on the road under study was collected for four consecutive years to obtain a broad picture of pavement conditions under various climatic and traffic situations. The Information on pavement distresses such as length of cracks, rut depths and area of potholes was obtained through field survey and measurement. Values of Equivalent Single Axle Load (ESAL) were also determined from the data on traffic characteristics of the road using equation 1:
n = Qf (DDF)(LDF)(Pt)(Favg)……………………………………………………... (1) Where
n = number of cumulative ESALs to be carried by critical lane over design period Qf = total number of estimated future vehicles during the design period, in both directions. DDF = Directional Distribution Factor (between 0.4 and 0.6) LDF = Lane Distribution Factor Pt = percent trucks, and Favg = average 8,200 kg single axle load equivalence factor from the TRUKWT program..
TRUKWT program (14) was used to transform different types of truckloads to 8,200 kg ESAL.
Owalabi and Abiola
Pavement Condition Scores (PCS) for different sections of the road were obtained using the parabolic equation (equation 2) developed by the Pavement Evaluation Unit of the Nigerian Federal Ministry of Works and Housing and the Texas Research and Development Foundation (15). For each surveyed road section, a descriptor for the distress category (potholes, cracks, ruts or patches) was inputted into equation 1 to obtain the PCS. The PCS is based on a scale of 1 to 100, where 1 indicates a very poor pavement and 100, a pavement in excellent condition. x2 PCS = Wi × 1 − i ……………………………………………………………. (2) 25 Where Wi = weighting factors for each distress category. xi = severity level of distress. The weighting factors (Wi) adopted for this study as recommended by Pavement Evaluation Unit of Federal Ministry of Works as suitable for evaluation of Nigerian road networks are 40%, 30%, 20% and 10% for potholes, cracks, ruts and patches respectively. International Roughness indices (IRI) for the road were sourced from the Pavement Evaluation Unit of the federal ministry of Works, Nigeria. IRI is an expression of irregularities in pavement surface that adversely affect the quality of ride of vehicles and also their operational cost. Values ranging between 0 and 1.5 indicate a highway with no surface imperfections while values greater than 5 are indicative of a highway with a lot of surface imperfections. An attempt was made to painstakingly assign priority indices ranging from 0 to 100 to various sections of the expressway. An index of 0 represented a situation where no maintenance operation was yet needed and 100 a case where maintenance was long overdue. The collected data were used in developing the priority index models. The descriptive statistics of some key data used for model development are given in Table 1. TABLE 1 Descriptive Statistics of Data Variable Mean Range IRI year 1 3.00 1.77 IRI year 2 4.64 3.44 IRI year 3 6.77 6.55 IRI year 4 8.92 8.83 PCS year 1 56.65 76.80 PCS year 2 59.38 64.00 PCS year 3 40.63 67.20 PCS year 4 32.52 67.20 Loge ESAL 16.14 1.450 PRIORITY INDEX (PI) MODEL DEVELOPMENT Analysis of collected data revealed that there was a relationship between PCS, IRI, ESAL and the Priority Index. Thus PCS, ESAL and IRI were chosen as independent variables for the Priority Index models. PCS incorporates various road defects such as cracks, ruts, patches and potholes while IRI is an indicator of quality of ride and vehicle operational cost. ESAL is a measure of the severity of the loading to which a road pavement is subjected and also an indicator of the economic importance of a road (16). As a result of large values of ESAL, the natural logarithms of ESAL were used.
Paper ICMPA093 8th International Conference on Managing Pavement Assets
The Prioritization Index models were developed using Multiple Linear Regression (MLR) and Artificial Neural Network (ANN). The models were evaluated in terms of forecasting errors and goodness of fit and the results were compared. Multiple Linear Regression Multiple linear regression modelling technique attempts to obtain the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. For this study the relationship between the dependent variable and independent variables was represented by the following equation: PI = β 0 + β1 ( PCS ) + β 2 ( IRI ) + β 3 ( Log e ESAL) + e ……………………………………… (3) Where: β0 = value of constant term β1, β2 and β3 = Coefficients of the independent variables e = error term. The ordinary least square method in which the best-fitting line for the observed data is calculated by minimizing the sum of the squares of the vertical deviations from each data point to the line was used for estimating the unknown coefficients β0, β1, β2, β3, and e with the aid of SPSS software. The developed model is given in equation 4: PI = 38.593 − 0.468 PCS + 0.968 IRI + 3.016 Log e ESAL ………………………………….. (4)
Artificial Neural Network(ANN) The Neural Network toolbox embedded in MATLAB was used in developing the ANN model due to its flexibility in structure specification and implementation of various training algorithms.ANN are parallel information processing systems inspired by the structure and functional aspects of biological neural networks Development of the ANN architecture involved determination of input and output variables, number of hidden layers and number of hidden neurons in each hidden layer. A three layer feed-forward network composed of an input layer, a hidden layer and an output layer was chosen for the study. The multilayer architecture of the neural network ensures nonlinear mapping of input to output (17). The input function governing the behaviour of units in a layer is given by equation 5. net i = ∑ wij x j + µ i ………………………………………………………………………… (5) j
Where: neti = result of net input xi impacting on unit i wij = weights connecting neuron j to i xj = output from neuron j µi = threshold for neuron i Each unit takes its net input and applies an output/ activation function to it. For this study, the sigmoid function was employed due to its concise form and differentiability. The activation function is given in equation 6.
g (netinput ) =
1 1+ e
− netinput
……………………………………………………………... (6)
Owalabi and Abiola
The same variables used for the regression model were employed for the ANN model. The data was divided into three distinct sets namely: training, testing and validation sets. The training set was the largest (60% of data) and was used for learning purpose. The testing set (20% of data) was used in estimating the generalisation ability of the supposedly trained network, while the validation set (20% of data) was used to carry out a final check on the performance of the trained network. The back propagation method- a supervised learning algorithm was employed in this study. The method used the data to adjust the network’s weight and thresholds so as to minimize the error in its prediction on the training set. Execution of the back propagation algorithm involved two steps. First, the training patterns (a set of known input and output pairs) were fed into the input layer of the network. These inputs were then propagated through the network until the output layer was reached. The output of each neuron was computed by the activation function given in equation 6 and then the forward pre-processing error was calculated using equation 7: E=
1 ( y i − d i ) 2 ………………………….............................................................. (7) ∑ 2 i
where yi is the activity level of the ith unit in the top layer and di is the desired output of the ith unit. In the second step, the calculated error was minimized by back propagation through the network. During this process, the individual error contribution caused by each layer was computed and distributed backward and the corresponding weight adjustments were made to minimise the error. Using a gradient descending method, the weight adjustment is given by equation 8. Training was considered complete when the error was reduced to an acceptable level. Wk +1 = Wk − α k g k + β k (Wk − Wk −1 ) .................................................................................(8) Where, Wk+1 = vector of weights and biases at iteration k+1; Wk = vector of weights and biases at iteration k; Wk-1 = vector of weights and biases at iteration k-1; αk = learning rate at iteration k and βk = momentum rate at iteration k. An appropriate ANN architecture (7-20-1) having twenty hidden neurons was chosen because it generated the minimum training and testing errors after series of alternative networks were tested. This is illustrated in figure 2.
Paper ICMPA093 8th International Conference on Managing Pavement Assets
Hidden Layer (20 Neurons)
PCS year 1
.
PCS year 2
. PCS year 3
. .
IRI year 1
PI year 4
. IRI year 2
.
IRI year 3 LogeESAL
FIGURE 2 Developed ANN Architecture PERFORMANCE EVALUATION OF MODELS The Artificial Neural Network and multiple Linear Regression models were evaluated in terms of forecasting errors and goodness of fit. In determining the forecasting errors, the Average Absolute Error (AAE) and Root Mean Square Error (RMSE) were computed for both ANN and MLR models using equations 9 and 10 respectively. The AAE and RMSE indicate how close the predicted values of PI are to the observed values. n
AAE =
∑o i =1
i
− pi ............................................................................................................. (9)
n
n
RMSE =
∑ (o i =1
i
− pi ) 2 n
....................................................................................................... (10)
where n = number of observations; oi = observed value of observation i and pi = predicted value of observation i.
Owalabi and Abiola
To examine the goodness of fit of the models graphs showing the relationship between forecasted PI and observed PI were plotted for the ANN and MLR models. A linear regression analysis was carried out to determine the trend line equations and the R2 values were calculated. A trend line equation: y=x corresponds to a situation of perfect fitness (R2 of 1) in which the observed PIs are equal to the forecasted PIs. Table 2 shows the comparison of the performance of MLR and ANN models while figures 3 and 4 illustrate the relationship between the predicted and observed PIs for both models.
TABLE 2 Comparison of ANN and Linear Regression Models ANN MLR 0.029 1.499 AAE 0.060 1.571 RMSE 0.95 0.98 R2
y = 0.7231x + 33.068
100
R2 = 0.9757
Predicted PI (y)
95 90 85 80 75 70 65 60 55 40
50
60
70 Observed PI (x)
FIGURE 3 Goodness of Fit of MLR Model
80
90
100
Paper ICMPA093 8th International Conference on Managing Pavement Assets
y = 0.7315x + 32.273
100
2
R = 0.95 95
Predicted PI (y)
90 85 80 75 70 65 60 55 40
50
60
70
80
90
100
Observed PI (x)
FIGURE 4 Goodness of Fit of ANN Model SIGNIFICANCE OF RESULTS Comparison of the performance of the ANN and MLR models shows that they have high goodness of fit as indicated by R2 values of 0.95 and 0.98 for ANN and MLR respectively. However, the Average Absolute Errors and Root Mean Square Errors obtained for the MLR model were higher than those of the ANN model indicating that the ANN model is better than the MLR model in terms of forecasting accuracy. On the overall, both models can be used satisfactorily to prioritise highway pavement maintenance. The implications of the priority indices are explained in table 3. Roads having PIs less than 55 have low maintenance priority. However, a PI of 56 to 70 indicates a critical situation in which if the pavement condition might quickly degenerate if the appropriate maintenance operation is not carried out on time, thereby raising the cost. A PI of 100 is an indication of extremely high priority, and at that point, the road has failed and requires reconstruction. The ratings provide engineers and decision makers with a rational basis for effective planning, programming and budgeting for road pavements maintenance operations in Nigeria and other developing countries of the world with similar climatic, soil and traffic conditions, using appropriate technology. TABLE 3 Priority Index Ratings PI Rating 0 – 35 Extremely Low 36 – 45 Very Low 46 – 55 Low 56 – 70 Critical 71 – 80 High 81 – 90 Very High 91- 100 Extremely High
Maintenance Required Little or no maintenance Routine maintenance Thin Overlay Thick Overlay Increasing thicker Overlay Surface reconstruction Reconstruction with possible sub grade stabilization
Owalabi and Abiola
CONCLUSION The efforts made in developing Priority Index models for pavement management system in Nigeria based on artificial neural network and multiple linear regression techniques have been discussed. Comprehensive investigations carried out on the expressway linking Lagos (the economic nerve of Nigeria) with Ibadan (the largest city in West Africa) showed that Pavement Condition Score, International Roughness Index and Equivalent Single Axle Load were germane to the developed models. These variables were combined into a convenient scale ranging from 0 to 100 to obtain a single priority index. The R2 values of 0.95 and 0.98 and the relatively small forecast errors show that both the Artificial Neural Network and Multiple Linear Regression model can be used satisfactorily to prioritize highway pavement maintenance. The results of this research will provide a method of effectively managing road pavements in Nigeria and other developing countries of the world with similar climatic, soil and traffic conditions. REFERENCES 1. Olugbekan, S. Road Development in Nigeria: Yesterday, Today and Tomorrow. The Nigerian Engineer, vol. 33, no 3, 1995, pp. 12-18 2. Shafik, J and A.H. Mehar. Development of a Pavement maintenance Management System (PMMS) for Gaza City. Journal of the Islamic University of Gaza (Series of Natural Studies & Engineering) Vol.13, No.1, 2005, pp. 119-138 3. Owolabi, A.O. Toward an Improved Road Network for the Survival of Nigerian Economy. Proceedings of the Maiden National Engineering Conference, Bauchi, 1996, pp.121-130. 4. Abiola, O.S. Pavement Performance Models for Lagos-Ibadan Express Road. Unpublished PhD Thesis, University of Agriculture, Abeokuta, Nigeria, 2010. 5. Snaith, M. S. and J. C. Burrow. Priority Assessment. In Transportation Research Record: Journal of Transportation Research Board No. 951, Washington, D. C., 1984, pp. 9-13. 6. Theberge, P. E. Development of Mathematical Models to Assess Highway Maintenance Needs and Establish Rehabilitation Threshold Levels. In Transportation Research Record: Journal of Transportation Research Board No. 1109, Washington, D. C., 1987, pp. 27-35. 7. Minnesota Department of Transportation. Distress Identification Manual. Office of Materials and Road Research, Pavement Management Unit, 2001. 8. Oguara, T.M. A Simple Highway Pavement Maintenance Management System. The Nigeria Engineers, Journal of the Nigerian Society of Engineers, Vol. 26, No. 1, 1991, pp. 1-13. 9. Abiola, O.S., Owolabi, A.O., Odunfa, S.O. and A. Olusola. Investigation into Causes of Premature Failure of Highway Pavements in Nigeria and Remedies. A paper presented at the Nigeria Institution of Civil Engineers (NICE) conference, 2010 10. Yang, J., Lu, J.J., Gunaratne, M and B. Dietrich. Comparison of Recurrent Markov Chains and Neural Networks for Modelling the Deterioration of Crack Conditions of Flexible Pavements. A paper presented at the TRB 85th Annual meeting, 2006, pp 18-25. 11. Yang, J., Lu, J.J., Gunaratne, M and Q. Xiang (2003). Forecasting Overall Pavement Condition with Neural Networks, Application on Florida Highway Network. In Transportation Research Record: Journal of Transportation Research Board No. 1853, National Research Council, Washington, D.C., 2003, pp. 3-12. 12. Lou Z., M. Gunaratne , J. J. Lu, and B. Dietrich. Application of Neural Network Model to Forecast Short-term Pavement Crack Condition: Florida Case Study. ASCE Journal of Infrastructure Systems, 7(4), 2001, pp. 166-171. 13. Owusu-Ababio S. Application of Neural Networks to Modeling Thick Asphalt Pavement Performance. Artificial Intelligence and Mathematical Methods in Pavement and Geomechanical Systems, 1998, pp. 23-30.
Paper ICMPA093 8th International Conference on Managing Pavement Assets
14. FMWH (1986): A Program to Determine Average Truck Axle Equivalence Factors from Axle Load survey Data. Nigerian Federal Ministry of Works and Housing’s Pavement Evaluation Unit, 1986. 15. Texas Research and Development Foundation. Development of Pavement Evaluation and Rehabilitation Design Procedure for Nigeria. Final project report-Phase II, 1986. 16. Oguara, T.M. Pavement Management Systems. Proceedings of the NSE National Workshop on Highway Maintenance, 2003, pp. 49-66 17. Sharma, S and A. Das. Back calculation of Pavement Layer Moduli from Falling Weight Deflectometer Data Using an Artificial neural network. Canadian Journal of Civil Engineering. Vol. 35, 2008, pp. 57-66.
