^{1}

^{2}

^{3}

^{4}

^{3}

^{1}

^{2}

^{3}

^{4}

Faulting prediction is the core of concrete pavement maintenance and design. Highway agencies are always faced with the problem of lower accuracy for the prediction which causes costly maintenance. Although many researchers have developed some performance prediction models, the accuracy of prediction has remained a challenge. This paper reviews performance prediction models and JPCP faulting models that have been used in past research. Then three models including multivariate nonlinear regression (MNLR) model, artificial neural network (ANN) model, and Markov Chain (MC) model are tested and compared using a set of actual pavement survey data taken on interstate highway with varying design features, traffic, and climate data. It is found that MNLR model needs further recalibration, while the ANN model needs more data for training the network. MC model seems a good tool for pavement performance prediction when the data is limited, but it is based on visual inspections and not explicitly related to quantitative physical parameters. This paper then suggests that the further direction for developing the performance prediction model is incorporating the advantages and disadvantages of different models to obtain better accuracy.

Transverse joint faulting is the common type of distress for jointed concrete pavement, which has negative effect on driving safety and resulting costly rehabilitation [

The paper first presents a comprehensive literature review that discusses previous work on the pavement performance prediction and its classification. Three different models including MNLR model, ANN model, and MC model are briefly introduced. These models are quantitatively evaluated and compared using a set of concrete pavement survey faulting data with varying design features, traffic, and climate data. These survey faulting data are taken for evaluating the performance of the three models. The results of these prediction models are presented. Then the strengths and weaknesses of these models are surveyed. Finally, the areas of concern in performance prediction and potential for future work are addressed. Suggestions for future research work are proposed by incorporating the advantages and disadvantages of different models.

According to the prediction results, the performance models can be divided into deterministic and probabilistic models. For the deterministic models, future condition of pavement section was predicted as the exact serviceability value or pavement condition index with the previous information of the pavement. The probabilistic models predict the performance of a pavement by giving the probability with which the pavement would fall into a particular condition state, describing the possible pavement conditions of the random process [

Deterministic models are perhaps the most common prediction method. The main advantages of using a deterministic model are easy to understand and develop. Disadvantage of deterministic models is that the regression equation may express the deterioration of a group of pavements well but do not predict the condition of individual sections very well [

Mechanistic models are based on the principles of mechanics of materials and use the input of wheel loads to predict the mechanistic responses, such as stress, strain, and deflection. The mechanistic models provide valuable insights into the performance of the pavements. There are some researchers focused on mechanistic model. Chua et al. established the distress model that defined a performance function in which the level of distress may be determined as a function of the controlling structural response according to some damage criterion [

Empirical approach is widely used in the prediction area, but it suffers from the limitations associated with the scope and range of available data. As an empirical model, the most important pavement performance model is created by American Association of State Highways Officials, and it is based on the results of actual road test [

There are also some JPCP transverse joint faulting empirical models developed under previous research. Yu develops two separate JPCP faulting models for doweled and nondoweled pavements as part of FHWA RPPR project. The development of these models identifies several pavement design features and site conditions that significantly affect transverse joint faulting. Teng develops separate mechanistic-empirical JPCP faulting models for doweled and nondoweled pavements for American Concrete Paving Association (ACPA) [

Mechanistic-empirical models are those in which responses predicted by mechanistic models were correlated with usage or environmental variable such as loadings or age to predict observed performance, such as distress. Most mechanistic-empirical models are used for the project level. Few were used for the network level. However, as the speed and capacity of microcomputers increase and the cost of collecting more structural information decreases, these mechanistic-empirical models are used more and more in prediction models [

In addition, especially for faulting model, there are also some research works on this. Under the FHWA Nationwide Pavement Cost Model (NAPCOM) study, Owusu-Antwi develops the following mechanistic-empirical faulting model for doweled and nondoweled JPCP. Titus Glove recalibrates NAPCOM JPCP transverse joint faulting model by LTPP data. But this model is recalibrated using LTPP data only [

Pavement performance is a stochastic process that varies widely with several factors, many of which are generally not captured by available data. Therefore, probabilistic models are often used to characterize performance. The following list summarizes the major advantages and disadvantages associated with probabilistic model [

The major advantages associated with probabilistic modeling approaches are as follows:

They provide a convenient way to incorporate field data into a prediction model.

They leave it to subjective inputs of experienced agency personnel.

They provide a mathematical means for obtaining performance predictions.

They provide a probabilistic distribution of the expected condition value with time, which will be required to identify those sections performing significantly differently than would be expected.

They reflect performance trends obtained from field observations regardless of nonlinear trends with time.

The major disadvantages associated with probabilistic models are listed:

They do not provide any guidance as to the physical factors that contribute to the change in condition.

They are time independent so that the probability of changing from one condition state to a lower condition state is not influenced by the age of the pavement and the probabilities are constant over time.

Probabilistic models include Markov models, survival analysis, and Bayesian approach.

Markov Chains based on the concept of probabilistic cumulative damage are the most commonly used stochastic techniques for predicting the performance of various infrastructure facilities such as highways and bridges. Lounis and Madanat combine the desired practicality of Markov Chain models and the accuracy of mechanistic models to improve the effectiveness of bridge maintenance management systems [

Survival analysis is generally defined as a set of methods for analyzing data where the outcome variable is the time until the occurrence of an event of interest, which has been used in the performance prediction. Survival methods include parametric, nonparametric, and semiparametric approaches. Parametric methods assume that the underlying distribution of the survival times follows certain known probability distributions. Weibull model is the popular one. Mishalani et al. develop a probabilistic model with Weibull distribution function in different areas [

Bayesian approach can be used with most approaches, except the truly mechanistic models [

ANN models are varied in implementation and interpretation. An ANN is a mathematical representation of how mammalian brains were believed to function [

The advantage of artificial neural networks is their ability to be trained on previous situations. Training is required to continuously adjust the connection weights until they reach values that allowed ANN to predict outputs that are very close to the actual outputs while being able to be generalized well on new cases [

Some of the disadvantages for ANN are as follows [

Prohibitively slow training times for large networks

Problems with previously unrepresented patterns in supervised training

Ideal network architectures and training algorithms remaining part of current research

Problems with local minima in training

Lack of ability to explain mechanisms in predictive models.

ANN can be used in the performance prediction in different areas. Tack and Felker used the ANN method to predict the performance and it is provided that this method performs well [

The overview of existing literature reflects some prominent problems in the prediction area. First, there are many types of prediction models. The advantages and disadvantages for each type are also introduced. But, based on the advantages and disadvantages, it is hard to estimate and compare the predicted performance for each model. Many models are able to perform well only in a dataset but not in different dataset. Hence, calibrations are required to adjust the parameter inputs so that the models can perform reasonably. Second, not all the prediction models can be used in the special case, for they may lack some parameters that cannot be acquired or there are not enough actual data to establish the model we are choosing. So evaluating the effectiveness of existing models on the same actual dataset that had variable design features, traffic, and climate is essentially useful for researchers.

For JPCP faulting models, existing researches identified a number of distinct relationships between faulting and traffic, age, and various climatic, site, and pavement design variables. All of the models indicate that design features have a significant effect on faulting. These models are almost either empirical models or mechanistic-empirical models, which also suffers from the disadvantages of these types of models. But the review of these developed transverse joint faulting models identified a number of variables that have been consistently found to significantly influence faulting.

Hence, in this paper we make a quantitative comparison of three different prediction models with actual survey data being conducted. Two are the JPCP faulting prediction models, while the other two are the prediction methods that can be used in this faulting prediction. It is hoped that the comparison results will provide crucial information for researchers and state DOTs on developing enhanced pavement performance models that can lead to a more accurate prediction for maintenance system and design system.

Actual pavement survey data used in the models are taken from interstate highway with varying design features, traffic, and climate data ([

Faulting distribution of training set and prediction set.

Based on the modeling methodology, it is found that different types of models have different characteristics. It is important to understand the feasibility of each prediction model by comparing their results. Since pavement performance deterioration process is complex and not completely understood, the pure mechanistic models developed so far cannot accurately predict the realistic pavement performance. Therefore, mechanistic model is not chosen in the paper.

MNLR model is a primal, useful technique which has been applied in all fields of engineering knowledge. ANN model, neither deterministic nor probabilistic, can be used in all the performance predictions and performs well [

Based on the previous study, eight important factors that have greater impacts on faulting are used in the modeling [

For the reasons listed above, MNLR model, ANN model, and MC model are used for comparative study. The modeling methods were described as follows.

Equation (

Artificial neural network (ANN) is mathematical models and algorithms designed to mimic the information processing and knowledge acquisition that takes place inside human brain. ANNs are capable of learning by example. The back propagation neural network (BPNN) developed by Rumelhart et al. is the most representative learning model for the ANN. BPNN is widely applied in a variety of scientific areas, especially in applications involving diagnosis and prediction [

Markov Chain (MC) model is a probabilistic model widely spread in the world. A Markov Chain is a special case of the Markov process whose development can be treated as a series of transitions between certain states. A stochastic process is considered as first-order. The probability of the future state in the Markov process depends only on the present state [

Transition probabilities are obtained from the increment of condition data to provide a better prediction [

When the predicted value is gotten, it is applied in next year’s prediction. Then the new transition probability matrix with the predicted value is computed and next year’s predicted value is obtained.

Three prediction models are used to evaluate the capability of different models for predicting the pavement performance. Here we present the results of three prediction models with 36 records. For comparing the capabilities of these proposed models, measured faulting and predicted faulting are both used. A summary of experimental results is presented in Figure

Predicted faulting versus measured faulting.

MNRL model

ANN model

MC model

Figure

Figure

Figure

Root mean squared error (RMSE) and mean absolute error (MAE) are used to quantify the prediction accuracy [

RMSE and MAE of predicted and measured values for the three prediction models are compared. As shown in Figure

Quantitative comparison of different models.

Figures

Although many researchers have developed pavement performance prediction models, the accuracy of the model is still a challenge. It is difficult to effectively compare the performance prediction models. Most researchers just focus on the optimization of the prediction model, but some researches do some work on the comparison of different models [

Based on the test results, it is concluded that MNLR model performs the worst and MC model performs the best. ANN model and MC model perform well, and the difference of the prediction capabilities of these two is not obvious. MC model shows its promising performance compared with other models when data is limited. It is concluded in our comparative study that MC model is a promising model in prediction, but it is just based on its past condition and not related to the design feature and other environment factors. This characteristic makes it only applied in pavement maintenance, not in pavement design. ANN model performs better than MNLR model. MNLR model for its low predicted capacities needs more data to calibrate and ANN model also needs more data for training the network to improve its accuracy.

In the future, more prediction models can be tested using the actual survey data and compared with each other effectively. A bigger dataset that is composed of more complex situation is also needed in the model comparison. For different models having different effectiveness and applicability, it is important to find a developing and improving model to predict the pavement performance. Further direction for developing the performance prediction model is incorporating the advantages and disadvantages of different models to obtain better accuracy.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This paper is sponsored by National Natural Science Foundation of China [51508064, 51408083], China Postdoctoral Science Foundation [2014M562287], Chongqing Science and Technology Commission [cstc2014jcyjA30018, cstc2016jcyjA0128], Department of Human Resource and Social Security of Chongqing [Xm2014094], and State and Local Engineering Laboratory for Civil Engineering Material of Chongqing Jiaotong University [LHSYS-2016-01].