Award Date

May 2017

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering and Construction

First Committee Member

Alexander Paz

Second Committee Member

Mohamed Kaseko

Third Committee Member

Moses Karakouzian

Fourth Committee Member

Pramen P. Shrestha

Fifth Committee Member

Ashok K. Singh

Number of Pages



The existing state-of-the-art approach of Clusterwise Regression (CR) to estimate pavement performance models (PPMs) pre-specifies explanatory variables without testing their significance; as an input, this approach requires the number of clusters for a given data set. Time-consuming ‘trial and error’ methods are required to determine the optimal number of clusters. A common objective function is the minimization of the total sum of squared errors (SSE). Given that SSE decreases monotonically as a function of the number of clusters, the optimal number of clusters with minimum SSE always is the total number of data points. Hence, the minimization of SSE is not the best objective function to seek for an optimal number of clusters.

In previous studies, the PPMs were restricted to be either linear or nonlinear, irrespective of which functional form provided the best results. The existing mathematical programming formulations did not include constraints that ensured the minimum number of observations required in each cluster to achieve statistical significance. In addition, a pavement sample could be associated with multiple performance models. Hence, additional modeling was required to combine the results from multiple models.

To address all these limitations, this research proposes a generalized CR that simultaneously 1) finds the optimal number of pavement clusters, 2) assigns pavement samples into clusters, 3) estimates the coefficients of cluster-specific explanatory variables, and 4) determines the best functional form between linear and nonlinear models. Linear and nonlinear functional forms were investigated to select the best model specification. A mixed-integer nonlinear mathematical program was formulated with the Bayesian Information Criteria (BIC) as the objective function. The advantage of using BIC is that it penalizes for including additional parameters (i.e., number of clusters and/or explanatory variables). Hence, the optimal CR models provided a balance between goodness of fit and model complexity. In addition, the search process for the best model specification using BIC has the property of consistency, which asymptotically selects this model with a probability of ‘1’.

Comprehensive solution algorithms – Simulated Annealing coupled with Ordinary Least Squares for linear models and All Subsets Regression for nonlinear models – were implemented to solve the proposed mathematical problem. The algorithms selected the best model specification for each cluster after exploring all possible combinations of potentially significant explanatory variables. Potential multicollinearity issues were investigated and addressed as required.

Variables identified as significant explanatory variables were average daily traffic, pavement age, rut depth along the pavement, annual average precipitation and minimum temperature, road functional class, prioritization category, and the number of lanes. All these variables were considered in the literature as the most critical factors for pavement deterioration.

In addition, the predictive capability of the estimated models was investigated. The results showed that the models were robust without any overfitting issues, and provided small prediction errors. The models developed using the proposed approach provided superior explanatory power compared to those that were developed using the existing state-of-the-art approach of clusterwise regression. In particular, for the data set used in this research, nonlinear models provided better explanatory power than did the linear models. As expected, the results illustrated that different clusters might require different explanatory variables and associated coefficients. Similarly, determining the optimal number of clusters while estimating the corresponding PPMs contributed significantly to reduce the estimation error.


Bayesian Information Criterion; Cluster analysis; Optimization; Pavement Management System; Regression analysis; Simulated Annealing


Civil Engineering | Statistics and Probability