Estimation of Latent Infrastructure Performance Models Using Time Series Analysis

We propose state-space specifications of autoregressive moving average models and structural time series models as a framework to develop and estimate incremental performance/deterioration models for transportation infrastructure facilities. State-space specifications are consistent with the latent performance modeling approach of (1), which means that they rigorously account for uncertainty in forecasting infrastructure condition when data are gathered using multiple technologies. Moreover, these specifications fit the optimization model of (2) to support maintenance and rehabilitation decision-making, which means that they constitute an alternative to the use of Markovian transition probabilities. Through an empirical study, we verify that the proposed methodology can be used to generate infrastructure condition forecasts when data are gathered with multiple technologies. The models in the study are estimated using deflection and pressure measurements generated by sensors embedded in an asphalt pavement. Analysis of the results corroborates earlier findings that question the universal validity of the Markovian assumption in the context of infrastructure deterioration. Chu and Durango-Cohen 4 INTRODUCTION Optimization models to support maintenance and rehabilitation (M&R) investment decisions for transportation infrastructure must evaluate both the short and long-term economic consequences associated with these investments. This involves processing data related to current infrastructure condition and using them to forecast the effect of M&R decisions on future condition. The economic consequences associated with these decisions are then predicted by assuming a correspondence between infrastructure condition and costs. Information about current infrastructure condition is obtained by collecting distress measurements. Examples of distresses on transportation infrastructure include roughness, type and extent of cracking, rut depth and profile, extent of surface patching, on pavements; and cracking, spalling, and chloride contamination on bridge decks. Information about future condition, i.e., condition forecasts, is generated with performance models. A performance model is a statistical expression that relates condition to a set of explanatory variables such as design characteristics, traffic loading, environmental factors, and history of M&R investments. From the previous paragraph, it follows that the ability to generate accurate condition forecasts is an essential part of developing efficient M&R policies. (1) introduced the latent performance modeling approach to rigorously address the problem of forecasting condition when multiple technologies are used to collect condition data. The key feature of the approach is that a facility's condition is represented by latent/unobservable variables that capture the ambiguity that exists in defining, and consequently in measuring infrastructure condition. Distress measurements are related to the latent condition through a measurement error model that accounts for systematic and random errors in the data-collection process, as well as, for the relationships between different technologies and distress measurements. Latent performance models also include a structural model that describes the relationship between a set of explanatory variables and infrastructure condition. Empirical studies by (1) and by (3) have shown that latent performance models are appropriate to generate condition forecasts of transportation infrastructure, i.e., the goodness-of-fit measures are better than those reported using other statistical methods. This, in turn, lead (4) to include latent performance models in a framework to support M&R decision-making by formulating the underlying optimization problem as a latent Markov Decision Process (MDP). While providing a rigorous framework to account for uncertainty (in the deterioration and in the data-collection process), the latent MDP suffers from computational limitations that make it impractical to support M&R decision-making for transportation infrastructure when multiple technologies are used simultaneously to measure (different) distresses. As discussed in (5), these limitations are derived from the fact that the state and decision variables in the model are defined over discrete sets. More importantly, these limitations are of practical significance as a plethora of advanced inspection technologies, e.g., sensors, satellite imaging, video, laser, and radar, have become commonplace in evaluating and measuring distresses on transportation infrastructure. To address the computational shortcomings of the latent MDP, (2) proposed a discrete time, stochastic optimal control framework to support M&R decision-making when condition data are gathered using multiple (advanced) inspection technologies. The framework consists of two components: a state-estimation problem that involves processing arrays of condition data and using them to develop condition forecasts; and an optimization problem whose solution yields M&R policies. The variables in the framework are defined over continuous spaces and the deterioration process is modeled as a time series. Time Series Analysis provides a broad class of incremental performance models that can be used to represent the evolution of Chu and Durango-Cohen 5 infrastructure performance, and that can be included in the aforementioned framework to support M&R decision-making. This paper complements the work in (2). Specifically, we describe and compare two classes of time series models to represent the evolution infrastructure performance: AutoRegressive Moving Average (ARMA) models and structural time series models. We consider state-space specifications of the models because they are consistent with the latent performance modeling approach of (1), and because they fit the optimization framework of (2). Through an empirical study, we verify that the proposed methodology is valid to forecast infrastructure performance when condition data are gathered with multiple technologies. The models in the study were estimated using deflection and pressure measurements generated by sensors embedded in an asphalt pavement section. The data was collected and generously provided by MnRoad, the road research division of the Minnesota Department of Transportation. The estimation results show that the history of the deterioration process is statistically significant, which means that the Markovian assumption that underlies the estimation of transition probabilities for the (latent) MDP framework may not be appropriate. The remainder of the paper is organized as follows. LITERATURE REVIEW provides an overview of the MDP approach and discusses characteristics that make this approach statistically unattractive to forecast the performance of transportation infrastructure. We also review state-space specifications of time series models. METHODOLOGY describes the methodology used in this paper which consists of the formulation and estimation of the infrastructure performance models as ARMA or structural time series models. EMPIRICAL STUDY details the empirical study used to validate the methodology. A summary of the contributions of the paper is provided in CONCLUSIONS.