Adaptive optimization methods in system-level bridge management

In 2012, over 25% of the bridges in the United States were rated as structurally deficient or functionally obsolete . Moreover, 35% of bridges are serving beyond their theoretical design lifespan and the number has been projected to increase over the next decade. The imperative needs of improving the overall condition of the bridge system has been impeded by the shortage of funding available for bridge repairs and maintenance. In 2006 the gap between Federal Highway Administration's (FHWA) estimates to eliminate the bridge maintenance backlog and the actual appropriations to bridges for repairs and maintenance from the Highway Bridge Program was $43. 4 Billion. In 2009, the gap increased to $65. 7 Billion. Such conflict has made effective bridge management more critical than ever. In bridge management, agencies collect bridge condition data and develop deterioration models that predict the bridges' future conditions and associated costs, based on which maintenance, rehabilitation and reconstruction (MR&R) decisions are made. It is therefore critical to have accurate deterioration models. However, limited availability of data and incomplete understanding of the deterioration process result in inaccurate models, which lead to sub-optimal MR&R decisions and significant cost increases. To address the inaccuracy stemming from limited bridge condition data, researchers have proposed Adaptive Control (AC) methods that update the deterioration models successively as new data become available. The underlying belief is that agencies can obtain more accurate deterioration models through updating and subsequently improve their MR&R decisions and achieve cost savings. State-of-the-art bridge management systems, such as Pontis, use a class of AC procedures known as Certainty Equivalent Control (CEC). The procedure used in Pontis updates the transition probabilities (i.e. , the parameters of the component deterioration models) after each condition survey, and uses the updated probabilities in subsequent planning of MR&R decisions. Unfortunately, CEC does not necessarily lead to more accurate models, or guarantee savings in system costs; in other words, updating of the type in Pontis is not necessarily beneficial. In the present dissertation, an AC method, Open-Loop Feedback Control (OLFC), is proposed for system-level bridge management. The performance of OLFC and the Pontis CEC is tested in a numerical study and empirical results show that OLFC has superior performance with respect to two criteria. In terms of improvement in model accuracy, the Pontis CEC yields systematic bias in model parameter estimates and therefore does not improve model accuracy. In all testing scenarios, the resulting deterioration models lead to faster deterioration than the true models. OLFC, on the other hand, results in consistent convergence to the true models in all testing scenarios and improves model accuracy. When evaluated by system costs, the Pontis CEC consistently results in higher system costs than the no-updating scenario. The increases are on the order of $180 Million at the level of the State of California. To the contrary, updating with OLFC consistently achieves system costs savings compared to the no-updating scenario, and results in system costs that do not differ significantly from the system costs when true models are used for MR&R decision-making. In addition, a computationally tractable optimization routine is developed for MR&R decision-making. The routine ensures strict conformity to system budget constraints and achieves satisfactory computational efficiency even given high levels of heterogeneity in bridge systems.