Stochastic processes for bridge deterioration assessment

Transcription

1 Stochastic processes for bridge deterioration assessment Palitha Manamperi, Wije Ariyaratne and Siva Perumynar Roads and Traffic Authority of NSW Khalid Aboura, Bijan Samali and Keith Crews Centre for Built Infrastructure Research Faculty of Engineering and Information Technology The University of Technology Sydney ABSTRACT The Roads and Traffic Authority of NSW (RTA) has over 5000 bridges in the road network under its jurisdiction. These structures were built from different materials, at different times, under different design codes with different articulations and are exposed to different environments. The levels and rate of deterioration of these structures vary greatly and are dependent on the effects of age, environment, magnitude and frequency of heavy traffic and construction quality. These factors make the management of these structures a real challenge to the RTA. In order for the RTA to improve the management of these bridge assets, the RTA is working with the University of Technology Sydney (UTS) to develop a statistical model to predict the future condition of bridges using the condition inspection data collected over the last 15 years. This paper will report on findings of the study conducted to identify a suitable model for prediction of future condition of bridges based on the available inspection data. The gamma process is considered in the development of the predictive model for the life of bridge components. In addition to the gamma process application, observations are made on the distribution of deterioration at different times that could lead to other stochastic processes for modeling time-dependent structural deterioration. BACKGROUND The Roads and Traffic Authority (RTA) manages more than 5000 bridges in its network. These bridges were built over the last 125 years using various materials and technology and to loading standards. These structures are exposed to different environments and subjected to various loading patterns and frequencies. In order to manage these bridges and ensure their safety the RTA has established a systematic condition rating procedure which rates bridge elements. The RTA has condition rated its bridge stock since 1992 and recorded condition rating data in its corporate data base, Bridge Information System (BIS). While the RTA has sufficient information to manage current bridge issues,

2 RTA does not have the capability to predict future condition of bridges. Therefore, RTA established a research and development project in collaboration with the University of Technology Sydney (UTS) to determine the following: The future condition of bridges for a given investment (intervention). The funding required to maintain at a pre-determined condition state of bridges. The aim of the collaborative research and development project with the UTS is to make full use of the condition rating information available in the RTA Bridge Information System, capture the deterioration of the bridge elements with time in a mathematical model and develop a rigorous and reliable statistical model to predict the future conditions of bridges. In order to manage the project effectively the following staged approach was adopted: Phase 1 Literature Review Phase 2 Analysis of Bridge Inspection data Phase 3 Development of a condition model Phase 4 Study of fit of stochastic deterioration theory and development of predictive model. LITERATURE REVIEW The UTS have reviewed various available models in the literature for determining structural deterioration of bridges and found the following model approaches: the simplest approach of lifetime analysis with probability distributions using the notion of failure rate function, the use of a Markov process model initially applied in bridge management systems, the extension of the idea of a reliability index introducing a time factor, the incorporation of the more modern concept of a random deterioration rate, and the use of mathematically and statistically sophisticated stochastic process approach. Failure Rate Model A lifetime distribution f(t) such as the Weibull distribution is used to model uncertainty in the time to failure of the structure. van Nootwijk and Klattter (2002) [1] determine lifetime distributions for concrete bridges and compute the expected cost of replacing a bridge stock. The uncertainty in the lifetime of a bridge is represented with a Weibull distribution. Markov Model In the Markov model, the deterioration takes discrete states and is modeled using a Markov Chain. The transition from one state to the other are characterised by transition probabilities. The transition probabilities can be determined from expert judgement or empirical observation. The Markov model is used in the bridge management system Pontis [2]. The Markov model provides a framework that accounts for the uncertainty and the bridge

3 maintenance optimisation can be solved using mathematical programming. The Markovian approach used in bridge management systems had several limitations, among these; Element deterioration is assumed to be a single step function Transition rates among condition states of a bridge element are not time dependent and Bridge system condition deterioration is not explicitly considered (see Madanat, Mishalani & Ibrahim (1995) [3]). Reliability Index The time-dependent Reliability Index approach relies on the fact that bridges built to the same standards and specifications require different maintenance. The notion of reliability index was used in code calibration and reliability based analysis and design. This approach is mostly used to simulate lifespan of a structure for scheduling of maintenance. The Stochastic Process Traditionally, bridge management systems were designed using a Markov chain model for the discrete states deterioration. While there are some promising models that have been proposed by researchers, most models are found to be simplistic and based on limited data. Therefore, their use as a predictive model is both limited and questionable. Our study concluded that the vast amount of condition rating data available to the RTA will allow the development of a refined, well tested and reliable predictive model for addressing the RTA needs. Time-based deterioration models introduce the time factor in modeling deterioration. Time based models consider the time between condition changes. These transition times are defined as the times needed for a structure or an element of the structure to change condition. If the condition states are discrete, then the transition times can vary from one structure to another due to the inherent stochastic nature of the deterioration process and the existence of explanatory variables (Morcous & Akhnoukh, 2006) [4]. The Markov model, a state-based deterioration modeling approach, as applied in Pontis for example, assumes that the time of transition from one state to another is distributed exponentially. This assumption allows the application of the Markov model and the associated memorylessness by which an old unit of element and a newer one are equally likely to move to the next condition state (Golabi & Shepard, 1997) [5]. A departure from the Markov assumption in order to take into account the time factor is the reliability based approach of Estes and Frangopol (1999) [6]. They proposed a system reliability based approach for optimizing the lifetime repair strategy for highway bridges. The method consisted of identifying relevant failure modes of the bridge, developing a system model of the overall bridge as a series-parallel combination of individual failure modes and computing the system reliability of the bridge. The idea is also implemented by Yang, Frangopol and Neves (2004) [7], using lifetime distribution functions to evaluate the overall system probability of survival of existing bridges over a

4 time period. The bridges are modeled as systems of independents and correlated components. The approach applies mainly to structures where the times to reach target failure can be estimated. The system reliability approach focuses on the safety and reliability aspects. However, it is not applicable in situations where severe deterioration of the structure elements is not observable in sufficient amount of data. It is often the case that structures are maintained so that severe deterioration occurs rarely. In addition, the assumption of independence of the lifetimes of elements of bridges is a hard one to make, while modeling correlation is an even harder task as stated in Yang, Frangopol & Neves (2004) [7]. Bridges suffer from a variety of degradation factors. They are the environment the bridge is subject to, the traffic load it carries daily, the quality and time of its construction and they all contribute to the deterioration process of the bridge. These factors have often been considered either in stratifying data or as explanatory variables in regression models. There are inherent deterioration processes in the materials of bridges, often due to the environment. These degradation processes do vary in influencing the deterioration of different structures, are time dependent. In addition the deterioration rates may not be constant. A statistical model that would consider non-linear rates of deteriorations would be more appropriate to model the deterioration of structures. Time dependent stochastic processes are sequences of random variables that can be used to model the deterioration at given points in time. The gamma process is a stochastic process proposed by Abdel-Hameed (1975) [8] for gradual deterioration modeling. A stochastic process such as the gamma process can capture the temporal variability of degradation. van Noortwijk (2009) [9] provides a comprehensive overview of the use of the gamma process in the maintenance of structures. ANALYSIS OF BRIDGE CONDITION DATA The RTA has over 5000 bridges under its control. It inspects these bridges regularly and has been recording condition rating of bridge elements in its corporate database since The RTA bridge condition rating system rates each bridge element of a bridge. Generally a bridge consists of 8 to 12 elements. Since 1992, the RTA has collected around 7 to 8 sets of condition rating data for each bridge every 2 to 3 years. The condition ratings of these elements are carried out in accordance with the RTA Bridge Inspection Procedure Manual which consists of three parts: A. Inspection Procedure for each element B. Description of each condition state for these each elements C. Photographs of element in different states The BIS database carries an accurate information of Level 2 inspections. As of July 2007, the BIS contained over 230,000 records spanning more than 15 years for 4945 bridges against 66 element types. While 15 years is a long time, compared to the design life of a bridge (100 years) it is relatively short. The data maybe not enough to build a statistical model for each structure. However it is considered that there is enough data to build statistical models

5 for elements that will enable evaluation and prediction. The work is divided into two parts: 1. Structure condition model based on element conditions 2. Statistical model for element behaviour over time. The RTA bridge condition rating system rates the quantity of each bridge element in different condition states and records it in the BIS. There are five condition states for steel elements, four for concrete and timber elements and three states for other ancillary elements. Since July 2007 this system has been changed to have four condition states for all elements. For example a concrete deck slab (CDSL) could have 60% in condition 1, 20% in condition 2, 15% in condition 3 & 5% in condition 4 (condition 4 being the worst condition). Even with today s computers capability of analysis of data, in the form it is recorded, it is not an easy task to analyse. Therefore to study the behavior of different elements and bridges it is necessary to develop consistent models for element condition and bridge condition. Analysis of the data confirmed that the use of a traditional Markov approach for developing a deterioration model will not correctly estimate future condition. This is due in part to the fact that the RTA bridges are normally maintained to remain above certain condition level (usually condition state 2). This means that some transitions in the Markov Chain will be rarely observed, leading to a poor estimation of their probabilities. DEVELOPMENT OF A CONDITION MODEL The Element condition The following models were examined before selecting a model to define the element condition index. Model 1. Defective Quantity Model 2. Weighted Deterioration Model 3. Defects and Severity factor Model 4. California Bridge Health Index The above models use the same condition data weighted in different ways and provide similar patterns of deterioration trends of elements over time. Therefore it is intended to use the California Bridge Health Index, which has been already tested and widely used. The California Bridge Health Index is derived for each element; the proportional quantity in each condition state is obtained from an inspection. These proportions are multiplied by factors reflecting the significance of the condition states to derive a numerical index called Element Condition Index (ECI). Element Condition Index= α 1 q 1 +α 2 q 2 +α 3 q 3 +α 4 q 4 +α 5 q 5 q 1 +q 2 +q 3 +q 4 +q 5 Where q 1, q 2, q 3, q 4 and q 5 are element quantities in condition states 1, 2, 3, 4 and 5 respectively and α 1, α 2, α 3, α 4,.α 5..are factors accounting for significance of the condition states.

6 Bridge Condition Index For the purpose of this project two separate Bridge Condition Indices (BCI) were established based on functional or performance categories as follows: BCIR - a BCI for strength or risk of structural failure BCID - a BCI for durability Each of these indices was derived based on the significance of the elements in a bridge to the performance in a specific category. For example the condition of a paint element will have no influence on strength or structural risk (BCIR) but significantly affect durability (BCID). These indices are derived based on condition of elements in a bridge (represented by ECI) as follows: BCIR or BCID= a 1 ECI 1 +a 2 ECI a n ECI n ECI 1 +ECI ECI n where a 1, a 2, a 3. a n are factors assigned to individual elements to account for their importance and influence in defining the specific functional aspect of the condition of the bridge. Assignment of zero to an element factor will eliminate the influence of that element on a functional index. These factors are to be integer values from 0 to 10 representing Nil contribution to Full contribution by the element. This will result in an index value between 0 and 10, and calculated to one decimal place, it can easily be visualised in terms of percentage if relevant (eg. BCIR=8.1 as 81%). The values for factors a 1, a 2, a 3. a n were chosen by practising bridge engineers with a confidence level of 95% for BCIR and 65% for BCID. However, the model is built in a manner that these values could be changed. Structure Condition Model Use of risk of failure weights Diagram 1 Diagrams 1 & 2 examines the behaviour of a bridge condition Index over time using different element condition models. Basically, all models provide a similar trend over time. As California Health Index is widely used and accepted, it was decided to use CA Health Index model to study the condition deterioration of bridges.

7 Use of maintenance weights Diagram 2 STUDY OF FIT OF STOCHASTIC DETERIORATION THEORY AND DEVELOPMENT OF PREDICTIVE MODEL. In developing a predictive model for deterioration of bridges/bridge elements it is vital to capture the continuous deterioration of elements over time. In the study of various models for structural deterioration, a stochastic process was considered to provide the best method for the estimation of continuous deterioration of elements over time. To verify its applicability, a study was conducted for the fit of various distributions in the data to corresponding probability distributions of the stochastic process. A strong fit was observed in the case of elements with larger data sets. Good fits and no rejections were observed for all other elements. In all cases, another distribution was also found to be a good fit. This leads to another stochastic process model. For the study of bridge element condition information is translated into a univariate model. This condition model departs from the Markov Chain sample space. The advantage of the univariate model is that stationarity is no longer a requirement. The univariate model is capable of capturing the time nonstationarity of deterioration. The deterioration rate is estimated from data without subjective interpretation. The use of a stochastic process, when used properly, leads to a good assessment of the past and future prediction of element conditions in a group of structures. Often, the data for each individual bridge aren t enough to estimate deterioration parameters properly. The approach used is to aggregate the data by dividing the bridges into classes in which the element of interest behaves similarly, in a probabilistic sense. Then the gamma process is applied. The approach results in good assessment and prediction. CURRENT DEVELOPMENTS AND FUTURE WORK As part of this project, a software platform is being developed to analyse the condition rating data and present deterioration of elements, bridges, group of bridges selected on a route, region, design era, material type, structure type etc. It is planned to test this software by experienced bridge engineers to validate the analyses and to find out what further modifications are necessary for the software to be a useful tool in bridge asset management.

8 Next stage of the development is to apply the gamma process in a predictive model and associated software to provide answer to the following questions. Element level deterioration prediction of a bridge/network with time Predicting of future condition of a bridge, type of bridges or bridges on a part of road network Estimating maintenance funding level for a pre-determined bridge condition state Predicting of network condition in terms of Bridge Condition Index for given level of funding. The authors intend to present the progress of the development of the predictive model at the bridge conference in May ACKNOWLEDGMENT The authors wish to express their thanks to the Chief Executive of the RTA for permission to present this paper. DISCLAIMER The opinions expressed in this paper are those of the authors and do not necessarily reflect the policies and practices of the RTA. REFERENCES [1] van Noortwijk, J.M. and Klatter, H.E., The use of lifetime distributions in bridge replacement modelling, First International Conference on Bridge Maintenance, Safety and Management, Barcelona, July, [2] Thompson, P. D., Small, E. P., Johnson, M., and Marshall, A. R., The Pontis bridge management system, Structural Engineering International, Zurich, vol. 8, no. 4, pp , [3] Madanat, S.M., Mishalani, R., and Wan Ibrahim, W.H., Estimation of infrastructure transition probabilities from condition rating data, Journal of Infrastructure Systems, Vol. 1, No. 2, pp , [4] Morcous, G. and Akhnoukh, A., Stochastic modeling of infrastructure deterioration: An application to concrete bridge decks, Joint International Conference on Computing and Decision Making in Civil and Building Engineering, June 14-16, Montreal, Canada, [5] Golabi, K. and Shepard, R., Pontis: A system for maintenance optimization and improvement of US bridge networks, Interfaces, Vol. 27, No. 1, pp , [6] Estes A.C. and Frangopol, D.M., Repair optimization of highway bridges using system reliability approach, Journal of Structural Engineering, ASCE, Vol. 125, No. 7, pp , 1999.

9 [7] Yang, S.-I., Frangopol, D.M., and Neves, L.C., Service life prediction of structural systems using lifetime functions with emphasis on bridges, Reliability Engineering and System Safety, Vol. 86, pp , [8] Abdel-Hameed, M., A gamma wear process, IEEE Transactions on Reliability, Vol. 24, No. 2, pp , [9] van Noortwijk, J.M., A survey of the application of gamma processes in maintenance, Reliability Engineering and System Safety, Vol. 94, pp. 2-21, 2009.