Bridge Deterioration Prediction Using Markov-Chain Model Based on the Actual Repair Status in Shanghai

Transcription

1 Bridge Deterioration Prediction Using Markov-Chain Model Based on the Actual Repair Status in Shanghai Li LI Associate Professor Key Laboratory of Road and Traffic Engineering of the Ministry of Education Tongji University No Cao an Road, Jiading District, , Shanghai, China TEL:(+8621) , 622lilian@tongji.edu.cn Feng LI Associate Professor Key Laboratory of Road Structure and Material of the Ministry of Transport Research Institute of Highway, Ministry of Transport No. 8 Xitucheng Road, Haidian District, , Beijing, China TEL:(+8610) , f.li@rioh.cn (Corresponding Author) Zhang CHEN Associate Professor Key Laboratory of Road and Traffic Engineering of the Ministry of Education Tongji University No Cao an Road, Jiading District, , Shanghai, China TEL:(+8621) , czy1620@gmail.com Lijun SUN Professor Key Laboratory of Road and Traffic Engineering of the Ministry of Education Tongji University No Cao an Road, Jiading District, , Shanghai, China TEL:(+8621) , ljsun@tongji.edu.cn Submitted for Presentation and Publication at the 2016 Annual Meeting of the Transportation Research Board Submission date: July 31, 2015 Revision date: November 15, 2015 Word count: 6977 with 3 tables and 4 figures

2 ABSTRACT Bridge condition prediction is crucial in preparing future conservation budgets and five-year capital programs for the construction and maintenance of bridges in Shanghai. A bridge management system (BMS) has been formally used and promoted for urban bridge management in Shanghai since 2004 and 16,623 bridge records have been accumulated. Although there are a large amount of data records, predicting bridge deterioration precisely is difficult because the data composition is complicated and the maintenance history is varied. Therefore, a Markov-chain model was applied as a decision aid to consider the different conservation strategies. More than 66,000 data records were used to calibrate the model. The modeling considered two conservation regimes: routine maintenance and minor repair, and medium and major repair. The repair rate was obtained through an actual conservation survey. Besides the influence of spatial distribution, different characteristics of bridges also were considered. Bridge conservation efforts were uneven at the city level in Shanghai. The condition of bridges in the central city is much better than those in suburban areas, although the proportion (55.6%, 2014) of suburban bridges is larger. Furthermore, based on the present status of Shanghai bridges, conservation efforts have been insufficient generally, and even worse in suburban areas. The medium and major repair level at present has had a significant impact on deck systems and superstructure, but quite a small impact on substructure and the whole bridge. Thus, the present conservation efforts cannot improve the overall bridge condition fundamentally. As a result, the condition of bridges in Shanghai has deteriorated rapidly. Key words: Markov chains; Bridge deterioration; Bridge prediction; Bridge repair

3 Other Number of bridge (2014) Li, Li, Chen and Sun INTRODUCTION The condition assessment and prediction of bridge infrastructure is crucial in preparing future conservation budgets and five-year capital programs for the construction and maintenance of bridges in Shanghai. A bridge management system (BMS) has been formally in use for urban bridge management in Shanghai since 2004, following an initial trial of the BMS in At present, the stable version of the BMS has successfully worked more than 11 years. All of the bridges are inspected once a year and 16,623 bridge assessment records have been accumulated. As small and moderately sized bridges make up the majority of the urban bridges, the data records in the Shanghai BMS all describe bridges belonging to categories II to V according to the Chinese technical code of urban bridges management CJJ [1], which excludes the super-large bridges (bridges with total span more than 1000 meters or single span more than 100 meters.). The technical status of bridges in the Shanghai BMS is quite complicated because bridges with different structure types and different material properties are included in the same database. Besides, the bridge age span is also large, as shown in Figure 1, which means that bridges at different stages of development coexist. Any reasonable performance assessment method should avoid the bias caused by this large span in bridge age. Apart from this, the bridge conservation status also exists in various forms, including routine maintenance and minor repair, medium repair, major repair and even reconstruction. Consequently, the precise prediction of bridge deterioration has become a challenge. A meaningful prediction modeling approach for such infrastructure is usually on the network-level, considering the necessary size of the data sample. The outcomes of network-level deterioration models are the prediction of condition changes with time of the given bridge network and can be used to plan maintenance, including repair and rehabilitation of bridges, and to calculate bridge life cycle cost [2]. This study only considered network-level deterioration modeling. Also, a prediction approach considering a variety of impact factors will be used Bridge age (year) Figure 1 Bridge Age Span in Shanghai, China (as of 2014) A prediction approach was sought that was capable of considering a variety of impact factors. Deterministic and stochastic methods are the most common ways by which to develop such a prediction method. The deterministic model assumes that the bridge deterioration tendency is certain, so regression analysis is commonly used to determine the infrastructure decay rate; an

4 exponential regression model is widely used [3 5]. Typically, these models are relatively convenient to calculate but fail to consider uncertainty and randomness of the bridge deterioration process [6]. Besides, a high quality data set is also required for regression analysis, which is usually hard to satisfy, and the preprocessing of data may cause too much risk of subjective judgement [3]. Comparatively, stochastic models are better in such aspects. Engineering experience can be used to describe the uncertain factors [7]. Although the deterioration processes of bridge components are continuous, discrete condition ratings are often used to reduce the complexity of continuous condition monitoring; this approach has been proved effective [8]. The discrete probability models are represented by the Markov process, which is based on the concept of probabilistic cumulative damage [9] and now commonly used in the performance prediction of infrastructure facilities [10]. It is believed that models based on the Markov process have three advantages [11]. Firstly, such models are able to reflect uncertainties of various aspects [12]. Secondly, the prediction of a future state is based on the present state, so the model is incremental [8]. And lastly, Markov-based models can be applied at network level with many facilities involved, improving calculation efficiency [13, 14]. Some bridge management systems, such as Pontis and BRIDGIT [15, 16], have adopted Markov models to predict the performance of bridges. Although the Markov process has been widely used in bridge performance prediction, most applications focus only on a particular bridge component such as a deck, or directly consider the bridge as a whole [11]. Besides, the sample size is not large enough in most applications [17]. Some research has attempted to model the different deterioration characteristics of different bridge components under certain maintenance regimes, but the bridge repair rates are all based on assumption or empirical estimation, which is not rigorous enough to reflect the real performance of bridges [18]. So there is often a performance gap between predictions and reality. Furthermore, in some big cities or large infrastructure networks, infrastructure status in the central city and suburban areas may be totally different due to the difference in the conservation investment level or in the importance of traffic infrastructure. So it is not so reasonable to consider the bridges in such situations as a whole even though the prediction is usually made on a network level. Rather, the effect of infrastructure distribution should be taken into account. The motivation of this study was to satisfy the need for a Markov-chain model that reflects the real impact of actual bridge conservation status in Shanghai and that can predict the performance deterioration tendency of different components of bridges in different areas (i.e., central city and suburban areas). As for the Markov model, the key problem was to estimate the transition probability matrixes (TPMs), a process also known as calibrating Markov models [19]. A stationary Markov model uses time-independent TPMs by assuming a homogeneous infrastructure deterioration pattern for a selected data set. Deterioration patterns of data sets with similar characteristics, without medium or major repair in between, can be assumed to be homogeneous when limited condition-rating data are available [2], and the stationary Markov model could be considered in this situation. In other words, a single TPM can be used. Therefore the actual objectives of this study were to calibrate a Markov-chain model using bridge condition-rating records in Shanghai to predict the deterioration process of local bridge infrastructures on a network level. To obtain actual bridge conservation data, a conservation

5 survey was also conducted by searching the BMS database and accessing the infrastructure industry reports from 2004 to 2013 [20]. MODEL AND ASSUMPTIONS Markov-chain model A Markov process describes a system that can be in one of several states. Each state can pass to another at each time step according to fixed probabilities. A Markov-chain model is a special case of the Markov process for which time and state parameters are both discrete. A Markov chain can be treated as a series of state transitions based on certain probabilities. A stochastic process whose transition probability of a future state depends only on the present state is defined as a first-order Markov process [21]. For a stochastic process {X(t), t T}, if the conditional probability can be expressed as Equation (1), {X(t), t T} is a Markov chain having discrete parameters. P(X t+1 = i t+1 X 0 = i 0, X 1 = i 1,, X t = i t ) = P(X t+1 = i t+1 X t = i t ) (1) In Equation (1), i t is the process state at time t; and P is the conditional probability of a future event. There are two assumptions about Markov chains. First, the future state of a stochastic process depends only on the present state and has nothing to do with the past. Second, the transition probability between two states should be constant. So the time step needs to be determined properly to assure simple-state transition. As mentioned above, urban bridges in Shanghai are inspected once a year, so the time interval for the model was set to one year. As the bridge condition is usually evaluated using several rating levels, the transition probabilities should be expressed as a transition probability matrix. A typical TPM, P, is shown in Equation (2). p 11 p 1n P = [( )] { p ij 0 i, j I p n1 p j I p ij = 1 i I nn In Equation (2), n is the number of bridge condition states; matrix element p ij represents the probability that the bridge condition will pass from state i to state j during a certain time step. Therefore, if the initial bridge condition is known, the future condition after t time intervals can be obtained using Equation (3), where C is the condition vector [22]. (2) C(t) = C(0) P t (3) The TPM is the key of the Markov-chain model and is commonly obtained by statistically analyzing the bridge condition data. Two methods can be used to calculate the transition probability matrix: the regression method based on nonlinear optimization [17, 23], and the percentage method [24]. The regression method is affected significantly by the prior maintenance actions, for which records may not be readily available. In the percentage method, the transition probability is estimated by the proportion of number of state changes to the total number of states

6 before the change. Thus, this method requires at least two consecutive condition records without any maintenance interventions [11], which usually reduces the magnitude of data processing. Because the requirement of the percentage method is comparatively easy to achieve, it was selected for use in this study. Model assumption and matrices simplification In China, urban bridge conditions are graded by five levels for small and moderate bridges [1], as shown in Table 1. For bridges with grades A to C, only routine maintenance and minor repair are needed. According to the conservation requirements in the Chinese technical regulation [1], the main work of the routine maintenance and minor repair is to mark the damaged area, find the suspicious damage and keep the affected areas tidy. Thus, in such a situation, the condition rating (CR) of a bridge should either maintain the original level or decay to the next lower level between two consecutive years. In other words, the bridge CR grade cannot decay more than one grade in a subsequent year. For bridges with grade D or E, more maintenance efforts are required, including medium or major repair and even reconstruction. In this case, the bridge condition can be improved, and thus the CR grade should be raised to any higher level according to the actual repair efforts. According to the Shanghai bridge conservation investigation conducted in this study, some universal principles can be summarized as follows: first, the medium repair is mainly for D-grade bridges and the major repair is for E-grade bridges; second, both D- and E-grade bridges will be improved to grade A after repair. However, there is also a situation that major repair is implemented on grade D bridges if there is a surplus maintenance budget after all of the grade E bridges are repaired. Table 1 Urban Bridge Condition Ratings in China Score Grade Definition Maintenance recommendations (100 mark system) A Intact Routine maintenance B Good Routine maintenance and minor repair C Qualified Minor repair D Unqualified/Bad Medium or major repair E Dangerous <50 Major repair or reconstruction Therefore, three basic assumptions were made in this study based on the analysis above. Assumption 1: in the circumstances of routine maintenance and minor repair, the CR of a bridge should maintain the original level or decay to the next lower level between two consecutive years. Assumption 2: medium repair is mainly for grade D bridges and major repair is for grade E bridges, but if there is a surplus maintenance budget, the major repair could be implemented on grade D bridges. Assumption 3: both D- and E-grade bridges will be improved to grade A after medium or major repair. Based on the CR definition in Table 1 and the assumptions above, the TPM in Equation (2)

7 can be simplified to Equation (4) and Equation (5), in which P routine and minor is the TPM under routine maintenance and minor repair, and P medium and major is the TPM under medium and major repair. P routine and minor = p 55 1 p 55 p 44 1 p 44 p 33 1 p 33 p 22 1 p 22 1 ] [ (4) p 55 1 p 55 p 44 1 p 44 P medium and major = p 33 1 p 33 p 25 (1 p 25 ) p 22 (1 p 25 ) (1 p 22 ) [ p 15 1 p 15 ] For ease of calculation, the state vector should be transformed from a qualitative rating [A, B, C, D, E] in Table 1 to an ordinal system [5, 4, 3, 2, 1], in which elements of the state vector are called status values. As urban bridges in Shanghai are inspected once a year, a one-year transition probability can be determined. In the circumstances of routine maintenance and minor repair, the probabilities for two (or more) state changes in two consecutive years should be negligible, according to Assumption 1. Besides, the rows of the transition matrix must sum to one. It follows that only five transition probabilities are needed to fully define a particular TPM in such a maintenance circumstance, as shown in Equation (4). Comparatively, the case for medium and major repair circumstances is a little more complex, as shown in Equation (5). For grades A to C (i.e., grades 5 to 3), only three transition probabilities are needed, just as for the routine maintenance and minor repair, according to Assumption 2. For grade D (grade 2), p 25 is its actual repair rate according to Assumption 3 and correspondingly the unrepair or neglect rate is 1 p 25. For these unrepaired grade D bridges, the probability of maintaining a D grade is (1 p 25 ) p 22, where p 22 is already determined in Equation (4). And the probability of that a grade D bridge will deteriorate to E grade is (1 p 25 ) (1 p 22 ). For grade E (grade 1) bridges, p 15 is the actual repair rate according to Assumption 3 and the neglect rate is 1 p 15. DATA PREPARATION AND CALCULATION OF TPMs Data profiles The stable operation of the Shanghai BMS started in 2004, thus bridge condition records for 2004 to 2014 were used in this study to calibrate the Markov-chain model. There are 16,623 bridge CR records in the BMS; each has three sub-records because a bridge can always be divided into three components: bridge deck system, superstructure and substructure. Each component is evaluated separately and the CR grade for the whole bridge is obtained by summing the weighted grades of all three components [1]. Thus, a single bridge actually has four data records and the available (5)

8 data size is actually 66,492. All records had to be preprocessed before using them in TPM calculations because (1) there may have been inspection errors in the BMS, and (2) all records had to be subjected to the three assumptions used in this study to make sure the single TPM was valid [2]. The result of data preparation is shown in Table 2. The number of valid data records for the bridge deck system was the smallest, probably because the deck inspections are based on visual observation and this technique has the greatest variability. On the contrary, the number of records for the inspection of substructure is steadiest over time, which means the decay of the substructure is slow or the defects are hard to inspect. Table 2 Number of valid data records Time interval Bridge parts Deck system Superstructure Substructure It must be noted that although the bridge type and its material characteristics are varied in the Shanghai BMS, data for concrete girder bridges comprise the majority (83.4% in terms of structure type) of the entire data set, while records for reinforced concrete bridges and pre-stressed concrete bridges accounted for 88.5% of the data set in terms of material type. Therefore the TPM calculation based on these data could be considered homogeneous [2] and all the discussions in this study mainly reflect the characteristics of such bridges in Shanghai. TPMs Calculation The 66,492 CR records of urban bridges in the Shanghai BMS from 2004 to 2014 (Table 2) were used to calculate the TPMs. All of the data were preprocessed and validated before being used in TPM calculations. The analysis of Equations (4) and (5) above shows that the transition probabilities in the circumstances of routine maintenance and minor repair are the basis of all calculations. Therefore the calculation of TPMs started using Equation (4). Besides, as mentioned before, each bridge component, as well as the whole bridge, usually has different deterioration characteristics, and the bridge conditions in the central city and suburban areas may also be different in Shanghai; thus, the TPMs should be calculated separately. Circumstances of routine maintenance and minor repair In this case, only four transition probabilities are needed for each situation. Every two-year period (consecutive years) has a group of transition probabilities. However, the final TPMs under routine maintenance and minor repair should be single for each bridge component and the whole bridge [2]. So the calculation results need to be further processed. As the distribution of transition probabilities for each grade is not uniform, the average value and standard deviation were used in this study to analyze these data. The transition probabilities

9 that exceeded the valid range were excluded, and the final transition probabilities are the average value of all valid values, as shown in Equation (6). This method has been proved effective for obtaining stable transition probabilities [18]. R i = p ii ± s i { i [5,4,3,2] (6) valid p ii = p ii p valid ii R i In Equation (6), R i is the valid range of transition probabilities for each grade i; p ii and s i are the average value and standard deviation, respectively, of transition probabilities through all valid years for each grade i; p ii is the final transition probabilities for each grade i; and p ii is the valid probabilities for each grade i. The data processing results can be found in Table 3. Table 3 Final transition probabilities under routine maintenance and minor repair and Category Bridge deck system Superstructure Substructure Whole bridge under medium and major repair Final probability Final probability (routine maintenance and minor repair ) (medium and major repair ) Element Entire Central Entire Central Suburbs Element city city city city Suburbs p p p p p p p p p p p p p p p p p p p p p p p p Circumstances of medium and major repair The case for medium and major repair is a little more complex because the probabilities of CR grades D and E for more than two state jumps in two years must be taken into consideration based on the actual repair rate. As noted previously, a conservation investigation was conducted to acquire the actual repair rate [20]. The transition probabilities for grades A to C are same as those under routine maintenance and minor repair, while the transition probabilities for grades D and E were calculated based on the actual repair rate. The final probabilities reflecting medium and major repair can also be found in Table 3. As shown in Table 3, the transition probabilities for bridges in the central city were much higher than those for bridges in suburban areas, indicating

10 that the bridge conservation intensity in the central city was greater than that in the suburban areas. The better economic development state of the central city may be the main reason for this result. It is should be noted that the transition probabilities named p 25 and p 15 in Table 3 were calculated based only on the survey results of whole bridge repair because more detailed conservation data about individual bridge components were not available. Thus, in this study all bridge components were considered to have the same repair rate as the whole bridge. BRIDGE DETERIORATION PREDICTION CR prediction based on present status of Shanghai Using the Markov TPMs and present status of urban bridges, the future status of bridge conditions at any year can be predicted. Taking the bridge condition in 2014 as the present status C(0), the status vector is defined by Equation (7), in which bridges in different locations are considered separately. Then the bridge condition during next t years C(t) can be predicted using Equation (8), in which P cir is the Markov TPM in a particular circumstance. [0.617, 0.289, 0.083, 0.011, 0] (if entire city ) C(0) = { [0.531, 0.336, 0.111, 0.021, 0] (if the suburb) [0.685, 0.251, 0.060, 0.004, 0] (if central city) C(t) = C(0) (P cir ) t t = 1, 2, 3, 4, 5 (8) The prediction results of all three bridge components and the whole bridge for the two conservatism regimes are displayed in Figure 2 and Figure 3. The prediction period is 10 years (i.e., ). (7)

11 Figure 2 Bridge prediction results under routine maintenance and minor repair. Letters A, B, C, D and E represent bridge grades according to the Chinese technical regulation.

12 Figure 3 Bridge prediction results under medium and major repair. Letters A, B, C, D and E represent bridge grades according to the Chinese technical regulation. CR prediction for a new bridge The deterioration process under different conservation regimes can be predicted using the Markov-chain model above for a new bridge with intact condition status in Shanghai. The

13 calculation method is described in Equation (9). In Equation (9), C(t) is the bridge CR grade (status value) after t years; C(0) is the status vector of the initial condition; P maintain is the TPM in certain conservation circumstance; and CR is the bridge condition rating vector, which is a constant vector in the case of new bridge. In this study CR= [5; 4; 3; 2; 1]. C(t) = C(0) (P maintain ) t CR (9) It was assumed that new bridges will deteriorate from the intact state during the forecast period of 20 years. Thus, the initial status vector C(0) was [1, 0, 0, 0, 0]. The bridge condition deterioration tendency for different components and for the whole bridge can be found in Figure 4, in which the ordinate scale 5 to 1 represents CR grades A to E, respectively.

14 Figure 4 Deterioration prediction over 20 years for a new bridge in Shanghai. The ordinate scale 5 to 1 (y axis) represents CR grades A to E, respectively. DISCUSSION Figure 2 and Figure 3 show that the bridge condition will deteriorate rapidly if only routine maintenance and minor repair are implemented. Comparatively, the bridge deck system has the fastest decline of the three bridge components analyzed. At the end of the prediction period (2024) the proportion of bridge deck systems with grade A will be less than 20%, while the proportion of grade E deck systems will be as much as 20%. This finding is quite worrying because the safety rating of a grade E bridge is dangerous. Medium and major repairs seem to have a significant positive impact on the bridge deck status in the central city, as shown in Figure 3(a) to Figure 3(f),

15 but this positive impact is not apparent for the suburban bridges. The latest data in the Shanghai BMS show that the proportion of suburban bridges is 55.6% (2014), thus their conditions have a large impact on the overall state of transport infrastructure in the city. Because the medium and major repair rate is too low in suburban areas of Shanghai (see Table 3), the bridge conditions in these areas cannot be improved significantly. The cases for the superstructure, substructure and the whole bridge are almost the same as for the bridge deck system. Bridges in the central city always have a better performance than their suburban counterparts, and the suburban bridges reduce the overall bridge quality level of the entire city, reflecting that investment on the repair of suburban bridges in Shanghai is very insufficient. Even in the central city, the present repair rate cannot fundamentally improve the technical condition of existing bridges. The results portrayed in Figure 2 and Figure 3 indicate that bridges in Shanghai have entered a rapid deterioration stage, and if the repair efforts cannot be strengthened from now, the future state of these bridges will be quite worrying. This conclusion is also consistent with the empirical findings of the Shanghai bridge management investigation conducted as part of this study. Figure 4 displays the predicted deterioration of a new bridge based on the present bridge conservation strategy in Shanghai. The medium and major repair efforts at present seem to have a significant impact on the bridge deck system and the superstructure, as shown in Figure 4(a) and Figure 4(b), and the impact will be apparent in 6 8 years. Regarding routine maintenance and minor repair, the location of a new bridge seems to have no influence on the bridge deterioration process. However, in the case of medium and major repair, the location effect is obvious and the performance decline of new suburban bridges is predicted to be far more rapid than that of new bridges in the central city. As with existing bridges, the present repair efforts are insufficient to improve the state of the substructures and the whole bridges, as shown in Figure 4(c) and Figure 4(d). CONCLUSIONS Bridge condition data spanning approximately 11 years in the Shanghai BMS were used in this study to calibrate a Markov-chain model to forecast the bridge condition, and also to find the deterioration tendency, of urban bridges in Shanghai. The bridge CR grades were used to generate the state vector space and the time step was set to one year, matching the bridge inspection frequency and simplifying the form of Markov TPMs. The modeling process considered two conservation strategies, and the actual repair rate was obtained through a conservation survey. The influence of bridge location also was considered. Results from the study support the following conclusions. Bridge conservation efforts (or investment levels) are uneven across the city, with those in the central city being much better than those in suburban areas, although the proportion of suburban bridges is higher (55.6%). Furthermore, the present level of bridge conservation efforts in central Shanghai is insufficient, and the condition in suburban areas is even worse. The medium and major repair efforts at present have a significant positive impact on the deck system and the superstructure of central city bridges, but the impact of these efforts on the substructure and the whole bridge is quite small, indicating that the present conservation strategy cannot improve the bridge conditions fundamentally. The positive impacts of conservation efforts on central city

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