Development of a Locally Adapted Deterioration Model for Bridges in the State of Rhode Island, USA

“One in nine of the nation’s bridges are rated as structurally deficient” and Rhode Island is not an exception – 56.5% of the state’s bridges are either structurally deficient or functionally obsolete [1]. Bridge Management Systems use prediction models to forecast the need of maintenance for bridges. Since those systems are based on general assumptions, it is of great interest to develop a locally adapted deterioration model to make those forecasts. In this study, a Markov Chain based deterioration Model has been developed. It is based on condition ratings provided through the National Bridge Inventory. Additionally to the development of the probabilistic deterioration model, correlations to several items of the National Bridge Inventory were investigated to gain a better understanding what types of bridges have the most issues with deterioration. Maps were created to analyze the spread of deterioration factors in the state of Rhode Island. The maps can be used to visualize the data in a more approachable way for decision makers. Additionally to the development of the Markov Chain based deterioration model, a short literature review for a more advanced model, the Bayesian Network, was given for future reference.


LIST OF TABLES
published Report card for Americas Infrastructure states, that America's grade in terms of infrastructure is D+. The nation's bridges are only rated slightly better with a C+, but by taking a deeper look into the numbers, even a C+ is not encouraging. "One in nine of the nation's bridges are rated as structurally deficient" and Rhode Island is not an exception [1]. In Rhode Island, 21.8% of bridges were deemed as structurally deficient.
Adding functionally obsolete bridges, results in 56.5% of unsatisfactory bridge ratings.
This grants Rhode Island the last place in a rating for the United States, followed by Massachusetts (52.5%) and Hawaii (43.9%) [2]. In the 2017 Infrastructure Report Card, the overall grade for bridges is still C+. The percentage of structural deficient bridges in Rhode Island increased to 24.9%, which still grants Rhode Island the last place in the ranking of all states [3].
Knowing these facts, it is not a question that something must change, but what is the best, given that an entire network of bridges within a state cannot be maintained overnight. Plans and decisions have to be made based on sound and objective data. Such data are stored in Bridge Management Systems (BMS), like the computer program Pontis, which is used by every Department of Transportation in the nation [4], [5]. BMS are not only supposed to store important data, they are also analyzing the data to support officials regarding their decisions. The analysis algorithms in Bridge Management Systems are universal, in order to account for numerous types of conditions.
In an attempt to gain a better understanding about bridge deterioration in Rhode Island, a locally adapted deterioration model is developed in this study. This model could help to improve decision making processes which are currently based on generic models as part of BMS.
The following sections will give a brief introduction to bridge management, bridge condition ratings and deterioration models. In order to maintain a continuous and precise record of the bridge, it is necessary to set up an inspection plan for every bridge and to follow certain techniques. Over the life span of a bridge the need for inspection changes and also the intensity of every inspections varies. The Manual for Bridge Evaluation defines 7 different types of inspections, which will be described hereafter [6]. In this chapter only basic types of inspections and their influence on bridge management will be discussed. Fracture-Critical Inspections, Underwater Inspections and other special inspections are not part of this work because of their very specific nature.

Initial Inspections
As soon as a bridge is built, it has to be inspected before the first usage. This Inspection is called Initial Inspection and also applies for bridges which have changed in the configuration of their structure, for instance through widenings or lengthenings.
In the case of the change of the owner this type of inspection should also be conducted [6].
The initial inspection pays attention to two topics: providing all Structure Inventory and Appraisal data (SI&A) and determining the structural condition of every structural member. For the determination of the structural condition of every member, the inspector has to identify and list any existing problems. In order to find every possible risk the inspector has to follow a strict plan [6].

Routine Inspections
Routine Inspections are conducted on a regular base, depending on the needs of the individual bridge. They consist of observations and measurements to obtain the physical and functional condition of the bridge accordingly to the requirements of the National Bridge Inspection Standards (NBIS). The purpose of routine inspections is to determine any differences from the initial or previously recorded conditions and to guarantee that the bridge still meets present service requirements. This applies not only to condition ratings (discussed in section 1.2) but also to parameters like average daily traffic (ADT) and average daily truck traffic (ADTT) since they are also subject to change [6].
Usually inspectors will conduct routine inspections from the deck, ground and/or water levels and from permanent work platforms and walkways. Any underwater parts of the bridge will only be observed during low-flow periods and will be probed for signs of undermining. Areas of special attention are determined by previous inspections or load rating calculations. Critical areas should be inspected according to the procedure described under "In-Depth Inspections", which follows later in this chapter [6].
The results should be well documented with photographs of any area which has any problems shown as well as appropriate measurements. Additionally, a written report including recommendations for maintenance and repair has to be issued. If necessary this report contains recommendations for scheduling any in-depth or other special inspections. The report should also include a re-evaluation of the load capacity to verify if any structural condition changes affect any previously recorded ratings. [6] Damage Inspections A damage inspection is defined as an unscheduled inspection after a structural damage occurred, to determine necessary emergency load restrictions or even the closure of the bridge to traffic. The extent of this type of inspections depends on the cause and the dimension of the damage. The inspector has to evaluate every fractured member and to determine the extent of section loss and loss of foundation support.
Additionally, the inspector should take measurements to obtain misalignment of members. In the case of severe damage, inspectors must be capable of making on-site calculations to determine emergency load restrictions. [6] Damage inspections should be complemented by a short-term in depth inspection if necessary to verify the field measurements and calculations and to refine the established load or speed restrictions. The documentation of this inspection has to contain recommendations for follow-up procedures and it must exercise the awareness of the potential for litigation. [6] In-Depth Inspections This type of inspections are usually scheduled either independently from a routine inspection or as a follow-up of a damage inspection. Depending on the size of the bridge either the complete bridge can be examined at once or the bridge can be divided into segments which are examined individually. [6] In-depth inspections require a close-up, hands-on inspection. Therefore, special equipment, such as under-bridge inspection equipment, staging and workboats are required. To maintain a high safety level for the inspector(s), special personnel to control the additional equipment is needed. The inspection includes the examination of all critical members of the chosen segment as well as nondestructive field tests, load tests and material tests. [6] The report for in-depth inspections should include all results of the performed tests as well as photos of critical areas. Also the defined segments of the bridge have to be clearly identified in the report to ensure that no part is missing and that future inspectors will choose segments according to the first in-depth inspection. [6] Planning of Inspections A well-planned inspection is essential for the success of a good bridge management. Therefore, the inspector who plans the bridge inspection should consult the local highway maintenance superintendent, who may point out some important local condition changes over the year and give recommendations for a good time to inspect a certain bridge. Additionally, all items of the following points should be considered to conduct an effective and safe inspection. [6]  Determination of the required type of inspection In this section a brief overview about single parts of a bridge record will be given, starting with general parts and ending with very specific data which have to be stored digitally in the correct format according to the Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges. [6] Beginning with the planning process for a new bridge, construction plans, shop and working drawings and "as-built" drawings have to be added to the bridge record.
All plans and drawings should be readable and available in an appropriate format. If the bridge record is stored electronically and in paper format, plans and drawings have to be cross referenced. In case of digital plans the responsible person should make sure to store the original files protected against changes and in appropriate formats to reuse them in the case of rehabilitation or replacement.
Not only structural computations and drawings have to be provided within a bridge record, but also pertinent material certificates, such as concrete delivery certificates, steel mill certificates and other manufacturers' certifications, must be included. In addition, to those certificates, material test and load test data can supplement the bridge record.
The recorded building progress in form of daily logs, memos, notes and pertinent letters should be included in the record. The As-Built-Status of the bridge should be documented by at least two photographs: one top view of the roadway and one side elevation view of the bridge. The record can be complemented by more photographs of any defects or areas of concern as applicable.
During the life span of a bridge maintenance and rehabilitation work will be done.
A report for each work has to be attached to the bridge record in chronological order. It should include the date, description of project, contractor and other related data, such as coating history, accident records and flood data. Further information which should be included are traffic data, permit loads ("significant special single-trip permits issued for use of the bridge" [6]) and rating records.  Some of these data do not need to be updated, but some of them need to. In later parts of this study, items which need to be updated (condition ratings, average daily traffic (ADT), average daily truck traffic (ADTT), etc.) will be referred to as timevariant parameters. Items, which do not need to be updated (year built, location, structure ID, etc.) will be referred to as time-invariant. The exact coding can be found in the Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges itself. In the following part only the most important items will be described in a general form.
Items related to structural components with operational characteristics need to be inspected by trained inspectors who must rate them following a specific rating system.
For the rating of the bridge deck, superstructure and substructure, a schema from 0-9 is used. Bridges with very good conditions would be rated as 9, failed bridges as 0. If a rating is not applicable for a single bridge, N would be the appropriate rating. The objective of the NBI condition rating system is to provide an overall characterization of the general condition of the bridge by comparing the existing to the as-built condition.
Any load bearing capacity shall not be used to describe the overall condition of a bridge since the fact that bridges were designed for different loads than nowadays, does not influence the overall condition of a bridge. [7] Items 58, 59 and 60 (Deck, Superstructure and Substructure) are the main items of the NBI condition rating, which are under investigation in this study. Concrete decks should be inspected with special attention towards cracking, scaling, chloride contamination, potholing and depth failures. During the inspection of steel grid decks, special attention should be payed for cracked welds, section loss and corrosion. Item 59 (superstructure condition rating), is rated according to signs of distress, cracking, deterioration and misalignment of bearings. The substructure, described through item number 60, is rated regarding its condition in terms of section loss, misalignment, scour, collision damage and corrosion. Most likely, a BMS includes not only NBI relevant data, but it can contain much more detailed information, like inspection records, photos or drawings. Which information a BMS ultimately stores depends on different factors among the decision makers within an agency. Different approaches to planning, programming and budgeting, individual characteristics of the transportation system of each agency and also the political environment can influence the stored data.
In general, a BMS contains the following components [4]:  Data Analysis Tool and  Decision Support [6].
Without a well-structured database, a BMS cannot work properly. Therefore, every BMS should include at least a bridge inventory and condition-, rating-, cost-, preservation-, and improvement-activity-data. These data are necessary to improve long-and short-term decisions regarding a healthy transportation network and financial constraints. [6]

Bridge Condition Ratings
The focal point of the decision process are bridge condition ratings, which are recorded according to the Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges [7]. The bridge data is stored within more than 100 numbered items, grouped by categories: identification, structure type and material, age and service, geometric data, navigation data, classification, condition, load rating and posting, appraisal, proposed improvements and inspections. Data which are not subject to change (time invariant data) work as a filter to ensure a consistent database. The sorting and verification will be explained in section 2.1. Data which are subject to change (time variant data) will be investigated regarding their behavior over time and their correlations to other items. Deck condition, superstructure condition and substructure condition (items number 58, 59 and 60) are considered for an in-depth investigation. Part of the investigation is to find correlations between each of the named items, as well as correlations to a number of other items. The process of finding correlation factors will be described in section 2.2.
The data utilized in this study can be found in several categories, the order of numbering is random and does not matter for the research itself. However, for a better reference the item numbers will be used next to the name of each item. An overview for items is enclosed in Appendix A. To name some items: structure number (item 8) and latitude and longitude (item 16 and 17) can be found in the category identification.
Structure type (item 43) though, can be found in the section structure type and material.

Appendix E shows every time-variant and time-invariant item which is used in this
study. Also, it shows the content of each item as well as the meaning of different ratings.

Deterioration Model
To describe deterioration, a mathematical model is needed. In this study the Markov Model is used and the Bayesian Network approach is discussed. The Markov Model uses a probability matrix and an initial state matrix to predict future conditions [8]. Hence, the model uses just one initial state to calculate further stateswhich makes the model easier to build and to compute. To handle a large number of dependent random variables at a time, Bayesian Networks can be used. Bayesian Networks use other common probabilistic models to describe the deterioration process, like the Markov Model, but it can combine different steps or cases with each other [9]. Both approaches will be discussed in Chapter 2.3 but only the Markov Model will be applied.

METHODOLOGY
The heart of this study is the bridge condition rating published by the Federal Highway Administration [10]. Those bridge condition ratings are coded files, which are available for every state within the United States from 1992 to 2016 [10]. The file format is defined in the Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation's Bridges [7]. According to this defined format, the data are imported into one excel spreadsheet document and are evaluated as described below.
In 2.1, the first step of processing the data is described. The data are sorted to ensure consistency by removing bridges for different reasons. Next, section 2.2 outlines how the data was analyzed and how correlation factors between different items were computed. Section 2.3 provides the reader with information on how the deterioration model was developed.

Filtering
After downloading all bridge records for Rhode Island, all files were imported to a single excel spreadsheet. As a first step, every existing structure ID had to be collected and stored to get an overview how many datasets can be obtained. All structure IDs were then stored within one sheet, along with items of interest, such as condition ratings or year built. Table 2 shows in detail which and why items were used for filtering. Based on observations of those items, datasets were excluded from further investigations to ensure data consistency. To be removed, datasets must have less than four consecutive inspection records, an average time period between two inspection records of less than 2.5 years, or missing parts of the condition rating. Considered as a missing part are either blanks within a dataset ormost likely for condition ratingsthe value 0 as a entry for one item. If a bridge is rated 0, the structure has failed. As an investigation of the available datasets has shown though, for a rating of 0, usually satisfying ratings were preceding. That and other observations, which will be discussed in chapter 3.1, was causing concern about the credibility of the data and therefore they were excluded. To develop a precise deterioration model, timespan between to inspections should be constant. If the average timespan between two inspections is longer than 2.5 years, the bridge was removed.

Data Analysis and Correlation Factors
In a similar study by Cruz for several states [8], bridges were divided into bridges with and without maintenance. This was done, due to increasing bridge deck ratings which does not reflect the real deteriorationratings should decrease. Therefore, the deterioration factor for bridges with maintenance was computed taking all instances of bridge deck rating into account. The deterioration factor for bridges without maintenance was computed by excluding all instances where the bridge deck rating increased [8].
The datasets in this study were not divided into bridges with and without maintenance. This decision was made because of the following reasons. First, Cruz did not state an exact threshold how to differ between bridges with or without maintenance.
That  Taking a general approach to compute the deterioration factor over all years and claim this bridge as a bridge with maintenance, the deterioration factor would be -0.083.
The approach in this thesis is, to divide the ratings in up to three time-periods, compute deterioration factors for each period and ultimately calculating the average deterioration factor. In the case of Figure 1, two time-periods should be considered. First from 1992 to 2001 (decreasing by 2) and second from 2002 to 2016 (decreasing by 3).
The deterioration factor for the first period is   In the multiple state study by Cruz, correlations between the bridge deck deterioration and time-invariant parameters were investigated [8]. In the present study, a similar approach is takenthe difference is, that more than just the bridge deck is under consideration. Based on the sorted data gained by evaluating the data according to Chapter 2.1, correlations between the deterioration of bridge deck, superstructure and substructure and several time-invariant as well as time-variant items are investigated.
Listed in Figure 3 is every correlation, which is considered within this study.   After dividing the datasets into the categories, the in Figure 3 listed items were stored next to the structure IDs into three different sheets to prepare the datasets for the next steps. All datasets were imported into MatLab to run curve fitting algorithms and create appropriate graphs for investigating correlations. The curve fitting algorithms were provided by the MatLab curve fitting toolbox [11].
Three different types of graphs were chosen as an appropriate way to show correlations between parameters. For discrete parameters such as design load, functional classification or type of service, box and whisker plots were generated. Non-discrete parameters, like year built, ADT or structure length are represented in scatter plots. If necessary, histograms are plotted next to those scatter plots were point overlapping is preventing a precise interpretation of the data.
For the investigation of correlations between the location and deterioration factors maps were created, using the 'MyMaps' feature of Google Maps.

Development Deterioration Model
After computing deterioration factors for each bridge, a deterioration model to predict future condition was developed. Deterioration can be defined as a random process where each incident is based on only the most recent previous incidentany other previous incidents are not considered [9]. In terms of this research, an incident is defined as the rating of a certain part of the bridge, during the most recent inspection.
In this section two different models will be explained. A widely used stochastic technique for predicting the performance of infrastructure is the Markov Model [12].
After discussing the Markov Model in section 2.3.1, another approachthe Bayesian Networkwill be explained in section 2.3.2.

Markov Model
In a previous study regarding this topic [8], the Markov Model is used, since it is considered to be an straightforward model. Therefore, the Markov Model is also the approach in this study.

According to Performance Prediction of Bridge Deck Systems using Markov
Chains, Markov Models are characterized by three advantages. First, they are able to reflect the uncertainty from different resources. Those different resources could be initial condition, applied stresses or the presence of condition assessment errors. The second big advantage is, that due to the computational efficiency, Markov Models can manipulate networks with many components. Also, they are incremental models, which accounts for present condition in predicting the future condition [12].
Morcous [12]  Actually, deterioration is a nonstationary process where "time elapsed in the initial state affects the probability of transition to the following state" [12].
To keep the straightforward manner of the Markov Model, the same limitations as for professional Bridge Management Systems are applied for the purpose of this study. Each element of the transition probability matrix represents the possibility of a bridge component to change from state (i) to state (j). It will be developed by evaluating all available bridge condition ratings [8], [12].
The prediction of the future condition for a bridge component can be determined as follows [8], [12]: and To develop the transition probability matrix, a probabilistic approach was taken.
Preprocessed data of the observed conditions served as base for a frequency analysis for every possible transition. For the computation of the transition probability matrix, ratings were expected to either decrease, stay constant or increase. Therefore, it was not necessary to differ between bridges with maintenance and without maintenance or to neglect additional bridges because of too many changes of ratings like shown in Figure   2. Due to this assumption, the developed model is capable of predicting the actual behavior of bridges.  6 … … … … … 5 … … … … … Figure 5: Example for computing the transition probability matrix

Bayesian Network
Bayesian networks (BN) are probabilistic graphical models which describe a set of random variables and their respective probabilistic dependencies [8]. They gained a lot of attention in medical applications and for other decision-making problems [13]. Its roots are in the artificial intelligence society [13]. The benefits of BNs are, that they are intuitive to build and can handle a large number of dependent random variables [9]. To explain the basics of BNs, an example inspired by Hulst [13] and Charniak [14] can be found in the following paragraph with illustrations in Figure 6 and Figure 8. there is also the possibility that they just forgot to turn it off after both were at home.
The related graph to this example can be found in Figure 6.
In Modeling physiological processes with dynamic Bayesian networks structure of graphs in BN applications is explained. A graph consists of two parts: nodes and edges, in the case of a BN edges are called arcs. There are two groups of nodes: parent-nodes and child-nodes. Within the student house example, the "Housemate at home"-node is a parent of the child-node "Outside light on" because it influences it directly.
"Housemate at home" and "Bike in shed" are in this case so called root-nodes since they do not have any predecessors [13]. BN can be either linear, converging or diverging, as shown in Figure 7   Theorem is stated in (3). In simple words it states that circles within BNs are not permitted [13].
The graph in Figure 6 shows the simple BN based on the student house example, but it does not help to find out if somebody is home yet. To be able to make that decision it needs the prior probabilities of all root nodes. Additionally, all conditional probabilities of non-root nodes with all possible combinations of their direct predecessors are necessary. Knowing those, a subset of the student house graph looks like as follows in Figure 8. The probabilities are randomly chosen for this example but need either to be calculated or estimated by experts for real scenarios [14]. A calculation of those values can be achieved by using for example the Markov Model approach from 2.3.1. The probabilities can be expressed within a condition probability table (CPT) [13]. The probabilities from the example are shown in a CPT in Table 3. As it can be observed, the nodes in the example can have two different stateseither true or false.   Assuming a BN for bridge ratings. Bridge ratings in the national bridge inventory can have ten different states, ratings between 0 and 9. The size of a CPT can be determined by using (4), where ri stands for states of the variable, rj stands for states of the parent and n is the number of nodes [13]. According to (4), the size of the CPT for this simple case is already 1000 (rj=10, ri=10, n=2). It can by observed, that the size of CPTs grows exponential to the number of parent-nodes. Therefore, this number should be kept as low as possible [13].
BNs in general are great to use for static problems. By adding a time dimension to a BN, BNs can be used to model dynamic systems and are therefore called dynamic Bayesian networks (DBN). In DBN one tries to model probability distributions over a semi-infinite collections of random variables [15]. Only discrete-time stochastic processes are considered, a next time-step can be added once new observations have been made [15].
To not be misleading: neither certain parameters nor the structure of the network would change in a DBN. Changing of parameters or the network structure itself, are part of Bayesian learning which is beyond the scope of this thesis. Introductions to Bayesian learning can be found in Modeling physiological processes with dynamic Bayesian networks and Bayesian networks without tears.

RESULTS
In this chapter, the results will be presented. Section 3.1 will evaluate the sorting process and the issues that occurred during this process. In 3.2 and its subsections, the reader will find the computed correlations between deck, superstructure, substructure and all previously mentioned time-variant and time-invariant items. Finally, section 3.3 will show the developed deterioration model.

Filtering Process
During the sorting process, several unusable datasets were found. Starting with obviously not usable data such as the rating of culverts, up to missing condition ratings within the datasets. Before sorting, data for 868 structures was availableafter sorting out 522 datasets, only 346 datasets were left. Table 4 shows how many datasets had to be removed, and for which reason. 147 Inconsistent condition rating. For some years, the dataset has a 0-rating which would indicate a failed structure. The data are not credible since most of the bridges which are removed for that reason have a rating above 5 in one year and in the next year a rating of 0. Also, bridges which have an N-rating (not applicable) are removed and counted in this category.

318
Inconsistent inspection period. Bridges should be inspected every two years. To account minor inconsistencies all bridges which have an average timespan between two inspections more than 2.5 years are removed.

26
Too less data. Bridges were built too recent than an appropriate amount of data could have been collected 31 Sum: 522 Special attention should be paid to inconsistent condition ratings. They are responsible for about 60% of removed datasets. It has also been observed, that most of the structure IDs, which were removed because of inconsistent condition ratings, are consecutive IDs. The cause removed data due to inconsistent condition ratings will be discussed in the following paragraphs.
Most of the data are not consistent, and due to concerns about the credibility of those datasets, they are removed. Taking structure ID 8370 or 3880 in Figure

Data Analysis and Correlations
In this section, the analysis-results are presented. It starts off with the results for the bridge deck, and goes on with results for superstructure and substructure. Each section will follow a certain patterndescribing the average deterioration factor, describing the correlation factors to certain time-variant and time-invariant items (cf. 2.2) and interpreting both of them. bridges show a deterioration factor between -0.09 and -0.12. Only 9 bridges have a higher deterioration rate than -0.2, the highest deterioration factor is -0.2857. The average bridge deck deterioration factor is -0.0725. Due to too many changes of the rating from one year to another, 28 bridges had to be neglected. During the analysis of the named data it became clear that correlations between the bridge deck and other time-invariant parameters are not very strong. In fact, the strongest correlation could be found between the deck deterioration factor and the year the bridge has been build. Figure 11 shows the related curve fittingin Table 5, all computed correlation factors are stated.

Figure 11: Correlation between Deck deterioration factor and year built
Shown in Figure 11, most bridges were built around 1960 and as seen in Figure 10, most of the deterioration factors are settled between -0.04 and-0.12. Remarkable as well is, that also bridges built in the 1880s have deterioration factors between -0.05 and -0.22 and not higher ones which one could expect.  The figure oben does not show a strong correlation between the parameters. An expected behavior could have been a higher deterioration rate for more lanes on a structure or even the opposite since more lanes on a structure could mean that a bridge is more important for the public so the maintenance intervals are shorter. The highest mean of deterioration factors can be observed for bridges with five lanes on them. One possible reason for such a higher deterioration rate could be an asymmetrical loading scenario which causes more damage to the structure itself than an even loading scenario.
To find the real reason for this is beyond the scope of this study.
Shown in Figure 13 is the box plot for Deck Deterioration Factor vs. Design Load.
As described in Appendix E, a rating of 0 stands for other or unknown design loads which makes it impossible to judge over this category. The average for categories 2 and 4 are higher than the overall average deterioration factor. In the categories of 5 and 6, the average deterioration factor is smaller than the overall average. Although in those categories there are more outlier than in other categories, the 75 th percentile is lower than for categories 2 and 4. The Box plot for Deck Deterioration Factor vs. Type of Service has also a rating of 0 which stands for other and makes it impossible to judge its influence on the deterioration factor. Category 1 stands for highways. In Figure 13, it was observed that the deterioration rates for higher loads are not necessarily higher than for smaller loads.
In the figure unterhalb, highways (category 1) have a mean deterioration factor smaller than the overall average. Railroads, covered by category 2, have a higher deterioration rate than highways. The reason for this should be investigated by analyzing the ADT on the two types to see if there is any correlation. Categories 6, 7 and 8 describe different levels of structures in interchanges, the majority of bridges of that type have smaller deterioration factors than the overall average is.  Figure 15 is the location analysis for the bridge deck deterioration factors.
A color scale is used to present the different deterioration rates. The scale reaches from red (highest deterioration rates) to blue (smallest deterioration rates). Grey dots stand for neglected bridges. This figure shows what Figure 10 already showed in a different way: the majority of bridges have a deterioration factor below -0.1. What also can be observed is, that most of the bridges are situated along major highways (I95 and I295).
It is also evident, that most of the bridges with higher deterioration rates are situated along those highways. In this category fewer parameter were under investigation. All parameters are shown in scatter graphs below, as well as the computed correlation factors in Table 6.
To not be misleading: the deterioration factor of each bridge is defined as constant, no updating of it is considered. Therefore, the bridge deck rating is considered as the reference factor in this section.
As it can be observed in Table 6, the correlation between ADT and bridge deck rating is similar to the correlation between ADTT and bridge deck rating. Therefore, just one curve fitting is shown (Figure 16   The correlation between deck rating and superstructure rating is the strongest correlation which was found for this section of the studyalthough an R-square of 0.3151 is not a really strong correlation. For the figure unterhalb, lots of data-points are overlapping. Therefore, histograms were plotted next to the scatter graph in the Appendix. Figure 17: Correlation between bridge deck rating and superstructure rating

Average Deterioration Factor
The split of the superstructure deterioration factor is shown in Figure 18. are in a range between -0.12 and -0.34. The highest deterioration factor for the superstructure is -0.34 which is higher than the highest deterioration factor for the bridge deck. Due to too many changes of the rating from one year to another, 17 bridges had to be neglected. The average superstructure deterioration factor is -0.0934. Figure 18: Deterioration rates superstructure

Correlations to time-invariant parameters
The analysis of the time-invariant parameter for the superstructure showed that there are no correlations. The highest R-square value was computed for the correlation between superstructure deterioration factor and year built with 0.00722 (see Table 7 for all values). That value is even smaller than the computed R-square for the bridge deck deterioration factor to year built (0.04483). Since this correlation is that weak, no graph is plotted here, although the produced graphs can be found in Appendix H. The following box plots show the spread of the superstructure deterioration factor versus traffic lanes on structure, design load and type of service. Those were also shown for the bridge deck analysis. For the superstructure also the main building material (kind of material, item 43A), as well as the type of the design (item 43B) are of interest and therefore shown in Figure 23 and Figure 22. The blue line shows the average superstructure deterioration factor of -0.0934. Figure 19 shows the superstructure deterioration factor vs traffic lanes on the structure. Observed in Figure 12, the deterioration rates for uneven numbers of traffic lanes on the structure were higher than for even numbers. This hypothesis cannot be supported by the observation of the superstructure deterioration rates in Figure 19. The highest rates can be observed for 2 and 4 lanes on the structure, with some outliers for 3 lanes on the structure.     The in Figure 24 shown map differs from the one in Figure 15 on the first sign: there are more light blue markers than dark blue ones. This was expected due to observations done in Figure 10 compared to Figure 18 (histograms of the deterioration rates of bridge deck and superstructure). It can also be observed, that higher deterioration rates are not only limited to bridges along bigger highways, they also can be found on less important routes. Thus, the bridges with the highest deterioration rates can be found along I95. Also similar to the bridge deck investigation are the correlations to other condition ratings. The correlation to the deck rating is slightly higher than to the substructure but can still not considered to be strong. Due to the high similarities graphs for those correlations are also not shown at this place, they can be found in Appendix H. Table 8 lists all computed correlation factors.

Average Deterioration Factor
The split of the superstructure deterioration factor is shown in Figure   vs. year built is not the highest factor. The highest correlation factor was computed for the correlation between substructure deterioration factor and structure length. Although this result was unexpected, it is not showing a strong relation which can be used for better predictions. The remaining correlation factors can be found in Table 9. Since all correlations are non-representative, no graphs are plotted here (graphs can be found in Appendix I). The following box plots show the spread of the substructure deterioration factor versus traffic lanes on structure, design load, type of service, main building material and type of the design. The blue line shows the average substructure deterioration factor of -0.08048.      Correlations to ADT and ADTT are similar to each other, however not strong at all. Therefore no scatter plot is shown here (it can be found in Appendix I).
Also, similar to the bridge deck investigation are the correlations to other condition ratings. The correlation to the superstructure rating is slightly higher than to the deck rating but can still not considered to be strong. Due to the high similarities, graphs for those correlations are also not shown at this place, they can be found in Appendix I as well. Table 10 lists all computed correlation factors.

Deterioration Model
Following the process described in 2.3.1, three transition probability matrices were developed. Each for bridge deck, superstructure and substructure, which are shown in Table 11 through Table 13. Like expected, it can be observed that all transition probability matrices have a similar form. Most values are settled around the diagonal of the matrix. Since maintenance is taken into account during the computations, it is possible that values under the diagonal appear. The first and last columnratings 9 and 0are filled with zeros. That is an expected behavior. However, those columns were not left out in order to use them as a form of check value to assure no invalid data was used for computation. Another check value is the sum of each row: it has to be equal to 1 [8].
In general, ratings are most likely to be constant between two inspections. Ratings between 8 and 6 are more likely to decrease than increase, whereas ratings below 6 are more likely to increase due to maintenance. The transition probability matrix for bridge deck and substructure both include the factor one for once. For the bridge deck this factor has its origin in two transitions and for the substructure in one transition.
Therefore, those factors should not be taken as representatives.  performed from an initial rating of 6, closely followed by initial ratings of 7 and 5. On average, 800 transitions have happened from 6 as an initial rating, 596 transitions have happened from 7 as an initial rating and 515 have happened from 5 as an initial rating.
Those initial ratings are the majority, which makes them the most reliable transition probabilities.
Using equation (2), a prediction for future conditions can be made. On the basis of the just stated observations, predictions are done for initial ratings of 5, 6 and 7 for one, five, ten, twenty-five and fifty years [8].

Summary
In this study, a Markov Chain based deterioration Model has been developed. After a brief description of Bridge Management in the US, bridge condition ratings are discussed in detail. Then, the approach for developing a deterioration model is discussed.
Chapter 2 shows how the process of developing a deterioration model was done.
First, the verification of the data was ensured by sorting out inconsistent datasets. The

Results and future work
During filtering the available datasets, more than 60% of the data had to be neglected due to various reasons. This decreases the credibility of the deterioration model and leaves room for further investigations why so much data is having errors. To compensate for time periods with missing data, special techniques could be used to simulate data. That could lead to more valid data and therefor to more credibility.
Additionally to simulate data, original inspection reports should be requested which might makes real condition ratings available which have not been submitted to the Federal Highway Administration (FHWA).
The computation of correlation between deterioration factors and time-invariant parameters, as well as computations of correlations between condition ratings and timevariant parameters did not bring strong correlations to daylight. This is an expected behavior, since it was also observed in previous studies [8].