Concept of Operations and High Level Requirements Framework for the
Development of a Computational Tool for Bridge Deterioration Analysis
by
Gabrielle Sue Leesman
A thesis submitted to the College of Engineering of
Florida Institute of Technology
in partial fulfillment of the requirements
for the degree of
Masters of Science
in
Systems Engineering
Melbourne, Florida
July, 2017
We the undersigned committee hereby approve the attached thesis, “Concept of
Operations and High Level Requirements Framework for the Development of a
Computational Tool for Bridge Deterioration Analysis” by Gabrielle Sue Leesman.
_________________________________________________
Dr. Luis Daniel Otero
Associate Professor of Engineering Systems
College of Engineering
_________________________________________________
Dr. Aldo Fabregas Ariza
Assistant Professor of Engineering Systems
College of Engineering
_________________________________________________
Dr. Munevver Subasi
Associate Professor of Mathematical Sciences
College of Science
_________________________________________________
Dr. Muzaffar Shaikh
Department Head of Engineering Systems
College of Engineering
Abstract
Concept of Operations and High Level Requirements Framework for the Development of a
Computational Tool for Bridge Deterioration Analysis
Author: Gabrielle Sue Leesman
Advisor: Luis Daniel Otero, Ph. D.
In developing the lifecycles of a system, maintenance and support must be considered.
Associated with this portion of the life cycle are periods between needs of maintenance and
the cost of each type of maintenance. Previously a few state deterioration models have
been created separately to better predict these maintenance cycles for varying ages,
materials, traffic flow, and environmental conditions in the deck, substructure, and
superstructure of bridges. A particular analysis tool from previous studies involves the
development of Markov Chain (MC) models. This paper presents a systematic process to
develop MC bridge deterioration models for state/federal transportation agencies. A stepby-step implementation of the process to develop MC bridge deterioration models using
data provided by the National Bridge Inventory (NBI) will be assessed. A description of a
computational procedure created in Microsoft Excel will also provide an initial analyses of
each states bridge deck deterioration models and areas of further study to ensure a more
accurate deterioration prediction model.
iii
Table of Contents
Table of Contents ................................................................................................... iv
List of Figures ...........................................................................................................v
List of Tables ........................................................................................................ viii
Acknowledgement .................................................................................................. ix
Dedication .................................................................................................................x
Chapter 1 Introduction ............................................................................................1
Chapter 2 Review of Relevant Literature ..............................................................3
Chapter 3 System Definition ...................................................................................6
Defining Stakeholders ..................................................................................................... 6
CONOPS .......................................................................................................................... 7
Defining Main Requirements ....................................................................................... 10
Defining Sub - Requirements ....................................................................................... 11
Redevelopment of the Software Requirements ........................................................... 18
Chapter 4 Proof of Concept ..................................................................................21
Excel Initial Data Analysis Tool ................................................................................... 21
Florida Bridge Data....................................................................................................... 21
Chapter 5 Markovian Deterioration Models .......................................................38
General Approach ......................................................................................................... 38
Florida Bridge Deterioration Curve Data ................................................................... 39
Chapter 6 Future Work and Conclusions............................................................41
References ...............................................................................................................42
Appendix State Bridge Deterioration Curves......................................................44
iv
List of Figures
Figure 1 — List of Primary Stakeholders ..................................................................6
Figure 2 — CONOPS ................................................................................................7
Figure 3 — Use Case Diagram ................................................................................10
Figure 4 — Main Requirements Diagram ................................................................11
Figure 5 — Requirement 1 Sub Requirements ........................................................12
Figure 6 — Requirement 2 Sub Requirements ........................................................13
Figure 7 — Requirement 3 Sub Requirements ........................................................14
Figure 8 — Requirement 4 Sub Requirements ........................................................15
Figure 9 — Requirement 5 Sub Requirements ........................................................16
Figure 10 — Requirement 6 Sub Requirements ......................................................17
Figure 11 — Requirement 7 Sub Requirements ......................................................17
Figure 12 — Updated CONOPS ..............................................................................18
Figure 13 — Updated Use Cases .............................................................................19
Figure 14 — Updated Excel Requirements Diagram ..............................................20
Figure 15 — Useability Requirements Diagram ......................................................20
Figure 16 — FL Age vs. Sufficiency Rating in 2016 ..............................................22
Figure 17 — FL Age Post Reconstruction vs. Sufficiency Rating in 2016 .............22
Figure 18 — FL Age vs. Structural Rating in 2016 .................................................23
Figure 19 — FL Age Post Reconstruction vs. Structural Rating in 2016 ................24
Figure 20 — FL Deck Condition Rating in 1992 ....................................................26
Figure 21 — FL Deck Condition Rating in 2016 ....................................................26
Figure 22 — FL Superstructure Condition Rating in 1992......................................27
Figure 23 — FL Superstructure Condition Rating in 2016......................................27
Figure 24 — FL Substructure Condition Rating in 1992 .........................................28
Figure 25 — FL Substructure Condition Rating in 2016 .........................................28
Figure 26 — FL Age vs. Deck Condition Rating in 2016 .......................................29
Figure 27 — FL Age vs. Superstructure Condition Rating in 2016 ........................29
Figure 28 — FL Age Substructure Condition Rating in 2016 .................................30
Figure 29 — FL Material Type in 2016 ...................................................................31
Figure 30 — FL Support Type in 2016 ....................................................................31
Figure 31 — FL Structure Type in 2016 ..................................................................33
Figure 32 — FL Structure Type without Culverts in 2016 ......................................33
Figure 33 — FL Type of Deck Wearing Surface in 2016........................................34
Figure 34 — FL Type of Deck Protection in 2016 ..................................................35
Figure 35 — FL Average Daily Traffic in all Bridges.............................................36
Figure 36 — FL Average Daily Truck Traffic in All Bridges .................................37
Figure 37 — FL Deterioration Curves All Bridges .................................................40
Figure 38 — AK Deterioration Curves All Bridges ................................................44
v
Figure 39 — AL Deterioration Curves All Bridges .................................................44
Figure 40 — AR Deterioration Curves All Bridges ................................................45
Figure 41 — AZ Deterioration Curves All Bridges .................................................45
Figure 42 — CA Deterioration Curves All Bridges ................................................46
Figure 43 — CO Deterioration Curves All Bridges ................................................46
Figure 44 — CT Deterioration Curves All Bridges .................................................47
Figure 45 — DC Deterioration Curves All Bridges ................................................47
Figure 46 — DE Deterioration Curves All Bridges .................................................48
Figure 47 — GA Deterioration Curves All Bridges ................................................48
Figure 48 — HI Deterioration Curves All Bridges ..................................................49
Figure 49 — IA Deterioration Curves All Bridges ..................................................49
Figure 50 — ID Deterioration Curves All Bridges ..................................................50
Figure 51 — IL Deterioration Curves All Bridges ..................................................50
Figure 52 — IN Deterioration Curves All Bridges ..................................................51
Figure 53 — KS Deterioration Curves All Bridges .................................................51
Figure 54 — KY Deterioration Curves All Bridges ................................................52
Figure 55 — LA Deterioration Curves All Bridges .................................................52
Figure 56 — MA Deterioration Curves All Bridges ................................................53
Figure 57 — MD Deterioration Curves All Bridges ................................................53
Figure 58 — ME Deterioration Curves All Bridges ................................................54
Figure 59 — MI Deterioration Curves All Bridges .................................................54
Figure 60 — MN Deterioration Curves All Bridges ................................................55
Figure 61 — MO Deterioration Curves All Bridges ................................................55
Figure 62 — MS Deterioration Curves All Bridges ................................................56
Figure 63 — MT Deterioration Curves All Bridges ................................................56
Figure 64 — NC Deterioration Curves All Bridges ................................................57
Figure 65 — ND Deterioration Curves All Bridges ................................................57
Figure 66 — NE Deterioration Curves All Bridges .................................................58
Figure 67 — NH Deterioration Curves All Bridges ................................................58
Figure 68 — NJ Deterioration Curves All Bridges ..................................................59
Figure 69 — NM Deterioration Curves All Bridges................................................59
Figure 70 — NV Deterioration Curves All Bridges ................................................60
Figure 71 — NY Deterioration Curves All Bridges ................................................60
Figure 72 — OH Deterioration Curves All Bridges ................................................61
Figure 73 — OK Deterioration Curves All Bridges ................................................61
Figure 74 — OR Deterioration Curves All Bridges ................................................62
Figure 75 — PA Deterioration Curves All Bridges .................................................62
Figure 76 — PR Deterioration Curves All Bridges .................................................63
Figure 77 — RI Deterioration Curves All Bridges ..................................................63
Figure 78 — SC Deterioration Curves All Bridges .................................................64
Figure 79 — SD Deterioration Curves All Bridges .................................................64
Figure 80 — TN Deterioration Curves All Bridges .................................................65
vi
Figure 81 — TX Deterioration Curves All Bridges .................................................65
Figure 82 — UT Deterioration Curves All Bridges .................................................66
Figure 83 — VA Deterioration Curves All Bridges ................................................66
Figure 84 — VT Deterioration Curves All Bridges .................................................67
Figure 85 — WA Deterioration Curves All Bridges ...............................................67
Figure 86 — WI Deterioration Curves All Bridges .................................................68
Figure 87 — WV Deterioration Curves All Bridges ...............................................68
Figure 88 — WY Deterioration Curves All Bridges ...............................................69
vii
List of Tables
Table 1 — FL Condition Ratings in 1992 ................................................................25
Table 2 — FL Condition Rating in 2016 .................................................................25
Table 3 — FL Bridge Material Types ......................................................................30
Table 4 — FL Structure Type in 2016 .....................................................................32
Table 5 — FL Type of Deck Wearing Surface in 2016 ...........................................34
Table 6 — FL Type of Deck Protection in 2016 .....................................................35
Table 7 — FL Average Daily Traffic in All Bridges ...............................................36
Table 8 — FL Average Daily Truck Traffic in All Bridges ....................................37
Table 9 — Probability of Transitioning in Percentages ...........................................39
Table 10 — Years Inbetween Condition Transitions ..............................................39
viii
Acknowledgement
This thesis would not be possible without the endless support and advice of many people
around me, only a small number of which I will be able to recognize here.
First I would like to thank Jacqueline Hetherington, Residence Life Coordinator of Mary
Star of the Sea at Florida Tech. She is an amazing colleague, ambitious leader, and expert
multitasker. She never failed to take time out of her day to help me and was a constant
guide on my journey through graduate school on both a personal and professional level.
Thank you for being my role model and friend throughout our time together in graduate
school.
I would also like to thank my family not only for their financial support, but also for their
patience and consistent efforts in encouraging me to pursue my dreams. This degree would
not be possible without their sacrifices and love that they have shown over the years.
A very special thank you to Andrew Luecker for introducing me to the technical
components of bridge building and inspections. His passion for the topic was a huge
inspiration in the thesis topic choice, and was a constant inspiration in continuing my work.
I would like to extend a final set of gratitude to the various faculty and students at the
Florida Institute of Technology for financial support, academic guidance, and on campus
opportunities that I was afforded to make my college experience memorable and beyond
supportive.
ix
Dedication
This thesis is dedicated to my fiancé, Christopher Branchaud, for supporting me and
encouraging me to continue in my efforts towards my degree despite numerous setbacks.
Repeatedly he proved to me that we are all capable of so much more than we think we can
handle. Not only must we persevere, but we can succeed in overcoming various obstacles.
x
1
Chapter 1
Introduction
When building a structure, the conception of the idea and development of the structure are
not the only important steps that need to be taken into consideration. The entire lifecycle of
a product must be developed at the initial point of system definition. The life cycle of a
product includes the conception of the idea, followed by its creation, maintenance
procedures, and eventually the product’s final retirement. Monitoring a product for needed
repairs and the repair process are vital in the continuous use of many products especially
those that are constantly utilized like bridges.
To better understand what costs and influences are associated with maintenance for
bridges, deterioration models can be created. These deterioration models will give insight
as too how long a bridge has under given parameters before its condition rating degrades.
These can also be used to predict maintenance intervals and eventual need for
reconstruction. Models on a national scale are already in use for the Departments of
Transportation across the United States of America. An academic trend has begun in
creating these deterioration models on a state level. State deterioration models have proven
to be statistically different from the national average for Michigan, Nebraska, and Florida,
providing more insight to the Departments of Transportation about these state’s bridges.
Development of the previously mentioned deterioration models is based on a variety of
factors. Bridges can be analyzed based on average daily traffic (ADT), average daily truck
traffic (ADTT), age, and material properties, for the bridge deck, superstructure, and
substructure of state bridges. Using these factors and Markov chains, it is possible to
develop individual state deterioration models.
2
The process of developing these deterioration models is nothing new, as previously stated.
However, it is important that this process is able to be replicated with ease for the states
that have not yet created their own bridge deterioration models. Developing a software
tool using Microsoft Excel, will allow for the process of creating deterioration models to be
a quick and easy process to do on an annual basis for each state.
In order to create an efficient and easily usable program in Excel, the stakeholders, use
cases, and requirements of the program must first be analyzed. With the knowledge of who
is a stakeholder in this program, the uses of the program, and the requirements needed to
construct the program, the various elements of software tools should require minimal
alterations in the future.
The next step will be to analyze the data that is being processed in a general sense. This is
done to better understand the types of bridges that each state has. For example: the ranges
of age and traffic will change a deterioration model. It is important to be able to identify
states with large age and traffic ranges. For the purposes of this software, Florida bridges
will be under examination. Florida bridges will be the results that verify the software’s
accuracy because deterioration models have already been created for this state.
The goal is to prove the feasibility of deterioration models that can be replicated using a
created. Understanding the components that can influence these deterioration models, and
producing initial findings for each of the 50 states plus the District of Columbia and Puerto
Rico.
Chapter 2
Review of Relevant Literature
3
The first element to review is the purpose of determining stakeholders, use cases and
requirements. All of these elements are part of project defining even for software products.
Stakeholders can be defined as those who have an affect or are affected by the product of
concern. Defining these stakeholders is essential because their needs can be diverse,
ranging from political involvement, product use, and company expectations (Ballejos
2011). Knowing the level of influences that each stakeholder has on the product will allow
for an in-depth look at how they will play a role in the products use cases.
Use cases are a method of documenting each person’s role in the activity chain of running
the program. Showing visual representation of when one person transfers control to the
program will allow for the requirements of information flow that will be needed to input
into the program and out from the program. It will also show how each stakeholder will
influence or be influenced by the process.
Requirements are some of the most important steps in project management. It has been
stated that requirement definition can be the most important and hardest part of the project.
However, preplanning for a project can minimize the problems arising in the later phases in
the project life cycle (Yang 2012). For software in particular defining the product quality
for the future users and maintainers of the software are key. Computer Standards and
Interfaces have defined six quality variables when designing software products: efficiency,
usability, maintainability, portability, reliability, and functionality (Curcio 2016).
Deterioration models have been a developing field of interest. Initially their applications to
bridges started with the work of G. Morcous who thoroughly explained the application of
deterioration models to the maintenance cycle of bridges. He also analyzed the various
components such as age, ADT, ADTT, protective surfaces and more on the bridges of
Nebraska and compared them to the national deterioration models, pointing out distinct
4
differences and similarities in the process (Morcous 2011). More developments have been
made when analyzing Florida and Michigan bridges to see some stark differences in the
bridge deterioration when in a coastal environment and an environment that includes larger
amounts of cold weather (Winn 2013) (Sobanjo 2011).
Bridge management is a decision process that includes determining when it is ideal to
conduct maintenance on bridges. A variety of methods has been previously attempted in
learning how to best make these prediction models including incremental and discrete
deterioration models, semiparametric hazard rate models, and Markovian models (Huang
2010). There is an increased demand for reliability assessments in the system development
process, such as those made when deciding maintenance routines for bridges
(Fazlollahtabar 2013). Bridge inspection are periodic tests that are undergone at a
predetermined state of time. When this occurs, the model is dependent on the state of the
bridge, the period of time in which the bridge stays in this state, and the new state in which
the bridge is transitioning (Papazoglou 2000).
The works of Winn and Sobanjo continued to redevelop deterioration models for bridges in
various states, finding the significant differences from the national deterioration models
used in most states. There has been no clear definition of how to replicate the process for
multiple states, or when the appropriate time frame would be to issue a new statewide
deterioration model.
The hope is to continue to develop these process for more states. Development of
deterioration models for each state’s bridge decks will provide us with insight on the
process of Markov Chains which is not fully documented in the bridge analysis of the
aforementioned states. Markov Chains have been used in other deterioration processes that
are not related to bridges, such as wastewater systems. In the process of applying the
Markov Chains to the wastewater system, the goal is to predict a future state of the system
using the present and past recorded states (Baik 2006). The states can be defined in a
variety of methods. For bridges there is a numerical scale provided by the National Bridge
5
Inventory (NBI) that will denote the past and present states of bridges in the inventory
(Svirsky 2016).
The process of applying the Markov Chains to bridges in the Netherland have been
documented mathematically, but once again, do not provide the context of a created
process that can be replicated beyond the use of condition based probability matrices. The
Netherlands discovered in their analysis of national bridges that the uncertainty was very
large due to the lack of information in their database, but also the natural variability of the
deterioration across the nation, a problem consistent with the United States (Kallen 2004).
The variability in deterioration only further proves the need for a smaller area of analysis
such as at a statewide level.
China has already begun the process of developing an artificial intelligence based approach
to bridge deterioration models. When new data enters the system, then the new AI based
approach will develop new models based on Bayesian theorem for the twelve districts of
Shanghai (Zhang 2015). A fully AI based system for the United States would however
require a change in the bridge inspection system that is currently in place. This is due to the
uncertainty and inaccuracy involved with using current inspection data to predict future
condition ratings (Callow 2013).
To increase the accuracy of such a system, the computational tool that is proposed will
allow for modifications as necessary from a user. This will allow for the user to remove
outliers from the data, and also remove years of deterioration models that prove to be
inaccurate in predicting the future condition ratings of the bridge.
Chapter 3
System Definition
6
Defining Stakeholders
“Stakeholders include anyone with interest in, or an effect on, the outcome of the project”
(Robertson 2013). The important portion of this quote is that stakeholders are those with an
impact on the end resulting product. This means that those who will have an interest in the
format or results of the bridge software
Initially the system in development included the production of the Deterioration Curve
Python and Excel Program, listed as numbers 3 and 4 in Figure 1. There are a variety of
devices, actors, and groups of individuals that will have an impact on the outcome.
Figure 1 — List of Primary Stakeholders
The NBI is listed as a device that will impact the outcome of the Deterioration Programs
because it will need to be format compatible for the Python code to read in the information.
The National and State Departments of Transportation and the Bridge Project Managers
will have a general interest in the outcome, as the results and deterioration curves will be
used in their departments to maintain bridges as well as for national and state statistics.
7
The program compiler and program maintainer, numbers 7 and 8 in Figure 1, will be more
interested in the software quality of the resulting code, as they will be dealing with the
direct lines of code and providing any necessary updates to the code over time.
CONOPS
The next important phase of stakeholder analysis is to understand the interactions between
devices, actors, and other stakeholders. This process is best displayed in the CONOPS in
Figure 2.
Figure 2 — CONOPS
8
The initial actor is the program compiler who will determine when to run the program and
what state the bridge information will be pulled for. The project compiler interacts with
three devices and one stakeholder. The initial interaction comes from the National Bridge
Inventory publishing new bridge inventory information that is now available to the
program compiler.
The program compiler then will choose to run the Deterioration Curve Python Program,
which will trigger the running of the Deterioration Curve Excel Program. Both of these
programs are to be maintained and upgraded as needed by the program maintainer. The
results are then passed back to the program compiler who passes the results on to the
project manager.
The bridge project manager will then share information with the State Department of
Transportation. The National Department of Transportation will get its traditional results
using the NBI. The state and nation departments can share information that they have
gathered.
Understanding the role of each of the various stakeholders, devices, and actors allows for
the generation of adequate use cases that describe the transferal portions of information and
the interactions between humans and devices.
Use cases are utilized to understand the correspondence between the devices and the
humans using them. The diagram for the main use case derived for the Deterioration Curve
Programs includes an un-mapped space for the system actions and how they correspond to
the outside environment including the program compiler and the NBI.
The use case in Figure 3 was generated in Cameo. It documents the process that the device
will undergo after the NBI posts new data. The program compiler will then compile the
program verifying that the files and tools needed to do so are on the computer and by
selecting the state to be evaluated.
9
Should the program compiler enter an incorrect state, the character variable will still be
transferred to the Python program, which will intern return an error statement to the user,
asking them to re-enter a correct state or ask if they would like to quit. A requirement can
also be developed from this location in the use case for example to require an error
message. A sub requirement can also be derived to state what should be included as
options in the error message.
If the program compiler should in fact enter a correct state, the program should run both in
Python and in Excel. This process includes reading in the data, solving the Markov Chain
Deterioration Curves and outputting the information correctly into the Excel format so that
it auto formats. The data auto formatting will then produce a variety of graphics,
distributions, and deterioration curves as needed to run the full report for that state’s
bridges.
The multitude of steps displayed in this use case can now be used to link requirements that
will be defined for the programs in both formats to their respective stakeholder.
Requirements derived from the use case can then be directly traced back to the stakeholder
of origin.
10
Figure 3 — Use Case Diagram
Defining Main Requirements
The requirements for the deterioration curve systems were easily determined from the use
case in Chapter 4. The seven main requirements are displayed in Figure 4 and traced to the
11
systems that they will impact. Each of the seven main requirements has its own subrequirements tree. The main requirements for the Python program focus on the ability of
the program to compile, maintenance components, data being read into the program, data
being used to calculate deterioration curves, and the data being transferred to the Excel
program.
Figure 4 — Main Requirements Diagram
The Excel program also has to be able to read the data that is being passed from the Python
program. Beyond that there are strict graphics requirements and guides to making the
Excel program easily maintainable as well.
Defining Sub - Requirements
Each of the seven main requirements has its own sub-requirements tree. Figure 5 is the
hierarchical tree of the compiling requirements.
12
Figure 5 — Requirement 1 Sub Requirements
Many of the compiling requirements focus on the interface that the program compiler will
be using and the error messages that the computer compiler would be receiving while the
program is running. In these requirements, it states that the compiler will need to input the
name of a state, which will be verified. If there is a valid state, the program will run using
that state’s information. If an invalid state is entered, then the program will produce an
error message with a possible option to exit the program.
Figure 6 is the requirements breakdown for the data that the program will need to be able
to read in. In this process, the program will need to be able to read in data from the
13
National Bridge Inventory, requiring format compatibility. The program will also need to
know how many years of data a state will have. Once the number of years of data is
determined, then the program will need to read in the data for the corresponding years,
storing them in separate variables.
Figure 6 — Requirement 2 Sub Requirements
After storing all of the data that is read in, the program will need to be able to calculate the
deterioration curves using the Markov Chains. The requirements process for this is outlined
in Figure 7. Requirements are meant to dictate the outcome of the product, not how the
outcomes are achieved, so the lack of mentioning the Markov Chains in these requirements
is intentional. The Markov chains are a common practice of how to achieve deterioration
models, but they may not be the only method allowed for the system to run functionally.
14
Figure 7 — Requirement 3 Sub Requirements
Instead, the requirements dictated in Figure 7 focus more on the formatting to be used in
the program. This will produce the physical aspects and interface of the program desired by
the maintainer and compiler.
15
Figure 8 — Requirement 4 Sub Requirements
Figure 8 displays the requirements for transferring the calculated and collected data from
the Python program into the Excel program. This focuses on where the data will be
transferred and that the Excel program will have designated locations for the data that will
be provided by the Python program. Both the National Bridge Inventory data and the
calculated deterioration curves will be transferred to the appropriate locations as designated
by the excel program.
Once the data is transferred into the Excel program, it will then automatically format the
graphics that will be provided to the compiler. These graphics have strict labeling, color,
unit, and legend guidelines that are to be followed. These requirements are thoroughly
outlined in Figure 9.
These graphics requirements have been made for the physical requirements that would be
set forth from the project manager who will be compiling reports on the bridges that have
been developed. It will also be much easier in the report o have strict unit distinction in the
16
printed graphics. The labels have similarly been defined to represent to easily differentiate
the graphics in the collection of report summary.
Figure 9 — Requirement 5 Sub Requirements
Both the Python and Excel program will need to be maintained by the program maintainer.
For the maintainers needs, two requirements have been derived. One for Python in Figure
10, and one for the Excel program in Figure 11.
These requirements are made to focus on leaving comments and traceability of how the
various program components interact. That way should a future programmer want a portion
of the program to adapt to a new purpose, or a maintainer needs to fix or update the
program, then the comments can alert these users of what other components will influence
their end goals in changing or adapting the program.
17
Figure 10 — Requirement 6 Sub Requirements
Figure 11 — Requirement 7 Sub Requirements
Redevelopment of the Software Requirements
18
Originally the method of reading in data from the NBI data base was to be written in
python. This would allow a simple user interface were the user would input the initial of a
state, and the deterioration model and resulting data would be output into a preformatted
excel. Although the software thought process was sound, the use of python was proved to
be infeasible.
Upon further research into the needs of the stakeholders, it was determined that having a
software tool that used one platform would be better for maintenance purposes. The
software size, system age, and the programming language can all have factors on the
degree of complexity of a software and directly impact the complexity of the maintenance
(Stafford 2003).
For the purpose of simplicity in development and maintenance, the program was modified
to only be in Excel. This process changed the stakeholder CONOPS, use cases, and
simplified the requirements which can be seen in Figure 12 through Figure 15.
Figure 12 — Updated CONOPS
19
Figure 13 — Updated Use Cases
20
Figure 14 — Updated Excel Requirements Diagram
Figure 15 — Useability Requirements Diagram
Chapter 4
Proof of Concept
21
Excel Initial Data Analysis Tool
The development of the Excel tool was essentially a method of computation and graphical
representation of the data input into the program. The user selects the data files that are
relevant to the state of their choosing. State in this connotation and all following
connotations includes the District of Columbia and Puerto Rico. These files are filled into
the appropriate tabs using the user instructions, and the preliminary data analysis and
deterioration curves are developed.
Data was collected from NBI for all of the states staring in 1992. Each state has a variety of
data. Not all data started in 1992, and if that was the case, then values were noted
accordingly to represent that the data collection did not begin until a later year. Each data
set was inserted into the corresponding year labeled tabs.
Each state that was input into the Excel program resulted in a series of tables and graphs to
represent the type of data that can be found. These elements are essential in determining
the unique characteristics of the bridge deck, superstructure, and substructure that can
influence the creation of deterioration curves. Each state will then need customized data
pulled based on this initial analysis.
Florida Bridge Data
Each bridge has been granted a sufficiency rating out of 100 percent. A graph showing
how the age influences the overall sufficiency rating of the bridge is shown in Figure 16.
Form this figure it can be noted that the sufficiency rating decreases as the age increases
for bridges in Florida.
22
Figure 16 — FL Age vs. Sufficiency Rating in 2016
Some bridges will experience reconstruction after enough deterioration has occurred.
Figure 17 shows the age as compared to the sufficiency rating using any reconstruction
dates.
Figure 17 — FL Age Post Reconstruction vs. Sufficiency Rating in 2016
23
For example a bridge built in 1940 and reconstructed in 1970 would now be represented as
having an age based off of the 1970 reconstruction date. Showing the correlation values of
R2, helps to determine that the existence of reconstruction dates has influenced some of the
outliers in the data set.
Sufficiency ratings are not the only way that bridges are characterized. Each bridge is also
given a structural rating from 0 to 9. These integer values are assigned by the bridge
inspector and can vary based on inspector judgements. The change between these states
provides a more solid definition in transitioning from a state 9 to a state 8, etc.
Figure 18 — FL Age vs. Structural Rating in 2016
Figure 18 and Figure 19 show these structural ratings compared to the age of each bridge.
The relationships are similar, but the definition of ratings from 0 to 9 has increased the
correlation eliminating some of the error associated with a larger range of assignment
option, like a 0 to 100 percent range.
24
Figure 19 — FL Age Post Reconstruction vs. Structural Rating in 2016
Condition ratings are also given to the components of a bridge like the deck,
superstructure, and substructure. The collection of data for 1992 is shown in Table 1,
while the table for data collected in 2016 is shown in Table 2.
25
Table 1 — FL Condition Ratings in 1992
Condition
Rating
0
1
2
3
4
5
6
7
8
9
N
Total
Deck
4585
6940
310
77
47
0
163
363
129
0
0
12614
Superstructure Substructure
4208
239
25
8
237
5
3
5
0
18
0
4748
12534
32
21
15
22
0
0
0
0
0
0
12624
By 2016, the data better represents a full distribution of the condition ratings.
Table 2 — FL Condition Rating in 2016
Condition
Rating
0
1
2
3
4
5
6
7
8
9
N
Total
Deck
3
0
2
2
27
221
1232
6794
1472
93
0
9846
Superstructure Substructure
3
2
5
7
54
306
1054
6454
1913
93
0
9891
3
0
5
18
98
361
1241
6181
1873
108
0
9888
26
Figure 20 — FL Deck Condition Rating in 1992
The differences noted between Figure 20 and Figure 21 display the changes in the decks
condition ratings between this time and the improvement in data gathering for Florida.
Figure 21 — FL Deck Condition Rating in 2016
27
Figure 22 and Figure 23 show the difference in condition rating frequencies in the
superstructure of the bridges.
Figure 22 — FL Superstructure Condition Rating in 1992
Figure 23 — FL Superstructure Condition Rating in 2016
And finally the substructure shows the largest change in condition rating distribution
change from Figure 24 to Figure 25.
28
Figure 24 — FL Substructure Condition Rating in 1992
Figure 25 — FL Substructure Condition Rating in 2016
It can be noted that more accurate data was acquired in 2016, so the continuation of
information displayed will be based off of the most recent 2016 data for Florida. As
previously stated, age and condition rating are directly related even when influenced by
varying characteristics. One of these components that influences the deterioration of
29
bridges is whether the condition rating is for the deck, superstructure, or the substructure.
For this reason age distributions for each of these components were created in Figure 26,
Figure 27, and Figure 28, respectively.
Figure 26 — FL Age vs. Deck Condition Rating in 2016
Figure 27 — FL Age vs. Superstructure Condition Rating in 2016
30
Figure 28 — FL Age Substructure Condition Rating in 2016
Another highly influential characteristic of deterioration is the material that the bridge is
constructed out of. The various types of bridge materials and their frequency of presence in
the 2016 are shown in Table 3.
Table 3 — FL Bridge Material Types
Material
Number
0
1
2
3
4
5
6
7
8
9
Total
Material
Other
Concrete
Concrete Continuous
Steel
Steel Continuous
Prestressed Concrete
Prestressed Concrete Continuous
Wood or Timber
Masonry
Aluminum, Wrought Iron, or Cast
Iron
Frequency Percentage
2
3628
741
836
556
5878
209
420
0
43
0.02
29.46
6.02
6.79
4.52
47.74
1.70
3.41
0.00
0.35
12313
100
31
Figure 29 — FL Material Type in 2016
From Figure 29 and Figure 30, it is clear that the primary materials for Florida is simple
prestressed concrete and regular concrete. This portion will vary per state. When creating
the Excel sheet for the deterioration graphs it is important to note that each state will need
customized data selection based on material types.
Figure 30 — FL Support Type in 2016
32
Table 4 — FL Structure Type in 2016
Material
Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Total
Structure
Other
Slab
Stringer/MultiBeam or Girder
Girder and Floor Beam System
Tee Beam
Box Beam or Girders - Multiple
Box Beam or Girders - Single or
Spread
Frame
Orthotropic
Truss - Deck
Truss - Thru
Arch - Deck
Arch - Thru
Suspension
Stayed Girder
Moveable Lift
Moveable Bascule
Moveable Swing
Tunnel
Culvert
Mixed Types
Segmental Box Girder
Channel Beam
Frequency Percentage
18
3306
5300
32
290
19
170
0.15
26.85
43.04
0.26
2.36
0.15
1.38
31
0
1
57
52
5
1
2
3
132
10
0
2421
0
80
383
12313
0.25
0.00
0.01
0.46
0.42
0.04
0.01
0.02
0.02
1.07
0.08
0.00
19.66
0.00
0.65
3.11
100
Bridges have a variety of structure types. These can also be components that will cause a
variation in the data beyond just age and condition ratings. The frequencies described in
Table 4 are also graphically represented in Figure 31 with a large culvert section.
33
Figure 31 — FL Structure Type in 2016
However, culverts are not a portion of the bridge elements that we are interested in creating
deterioration curves for, so Figure 32 shows the frequency of structure distributions
without culverts.
Figure 32 — FL Structure Type without Culverts in 2016
34
Table 5 — FL Type of Deck Wearing Surface in 2016
Material
Number
0
1
2
3
4
5
6
7
8
9
N
Total
Deck Wearing Surface
Frequency
Percentage
None
Concrete
Type 4BD-SF (Silica Fume)
Latex Concrete
Low Slump Concrete
Epoxy Overlay
Bituminous
Timber
Gravel
Other
Not Applicable
5936
1125
154
1
3
59
2425
199
3
95
2313
12313
48.21
9.14
1.25
0.01
0.02
0.48
19.69
1.62
0.02
0.77
18.79
100.00
Decks do have wearing surfaces and protection. The combination of these material choices
can also influence the deterioration of the bridge condition ratings. The frequency of the
deck wearing surfaces outlined in Table 5 are displayed in Figure 33.
Figure 33 — FL Type of Deck Wearing Surface in 2016
35
Table 6 — FL Type of Deck Protection in 2016
Material
Number
0
1
2
3
4
5
6
7
8
9
N
Total
Deck Protection
None
Epoxy Coated
Reinforcing
Galvanized Reinforcing
Other Coated
Reinforcing
Cathodes Protection
Polymer Impregnated
Internally Sealed
Unknown
Other
Not Applicable
Frequency Percentage
9755
62
79.23
0.50
1
0
0.01
0.00
0
0
16
3
103
13
2360
12313
0.00
0.00
0.13
0.02
0.84
0.11
19.17
100.00
Similarly the deck protection frequency distribution from Table 6 is represented in Figure
34.
Figure 34 — FL Type of Deck Protection in 2016
36
Table 7 — FL Average Daily Traffic in All Bridges
ADT Category
ADT < 100
100 <= ADT <
1000
1000 <= ADT <
5000
ADT >= 5000
1995
1099
1938
2000
1050
1966
2005
947
2015
2010
995
2090
2015
854
1785
3986
3854
3861
4078
3462
6932
8099
8949
9560
6888
The final characteristic of influence on the deterioration curves are the Average Daily
Traffic (ADT) in number of cars, and the Average Daily Track Traffic (ADTT) in number
of trucks. Data has been collected for years in an increment of 5 years for the State of
Florida. The ADT was broken up for these bridges in Table 7. The distribution for each
year can be seen in Figure 35. From this we can see that time hasn’t severely impacted the
frequency of bridges in the ADT categories. However, more bridges do experience a high
daily traffic rate.
Figure 35 — FL Average Daily Traffic in all Bridges
37
Table 8 — FL Average Daily Truck Traffic in All Bridges
ADTT Category
ADTT < 100
100 <= ADTT <
500
ADTT >= 500
1995
6060
2223
2000
4172
2428
2005
3716
2323
2010
3708
2440
2015
3535
2756
3854
5531
6074
5981
5879
Similarly ADTT has been categorized in Table 8. The frequencies of truck traffic have
shifted for several Florida bridges over time as shown in Figure 36. This will impact the
deterioration curves developed for Florida bridges depending on the years of data included
in the deterioration calculations.
Figure 36 — FL Average Daily Truck Traffic in All Bridges
All of these characteristics are elements that will later need to be used to develop
customizable deterioration curves for each state. For example, a deterioration curve can be
made for Florida bridges made from concrete with a high ADT and low ADTT.
Chapter 5
Markovian Deterioration Models
38
General Approach
The goal of this program was simply to prove that deterioration curves for each state could
be replicated independent of the chosen factors that will influence each state’s deterioration
curves. For this purpose, the decks will be analyzed for all states. Florida will be shown as
the example, and initial analysis and deterioration curves for other state can be found in the
Appendix A.
Markov Chains are probability based calculations to predict the transition from one state to
the next. In the case of bridges, the states are the level of condition ratings. Markov Chains
are only interested in the current and previous set of data, so the transition probabilities
come from the current year and prior year’s data collected on the condition ratings (Riveros
2010).
The assumption is made that each bridge will start at a state of 9, full health. The
probability the bridge will change to an 8 is based on the percent of bridges labeled at a 9
that do transition to an 8 from the years of data being looked at.
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 9 𝑡𝑜 8 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐵𝑟𝑖𝑑𝑔𝑒𝑠 𝑎𝑡 𝑎 9 𝑖𝑛𝑖𝑡𝑖𝑎𝑙𝑙𝑦
The inverse of this value is the years that it will take for the bridge to deteriorate from a 9
to and 8. After the number of years for each state transition are calculated, they can be
plotted on a time graph to represent the deterioration curve for the current year’s data.
𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝐷𝑒𝑡𝑒𝑟𝑖𝑜𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 9 𝑡𝑜 8 =
1
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦
39
Florida Bridge Deterioration Curve Data
A deterioration curve for all bridge decks in Florida was calculated for each year. The
probabilities calculated for the transitions are shown in Table 9.
Table 9 — Probability of Transitioning in Percentages
Condition
Rating
9
8
7
6
5
1994
0.000
3.052
7.902
34.789
36.500
1995
1996
1997
1998
0.000 0.000 0.000 0.000
5.294 2.702 1.989 3.283
8.957 5.387 6.018 5.889
35.102 48.370 38.598 55.122
80.143 34.111 41.000 43.583
Then these probabilities were used to find the estimated time of residence in each state.
These values are shown in Table 10.
Table 10 — Years Inbetween Condition Transitions
Initial
Condition
Rating
9
8
7
6
5
1994
0.000
3.052
10.953
45.742
82.242
1995
1996
1997
1998
0.000
0.000 0.000
0.000
5.294
2.702 1.989
3.283
14.251 8.090 8.006
9.172
49.353 56.460 46.604 64.293
129.496 90.571 87.604 107.877
The data in Figure 37 shows the deterioration curve as if it was calculated in the labeled
year. For Florida there is little variation in the prediction of time for a bridge to deteriorate
from a 9 to an 8 and an 8 to a 7. After that point, the percentages begin to vary widely. The
bridge deterioration curves do not include transitions from state 5 to below because there is
not sufficient information to produce an accurate probability.
40
Figure 37 — FL Deterioration Curves All Bridges
Looking at the years that were included in Figure 37, 1993 was not included because there
was not sufficient transition data between 1992 and 1993. The year 2011 was also not
included for a similar reason in all state graphs. In other states, which can be references in
the Appendices, some states did not have data that changed between the years providing a
probability that the bridge would indefinitely remain in one condition rating state. If that
was the case, these years were excluded from the graph.
Chapter 6
Future Work and Conclusions
41
After using Markov Chains to develop Florida bridge deck deterioration models, the
process of creating a repeatable process to produce deterioration models has been proven to
be feasible with the understanding that modifications will need to be made by the user.
More research should be done on the feasibility of creating automatic customized models
that are specific to the state’s needs. For example, Florida uses mostly prestressed and
simple concrete. A model that can understand this and pull the data to create a prestressed
concrete and regular concrete deterioration model would be ideal. These results would be
easily replicated for the superstructure and substructure decks.
This program was also able to analyze the variables that would affect the deterioration
models. It compared age to various condition ratings, the varying levels of ADT and
ADTT, the deck wearing surfaces and the deck protection used. More research could also
be done with elements that are not on NBI, such as environmental impacts of heat and
water.
The ability to produce data for the 50 states and the District of Columbia and Puerto Rico
was proven, and able to be referenced in Appendix A. Some states have data that was
incapable of producing a variety of deterioration curves while others produced several
similar deterioration curves. The outcome was dependent on the data collection for each
state. Future work can be done to compare these findings to the national average to see if
there are geographical patterns or methods of predicting deterioration curve developments
as time progresses.
References
42
Baik, H. C., et. al. (2006). Estimating Transition Probabilities in Markov Chain-Based
Deterioration Models for Management of Wastewater Systems. Journal of Water
Resources Planning and Management, 132(1), 15-24.
Ballejos, L. C., & Montagna, J. M. (2011). Modeling stakeholders for information systems
design processes. Requirements Engineering, 16(4), 281-296.
Callow, D., et. al. (2013). Development of Hybrid Optimization Method for Artificial
Intelligence Based Bridge Deterioration Model – Feasibility Study. Automation in
Construction, vol. 31, 83-91.
Curcio, K., et. al. (2016). An analysis of the factors determining software product quality:
A comparative study. Computer Standards & Interfaces, 48, 10-18.
Fazlollahtabar, H., & Naini, S.G. (2013) Adapted Markovian Model to Control Reliability
Assessment in Multiple AGV Manufacturing System. Scientia Iranica.
Transaction E, Industrial Engineering, 20(6), 2244-2237.
Huang, Y. (2010). Artificial Neural Network Model of Bridge Deterioration. Journal of
Performance of Constructed Facilities, 24(6), 597-602.
Kallen, M. J., & Van Noortwijk, J. M. (2004). Statistical Inference for Markov
Deterioration Models of Bridge Conditions in the Netherlands. HKV Consultants,
Lelystad and Delft University of Technology, Delft, Netherlands.
Morcous, G. (2011). Developing Deterioration Models for Nebraska Bridges. Nebraska
Department of Roads (NDOR), 1-106.
Papazoglou, I.A. (2000). Semi-Markovian Reliability Models for Systems with Testable
Components and General Test/Outage Times. Reliability Engineering & System
Safety, 68(2), 121-133.
Robertson, S., & Robertson, J. (2013). Mastering the Requirements Process: Scoping the
Business Problem. Pearson Education, Inc., ed. 3. 43-50.
Riveros, G. S., & Arredondo, E. (2010). Guide to the Development of a Deterioration Rate
Curve Using Condition State Inspection Data. US Army Corps of Engineers, 2-12.
Sobanjo, J. (2011). Determining Deterioration Models Using Inspection Data in Florida.
Florida State University, Tallahassee, Florida.
43
Stafford (2003). Software Maintenance as Part of the Software Life Cycle. Tufts
University: Department of Computer Science.
Svirsky, A. (2016). National bridge inventory database search - 2015. National Bridges.
Winn, E., & Burgueno, R. (2013). Development and Validation of Deterioration Models
for Concrete Bridge Decks. Michigan State University, East Lansing, Michigan.
Yang, L. R., et. al. (2012). Requirements Definition and Management Practice to Improve
Project Outcomes. Journal of Civil Engineering and Management, 18(1), 114-124.
Zhang, C., et. Al. (2015). Application of Artificial Intelligence for Bridge Deterioration
Model. The Scientific World Journal, vol. 15, 1-6.
Appendix
State Bridge Deterioration Curves
Figure 38 — AK Deterioration Curves All Bridges
Figure 39 — AL Deterioration Curves All Bridges
44
45
Figure 40 — AR Deterioration Curves All Bridges
Figure 41 — AZ Deterioration Curves All Bridges
46
Figure 42 — CA Deterioration Curves All Bridges
Figure 43 — CO Deterioration Curves All Bridges
47
Figure 44 — CT Deterioration Curves All Bridges
Figure 45 — DC Deterioration Curves All Bridges
48
Figure 46 — DE Deterioration Curves All Bridges
Figure 47 — GA Deterioration Curves All Bridges
49
Figure 48 — HI Deterioration Curves All Bridges
Figure 49 — IA Deterioration Curves All Bridges
50
Figure 50 — ID Deterioration Curves All Bridges
Figure 51 — IL Deterioration Curves All Bridges
51
Figure 52 — IN Deterioration Curves All Bridges
Figure 53 — KS Deterioration Curves All Bridges
52
Figure 54 — KY Deterioration Curves All Bridges
Figure 55 — LA Deterioration Curves All Bridges
53
Figure 56 — MA Deterioration Curves All Bridges
Figure 57 — MD Deterioration Curves All Bridges
54
Figure 58 — ME Deterioration Curves All Bridges
Figure 59 — MI Deterioration Curves All Bridges
55
Figure 60 — MN Deterioration Curves All Bridges
Figure 61 — MO Deterioration Curves All Bridges
56
Figure 62 — MS Deterioration Curves All Bridges
Figure 63 — MT Deterioration Curves All Bridges
57
Figure 64 — NC Deterioration Curves All Bridges
Figure 65 — ND Deterioration Curves All Bridges
58
Figure 66 — NE Deterioration Curves All Bridges
Figure 67 — NH Deterioration Curves All Bridges
59
Figure 68 — NJ Deterioration Curves All Bridges
Figure 69 — NM Deterioration Curves All Bridges
60
Figure 70 — NV Deterioration Curves All Bridges
Figure 71 — NY Deterioration Curves All Bridges
61
Figure 72 — OH Deterioration Curves All Bridges
Figure 73 — OK Deterioration Curves All Bridges
62
Figure 74 — OR Deterioration Curves All Bridges
Figure 75 — PA Deterioration Curves All Bridges
63
Figure 76 — PR Deterioration Curves All Bridges
Figure 77 — RI Deterioration Curves All Bridges
64
Figure 78 — SC Deterioration Curves All Bridges
Figure 79 — SD Deterioration Curves All Bridges
65
Figure 80 — TN Deterioration Curves All Bridges
Figure 81 — TX Deterioration Curves All Bridges
66
Figure 82 — UT Deterioration Curves All Bridges
Figure 83 — VA Deterioration Curves All Bridges
67
Figure 84 — VT Deterioration Curves All Bridges
Figure 85 — WA Deterioration Curves All Bridges
68
Figure 86 — WI Deterioration Curves All Bridges
Figure 87 — WV Deterioration Curves All Bridges
69
Figure 88 — WY Deterioration Curves All Bridges