Stochastic Preservation Model for Transportation Infrastructure

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Electronic Theses, Treatises and Dissertations The Graduate School
2011
Stochastic Preservation Model for
Transportation Infrastructure
Omar St. Aubyn Alexander Thomas
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF ENGINEERING
STOCHASTIC PRESERVATION MODEL FOR TRANSPORTATION
INFRASTRUCTURE
By
OMAR ST. AUBYN ALEXANDER THOMAS
A Dissertation submitted to the
Department of Civil and Environmental Engineering
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree Awarded:
Summer Semester, 2011
The members of the committee approve the dissertation of Omar St. Aubyn Alexander
Thomas defended on June 16, 2011.
John Sobanjo
Professor Directing Dissertation
Eric Chicken
University Representative
Lisa Spainhour
Committee Member
Primus Mtenga
Committee Member
Approved:
Kamal Tawfiq, Chair, Department of Civil and Environmental Engineering
John Collier, Dean, College of Engineering
The Graduate School has verified and approved the above-named committee members.
ii
I’ll like to dedicate this dissertation to my darling wife, Tamika, my parents Audley and
Ivy Thomas, and the rest of my family who have been supportive throughout the entire
process. Thanks to Almighty God, Who through all things are possible!
iii
ACKNOWLEDGMENTS
I would like to thank my major professor, Dr. John Sobanjo, for his guidance throughout my
PhD. process. I had the tremendous opportunity to learn from his wealth of experience and
mentorship over the years. I also would like to thank the rest of my committee members,
Dr. Lisa Spainhour, Dr. Primus Mtenga and Dr. Eric Chicken. I appreciate the knowledge
I have gained from their instructions and interactions throughout my years of research and
studies at the Florida State University. The knowledge gained has not only enabled me to
be successful in my studies, but has equipped me for life.
I acknowledge my colleagues and friends who have all been a source of strength and
encouragement to me every step of the way. Thanks to the faculty and staff of the Depart-
ment of Civil and Environmental Engineering, who I have gotten to know and respect over
the years. I am grateful to the staff for their kindness and genuine interest in my success,
and I acknowledge the faculty for the high standard of education they have imparted to me
and others over the years, which is priceless.
Love and much thanks to my beautiful wife, Tamika, who shared this dissertation jour-
ney with me from beginning to end, and who have been a constant support in every way.
Many thanks to my wonderful parents Audley and Ivy Thomas, who have always believed
in me. I am also grateful to my siblings Carolin, Kim, Shaun and Karen, for their prayers
and words of encouragement. Thanks to Almighty God, the Alpha and Omega.
iv
TABLE OF CONTENTS
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1 INTRODUCTION 1
1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Background on Pavement Management . . . . . . . . . . . . . . . . . . . . . 3
1.4 Background on Bridge Management . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Stochastic Preservation Models . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 LITERATURE REVIEW 10
2.1 Stochastic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Ng (1996)’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 DeStefano (1998)’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Ng and Moses (1999)’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Black et al. (2005a,b)’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Cox Proportion Hazards Model . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 Rehabilitation-Cost Effectiveness: Existing Methodologies/Theories for Op-
timization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7.1 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7.2 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7.3 Multiobjective optimization . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Adaptive Control Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 COMPARISON OF SEMI-MARKOV AND TRADITIONAL MARKOV
CHAIN MODELS 21
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Training and Test Data . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Markov Chain Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.4 Semi-Markov Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.5 Simulation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
v
3.2.6 Actual Pavement Deterioration based on Test Data . . . . . . . . . . 32
3.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Transition Probabilities based on the Markov Chain Model . . . . . 35
3.3.2 Transition Probabilities based on the Semi-Markov Model . . . . . . 35
3.3.3 Comparison of the Markov Chain Model, Semi-Markov Model and
Actual Pavement Deterioration Behavior . . . . . . . . . . . . . . . . 45
3.4 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4 SEMI-MARKOV APPROACH FOR MODELING THE DETERIORA-
TION OF BRIDGE ELEMENTS 50
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Methodology based on Black et al. (2005a,b) . . . . . . . . . . . . . . . . . 52
4.2.1 Filtering Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.2 Model Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.3 Markov Chain Model based on Regression Method . . . . . . . . . . 55
4.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.1 Bare Concrete Deck . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.2 Pourable Joint Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.3 Reinforced Concrete Abutment . . . . . . . . . . . . . . . . . . . . . 78
4.4 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 BAYESIAN UPDATE TECHNIQUE FOR INTERVAL DEPENDENT
TRANSITION PROBABILITIES 83
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Bayesian Update of Transition Probabilities: A Theoretical Explanation . . 83
5.2.1 Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.2 Prior Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.3 Posterior Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4.1 Prior Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . 89
5.4.2 Observed (Likelihood) Transition Probabilities . . . . . . . . . . . . 90
5.4.3 Updated (Posterior) Transition Probabilities . . . . . . . . . . . . . 91
5.4.4 Bridge Element Deterioration Predictions using Updated Transition
Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4.5 Pourable Joint Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.6 Bare Concrete Deck and Reinforced Concrete Abutment . . . . . . . 96
5.5 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6 CONDITION INDEX-BASED SEMI-MARKOV MODELS OF BRIDGE
ELEMENT DETERIORATION 102
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.1 Expected Condition State . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.2 Yearly Transition Probabilities based on the Semi-Markov Process . 104
vi
6.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 ADAPTIVE CONTROL APPROACH TO BRIDGE MANAGEMENT
SYSTEM 119
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.1 Network Level Optimization . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.2 Project Level Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2.3 Modeling of Deterioration Using Semi-Markov Processes . . . . . . . 121
7.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3.1 Discount Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3.2 The Laplace transform (s-transform) . . . . . . . . . . . . . . . . . . 122
7.3.3 Semi-Markov Decision Process with Discounting . . . . . . . . . . . 123
7.3.4 Do-nothing Action (Action ‘d’) . . . . . . . . . . . . . . . . . . . . . 125
7.3.5 Maintenance Action (Action ‘m’) . . . . . . . . . . . . . . . . . . . . 126
7.3.6 Rehabilitation Action (Action ‘r’) . . . . . . . . . . . . . . . . . . . 128
7.3.7 Action Unit Cost for SMDP and MDP models . . . . . . . . . . . 128
7.4 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.4.1 The ‘Inputs’ for Do-nothing Actions . . . . . . . . . . . . . . . . . . 131
7.4.2 The ‘Inputs’ for Maintenance Action . . . . . . . . . . . . . . . . . . 133
7.4.3 Results of the Semi-Markov Decision Processes Model to FHWA
Cost Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
⃝R
7.4.4 Results of the Semi-Markov Decision Processes Model to Florida (Pontis )
Cost Data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.5 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8 MODELING SERVICE LIVES OF PAVEMENT AND BRIDGE ELE-
MENTS 141
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
8.2.1 Pavement: Service Life . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.2.2 Bridge Element: Service Life . . . . . . . . . . . . . . . . . . . . . . 142
8.2.3 Parametric Model: Weibull Model . . . . . . . . . . . . . . . . . . . 142
8.2.4 Semi-Parametric Model: Cox Model . . . . . . . . . . . . . . . . . . 143
8.2.5 Nonparamteric Analysis: Kaplan-Meier . . . . . . . . . . . . . . . . 143
8.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.3.1 Survival Analysis: Service Life for Flexible Pavement . . . . . . . . . 144
8.3.2 Survival Analysis: Service Life for Concrete Bare Deck . . . . . . . . 147
8.4 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9 DISCUSSION AND CONCLUSION 152
9.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
vii
Bibliography 156
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
viii
LIST OF TABLES
2.1 Number of transformers in each paintwork class grouped by the number of
years since the last refurbishment (Source: Black et al. (2005b)) . . . . . . . 14
3.1 The Range of Crack Indices and Corresponding Condition States . . . . . . . 23
3.2 Transition Probabilities of the Embedded Markov Chain of the Semi-Markov
Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Results based on Maximum Likelihood Estimation of the Scale (α) and Shape
(β) Parameters for the Holding Time (Weibull) Distributions in Condition
State i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Means and Standard Deviations of Sojourn Times (Weibull) . . . . . . . . . 42
3.5 Goodness-of-Fit Test on Pavement Sojourn Times (Weibull) . . . . . . . . . 43
4.1 Example of a condition record for Pourable Joint Seal (element 301) . . . . . 51
4.2 Estimated Scale and Shape Parameters, Mean and Standard Deviation for the
Sojourn Times in Each Condition States for Bare Concrete Deck . . . . . . . 58
4.3 Computed Condition State 1 probabilities for Bare Concrete Deck . . . . . . 59
4.4 Estimated Scale and Shape Parameters, Mean and Standard Deviation for the
Sojourn Times in Each Condition States for Pourable Joint Seal . . . . . . . 69
4.5 Computed Condition State 1 probabilities for Pourable Joint Seal . . . . . . 69
4.6 Estimated Scale and Shape Parameters, Mean and Standard Deviation for the
Sojourn Times in Each Condition States for Reinforced Concrete Abutment . 78
5.1 ‘Number’ of Pourable Joint Seal in each condition state for years 2007 and 2008 90
5.2 Transition Probabilities and Proportions in Condition State i for Pourable
Joint Seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Prior Transition Probability Weights and Updated Transition Probabilities for
Pourable Joint Seals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
ix