Probabilistic models for life‐cycle performance of deteriorating structures: review and future directions

In comparison with the well-researched field of analysis and design of structural systems, the life-cycle performance prediction of these systems under no maintenance as well as under various maintenance scenarios is far more complex, and is a rapidly emergent field in structural engineering. As structures become older and maintenance costs become higher, different agencies and administrations in charge of civil infrastructure systems are facing challenges related to the implementation of structure maintenance and management systems based on life-cycle cost considerations. This article reviews the research to date related to probabilistic models for maintaining and optimizing the life-cycle performance of deteriorating structures and formulates future directions in this field.

[1]  Samer Madanat,et al.  Optimization of Infrastructure Systems Maintenance and Improvement Policies , 1999 .

[2]  Nozer D. Singpurwalla,et al.  Survival in Dynamic Environments , 1995 .

[3]  Ülkü Gürler,et al.  A maintenance policy for a system with multi-state components: an approximate solution , 2002, Reliab. Eng. Syst. Saf..

[4]  Rüdiger Rackwitz.  Optimizing systematically renewed structures , 2001, Reliab. Eng. Syst. Saf..

[5]  M. Abdel-Hameed.  Inspection and maintenance policies of devices subject to deterioration , 1987, Advances in Applied Probability.

[6]  Mahmut Parlar,et al.  A survey of maintenance models for multi-unit systems , 1991 .

[7]  S E Lipkus.  BRIDGIT - BRIDGE MANAGEMENT SYSTEM SOFTWARE , 1993 .

[8]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .

[9]  Ludo Gelders,et al.  Maintenance management decision making , 1992 .

[10]  Dan M. Frangopol,et al.  Cost-Reliability Interaction in Life-Cycle Cost Optimization of Deteriorating Structures , 2004 .

[11]  D. G. Robinson.  A survey of probabilistic methods used in reliability, risk and uncertainty analysis: Analytical techniques 1 , 1998 .

[12]  Mark G. Stewart,et al.  Reliability-based assessment of ageing bridges using risk ranking and life cycle cost decision analyses , 2001, Reliab. Eng. Syst. Saf..

[13]  Y. S. Sherif,et al.  Optimal maintenance models for systems subject to failure–A Review , 1981 .

[14]  Mohamed Abdel-Hameed,et al.  OPTIMAL REPLACEMENT POLICIES FOR DEVICES SUBJECT TO A GAMMA WEAR PROCESS**Research supported in part by the Air Force Office of Scientific Research, AFSC, USAF, under Grant AFOSR-76-2999 and Office of Naval Research Contract N00014-76-C-0840. , 1977 .

[15]  Antoine Grall,et al.  A condition-based maintenance policy for stochastically deteriorating systems , 2002, Reliab. Eng. Syst. Saf..

[16]  Tarek Zayed,et al.  Life-Cycle Cost Analysis using Deterministic and Stochastic Methods: Conflicting Results , 2002 .

[17]  Dimitri A. Grivas,et al.  Method for Estimating Transition Probability in Bridge Deterioration Models , 1998 .

[18]  Kelvin C. P. Wang,et al.  20/30 HINDSIGHT -- THE NEW PAVEMENT OPTIMIZATION IN THE ARIZONA STATE HIGHWAY NETWORK. , 1996 .

[19]  Eric V. Denardo,et al.  Dynamic Programming: Models and Applications , 2003 .

[20]  Antoine Grall,et al.  Sequential condition-based maintenance scheduling for a deteriorating system , 2003, Eur. J. Oper. Res..

[21]  Jan M. van Noortwijk,et al.  Optimal Sand Nourishment Decisions , 2000 .

[22]  J. D. Bakker.  MODEL OF LIFETIME-EXTENDING MAINTENANCE , .

[23]  Ross B. Corotis,et al.  Reliability-based bridge design and life cycle management with Markov decision processes☆ , 1994 .

[24]  Dan M. Frangopol,et al.  Updating Reliability of Steel Miter Gates on Locks and Dams Using Visual Inspection Results , 2004 .

[25]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[26]  Hongzhou Wang,et al.  A survey of maintenance policies of deteriorating systems , 2002, Eur. J. Oper. Res..

[27]  J. M. van Noortwijk,et al.  Optimal inspection decisions for the block mats of the Eastern-Scheldt barrier , 1999 .

[28]  Y. S. Sherif,et al.  Reliability analysis : Optimal inspection and maintenance schedules of failing systems , 1982 .

[29]  Samer Madanat,et al.  Computation of Infrastructure Transition Probabilities using Stochastic Duration Models , 2002 .

[30]  Diederik J.D. Wijnmalen,et al.  Optimum condition-based maintenance policies for deteriorating systems with partial information , 1996 .

[31]  Nozer D. Singpurwalla.  Gamma Processes and their Generalizations: An Overview , 1997 .

[32]  Antoine Grall,et al.  Continuous-time predictive-maintenance scheduling for a deteriorating system , 2002, IEEE Trans. Reliab..

[33]  Kamal Golabi.  A Markov Decision Modeling Approach to a Multi-Objective Maintenance Problem , 1983 .

[34]  Dan M. Frangopol,et al.  Cost of life extension of deteriorating structures under reliability-based maintenance , 2004 .

[35]  Jan M. van Noortwijka.  Explicit formulas for the variance of discounted life-cycle cost , 2003 .

[36]  Samer Madanat,et al.  Optimal infrastructure management decisions under uncertainty , 1993 .

[37]  Bruce R. Ellingwood,et al.  MAINTAINING RELIABILITY OF CONCRETE STRUCTURES. I: ROLE OF INSPECTION/REPAIR , 1994 .

[38]  Palle Thoft-Christensen,et al.  Assessment of the Reliability Profiles for Concrete Bridges , 1998 .

[39]  Richard M. Feldman,et al.  A survey of preventive maintenance models for stochastically deteriorating single-unit systems , 1989 .

[40]  Kamal Golabi,et al.  A Statewide Pavement Management System , 1982 .

[41]  Palle Thoft-Christensen,et al.  Optimal strategy for inspection and repair of structural systems , 1987 .

[42]  Dan M. Frangopol,et al.  Updating Bridge Reliability Based on Bridge Management Systems Visual Inspection Results , 2003 .

[43]  L. Manuel,et al.  Optimal inspection scheduling with alternative fatigue reliability formulations for steel bridges , 2003 .

[44]  R. Cooke,et al.  Optimal Maintenance Decisions for the Sea-Bed Protection of the Eastern-Scheldt Barrier , 1997 .

[45]  Michael P. Enright,et al.  Maintenance Planning for Deteriorating Concrete Bridges , 1999 .

[46]  Antoine Grall,et al.  A sequential condition‐based repair/replacement policy with non‐periodic inspections for a system subject to continuous wear , 2003 .

[47]  Pieter van Gelder,et al.  Optimal maintenance decisions for berm breakwaters , 1996 .

[48]  B. Ellingwood,et al.  Directional methods for structural reliability analysis , 2000 .

[49]  A. H. Christer,et al.  A prototype cost model of functional check decisions in reliability-centred maintenance , 2002, J. Oper. Res. Soc..

[50]  P. Thompson,et al.  The Pontis Bridge Management System, Structural Engineering International , 1998 .

[51]  Mahesh D. Pandey,et al.  Probabilistic models for condition assessment of oil and gas pipelines , 1998 .

[52]  Dan M. Frangopol,et al.  Minimum expected cost-oriented optimal maintenance planning for deteriorating structures: application to concrete bridge decks , 2001, Reliab. Eng. Syst. Saf..

[53]  Achintya Haldar,et al.  FATIGUE-RELIABILITY EVALUATION OF STEEL BRIDGES , 1994 .

[54]  George Hearn,et al.  Integration of Bridge Management Systems and Nondestructive Evaluations , 1998 .

[55]  William P. Pierskalla,et al.  A survey of maintenance models: The control and surveillance of deteriorating systems , 1976 .

[56]  Ross B. Corotis,et al.  INSPECTION, MAINTENANCE, AND REPAIR WITH PARTIAL OBSERVABILITY , 1995 .

[57]  F. Dufresne,et al.  Risk Theory with the Gamma Process , 1991, ASTIN Bulletin.

[58]  Michael P. Enright,et al.  Condition Prediction of Deteriorating Concrete Bridges Using Bayesian Updating , 1999 .

[59]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[60]  M. Abdel-Hameed.  A Gamma Wear Process , 1975, IEEE Transactions on Reliability.

[61]  Kamal Golabi,et al.  INNOVATIVE PAVEMENT MANAGEMENT AND PLANNING SYSTEM FOR ROAD NETWORK OF PORTUGAL , 2003 .

[62]  Roger M. Cooke,et al.  OPTIMAL MAINTENANCE DECISIONS FOR DIKES , 2000, Probability in the Engineering and Informational Sciences.

[63]  Samer Madanat,et al.  Poisson Regression Models of Infrastructure Transition Probabilities , 1995 .

[64]  Dan M. Frangopol,et al.  Optimum Lifetime Planning of Bridge Inspection and Repair Programs , 1999 .

[65]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[66]  Dan M. Frangopol,et al.  Repair Optimization of Highway Bridges Using System Reliability Approach , 1999 .

[67]  Jan M. van Noortwijk,et al.  Optimal Replacement Decisions for Structures under Stochastic Deterioration , 2004 .

[68]  Rommert Dekker,et al.  On the impact of optimisation models in maintenance decision making: the state of the art , 1998 .

[69]  Rommert Dekker,et al.  Applications of maintenance optimization models : a review and analysis , 1996 .

[70]  Dan M. Frangopol,et al.  Life-cycle performance of deteriorating structures : assessment, design, and management , 2003 .

[71]  Dan M. Frangopol,et al.  Cost of reliability improvement and deterioration delay of maintained structures , 2003 .

[72]  J. Kingman.  A FIRST COURSE IN STOCHASTIC PROCESSES , 1967 .

[73]  Diederik J.D. Wijnmalen,et al.  Review of a Markov decision algorithm for optimal inspections and revisions in a maintenance system with partial information , 1992 .

[74]  Kyung S. Park,et al.  Optimal replacement of an item subject to cumulative damage under periodic inspections , 1997 .

[75]  Dan M. Frangopol,et al.  Probabilistic Performance Prediction of Deteriorating Structures Under Different Maintenance Strategies: Condition, Safety and Cost , 2003 .

[76]  Palle Thoft-Christensen,et al.  Structural Reliability Theory and Its Applications , 1982 .

[77]  J. McCall.  Maintenance Policies for Stochastically Failing Equipment: A Survey , 1965 .

[78]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[79]  Bruce R. Ellingwood,et al.  MAINTAINING RELIABILITY OF CONCRETE STRUCTURES. II: OPTIMUM INSPECTION/REPAIR , 1994 .

[80]  Samer Madanat,et al.  Estimation of infrastructure transition probabilities from condition rating data , 1995 .

[81]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[82]  Tarek Zayed,et al.  Statewide Performance Function for Steel Bridge Protection Systems , 2002 .

[83]  Yehuda Kleiner,et al.  Scheduling Inspection and Renewal of Large Infrastructure Assets , 2001 .

[84]  Parag C. Das.  Application of reliability analysis in bridge management , 1998 .

[85]  Palle Thoft-Christensen.  RELIABILITY PROFILES FOR CONCRETE BRIDGES , 1996 .

[86]  P C Das.  RELIABILITY BASED BRIDGE MANAGEMENT PROCEDURES , 2000 .

[87]  K Smilowitz,et al.  OPTIMAL INSPECTION AND MAINTENANCE POLICIES FOR INFRASTRUCTURE SYSTEMS UNDER MEASUREMENT AND PREDICTION UNCERTAINTY , 2000 .

[88]  Hugh Hawk,et al.  The BRIDGIT Bridge Management System , 1998 .

[89]  Ross B. Corotis,et al.  Reliability-Based Structural Design with Markov Decision Processes , 1995 .

[90]  Bruce R. Ellingwood,et al.  Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants , 1993 .

[91]  J. M. van Noortwijk,et al.  Inspection and maintenance decisions based on imperfect inspections , 2003 .

[92]  Allen R. Marshall,et al.  The PONTIS bridge management system , 1998 .

[93]  Henk Tijms,et al.  A Markov decision algorithm for optimal inspections and revisions in a maintenance system with partial information , 1985 .

[94]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[95]  Dan M. Frangopol,et al.  Bridge Deck Replacement for Minimum Expected Cost Under Multiple Reliability Constraints , 2004 .

[96]  Erik H. Vanmarcke,et al.  Modeling Bridge Deterioration with Markov Chains , 1992 .

[97]  David Z. Yankelevsky,et al.  Optimization problem solution in reliability analysis of reinforced concrete structures , 1996 .

[98]  Andrzej S. Nowak,et al.  Lifetime Reliability Profiles for Steel Girder Bridges , 1997 .

[99]  William T. Scherer,et al.  Markovian Models for Bridge Maintenance Management , 1994 .

[100]  Dan M. Frangopol,et al.  Life-cycle cost design of deteriorating structures , 1997 .

[101]  Palle Thoft-Christensen,et al.  Probability‐Based Bridge Inspection Strategy , 1993 .

[102]  Ross B. Corotis,et al.  Optimal Life-Cycle Costing with Partial Observability , 2000 .

[103]  Chris P. Tsokos,et al.  The theory and applications of reliability with emphasis on Bayesian and nonparametric methods , 1978 .

[104]  Kyung S. Park,et al.  Optimal continuous-wear limit replacement under periodic inspections , 1988 .

[105]  T. Ferguson,et al.  A Representation of Independent Increment Processes without Gaussian Components , 1972 .

[106]  Kevin L. Rens,et al.  BRIDGE MANAGEMENT SYSTEM FOR THE CITY AND COUNTY OF DENVER , 1999 .

[107]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[108]  S. C. Yang,et al.  LIFE-CYCLE RELIABILITY-BASED MAINTENANCE COST OPTIMIZATION OF DETERIORATING STRUCTURES WITH EMPHASIS ON BRIDGES , 2003 .

[109]  Melvin L. Baron,et al.  Journal of the Engineering Mechanics Division , 1956 .

[110]  C A Cornell,et al.  A PROBABILITY BASED STRUCTURAL CODE , 1969 .

[111]  Kamal Golabi,et al.  Pontis: A System for Maintenance Optimization and Improvement of US Bridge Networks , 1997 .

[112]  R. Cooke,et al.  A Bayesian failure model based on isotropic deterioration , 1995 .

[113]  Dan M. Frangopol,et al.  Reliability- and Cost-Oriented Optimal Bridge Maintenance Planning , 2000 .

[114]  E. Çinlar,et al.  STOCHASTIC PROCESS FOR EXTRAPOLATING CONCRETE CREEP , 1977 .

[115]  Dan M. Frangopol,et al.  Optimal Network-Level Bridge Maintenance Planning Based on Minimum Expected Cost , 2000 .

[116]  Dan M. Frangopol,et al.  RELIABILITY-BASED LIFE-CYCLE MANAGEMENT OF HIGHWAY BRIDGES , 2001 .

[117]  Jan M. van Noortwijk,et al.  Explicit formulas for the variance of discounted life-cycle cost , 2003, Reliab. Eng. Syst. Saf..