Algorithms for Bayesian network modeling and reliability assessment of infrastructure systems

Novel algorithms are developed to enable the modeling of large, complex infrastructure systems as Bayesian networks (BNs). These include a compression algorithm that significantly reduces the memory storage required to construct the BN model, and an updating algorithm that performs inference on compressed matrices. These algorithms address one of the major obstacles to widespread use of BNs for system reliability assessment, namely the exponentially increasing amount of information that needs to be stored as the number of components in the system increases. The proposed compression and inference algorithms are described and applied to example systems to investigate their performance compared to that of existing algorithms. Orders of magnitude savings in memory storage requirement are demonstrated using the new algorithms, enabling BN modeling and reliability analysis of larger infrastructure systems.

[1]  Armen Der Kiureghian,et al.  Multi-scale reliability analysis and updating of complex systems by use of linear programming , 2008, Reliab. Eng. Syst. Saf..

[2]  Kevin Murphy,et al.  Bayes net toolbox for Matlab , 1999 .

[3]  Daniel Straub,et al.  Stochastic Modeling of Deterioration Processes through Dynamic Bayesian Networks , 2009 .

[4]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

[5]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[6]  Christine M. Anderson-Cook,et al.  System Reliability Theory: Models, Statistical Methods, and Applications (2nd ed.) (Book) , 2004 .

[7]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[8]  Radford M. Neal.  Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .

[9]  Kasturi Narasimhan,et al.  Reliability Engineering: Theory and Practice, 4th edition , 2005 .

[10]  Changhe Yuan,et al.  Importance sampling algorithms for Bayesian networks: Principles and performance , 2006, Math. Comput. Model..

[11]  A. Hasman,et al.  Probabilistic reasoning in intelligent systems: Networks of plausible inference , 1991 .

[12]  Wei-Chang Yeh.  A new algorithm for generating minimal cut sets in k-out-of-n networks , 2006, Reliab. Eng. Syst. Saf..

[13]  Joanne Bechta Dugan,et al.  A discrete-time Bayesian network reliability modeling and analysis framework , 2005, Reliab. Eng. Syst. Saf..

[14]  Alessandro Birolini.  Reliability Engineering: Theory and Practice , 1999 .

[15]  S. Ahmed,et al.  Bayesian Networks and Decision Graphs (2nd ed.), by F. V. Jenson and T. D. Nielsen , 2008 .

[16]  Anders L. Madsen,et al.  Belief update in CLG Bayesian networks with lazy propagation , 2006, Int. J. Approx. Reason..

[17]  P.D.T. O'Connor,et al.  System Reliability. Evaluation and Prediction in Engineering , 1987 .

[18]  J. Koh,et al.  An algorithm for generating minimal cutsets of undirected graphs , 1998 .

[19]  Marvin Rausand,et al.  System Reliability Theory , 2020, Wiley Series in Probability and Statistics.

[20]  Iris Tien,et al.  Compression algorithm for Bayesian network modeling of binary systems , 2014 .

[21]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[22]  Carl K. Chang,et al.  Algorithms for the minimal cutsets enumeration of networks by graph search and branch addition , 2000, Proceedings 25th Annual IEEE Conference on Local Computer Networks. LCN 2000.

[23]  Natasha Smith,et al.  Bayesian networks for system reliability reassessment , 2001 .

[24]  Luigi Portinale,et al.  Improving the analysis of dependable systems by mapping fault trees into Bayesian networks , 2001, Reliab. Eng. Syst. Saf..

[25]  Nasser Fard.  Determination of minimal cut sets of a complex fault tree , 1997 .

[26]  Mohammad Modarres,et al.  Reliability engineering and risk analysis : a practical guide , 2016 .

[27]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[28]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[29]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[30]  Zhibin Tan.  Minimal cut sets of s-t networks with k-out-of-n nodes , 2003, Reliab. Eng. Syst. Saf..

[31]  Thomas D. Nielsen,et al.  Using ROBDDs for Inference in Bayesian Networks with Troubleshooting as an Example , 2000, UAI.

[32]  David J. Spiegelhalter,et al.  Bayesian analysis in expert systems , 1993 .

[33]  Luis Enrique Sucar,et al.  Bayesian Networks for Reliability Analysis of Complex Systems , 1998, IBERAMIA.

[34]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[35]  Michelle Terese Bensi,et al.  A Bayesian Network Methodology for Infrastructure Seismic Risk Assessment and Decision Support , 2010 .

[36]  Li Jie,et al.  Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks , 2007 .

[37]  Michel Gondran,et al.  System reliability: evaluation & prediction in engineering , 1986 .

[38]  Marvin Rausand,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2003 .

[39]  Daniel Straub,et al.  Efficient Bayesian network modeling of systems , 2013, Reliab. Eng. Syst. Saf..

[40]  Man Cheol Kim,et al.  Reliability block diagram with general gates and its application to system reliability analysis , 2011 .

[41]  Mohamed Benaddy,et al.  Cutset Enumerating and Network Reliability Computing by a new Recursive Algorithm and Inclusion Exclusion Principle , 2012 .

[42]  Wei Liu,et al.  Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks , 2007 .

[43]  A. Salmerón,et al.  Importance sampling in Bayesian networks using probability trees , 2000 .

[44]  Seung-Yong Ok,et al.  Multi-scale system reliability analysis of lifeline networks under earthquake hazards , 2009 .

[45]  Iris Tien,et al.  Bayesian Network Methods for Modeling and Reliability Assessment of Infrastructure Systems , 2014 .