Probabilistic Indicators of Structural Redundancy in Mechanics

Affiliation(s)

Department of Mechanical Engineering and Naval Architecture, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), University of Split, Split, Croatia.

Department of Ship Structures, Faculty of Mechanical Engineering and Naval Architecture (FSB), University of Zagreb, Zagreb, Croatia.

Department of Mechanical Engineering and Naval Architecture, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), University of Split, Split, Croatia.

Department of Ship Structures, Faculty of Mechanical Engineering and Naval Architecture (FSB), University of Zagreb, Zagreb, Croatia.

ABSTRACT

The paper in the introductory part reviews various definitions and interpretations of structural redundancy in mechanics. The study focuses on the general structural redundancy of systems after sequences of component failures followed by possible load redistributions. The second section briefly summarizes the Event Oriented System Analysis and structural redundancy in terms of the conditional probabilistic entropy. Mechanical responses to adverse loads in this approach are represented by random operational and failure events in the lifetime. The general redundancy measure in the third section of the paper employs the information entropy and goes beyond existing formulations since it includes all functional modes in service. The paper continues with a summary of traditional redundancy indices. In addition, it proposes an alternative redundancy index that accounts for the transition to secondary functional level in case of failures of primary components. The example of a ship structure illustrates the usage of the conditional entropy of subsystems of operational events and compares it to the traditional and newly proposed redundancy indices. The study at the end investigates how to enhance the safety of structures by using the redundancy based design.

The paper in the introductory part reviews various definitions and interpretations of structural redundancy in mechanics. The study focuses on the general structural redundancy of systems after sequences of component failures followed by possible load redistributions. The second section briefly summarizes the Event Oriented System Analysis and structural redundancy in terms of the conditional probabilistic entropy. Mechanical responses to adverse loads in this approach are represented by random operational and failure events in the lifetime. The general redundancy measure in the third section of the paper employs the information entropy and goes beyond existing formulations since it includes all functional modes in service. The paper continues with a summary of traditional redundancy indices. In addition, it proposes an alternative redundancy index that accounts for the transition to secondary functional level in case of failures of primary components. The example of a ship structure illustrates the usage of the conditional entropy of subsystems of operational events and compares it to the traditional and newly proposed redundancy indices. The study at the end investigates how to enhance the safety of structures by using the redundancy based design.

KEYWORDS

Reliability; Event-Oriented System Analysis; Entropy; Redundancy; Redundancy Index; Structures

Reliability; Event-Oriented System Analysis; Entropy; Redundancy; Redundancy Index; Structures

Cite this paper

nullB. Blagojević and K. Žiha, "Probabilistic Indicators of Structural Redundancy in Mechanics,"*World Journal of Mechanics*, Vol. 2 No. 5, 2012, pp. 229-238. doi: 10.4236/wjm.2012.25028.

nullB. Blagojević and K. Žiha, "Probabilistic Indicators of Structural Redundancy in Mechanics,"

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[26] K. ?iha, “Event –oriented Analysis of Series Structural Systems,” Structural Safety, Vol. 23, 2001, pp 1-29. doi:10.1016/S0167-4730(00)00022-9

[27] K. ?iha, “Redun-dancy and Robustness of Systems of Events,” Probabilistic Engineering Mechanics, Vol. 15, No. 4, 2000, pp. 347-357. doi:10.1016/S0266-8920(99)00036-3

[28] C. Palion, M. Shi-nozuka and Y. N. Chen, “Reliability Analysis of Offshore Structures,” Marine Structural Reliability Symposium, New York, 1987.

[29] R. S. De, A. Karamchandani and C. A. Cor-nell, “Study of redundancy in near-ideal parallel structural sys-tems,” Structural Safety and Reliability, No. 2, 1990, pp. 975-982.

[30] S. Hendawi and D. M. Frangopol, “System Reliability and Redundancy in Structural Design and Evalua-tion,” Structural Safety, No. 16, 1994, pp. 47-71. doi:10.1016/0167-4730(94)00027-N

[31] K. ?iha, “Redun-dancy based design by event oriented analysis,” Transactions of FAMENA, Vol. 27, No. 2, 2003, pp. 1-12.

[32] K. ?iha, “Event-oriented analysis of fail-safe objects,” Transactions of FAMENA, Vol. 27, No. 1, 2003, pp. 11-22.

[33] B. Blagojevi? and K. ?iha, “On the assessment of redundancy of ship struc-tural components,” Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008, Estoril 2008, pp. 256-262.

[34] Ship's Load and Strength Manual. Oslo: Det Norske Veritas; 1995.

[35] Rules for Classification of Ships. Oslo: Det Norske Veritas; 2007.

[36] I. A. Assakkaf, “Reliability-Design of Panels and Fatigue Details of Ship Structures,” University of Maryland, 1998.

[37] C. Guedes Soares and P. M. Dogliani, “Probabilistic modelling of time-varying still-water load effects in tankers,” Marine Structures, No.13, 2000, pp. 129–143. doi:10.1016/S0951-8339(00)00006-X

[38] K. Atua, I. A. As-sakkaf and M. Ayyub, “Statistical Characteristics of Strength and Load Random Variable of Ship Structures. Proceedings of the 7th Specialty Conference on Probabilistic Mechanisms and Structural Reliability, Massachusetts, 1996.

[39] J. Parunov, I. Senjanovi? and C. Guedes Soares, “Hull-girder reliability of new generation oil tanker,” Marine Structures, Vol. 20, No. 1-2, 2007, pp. 49-70.

[1] M. Arvidsson and I. Gremyr, “Principles of Robust Design Methodology,” Quality and Reliability Engineering International, No. 24, 2008, pp. 24-35.

[2] G. Taguchi, S. Chowdhury and S. Taguchi, “Robust Engineering-Learn How to Boost Quality While Reducing Costs and Time to Market,” McGraw-Hill, New York, 2000.

[3] J. Agarwal, D. I. Blockley and N. J. Woodman, “Vulnerability of structural systems,” Structural Safety , No.25, 2003, pp. 263–86. doi:10.1016/S0167-4730(02)00068-1

[4] A. Eriksson and A. Gunnar Tibert, “Redundant and force-differentiated systems in engineering and nature,” Computer Methods in Applied Me-chanics and Engineering , Vol.195, No.41, 2006, pp. 5437-5453. doi:10.1016/j.cma.2005.11.007

[5] J. W. Baker, M. Schubert and M. H. Faber, “On the assessment of robustness,” Structural Safety , Vol.30, No.3, 2008, pp. 253-267. doi:10.1016/j.strusafe.2006.11.004

[6] B. W. Schafer and P. Bajpai, “Stability degradation and redundancy in damaged structures,” Engineering Structures, Vol.27, No.11, 2005, pp. 1642-1651. doi:10.1016/j.engstruct.2005.05.012

[7] L. Due?as-Osorio and S.M. Vemuru, “Cascading failures in complex infrastructure systems,” Structural Safety, Vol.31, No.2, 2009, pp. 157-167. doi:10.1016/j.strusafe.2008.06.007

[8] Z. Tian and M. J. Zuo, “Redundancy allocation for multi-state systems using physical programming and genetic algorithms,” Reliability Engineering and System Safety, Vol.91, No.9, 2006, pp. 1049–56. doi:10.1016/j.ress.2005.11.039

[9] J. England, J. Agarwal and D. Blockley, “The vulnerability of structures to unforeseen events,” Computers & Structures, Vol.86, No.10, 2008, pp. 1042-1051. doi:10.1016/j.compstruc.2007.05.039

[10] S.G. Stiansen, “In-terrelation between Design, Inspection and Redundancy in Ma-rine Structures,” National Academy Press , Washington D.C., 1984.

[11] Y. Feng, “The Theory of Structural Redundancy and its effect on structural design,” Computers & Structures, Vol. 28, No.1, 1988, pp. 15-24. doi:10.1016/0045-7949(88)90087-9

[12] K. Chen and S. Zhang, “Semi-probabilistic method for evaluating systems redundancy of existing offshore structures,” Ocean Engineering, Vol. 23, No.6, 1996, pp. 455-464. doi:10.1016/0029-8018(95)00051-8

[13] C. E. Shannon and W. Weaver, “The mathematical theory of communication,” Urbana University of Illinois Press, 1949.

[14] A. Rényi, “Probability theory,” Amsterdam North-Holland, 1970.

[15] J. Aczel and Z. Daroczy, “On measures of information and their characteriza-tion,” Academic Press, New York, 1975.

[16] A. I. Khinchin, “Mathematical Foundations of Information Theory,” Dover Publications, 1957.

[17] K. ?iha, “Event Oriented System Analysis,” Probabilistic Engineering Mechanics, Vol. 15, No. 3, 2000, pp. 261-275. doi:10.1016/S0266-8920(99)00025-9

[18] M. Hoshiya, K. Yamamoto and H. Ohno, “Redundancy index of lifelines for mitigation measures against seismic risk,” Probabilistic Engi-neering Mechanics, Vol. 19, No. 3, 2004, pp. 205-210. doi:10.1016/j.probengmech.2004.02.003

[19] H. Madsen, S. Krenk and N. C. Lind, “Methods of Structural Safety,” Prentice Hall, Englewood Cliffs NJ, 1986.

[20] A. H. S. Ang and W. H. Tang, “Probability concepts in engineering,” John Wiley, New York, 2007.

[21] S. K. Choi, R. V. Grandhi and R. A. Canfield, “Reliability-based Structural Design,” Springer, New York, 2007.

[22] M. Rausand and A. H?yland, “System Reliability Theory: Models, Statistical Methods, and Applications,” Wi-ley-Interscience, New York, 2003.

[23] R. Y. Rubinstein and D. P. Kroese, “Simulation and the Monte Carlo Method,” Wi-ley-Interscience, New York, 2007. doi:10.1002/9780470230381

[24] M. S. Hamada, A. Wilson, C. S. Reese and H. F. Martz, “Bayesian Reliability,” Springer, New York, 2008. doi:10.1007/978-0-387-77950-8

[25] D. L. Kreher and D. R. Stinson, “Combinatorial Algorithms: Generation, Enumeration, and Search,” CRC Press, 1998.

[26] K. ?iha, “Event –oriented Analysis of Series Structural Systems,” Structural Safety, Vol. 23, 2001, pp 1-29. doi:10.1016/S0167-4730(00)00022-9

[27] K. ?iha, “Redun-dancy and Robustness of Systems of Events,” Probabilistic Engineering Mechanics, Vol. 15, No. 4, 2000, pp. 347-357. doi:10.1016/S0266-8920(99)00036-3

[28] C. Palion, M. Shi-nozuka and Y. N. Chen, “Reliability Analysis of Offshore Structures,” Marine Structural Reliability Symposium, New York, 1987.

[29] R. S. De, A. Karamchandani and C. A. Cor-nell, “Study of redundancy in near-ideal parallel structural sys-tems,” Structural Safety and Reliability, No. 2, 1990, pp. 975-982.

[30] S. Hendawi and D. M. Frangopol, “System Reliability and Redundancy in Structural Design and Evalua-tion,” Structural Safety, No. 16, 1994, pp. 47-71. doi:10.1016/0167-4730(94)00027-N

[31] K. ?iha, “Redun-dancy based design by event oriented analysis,” Transactions of FAMENA, Vol. 27, No. 2, 2003, pp. 1-12.

[32] K. ?iha, “Event-oriented analysis of fail-safe objects,” Transactions of FAMENA, Vol. 27, No. 1, 2003, pp. 11-22.

[33] B. Blagojevi? and K. ?iha, “On the assessment of redundancy of ship struc-tural components,” Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008, Estoril 2008, pp. 256-262.

[34] Ship's Load and Strength Manual. Oslo: Det Norske Veritas; 1995.

[35] Rules for Classification of Ships. Oslo: Det Norske Veritas; 2007.

[36] I. A. Assakkaf, “Reliability-Design of Panels and Fatigue Details of Ship Structures,” University of Maryland, 1998.

[37] C. Guedes Soares and P. M. Dogliani, “Probabilistic modelling of time-varying still-water load effects in tankers,” Marine Structures, No.13, 2000, pp. 129–143. doi:10.1016/S0951-8339(00)00006-X

[38] K. Atua, I. A. As-sakkaf and M. Ayyub, “Statistical Characteristics of Strength and Load Random Variable of Ship Structures. Proceedings of the 7th Specialty Conference on Probabilistic Mechanisms and Structural Reliability, Massachusetts, 1996.

[39] J. Parunov, I. Senjanovi? and C. Guedes Soares, “Hull-girder reliability of new generation oil tanker,” Marine Structures, Vol. 20, No. 1-2, 2007, pp. 49-70.