Research Papers

A Comparative Study of Evidence Theories in the Modeling, Analysis, and Design of Engineering Systems

[+] Author and Article Information
K. K. Annamdas

Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33146

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 4, 2012; final manuscript received March 28, 2013; published online May 9, 2013. Assoc. Editor: Zissimos P. Mourelatos.

J. Mech. Des 135(6), 061006 (May 09, 2013) (10 pages) Paper No: MD-12-1297; doi: 10.1115/1.4024229 History: Received June 04, 2012; Revised March 28, 2013

The application of different types of evidence theories in the modeling, analysis and design of engineering systems is explored. In most studies dealing with evidence theory, the Dempster–Shafer theory (DST) has been used as the framework not only for the characterization and representation of uncertainty but also for combining evidence. The versatility of the theory is the motivation for selecting DST to represent and combine different types of evidence obtained from multiple sources. In this work, five evidence combination rules, namely, Dempster–Shafer, Yager, Inagaki, Zhang, and Murrphy combination rules, are considered. The limitations and sensitivity of the DST rule in the case of conflicting evidence are illustrated with examples. The application of all the five evidence combination rules for the modeling, analysis and design of engineering systems is illustrated using a power plant failure example and a welded beam problem. The aim is to understand the basic characteristics of each rule and develop preliminary guidelines or criteria for selecting an evidence combination rule that is most appropriate based on the nature and characteristics of the available evidence. Since this work is the first one aimed at developing the guidelines or criteria for selecting the most suitable evidence combination rule, further studies are required to refine the guidelines and criteria developed in this work.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Dempster, A. P., 1967, “Upper and Lower Probabilities Induced by a Multivalued Mapping,” Ann. Math. Stat., 38, pp. 325–339. [CrossRef]
Shafer, G., 1976, A Mathematical Theory of Evidence, Princeton University Press, Princeton, NJ.
Ha-Rok, B., 2004, “Uncertainty Quantification and Optimization of Structural Response Using Evidence Theory,” Ph.D. dissertation, Wright State University, Dayton, OH.
Sentz, K., and Ferson, S., 2002, “Combination of Evidence in Dempster-Shafer Theory,” Sandia Report SAND2002-0835, Sandia National Laboratories, Albuquerque, NM.
Yong, D., WenKang, S., ZhenFu, Z., and Qi, L., 2004, “Combining Belief Functions Based on Distance of Evidence,” Decision Support Sys., 38, pp. 489–493. [CrossRef]
Oberjampf, W. L., and Helton, J. C., 2002, “Investigation of Evidence Theory for Engineering Applications,” American Institute of Aeronautics and Astronautics, Reston, VA, AIAA Paper No. 2002-1569.
Ruthven, I., and Lalmas, M., 2002, “Using Dempster Shafer's Theory of Evidence to Combine Aspects of Information Use,” J. Intell. Inf. Syst., 19(3), pp. 267–301. [CrossRef]
Zadeh, L., 1986, “A Simple View of the Dempster-Shafer Theory of Evidence and Its Implication for the Rule of Combination,” AI Mag., 7(2), pp. 85–90.
Yager, R., 1987, “On the Dempster-Shafer Framework and New Combination Rules,” Inf. Sci., 41, pp. 93–137. [CrossRef]
Mourelatos, Z. P., and Zhou, J., 2006, “A Design Optimization Method Using Evidence Theory,” ASME J. Mech. Des., 128(4), pp. 901–908. [CrossRef]
Rao, S. S., and Annamdas, K. K., 2009, “Evidence-Based Fuzzy Approach for the Safety Analysis of Uncertain Systems,” AIAA J., 46(9), pp. 2383–2387. [CrossRef]
Inagaki, T., 1991, “Interdependence Between Safety-Control Policy and Multiple-Sensor Schemes via Dempster-Shafer Theory,” IEEE Trans. Reliab., 40(2), pp. 182–188. [CrossRef]
Zhang, L., 1994, “Representation, Independence, and Combination of Evidence in the Dempster-Shafer Theory,” Advances in the Dempster-Shafer Theory of Evidence, R. R.Yager, J.Kacprzyk, and M.Fedrizzi, John Wiley, New York, pp. 51–69.
Murphy, C. K., 2000, “Combining Belief Functions When Evidence Conflicts,” Decision Support Sys., 29, pp. 1–9. [CrossRef]
Dempster, A. P., 2008, “The Dempster Shafer Calculus for Statisticians,” Int. J. Approx. Reason., 48(2), pp. 365–377. [CrossRef]
Liu, W., 2006, “Analyzing the Degree of Conflict Among Belief Functions,” Artif. Intell., 170, pp. 909–924. [CrossRef]
Rao, S. S., 2009, Engineering Optimization Theory and Practice, 4th ed., John Wiley, Hoboken, NJ.


Grahic Jump Location
Fig. 1

Belief (Bel) and Plausibility (Pl) of a proposition A

Grahic Jump Location
Fig. 2

Inagaki's unified rule of combination with different values of the parameter k



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In