Fractal-wavelet-fusion-based re-ranking of joint roughness coefficients

Abstract

Nowadays, Barton’s Joint Roughness Coefficients (JRC) are widely used as the index for roughness and as a challenging fracture property. When JRC ranking is the goal, deriving JRC from different fractal/wavelet procedures can be conflicting. Complexity increases when various rankings outcome from different calculation methods. Therefore, using Barton’s JRC, we cannot make a decision based on the proven mathematical theories because each method has a different rank. Ideally, these rankings must be equal but, in practice, they are different for each method. To solve this problem and to achieve a robust and valid ranking for JRC, Condorcetand Borda count methods have been used. These methods have been proposed as fusion approaches. Re-ranking of JRC using different methods integrated with Condorcet showed confusion in ranking of the JRC4, JRC5, and JRC6 profiles. This ambiguity is equal to equalizing decision conditions about all the three at the examination of the winners, losers, and draws in pairwise matrices. Therefore, Borda Count was applied and resulted in robust rankings. In fact, a new approach for a roughness measurement is presented. A new JRC ranking called JRCN is introduced. This new ranking shows a lower sum of squared errors (0.00390) in comparison with the original JRC ranking method (0.00410) and ranked JRCN1 to JRCN10. Thus it is proposed to consider JRCN as a new and improved version of JRC rankings.