New CBR adaptation method combining with problem–solution relational analysis for mechanical design

• A CBR adaptation way using weighted mean and grey relational analysis is present.
• Problem–solution relational information is analyzed before adapting similar cases.
• A weighting strategy with relational information is proposed in weighted mean.
• The priority of proposed CBR adaptation is validated by empirical comparison.

Case based reasoning (CBR) methodology is proved to be a promising methodology on determining the parameter values of new mechanical product by adapting previously successful solutions to current problems. Compared with the sophisticated case retrieval technique, the case adaptation under K-nearest neighbour is still a bottleneck problem in CBR researches, which needs to be resolved urgently. According to the characteristics of parametric machinery design (PMD), i.e., less data and many parameters, this paper employs weighted mean (WM) as a basic model, and presents a new CBR adaptation method for PMD by integrating with problem–solution (PS) relational information. In our proposed adaptation method, prior to adapting the similar cases, the grey relational analysis (GRA) is utilized to investigate the PS relational information hidden in K retrieved cases, and the proposed method is called as GRA-WM. Different from classical WM method, the weighting factor of retrieved case for each solution element adaptation is calculated by multiplying similarity matrix (SM) and relational matrix (RM), and the adapted solution values of new mechanical product are subsequently obtained by calculating the weighted average of solution values of K similar cases. A case study on the power transformer design is given to prove the industrial applicability of GRA-WM. Moreover, the empirical comparisons between GRA-WM and other adaptation methods are carried out to validate its superiority. The empirical results indicate that GRA-WM can offer an acceptable adaptation proposal in application of CBR for mechanical design.