Extended Hierarchical Cluster Analysis for the Decomposition of Complex Design Problems

This paper presents a new decomposition method for partitioning complex design problems based on an extended Hierarchical Cluster Analysis (HCA). After a complex design problem is represented using a function-parameter incidence matrix, this new decomposition method allows transforming the originally unorganized matrix into a block-angular form matrix. By means of the resulting matrix, a coordination part and design blocks can be further identified and obtained. In particular, the extended HCA plays an important role in this method, contributive to aligning all non-zero elements, also known as 1s elements, of the matrix along its main diagonal as compactly as possible. As such, a post process, called Partition Point Analysis (PPA), can be further applied to the matrix to finally form the coordination part and the related design blocks, subject to such decomposition criteria as block size and coordination size limits. A powertrain design example is employed for illustration of the decomposition method newly developed.