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Determining optimal granularity level of modular product with hierarchical clustering and modularity assessment

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Modular product architecture is beneficial for the product maintenance, upgrade, components’ concurrent design through team work, and achieving the mass customization eventually. Recent researches tend to group elements into modules as a flat map, but this is inconsistent with the nested composition in product final assembly. Finding the hierarchical modular partition for elements of a product and obtaining its optimal granularity level are still necessary to ease the partition and combination for sub-design tasks. We use the design structure matrix (DSM) to represent the relationships among elements of a product. The hierarchical clustering functions such as pdist and linkage within MATLAB software are utilized to form the hierarchical dendrogram for DSM elements, and the modularity index Q is applied to assess the modular clustering results. The partitions are acquired by various distance threshold values in the vertical axis of the hierarchical dendrogram. The ‘cityblock’ and ‘average’ are found as preferred parameters for pdist and linkage functions, respectively, from loop test experiments. Combining the modularity formula in a research literature, a hierarchical modular architecture design methodology is proposed in this work to determine the optimal granularity level of a modular product and to provide solutions for designer selection. Case studies and comparisons in a benchmark problem and a concrete spraying machine illustrate the effectiveness and efficiency of the proposed method. It is characterized by being able to find stable modular partition results for both float and binary DSM elements and satisfying the recommended modular number rule simultaneously.

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Abbreviations

DSM:

Design structure matrix

FCM:

Fuzzy c-means algorithm

GGA:

Group genetic algorithm

HC:

Hierarchical clustering

IC:

Integrative complexity

LCA:

Life cycle assessment

MDL:

Minimum description length

MDS:

Multi-dimensional scaling

MI:

Modularity index

MSI:

Module strength indicator

OMI:

Overall modularity index

PC(c):

Partition coefficient c

Q :

A modularity index named Q

R-IGTA:

Revised algorithm on Image and Graphics Technologies and Applications

Sil :

Silhouette index

SMACOF:

Scaling by minimizing a convex function

WCA:

Weighted combined algorithm

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Acknowledgements

The support for this work by Fundamental Research Funds for the Central Universities of China (2017XKQY040) and Priority Academic Program Development of Jiangsu Education Department of China (PAPD) is gratefully acknowledged. We thank Dr Shuzhe Tang at China University of Mining & Technology for improving the context and also for the constructive comments of the anonymous reviewers.

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  1. School of Mechatronics Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Zhong-kai Li, Shuai Wang & Wen-wei Yin

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  1. Zhong-kai Li
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  2. Shuai Wang
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Correspondence to Zhong-kai Li.

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Li, Zk., Wang, S. & Yin, Ww. Determining optimal granularity level of modular product with hierarchical clustering and modularity assessment. J Braz. Soc. Mech. Sci. Eng. 41, 342 (2019). https://doi.org/10.1007/s40430-019-1848-y

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