<p>Module partition is a challenging topic in modular design, and various methods have been proposed for that. Many methods for partitioning complex products utilize modularity as a metric to evaluate the quality of the partitioning results. These methods attempt to partition modules based on maximizing modularity. However, modularity maximization may encounter issues pertaining to resolution limit, which may prevent detection of modules that are smaller than a specific scale. To address such problems, in this paper, a graph spectral sparsification algorithm based on null model is proposed, specifically designed to extract critical correlation edges in the weighted graph model of complex products. Firstly, this algorithm employs the null model to calculate the statistical significance probabilities of the correlation strengths between complex product components, subsequently generating a Minimum Spanning Tree (MST) of the product based on these calculations. Following this, critical edges between components, identified through screening based on the statistical significance probability and relative condition number, are added to the MST, serving as the sparse graph for the complex product. Finally, the validity and feasibility of the proposed method are verified by applying it to both a light water reactor and a hydraulic excavator system. </p>

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Module partition in weighted complex product graphs beyond the resolution limit

  • Zhichao Wang,
  • Shaopeng Xia,
  • Qi Wang,
  • Wei Guo

摘要

Module partition is a challenging topic in modular design, and various methods have been proposed for that. Many methods for partitioning complex products utilize modularity as a metric to evaluate the quality of the partitioning results. These methods attempt to partition modules based on maximizing modularity. However, modularity maximization may encounter issues pertaining to resolution limit, which may prevent detection of modules that are smaller than a specific scale. To address such problems, in this paper, a graph spectral sparsification algorithm based on null model is proposed, specifically designed to extract critical correlation edges in the weighted graph model of complex products. Firstly, this algorithm employs the null model to calculate the statistical significance probabilities of the correlation strengths between complex product components, subsequently generating a Minimum Spanning Tree (MST) of the product based on these calculations. Following this, critical edges between components, identified through screening based on the statistical significance probability and relative condition number, are added to the MST, serving as the sparse graph for the complex product. Finally, the validity and feasibility of the proposed method are verified by applying it to both a light water reactor and a hydraulic excavator system.