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Hierarchical Structural Analysis Method for Complex Equation-Oriented Models

Author

Listed:
  • Chao Wang

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Li Wan

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Tifan Xiong

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Yuanlong Xie

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
    Guangdong Intelligent Robotics Institute, Dongguan 523808, China)

  • Shuting Wang

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
    Guangdong Intelligent Robotics Institute, Dongguan 523808, China)

  • Jianwan Ding

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Liping Chen

    (School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China)

Abstract

Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the large-scale equations in complex models make structural analysis difficult. Aimed to address the issue, this study proposes a hierarchical structural analysis method by exploring the relationship between the singularities of the hierarchical equation-oriented model and its components. This method obtains the singularity of a hierarchical equation-oriented model by analyzing a dummy model constructed with the parts from the decomposing results of its components. Based on this, the structural singularity of a complex model can be obtained by layer-by-layer analysis according to their natural hierarchy. The hierarchical structural analysis method can reduce the equation scale in each analysis and achieve efficient structural analysis of very complex models. This method can be adaptively applied to nonlinear-algebraic and differential-algebraic equation models. The main algorithms, application cases and comparison with the existing methods are present in this paper. The complexity analysis results show the enhanced efficiency of the proposed method in the structural analysis of complex equation-oriented models. Compared with the existing methods, the time complexity of the proposed method is improved significantly.

Suggested Citation

  • Chao Wang & Li Wan & Tifan Xiong & Yuanlong Xie & Shuting Wang & Jianwan Ding & Liping Chen, 2021. "Hierarchical Structural Analysis Method for Complex Equation-Oriented Models," Mathematics, MDPI, vol. 9(21), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2660-:d:661376
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    References listed on IDEAS

    as
    1. Mattsson, Sven Erik, 1995. "Simulation of object-oriented continuous time models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(5), pages 513-518.
    2. Cinzia Bernardeschi & Pierpaolo Dini & Andrea Domenici & Maurizio Palmieri & Sergio Saponara, 2020. "Formal Verification and Co-Simulation in the Design of a Synchronous Motor Control Algorithm," Energies, MDPI, vol. 13(16), pages 1-23, August.
    3. H. W. Kuhn, 2005. "The Hungarian method for the assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 7-21, February.
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