Hierarchical Structural Analysis Method for Complex Equation-oriented Models

TL;DR

This paper introduces a hierarchical structural analysis method that efficiently analyzes complex equation-oriented models by leveraging their natural hierarchy, significantly reducing computational complexity compared to existing approaches.

Contribution

The paper presents a novel hierarchical analysis technique that analyzes models layer-by-layer, improving efficiency and scalability for large-scale complex models.

Findings

Reduces equation scale in analysis of complex models

Achieves significant improvement in time complexity

Applicable to nonlinear and differential-algebraic models

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.