Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening the hierarchical models into an equation system for analysis. However, the large-scale equations in complex models make the 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 the 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 the paper. Complexity analysis results show the enhanced efficiency of the proposed method in structural analysis of complex equation-oriented models. As compared with the existing methods, the time complexity of the proposed method is improved significantly.

中文翻译：

---

面向复杂方程模型的层次结构分析方法

结构分析是一种在工业系统设计中验证面向方程模型的方法。现有的结构分析方法需要将层次模型展平成方程系统进行分析。然而，复杂模型中的大规模方程使得结构分析变得困难。针对这一问题，本研究通过探索层次方程导向模型的奇异点与其组成部分之间的关​​系，提出了层次结构分析方法。该方法通过分析由零件构成的虚拟模型，从零件的分解结果中得到层次方程导向模型的奇异性。在此基础上，复杂模型的结构奇异性可以根据其自然层次结构进行逐层分析。层次结构分析方法可以减少每次分析中的方程规模，实现非常复杂模型的高效结构分析。该方法可以自适应地应用于非线性代数和微分代数方程模型。论文中介绍了主要算法、应用案例以及与现有方法的比较。复杂性分析结果表明，该方法在复杂面向方程模型的结构分析中具有更高的效率。与现有方法相比，所提方法的时间复杂度显着提高。该方法可以自适应地应用于非线性代数和微分代数方程模型。论文中介绍了主要算法、应用案例以及与现有方法的比较。复杂性分析结果表明，该方法在复杂面向方程模型的结构分析中具有更高的效率。与现有方法相比，所提方法的时间复杂度显着提高。该方法可以自适应地应用于非线性代数和微分代数方程模型。论文中介绍了主要算法、应用案例以及与现有方法的比较。复杂性分析结果表明，该方法在复杂面向方程模型的结构分析中具有更高的效率。与现有方法相比，所提方法的时间复杂度显着提高。