  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.
