Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for polynomial systems of differential-algebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a full-rank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differential-algebraic equations on all components of constraints.

翻译：现有结构分析方法可能在参数取某些特定值时，无法完全发现包含参数的微分代数方程系统的所有隐式约束。针对多项式型微分代数方程系统，本文提出了基于数值实代数几何的数值方法以解决此类问题。首先，我们提出一种嵌入方法，该方法能够为给定实解析系统构造一个具有满秩雅可比矩阵的等价系统。其次，引入一种见证点方法，可用于检测此类系统约束所有分量上的退化现象。最后，上述两种方法共同形成了一种针对结构不适定微分代数方程约束全分量的数值全局结构分析方法。