ABSTRACT This work presents a new methodology for computing parameter sensitivities of differential algebraic system of equations with higher differential index. This methodology is particularly adequate for performing sensitivity analysis of object-oriented models described by modern universal modelling languages. By employing the same concepts and tools adopted by these languages for structural analysis of systems of equations, it is shown that the computational graphs of a differential algebraic system of equations and its corresponding sensitivity equation are structurally isomorphic. As a consequence, the structural index of both systems of equations are proven to be equal. Based on this result, an efficient strategy for index reduction of sensitivity equations is designed.

中文翻译：

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灵敏度方程系统的结构指标

摘要 这项工作提出了一种计算具有较高微分指数的微分代数方程组参数灵敏度的新方法。这种方法特别适用于对现代通用建模语言描述的面向对象模型进行敏感性分析。通过使用这些语言所采用的相同概念和工具对方程组进行结构分析，表明微分代数方程组的计算图及其对应的灵敏度方程在结构上是同构的。因此，两个方程组的结构指数被证明是相等的。在此结果的基础上，设计了一种有效的灵敏度方程指标降阶策略。