Structural analysis is essential for understanding the characteristics of integro differential algebraic equations (idaes) before numerical solving. The \(\Sigma \) - method uses the signature matrix to efficiently analyze differential algebraic equations (daes), and attempts have been to extend it to idaes. Challenges arise when the signature matrix becomes undefined or overestimated due to derivatives in integrands of idaes. Additionally, when a singular Jacobian matrix is obtained after applying the \(\Sigma \) -method, there is no guarantee for termination by using the existing conversion methods. This paper addresses these issues by partitioning an idae into two parts, an analytic dae part and a polynomial integro algebraic equations (iae) part. We redefine the signature matrix for each part and introduce a new concept degrees of freedom measure to ensure termination of our algorithm. Finally, a generalized embedding method is given to regularize nonlinear idaes for both symbolic cancellation and numerical degeneration. When coupled with the collocation method, our method can effectively solve such idae numerically with high accuracy.
