Research and Implementation of Solution and Optimization Methods for Nested Algebraic Loops

To improve simulation efficiency and accuracy of simulation results, point at communication errors and data transmission issues caused by temporal variability between simulation models, Using Kosaraju - Breadth Bidirectional search method to detect the nested algebraic loop structure in the simulation system. On the basis of studying the traditional solution method of nonlinear equations, the structure of Jacobi matrix in the imprecise Newton's method is adjusted by using the iteration between H and S matrix in the NPHSS method, the Newton NPHSS iterative method is obtained to improve the low efficiency of imprecise Newton's method for solving large dimension algebraic loops, and improve the efficiency of the algorithm. The error analysis of the Newton NPHSS iterative method and the iterative results of Newton method and inexact Newton method show that the Newton NPHSS iterative method converges faster and has less iteration. And the new algorithm was applied to the FMI simulation system constructed by Simulink, achieving fast detection and effective solution of nested algebraic loops, verifying its effectiveness and feasibility in practical applications.