Abstract: Both for the cases when a failure field and a super-ellipsoid convex set interfere or don't interfere with each other, there exists insufficiency of both the super-ellipsoid convex sets non-probabilistic reliability index and non-probabilistic reliability degree index. In view of this, this paper presents a definition of reliability comprehensive index based on multi-ellipsoid convex sets by combining the above two definition indexes. The comprehensive index is calculated by the combined method of modified limit step iteration algorithm (MLSA) and the Monte-Carlo method. The modified limit step length iteration algorithm is presented based on the limit step length iteration algorithm. A new merit function is proposed based on the extreme value condition of the extensive Lagrange function. Golden section method is introduced for one dimension search of the step length and convergence is accelerated. Numerical examples show the validity of the iteration results of the multi-ellipsoid convex sets non-probabilistic reliability index obtained by MLSA, and the algorithm also exhibits better convergence. The structural buckling non-probabilistic reliability degree of a supercavitating projectile is evaluated by the super-ellipsoid convex sets reliability comprehensive index with more satisfactory results.

Key words: super-ellipsoid convex set, reliability comprehensive index, modified limit step length iteration algorithm, Monte-Carlo method, merit function, supercavitating projectile, buckling reliability