Abstract This paper presents an ellipsoidal Newton’s iteration method for predicting the response of nonlinear structural systems with uncertain-but-bounded parameters. In the study, the uncertainty in parameters is expressed in terms of an ellipsoid set in an appropriate vector space and the bounds for the solution set of the nonlinear equations are aiming to be calculated effectively. In the framework of the convex set theory and Taylor series expansion, the ellipsoidal Newton’s iteration scheme is established. Two various models of the scheme depending on the different models of quantifying the region of the iterative solution in iterative calculation are discussed. The bounds of the solution are updated iteratively by using the maximum and minimum values of the solution increment, which can be obtained by solving the optimization problem. The convergence of the scheme is proved and the general procedure for its implementation is also presented. Three numerical examples are employed to illustrate the feasibility and accuracy of the proposed method in evaluating the bounds of nonlinear structural systems with uncertain-but-bounded parameters in comparison with the Monte-Carlo Simulation and the point-based iteration method.

中文翻译：

---

参数不确定但有界非线性结构系统的椭球牛顿迭代法

摘要 本文提出了一种用于预测参数不确定但有界的非线性结构系统的响应的椭球牛顿迭代法。在研究中，参数的不确定性用一个在适当向量空间中的椭球集来表示，并且旨在有效地计算非线性方程组的解集的界限。在凸集理论和泰勒级数展开的框架内，建立了椭球牛顿迭代方案。根据迭代计算中量化迭代解区域的不同模型，讨论了该方案的两种不同模型。解的边界通过使用解增量的最大值和最小值迭代更新，这可以通过求解优化问题获得。证明了该方案的收敛性，并给出了其实现的一般过程。通过三个数值算例，与蒙特卡洛模拟和基于点的迭代方法相比，该方法在评估具有不确定但有界参数的非线性结构系统的边界时具有可行性和准确性。