基于脉冲暂态混沌神经网络的可靠度分析方法

工程中计算结构可靠度系数β可以看做一个优化问题。考虑极限状态函数的非线性程度很高且存在非凸失效域时，传统的求解非线性优化方法，如序列二次规划（SQP）法、罚函数法和梯度投影法等都有其使用范围和局限性，无法解决局部极小解问题。如何避免局部极小解问题并且兼顾计算精度和效率目前仍很难处理。提出一种新的可靠度计算方法：将求解转化为带有约束条件的非线性规划问题，利用罚函数法转化成无约束条件的非线性规划问题，引入脉冲暂态混沌神经网络（PTCNN）模型快速有效地进行全局寻优，从而解决具有局部极小解的约束非线性规划问题。最后采用不同类型的非线性极限状态函数算例进行算法验证，验证该方法在处理高维、高非线性、不可微、非凸失效域问题时具有可行性、高效性。

Pulse Transiently Chaotic Neural Network for the Analysis Method of Reliability

The structural reliability index β can be solved as an optimization problem in engineering design. However, when the limited state function is high nonlinearity with concave failure domain, the classic methods of solving nonlinear programming such as sequential quadratic programming (SQP) method, penalty function method, and gradient projection method etc, have disadvantages in solving the local minimum solution. It is still difficult to deal with how to solve local minimum solution taking into account the calculation accuracy and efficiency. This paper presents a new method of reliability that the problem for solving reliability indexes is transformed into the nonlinear programming problem with constraint condition. Penalty function method is used to convert the problem into unconstrained nonlinear programming one. Pulse transiently chaotic neural network (PTCNN) is introduced to optimize globally so as to solve constrained nonlinear programming problems with local minimum solution quickly and efficiently. Finally the examples of different types of non-linear limit state functions are presented to prove that this method is feasible and efficient to address the problem with high dimension, highly nonlinear, non-differentiable and non-convex failure domain.