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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。
Engineering calculation of structural reliability coefficient β can be seen as an optimization problem. Considering the nonlinearity of the limit state function and the existence of non-convex inefficiencies, the traditional nonlinear optimization methods such as Sequential Quadratic Programming (SQP), Penalty Function and Gradient Projection have their scope of use and Limitations, unable to solve the problem of local minimum solution. How to avoid the problem of local minutiae and the balance of calculation accuracy and efficiency is still hard to deal with. A new method of reliability calculation is proposed: the solution is transformed into a nonlinear programming problem with constraints, and the penalty function method is used to transform the nonlinear programming problem into an unconstrained condition. The impulsive transient chaotic neural network (PTCNN) model Quickly and efficiently global optimization, so as to solve the constrained nonlinear programming problem with local minimum solution. Finally, different types of non-linear limit state function examples are used to verify the algorithm. It is proved that this method is feasible and efficient in dealing with the problems of high dimensional, high nonlinearity, non-differentiable and non-convex inefficiencies.