摘要
针对目前在结构可靠性计算中被广泛应用的传统响应面法存在计算量大,精确度不高,容易产生奇异解,必须知道功能函数才能计算等问题。首先根据最小二乘原理,在只需知道设计验算点对应的功能函数值的情况下,利用权函数的紧支性、非负性、光滑性、递减性等性质,在影响域内应用选取的设计验算点,提出了用移动最小二乘法通过迭代生成响应面函数,然后结合一阶可靠性方法,计算结构的最大失效点与可靠性指标。通过反复迭代,直到计算的相邻两次的可靠性指标满足所给的误差为止。给出了切实可行的算法,该算法不需要知道功能函数,甚至不需要知道功能函数的类型就可以进行计算。算例表明,文中方法以较少的迭代次数,可以获取高精度的最大失效点与可靠性指标。
For the problems as large amount of calculation,not high accuracy,easy to produce singular solution and calculation can be done only performance function is known in the conventional response surface methodology widely adopted for structural reliability computation,first,based on the principle of least squares,under the condition that only the performance function value corresponding to the design checking point is known,by using the properties of weight function as compactly supported,non-negativity,smoothness,decrease,and selecting the design checking point in the domain of influence,the paper presents that most probable failure point and reliability index of the structure can be calculated by applying the least squares method to generate response surface function through iteration and the combining with first order reliability method,until the calculated adjacent two reliability indexes can meet the given error.The paper gives a feasible algorithm,which can carry out calculation without necessary to know the performance function,even the type of the performance function.Examples show that this method with less number of iterations,can obtain the most probable failure point and reliability index of structure in the higher accuracy and with less number of iterations.
出处
《机械设计》
CSCD
北大核心
2013年第7期10-14,共5页
Journal of Machine Design
基金
江苏省自然科学基金资助项目(BK2008197)
关键词
移动最小二乘法
响应面函数
结构
可靠性
moving least squares approximation
response surface function
structure
reliability
