响应面的移动最小二乘法结构可靠性计算
|
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.
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.
引文
[1]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996:53-64.
[2]何水清,王善.结构可靠性分析与设计[M].北京:国防工业出版社,1993:112-118.
[3]谭海涛,徐定海,王善.一种计算结构可靠度的一元分解法[J].哈尔滨工程大学学报,2009,30(8):883-886.
[4]Rackwitz R.Reliability analysis-a review and some per-spectives[J].Structural Safety,2001,23(4):365-395.
[5]Liu P L,Der Kiureghian A.Optimization algorithmsfor structural reliability[J].Structural Safety,1991(9):61-77.
[6]Bucher C G,Most T.A comparison of approximate re-sponse functions structural reliability analysis[J].Probabi-listic Engineering Mechanics,2008,82:54-63.
[7]Bucher C G,Bourgund U.A fast and efficient responsesurface approach for structural reliability problems[J].Structural Safety,1990:7(1):57-66.
[8]吴子燕,王其昂,韩晖,等.基于响应面法的桥梁地震易损性分析研究[J].西北工业大学学报,2011,29(1):103-108.
[9]Rajashekhar M R,Ellingwood B R.A new look at the re-sponse surface approach for reliability analysis[J].Struc-tural Safety,1993:12(3):5-20.
[10]Irfan Kaymaz,Chris A McMahon.Aresponse surface meth-od based on weighted regression for structural reliability a-nalysis[J].Probabilistic Engineering Mechanics,2005,20:11-17.
[11]曾清红,卢德堂.基于移动最小二乘法的曲线曲面拟合[J].工程图学学报,2004(1):84-89.
[12]苏永华,方祖烈,高谦.用响应面方法分析特殊地下岩体空间的可靠性[J].岩石力学与工程学报,2000,19(1):55-58.
[13]Kaymaz I,McMahon C A.A response surface method basedon weighted regression for structural reliability analysis[J].Probabilistic Engineering Mechanics,2005,20:11-7.
[14]Dupart F,Sellier A.Probabilistic approach to corrosionrisk due to carbonation via an adaptive response surfacemethod[J].Probabilistic Engineering Mechanics,2006,21:7-16.
[15]Yi P,Cheng G,Liang L.A sequential approximate pro-gramming strategy for performance-measure-based probabi-listic structural design optimization[J].Structural Safety,2008,30(2):92-109.
[16]Choi SK,Grandhi RV,Canfield RA.Reliability-based structural design[M].Springer,2007.
[2]何水清,王善.结构可靠性分析与设计[M].北京:国防工业出版社,1993:112-118.
[3]谭海涛,徐定海,王善.一种计算结构可靠度的一元分解法[J].哈尔滨工程大学学报,2009,30(8):883-886.
[4]Rackwitz R.Reliability analysis-a review and some per-spectives[J].Structural Safety,2001,23(4):365-395.
[5]Liu P L,Der Kiureghian A.Optimization algorithmsfor structural reliability[J].Structural Safety,1991(9):61-77.
[6]Bucher C G,Most T.A comparison of approximate re-sponse functions structural reliability analysis[J].Probabi-listic Engineering Mechanics,2008,82:54-63.
[7]Bucher C G,Bourgund U.A fast and efficient responsesurface approach for structural reliability problems[J].Structural Safety,1990:7(1):57-66.
[8]吴子燕,王其昂,韩晖,等.基于响应面法的桥梁地震易损性分析研究[J].西北工业大学学报,2011,29(1):103-108.
[9]Rajashekhar M R,Ellingwood B R.A new look at the re-sponse surface approach for reliability analysis[J].Struc-tural Safety,1993:12(3):5-20.
[10]Irfan Kaymaz,Chris A McMahon.Aresponse surface meth-od based on weighted regression for structural reliability a-nalysis[J].Probabilistic Engineering Mechanics,2005,20:11-17.
[11]曾清红,卢德堂.基于移动最小二乘法的曲线曲面拟合[J].工程图学学报,2004(1):84-89.
[12]苏永华,方祖烈,高谦.用响应面方法分析特殊地下岩体空间的可靠性[J].岩石力学与工程学报,2000,19(1):55-58.
[13]Kaymaz I,McMahon C A.A response surface method basedon weighted regression for structural reliability analysis[J].Probabilistic Engineering Mechanics,2005,20:11-7.
[14]Dupart F,Sellier A.Probabilistic approach to corrosionrisk due to carbonation via an adaptive response surfacemethod[J].Probabilistic Engineering Mechanics,2006,21:7-16.
[15]Yi P,Cheng G,Liang L.A sequential approximate pro-gramming strategy for performance-measure-based probabi-listic structural design optimization[J].Structural Safety,2008,30(2):92-109.
[16]Choi SK,Grandhi RV,Canfield RA.Reliability-based structural design[M].Springer,2007.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心