区间模型非概率可靠性指标的改进型仿射算法
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摘要
针对标准区间运算易引发误差爆炸,常规的仿射运算没能考虑计算过程中出现的使用同一噪声元表达的一次项、二次项,乃至多次项、非线性项之间存在相关性而造成的计算误差,提出以仿射运算为主体,在遇到这种相关项时,借助区间运算计算出相关项总体取值的上下界,再利用上下界信息,引入新噪声的仿射型代替它们。这种借助区间运算对常规的仿射运算进行改进的方法,应用于区间模型非概率可靠性指标的计算结果,精度高于区间运算和常规的仿射运算,有较强的实际意义。
Aimed at that standard interval arithmetic is easy to cause error explosion, as well as traditional affine arithmetic is easy to cause calculation error due to not considering the correlation among the first degree item, quadratic term, even the multiple-item and the nonlinear term expressed by the same noise, an improved algorithm was proposed which took affine algorithm operation as the main body. When there are those correlation items, the upper bound and lower bound of their total value were calculated by interval arithmetic, then uses the bound information and introduces the new noise affine form to instead of those terms. The method improved the conventional affine operation by combining interval arithmetic. When it applied to calculate the non-probabilistic reliability index, the calculation results has higher accuracy than the interval arithmetic and the conventional affine algorithm, and it hasimportant practical significance.
Aimed at that standard interval arithmetic is easy to cause error explosion, as well as traditional affine arithmetic is easy to cause calculation error due to not considering the correlation among the first degree item, quadratic term, even the multiple-item and the nonlinear term expressed by the same noise, an improved algorithm was proposed which took affine algorithm operation as the main body. When there are those correlation items, the upper bound and lower bound of their total value were calculated by interval arithmetic, then uses the bound information and introduces the new noise affine form to instead of those terms. The method improved the conventional affine operation by combining interval arithmetic. When it applied to calculate the non-probabilistic reliability index, the calculation results has higher accuracy than the interval arithmetic and the conventional affine algorithm, and it hasimportant practical significance.
引文
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[10]王新刚,张义民,王宝艳.基于非概率可靠性灵敏度方法的研究[J].机械设计,2010,27(3):71-74.
[11]张建国,陈建军,江涛,等.关于不确定结构非概率可靠性计算的研究[J].机械强度,2007,29(1):58-62.
[12]马景槐,朱福先.区间模型结构非概率可靠性度量研究[J].机械强度,2012,34(1):48-52.
[13]江涛,陈建军,张弛江.区间模型非概率可靠性指标的仿射算法[J].机械强度,2007,29(2):251-255.
[14]江涛.结构系统非概率可靠性算法研究[D].西安:西安电子科技大学,2006.
[2]王登刚,李杰.计算不确定结构系统静态响应的一种可靠方法[J].计算力学学报,2003,20(6):662-668.
[3]刘长虹,陈虬.基于粗糙集理论下的结构随机分析中的有限元法[J].机械强度,2004,26(3):274-277.
[4]郭书祥,吕震宙.区间运算和静力区间有限元[J].应用数学和力学,2001,22(12):1249-1254.
[5]王晓军,邱志平.结构振动的鲁棒可靠性[J].北京航空航天大学学报,2003,29(11):1006-1010.
[6]Goldenstein K S,Vogler C,Metaxas D.Statistical cue integration in DAG deformable models[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2003,25(7):801-813.
[7]谢永强,陈建军.不确定系统稳定性的仿射不等式分析[J].高技术通讯,2008(4):867-871.
[8]Femia N,Spagnuolo G.True worst-case circuit tolerance analysis using genetic algorithms and affine arithmetic[J].IEEE Transactions on Circuits and Systems,2000,47(9):1285-1296.
[9]Martin R,Shou Hua-hao,Voculescu I,et al.Comparison of interval methods for plotting algebraic curves[J].Computer Aided Geometric Design,2002,19:553-587.
[10]王新刚,张义民,王宝艳.基于非概率可靠性灵敏度方法的研究[J].机械设计,2010,27(3):71-74.
[11]张建国,陈建军,江涛,等.关于不确定结构非概率可靠性计算的研究[J].机械强度,2007,29(1):58-62.
[12]马景槐,朱福先.区间模型结构非概率可靠性度量研究[J].机械强度,2012,34(1):48-52.
[13]江涛,陈建军,张弛江.区间模型非概率可靠性指标的仿射算法[J].机械强度,2007,29(2):251-255.
[14]江涛.结构系统非概率可靠性算法研究[D].西安:西安电子科技大学,2006.