结构可靠性分析区间模型的若干问题研究
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摘要
结构在工作时,其性能受到来自多方面不确定性因素的影响,如结构材料参数、几何参数或载荷等的不确定性。为确保结构在规定的使用条件和环境下,在给定的使用寿命期间有效地承受载荷和耐受环境而正常工作,对其进行可靠性分析就显得尤为重要。为建立合理的可靠性分析模型,保证可靠性分析结果的有效性,应该充分了解和认识结构分析过程中存在的不确定性,以便采用适当的不确定性处理方法。区间分析理论在处理不确定性方面具有不需要考虑变量分布形式、计算简单、易于进行等特点,而且区间运算可以自动跟踪计算过程中出现的截断误差和舍入误差。因此,基于区间分析的结构区间可靠性分析方法成为学术界研究的热点问题。结构区间可靠性分析方法作为一种非概率可靠性分析方法,是概率可靠性分析方法的有益补充,它可以弥补概率可靠性分析方法的不足。但是,结构区间可靠性分析还远没有形成完整的、规范化的理论体系。因此,本文就结构区间可靠性分析中的相关问题展开研究,将结构可靠性分析区间模型理论进一步系统化和规范化。
在结构区间可靠性分析过程中,一般会涉及到两个区间量之间的比较,如广义区间强度和广义区间应力的比较等等,因此本文对区间数的比较方法作了详尽评述,作为结构区间可靠性分析的前提。
提出区间变量的定义。提出基于区间功能函数法和区间应力-区间强度干涉模型的结构区间可靠性分析方法。修正了区间可靠性指标,通过定义标准变换,详细分析了区间可靠性指标的几何意义;提出结构区间可靠性分析的可能度法,提出结构安全可能度定义,详细分析了结构安全可能度的性质;分析了当强度和应力在其取值区间内服从均匀分布时,结构安全可能度与概率可靠度间的关系。得到:在没有足够数据信息进行概率可靠性分析时,安全可能度可以对结构的安全程度做出合理的估计。
在系统单元可靠度的界已知及单元可靠性独立假设下,研究了典型系统的区间可靠性。分析了典型系统的区间可靠性与单元区间可靠性的关系,研究得到典型系统的区间可靠性在准一致性意义下保持了其点可靠性的特性。
The performance of structures in service will be affected by uncertainties from many aspects, such as structural material parameters, geometrical parameters, loads, and etc. To ensure proper performance of a structure for supporting loads and bearing environment and normally working, it is essential to give a reliability analysis of this structure under service environment, assigned condition and design lifetime. In order to set up a reasonable reliability model and guarantee validity of reliability analysis, well-understanding of these uncertainties should be emphasized. Because theory of interval analysis representing uncertainty with simple interval arithmetic computation has no need for consideration of probability distribution, it’s more practical and can be easily done; and interval arithmetic could track truncated error and rounded error automatically during calculation. So reliability analysis based on theory of interval analysis, named structural interval reliability analysis prevails in recent years, which as one of the non-probabilistic reliability analysis methods is one useful supplement to probabilistic reliability analysis, and could make up some drawbacks of probabilistic methods, such as a great number of data are required to determine the probability density function for stochastic methods and membership function for fuzzy methods, and practically high cost will pay out for acquiring these probability information, and little error in initial probability information will result in big error in reliability analysis, and the like. Thus far, there is still a long way to go for integral and regular system info of structural interval reliability analysis. So, this paper pays more attentions to some problems of structural interval reliability analysis.
In structural interval reliability analysis, comparison between two interval variables will often be involved, such as the comparison between generalized interval strength and generalized interval stress, etc. Thus a detailed survey on comparing interval numbers is presented; which provides us the premise for structural interval analysis.
After the survey on methods for comparison between interval numbers and definition given on interval variable, structural interval reliability analysis methods based on interval performance function and interval stress-interval strength interference model are analyzed. The interval reliability index was modified, and its geometrical meaning is deeply investigated following the definition of a standard transformation. Possibility degree based method for structural interval reliability is presented, and structural safety possibility degree (SPD), to characterize the safety of structure, is given. The characters of SPD are analyzed. When strength and stress are uniformly distributed in their interval fields, the relationship between structural SPD based on interval analysis and probability reliability degree based on probability analysis is investigated. It is concluded that SPD could provide us a reasonable estimation for the safety state of structures, even if there is no enough data for probability reliability analysis.
In the presence of upper bound and lower bound of elements’reliability degree and independence of reliability among elements, interval reliability of some typical systems and its relation to elements’interval reliability are investigated. It is concluded that the properties of system point reliability (i.e. traditional probability reliability) are hold with quasi-consistency by system interval reliability.
在结构区间可靠性分析过程中,一般会涉及到两个区间量之间的比较,如广义区间强度和广义区间应力的比较等等,因此本文对区间数的比较方法作了详尽评述,作为结构区间可靠性分析的前提。
提出区间变量的定义。提出基于区间功能函数法和区间应力-区间强度干涉模型的结构区间可靠性分析方法。修正了区间可靠性指标,通过定义标准变换,详细分析了区间可靠性指标的几何意义;提出结构区间可靠性分析的可能度法,提出结构安全可能度定义,详细分析了结构安全可能度的性质;分析了当强度和应力在其取值区间内服从均匀分布时,结构安全可能度与概率可靠度间的关系。得到:在没有足够数据信息进行概率可靠性分析时,安全可能度可以对结构的安全程度做出合理的估计。
在系统单元可靠度的界已知及单元可靠性独立假设下,研究了典型系统的区间可靠性。分析了典型系统的区间可靠性与单元区间可靠性的关系,研究得到典型系统的区间可靠性在准一致性意义下保持了其点可靠性的特性。
The performance of structures in service will be affected by uncertainties from many aspects, such as structural material parameters, geometrical parameters, loads, and etc. To ensure proper performance of a structure for supporting loads and bearing environment and normally working, it is essential to give a reliability analysis of this structure under service environment, assigned condition and design lifetime. In order to set up a reasonable reliability model and guarantee validity of reliability analysis, well-understanding of these uncertainties should be emphasized. Because theory of interval analysis representing uncertainty with simple interval arithmetic computation has no need for consideration of probability distribution, it’s more practical and can be easily done; and interval arithmetic could track truncated error and rounded error automatically during calculation. So reliability analysis based on theory of interval analysis, named structural interval reliability analysis prevails in recent years, which as one of the non-probabilistic reliability analysis methods is one useful supplement to probabilistic reliability analysis, and could make up some drawbacks of probabilistic methods, such as a great number of data are required to determine the probability density function for stochastic methods and membership function for fuzzy methods, and practically high cost will pay out for acquiring these probability information, and little error in initial probability information will result in big error in reliability analysis, and the like. Thus far, there is still a long way to go for integral and regular system info of structural interval reliability analysis. So, this paper pays more attentions to some problems of structural interval reliability analysis.
In structural interval reliability analysis, comparison between two interval variables will often be involved, such as the comparison between generalized interval strength and generalized interval stress, etc. Thus a detailed survey on comparing interval numbers is presented; which provides us the premise for structural interval analysis.
After the survey on methods for comparison between interval numbers and definition given on interval variable, structural interval reliability analysis methods based on interval performance function and interval stress-interval strength interference model are analyzed. The interval reliability index was modified, and its geometrical meaning is deeply investigated following the definition of a standard transformation. Possibility degree based method for structural interval reliability is presented, and structural safety possibility degree (SPD), to characterize the safety of structure, is given. The characters of SPD are analyzed. When strength and stress are uniformly distributed in their interval fields, the relationship between structural SPD based on interval analysis and probability reliability degree based on probability analysis is investigated. It is concluded that SPD could provide us a reasonable estimation for the safety state of structures, even if there is no enough data for probability reliability analysis.
In the presence of upper bound and lower bound of elements’reliability degree and independence of reliability among elements, interval reliability of some typical systems and its relation to elements’interval reliability are investigated. It is concluded that the properties of system point reliability (i.e. traditional probability reliability) are hold with quasi-consistency by system interval reliability.
引文
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