稳健可靠性理论及优化方法研究
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摘要
不确定性因素的处理在可靠性工程中起着至关重要的作用,与之相联系的可靠性各种研究方法也日益引起诸多学者的关注。经过几十年的发展,基于概率模型的常规可靠性理论已广泛应用于各个领域,其成熟性毋庸置疑,但是这种方法对于统计数据缺乏或者信息不完备的情况以及概率论本身固有的缺陷却无能为力,而非概率可靠性却可以弥补这一不足。本文在前人工作的基础上,对非概率的稳健可靠性理论及其应用做了进一步的研究和探讨,其主要内容如下:
(1)对机械静强度稳健可靠性理论进行了分析和研究,给出了机械零件静强度稳健可靠性设计准则;对振动构件的稳健可靠性进行了分析和探讨,给出了振动构件的稳健可靠性设计准则:对概率可靠性和基于非概率的稳健可靠性方法进行了对比研究。
(2)提出了一种新的稳健可靠性指标度量方法和设计准则,并进行了相应的系统稳健可靠性的研究,对简单的振动系统的稳健可靠性进行了分析。将本文提出的稳健可靠性度量方法与Ben-Haim教授提出的度量准则进行了比较。
(3)针对在实际工程中影响可靠性的不确定性因素具有多样性和复杂性的特点,为了更充分合理地利用现有的数据来处理实际工程中的可靠性问题,研究了稳健可靠性与传统可靠性以及模糊可靠性的融合问题。对于不确定性变量较多的复杂系统,分析了如何建立将稳健可靠性和传统的可靠性以及模糊可靠性结合的混合可靠性分析模型,综合各模型的优点最大限度地将已有的信息利用到产品的可靠性分析中去。对数据掌握得较多的不确定性变量应考虑采用概率可靠性来分析,而对一些数据掌握较少或数据不完备的情况则考虑采用集合模型来描述,然后建立混合的可靠性模型,并对模型进行了求解。
(4)对稳健可靠性优化方法进行了研究。对数据信息缺乏或不完备的不确定结构的可靠性优化设计,考虑用非概率模型求解。基于不确定性的凸集模型描述,研究了非概率优化设计模型,在此模型基础上给出了概率信息和非概率信息同时并存的非概率可靠性优化模型。基于物理规划方法研究机械结构的稳健可靠性优化问题,用凸集模型描述结构设计中存在的不确定性,借助于物理规划方法描述不确定性参数的不满意度函数,极小化不满意度函数最劣值来实现目标函数的稳健性,采用最坏情况分析方法实现约束函数的稳健性,进行结构的稳健可靠性优化设计。研究了基于灵敏度分析的稳健可靠性优化方法,提出一种在以可靠度为目标函数或者约束函数的可靠性优化设计中加入灵敏度约束作为附加目标函数来实现稳健性的稳健可靠性优化设计方法,建立了三种稳健可靠性优化设计模型,这三种模型是分别考虑目标函数的灵敏度、约束函数的灵敏度、目标函数和约束函数的灵敏度分析产生的附加目标函数来实现的。用MATLAB优化工具箱求解优化问题。
稳健可靠性理论的提出具有重大的理论和现实意义。虽然该理论还不成熟、完善,
Uncertain factors are critical in the applications of reliability engineering. The study on methods of reliability theory has been gaining increasing attentions to many researchers. During the past several decades, the traditional reliability approach based on probability theory has been widely applied to various engineering fields and has demonstrated its maturity. However, that method is not capable to deal with the situation when the statistical data or information is lacking. It can not overcome the limitations of the probability theory either. To overcome those barriers, a new reliability theory called the non-probabilistic reliability is proposed as a complement to the traditional reliability theory. This dissertation further develops the non-probabilistic reliability theory and studies its applications based on the exiting work in literature. The contributions of this paper include the following aspects:(1) The robust reliability theory of mechanical static strength is investigated and analyzed. The corresponding design criterion for mechanical components is proposed. The robust reliability of vibration components is analyzed, and the corresponding design criterion is established. We also compare the present robust reliability method with the traditional reliability method.(2) A new measure and a design criterion of the robust reliability theory are proposed. They are applied to study the system robust reliability. An example of the robust reliability analysis of a simple vibration system is used to demonstrate the validity of the proposed method. We compare the proposed robust reliability index with the Ben-Haim's robust reliability index.(3) Considering the variety and complexity of the uncertain factors with impact on the reliability in engineering practice, it is necessary to study the combination of the robust reliability, the traditional reliability, and the fuzzy reliability. To handle the real reliability problems, hybrid reliability models are established to fully utilizing available data. When we have sufficient data to describe the probabilistic characteristics of uncertain parameters, probabilistic reliability models or fuzzy reliability models can be adopted. When there is insufficient data, non-probabilistic set models should be chosen. When the above three conditions exist at the same time, we may choose to use hybrid reliability models. In engineering analysis, the ability of different possible reliability methods allows for mutual compensation for the disadvantages inherent in each individual method. After establishing the hybrid models, programs can be built to obtain corresponding solutions.(4) The robust reliability optimization methods are studied. In the lacking of data or deficiency of information on the uncertain structures, non-probabilistic models are proposed to be used to solve robust reliability optimization design problems. Based on convex models
for uncertainty description, structural design models of the non-probabilistic optimization are established. Furthermore, non-probabilistic reliability models are proposed in the presence of both probabilistic and non-probabilistic information. Based on the physical programming method, the robust reliability optimization of mechanical structures is investigated. The uncertainties in mechanical structures are described by convex models. The unsatisfactory functions are created by means of the physical programming. The robustness of objective functions is achieved by minimizing the unfavorable unsatisfactory functions. The robustness of constraints is ensured by a sub-optimization of the worst case scenario. Treating the reliability index as constraint functions or objective functions, another new method of the robust reliability optimization is presented by adding sensitivities as additive objectives. Three models of the robust reliability optimization are developed based on the conventional reliability optimization models with the additive objective functions. They are created respectively considering the sensitivity of objective functions, constraint functions, and the objective and constraint functions, with respect to design parameters. Optimization problems are solved by the optimization toolbox of MATLAB.The research on the robust reliability theory is important not only in academic research, but also in engineering applications. Although the robust reliability theory is not yet a mature theory, its idea is innovative providing a new method for the reliability engineering. This method is suited to the scarce statistical information, severe uncertainties, and the problems which the traditional reliability methods can deal with.
(1)对机械静强度稳健可靠性理论进行了分析和研究,给出了机械零件静强度稳健可靠性设计准则;对振动构件的稳健可靠性进行了分析和探讨,给出了振动构件的稳健可靠性设计准则:对概率可靠性和基于非概率的稳健可靠性方法进行了对比研究。
(2)提出了一种新的稳健可靠性指标度量方法和设计准则,并进行了相应的系统稳健可靠性的研究,对简单的振动系统的稳健可靠性进行了分析。将本文提出的稳健可靠性度量方法与Ben-Haim教授提出的度量准则进行了比较。
(3)针对在实际工程中影响可靠性的不确定性因素具有多样性和复杂性的特点,为了更充分合理地利用现有的数据来处理实际工程中的可靠性问题,研究了稳健可靠性与传统可靠性以及模糊可靠性的融合问题。对于不确定性变量较多的复杂系统,分析了如何建立将稳健可靠性和传统的可靠性以及模糊可靠性结合的混合可靠性分析模型,综合各模型的优点最大限度地将已有的信息利用到产品的可靠性分析中去。对数据掌握得较多的不确定性变量应考虑采用概率可靠性来分析,而对一些数据掌握较少或数据不完备的情况则考虑采用集合模型来描述,然后建立混合的可靠性模型,并对模型进行了求解。
(4)对稳健可靠性优化方法进行了研究。对数据信息缺乏或不完备的不确定结构的可靠性优化设计,考虑用非概率模型求解。基于不确定性的凸集模型描述,研究了非概率优化设计模型,在此模型基础上给出了概率信息和非概率信息同时并存的非概率可靠性优化模型。基于物理规划方法研究机械结构的稳健可靠性优化问题,用凸集模型描述结构设计中存在的不确定性,借助于物理规划方法描述不确定性参数的不满意度函数,极小化不满意度函数最劣值来实现目标函数的稳健性,采用最坏情况分析方法实现约束函数的稳健性,进行结构的稳健可靠性优化设计。研究了基于灵敏度分析的稳健可靠性优化方法,提出一种在以可靠度为目标函数或者约束函数的可靠性优化设计中加入灵敏度约束作为附加目标函数来实现稳健性的稳健可靠性优化设计方法,建立了三种稳健可靠性优化设计模型,这三种模型是分别考虑目标函数的灵敏度、约束函数的灵敏度、目标函数和约束函数的灵敏度分析产生的附加目标函数来实现的。用MATLAB优化工具箱求解优化问题。
稳健可靠性理论的提出具有重大的理论和现实意义。虽然该理论还不成熟、完善,
Uncertain factors are critical in the applications of reliability engineering. The study on methods of reliability theory has been gaining increasing attentions to many researchers. During the past several decades, the traditional reliability approach based on probability theory has been widely applied to various engineering fields and has demonstrated its maturity. However, that method is not capable to deal with the situation when the statistical data or information is lacking. It can not overcome the limitations of the probability theory either. To overcome those barriers, a new reliability theory called the non-probabilistic reliability is proposed as a complement to the traditional reliability theory. This dissertation further develops the non-probabilistic reliability theory and studies its applications based on the exiting work in literature. The contributions of this paper include the following aspects:(1) The robust reliability theory of mechanical static strength is investigated and analyzed. The corresponding design criterion for mechanical components is proposed. The robust reliability of vibration components is analyzed, and the corresponding design criterion is established. We also compare the present robust reliability method with the traditional reliability method.(2) A new measure and a design criterion of the robust reliability theory are proposed. They are applied to study the system robust reliability. An example of the robust reliability analysis of a simple vibration system is used to demonstrate the validity of the proposed method. We compare the proposed robust reliability index with the Ben-Haim's robust reliability index.(3) Considering the variety and complexity of the uncertain factors with impact on the reliability in engineering practice, it is necessary to study the combination of the robust reliability, the traditional reliability, and the fuzzy reliability. To handle the real reliability problems, hybrid reliability models are established to fully utilizing available data. When we have sufficient data to describe the probabilistic characteristics of uncertain parameters, probabilistic reliability models or fuzzy reliability models can be adopted. When there is insufficient data, non-probabilistic set models should be chosen. When the above three conditions exist at the same time, we may choose to use hybrid reliability models. In engineering analysis, the ability of different possible reliability methods allows for mutual compensation for the disadvantages inherent in each individual method. After establishing the hybrid models, programs can be built to obtain corresponding solutions.(4) The robust reliability optimization methods are studied. In the lacking of data or deficiency of information on the uncertain structures, non-probabilistic models are proposed to be used to solve robust reliability optimization design problems. Based on convex models
for uncertainty description, structural design models of the non-probabilistic optimization are established. Furthermore, non-probabilistic reliability models are proposed in the presence of both probabilistic and non-probabilistic information. Based on the physical programming method, the robust reliability optimization of mechanical structures is investigated. The uncertainties in mechanical structures are described by convex models. The unsatisfactory functions are created by means of the physical programming. The robustness of objective functions is achieved by minimizing the unfavorable unsatisfactory functions. The robustness of constraints is ensured by a sub-optimization of the worst case scenario. Treating the reliability index as constraint functions or objective functions, another new method of the robust reliability optimization is presented by adding sensitivities as additive objectives. Three models of the robust reliability optimization are developed based on the conventional reliability optimization models with the additive objective functions. They are created respectively considering the sensitivity of objective functions, constraint functions, and the objective and constraint functions, with respect to design parameters. Optimization problems are solved by the optimization toolbox of MATLAB.The research on the robust reliability theory is important not only in academic research, but also in engineering applications. Although the robust reliability theory is not yet a mature theory, its idea is innovative providing a new method for the reliability engineering. This method is suited to the scarce statistical information, severe uncertainties, and the problems which the traditional reliability methods can deal with.
引文
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