非正态分布参数的机械构件的可靠性灵敏度与可靠性稳健设计
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摘要
机械结构的安全可靠是通过设计、生产和管理来实现的,设计决定着产品的固有可靠性,可见设计对产品质量有着重要的贡献率,可赋予产品先天优劣本质特性。在实际工程中,由于结构中存在各种不确定因素,如结构所承受的载荷、结构参数(材料、几何尺寸等)都具有随机性,导致了具有随机参数的随机结构,可见研究随机结构的可靠性问题具有十分重要的意义。另外,可靠性研究可以帮助工程设计人员合理地建立结构的安全容限和控制随机参数对结构安全的影响,使结构的预测工作性能与实际工作性能更加符合,并且可靠性研究能够得到具有足够的可靠性和经济性的优化结构。结构的可靠性作为产品质量的主要指标和最重要的技术指标之一,受到国内外的普遍重视,因此结构可靠性理论和设计方法研究得到了迅速发展。
机械结构的可靠性灵敏度设计,是在可靠性基础上进行结构的灵敏度设计,可以评价设计参数的改变对结构可靠性的影响,即结构可靠性对设计参数变异的敏感性。可靠性灵敏度分析在可靠性设计和修改、可靠性优化设计、可靠性维护等方面均有重要的应用。目前可靠性灵敏度的计算方法很多,通常在可靠性的分析方法基础上都可以进行可靠性灵敏度设计。
机械结构的可靠性稳健设计是在可靠性优化设计理论的基础上的一种低成本和高质量的设计方法,是把可靠性优化设计与可靠性灵敏度设计相融合的一种工程设计方法。它的基本思想是当设计参数发生微小的变差时,在制造或使用中都能保证产品质量的稳健性要求。因此,可靠性稳健设计方法的研究在机械结构的可靠性设计领域具有非常重要的意义。
本文针对非正态分布参数的机械构件的可靠性灵敏度与可靠性稳健设计进行了研究,采用随机摄动方法、四阶矩技术、灵敏度分析方法,建立以四阶矩技术为基础的可靠性灵敏度分析方法,并通过数值算例与Edgeworth级数法、Monte Carlo方法进行比较,证明了所研究方法的设计实用性,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对机械构件的可靠性的影响。
本文共分为八章,主要研究内容如下：
第1章,对课题来源、选题依据和背景、主要研究内容、课题的学术理论意义和实际应用价值等进行了论述,阐述了可靠性的发展历程以及可靠性灵敏度、可靠性稳健设计的研究现状。
第2章,主要概述了机械构件可靠性设计的常用方法,列举了可靠性设计所涉及的基本数学理论,针对随机参数服从任意分布的情况进行研究,采用随机摄动方法和四阶矩技术等,提出了以四阶矩技术为基础的可靠性设计方法,并通过数值算例与Monte Carlo方法、Edgeworth级数法进行比较,证明了所研究方法的有效性与实用性。
第3章,阐述了目前可靠性灵敏度的设计方法,在本文所提出的四阶矩可靠性设计方法的基础上,提出了基于四阶矩技术的可靠性灵敏度设计方法,通过数值算例结果与Edgeworth级数法结果进行比较,证明了所提方法的有效性,得到了机械构件的随机参数对可靠性的影响规律,研究了设计参数的改变对机械构件的可靠性的影响。
第4章,基于机械构件的工程优化模型、可靠性优化方法、灵敏度分析方法和稳健设计理论,研究了基于四阶矩技术的非正态分布参数的机械构件的可靠性稳健设计方法,并与一般优化设计方法进行比较,证明了通过本文提出的可靠性稳健设计方法的实用有效性。
第5章,论述了相关系数可靠性灵敏度设计方法,提出了相关系数量值的选取原则,给出了随机参数之间相关程度的判别依据,并且通过数值算例说明,根据此理论原则是获取随机参数的相关系数量值既简便又有效的途径。
第6章,对航空发动机涡轮盘进行可靠性灵敏度设计,利用ISIGHT集成PRO/E、PATRAN/NASTRAN进行应力应变的分析。采用三维建模软件PRO/E和有限元软件PATRAN对涡轮盘进行了确定性静应力分析。利用结构可靠性分析软件NESSUS建立与PRO/E和PATRAN的接口技术,进行可靠度和可靠性灵敏度的计算与分析。再者,采用神经网络拟合技术,得到应力极限状态方程的显式表达式,而后应用摄动可靠性方法进行了发动机涡轮盘的可靠度和可靠性灵敏度的计算与分析,并与NESSUS可靠度和可靠性灵敏度分析结果进行了对比,对两种方法的分析结果进行了有效的相互验证。
第7章,对两类可靠性实用软件库(①车辆零部件可靠性设计实用软件库(登记号：2009SR06661)②机械基础件可靠性设计实用软件库(登记号：2009SR06662))的研制开发做了简述,对软件的使用操作做了简单介绍。
第8章,对本文的研究内容做了概括总结,并对课题的今后工作做了进一步的展望。
The security and reliability of structural systems is realized through design, manufacturing and management. Among them the design determines the inherent reliability of the product. Therefore, design has an important contribution to the quality of the product, and endows the congenital essential characteristics of the product. Because of the existence of uncertain factors in structures, such as the load, material properties, and geometry parameters, the problem hence becomes a stochastic system with random parameters. The study of the reliability of stochastic structural systems is of important significance. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and govern the fluctuations of the system parameters for safe operations. In the end, the reasonable mechanical structures could be designed with enough reliability and little cost. Structural reliability which is of universal attention at home and abroad is the main index and on the most important technique index of product quality, and the reliability theory and reliability-based design methods have been developed rapidly in the past decades.
Reliability sensitivity analysis of structural systems is the sensitivity design based on reliability, which can be used to evaluate the influence of the change of parameters on the reliability of structural systems. That is to say, the sensitivity of the reliability of structural systems with respect to the variance of design parameters can be determined by reliability sensitivity analysis. Reliability sensitivity analysis is of important implication in reliability design and modification, reliability based optimization design, reliability maintenance and so on. Nowadays, there are many methods in reliability analysis. In general, reliability analysis can always be performed based on the reliability analysis.
The reliability-based robust design which is based on reliability based optimization design is a low cost and high quality design method. This method integrates the reliability sensitivity design into the reliability optimization design. Its basic concept is that the robust of the product quality can always be ensured when the design parameters have small variances. There the study of reliability based robust design is of very important significance in the field of reliability design of mechanical structures.
Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was proposed. A numerical comparison was made among other methods, such as Edgeworth method and Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.
There are eight chapters in the thesis, the main contents are as follows:
Chapter1We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability theory, reliability sensitivity method and reliability-based robust design, and set forth the significant meaning of the study.
Chapter2:The common methods for reliability design of mechanical components are introduced. Mathematics theories and methods used in this dissertation are briefly listed. Techniques from the perturbation method and the fourth moment method are used to propose a practical and effective numerical method of reliability analysis with arbitrary distribution parameters. A numerical comparison was made among other methods, such as Edgeworth method, Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical.
Chapter3Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was built. A numerical comparison was made among other methods, such as Edgeworth method. The results showed out that the method proposed here is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.
Chapter4Based on the engineering optimization model, reliability optimization method, reliability sensitivity technique and robust design theory, a reliability-based robust design. method for mechanical components with non-normal parameters was proposed based on the fourth moment technique. A comparison was made among different methods, which proved that the reliability-based robust design method proposed herein is practical.
Chapter5A method of reliability-based sensitivity with respect to correlation coefficients was proposed. The principle of choosing the correlation coefficients and criterions for determining correlation degree among the random parameters were put forward. Results of numerical examples indicated that the method proposed is a convenient and practical approach to obtain the values of the correlation coefficients among random parameters.
Chapter6A deterministic static stress analysis on a turbine disk was conducted by using three-dimensional modeling software PRO/E and the finite element software PATRAN. By using ISIGHT, PRO/E and PATRAN/NASTRAN are integrated to carry out the stress and strain analysis. The randomness of parameters are taken into account, sample points of the dangerous area are generated by the experiment design of ISIGHT. Artificial neural network technology was adopted for the purpose of sample fitting. The approximate nonlinear function acquired by using Back Propagation network (BP network) was employed as the limit state function with an explicit expression. Hence, the reliability and reliability sensitivity analysis can be conducted with the method proposed herein. Using of the structural reliability analysis software NESSUS, a connector with PRO/E and PATRAN is established. The reliability and reliability sensitivity analysis are carried out in NESSUS. The results obtained in NESSUS are compared with that obtained by using the proposed method.
Chapter7Two sets of software library on the reliability design were developed, which helps to solve the core problems on the analysis of reliability in the mechanical area in our country (A practical software library for reliability based design of mobile components:China,2009SR06661; A practical software library for reliability based design of mechanical components:China,2009SR06661).
Chapter8The main conclusions of this dissertation are summarized and the prospects of the applications of reliability design in mechanical structures are discussed.
机械结构的可靠性灵敏度设计,是在可靠性基础上进行结构的灵敏度设计,可以评价设计参数的改变对结构可靠性的影响,即结构可靠性对设计参数变异的敏感性。可靠性灵敏度分析在可靠性设计和修改、可靠性优化设计、可靠性维护等方面均有重要的应用。目前可靠性灵敏度的计算方法很多,通常在可靠性的分析方法基础上都可以进行可靠性灵敏度设计。
机械结构的可靠性稳健设计是在可靠性优化设计理论的基础上的一种低成本和高质量的设计方法,是把可靠性优化设计与可靠性灵敏度设计相融合的一种工程设计方法。它的基本思想是当设计参数发生微小的变差时,在制造或使用中都能保证产品质量的稳健性要求。因此,可靠性稳健设计方法的研究在机械结构的可靠性设计领域具有非常重要的意义。
本文针对非正态分布参数的机械构件的可靠性灵敏度与可靠性稳健设计进行了研究,采用随机摄动方法、四阶矩技术、灵敏度分析方法,建立以四阶矩技术为基础的可靠性灵敏度分析方法,并通过数值算例与Edgeworth级数法、Monte Carlo方法进行比较,证明了所研究方法的设计实用性,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对机械构件的可靠性的影响。
本文共分为八章,主要研究内容如下：
第1章,对课题来源、选题依据和背景、主要研究内容、课题的学术理论意义和实际应用价值等进行了论述,阐述了可靠性的发展历程以及可靠性灵敏度、可靠性稳健设计的研究现状。
第2章,主要概述了机械构件可靠性设计的常用方法,列举了可靠性设计所涉及的基本数学理论,针对随机参数服从任意分布的情况进行研究,采用随机摄动方法和四阶矩技术等,提出了以四阶矩技术为基础的可靠性设计方法,并通过数值算例与Monte Carlo方法、Edgeworth级数法进行比较,证明了所研究方法的有效性与实用性。
第3章,阐述了目前可靠性灵敏度的设计方法,在本文所提出的四阶矩可靠性设计方法的基础上,提出了基于四阶矩技术的可靠性灵敏度设计方法,通过数值算例结果与Edgeworth级数法结果进行比较,证明了所提方法的有效性,得到了机械构件的随机参数对可靠性的影响规律,研究了设计参数的改变对机械构件的可靠性的影响。
第4章,基于机械构件的工程优化模型、可靠性优化方法、灵敏度分析方法和稳健设计理论,研究了基于四阶矩技术的非正态分布参数的机械构件的可靠性稳健设计方法,并与一般优化设计方法进行比较,证明了通过本文提出的可靠性稳健设计方法的实用有效性。
第5章,论述了相关系数可靠性灵敏度设计方法,提出了相关系数量值的选取原则,给出了随机参数之间相关程度的判别依据,并且通过数值算例说明,根据此理论原则是获取随机参数的相关系数量值既简便又有效的途径。
第6章,对航空发动机涡轮盘进行可靠性灵敏度设计,利用ISIGHT集成PRO/E、PATRAN/NASTRAN进行应力应变的分析。采用三维建模软件PRO/E和有限元软件PATRAN对涡轮盘进行了确定性静应力分析。利用结构可靠性分析软件NESSUS建立与PRO/E和PATRAN的接口技术,进行可靠度和可靠性灵敏度的计算与分析。再者,采用神经网络拟合技术,得到应力极限状态方程的显式表达式,而后应用摄动可靠性方法进行了发动机涡轮盘的可靠度和可靠性灵敏度的计算与分析,并与NESSUS可靠度和可靠性灵敏度分析结果进行了对比,对两种方法的分析结果进行了有效的相互验证。
第7章,对两类可靠性实用软件库(①车辆零部件可靠性设计实用软件库(登记号：2009SR06661)②机械基础件可靠性设计实用软件库(登记号：2009SR06662))的研制开发做了简述,对软件的使用操作做了简单介绍。
第8章,对本文的研究内容做了概括总结,并对课题的今后工作做了进一步的展望。
The security and reliability of structural systems is realized through design, manufacturing and management. Among them the design determines the inherent reliability of the product. Therefore, design has an important contribution to the quality of the product, and endows the congenital essential characteristics of the product. Because of the existence of uncertain factors in structures, such as the load, material properties, and geometry parameters, the problem hence becomes a stochastic system with random parameters. The study of the reliability of stochastic structural systems is of important significance. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and govern the fluctuations of the system parameters for safe operations. In the end, the reasonable mechanical structures could be designed with enough reliability and little cost. Structural reliability which is of universal attention at home and abroad is the main index and on the most important technique index of product quality, and the reliability theory and reliability-based design methods have been developed rapidly in the past decades.
Reliability sensitivity analysis of structural systems is the sensitivity design based on reliability, which can be used to evaluate the influence of the change of parameters on the reliability of structural systems. That is to say, the sensitivity of the reliability of structural systems with respect to the variance of design parameters can be determined by reliability sensitivity analysis. Reliability sensitivity analysis is of important implication in reliability design and modification, reliability based optimization design, reliability maintenance and so on. Nowadays, there are many methods in reliability analysis. In general, reliability analysis can always be performed based on the reliability analysis.
The reliability-based robust design which is based on reliability based optimization design is a low cost and high quality design method. This method integrates the reliability sensitivity design into the reliability optimization design. Its basic concept is that the robust of the product quality can always be ensured when the design parameters have small variances. There the study of reliability based robust design is of very important significance in the field of reliability design of mechanical structures.
Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was proposed. A numerical comparison was made among other methods, such as Edgeworth method and Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.
There are eight chapters in the thesis, the main contents are as follows:
Chapter1We explicate the engineering background, the aim and meaning of the research; introduce the rise, the concept, the development of reliability theory, reliability sensitivity method and reliability-based robust design, and set forth the significant meaning of the study.
Chapter2:The common methods for reliability design of mechanical components are introduced. Mathematics theories and methods used in this dissertation are briefly listed. Techniques from the perturbation method and the fourth moment method are used to propose a practical and effective numerical method of reliability analysis with arbitrary distribution parameters. A numerical comparison was made among other methods, such as Edgeworth method, Monte Carlo Simulation. The results showed out that the method proposed in the thesis is practical.
Chapter3Based on the stochastic perturbation method, fourth moment technique and reliability sensitivity method, an analytical method of reliability sensitivity with respect to random variables with non-normal distribution was built. A numerical comparison was made among other methods, such as Edgeworth method. The results showed out that the method proposed here is practical. The numerical example gave out the variation of the reliability sensitivity. The impact of mutative design parameters on the reliability of mechanical structures was widely studied.
Chapter4Based on the engineering optimization model, reliability optimization method, reliability sensitivity technique and robust design theory, a reliability-based robust design. method for mechanical components with non-normal parameters was proposed based on the fourth moment technique. A comparison was made among different methods, which proved that the reliability-based robust design method proposed herein is practical.
Chapter5A method of reliability-based sensitivity with respect to correlation coefficients was proposed. The principle of choosing the correlation coefficients and criterions for determining correlation degree among the random parameters were put forward. Results of numerical examples indicated that the method proposed is a convenient and practical approach to obtain the values of the correlation coefficients among random parameters.
Chapter6A deterministic static stress analysis on a turbine disk was conducted by using three-dimensional modeling software PRO/E and the finite element software PATRAN. By using ISIGHT, PRO/E and PATRAN/NASTRAN are integrated to carry out the stress and strain analysis. The randomness of parameters are taken into account, sample points of the dangerous area are generated by the experiment design of ISIGHT. Artificial neural network technology was adopted for the purpose of sample fitting. The approximate nonlinear function acquired by using Back Propagation network (BP network) was employed as the limit state function with an explicit expression. Hence, the reliability and reliability sensitivity analysis can be conducted with the method proposed herein. Using of the structural reliability analysis software NESSUS, a connector with PRO/E and PATRAN is established. The reliability and reliability sensitivity analysis are carried out in NESSUS. The results obtained in NESSUS are compared with that obtained by using the proposed method.
Chapter7Two sets of software library on the reliability design were developed, which helps to solve the core problems on the analysis of reliability in the mechanical area in our country (A practical software library for reliability based design of mobile components:China,2009SR06661; A practical software library for reliability based design of mechanical components:China,2009SR06661).
Chapter8The main conclusions of this dissertation are summarized and the prospects of the applications of reliability design in mechanical structures are discussed.
引文
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