基于功能度量法的概率结构优化设计
发布时间：2018-08-24 18:55
【摘要】：由于资源能源的短缺,工程结构优化设计的研究在近年来得到了高度重视。传统的结构优化设计方法由于未能充分考虑工程结构中的不确定性而经常会导致所设计的结构或因可靠度太低而无法满足结构预定功能,或因可靠度太高而造成资源的浪费。为解决传统优化设计方法的弊端,人们提出了概率结构优化设计。然而,概率优化设计计算量大的缺点在很大程度上限制了其在工程中的应用,因此,研究高效稳定的概率结构优化设计算法具有重要意义。本文研究内容可概括为以下几点：1.介绍了概率结构优化设计的常用计算方法,如可靠指标法(RIA)、功能度量法(PMA)、单循环单变量方法(SLSV)以及序列优化与可靠度评定方法(SORA)。因为功能度量法比传统可靠指标法效率高、稳定性好,本文主要基于功能度量法和以此为基础的SORA开展研究工作。因此还详细介绍了功能度量法中概率功能度量求解的计算方法：改进均值法(AMV)、混合均值法(HMV)、混沌控制法(CC)以及改进混沌控制法(MCC)。2.针对AMV方法求解概率功能度量时容易出现周期振荡、混沌等不收敛现象,本文通过引入一个“新”的步长来改善迭代序列的收敛性能,提出了自适应步长法(SLA)在迭代过程中,该步长可能保持不变,也可能采用一种简单的自适应策略逐渐减小。通过证明可知,AMV方法为步长趋近于无穷时SLA方法的一个特例。SLA方法迭代格式简单,且不需要功能函数凹凸性等先验信息。多个算例表明,与AMV、HMV、CC等常用概率功能度量求解方法相比,SLA方法更加高效、稳定。采用SLA方法继续进行概率结构优化设计,同样表明基于SLA方法的概率结构优化设计比基于AMV、HMV、CC等方法的概率结构优化设计稳定、高效。3.基于SORA方法的概念,本文提出了近似序列优化与可靠度评定方法(ASORA),该方法在每次可靠度评估中采用近似最小功能目标点,而不是精确的最小功能目标点。在每一次循环中,利用上一次循环中得到的近似最小功能目标点及该点处功能函数的灵敏度来构建优化设计中的近似约束,并求得新的近似最小功能目标点。由于采用了近似可靠度分析,在可靠度评定过程中概率功能度量求解不再需要进行多次迭代,这大大减少了功能函数调用次数,显著提高了概率结构优化设计的计算效率。另外,由于近似最小功能目标点及该点处灵敏度被用来构建约束的线性泰勒展开,因此在确定性优化过程中也不再计算功能函数,这同样减少了功能函数计算次数,提高效率。数值算例表明,随着设计变量收敛到最优设计点,近似最小功能目标点也逐步收敛到了精确最小功能目标点,优化设计和可靠性评定实现了同步收敛。多个算例证明了本文所提出ASORA方法的高效、稳定。
[Abstract]:Due to the shortage of resources and energy, the research on optimal design of engineering structures has been paid great attention in recent years. The traditional structural optimization design method often leads to the failure to take full account of the uncertainty in engineering structure, which results in the structure being too low in reliability to satisfy the predefined function of the structure, or the waste of resources due to the high reliability. In order to solve the drawback of the traditional optimization design method, the probabilistic structure optimization design is proposed. However, the disadvantages of large computational complexity in probabilistic optimization design limit its application in engineering to a great extent. Therefore, it is of great significance to study the efficient and stable probabilistic structure optimization design algorithm. The contents of this paper can be summarized as follows: 1. This paper introduces the common calculation methods of probabilistic structural optimization design, such as reliability index method, (RIA), function metric method, (PMA), single cycle univariate method (SLSV), sequence optimization and reliability evaluation method (SORA). Because the function measure method is more efficient and stable than the traditional reliable index method, this paper mainly based on the function measure method and the SORA based on it. Therefore, the calculation methods of probabilistic function metric in function metric are introduced in detail: improved mean method (AMV), mixed mean method (HMV), chaos control method (CC) and improved chaos control method (MCC). 2. In order to solve the problem of periodic oscillation and chaotic nonconvergence in solving probabilistic function measurement by AMV method, this paper introduces a new step size to improve the convergence performance of iterative sequence, and proposes an adaptive step size method (SLA) in the iterative process. The step size may remain the same, or a simple adaptive strategy may be adopted. It is proved that the SLA method has a simple iterative format and does not require prior information such as convexity and concavity of function when the step size is approaching infinity. A number of examples show that the AMV,HMV,CC method is more efficient and stable than the usual probabilistic function measurement methods such as AMV,HMV,CC. The probabilistic structure optimization design based on SLA method also shows that the probabilistic structure optimization design based on SLA method is more stable and efficient than the probabilistic structure optimization design based on AMV,HMV,CC method. Based on the concept of SORA method, an approximate sequence optimization and reliability evaluation method, (ASORA), is proposed in this paper. In each reliability evaluation, the approximate minimum function target point is used instead of the exact minimum function target point. In each cycle, the approximate minimum function target point and the sensitivity of the function at the last cycle are used to construct the approximate constraints in the optimization design, and a new approximate minimum function target point is obtained. Because of the use of approximate reliability analysis, in the process of reliability evaluation, the calculation of probabilistic function measurement does not need multiple iterations, which greatly reduces the number of functional function calls and improves the computational efficiency of the optimization design of probabilistic structure. In addition, the approximate minimum functional target point and its sensitivity are used to construct the constrained linear Taylor expansion, so the function is not calculated in the deterministic optimization process, which also reduces the number of functional function calculations and improves the efficiency. Numerical examples show that as the design variables converge to the optimal design point, the approximate minimum functional target point converges to the exact minimum functional objective point gradually, and the optimal design and reliability evaluation achieve synchronous convergence. Several examples show that the proposed ASORA method is efficient and stable.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TU318
本文编号：2201726
[Abstract]:Due to the shortage of resources and energy, the research on optimal design of engineering structures has been paid great attention in recent years. The traditional structural optimization design method often leads to the failure to take full account of the uncertainty in engineering structure, which results in the structure being too low in reliability to satisfy the predefined function of the structure, or the waste of resources due to the high reliability. In order to solve the drawback of the traditional optimization design method, the probabilistic structure optimization design is proposed. However, the disadvantages of large computational complexity in probabilistic optimization design limit its application in engineering to a great extent. Therefore, it is of great significance to study the efficient and stable probabilistic structure optimization design algorithm. The contents of this paper can be summarized as follows: 1. This paper introduces the common calculation methods of probabilistic structural optimization design, such as reliability index method, (RIA), function metric method, (PMA), single cycle univariate method (SLSV), sequence optimization and reliability evaluation method (SORA). Because the function measure method is more efficient and stable than the traditional reliable index method, this paper mainly based on the function measure method and the SORA based on it. Therefore, the calculation methods of probabilistic function metric in function metric are introduced in detail: improved mean method (AMV), mixed mean method (HMV), chaos control method (CC) and improved chaos control method (MCC). 2. In order to solve the problem of periodic oscillation and chaotic nonconvergence in solving probabilistic function measurement by AMV method, this paper introduces a new step size to improve the convergence performance of iterative sequence, and proposes an adaptive step size method (SLA) in the iterative process. The step size may remain the same, or a simple adaptive strategy may be adopted. It is proved that the SLA method has a simple iterative format and does not require prior information such as convexity and concavity of function when the step size is approaching infinity. A number of examples show that the AMV,HMV,CC method is more efficient and stable than the usual probabilistic function measurement methods such as AMV,HMV,CC. The probabilistic structure optimization design based on SLA method also shows that the probabilistic structure optimization design based on SLA method is more stable and efficient than the probabilistic structure optimization design based on AMV,HMV,CC method. Based on the concept of SORA method, an approximate sequence optimization and reliability evaluation method, (ASORA), is proposed in this paper. In each reliability evaluation, the approximate minimum function target point is used instead of the exact minimum function target point. In each cycle, the approximate minimum function target point and the sensitivity of the function at the last cycle are used to construct the approximate constraints in the optimization design, and a new approximate minimum function target point is obtained. Because of the use of approximate reliability analysis, in the process of reliability evaluation, the calculation of probabilistic function measurement does not need multiple iterations, which greatly reduces the number of functional function calls and improves the computational efficiency of the optimization design of probabilistic structure. In addition, the approximate minimum functional target point and its sensitivity are used to construct the constrained linear Taylor expansion, so the function is not calculated in the deterministic optimization process, which also reduces the number of functional function calculations and improves the efficiency. Numerical examples show that as the design variables converge to the optimal design point, the approximate minimum functional target point converges to the exact minimum functional objective point gradually, and the optimal design and reliability evaluation achieve synchronous convergence. Several examples show that the proposed ASORA method is efficient and stable.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TU318
【参考文献】
相关期刊论文 前4条
1 贺谦;李元生;敖良波;温志勋;岳珠峰;;基于单循环方法的涡轮叶片可靠性及多学科设计优化[J];推进技术;2011年05期
2 杨迪雄;易平;;概率约束评估的功能度量法的混沌控制[J];计算力学学报;2008年05期
3 隋允康;李善坡;;结构优化中的建模方法概述[J];力学进展;2008年02期
4 陈新度，王石刚，，张新访，余俊;大型板结构的一种优化准则法[J];华中理工大学学报;1995年06期
相关博士学位论文 前4条
1 陈振中;基于可靠性的设计优化中精确解耦与高效抽样技术研究[D];华中科技大学;2013年
2 戴伟;基于响应面方法的立管结构可靠性研究[D];哈尔滨工程大学;2012年
3 易平;概率结构优化设计的高效算法研究[D];大连理工大学;2007年
4 许林;基于可靠度的结构优化研究[D];大连理工大学;2004年
本文编号：2201726
本文链接：https://www.wllwen.com/guanlilunwen/chengjian/2201726.html
