基于功能度量法的概率結(jié)構(gòu)優(yōu)化設(shè)計
發(fā)布時間：2018-08-24 18:55
【摘要】：由于資源能源的短缺,工程結(jié)構(gòu)優(yōu)化設(shè)計的研究在近年來得到了高度重視。傳統(tǒng)的結(jié)構(gòu)優(yōu)化設(shè)計方法由于未能充分考慮工程結(jié)構(gòu)中的不確定性而經(jīng)常會導(dǎo)致所設(shè)計的結(jié)構(gòu)或因可靠度太低而無法滿足結(jié)構(gòu)預(yù)定功能,或因可靠度太高而造成資源的浪費。為解決傳統(tǒng)優(yōu)化設(shè)計方法的弊端,人們提出了概率結(jié)構(gòu)優(yōu)化設(shè)計。然而,概率優(yōu)化設(shè)計計算量大的缺點在很大程度上限制了其在工程中的應(yīng)用,因此,研究高效穩(wěn)定的概率結(jié)構(gòu)優(yōu)化設(shè)計算法具有重要意義。本文研究內(nèi)容可概括為以下幾點：1.介紹了概率結(jié)構(gòu)優(yōu)化設(shè)計的常用計算方法,如可靠指標法(RIA)、功能度量法(PMA)、單循環(huán)單變量方法(SLSV)以及序列優(yōu)化與可靠度評定方法(SORA)。因為功能度量法比傳統(tǒng)可靠指標法效率高、穩(wěn)定性好,本文主要基于功能度量法和以此為基礎(chǔ)的SORA開展研究工作。因此還詳細介紹了功能度量法中概率功能度量求解的計算方法：改進均值法(AMV)、混合均值法(HMV)、混沌控制法(CC)以及改進混沌控制法(MCC)。2.針對AMV方法求解概率功能度量時容易出現(xiàn)周期振蕩、混沌等不收斂現(xiàn)象,本文通過引入一個“新”的步長來改善迭代序列的收斂性能,提出了自適應(yīng)步長法(SLA)在迭代過程中,該步長可能保持不變,也可能采用一種簡單的自適應(yīng)策略逐漸減小。通過證明可知,AMV方法為步長趨近于無窮時SLA方法的一個特例。SLA方法迭代格式簡單,且不需要功能函數(shù)凹凸性等先驗信息。多個算例表明,與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、穩(wěn)定。采用SLA方法繼續(xù)進行概率結(jié)構(gòu)優(yōu)化設(shè)計,同樣表明基于SLA方法的概率結(jié)構(gòu)優(yōu)化設(shè)計比基于AMV、HMV、CC等方法的概率結(jié)構(gòu)優(yōu)化設(shè)計穩(wěn)定、高效。3.基于SORA方法的概念,本文提出了近似序列優(yōu)化與可靠度評定方法(ASORA),該方法在每次可靠度評估中采用近似最小功能目標點,而不是精確的最小功能目標點。在每一次循環(huán)中,利用上一次循環(huán)中得到的近似最小功能目標點及該點處功能函數(shù)的靈敏度來構(gòu)建優(yōu)化設(shè)計中的近似約束,并求得新的近似最小功能目標點。由于采用了近似可靠度分析,在可靠度評定過程中概率功能度量求解不再需要進行多次迭代,這大大減少了功能函數(shù)調(diào)用次數(shù),顯著提高了概率結(jié)構(gòu)優(yōu)化設(shè)計的計算效率。另外,由于近似最小功能目標點及該點處靈敏度被用來構(gòu)建約束的線性泰勒展開,因此在確定性優(yōu)化過程中也不再計算功能函數(shù),這同樣減少了功能函數(shù)計算次數(shù),提高效率。數(shù)值算例表明,隨著設(shè)計變量收斂到最優(yōu)設(shè)計點,近似最小功能目標點也逐步收斂到了精確最小功能目標點,優(yōu)化設(shè)計和可靠性評定實現(xiàn)了同步收斂。多個算例證明了本文所提出ASORA方法的高效、穩(wěn)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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TU318
本文編號：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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TU318
【參考文獻】
相關(guān)期刊論文 前4條
1 賀謙;李元生;敖良波;溫志勛;岳珠峰;;基于單循環(huán)方法的渦輪葉片可靠性及多學(xué)科設(shè)計優(yōu)化[J];推進技術(shù);2011年05期
2 楊迪雄;易平;;概率約束評估的功能度量法的混沌控制[J];計算力學(xué)學(xué)報;2008年05期
3 隋允康;李善坡;;結(jié)構(gòu)優(yōu)化中的建模方法概述[J];力學(xué)進展;2008年02期
4 陳新度，王石剛，，張新訪，余俊;大型板結(jié)構(gòu)的一種優(yōu)化準則法[J];華中理工大學(xué)學(xué)報;1995年06期
相關(guān)博士學(xué)位論文 前4條
1 陳振中;基于可靠性的設(shè)計優(yōu)化中精確解耦與高效抽樣技術(shù)研究[D];華中科技大學(xué);2013年
2 戴偉;基于響應(yīng)面方法的立管結(jié)構(gòu)可靠性研究[D];哈爾濱工程大學(xué);2012年
3 易平;概率結(jié)構(gòu)優(yōu)化設(shè)計的高效算法研究[D];大連理工大學(xué);2007年
4 許林;基于可靠度的結(jié)構(gòu)優(yōu)化研究[D];大連理工大學(xué);2004年
本文編號：2201726
本文鏈接：http://sikaile.net/guanlilunwen/chengjian/2201726.html
最近更新
教材專著
