代理模型近似技术研究及其在结构可靠度分析中的应用
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摘要
近几十年来，伴随着新材料、先进制造工艺和以科学计算为基础的仿真分析均出现重大技术进步，工程结构分析与设计技术也呈现出多样化发展的趋势。以结构多目标优化、多学科协同优化设计、结构可靠度分析与设计以及鲁棒设计等为代表的先进结构设计思想已经在实际工程结构设计应用中得到体现，这也契合了当前日益攀升的工程结构设计要求，即缩短设计周期，降低开发成本，提高设计质量，及对环境与客户更友好等。另一方面，尽管计算机仿真能力与计算效率已经取得较大进展，但新材料与新结构形式在工程结构设计中的广泛应用仍可能使传统的结构分析手段出现困难，不论是采用结构试验还是复杂仿真分析来辅助结构设计，都对上述结构设计要求提出挑战。因此，非常有必要研究各种适应结构分析能力现状的设计技术，而对代理模型技术的研究及其对于辅助结构分析与设计方面的应用已经成为当前国内外的热门研究课题。
本文围绕代理模型在结构分析与设计中的应用展开研究，分别探讨了基于结构试验的复合材料冲击损伤表征及基于有限元仿真计算的结构可靠度分析问题，其中研究重点放在新型代理模型技术在结构可靠度分析中的应用。本文提出了一种改进的人工神经网络建模技术，实现了该方法在复合材料结构冲击损伤表征中的应用；基于各基本结构可靠度分析方法的不足，提出了一种新型结构可靠度分析的Two-Phase混杂模型；将移动最小二乘技术推广于结构可靠度分析领域，并基于失效概率计算特征提出了新型双加权移动最小二乘方法，以提高分析效率；研究了有限元分析中的灵敏度计算原理，具体推导了灵敏度信息辅助Kriging插值的建模方法，并提出了两种基于灵敏度信息的结构可靠度分析方法。主要研究工作及结论如下：
(1)建立了改进的人工神经网络模型，并实现了该模型在复合材料冲击损伤表征中的应用
针对实际复合材料飞机结构设计中冲击损伤表征出现的困难，提出了以结构试验结果作为训练样本，构建人工神经网络模型(Artificial Neural Network,ANN)来定义结构冲击响应与影响参数之间的函数关系。基于训练样本点的数据特征，对传统的人工神经网络训练方法进行了改进，提出了利用交叉验证技术(Cross-Validation, CV)确定最佳网络结构与初始参数的方法。为了验证所提出方法的有效性，将其应用于复杂非线性函数和蜂窝夹层结构冲击损伤表征问题中。结果显示所提方法均能够有效地建立人工神经网络模型对未知函数关系进行近似，且表现出比采用传统神经网络建模方法更稳定的特征；
(2)提出了结构可靠度分析的两阶段(Two-Phase)混杂模型
鉴于含隐式极限状态函数的结构可靠度分析问题中，一次二阶矩法、Monte Carlo法与经典响应面法都存在各自的优点与不足，提出了一种能够凸显三种方法分析优势、避免各自计算缺陷的可靠度分析Two-Phase混杂模型。在Two-Phase混杂模型中，基于一次二阶矩法与代理模型的新型序列自适应抽样技术保证了在1st Phase中能够在极限状态曲面附近抽取更多的样本点，这对于提高2nd Phase中基于Monte Carlo法的失效概率Pf计算精度与效率有直接影响。通过4个典型可靠度分析算例，验证了所提方法能够有效实现将样本点布置在极限状态曲面附近，计算结果与其它可靠度方法相比也存在明显优势，即Two-Phase混杂模型可以在失效概率Pf的计算精度与计算效率上同步得到改进。
(3)开展了双加权移动最小二乘技术在结构可靠度分析中的应用研究
为了将移动最小二乘技术(Moving Least Square,MLS)推广于结构可靠度分析应用中，首先介绍了其基本理论，并结合结构可靠度分析中失效概率计算的基本原理，提出了一种改进的双加权移动最小二乘法并使其能更适应可靠度分析问题特征。新的加权方案能够将随机变量空间中靠近极限状态曲面或最可能失效点的样本点分配更大的权系数值，因此能够提高极限状态曲面或最可能失效点的近似精度。而这对于提高失效概率计算精度有促进作用。3个典型算例的结果表明，与其它近似代理模型相比，移动最小二乘法能够有效地应用于结构可靠度分析问题，且采用双加权移动最小二乘模型比采用普通移动最小二乘模型具备更高的失效概率计算精度。
(4)提出了基于仿真灵敏度信息的结构可靠度分析模型
将计算机仿真程序特征与结构可靠度分析特征综合考虑，研究了提高失效概率Pf计算效率的一种新方法。以主流有限元软件均能提供的仿真灵敏度信息利用为例，提出了两种利用仿真灵敏度信息辅助进行结构失效概率计算的方法：1.将仿真灵敏度信息转化为一次二阶矩法中极限状态函数对随机变量的偏导数。三个工程算例的结果表明，灵敏度信息极大地提高了失效概率计算效率，但是计算精度存在限制；2.推导了包含仿真灵敏度信息的Kriging建模方法(SEK)，通过已知函数近似问题验证了SEK在提高近似精度与效率方面的优势。基于Kriging、SEK与Two-Phase混杂模型的思路，发展出四种不同结构可靠度分析方法，两个典型数值算例的分析结果也表明：在保证失效概率分析精度的前提下，仿真灵敏度信息对于提高计算效率有很大的促进作用。
In recent decades, along with the significant technical progress of new materials,advanced manufacturing technology and simulation analysis based on scientific computing,engineering structural analysis and design techniques are also showing a diversifieddevelopment trend. Several advanced structure design ideologies, which includemulti-objective structure optimization, multidisciplinary design optimization(MDO),structural reliability analysis and design, and robust design, has to be reflected in the actualengineering structural design applications. These new design principles also fulfill currentescalating structural design requirements, which means shorten the design cycle, reducedevelopment costs, improve design quality, and more friendly to the environment andcustomers. On the other hand, even the computer simulation capacity and computationalefficiency has made great progress, widely usage of new materials and new structures designcould still make traditional structure analysis theory of too difficult or complex in assistingstructure designs and fulfilling the structure design requirements. Therefore, it is necessary tostudy new design technologies which adapt to contemporary structural analysis capabilities.As an efficient solution to these problems in structure design, surrogate modeling techniqueshad become a popular research topic. The research focus of this dissertation lays on severalcritical issues related to approximation of surrogate models and its applicability in structuralreliability analysis. The content of dissertation can be summarized as follows:
(1)Improved Artificial Neural Networks models and application in characterizing impactdamage of composite structures
As the structure design application of composite is still advanced than its correspondinganalytical model development, the artificial neural network model (ANN) was studied andextended to composite structure designs based on abundant physical test results on composite materials. It is necessary to improve the traditional modeling process of ANN because of thefeature of training sample data from physical structure test. A cross-validation scheme isutilized to determine the optimal network structural and initial parameters. The complexnonlinear function approximation problem has verified the applicability of proposed ANNmodeling method. The internal damages induced in honeycomb sandwich structure are thencharacterized and predicted with proposed ANN model whose training sample data comesfrom standard low-velocity impact tests and non-destructive damage testing. The results haveproved the hypothesis that surrogate ANN models can approximate responses of compositestructures efficiently, which enabled a possible option in assisting composite structure designs
(2) A Two-Phase Hybrid model for structural reliability analysis
A Two-Phase Hybrid Method (TPHM) aiming at structural reliability analysis isproposed in current research based on complete performance discussion on basic reliabilitymethods. The TPHM is expected to highlight the advancements of each basic reliabilitymethod and obtain the structure failure probabilityPf efficiently. In the first phase, the firstorder reliability methods (FORM) are utilized to promote the sampling efficiency of surrogatemodels, while FORM can help to locate newly added sample points as close as possible to thelimit state surface. In the second phase, the Monte Carlo method and surrogate models isadopted to estimate the structure failure probabilityPf accurately. The chosen4test examplesdemonstrated the success of sequential adaptive sampling schemes and verified theapplicability of TPHM.
(3)Doubly weighted moving least square method and its application in structuralreliability analysis
The object of this research is extending the moving least square method (MLS) tostructural reliability analysis, so the basic hypothesis and principle is firstly explained in detail.However, it is necessary to improve the traditional MLS in order to further embody thefeature of structural reliability analysis. Besides the original weight system in MLS, anadditional weight system to sample points is devised, which enable to assign more weightfactors to sample points that locate more closer to limit state surface or most probable failurepoint. The highlight of sample points close to limit state surface or most probable failure pointcan promote the approximate of themselves, which would do great good to failure probabilityestimation.3numerical test problems had verified the applicability of MLS and doubly weighted MLS in structural reliability analysis, furthermore, the second additional weightsystem enhanced the performance of failure probability estimations.
(4)Utilization of simulation sensitivity information in boosting structural reliabilityanalysis
The possibility of combining both the property of computer simulation tools andstructural reliability analysis is discussed in current study. The sensitivity information, whichhad been able to calculated inexpensively by commercial finite element programs, is studiedto boost the capability of structural reliability methods and two possible methodsproposed:1.the simulation sensitivity information outputed by finite element code are treat asthe partial derivatives of performance function to random variables in first order reliabilityanalysis, and three practical engineering structure analysis verified that the cheap sensitivityinformation do great good to convergence of FORM, which is exactly the reason why theaccuracy of failure probability is unacceptable for many problem;2. A sensitivity enhancekriging (SEK) is reformulated based on discussion of kriging theory, and the numericalexample help conclude that the sensitivity information can promote the approximation ofsurrogate models remarkably. An analogical Two-Phase Hybrid Method (TPHM) based onsensitivity information and SEK is proposed and two reliability problems are tested. The testproblem have demonstrated the utilization of sensitivity information in estimating failureprobabilities.
本文围绕代理模型在结构分析与设计中的应用展开研究，分别探讨了基于结构试验的复合材料冲击损伤表征及基于有限元仿真计算的结构可靠度分析问题，其中研究重点放在新型代理模型技术在结构可靠度分析中的应用。本文提出了一种改进的人工神经网络建模技术，实现了该方法在复合材料结构冲击损伤表征中的应用；基于各基本结构可靠度分析方法的不足，提出了一种新型结构可靠度分析的Two-Phase混杂模型；将移动最小二乘技术推广于结构可靠度分析领域，并基于失效概率计算特征提出了新型双加权移动最小二乘方法，以提高分析效率；研究了有限元分析中的灵敏度计算原理，具体推导了灵敏度信息辅助Kriging插值的建模方法，并提出了两种基于灵敏度信息的结构可靠度分析方法。主要研究工作及结论如下：
(1)建立了改进的人工神经网络模型，并实现了该模型在复合材料冲击损伤表征中的应用
针对实际复合材料飞机结构设计中冲击损伤表征出现的困难，提出了以结构试验结果作为训练样本，构建人工神经网络模型(Artificial Neural Network,ANN)来定义结构冲击响应与影响参数之间的函数关系。基于训练样本点的数据特征，对传统的人工神经网络训练方法进行了改进，提出了利用交叉验证技术(Cross-Validation, CV)确定最佳网络结构与初始参数的方法。为了验证所提出方法的有效性，将其应用于复杂非线性函数和蜂窝夹层结构冲击损伤表征问题中。结果显示所提方法均能够有效地建立人工神经网络模型对未知函数关系进行近似，且表现出比采用传统神经网络建模方法更稳定的特征；
(2)提出了结构可靠度分析的两阶段(Two-Phase)混杂模型
鉴于含隐式极限状态函数的结构可靠度分析问题中，一次二阶矩法、Monte Carlo法与经典响应面法都存在各自的优点与不足，提出了一种能够凸显三种方法分析优势、避免各自计算缺陷的可靠度分析Two-Phase混杂模型。在Two-Phase混杂模型中，基于一次二阶矩法与代理模型的新型序列自适应抽样技术保证了在1st Phase中能够在极限状态曲面附近抽取更多的样本点，这对于提高2nd Phase中基于Monte Carlo法的失效概率Pf计算精度与效率有直接影响。通过4个典型可靠度分析算例，验证了所提方法能够有效实现将样本点布置在极限状态曲面附近，计算结果与其它可靠度方法相比也存在明显优势，即Two-Phase混杂模型可以在失效概率Pf的计算精度与计算效率上同步得到改进。
(3)开展了双加权移动最小二乘技术在结构可靠度分析中的应用研究
为了将移动最小二乘技术(Moving Least Square,MLS)推广于结构可靠度分析应用中，首先介绍了其基本理论，并结合结构可靠度分析中失效概率计算的基本原理，提出了一种改进的双加权移动最小二乘法并使其能更适应可靠度分析问题特征。新的加权方案能够将随机变量空间中靠近极限状态曲面或最可能失效点的样本点分配更大的权系数值，因此能够提高极限状态曲面或最可能失效点的近似精度。而这对于提高失效概率计算精度有促进作用。3个典型算例的结果表明，与其它近似代理模型相比，移动最小二乘法能够有效地应用于结构可靠度分析问题，且采用双加权移动最小二乘模型比采用普通移动最小二乘模型具备更高的失效概率计算精度。
(4)提出了基于仿真灵敏度信息的结构可靠度分析模型
将计算机仿真程序特征与结构可靠度分析特征综合考虑，研究了提高失效概率Pf计算效率的一种新方法。以主流有限元软件均能提供的仿真灵敏度信息利用为例，提出了两种利用仿真灵敏度信息辅助进行结构失效概率计算的方法：1.将仿真灵敏度信息转化为一次二阶矩法中极限状态函数对随机变量的偏导数。三个工程算例的结果表明，灵敏度信息极大地提高了失效概率计算效率，但是计算精度存在限制；2.推导了包含仿真灵敏度信息的Kriging建模方法(SEK)，通过已知函数近似问题验证了SEK在提高近似精度与效率方面的优势。基于Kriging、SEK与Two-Phase混杂模型的思路，发展出四种不同结构可靠度分析方法，两个典型数值算例的分析结果也表明：在保证失效概率分析精度的前提下，仿真灵敏度信息对于提高计算效率有很大的促进作用。
In recent decades, along with the significant technical progress of new materials,advanced manufacturing technology and simulation analysis based on scientific computing,engineering structural analysis and design techniques are also showing a diversifieddevelopment trend. Several advanced structure design ideologies, which includemulti-objective structure optimization, multidisciplinary design optimization(MDO),structural reliability analysis and design, and robust design, has to be reflected in the actualengineering structural design applications. These new design principles also fulfill currentescalating structural design requirements, which means shorten the design cycle, reducedevelopment costs, improve design quality, and more friendly to the environment andcustomers. On the other hand, even the computer simulation capacity and computationalefficiency has made great progress, widely usage of new materials and new structures designcould still make traditional structure analysis theory of too difficult or complex in assistingstructure designs and fulfilling the structure design requirements. Therefore, it is necessary tostudy new design technologies which adapt to contemporary structural analysis capabilities.As an efficient solution to these problems in structure design, surrogate modeling techniqueshad become a popular research topic. The research focus of this dissertation lays on severalcritical issues related to approximation of surrogate models and its applicability in structuralreliability analysis. The content of dissertation can be summarized as follows:
(1)Improved Artificial Neural Networks models and application in characterizing impactdamage of composite structures
As the structure design application of composite is still advanced than its correspondinganalytical model development, the artificial neural network model (ANN) was studied andextended to composite structure designs based on abundant physical test results on composite materials. It is necessary to improve the traditional modeling process of ANN because of thefeature of training sample data from physical structure test. A cross-validation scheme isutilized to determine the optimal network structural and initial parameters. The complexnonlinear function approximation problem has verified the applicability of proposed ANNmodeling method. The internal damages induced in honeycomb sandwich structure are thencharacterized and predicted with proposed ANN model whose training sample data comesfrom standard low-velocity impact tests and non-destructive damage testing. The results haveproved the hypothesis that surrogate ANN models can approximate responses of compositestructures efficiently, which enabled a possible option in assisting composite structure designs
(2) A Two-Phase Hybrid model for structural reliability analysis
A Two-Phase Hybrid Method (TPHM) aiming at structural reliability analysis isproposed in current research based on complete performance discussion on basic reliabilitymethods. The TPHM is expected to highlight the advancements of each basic reliabilitymethod and obtain the structure failure probabilityPf efficiently. In the first phase, the firstorder reliability methods (FORM) are utilized to promote the sampling efficiency of surrogatemodels, while FORM can help to locate newly added sample points as close as possible to thelimit state surface. In the second phase, the Monte Carlo method and surrogate models isadopted to estimate the structure failure probabilityPf accurately. The chosen4test examplesdemonstrated the success of sequential adaptive sampling schemes and verified theapplicability of TPHM.
(3)Doubly weighted moving least square method and its application in structuralreliability analysis
The object of this research is extending the moving least square method (MLS) tostructural reliability analysis, so the basic hypothesis and principle is firstly explained in detail.However, it is necessary to improve the traditional MLS in order to further embody thefeature of structural reliability analysis. Besides the original weight system in MLS, anadditional weight system to sample points is devised, which enable to assign more weightfactors to sample points that locate more closer to limit state surface or most probable failurepoint. The highlight of sample points close to limit state surface or most probable failure pointcan promote the approximate of themselves, which would do great good to failure probabilityestimation.3numerical test problems had verified the applicability of MLS and doubly weighted MLS in structural reliability analysis, furthermore, the second additional weightsystem enhanced the performance of failure probability estimations.
(4)Utilization of simulation sensitivity information in boosting structural reliabilityanalysis
The possibility of combining both the property of computer simulation tools andstructural reliability analysis is discussed in current study. The sensitivity information, whichhad been able to calculated inexpensively by commercial finite element programs, is studiedto boost the capability of structural reliability methods and two possible methodsproposed:1.the simulation sensitivity information outputed by finite element code are treat asthe partial derivatives of performance function to random variables in first order reliabilityanalysis, and three practical engineering structure analysis verified that the cheap sensitivityinformation do great good to convergence of FORM, which is exactly the reason why theaccuracy of failure probability is unacceptable for many problem;2. A sensitivity enhancekriging (SEK) is reformulated based on discussion of kriging theory, and the numericalexample help conclude that the sensitivity information can promote the approximation ofsurrogate models remarkably. An analogical Two-Phase Hybrid Method (TPHM) based onsensitivity information and SEK is proposed and two reliability problems are tested. The testproblem have demonstrated the utilization of sensitivity information in estimating failureprobabilities.
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