复杂工程结构可靠度分析的高斯过程动态响应面方法研究
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摘要
中国正处在土木建筑行业的黄金机遇期,大型结构如雨后春笋,复杂程度越来越高,不确定因素越来越多,随着而来的是安全问题越来越重要。这就要求提出结构可靠度评估的与信息化时代相吻合的新理论和新方法。本文将针对大型复杂结构对应的功能函数具有计算代价高、隐式表达和高度非线性等特征,而传统方法难以或准确或快速地解决的问题,利用高斯过程机器学习方法善于处理高维数、小样本、非线性等复杂问题、能自适应获取最优超参数、预测结果具有概率意义等优点,在动态更新学习样本的基础上,采用高斯过程模型重构复杂结构的隐式功能函数,进而结合传统可靠度分析方法求解结构的可靠度问题,能较为高效快速地求解复杂结构可靠度问题。
本文的主要研究工作如下：
1.基于蒙特卡罗的高斯过程分类法研究。采用高斯过程分类模型来重构功能函数,基于马尔可夫链的样本生成机制,并将高精度的蒙特卡罗可靠度分析方法与分类性能优异的高斯过程分类模型相结合,在构建响应面拟合误差自适应修正机制的基础上,提出基于高斯过程分类-MCS动态响应面的结构可靠度分析方法,为含有隐式功能函数的复杂工程结构可靠度的高速求解提供一个新的选择。
2.基于Breitung法的高斯过程回归动态响应面法研究。该方法利用有限元分析程序构造少量训练样本,利用训练后的高斯过程回归模型构建响应面,实现小样本条件下功能函数及其偏导数的显式表达,通过构造合理的迭代方式,利用各迭代步的验算点信息不断修正响应面的拟合误差,动态提升响应面对失效概率贡献较大区域的重构精度,进而结合Breitung法快速推求结构的可靠度指标。与传统响应面法相比较,该方法具有较高的计算精度与计算效率,且易于与既有的有限元软件相结合。
3.基于蒙特卡罗的高斯过程回归动态响应面法研究。该方法利用有限元分析程序构造少量训练样本,据此利用高斯过程回归模型构建响应面,实现小样本条件下高度非线性隐式功能函数的高精度逼近与显式化,并采用蒙特卡罗随机抽样快速估计失效域中最可能失效点,通过迭代循环,利用最可能失效点信息不断修正响应面的拟合误差,从而动态提升响应面对失效概率贡献较大区域的重构精度,进而结合蒙特卡罗模拟快速推求结构失效概率。该方法简单易行,具有高效高精度的优点,适用于大型复杂工程结构的可靠度分析。
4.基于粒子群优化的高斯过程动态响应面法研究。该方法将可靠度求解问题转化为最优化问题,在采用有限元法生成少量样本的基础上,采用高斯过程回归模型构建功能函数的响应面,实现小样本条件下隐式非线性功能函数的显式表达,进而利用粒子群优化算法搜索的全局最可能失效点,并构造合理的迭代方式,利用各迭代步的最可能失效点信息动态提升响应面对失效概率贡献较大区域的重构精度。最后,以迭代完成后的最可能失效点为抽样中心,采用重要抽样方法进一步推求结构失效概率。该方法是解决多峰值性质功能函数可靠度问题的有效方法。
5.将上述成果应用于实际的大型复杂结构进行结构可靠度计算,进一步验证了本文方法的先进性和可行性,为大型复杂结构的可靠度评估提供了参考。
China is at a golden opportunity to develop civil construction industry.With the rapid appearance of large-scale structures, complexity is higher and higher, uncertain factors are increasing, security problem following is more and more important. It is required that the new theory and analysis methods are proposed to face new challenges in the area of structure reliability assessment. The performance function of large-scale complex structures has many features, such as high computational cost, implicit expression, highly nonlinear and the traditional method is often difficult to solve it. Because GP model is good at dealing with high dimensions, small samples, nonlinear complexities problems and can obtain optimal super-parameter self-adaptively and forecast results of probability, this paper will focus on approximating the implicit performance function by GP model and combining traditional structure reliability analysis method to handle the issues of structure reliability assessment, which is based on dynamic updating of learning samples.
Four methods are proposed in this paper for reliability analysis which are based on GP model:GPC-based MCS, which combined the GPC with MCS simulation (MCS),GPR-based Breitung, which combined the GPR with Breitung method, GPR-based MCS,which combined the GPR with MCS simulation (MCS) and GPR-based PSO,which combined the GPR with Particle Swarm Optimization (PSO).Then, those methods are applied to large-scale structure existed, which provides a new choice to solve this problem quickly and accurately. In sum, the main works and results are listed as follows:
1. MCS-GPC. Based on markov chain sample generation mechanism and GPC model which is used to approximate the implicit performance function,GPC are combined with MCS to solve the issues of structure reliability assessement.In this method,fitting error is self-adaptively in the aspects of approximating the response surface,which provides a new choice to solve this problem quickly and accurately.
2. Breitung-.GPR. The small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the implicit performance and its derivatives were approximated by the GPR with explicit formulation. Then, an iterative algorithm is presented to reduce the errors of GPR response surface by information of design point in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, the classical Breitung method combined with GRP response surface was applied to calculate the structural reliability index. The results show that the proposed method has higher efficiency and higher accuracy compared to traditional response surface method. It can directly take advantage of existing engineering FEM code without modification.
3. MCS-GPR.The small number of training samples were created using FEM code for building the GPR response surface. The highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is predicted quickly using MCS Simulation without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, MCS method combined with GRP surface is applied to get the structure of failure probability. The proposed method has advantages of high efficiency and high precision compared to traditional response surface method.and thus it is very suitable for reliability analysis of large-scale complicated engineering structure.
4. PSO-GPR. The calculation of reliability index converted to optimization problem. Then, the small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is searched quickly using PSO without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Finally, Important simulation method (ISM) combined with GRP surface is applied to calculate the failure probability.It is a effective method to solve the issues of structure reliability assessment which involve multiple peak values function.
Finally,the methods above are applied to calculate the structural reliability index for large-scale complex structures. It show that a series of methods proposed in this paper are more accurate, efficient, scientific and feasible, which can be a good reference for large-scale complex structure reliability assessment.
本文的主要研究工作如下：
1.基于蒙特卡罗的高斯过程分类法研究。采用高斯过程分类模型来重构功能函数,基于马尔可夫链的样本生成机制,并将高精度的蒙特卡罗可靠度分析方法与分类性能优异的高斯过程分类模型相结合,在构建响应面拟合误差自适应修正机制的基础上,提出基于高斯过程分类-MCS动态响应面的结构可靠度分析方法,为含有隐式功能函数的复杂工程结构可靠度的高速求解提供一个新的选择。
2.基于Breitung法的高斯过程回归动态响应面法研究。该方法利用有限元分析程序构造少量训练样本,利用训练后的高斯过程回归模型构建响应面,实现小样本条件下功能函数及其偏导数的显式表达,通过构造合理的迭代方式,利用各迭代步的验算点信息不断修正响应面的拟合误差,动态提升响应面对失效概率贡献较大区域的重构精度,进而结合Breitung法快速推求结构的可靠度指标。与传统响应面法相比较,该方法具有较高的计算精度与计算效率,且易于与既有的有限元软件相结合。
3.基于蒙特卡罗的高斯过程回归动态响应面法研究。该方法利用有限元分析程序构造少量训练样本,据此利用高斯过程回归模型构建响应面,实现小样本条件下高度非线性隐式功能函数的高精度逼近与显式化,并采用蒙特卡罗随机抽样快速估计失效域中最可能失效点,通过迭代循环,利用最可能失效点信息不断修正响应面的拟合误差,从而动态提升响应面对失效概率贡献较大区域的重构精度,进而结合蒙特卡罗模拟快速推求结构失效概率。该方法简单易行,具有高效高精度的优点,适用于大型复杂工程结构的可靠度分析。
4.基于粒子群优化的高斯过程动态响应面法研究。该方法将可靠度求解问题转化为最优化问题,在采用有限元法生成少量样本的基础上,采用高斯过程回归模型构建功能函数的响应面,实现小样本条件下隐式非线性功能函数的显式表达,进而利用粒子群优化算法搜索的全局最可能失效点,并构造合理的迭代方式,利用各迭代步的最可能失效点信息动态提升响应面对失效概率贡献较大区域的重构精度。最后,以迭代完成后的最可能失效点为抽样中心,采用重要抽样方法进一步推求结构失效概率。该方法是解决多峰值性质功能函数可靠度问题的有效方法。
5.将上述成果应用于实际的大型复杂结构进行结构可靠度计算,进一步验证了本文方法的先进性和可行性,为大型复杂结构的可靠度评估提供了参考。
China is at a golden opportunity to develop civil construction industry.With the rapid appearance of large-scale structures, complexity is higher and higher, uncertain factors are increasing, security problem following is more and more important. It is required that the new theory and analysis methods are proposed to face new challenges in the area of structure reliability assessment. The performance function of large-scale complex structures has many features, such as high computational cost, implicit expression, highly nonlinear and the traditional method is often difficult to solve it. Because GP model is good at dealing with high dimensions, small samples, nonlinear complexities problems and can obtain optimal super-parameter self-adaptively and forecast results of probability, this paper will focus on approximating the implicit performance function by GP model and combining traditional structure reliability analysis method to handle the issues of structure reliability assessment, which is based on dynamic updating of learning samples.
Four methods are proposed in this paper for reliability analysis which are based on GP model:GPC-based MCS, which combined the GPC with MCS simulation (MCS),GPR-based Breitung, which combined the GPR with Breitung method, GPR-based MCS,which combined the GPR with MCS simulation (MCS) and GPR-based PSO,which combined the GPR with Particle Swarm Optimization (PSO).Then, those methods are applied to large-scale structure existed, which provides a new choice to solve this problem quickly and accurately. In sum, the main works and results are listed as follows:
1. MCS-GPC. Based on markov chain sample generation mechanism and GPC model which is used to approximate the implicit performance function,GPC are combined with MCS to solve the issues of structure reliability assessement.In this method,fitting error is self-adaptively in the aspects of approximating the response surface,which provides a new choice to solve this problem quickly and accurately.
2. Breitung-.GPR. The small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the implicit performance and its derivatives were approximated by the GPR with explicit formulation. Then, an iterative algorithm is presented to reduce the errors of GPR response surface by information of design point in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, the classical Breitung method combined with GRP response surface was applied to calculate the structural reliability index. The results show that the proposed method has higher efficiency and higher accuracy compared to traditional response surface method. It can directly take advantage of existing engineering FEM code without modification.
3. MCS-GPR.The small number of training samples were created using FEM code for building the GPR response surface. The highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is predicted quickly using MCS Simulation without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Then, MCS method combined with GRP surface is applied to get the structure of failure probability. The proposed method has advantages of high efficiency and high precision compared to traditional response surface method.and thus it is very suitable for reliability analysis of large-scale complicated engineering structure.
4. PSO-GPR. The calculation of reliability index converted to optimization problem. Then, the small number of training samples were created using Finite Element method (FEM) code for building the GPR response surface. Thus, the highly nonlinear and implicit performance function is approximated by GPR with explicit formulation under small sample condition. Then, the most probable point (MPP) is searched quickly using PSO without any extra FEM analysis. Furthermore, an iterative algorithm is presented to reduce the errors of GPR by using information of MPP in order to improve constantly the reconstructing precision at the important region, which contributes to the failure probability significantly. Finally, Important simulation method (ISM) combined with GRP surface is applied to calculate the failure probability.It is a effective method to solve the issues of structure reliability assessment which involve multiple peak values function.
Finally,the methods above are applied to calculate the structural reliability index for large-scale complex structures. It show that a series of methods proposed in this paper are more accurate, efficient, scientific and feasible, which can be a good reference for large-scale complex structure reliability assessment.
引文
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