本文選題：Kriging模型　切入點：增量構造方法　出處：《華中科技大學》2015年博士論文　論文類型：學位論文

【摘要】：在科學技術不斷發(fā)展的今天,為了應對越來越復雜的工程設計優(yōu)化問題,出現(xiàn)了各種不同的設計策略和研究方法�；陧憫婺Ｐ偷娜纸婆c仿真優(yōu)化方法是目前工程設計領域的焦點之一。這類方法主要利用計算機試驗設計、響應面構造以及響應面給出的有效信息來實現(xiàn)模型的全局近似和最優(yōu)解的獲珥取,特別適合求解需要“昂貴”估值的“黑箱”函數(shù)或計算機仿真模型的近似優(yōu)化問題。作為一種高精度插值響應面模型,Kriging模型是目前應用較為廣‘泛的響應面模型之一,它能夠靈活地代替多峰或非線性函數(shù)進行“最優(yōu)參數(shù)”估計和近似模型的精度評價。在優(yōu)化過程中,來自于Kriging模型的函數(shù)估值和估計方差等信息能夠有效地指導優(yōu)化搜索朝著全局的方向進行。因此,基于Kriging模型的全局近似和優(yōu)化方法已被融入到方案設計、結構優(yōu)化、大數(shù)據(jù)統(tǒng)計分析以及多學科設計優(yōu)化過程中,并廣泛應用于航空航天、機械工程、車輛工程、地質(zhì)工程等諸多領域。鑒于此,進一步研究基于Kriging模型的全局近似和優(yōu)化方法具有一定的理論意義和應用價值。 針對確定性的“黑箱”函數(shù)或仿真模型,本文基于Kriging模型研究全局近似和優(yōu)化方法,包括：Kriging模型的增量構造以及全局近似方法：基于正則對偶變換和信任域策略的高效無約束優(yōu)化方法：并行多采樣點的無約束全局優(yōu)化方法：存在不可行采樣點的約束全局優(yōu)化方法。這些方法拓展和完善了基于響應面的全局近似和優(yōu)化體系,為具有昂貴估值的優(yōu)化問題提供了有效的解決方法。本文的研究成果主要體現(xiàn)在如下幾個方面： (1)深入分析了標準Kriging模型的結構和參數(shù),提出了Kriging模型的增量構造方法。該方法能夠在損失很少精度的前提下,大幅度地提高建模效率。為基于序列采樣的全局近似方法提供了理論依據(jù)。 (2)依據(jù)增量Kriging方法,提出了一種以提高建模效率為目的、在序列優(yōu)化過程中實現(xiàn)模型全局近似的方法。在確保Kriging模型的穩(wěn)定性和有效性的前提下對一次增加一個采樣點的序列增量構造進行了研究,利用最大化估計方差的方法來尋優(yōu)下一個采樣點,以六西格瑪更新準則為判斷標準,決定使用計算機試驗設計與分析(DACE-Design and Analysis of Computer Experiments)建模或增量Kriging建模。 (3)結合正則對偶/三對偶理論和基于響應面的信任域策略,提出了一種基于Kriging模型的全局優(yōu)化方法。其中,正則對偶變換能將非凸的Krging模型優(yōu)化問題轉化為凸優(yōu)化問題,而三對偶原理證明了對偶變換后問題中的所有極值點與原問題所有極值點之間的映射關系,并確保在對偶變量大于0的條件下能夠直接獲取問題的全局最優(yōu)點。該方法結合Kriging模型和信任域策略的特點,根據(jù)迭代過程中的最優(yōu)解信息自動調(diào)用區(qū)間縮減方法來搜索更優(yōu)的迭代點,有效地改善了復雜無約束問題的收斂效率和精度。 (4)研究了一種基于Kriging模型的多采樣點并行序列全局優(yōu)化算法。該算法利用中點距離最小舍棄方法處理樣本中的所有中點,根據(jù)目標和方差的近似估計來獲取多個新采樣點;基于廣義EGO (Efficient Global Optimization)方法,利用改進的廣義期望改善(GEI-Generalized Expected Improvement)作為填充采樣準則(ISC-Infill Sampling Criterion)對新采樣點進行并行優(yōu)化。該算法有效地減少了函數(shù)的估值次數(shù),較好地平衡局部搜索與全局搜索,大大提高了優(yōu)化效率。 (5)提出了一種基于Kriging模型的約束全局優(yōu)化方法。在初始試驗設計不存在可行采樣點且目標函數(shù)和約束函數(shù)都是“黑箱”函數(shù)的情況下,該算法通過最大化“滿足所有約束的概率”來獲取可行采樣點；利用目標估計的下限和均方根誤差估計的上限建立填充采樣準則,通過最小化填充采樣準則,確保能夠以盡可能少的函數(shù)估值次數(shù)得到一個可行的全局近似最優(yōu)解。此外,針對尋優(yōu)過程中連續(xù)出現(xiàn)多個不可行采樣點的情況,利用近似約束校正方法將處于可行邊界的采樣點拉回到實際的可行域內(nèi)。 (6)基于多學科優(yōu)化平臺FlowComputer,利用開源優(yōu)化工具包DAKOTA,開發(fā)了基于響應面組件的仿真優(yōu)化模塊,實現(xiàn)了經(jīng)典的EGO及本文中所提出的近似優(yōu)化算法。最后,通過一個重型汽車燃油經(jīng)濟性的仿真優(yōu)化問題來驗證本文方法的有效性。
[Abstract]:In the continuous development of science and technology today, in order to cope with the increasingly complex optimization problems in engineering design, presents the design strategy and research various methods. The approximate optimization method and simulation is one of the focuses in the field of global engineering design based on response surface model. This kind of method by means of computer experimental design, response surface structure and effective the information given by response surface model to achieve global optimal solution by Joel and approximation, especially suitable for solving the needs of "expensive" valuation of the "black box" function or a computer simulation model of the approximate optimization problem. As a kind of high precision interpolation response surface model, the Kriging model is more widely the response surface model one of the applications, it can replace the multi peak function or nonlinear optimal parameter estimation and approximation accuracy evaluation. In the optimization process. The function of valuation and estimation of variance information from Kriging model can effectively guide the search toward the global direction. Therefore, optimizing the structure of global Kriging model approximation and optimization methods have been integrated into the design, based on the statistical analysis of large data and multidisciplinary design optimization process, and is widely used in aviation aerospace, mechanical engineering, vehicle engineering, geological engineering and other fields. In view of this, further study on global Kriging model approximation and optimization method has certain theoretical significance and application value based.
According to the uncertainty of the "black box" function or simulation model, this paper studies the global Kriging model and approximate optimization method based on Kriging model including incremental construction and global approximation method: canonical dual transformation and trust region strategy, unconstrained optimization method based on unconstrained global optimization method for parallel multi sampling points: there is no feasible sampling the constrained global optimization method. These methods to expand and improve the response surface approximation and global optimization based system provides an effective solution to the optimization problem with expensive valuation. The research results of this paper are mainly embodied in the following aspects:
(1) in-depth analysis of the structure and parameters of the standard Kriging model. The incremental construction method of Kriging model is proposed. This method can greatly improve the modeling efficiency under the premise of little loss accuracy, which provides a theoretical basis for the global approximation method based on sequential sampling.
(2) based on the incremental Kriging method, put forward a kind of in order to improve the efficiency of modeling methods, implementation model of global approximation in the sequence optimization process. In the premise of ensuring the stability of the Kriging model and the effectiveness of the time for a sampling point sequence of incremental construction were studied, using the maximum estimate the variance method to optimize the next sampling point, with six sigma criteria for judgment standard, decided to use the design and analysis of computer experiments (DACE-Design and Analysis of Computer Experiments) modeling or incremental Kriging modeling.
(3 / three) combined with the canonical dual duality theory and the response surface based trust region strategy, this paper presents a global optimization method based on Kriging model. The canonical dual transformation can be non convex Krging model optimization problem into a convex optimization problem, and proves that the three principle of duality mapping between all extreme points of dual transformation after the problems in the original problem and all extreme points, and to ensure that global direct access to the problem of more than 0 conditions in the dual variables of the most advantages. This method combines the characteristics of Kriging model and trust region strategy, according to the optimal solution of the iterative process of information automatic call interval reduction method to search the iteration point better and effectively improve the complexity of the unconstrained problem of convergence efficiency and accuracy.
(4) on a Kriging model of multi sample parallel global optimization algorithm based on sequence. The algorithm uses minimum distance method to handle all abandon the midpoint in the sample according to the approximate midpoint, estimation of target and variance to obtain multiple sampling points; based on the generalized EGO (Efficient Global Optimization) method, using generalized expectation improvement the improved (GEI-Generalized Expected Improvement) as the filling sampling criteria (ISC-Infill Sampling Criterion) of the new sampling points for parallel optimization. This algorithm can reduce the number of times the valuation function, better balance between global search and local search, improves the efficiency of optimization.
(5) proposed a global optimization method based on Kriging model. In the initial design there is no feasible sampling points and the objective function and constraint function are the "black box" function, the algorithm to obtain the feasible sampling points by maximizing the "probability" of all constraints by using the lower bound estimation of the target; and the root mean square error estimation of the upper bound of a packed sampling criterion, by minimizing the sampling criteria to ensure the filling, function evaluation times as little as possible to obtain a feasible global optimal solution. In addition, for a number of feasible sampling points of consecutive optimization process, using the correction method of approximate constraint will be feasible in the the boundary of the feasible domain sampling point back to the actual.
(6) multidisciplinary design optimization platform based on FlowComputer, using open-source DAKOTA toolkit to develop the simulation optimization, response surface optimization module based on component, realizes the approximate optimization algorithm proposed by EGO and the classic in. Finally, through a heavy vehicle fuel economy simulation optimization problem to verify the validity of this method.

【學位授予單位】：華中科技大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：U462.34;TB21

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