基于響應(yīng)面的復(fù)雜黑箱模型優(yōu)化算法研究
發(fā)布時(shí)間：2018-08-12 18:38
【摘要】：當(dāng)今在對(duì)復(fù)雜機(jī)械系統(tǒng)進(jìn)行設(shè)計(jì)時(shí),往往需要建立系統(tǒng)的計(jì)算機(jī)仿真模型,并基于仿真分析模型對(duì)系統(tǒng)的相關(guān)參數(shù)進(jìn)行調(diào)整,使系統(tǒng)性能達(dá)到較優(yōu)的水平。這種基于計(jì)算機(jī)仿真模型的優(yōu)化設(shè)計(jì)屬于典型的仿真優(yōu)化問(wèn)題,其特點(diǎn)是優(yōu)化問(wèn)題的目標(biāo)和約束與設(shè)計(jì)變量的關(guān)系不能顯式的表述,在優(yōu)化迭代過(guò)程中目標(biāo)或約束每進(jìn)行一次估值均需要調(diào)用仿真模型執(zhí)行一次計(jì)算分析。這種計(jì)算仿真模型對(duì)于工程人員來(lái)說(shuō)就是一種黑箱模型。由于現(xiàn)代機(jī)械系統(tǒng)日趨復(fù)雜,計(jì)算機(jī)輔助分析模型的精度也越來(lái)越高,因此仿真模型所需的計(jì)算時(shí)間也越來(lái)越長(zhǎng)。盡管計(jì)算機(jī)的計(jì)算處理能力較之以前相比有了大幅的提升,但是在求解一些基于復(fù)雜、高保真度的仿真模型參數(shù)優(yōu)化問(wèn)題時(shí),整個(gè)優(yōu)化過(guò)程所需的時(shí)間過(guò)長(zhǎng)甚至于無(wú)法采用傳統(tǒng)優(yōu)化方法來(lái)實(shí)現(xiàn)。為了減少計(jì)算開(kāi)銷(xiāo),基于響應(yīng)面模型的優(yōu)化理論應(yīng)運(yùn)而生,并且在近20年來(lái)不斷得到發(fā)展和完善,已經(jīng)被工程人員廣泛的應(yīng)用于航空航天、車(chē)輛工程、化工、船舶海洋工程、機(jī)械工程、生物等諸多領(lǐng)域。該方法通過(guò)在優(yōu)化過(guò)程中建立原復(fù)雜黑箱模型的近似數(shù)學(xué)表達(dá),并合理的分配計(jì)算資源,最大限度的減少真實(shí)仿真分析(“昂貴估值”)的次數(shù),盡可能的利用近似數(shù)學(xué)模型代替仿真模型進(jìn)行求解計(jì)算(“廉價(jià)估值”),以減少整個(gè)優(yōu)化過(guò)程中的計(jì)算開(kāi)銷(xiāo)。響應(yīng)面模型是描述仿真模型輸入變量與輸出響應(yīng)間的近似函數(shù)關(guān)系,其構(gòu)造過(guò)程是先通過(guò)實(shí)驗(yàn)設(shè)計(jì)方法獲取一系列的數(shù)據(jù)采樣點(diǎn),再對(duì)采樣點(diǎn)進(jìn)行仿真計(jì)算得到對(duì)應(yīng)的輸出響應(yīng)值,從而建立輸入-輸出的函數(shù)關(guān)系。而基于響應(yīng)面的優(yōu)化則需要在現(xiàn)有響應(yīng)面模型的基礎(chǔ)上,均衡未知區(qū)域的空間探索與響應(yīng)面模型最優(yōu)值區(qū)域的分析采樣,并合理的分配計(jì)算開(kāi)銷(xiāo)以確定搜索過(guò)程中的迭代點(diǎn)。整個(gè)過(guò)程涉及到實(shí)驗(yàn)設(shè)計(jì)理論,響應(yīng)面方法以及全局優(yōu)化方法等多個(gè)方面。本文針對(duì)復(fù)雜黑箱模型優(yōu)化問(wèn)題,采用響應(yīng)面方法對(duì)無(wú)約束優(yōu)化問(wèn)題、約束優(yōu)化問(wèn)題、混合整數(shù)優(yōu)化問(wèn)題以及多目標(biāo)優(yōu)化問(wèn)題進(jìn)行了一系列研究探索,主要研究?jī)?nèi)容可概括為以下幾點(diǎn)：(1)分析了目前常用的幾種響應(yīng)面模型的特點(diǎn)及其適用處理的問(wèn)題,針對(duì)目前大多數(shù)響應(yīng)面模型優(yōu)化方法均是基于單一一種響應(yīng)面模型的現(xiàn)狀,提出了AMGO(Adaptive Metamodel-based Global Optimization)算法,在優(yōu)化過(guò)程中采用混合響應(yīng)面模型對(duì)仿真模型進(jìn)行近似擬合,以結(jié)合多個(gè)響應(yīng)面模型的特點(diǎn),增強(qiáng)混合模型的適用性和穩(wěn)定性。在該算法中,考慮到搜索迭代時(shí)不僅僅要對(duì)當(dāng)前響應(yīng)面模型最優(yōu)值附近區(qū)域進(jìn)行采樣分析,而且要進(jìn)一步探索當(dāng)今尚未探索的區(qū)域,提出了一種新的迭代點(diǎn)選擇策略,其能夠一定程度的均衡算法的局部搜索與全局探索能力。論文通過(guò)數(shù)值實(shí)驗(yàn)將AMGO算法與現(xiàn)有的三種具有代表性的響應(yīng)面優(yōu)化方法進(jìn)行比較,驗(yàn)證了本算法的有效性,而后將其應(yīng)用于內(nèi)嚙合轉(zhuǎn)子泵的優(yōu)化設(shè)計(jì)問(wèn)題中,有效的提升了該轉(zhuǎn)子泵的流量特性。(2)針對(duì)帶復(fù)雜約束的黑箱函數(shù)優(yōu)化問(wèn)題,提出了基于響應(yīng)面模型的約束優(yōu)化方法。該方法對(duì)黑箱目標(biāo)函數(shù)和每個(gè)黑箱約束函數(shù)均建立其近似響應(yīng)面模型,而不是簡(jiǎn)單地采用懲罰函數(shù)法來(lái)處理,避免了罰因子選擇不當(dāng)以及近似罰函數(shù)劇烈波動(dòng)的數(shù)值特性對(duì)響應(yīng)面優(yōu)化算法搜索迭代造成的不良影響。算法具體分為兩個(gè)階段：第一個(gè)階段是在初始采樣點(diǎn)均不可行時(shí)利用現(xiàn)有數(shù)據(jù)信息搜索一個(gè)初始可行解：第二階段是在已有初始可行點(diǎn)的基礎(chǔ)上搜尋更優(yōu)的設(shè)計(jì)點(diǎn)。該算法并且不要求設(shè)計(jì)人員在算法初始時(shí)提供可行初始點(diǎn),并利用目標(biāo)與約束函數(shù)響應(yīng)面模型的梯度信息對(duì)搜索過(guò)程中違反約束程度較小的迭代點(diǎn)進(jìn)行近似約束矯正,以期望在較小的計(jì)算開(kāi)銷(xiāo)下獲取更多的可行點(diǎn)。(3)分析了基于響應(yīng)面的優(yōu)化方法在求解基于仿真模型的混合整數(shù)優(yōu)化問(wèn)題時(shí)的優(yōu)勢(shì),并將細(xì)分矩形算法擴(kuò)展且與響應(yīng)面優(yōu)化方法結(jié)合提出了METADIR算法(METAmodel and DIRect method).在搜索迭代時(shí),METADIR算法首先利用細(xì)分矩形方法對(duì)設(shè)計(jì)空間不斷的細(xì)分,并識(shí)別潛在的最優(yōu)子空間,通過(guò)區(qū)域采樣點(diǎn)密度函數(shù)分析當(dāng)今最優(yōu)子區(qū)域內(nèi)的數(shù)據(jù)點(diǎn)聚集程度。當(dāng)密度達(dá)到一定閥值,則終止設(shè)計(jì)域的細(xì)分進(jìn)程,并在當(dāng)前最優(yōu)子區(qū)域內(nèi)建立局部響應(yīng)面模型,再利用響應(yīng)面優(yōu)化方法求得對(duì)原混合整數(shù)優(yōu)化問(wèn)題的近似最優(yōu)解。(4)在詳細(xì)分析討論Kriging模型對(duì)未采樣點(diǎn)預(yù)測(cè)誤差及不確定性估計(jì)的基礎(chǔ)上,將Kriging響應(yīng)面模型與粒子群算法結(jié)合以解決多目標(biāo)黑箱函數(shù)優(yōu)化問(wèn)題。多目標(biāo)粒子群算法由于其較好的魯棒性,簡(jiǎn)單的算法流程以及無(wú)需對(duì)多目標(biāo)問(wèn)題的預(yù)先假設(shè)信息使得其受到許多設(shè)計(jì)人員的青睞。但是由于粒子群算法迭代過(guò)程中所需的仿真次數(shù)過(guò)多,容易陷入局部最優(yōu),限制了其在仿真優(yōu)化問(wèn)題中的應(yīng)用。本文在多目標(biāo)粒子群的迭代過(guò)程中,利用已有粒子的分析數(shù)據(jù),構(gòu)建Kriging響應(yīng)面集以近似擬合原仿真模型與設(shè)計(jì)變量間的函數(shù),然后通過(guò)求解基于近似模型的多目標(biāo)問(wèn)題,利用其非支配解指導(dǎo)粒子種群的更新,以提升算法的全局搜索能力。同時(shí),基于Kriging模型的預(yù)測(cè)能力提出了廣義的期望改善以判斷哪些粒子需要進(jìn)行昂貴估值,剩余的粒子可以通過(guò)響應(yīng)面估值,以便大幅減少算法的仿真計(jì)算開(kāi)銷(xiāo)。(5)基于多學(xué)科優(yōu)化平臺(tái)MDesigner,采用Matlab引擎技術(shù)和mex應(yīng)用程序接口實(shí)現(xiàn)MDesigner與Matlab的集成,為多學(xué)科優(yōu)化設(shè)計(jì)提供基礎(chǔ)。本文基于Matlab引擎技術(shù)和mex應(yīng)用程序接口,使得MDesigner平臺(tái)可以直接調(diào)用Matlab環(huán)境下的響應(yīng)面優(yōu)化算法。最后通過(guò)對(duì)齒輪箱的優(yōu)化設(shè)計(jì)展示了在MDesigner平臺(tái)下實(shí)現(xiàn)響應(yīng)面優(yōu)化的整個(gè)流程,有效的展示了方法的有效性和平臺(tái)的廣泛應(yīng)用性。最后,對(duì)本文的研究進(jìn)行了總結(jié),并對(duì)下一步工作和研究進(jìn)行展望,探討了未來(lái)基于響應(yīng)面優(yōu)化方法的研究熱點(diǎn)和趨勢(shì)。
[Abstract]:Nowadays, when designing complex mechanical systems, it is often necessary to establish a computer simulation model of the system and adjust the relevant parameters of the system based on the simulation analysis model so as to achieve a better performance level. The relationship between the objective and constraints of the problem and the design variables can not be expressed explicitly. In the process of optimization iteration, the objective or constraints need to call the simulation model to perform a computational analysis for each evaluation. This computational simulation model is a black box model for engineers. The accuracy of the auxiliary analysis model is higher and higher, so the computational time of the simulation model is longer and longer. Although the computational capacity of the computer has been greatly improved compared with the previous, the whole optimization process takes too long to solve some complex and high fidelity simulation model parameters optimization problems. In order to reduce the computational cost, the optimization theory based on response surface model (RSM) emerged and has been developed and perfected in the past 20 years. It has been widely used by engineers in aerospace, vehicle engineering, chemical engineering, marine engineering, mechanical engineering, biology and many other fields. Methods By establishing the approximate mathematical expression of the original complex black box model in the optimization process and allocating computing resources reasonably, the number of real simulation analysis ("expensive valuation") is minimized, and the approximate mathematical model is used instead of the simulation model as much as possible to solve the calculation ("cheap valuation") in order to reduce the whole optimization process. Response surface model describes the approximate functional relationship between input variables and output responses of the simulation model. The construction process is to obtain a series of data sampling points through experimental design method, and then to simulate the sampling points to get the corresponding output response values, thus establishing the input-output functional relationship. On the basis of the existing response surface model, the optimization of response surface needs to balance the spatial exploration of the unknown area with the analysis and sampling of the optimal value area of the response surface model, and allocate the computational cost reasonably to determine the iterative point in the search process. In this paper, a series of research and exploration are carried out on unconstrained optimization, constrained optimization, mixed integer optimization and multi-objective optimization problems. The main research contents can be summarized as follows: (1) Several commonly used response surface models are analyzed. Aiming at the current situation that most of the response surface model optimization methods are based on a single response surface model, the AMGO (Adaptive Metamodel-based Global Optimization) algorithm is proposed. In the optimization process, the hybrid response surface model is used to approximate the simulation model to combine multiple responses. In this algorithm, considering that the search iteration not only needs to sample and analyze the region near the optimal value of the current response surface model, but also needs to explore the region which has not been explored yet, a new iterative point selection strategy is proposed, which can be used to a certain extent. This paper compares the AMGO algorithm with three representative response surface optimization methods to verify the validity of the proposed algorithm, and then applies it to the optimization design of the internal meshing rotor pump, which effectively improves the flow characteristics of the rotor pump. (2) To solve the problem of black box function optimization with complex constraints, a constrained optimization method based on response surface model (RSM) is proposed. This method establishes an approximate response surface model for both the black box objective function and each black box constraint function, instead of simply using penalty function method to deal with the problem, avoiding improper selection of penalty factors and severe approximate penalty function. The algorithm is divided into two stages: the first stage is to search an initial feasible solution by using the existing data information when the initial sampling point is not feasible; the second stage is to search for a better design point on the basis of the existing initial feasible point. The algorithm does not require the designer to provide feasible initial points at the beginning of the algorithm, and uses the gradient information of the objective and constraint function response surface model to approximate the constraint correction of iteration points which violate less constraint degree in the search process, in order to obtain more feasible points with less computational cost. (3) The response surface based method is analyzed. The advantages of the optimization method in solving mixed integer optimization problems based on simulation models are discussed. The subdivision rectangle algorithm is extended and combined with the response surface optimization (RSO) method, METADIR algorithm (METAmodel and DIRect method) is proposed. Potential optimal subspace is used to analyze the aggregation degree of data points in the optimal subspace. When the density reaches a certain threshold, the subdivision process of the design domain is terminated, and a local response surface model is established in the current optimal subspace. Then the original mixed integer optimization problem is solved by the response surface optimization method. (4) Based on the detailed analysis and discussion of Kriging model, Kriging response surface model is combined with particle swarm optimization to solve the problem of multi-objective black box function optimization. The presupposition information of multi-objective problem makes it popular among many designers. However, the number of simulations required in the iteration process of particle swarm optimization is too many to fall into local optimum, which limits its application in simulation optimization problems. The Kriging response surface set is constructed to approximate the function between the original simulation model and the design variables. Then, by solving the multi-objective problem based on the approximate model and using its non-dominated solution to guide the updating of the particle population, the global searching ability of the algorithm is improved. Determine which particles need expensive valuation, and the remaining particles can be estimated by response surface method, so as to greatly reduce the computational cost of the algorithm. (5) Based on MDesigner, the integration of MDesigner and MATLAB is realized by using MATLAB engine technology and mex application program interface. Based on the technology of MATLAB engine and mex application program interface, the MDesigner platform can directly invoke the response surface optimization algorithm under the environment of MATLAB. Finally, through the optimization design of gearbox, the whole process of response surface optimization under the MDesigner platform is demonstrated, which effectively demonstrates the effectiveness of the method and the wide application of the platform. Finally, the research of this paper is summarized, and the future work and research are prospected, and the future research hotspots and trends based on response surface optimization method are discussed.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TP18
本文編號(hào)：2179947
[Abstract]:Nowadays, when designing complex mechanical systems, it is often necessary to establish a computer simulation model of the system and adjust the relevant parameters of the system based on the simulation analysis model so as to achieve a better performance level. The relationship between the objective and constraints of the problem and the design variables can not be expressed explicitly. In the process of optimization iteration, the objective or constraints need to call the simulation model to perform a computational analysis for each evaluation. This computational simulation model is a black box model for engineers. The accuracy of the auxiliary analysis model is higher and higher, so the computational time of the simulation model is longer and longer. Although the computational capacity of the computer has been greatly improved compared with the previous, the whole optimization process takes too long to solve some complex and high fidelity simulation model parameters optimization problems. In order to reduce the computational cost, the optimization theory based on response surface model (RSM) emerged and has been developed and perfected in the past 20 years. It has been widely used by engineers in aerospace, vehicle engineering, chemical engineering, marine engineering, mechanical engineering, biology and many other fields. Methods By establishing the approximate mathematical expression of the original complex black box model in the optimization process and allocating computing resources reasonably, the number of real simulation analysis ("expensive valuation") is minimized, and the approximate mathematical model is used instead of the simulation model as much as possible to solve the calculation ("cheap valuation") in order to reduce the whole optimization process. Response surface model describes the approximate functional relationship between input variables and output responses of the simulation model. The construction process is to obtain a series of data sampling points through experimental design method, and then to simulate the sampling points to get the corresponding output response values, thus establishing the input-output functional relationship. On the basis of the existing response surface model, the optimization of response surface needs to balance the spatial exploration of the unknown area with the analysis and sampling of the optimal value area of the response surface model, and allocate the computational cost reasonably to determine the iterative point in the search process. In this paper, a series of research and exploration are carried out on unconstrained optimization, constrained optimization, mixed integer optimization and multi-objective optimization problems. The main research contents can be summarized as follows: (1) Several commonly used response surface models are analyzed. Aiming at the current situation that most of the response surface model optimization methods are based on a single response surface model, the AMGO (Adaptive Metamodel-based Global Optimization) algorithm is proposed. In the optimization process, the hybrid response surface model is used to approximate the simulation model to combine multiple responses. In this algorithm, considering that the search iteration not only needs to sample and analyze the region near the optimal value of the current response surface model, but also needs to explore the region which has not been explored yet, a new iterative point selection strategy is proposed, which can be used to a certain extent. This paper compares the AMGO algorithm with three representative response surface optimization methods to verify the validity of the proposed algorithm, and then applies it to the optimization design of the internal meshing rotor pump, which effectively improves the flow characteristics of the rotor pump. (2) To solve the problem of black box function optimization with complex constraints, a constrained optimization method based on response surface model (RSM) is proposed. This method establishes an approximate response surface model for both the black box objective function and each black box constraint function, instead of simply using penalty function method to deal with the problem, avoiding improper selection of penalty factors and severe approximate penalty function. The algorithm is divided into two stages: the first stage is to search an initial feasible solution by using the existing data information when the initial sampling point is not feasible; the second stage is to search for a better design point on the basis of the existing initial feasible point. The algorithm does not require the designer to provide feasible initial points at the beginning of the algorithm, and uses the gradient information of the objective and constraint function response surface model to approximate the constraint correction of iteration points which violate less constraint degree in the search process, in order to obtain more feasible points with less computational cost. (3) The response surface based method is analyzed. The advantages of the optimization method in solving mixed integer optimization problems based on simulation models are discussed. The subdivision rectangle algorithm is extended and combined with the response surface optimization (RSO) method, METADIR algorithm (METAmodel and DIRect method) is proposed. Potential optimal subspace is used to analyze the aggregation degree of data points in the optimal subspace. When the density reaches a certain threshold, the subdivision process of the design domain is terminated, and a local response surface model is established in the current optimal subspace. Then the original mixed integer optimization problem is solved by the response surface optimization method. (4) Based on the detailed analysis and discussion of Kriging model, Kriging response surface model is combined with particle swarm optimization to solve the problem of multi-objective black box function optimization. The presupposition information of multi-objective problem makes it popular among many designers. However, the number of simulations required in the iteration process of particle swarm optimization is too many to fall into local optimum, which limits its application in simulation optimization problems. The Kriging response surface set is constructed to approximate the function between the original simulation model and the design variables. Then, by solving the multi-objective problem based on the approximate model and using its non-dominated solution to guide the updating of the particle population, the global searching ability of the algorithm is improved. Determine which particles need expensive valuation, and the remaining particles can be estimated by response surface method, so as to greatly reduce the computational cost of the algorithm. (5) Based on MDesigner, the integration of MDesigner and MATLAB is realized by using MATLAB engine technology and mex application program interface. Based on the technology of MATLAB engine and mex application program interface, the MDesigner platform can directly invoke the response surface optimization algorithm under the environment of MATLAB. Finally, through the optimization design of gearbox, the whole process of response surface optimization under the MDesigner platform is demonstrated, which effectively demonstrates the effectiveness of the method and the wide application of the platform. Finally, the research of this paper is summarized, and the future work and research are prospected, and the future research hotspots and trends based on response surface optimization method are discussed.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：TP18
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