基于响应面的复杂黑箱模型优化算法研究

发布时间：2018-08-12 18:38

【摘要】：当今在对复杂机械系统进行设计时,往往需要建立系统的计算机仿真模型,并基于仿真分析模型对系统的相关参数进行调整,使系统性能达到较优的水平。这种基于计算机仿真模型的优化设计属于典型的仿真优化问题,其特点是优化问题的目标和约束与设计变量的关系不能显式的表述,在优化迭代过程中目标或约束每进行一次估值均需要调用仿真模型执行一次计算分析。这种计算仿真模型对于工程人员来说就是一种黑箱模型。由于现代机械系统日趋复杂,计算机辅助分析模型的精度也越来越高,因此仿真模型所需的计算时间也越来越长。尽管计算机的计算处理能力较之以前相比有了大幅的提升,但是在求解一些基于复杂、高保真度的仿真模型参数优化问题时,整个优化过程所需的时间过长甚至于无法采用传统优化方法来实现。为了减少计算开销,基于响应面模型的优化理论应运而生,并且在近20年来不断得到发展和完善,已经被工程人员广泛的应用于航空航天、车辆工程、化工、船舶海洋工程、机械工程、生物等诸多领域。该方法通过在优化过程中建立原复杂黑箱模型的近似数学表达,并合理的分配计算资源,最大限度的减少真实仿真分析(“昂贵估值”)的次数,尽可能的利用近似数学模型代替仿真模型进行求解计算(“廉价估值”),以减少整个优化过程中的计算开销。响应面模型是描述仿真模型输入变量与输出响应间的近似函数关系,其构造过程是先通过实验设计方法获取一系列的数据采样点,再对采样点进行仿真计算得到对应的输出响应值,从而建立输入-输出的函数关系。而基于响应面的优化则需要在现有响应面模型的基础上,均衡未知区域的空间探索与响应面模型最优值区域的分析采样,并合理的分配计算开销以确定搜索过程中的迭代点。整个过程涉及到实验设计理论,响应面方法以及全局优化方法等多个方面。本文针对复杂黑箱模型优化问题,采用响应面方法对无约束优化问题、约束优化问题、混合整数优化问题以及多目标优化问题进行了一系列研究探索,主要研究内容可概括为以下几点：(1)分析了目前常用的几种响应面模型的特点及其适用处理的问题,针对目前大多数响应面模型优化方法均是基于单一一种响应面模型的现状,提出了AMGO(Adaptive Metamodel-based Global Optimization)算法,在优化过程中采用混合响应面模型对仿真模型进行近似拟合,以结合多个响应面模型的特点,增强混合模型的适用性和稳定性。在该算法中,考虑到搜索迭代时不仅仅要对当前响应面模型最优值附近区域进行采样分析,而且要进一步探索当今尚未探索的区域,提出了一种新的迭代点选择策略,其能够一定程度的均衡算法的局部搜索与全局探索能力。论文通过数值实验将AMGO算法与现有的三种具有代表性的响应面优化方法进行比较,验证了本算法的有效性,而后将其应用于内啮合转子泵的优化设计问题中,有效的提升了该转子泵的流量特性。(2)针对带复杂约束的黑箱函数优化问题,提出了基于响应面模型的约束优化方法。该方法对黑箱目标函数和每个黑箱约束函数均建立其近似响应面模型,而不是简单地采用惩罚函数法来处理,避免了罚因子选择不当以及近似罚函数剧烈波动的数值特性对响应面优化算法搜索迭代造成的不良影响。算法具体分为两个阶段：第一个阶段是在初始采样点均不可行时利用现有数据信息搜索一个初始可行解：第二阶段是在已有初始可行点的基础上搜寻更优的设计点。该算法并且不要求设计人员在算法初始时提供可行初始点,并利用目标与约束函数响应面模型的梯度信息对搜索过程中违反约束程度较小的迭代点进行近似约束矫正,以期望在较小的计算开销下获取更多的可行点。(3)分析了基于响应面的优化方法在求解基于仿真模型的混合整数优化问题时的优势,并将细分矩形算法扩展且与响应面优化方法结合提出了METADIR算法(METAmodel and DIRect method).在搜索迭代时,METADIR算法首先利用细分矩形方法对设计空间不断的细分,并识别潜在的最优子空间,通过区域采样点密度函数分析当今最优子区域内的数据点聚集程度。当密度达到一定阀值,则终止设计域的细分进程,并在当前最优子区域内建立局部响应面模型,再利用响应面优化方法求得对原混合整数优化问题的近似最优解。(4)在详细分析讨论Kriging模型对未采样点预测误差及不确定性估计的基础上,将Kriging响应面模型与粒子群算法结合以解决多目标黑箱函数优化问题。多目标粒子群算法由于其较好的鲁棒性,简单的算法流程以及无需对多目标问题的预先假设信息使得其受到许多设计人员的青睐。但是由于粒子群算法迭代过程中所需的仿真次数过多,容易陷入局部最优,限制了其在仿真优化问题中的应用。本文在多目标粒子群的迭代过程中,利用已有粒子的分析数据,构建Kriging响应面集以近似拟合原仿真模型与设计变量间的函数,然后通过求解基于近似模型的多目标问题,利用其非支配解指导粒子种群的更新,以提升算法的全局搜索能力。同时,基于Kriging模型的预测能力提出了广义的期望改善以判断哪些粒子需要进行昂贵估值,剩余的粒子可以通过响应面估值,以便大幅减少算法的仿真计算开销。(5)基于多学科优化平台MDesigner,采用Matlab引擎技术和mex应用程序接口实现MDesigner与Matlab的集成,为多学科优化设计提供基础。本文基于Matlab引擎技术和mex应用程序接口,使得MDesigner平台可以直接调用Matlab环境下的响应面优化算法。最后通过对齿轮箱的优化设计展示了在MDesigner平台下实现响应面优化的整个流程,有效的展示了方法的有效性和平台的广泛应用性。最后,对本文的研究进行了总结,并对下一步工作和研究进行展望,探讨了未来基于响应面优化方法的研究热点和趋势。
[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.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP18

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