摘要
基于工程发展的客观现实需求,以及异于传统优化设计理论和方法的突出优点,近年来,鲁棒优化设计理论和方法在自然科学、工程技术、经济管理等各个领域得到了广泛的发展和应用,无论在鲁棒优化方法和理论体系的构建,还是在实际工程问题的求解算法研究等方面,都取得了长足的进步。但总体来说,与其他学科或专业比较,电磁场逆问题鲁棒优化设计的研究成果还很不成熟和完善,电磁场逆问题鲁棒优化理论和算法研究仍处于起步阶段。其中主要问题之一就是现有研究成果都是以牺牲算法的计算效率为代价换取鲁棒性能参数的分析和计算。考虑到电磁场逆问题的求解需要反复进行电磁场正问题的数值分析和计算,应用现有成果进行电磁场逆问题鲁棒优化设计研究,对于计算机的资源要求来说无疑是雪上加霜。所以如何提高计算效率是电磁场逆问题鲁棒优化设计理论和算法研究必须解决的“瓶颈”问题。
在综合国内外研究成果的基础上,本文对进化类鲁棒优化算法进行了系统分析和深入研究。针对电磁场逆问题的特点,重点解决鲁棒性能参数计算依赖巨大计算资源这一瓶颈问题。同时,为保证算法的全局寻优能力,对算法的结构和参数赋值机制等问题亦进行了相应的改进研究,以期在提高算法的计算效率的同时,也能够保证算法最终解的质量。此外,还探讨了电磁场逆问题鲁棒优化设计的若干关键技术问题。
首先,提出了一种电磁场逆问题粒子群鲁棒优化算法。根据鲁棒优化问题的特点,重新定义了粒子邻域、提出了一种有效的期望适值赋值机制、新点的产生规则,以及基于距离的期望适值计算式。此外,为适应电磁场逆问题鲁棒优化分析计算的需求,对算法的结构和参数进行了改进研究。主要工作包括速度和位置矢量更新算法、年龄变量的引入、越界控制等。
其次,将一种新的基于概率模型的进化算法——交叉熵算法,成功推广应用于电磁场逆问题的鲁棒优化设计。为此,提出了一种平滑参数的自适应调节算法、引入简单而有效的变异操作、基于交叉熵算法固有特点的设计的鲁棒参数赋值新机制、保证约束条件成立的可行性概率模型,以及算法终止的新规则。
再次,对电磁场逆问题鲁棒优化设计的若干关键技术问题进行了研究。(1)基于机器学习领域最新的研究成果：支持向量机,提出了一种新的表面响应模型,并将其与进化算法结合,提出了一种鲁棒优化设计的快速求解策略；(2)通过将多项式混沌展开作为典型随机扰动的随机响应面模型,提出了一种鲁棒性能参数的快速计算方法,并将其与进化算法结合,提出了电磁场逆问题鲁棒优化的另一种快速优化策略；(3)基于交替使用不同性能参数评价中间解的新思路,提出了一种同时求解鲁棒最优解和全局最优解的求解方法。
最后,为验证和说明理论成果的正确性,对系列工程电磁场逆问题进行了实例分析和计算。首先,以倒S形天线的鲁棒优化设计、模型天线制作以及天线性能测试结果的分析等工程实例来证明理论成果的正确性、可靠性和优越性。然后,应用天线阵鲁棒优化设计和标准TEAM (Testing of Electromagnetic Analysis Method) Workshop Problem基准算例等工程电磁场逆问题对本文提出的鲁棒优化算法和技术进行了全面的分析和验证。
Synchronizing with the ever-increasing demand on high quality products to function in variable operating conditions and environments, the study of robust design methodologies and techniques has become a new topical area in design optimizations in nearly all engineering and applied science disciplines. Nowadays the robust design technique has become the state of the art for making product performance insensitive to varying manufacturing conditions, environmental and product-to-product variations. Although its immense importance has been widely acknowledged for different engineering disciplines, there are still many open issues both in practical and theoretical aspects that need to be addressed, especially in the computation of electromagnetic fields. In other words, the computational burden for a robust optimizer is significantly higher than that for its global counterpart, and in this regard, the available robust methodologies may become computationally inefficient for inverse problems where high fidelity models and analysis are commonly used for performance evaluations.
Based on the available robust design methodologies of fellow researchers from different engineering disciplines, a comprehensive and symmetric study of robust optimal design methodologies and techniques, especially the evolutionary algorithm is conducted. More concretely, the study focuses on issues such as the measures and approaches to reduce the huge computational burden of solution strategies, the improvements of evolutionary algorithm in both algorithm structures and parameter updating mechanisms, as well some special key techniques.
Firstly, a robust oriented particle swarm optimization algorithm is proposed for inverse problem. In the proposed algorithm; the neighborhood is redefined; a strategy for efficient expected fitness assignments, and the mechanism for generating new neighborhood solutions, as well as the distance weighted formulation for expected fitness computation are proposed. Also, improvements on algorithm structures and parameters such as new updating formulae for velocity and position vector, the introduction of an age variable, and the out of boundary control are included.
Secondly, an evolutionary algorithm based on Probabilistic Models, a cross entropy method is extended successfully to study the robust optimization of inverse problem. To efficiently compute the robust performances, the normal distribution function is used as the probability density function, and a methodology for evaluating and assigning robust performance to promising solutions is proposed.
Thirdly, some key issues for robust optimizations of inverse problems are addressed. To summary up, the support vector machine is proposed as a response surface model of the objective and constraint function, and combined with evolutionary algorithm to develop an efficient numerical methodology; the polynomial chaos expansion is used as a stochastic response surface model for efficient computations of the expectancy metric of the objective function; and a novel driving mechanism to bias the next iteration cycles to search for both global and robust optimal solutions is introduced.
To validate the proposed methodology and method, they are extensively experienced on different case studies. The case studies include the optimal designs of inverted-S antenna, antenna arrays, and the TEAM (Testing of Electromagnetic Analysis Method) Workshop Problem22. The numerical results as reported positively confirm the feasibility and advantage of the present work.
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