基于替代模型和良率估计的柔性天线多目标优化算法

随着物联网、智能穿戴设备等领域的迅速发展，对通信设备的要求更加严格。 柔性天线为这些应用带来了全新的可能性。相比于传统刚性天线，柔性天线具有 更大的设计自由度和适应性，可以灵活应对不同的应用场景，为用户提供更加稳 定、高效的通信服务。因此，研究柔性天线及其优化技术，对于推动智能通信设备 的发展和应用具有重要意义。目前柔性天线的设计面临由于设计变量较多、电磁 仿真耗时长而导致设计成本较高的问题，使用智能优化算法调用电磁仿真软件评 估每个种群个体的表现并求解天线设计参数的方式虽然解决了依靠经验设计天线 的问题，但是仍然消耗很大计算成本，限制了天线的优化效率。基于替代模型的 设计方法在微波器件设计领域逐渐被研究人员经常使用，它通过计算成本较低的 替代模型来引导电磁仿真模型快速找到最优解，极大提高了复杂器件的设计效率。 本文基于替代模型的优化方法，将良率作为柔性天线的目标函数，对柔性天线 的电磁性能进行高效率优化。主要研究工作及成果概括如下:(1) 针对柔性天线形变 时谐振频率偏移和带宽变窄的问题设计了良率优化框架，通过神经网络作为柔性 电小天线替代模型，拟合了天线的尺寸及形变量和回波损耗之间的映射关系，解 决了良率计算过程中需要多次计算天线响应耗费大量时间的问题。以一柔性电小 天线为实例，通过全波仿真改变形变量检验了算法的有效性，测试中弯曲情况下 的带宽保持在目标带宽的 91% 以上，同时最大谐振频率偏移量小于目标谐振频率 的 0.85%。(2) 针对柔性天线的响应和设计变量数据之间非线性程度高、建模复杂、 且需要大量样本点的问题，通过基于特征的替代模型降低了输入和输出数据之间 的非线性程度，降低了替代模型结构复杂度，减少了建模需要的样本点，提高了 设计效率。将模型应用到良率优化框架并以电小天线为例，实现了该天线弯曲时 谐振点偏移量在目标谐振频率的 1.5% 以内，最小带宽超过目标带宽 5%，最大带 宽超过目标带宽 10%。(3) 针对柔性天线多目标优化问题，通过良率优化框架和基 于特征的替代模型设计了多目标优化算法，得到了四个目标之间互不占有的解集。 最后对一种双频柔性天线进行全波仿真验证了算法产生的解集，以天线双频带的 谐振频率稳定性和带宽为目标，结果显示优化后的天线具有更高的带宽和稳定的 稳定的谐振频率，设计者可以根据解集中的结果选择设计方案。

With the rapid development of the Internet of Things, smart wearable devices, and other fields, the demands for communication devices have become increasingly stringent. Flexible antennas, as a novel solution, introduce entirely new possibilities for these applications. Compared to traditional rigid antennas, flexible antennas offer greater design freedom and adaptability, enabling them to respond flexibly to diverse application scenarios and provide users with more stable and efficient communication services. Therefore, studying flexible antennas and their optimization technologies is of significant importance in advancing the development and application of communication equipment. The current design of flexible antennas faces the same difficulties as other antennas—high design costs due to numerous design variables and time-consuming electromagnetic simulations. Although the traditional approach of employing intelligent optimization algorithms to invoke electromagnetic simulation software to evaluate the performance of each population individual and solve antenna design parameters addresses the issue of relying on experience to design antennas, it still incurs significant computational costs, thus limiting the optimization efficiency of antennas. The surrogate model-based design method is often used by researchers in the field of microwave device design. This method guides the electromagnetic simulation model to quickly find the optimal solution through the surrogate model, which has a low computational cost. As a result, it greatly improves the design efficiency of microwave devices with complex structures. In this paper, based on the optimization method of the surrogate model, the yield is taken as the objective function of the electromagnetic performance stability of the flexible antenna after deformation, and the electromagnetic performance of the flexible antenna is optimized with high efficiency. The main research work and achievements are summarized as follows: (1) A yield optimization framework is designed to solve the problem of resonant frequency shift and bandwidth narrowing when the flexible antenna is deformed, and the neural network is used as a surrogate model for the flexible electric small antenna, and the mapping relationship between the size and deformation of the antenna and the return loss is fitted, which solves the problem of time-consuming calculation of the antenna response in the process of yield calculation. Taking a small flexible antenna as an example, the effectiveness of the algorithm is verified, in the test, the bandwidth in the bending case is maintained at more than 91% of the target bandwidth, and the resonant frequency offset is 0.14%-0.85% of the target resonant frequency. (2) In order to solve the problem that the response of the flexible antenna and the design variable data are high and the model needs to be re-established after changing the design target, the feature-based surrogate model reduces the degree of nonlinearity between the input and output data, reduces the structural complexity of the surrogate model, increases the flexibility of the surrogate model in yield optimization, and improves the design efficiency. The model is applied to the yield optimization framework and the electric small antenna is taken as an example, and the resonant point offset of the antenna is less than 1.5% of the target resonant frequency when the antenna is bent, the minimum bandwidth exceeds the target bandwidth by 5%, and the maximum bandwidth exceeds the target bandwidth by 10%. (3) In order to solve the problem that there are many optimization targets for flexible antennas, a multi-objective optimization algorithm is designed through the yield optimization framework and a feature-based surrogate model, and the solution set is iteratively updated to generate the solution set by iteratively updating the response of random samples to meet the design indicators. The results show that the optimized antenna has higher bandwidth and stable resonant frequency, and the designer can choose the design scheme according to the results in the solution set.

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