大型天线反射面保型与机电综合优化设计
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摘要
在国家重大基础科研（国防973）项目的支持下，基于前人的工作，本文对大型反射面天线的保型设计与机电综合优化问题进行了研究。完成的主要工作和取得的成果如下：
1.为了减小赋形曲面天线在各个工作仰角的弹性变形对电性能的不利影响，提出了一种分段拟合与副面补偿方法。首先，采用标准抛物线对赋形面的母线数据进行分段拟合，通过旋转得到一组标准抛物环面。其次，用该组抛物环面吻合天线在各个仰角时的变形主面，同时保证各抛物环面的焦点落在设计理论面的焦线段上，得到一组主面吻合参数。最后，根据主副面之间的匹配关系，得到了天线在各个仰角时的副面调整参数。
2.基于电磁场与结构位移场的场耦合理论模型，研究了反射面天线的机电综合拓扑优化问题。提出了大型天线背架结构拓扑优化的基结构确定方法。该部分讨论了场耦合分析模型的分析方法和计算流程，并指出将拓扑变量引入机电综合优化模型时带来的问题。进而以背架结构的尺寸和拓扑变量以及副面补偿量为设计变量，以天线电性能为目标，同时考虑天线的自重和强度等约束，建立了反射面天线的多工况机电综合拓扑优化模型。
3.采用机电综合拓扑优化模型对某65m口径的反射面天线进行了优化设计，得到了改进的结构方案，提高了天线的电性能。计算结果表明，采用机电综合拓扑优化方法可使口径场的相位误差分布趋于合理，在保证天线增益不下降的情况下，可明显降低副瓣电平。
4.杆系结构拓扑优化结果中，往往出现杆件的交叉现象，给结构的制造和装配带来工艺上的不便。为此，本文提出一种避免交叉现象的拓扑优化方法。根据节点和杆件单元的几何位置信息，采用Heaviside函数将是否出现交叉的判断准则表示为杆件横截面积的连续函数。将交叉约束以连续函数的形式加入拓扑优化模型，从而便于采用成熟的数学规划法求解该问题。
5.针对现有离散变量结构优化方法在解决大型工程结构设计问题上的不足之处，提出一种新的离散变量结构优化方法。采用带有罚因子的光滑函数逼近阶梯函数，将离散变量优化问题转化为连续变量优化问题。通过调整罚因子的取值，保证设计变量最优值落在给定的离散值附近。与已有方法相比，该方法在计算规模和计算量上均有明显优势。本文将该方法应用于某大型相控阵雷达的精密补偿平台设计之中，得到了满意的设计方案。
This work was supported by a grant from the National Program on Key BasicResearch Project (973Program). On the basis of the predecessor work, this thesis ismainly concerned with the homology design and electromechanical syntheticoptimization of large radar and antenna. The main research work can be described asfollows.
1. On the degradation of electrical performance due to the main reflectordeformation of large shaped Cassegrain antennas, a method for compensation bymoving sub-reflector is presented. First of all, a group of best-fit paraboloids are foundby least-square fitting to the theoretical discrete data. Second, the group of paraboloidsis used to fit the deformed main reflector, with the constraint of all these focuses beingin line. At last, the best-fit parameters are optimized and the adjustments of sub-reflectorare derived with the ratio of main reflector and sub-reflector.
2. Based on the field-coupling model about the electromagnetic field and thestructural displacement field, a topology electromechanical synthetic optimization ofreflector antenna is studied. The selection criterion of ground structure is proposed forthe topology optimization of antenna structure. This chapter discusses the method andprocess of the field-coupling model in detail, and points out the problem of adding thetopology variables into the optimization model. The main contribution of this chapter isto establish the optimization design model treating the antenna electrical properties astarget, taking the size, shape, topology of antenna structure and compensation quantityof sub-reflector as design variables. At the same time, the constraints of weight, strengthis satisfied.
3. Simulation results of65m antenna show that electrical performances areimproved by the electro-mechanical integrated optimization model. The greatest benefitafter the topology change is to flat the phase error of aperture, thus the side-lobes arereduced, so as to reach the engineering design requirements. At the same time, the gainof antenna is satisfied.
4. The intersection elements exist in the result of topology optimizationfrequently. It is not reasonable to delete the intersection elements. It will give thestructure of manufacturing and assembly inconvenience. Generally speaking, theintersection is avoided for engineering design. The contribution is that elementintersection is described in terms of a continuous intersection factor. A Heaviside function is used to map element cross-section area to intersection properties. Therefore,the intersection feature is described by a continuous and differentiable function.According to this, the intersection constraint is added to the topology optimization couldbe calculated by mature mathematical programming method.
5. Considering the inadequacies of the method about multi-discrete structuraloptimization at present. This part constructs a new mathematical model of discretevariables. The ultimate optimal results fall near the discrete values through the mappingof the continuous variables. A piecewise function is constructed to punish thecontinuous variables on each interval of all adjacent discrete variables. The solvingscale is smaller compared to the branch and bound method. Finally, the problem of amulti-variable topology optimization is transformed into a general nonlinearoptimization problem. Finally, case verification is conducted on the largest phased arrayradar and a better optimization result is obtained. The design will be applied toengineering.
1.为了减小赋形曲面天线在各个工作仰角的弹性变形对电性能的不利影响，提出了一种分段拟合与副面补偿方法。首先，采用标准抛物线对赋形面的母线数据进行分段拟合，通过旋转得到一组标准抛物环面。其次，用该组抛物环面吻合天线在各个仰角时的变形主面，同时保证各抛物环面的焦点落在设计理论面的焦线段上，得到一组主面吻合参数。最后，根据主副面之间的匹配关系，得到了天线在各个仰角时的副面调整参数。
2.基于电磁场与结构位移场的场耦合理论模型，研究了反射面天线的机电综合拓扑优化问题。提出了大型天线背架结构拓扑优化的基结构确定方法。该部分讨论了场耦合分析模型的分析方法和计算流程，并指出将拓扑变量引入机电综合优化模型时带来的问题。进而以背架结构的尺寸和拓扑变量以及副面补偿量为设计变量，以天线电性能为目标，同时考虑天线的自重和强度等约束，建立了反射面天线的多工况机电综合拓扑优化模型。
3.采用机电综合拓扑优化模型对某65m口径的反射面天线进行了优化设计，得到了改进的结构方案，提高了天线的电性能。计算结果表明，采用机电综合拓扑优化方法可使口径场的相位误差分布趋于合理，在保证天线增益不下降的情况下，可明显降低副瓣电平。
4.杆系结构拓扑优化结果中，往往出现杆件的交叉现象，给结构的制造和装配带来工艺上的不便。为此，本文提出一种避免交叉现象的拓扑优化方法。根据节点和杆件单元的几何位置信息，采用Heaviside函数将是否出现交叉的判断准则表示为杆件横截面积的连续函数。将交叉约束以连续函数的形式加入拓扑优化模型，从而便于采用成熟的数学规划法求解该问题。
5.针对现有离散变量结构优化方法在解决大型工程结构设计问题上的不足之处，提出一种新的离散变量结构优化方法。采用带有罚因子的光滑函数逼近阶梯函数，将离散变量优化问题转化为连续变量优化问题。通过调整罚因子的取值，保证设计变量最优值落在给定的离散值附近。与已有方法相比，该方法在计算规模和计算量上均有明显优势。本文将该方法应用于某大型相控阵雷达的精密补偿平台设计之中，得到了满意的设计方案。
This work was supported by a grant from the National Program on Key BasicResearch Project (973Program). On the basis of the predecessor work, this thesis ismainly concerned with the homology design and electromechanical syntheticoptimization of large radar and antenna. The main research work can be described asfollows.
1. On the degradation of electrical performance due to the main reflectordeformation of large shaped Cassegrain antennas, a method for compensation bymoving sub-reflector is presented. First of all, a group of best-fit paraboloids are foundby least-square fitting to the theoretical discrete data. Second, the group of paraboloidsis used to fit the deformed main reflector, with the constraint of all these focuses beingin line. At last, the best-fit parameters are optimized and the adjustments of sub-reflectorare derived with the ratio of main reflector and sub-reflector.
2. Based on the field-coupling model about the electromagnetic field and thestructural displacement field, a topology electromechanical synthetic optimization ofreflector antenna is studied. The selection criterion of ground structure is proposed forthe topology optimization of antenna structure. This chapter discusses the method andprocess of the field-coupling model in detail, and points out the problem of adding thetopology variables into the optimization model. The main contribution of this chapter isto establish the optimization design model treating the antenna electrical properties astarget, taking the size, shape, topology of antenna structure and compensation quantityof sub-reflector as design variables. At the same time, the constraints of weight, strengthis satisfied.
3. Simulation results of65m antenna show that electrical performances areimproved by the electro-mechanical integrated optimization model. The greatest benefitafter the topology change is to flat the phase error of aperture, thus the side-lobes arereduced, so as to reach the engineering design requirements. At the same time, the gainof antenna is satisfied.
4. The intersection elements exist in the result of topology optimizationfrequently. It is not reasonable to delete the intersection elements. It will give thestructure of manufacturing and assembly inconvenience. Generally speaking, theintersection is avoided for engineering design. The contribution is that elementintersection is described in terms of a continuous intersection factor. A Heaviside function is used to map element cross-section area to intersection properties. Therefore,the intersection feature is described by a continuous and differentiable function.According to this, the intersection constraint is added to the topology optimization couldbe calculated by mature mathematical programming method.
5. Considering the inadequacies of the method about multi-discrete structuraloptimization at present. This part constructs a new mathematical model of discretevariables. The ultimate optimal results fall near the discrete values through the mappingof the continuous variables. A piecewise function is constructed to punish thecontinuous variables on each interval of all adjacent discrete variables. The solvingscale is smaller compared to the branch and bound method. Finally, the problem of amulti-variable topology optimization is transformed into a general nonlinearoptimization problem. Finally, case verification is conducted on the largest phased arrayradar and a better optimization result is obtained. The design will be applied toengineering.
引文
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