Study On Integrated Structural Electromagnetic Optimization Design Of Reflector Antennas

Reflector antennas are widely used in radar, telecommunication, radio astronomy and other applications. With the trend of large diameter, high frequency and high accuracy, the harsh design requirements on reflector antennas become more demanding, and the antenna design concept has already been transformed from traditional simple structural design (to achieve its electromagnetic performance) to the concept of integrated structural electromagnetic optimization design. The key points on the integrated structural electromagnetic optimization design of reflector antennas are investigated in this thesis, and the main research is described as follows.1. An approximation method of pattern analysis for distorted reflector antennas is presented based on structural finite element shape functions. The previous work of approximation expression using a second-order Taylor series about exponential term caused by structural deformation is further developed. The shape functions in structural analysis are employed as a local interpolation scheme in the electromagnetic integral computation. The concepts of "element stiffness matrix", "global stiffness matrix", "finite element assembly" in structural finite element method are introduced in the approximation pattern analysis for distorted reflector antennas, which makes the far field integral computation and structural deformation separated, and the far field electrical vector is derived as a function of structural nodal displacements in a simple matrix form by assembling the integrals on structural elements. This method costs less time to obtain the far field pattern with different surface deformations during the iterations of integrated optimization design. The effectiveness of the proposed method is verified by simulation results.2. The sensitivity of far field electromagnetic performance of reflector antennas with respect to surface nodal displacements is presented. On the basis of structural finite element model, the same shape functions in structural finite element method are adopted as a local interpolation scheme in the far field integral. The surface normal vector and additional phase error in exponential term caused by surface nodal displacements are expanded, and the gradient of far field electromagnetic performance-directivity with respect to surface nodal displacement is thus obtained by the partial derivative. The sensitivity analysis of maximum directivity, sidelobe level and cross-polarization level is performed respectively and some interesting achievements are concluded.3. An integrated structural electromagnetic shape control of cable mesh reflector antennas is presented. In this integrated model, the boresight directivity is directly chosen as the object function and the initial cable lengths are chosen as design variables. The prior work on "approximation method" and "sensitivity analysis" is applied in this multidisciplinary model, which makes the procedure characterized by a sequential quadratic programming model. The gradient and Hessian matrix of boresight directivity with respect to adjustable cable lengths are obtained by the sensitivity of boresight directivity with respect to surface nodal displacements and the sensitivity of surface nodal displacements with respect to adjustable cable lengths. The finite positive of Hessian matrix of object function is proofed and the shape control procedure is implemented by establishing and solving the sequential quadratic programming model iteratively. The effectiveness of the proposed method is verified by simulation results.4. An integrated structural electromagnetic analysis procedure of cable mesh reflector antennas with structural random errors is presented. Considering the randomness of truss nodal positions and cable member dimensions, the structural random parameters are modeled by the random factor method. The numerical characteristics of cable surface nodal displacements are obtained by the sensitivity analysis of surface nodal displacements with respect to truss nodal positions and the sensitivity analysis of surface nodal displacements with respect to cable member dimensions. By the analysis of gradient of far field directivity with respect to surface nodal displacements, the computational expressions of the mean value and variance of the far field directivity are developed by means of random factor method and random variable’s functional moment method.5. An integrated structural electromagnetic beam pattern synthesis method of cable mesh reflector antennas is presented. In this integrated method, the beam pattern requirement is chosen as object function and the cable member dimensions are chosen as design variables. Based on the sensitivity analysis of cable mesh reflector antennas, the gradient of far field directivity with respect to cable member dimensions is added in the integrated beam pattern synthesis and the object is expressed as a function of structrual design parameters. Sequential linear programming method is adopted in solving of the optimization model for a cable mesh reflector antenna. The method provides a therorical basis for the reality of contour beam pattern synthesis of cable mesh reflector antennas in engineering.