The Application Of CGP Function Modeling In Wire Antenna Design

With the rapid development of electronic computers, function modeling becomes more and more concerned, function modeling in the real world is importance, it is mainly used in the general engineering field(such as mechanical, electrical, civil engineering, water resources engineering technology), high-tech areas (such as telecommunications, aerospace, electronics, automation, and other high-tech), and other related fields. The so-called function modeling is that the actual variable relationship of problems is represented by function. It uses the image and nature to come to the conclusion of mathematics to solve real problems.In the field of evolvable hardware, people user the way of evolution of circuit functions and connection between a series of arithmetic logic gates, so the study of truth table begins to growing in this area. The genetic algorithm (GA) and linear integer chromosomes are used to represent the connection relations of arithmetic cells. It is clear that this representation of digital circuits has been promoted, which makes the solution of problem is not limited in the scope of binary. This general form of the construction is Cartesian Genetic Programming (CGP).Cartesian Genetic Programming (CGP) is a form of diagram, which is based on the genetic program; it comes from the evolution of digital circuits. In essence, its feature is that it uses integer string to encode, so as to represent functions and connections between nodes, and the program input and output interface. This gives it a great general, so that it can represent neural networks, programs, circuits, and much other computing architecture.The CGP is widely implicated in the evolution of digital circuit, for example, Miller, Thompson and Fogarty took the lead in this evolutionary algorithm to design the arithmetic logic circuit. This technology of evolution related functions and arithmetic cell matrix can easily be mapped to a programmable logic array, which is the FPGA.Since Julian F.Miller proposed CGP’s theory, the development of CGP is mainly used in circuit design, few people apply it in the field of function modeling, in the paper of Europe2009"Self Modifying Construction of Cartesian Genetic Programming:Fibonacci, Squares, the Regression and Summing ", it firstly proposed the CGP function modeling, but is slightly over.CGP in function modeling in this area, so it still has big space of research and exploration. In this paper, we propose a new method of function modeling, which is using the principle of CGP to implement function modeling. Firstly, we abstract out the CGP cell matrix of the problem, and then analyze the structure according to the requirement of the problem, and determine the input and output interface, while we design the function of every cell in the matrix. When the CGP architecture is achieved, we use the genetic algorithm to encode, decode and make genetic operation for the related problem, and make the evolution for it. Finally, we compare the two methods of function modeling; one is the method of our CGP function modeling, the other is the ParetoGP system which is proposed in the paper of2009TEC "Order of non-linearity as a complexity measure for models generated by symbolic regression via Pareto genetic programming" writhed by Vladislavleva. We test the same eight classic problems through the experiment for these two methods, and compare the results, and then we can know that the method of using CGP to implement function modeling is feasible, effective and has its advantages.On this basis, we try to apply CGP to the practical problem, which is the antenna design problem. The antenna design problem is a super multi-constrained highly nonlinear, steep, multi-peak, non-conductive and not even continuous optimization problem; the general algorithm often cannot meet the constraints on a feasible solution, and cannot find the global optimal solution. In the modern wire design, we commonly used the methods of moments (MOM), finite element method (FEM), and the geometrical theory of diffraction (GTD) and so on to analysis the antenna, but using the above methods often encounters the following difficulties in the antenna design:1) In accordance with a traditional antenna design method to complete the antenna design, we must need to have rich experience in the design, complex authentication methods and a variety of counseling test tools to solve such as RF interference, antenna matching, receiver sensitivity, antenna coupling sensitivity, the device parameters and so many problems. The cycle of completing the design and implementation is relatively long, and if we change the demand, it will increase the difficulty and cycle of antenna design.2) Under the guidance of the development trend of the miniaturization of electronic devices, it not only requires the development of miniaturized antenna, and also requires the antenna and other electronic devices integrated together. But these may interfere with each other, when the components get too close to the antenna and it will have a greater interference, resulting in lower signal quality and equipment performance, it is necessary to introduce other algorithms to optimize the electromagnetic compatibility between the antenna and other electronic devices.3) When the height of is required to be smaller and smaller, the matching circuit in practice may result in the adverse effects of the distribution parameters, if the circuit layout is not good or welding repeated operation, so this effect is particularly evident.In recent years, the use of evolutionary algorithms to design the antenna is to be better resolves on these issues.In this paper, we use a new principle that applies the principle of CGP function modeling to build an antenna model, and then get a reasonable antenna through the improved evolutionary algorithm, and make a performance comparison between the antenna designed by CGP and ST5antenna designed by NASA designed through the experiments. By the comparison, we can validate the feasibility, effectiveness, and its unique comparative advantages in our application of the CGP principle in practical engineering problems. In this paper, we use the CGP principle to make antenna design and it has the following three characteristics:(1) Since the CGP theory proposed by Julian F. Miller, in recent years, the research and development mainly trends in circuit design, there are little relevant scholars to research in the field of function modeling. In this paper, we propose a new function modeling method that is the application of the CGP principle in function modeling, and it reflects the novelty and superiority compared with the general function modeling method.(2) We boldly attempt to apply principle of the CGP modeling to the actual process of problem:antenna design. By the experiment and compare with the ST5wire antenna, we find that the designed wire antenna can meet the requirement of function, and it has the comparative advantage in the aspect of VSWR.(3) Because the CGP method is based on the basis of available FPGA resources, so whether it is for function modeling and its application in antenna problems, it can be relatively easy to map directly to the FPGA hardware, so it make our antenna design to be more intelligent.