Paper ID# USING A GENETIC ALGORITHM TO DETERMINE AN OPTIMAL POSITION FOR AN ANTENNA MOUNTED ON A PLATFORM

Transcription

1 Paper ID# USING A GENETIC ALGORITHM TO DETERMINE AN OPTIMAL POSITION FOR AN ANTENNA MOUNTED ON A PLATFORM Jamie M. Knapil Infantolino (), M. Jeffrey Barney (), and Randy L. Haupt (2) () Remcom, Inc, State College, PA, USA (2) The Applied Research Lab, State College, PA, USA ABSTRACT Determining an optimal position of an antenna on a platform is not always intuitive. This paper examines the implementation ofa Genetic Algorithm (GA) within XFdtd, a Finite Difference Time Domain (FDTD) solver, for its effectiveness in determining an optimal antenna position when compared to a bruteforce method. XFdtd uses the FDTD method [J to solve general electromagneticproblems. Built into XFdtd is the concept of Feature Based Modeling (FBM), which uses relative coordinate systems to position antennas in a geometry in relation to other parts. The GA, written in C++, is available to XFdtd's Scripting API Through scripting a user specifies the antenna to move and provides bounded regions where the antenna can be located for maximum efficiency. INTRODUCTION Adding new wireless systems to existing platforms is difficult due to physical and electromagnetic constraints. Finding space on an already crowded platform is difficult. Blockage, scattering, and interference with other communications and radar systems must be taken into account. For instance, jammers on a vehicle used to disable improvised explosive devices (led) can interfere with the tactical communication systems on that same vehicle as well as other nearby vehicles. Designers ofthese jamming systems need a way to optimally place the ~ammer antennas on the platform while minimizing the Im~act on tactical communication systems. Traditionally, designers use experience and intuition to place the antennas on a platform. The large number of wireless systems on a platform, interactions between the antenna and its environment, and complex requirements like low radar cross section, contribute to the complexity of the antenna placement problem. ~ full wave electromagnetics model like FDTD is required In order to understand the antenna's behavior in the presence of the platform and environment. An exhaustive search of all combinations of the antenna shape, size, material, and location is not practical, because an antenna designer must conduct many computationally and time intensive simulations and evaluate each one against the others to arrive at the best performing antenna. Not only is the antenna design process time consuming and laborious, but there are no guarantees that the design chosen is optimal. The Genetic Algorithm (GA) is a global optimization computer program that automatically guides the engineer towards the best performing antenna design for an application. The GA begins with some random guesses for the location of an antenna on a platform and proceeds to finding an optimal location using rules based upon genetics and natural selection. This paper presents results from incorporating a GA in the FDTD algorithm XFdtd in order to optimally place antennas on platforms. XFdtd provides the needed accuracy of the electromagnetics model while the GA is capable of finding an excellent solution within a reasonable run time. Results for the optimal placement of a jamming antenna on a Humvee are much better than the results obtained from the best intuitive guess. GENETIC ALGORITHM A GA works by evaluating a cost function to determine the optimal solution to a problem. The cost function, in this case, consists of the electromagnetic functions which are to be minimized or maximized. Some examples of cost ~unctions are radiation pattern, radiation efficiency, input Impedance, and S parameters. Some of these functions may also involve manufacturing costs or other nonelectromagnetic factors such as antenna placement location, frequency, dielectric value, or perhaps the cost of a material used in the antenna design. Using a GA can maximize or minimize the cost function that employs real and integer variables in calculating the cost. Optimization algorithms that minimize real and integer values are known as mixed integer optimization algorithms, so this GA is known as a mixed integer GA [2]. In order to increase the GA's flexibility, all variables are mapped to continuous values between 0 and /09/$ IEEE

2 The population npop x nvar matrix for this GA is represented by; v I, VI,2 p= v 2, V2,2 v npop, X n = x max - x min vm,n + X min In = rounddown I max - I min + Vm,n + I min b; = round vm,n VI,nvar Vnpop,nvar where vm,n = variable n In chromosome m with 0 ::; vm,n ::;. Each row is a chromosome, and the values are initially created by a uniform random number generator. A continuous variable, vm,n is converted to either a real variable, x n ' an integer, In, or a binary digit, s; Where min and max represent variable bounds specified by the GA. X m i n ::; X n ::; X m a, rounddown is a function that rounds to the next lowest integer, and round is a function that rounds to the nearest integer. A grouping of binary digits forms a gene in the binary GA. The benefit of this approach is that all the scaling, quantizing, and rounding happen in the cost function, so the GA operates independent of the variable type. There is no need for a binary GA, a real GA, and a mixed integer GA, because the operators work with any combination ofvariable types. A chromosome can have any mix of real, integer, and binary variables. For instance, the chromosome may contain the number of antennas (integer), the location of the antennas in three-dimensional space (constrained continuous), the material properties of a nearby object (binary), and the location ofa handrail. Chromosome survival may be determined in a number of different ways. Here, the top 50% of the chromosomes survive to be part of the mating pool. Tournament selection with two chromosomes per tournament is used. Roulette wheel selection with rank ordering would give nearly equivalent results [2]. At this point, mating between two selected chromosomes can be done using one of the many different real GA or binary crossovers [2]. Uniform crossover provides a larger exploration of the cost surface than other approaches to crossover [2], so it is implemented in this algorithm. First, a random binary mask is created. A in the mask column means the offspring receives the variable value in parent#. If it has a 0, then the offspring receives the variable value in parent#2. parent #=Vm,l Vm,2 Vm,3 Vm,4 Vm,5 Vm,6 Vm,7 Vm,8 parent#2 =V n,l Vn,2 Vn,3 Vn,4 Vn,5 Vn,6 Vn,7 Vn,8 mask = offspring =V n,l Vn,2 Vm,3 Vn,4 Vn,5 Vm,6 Vn,7 Vm,8 In this approach, only one offspring is created for every two parents selected. This type of crossover results in a diversity of values if the values are binary, but only interchanges values between chromosomes if the values are integer or continuous. Consequently, the mutation introduces new values within the population of continuous values. A continuous crossover would also work in this algorithm. One approach to mutation is to randomly select variables in the population and replace them with uniform random values. Another approach is to add a random correction factor. The correction factor may be created by multiplying each element within a chromosome by a random number ( - s firm s ) and multiplying the entire chromosome by a mutation factor ( 0 ::; a, S ). where rem is the remainder function (digits to the left of the decimal point are dropped). This type of mutation modifies the entire chromosome rather than a single variable. GENETIC ALGORITHM IN XFDTD XFdtd' s theory is based on the FDTD method presented by Kunz and Luebbers []. Built into XFdtd is the concept of Feature Based Modeling (FBM), which allows relative coordinate system definitions among parts in a model. The GA [2], written in C++, is available through XFdtd's Scripting API. Through scripting, a user defines the antenna and the acceptable regions on a platform where the antenna can be located. This GA has a population size of 8 and a mutation rate of 5%. During an optimization, a single region from the list ofpossible regions, as well as a position on that region, are Page 2 of6

3 randomly selected. The resulting spatial location is where the antenna is placed for the next cost function evaluation. Each cost function evaluation is a call to a script function that executes the calculation engine, calculates the cost (antenna pattern, impedance, bandwidth, etc.) and passes that value back to the GA as the cost. The GA keeps 50% of the best chromosomes then performs mating and mutation to find the next generation. This process continues until an acceptable solution is found or a set number of iterations are performed. Figure is a flowchart of the process. dipole --+ I 9 mm 90 = j PEe plate I +, C++ GA Initial pop ulation = 8 Movab le structure and acceptab le regions mut ation rate = 5% 2000 rnm t, Figure 2: Analytic geometry Results IscriPti ng Language Passes cost to GA The cost threshold was set at 4.5dBi and the GA optimized for a maximum cost. The cost function executed XFdtd's calculation engine (CalcFDTD) which calculated the far zone gain. The minimum gain was returned as the cost. By maximizing the minimum gain, an omni-directional pattern was found. After 29 evaluations of the cost function, the GA reached its cost threshold at 4.53dBi. The associated dipole location was at (le-24,.8) mm. The optimization occurred in 22min. SIDPMODEL C++GA Translates GA chromoso me into XFdtd design variables XFdtd Builds model Performs gridding Does calculations Performs natural C++GA selection. mating.. A crude model of a ship was generated inside XFdtd and is shown in Figure 3. The dimensions were as follows: and mut ation. then iterates Figure : Flowchart for GA process DIPOLE OVER METAL PLATE XFdtd's GA implementation was first verified with an analytic model with a known solution before proceeding to a more complicated model, with an unknown solution. The analytic model consisted of a dipole located over a circular plate (Figure 2). It used a design frequency of.5 GHz with a wavelength of 200mm. The vertically polarized short dipole had a length of 9mm. The dipole was placed over a circular PEC plate a distance of 90mm. The plate had a 000mm radius and is centered at (0,0). The dipole was constrained to being directly over the plate. The optimization attempted to find a position that produced an omni-directional pattern. The center of the plate was the obvious solution. An initial test was run with a centered dipole and a minimum gain of 4.76dBi is computed. The grid contains million FDTD cells, the calculation engine uses 52MB, and it took 49s to run the initial test. The smoke stack had a m radius, was 4m long, 3.577m tall The box was 3 x 3 x.5m The distance between the base of the smoke stack and box was m The deck was a maximum of 8.3m wide and 7.7m long The vertically polarized monopole was m tall which is a quarter-wavelength at 800MHz Figure 3: Crude model of ship An initial test started with the monopole located half way between the smoke stack and box. The discretized model contained million FDTD cells. CalcFDTD used Page 3 of6

4 Gain vs An9e 90 80MB and took 3min 30sec to determine a solution. The computed radiation pattern had values ranging from 5.8dBi to 4.9dBi. The local origin of the monopole was constrained to the top of the deck, excluding regions around the smoke stack and box. The cost function executed CalcFDTD, analyzed the far zone pattern, and returned the minimum gain value found. Again, by maximizing the minimum gain, an omnidirectional pattern was found. The cost threshold was 20dBi. After 22 evaluations of the cost function, the threshold was reached at 2.2dBi when the monopole was placed in front of the smokestack. The optimization took 29 min. The optimal location is represented by the red dot in Figure 4. The optimized far zone radiation pattern ranged from 2.2dBi to 54.8dBi. The full 3D pattern can be seen in Figure 5. Figure 6 compares a conical surface (theta=75 degrees from the vertical axis) from the optimal pattern, drawn in green, with the same conical surface from the starting pattern, drawn in blue Figure 6: Optimized vs unoptimized location comparison This optimization found that placing the monopole in front of the smoke stack generated a more omni-directional pattern and produced greater gain at nearly all angles when compared to a location between the smoke stack and box. RESULTS The GA was used to find an optimal location for an led jammer antenna on a Humvee. The first location was chosen to mimic an antenna that was already located on the platform. Figure 7 depicts the first guess for the optimal antenna location. This was the first guess used to initialize the GA. Figure 4: Optimal location of monopole Figure 7: First Guess for Optimal Antenna Location z x Figure 5: Optimized far zone radiation pattern The goal of the jammer was to project as much power on the target (the suspected led) as possible. This can be simulated using XFdtd. It was assumed the led was close to the ground. Figure 8 depicts the results of the first guess for optimal antenna location. XFdtd indicates that very little energy from the transmitter reached the ground. This seed was placed into the initial GA population to see if a better location for the antenna could be found. By the sixth generation, all of the locations that were on the front Page 4 of6

5 bumper were discarded. This seems counterintuitive, but the GA determined it was not the optimal location. It turns out that the optimal location was on the front hood and not on the front bumper. This might be due to the fact the air intake acted like a reflector. The second most optimal location was on the driver side front bumper. FUTURE WORK.35 The next step is to start using more complex geometries with the GA. The Humvee is a simple model compared to other military applications. For example, a platform that already has a dozen antennas on it has more interactions than the Humvee. Further investigation is needed to determine how complex of a geometry the GA can handle. 28 Figure 8 Cross Section SSE of First Guess Antenna Location The GA ran 3 generations. The optimal location found is depicted in Figure 9 with the power down range depicted in Figure 0. One of the problems with the current GA is runtime limitations. This GA takes 3 generations for a total of 36 hours to complete. This is an unrealistic runtime for some applications. One way to help with the runtime is to use a Graphic Processor Unit (GPU) to do the calculations. More research is required to better utilize these devices; initial studies have shown speed ups of 20X, and speed ups of 30X-50X are theoretically possible. The Humvee example took 2 hours with the use of a GPU, making this technology more practical. CONCLUSIONS The GA was useful in determining the location for an led jammer antenna on a platform like a Humvee. It provided an answer with very little guess work. The GA was also able to account for interactions with other elements of the platform. The Humvee has irregular surfaces which could impact the performance of an antenna due to interactions between the antenna and the environment. XFdtd was able to model these interactions properly and then feed the GA the correct data. Figure 9: Optimal Location Found by GA It has been demonstrated that the GA can produce an optimal location for an antenna on a platform. It takes away some of the guess work that is currently employed within this field. The GA can be used to solve problems, such as designing effective jammers, faster and more efficient than what is being used currently. REFERENCES Figure 0: Power down range for Optimally Placed Antenna [] K.S. Kunz and RJ. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, sl edition, CRC Press, 993. Page 5 of6

6 [2] R.L. Haupt and S.E. Haupt, Practical Genetic Algorithms, 2 nd edition, New York: John Wiley & Sons, [3] R.L. Haupt, "A Mixed Integer Genetic Algorithm for Electromagnetics Applications," IEEE AP-S Trans., Vol. 55, No.3, Mar Page 6 of6