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10
1.РАДЮЕЛЕКТРОН1КА
УДК 621.326
OPTIMIZING RADIATION PATTERN OF BROADSIDE ARRAY ANTENNA BY AMPLITUDE-POSITION PERTURBATIONS USING A GENETIC
ALGORITHM
Chao-Hsing Hsu, Kang K. Yen, Tadeusz Babij
В статье описана реализация антенны с амплитудно-позиционным возбуждением. Генетический алгоритм используется для оптимизации паттерна излучения антенны.
This paper presents the implementation of the broadside antenna by using adaptive array antenna. Even though this kind of broadside antenna is little bit costly compared with the conventional ones, its performance can be improved because it is possible to null the interfering signals and maximize the main lobe towards the array normal at the same time. Thus the optimal radiation pattern can be obtained. In many applications, it is required to have the maximum radiation of an array directed toward the array normal. An optimal radiation pattern design for a broadside array antenna is not only to derive the maximum power radiation at the array normal direction but also to suppress interference by placing a null at the direction of the interfering sources. The Signal Interference Ratio (SIN) can be maximized. Genetic algorithms are used for the search of the optimal radiation pattern by amplitude-position perturbations. Details on the structure of the system, radiation pattern formulation, the application of the genetic algorithm and simulation results are given.
1 INTRODUCTION
Conventional broadside antennas can form a main lobe always towards the array normal. Their structures are simple, but they are not able to compress the interferences. As the development of the modern communications, higher and higher communication quality is required by users for different kinds of antennas. In order to improve the performance of the broadside antenna, implementing the function of the broadside antennas with adaptive antenna array is a possible approach.
A broadside array antenna must keep maximum radiation toward array normal. In the previous papers [1-6], adaptive pattern nulling technique has been studied in the optimal radiation pattern search. Adaptive pattern nulling technique means minimizing the power of the interfering signal coming from any direction by putting a null in its direction. In this paper, the optimal radiation pattern of broadside array will not only be able to suppress interferences by placing nulls but also be able to derive the maximum power radiation in the array normal direction. A deduced formula of the radiation pattern of broadside array antennas is suitable for the
optimal solution search. The formula can always keep maximum radiation of a broadside array antenna toward array normal. At the same time, it can cancel all the interferences from the interfering sources. A perturbation method consists of small perturbations with the element parameters. The technique features are amplitude and position perturbations. As known, compared with gradient-based search methods, genetic algorithms can derive a global search by mutation technique and avoid being trapped in local optima. A search procedure based on the genetic algorithm is used to obtain the required perturbations for the designed optimal radiation patterns.
This paper first presents the structure of the adaptive antenna, which will be used as a broadside antenna. The idea is trying to simplify the structure as much as possible so as not to increase the cost much. Second, the formulation of the radiation pattern is deduced based on the characteristics of the broadside antenna. Third, the application of the genetic algorithms to the optimal radiation pattern design of the broadside antenna is explained. Last, the simulation results are given.
2 DEDUCING RADIATION PATTERN FORMULA
FOR SEARCHING OPTIMAL SOLUTION
For an adaptive linear array of 2N equispaced sensor elements as Figure 1, an interfering signal with wavelength l impinges on any two adjacent element n and element n + 1 by a distance d from the direction 9 with respect to array normal as shown in Figure 2. To reach any two adjacent elements, there is a time delay t as follows [7-8]:
v
v is the propagation speed of radio wave. t corresponds to a phase shift of y .
2 P
y = -T-dsin9 = kdsin9 . (2)
Array Normal
N
elements
amplitude weights
Figure 1 - Diagram of an adaptive linear array designed by amplitude-only perturbations using a genetic algorithm
AF(0) = 2 £ ancos[(n - 0,5)y]
n = 1
(5)
In order to increase the performance of adaptive array, the antenna position perturbations in even symmetry are added. The array factor becomes as
N
AF (9) = 2 £ an cos [( n - 0,5 ) k (d + (Ad/( n - 0,5 ))) sin 9], (6)
n = 1
where Adn is the position weight at element n .
The equation (6) can always keep maximum radiation toward array normal however the weights change. In addition, it is suitable for optimal solution searching.
3 GENETIC ALGORITHM APPROACH FOR OPTIMIZING RADIATION PATTERN
Array
Figure 2 - The incident signal reaching any two adjacent elements
The array factor of adaptive linear array for far field using phase perturbations is given by
2 N
AF(0) = £ aneJ(n- 1 )y , (3)
n = 1
where an - amplitude weight at element n .
If the reference point is at the physical center of the array, the array factor becomes
2 N
AF(0) = 2 £ aneJ(n -N- 0>5)y , (4)
n = 1
where 2N - number of elements, 0 - incident angle of interfering signal or desired signal.
If amplitude weights are in even symmetry, the equation (4) can be simplified to
With fitness function given by the square of AF(0) in equation (6), a genetic algorithm is used to adjust the position weights based on the power of the array in the interfering direction [9-10]. The goals are to minimize the total output power of the interfering signal. During the process of genetic iteration, the weight vector kept for the next step iteration should make the output power of the interfering signal to be decreased monotonically. Owing to a broadside array, the main lobe is always toward 0 ° with respect to array normal using equation (6), the radiation pattern could
not only make the main lobe is always toward 0° or 180° but also minimize the total output power of the interfering signal at same time. Obviously, this technique can maximize the signal to interference ratio (SIR) for an broadside array antenna. The flow chart is shown in Figure 3. Steps of genetic algorithm are as follows:
Step 1. Initialization: A set of chromosomes is randomly generated. A chromosome (weight vector) is composed of genes (weights). For this problem, the genes are an and
Ddn . So, The initial step is generating a collection of random matrix vectors [an;Ddn] , n = 1, 2,..., N,
m =1, 2,., P . The number of genes is 2N. P is the number of chromosomes or population size. Define a vector and variable to which the gradually optimized chromosome and its fitness are saved separately. Their initial values are the first chromosome of the generated chromosome set and its fitness.
Step 2. Evaluation: For every chromosome, two objective functions are calculated for evaluating its fitness. One is the output power of the desired signal; the other is the output power of the interfering signal. Check every chromosome's fitness step by step. Compared with the present best fitness, if one chromosome can not only give the higher output power of the desired signal but also the lower output power of the interfering signal, renew the value of the defined vector and variable with this chromosome and its fitness. Otherwise, keep their values unchanged.
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ISSN 1607-3274 "Paäioe^eKTpoHiKa. iH^opMaTHKa. YnpaBëiHHfl" № 1, 2003
Step 3. Selection: A random number generator is used to generate random numbers whose values are between 0 and 1. If the value of random number is smaller than p , this chromosome survives; otherwise, it dose not survive. The best fitness of the population always survives.
Step 4. Crossover: Pairs of parents are selected from these survivors. Single point crossover is selected to produce the next generation. The weight string from the beginning of chromosome to the crossover point is copied from one parent and the rest is copied from the second parent.
Step 5. Mutation: The basic mutation operator randomly generates a number as the crossover position and then changes the value of this gene randomly.
Step 6. Termination: Steps 2-5 are repeated till the predefined number of generations has been reached.
The best set of weights (amplitude and position weights) can be generated after Termination.
The flow chart of genetic algorithms is as follows:
Case and Result: With respect to array normal, the interfering signal directions are from 40° and -20 ° respectively,
and main lobe is toward 0 °. The genetic algorithm is going to stop after 10000 iterations. The results are as showed in Table 1 and Figure 5. The optimal radiation pattern is derived. The SIN=125dB so that the interfering noise can be completely ignored.
Table 1 The weight for the optimal radiation pattern
Main lobe toward 0° Nulling direction in from 40° and -20°
a1 = 0,572 Ad1 = 0,158
a 2 = 0,965 Ad2 = 0,077
a 3 = 0,506 Ad3 = -0,161
a4 = 0,949 Ad4 = -0,005
a5 = 0,761 Ad5 = -0,078
a6 = 0,986 Ad6 = -0,168
a7 = 0,678 Ad7 = -0,240
a8 = 0,922 Ad8 = -0,197
a9 = 0,830 Ad9 = -0,024
a10 = 0,166 Ad 10 = 0,132
The relative power pattern is getting convergent as Figure 4. It can be seen that SIR reaches to 100dB only in the 45 th generation. So, the efficiency of genetic algorithm approach is very high and the interference can be completely ignored in real time signal processing.
Figure 3 - Flow chart of genetic algorithm
4 SIMULATION RESULTS
For this problem, the necessary variables of genetic algorithm are defined as follows: population size p equals to 20; the selected survival rate ps equals to 0,5; the probability of crossover is 0,5; the proportion of mutated genes is 0,5.
In this problem, assumed a linear antenna array is composed of 20 isotropic elements. So, N equals 10.
1 < n < N. The distance d of two adjacent elements is half of l. The optimal radiation pattern technique features are by position perturbations. The fitness function is given by the square of AF(9) in equation (6). Both amplitude weights and position weights are in even symmetry. The value of an is set between 0,1 and 1. The value of Ad is set between -0,24 and 0,24.
Figure 4 - Relative power pattern getting convergent using iteration
Mtp 11 n-mi
Figure 5 - Adaptive radiation pattern of broadside array antenna for main lobe toward 0° and interfering source at 40° and -20°
The interfering signal directions are from 40 ° and -20 °
(i.e. 340° ) respectively, and the maximum radiation toward
0 °. The radiation patterns are mapped from 90 ° to 270 ° as showed in Figure 6 in dB scale and in Figure 7 in decimal scale.
5 CONCLUSIONS
The optimal radiation pattern design of broadside array antenna based on amplitude-position perturbations using a genetic algorithm is proposed and achieved. For a broadside array, the desired signal direction is always at 0 ° with respect to array normal. In the paper, first, the output power formula based on amplitude and position for broadside array antenna composed by adaptive antenna array is deduced. In order to be able to adopt genetic algorithm to search the optimal radiation pattern, the formula is reformed through assuming amplitude and position weights are in even symmetry. Genetic algorithms are applied to find the optimal radiation pattern of the proposed adaptive antenna. As the optimal radiation pattern means that the power of desired signal should be highest and the power of interfering signals should be lowest as much as possible at the same time. In this paper, the optimal radiation pattern of broadside array was obtained. The convergence curves of genetic algorithm iteration show that it is effective for this problem. The approach of genetic algorithm in an adaptive linear array places nulls in the directions of interference and forms maximum main lobe in the direction of array normal to the far-field radiation pattern. The adaptive radiation pattern of broadside array antenna has been derived in this paper.
un a }«î :< : 'iMhnng sais J jO # L»js-j:
ît
Figure 6 - The whole radiation pattern of adaptive broadside array antenna in dB scale
i» ■ h '■>■ I > ■ j JO 094 ari ■+>■'■.■ ■ t':'. -i JO H -4 -:■
Figure 7 - The whole radiation pattern of adaptive broadside array antenna in decimal scale
REFERENCES
1. Alan J. Fenn, "Theoretical Near Field Cluster and Interference Cancellation for an Adaptive Phased Array Antenna," Proceedings of International Symposium Digest, Antennas and Propagation, pp. 47-49, 1987.
2. M. H. Er, "Synthesis of Antenna Array Pattern with Broad Null Constraints," Journal of Electrical and Electronics Engineering, Australia-IE Aust. & IREE Aust., vol. 10, no. 2, pp. 136145, June 1990.
3. C. H. Hsu and T. M. Babij, "Pattern Nulling of Adaptive Antenna by Phase and Amplitude Perturbations Using Genetic Algorithm," Knowledge-Based Intelligent information Engineering Systems & Allied Technologies, KES'2001, Part 2, pp.1047-1051, 2001.
4. Wen-Pin Liao and Fu-Lai Chu, "Array pattern Nulling by Phase and Position Perturbations with the Use of the Genetic Algorithm" Microwave and Optical Technology Letters, Vol. 15, No. 4, pp. 251-256, 1997.
5. You Chung Chung and Randy L. Haupt, "Amplitude and Phase Adaptive Nulling with A Genetic Algorithm," Proceedings of 15th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, vol. 1, pp. 359-364, CA Mar. 1520, 1999.
6. A. Tennant, M. M. Dawoud and A. P. Anderson, "Array Pattern Nulling by Element PositionPerturbations Using a Genetic Algorithm," Electronics Letters, Vol. 30, No. 3, pp. 174-176, 3rd February 1994.
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ISSN 1607-3274 "PaâioeëeKTpoHiKa. Ii^opMaTHKa. YnpaBëiHHfl" № 1, 2003
В.А.Дзензерский, С.В.Плаксин, И.И.Соколовский: РАДИОФИЗИЧЕСКИЙ ПОДХОД К ИЗМЕРЕНИЮ СКОРОСТИ ГАЗОВЫДЕЛЕНИЯ В СВИНЦОВО-КИСЛОТНЫХ АККУМУЛЯТОРНЫХ БАТАРЕЯХ
7. Monzingo, Miller, "Introduction to Adaptive Arrays" weley, New York, 1968.
8. Chao-Hsing Hsu and Kang Yen, "Optimizing Adaptive Linear Array Pattern by Phase-Position Perturbations" The 2nd International Conference on Information, pp. 56-59, July 24-28, 2002.
9. J. S. Pan, F. R. Mclnnes and M.A. Jack, "Codebook Design Using Genetic Algorithms" IEE Electronics Letters, Vol. 31, No. 17, pp.1418-1419, 1995.
10. D. E. Golderg, "Genetic Algorithms in Search Optimization and Machine Earning", Addison-Wesley publishing Company, 1989.
УДК 621.355.1.035.32
РАДИОФИЗИЧЕСКИЙ ПОДХОД К ИЗМЕРЕНИЮ СКОРОСТИ ГАЗОВЫДЕЛЕНИЯ В СВИНЦОВО-КИСЛОТНЫХ АККУМУЛЯТОРНЫХ БАТАРЕЯХ
В.А.Дзензерский, С.В.Плаксин, И.И.Соколовский
Запропонований рад1оф1зичний метод контролю газов-udi-лення в свинцево-кислотних акумуляторах, заснований на 3Miii розnодiлу електричного поля в хвилеводнш електро-динамiчнiй системi, що мiститъ стабiлiзований наniвnровiд-никовий ганновсъкий генератор. 1нформащя про швидкiстъ газовидiлення дозволяе ощнити мiру саморозряду i стутнъ зарядженностi акумуляторноЧ батареЧ, оnтимiзувати режим заряду акумуляторноЧ батареЧ.
Предложен радиофизический метод контроля газовыделения в свинцово-кислотных аккумуляторах, основанный на изменении распределения электрического поля в волноводной электродинамической системе, содержащей стабилизированный полупроводниковый ганновский генератор. Информация о скорости газовыделения позволяет оценитъ меру саморазряда и степенъ заряженности аккумуляторной батареи, оптими-зироватъ режим заряда аккумуляторной батареи.
The radiophysical method of control of gassing in the lead-acid accumulators, based on the change of distribution of the electric field in the waveguide electrodynamic system containing the stabilized semiconductor Gann-generator, is offered. Information about the gassing rate allows to estimate the measure of self-discharge and degree of charge of accumulator battery, to optimize the mode of charge of accumulator battery.
ВВЕДЕНИЕ
Одной из причин снижения ресурсных характеристик свинцово-кислотных аккумуляторных батарей (стартер-ных, стационарных, тяговых) является чрезмерный разряд и неконтролируемое время нахождения их в разряженном состоянии. Чрезмерный разряд при этом может быть связан как с условиями эксплуатации батарей, так и с саморазрядом. Саморазряд батарей проявляется при хранении их на складе или при длительных перерывах в их эксплуатации. Под саморазрядом подразумевают потерю емкости аккумуляторной батареи с разомкнутой цепью, и происходить он может за счет токов утечки по поверхности батареи, смоченной электролитом, между выводами токоведущих мостиков, за счет токов утечки системы электропитания транспортного средства, а также за счет определенных физико-химических механизмов в аккумуляторе, включающих анодную реакцию ионизации металла и катодный восстановительный процесс. С точки
зрения термодинамики причина саморазряда (и коррозии металла токоотвода) обусловлена термодинамической неустойчивостью металлического свинца и диоксида свинца при работе их в качестве электродов аккумулятора. РЬ02-электрод располагается в зоне термодинамической
неустойчивости воды диаграммы Пурбе (Е0= +1,629 В) и взаимодействует с водой с выделением кислорода. РЬ -электрод также расположен в зоне термодинамической
неустойчивости воды (Е0= -0,356 В) и должен взаимодействовать с водой с выделением водорода. И в этом смысле саморазряд свинцово-кислотных аккумуляторов и сопряженное с этим газовыделение является неизбежным. Контроль скорости газовыделения является поэтому важной процедурой, так как позволяет прогнозировать меру саморазряда и степень заряженности аккумуляторной батареи без контрольных измерений.
Кроме того, в реальных условиях у всех металлов, являющихся добавками или встречающихся в качестве примесей в сырье аккумуляторных электродов, значение водородного перенапряжения ниже, чем на чистом свинце. Снижение энергетического барьера процесса 2Н+ + 2е ® Н2 повышает скорость реакций РЬ - 2е + + S0-2 ® РЬ80^ , то есть скорость выделения водорода прямо связана с коррозией. Поэтому разработка надежного метода контроля темпа газовыделения будет способствовать выявлению добавок, повышающих коррозию, и облегчит поиск иных добавок, снижающих коррозию.
1 МОТИВАЦИЯ РАЗРАБОТКИ ИЗМЕРИТЕЛЯ СКОРОСТИ ГАЗОВЫДЕЛЕНИЯ
Имеется еще один мотив для проведения исследований по обеспечению надежных измерений скорости газовыделения. Как указывалось выше, саморазряд и коррозия отрицательного электрода связаны с взаимодействием растворенного в электролите кислорода со свинцом:
Pb + ;-o2 + h2so4 ® PbSO4 + h2o
