改良式基因演算法在適應性無限脈衝響應主動式噪因控制之研究

行政院國家科學委員會補助專題研究計畫成果報告

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※ 改良式基因演算法在適應性無限脈衝響應主動式噪音控制之研究※

※ Adaptive IIR Active Noise Control using Memetic Algorithm

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行政院國家科學委員會專題研究計畫成果報告

改良式基因演算法在適應性無限脈衝響應主動式噪音控制之研究

Adaptive IIR Active Noise Control using Memetic Algorithm

計劃編號: NSC 90-2213-E-151-009

執行期間: 90 年 08 月 01 日至 91 年 7 月 31 日止

主持人: 蘇德仁 教授 國立高雄應用科技大學

研究助理人: 盧建余 趙珮如 石文傑 張懷陽

Abstract

Genetic Algorithm (GA) has been shown to be optimization algorithm for an active noise control (ANC) with infinite impulse response (IIR) filter structure. But there exist some disadvantage in genetic algorithms such as premature convergence and long convergence time. In this paper, we present a method called Memetic Algorithm (MA) to solve active noise control with adaptive IIR problem and improve its convergence time successfully. Computer simulation is given to demonstrate the effectiveness of the proposed method.

Keywords：Genetic Algorithm, Memetic Algorithm,

Infinite Impulse Response, Active Noise Control

1. Introduction

Acoustic noise problems are more and more evident as increased numbers of industrial equipment such as engines, blowers, transformers, fans and compressors[1]. The active noise control system was first proposed in 1936 by Lueg[2], used an artificial signal to cancel the acoustic noise. Active noise control involves an electroacoustical or electromechanical system that cancels the source (unwanted) noise based on the principle of superposition, specially, an anti-noise of equal amplitude and opposite phase is generated and combined with the source noise, thus resulting in the cancellation of noises [3].

Conventional ANC's control structures are finite impulse response (FIR) filters and their control algorithms are stochastic gradient algorithms such a filtered-x least mean square (FXLMS)[4]. Up to now, various adaptive algorithms have been proposed for adaptive filtering. The "adaptive" notion derives from the people desire to emulate living systems found in nature, which adapts to their environments in various

ways. According to this direction, several researchers have proposed adaptive algorithms for digital filtering, which are all based on the Darwinian concept of "natural selection"[5]. Mayyas[6]and Yim et al.[7] propose IIR filter as controller structure to reduce computational complexity and genetic algorithm as adaptation mechanism to solve local minimum and eigenvalue disparity problems.

s

In this paper, we present Memetic Algorithm to solve wide variety of active noise control with adaptive IIR problem and improve its convergence speed. MA is the combination of improvement procedures which are combining a hill-climber local search heuristic and genetic algorithm.

Genetic algorithms are well known in many disciplines for their efficient optimization capabilities[8]. Sundaralingam and Sharman[9] presented a computationally efficient adaptive IIR filtering approach for a number of DSP applications. Yim et al.[10] presented an IIR controller whose adaptation mechanism was based on genetic algorithm. Proposed genetic based active controller can be learned by one sample set per generation, but there exist some disadvantage in genetic algorithms such as premature convergence and long convergence time.

The term 'Memetic Algorithm' was introduced by Moscato and Norman[11]. A formal study has been presented by Radcliffe and Surry [12]. Memetic algorithms use local improvement procedures as part of the evaluation of individuals. For many problems there exists a well-developed, efficient search strategy for local improvement, e.g., hill-climber for optimization. These local search strategies compliment the global search strategy of the genetic algorithm, yielding a more efficient overall search strategy.

2. Active Noise Control with Adaptive IIR

Filter

Traditionally, adaptive signal processing has been carried out using FIR filters. The property of their mean square error surfaces allows adaptive algorithms based on gradient search techniques to be applied. Additionally, stability of the FIR filter can be

Σ

e(n)

d(n)

+

Noise

Source Unknown _Plant

Adaptive IIR Filter Memetic Algorithm y(n) x(n)

_

Fig 2：ANC System with a Adaptive

Memetic Algorithm

Using this structure, it is possible to use one sample set to learn one generation. The sample set is independent of population size.

The unknown plant uses uniformly distributed white noise as the input for simplicity, while the adaptive system whose coefficients are updated by memetic algorithm.

In adaptive filtering, we proposed the MA to automatically determine the adapting probabilities for allele exchange of uniform crossover was investigated by White and Oppacher in [19].

The adaptive technique for computing the data associated with each operator is as follows:

(

)

(

)

, 1 , max max P P c else f ave f f indi f P c then f ave f indi if = − − = ≥ (7) where is individual fitness value, is average fitness value of the population, is maximum fitness value of the population, and is the last probability of crossover.

f_indi f_ave

f_max P1 The procedure of adaptive MA for ANC system is shown as follows:

(a) Initial population: Given a fixed IIR structure initialized the filter coefficients by some small real random numbers.

(b) Acoustic signal acquisition.

(c) Calculation the system error by equations

(1) and (5).

) (n e

(d) If less than the tolerance, then stop, otherwise update filter coefficients.

) (n e

(e) Mutation and crossover of controller coefficients. (f) Adaptive search by equation (7).

(g) Local search(hill-climber). (h) Check the ending conditions. (i) If satisfied then end; else go to (b).

The structure of the procedure for hill-climber is given as follows:

{

}

; ; : ); ( : ) ( ; ) ( ) ( ); ( : ) ( ); ( : ); ( : ) ( : ) ( ; : : lim ' ' ' ' ' ' end e e impossible is extension until e q e q e e then e q e q if e quality e q e extension e repeat e quality e quality e q solution initial e e e ber C Hill procedure loc loc loc loc loc loc o = = = > = = = = = =

5. Simulation Result

The memetic algorithm has been used here for adaptive IIR filtering to improve the performance of the genetic algorithm. We restrict ourselves to the synthesis of second-order IIR structures with the transfer function z a z a z b z b b z H ₂ 2 1 1 2 2 1 1 0 1 ) ( ₋− ₋− + + + + =

which can be used in cascade or in parallel for the realization of high-order transfer functions of order more than two. The unknown plant uses uniformly distributed white noise as the input.

The defining parameters for the MA are as follows : population size=20, probability of crossover =0.65, probability of mutation=0.008. The adaptive IIR filter is second-order (L=2; M=1) with

5 . 0 , 33 . 0 2 1= a = a andb0=2.3,b1=−1.7,b2=0.81. The

simulation is depicted in Figure 3. From Figure 3, it can be shown that the MA convergence to the optimal solution with residual error after the 150 generations.

Figure 3: Residual Error vs. Generations

The simulation in GA [11] shown that the GA can

convergence to the optimal solution after the 450 generations.

From Figure, we can find the MA has a merit of fast convergence than that proposed in GA [11].

6. Conclusion

In this paper, an approach for active noise control with adaptive IIR problem is presented. The approach is based on the combination of local search heuristics and genetic algorithm.

The simulation results indicate that an adaptive memetic algorithm approach to the IIR system shows some promise. The adaptive memetic algorithm takes fast convergence than that of genetic algorithm.

7. References

1. S. M. Kuo and D. R. Morgan, "Active Noise Control : A Tutorial Review", Proceedings of the IEEE, Vol. 87, No. 6, pp. 943-973, June, 1999.

2. P. Lueg, "Process of Silencing Sound Oscillations", U.S. Patent No. 2043416, June 9, 1936.

3. C. H. Hansen and S. D. Snyder, "Active Control of Noise and Vibration", London, U. K., E&FN Spon, 1997.

4. S. M. Kuo and D. R. Morgan, "Active Noise Control Systems: Algorithms and DSP Implementations. New York, Wiley, 1996.

5. R. Dawkins, "The Selfish Gene", Oxford University Press, 1976.

6. K. Mayyas and T. Abolnasr, "A Globally Convergent Modified OE IIR Adaptive Filter for Sufficient Modeling ", IEEE ICASSP'98, pp. 1729-1732, May, 1998.

7. Kook Hyum Yim, Jong Boo Kim, Tae Pyo Lee and Soo Ahn Doo, "A Genetic Learning Active

Controller", Automation, Robotics, pp.115-118, March, 1999.

8. D. E. Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison-Wesley Publishing Company, 1989. 9. S. Sundaralingam and K. C. Sharman, "Genetic

Evolution of Adaptive Filters,'' Proceedings of DSP-97, London, pp. 47-53, December 1997. 10. Kook Hyum Yim, Jong Boo Kim and Tae Pyo

Lee, "A Genetic Based Control Structure for Active Control", Proceedings of the IEEE Inter. Symposium on Intelligent Control/Intelligent Systems and Semiotics, pp. 381-386, Sep. 1999. 11. P. Moscato and M. G. Norman," A 'Memetic'

Approach for the Travelling Salesman Problem-Implementation of a Computational Ecology for Combinatorial Optimization on Message-Passing Systems", Proceedings of the International Conference on Parallel Computing and computer Applications, IOS Press, 1992. 12. N. J. Radcliffe and P. D. Surry, "Formal

Memetic Algorithms", Lecture of computer science, Springer Verlag, 1995.

13. S. J. Flockton and M. S. White, "The Application of Genetic Algorithms to Infinite Impulse Response Adaptive Filters", IEE Colloquium Digest1993/039, pp. 9/1-9/4, 1993. 14. John J. Shynk, "Adaptive IIR Filtering", IEEE

ASSP Magazine, Vol. 6, No. 2, pp.4-21, 1989. 15. B. Freisleben and P. Merz., "A Genetic Local

Search Algorithm for Solving Symmetric and Asymmetric Travelling Salesman Problems", Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 616-621, IEEE Press, 1996.

16. Joshua D. Knowles and David W. Corne, "M-PAES: A Memetic Algorithm for Multi-objective Optimization", Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 325-332, Vol. 1, July, 2000.

17. P. Moscato, "Memetic Algorithms: A Short Introduction", In D. Corne, F. Glover and M. Dorigo, editors, New Ideas in Optimization, pp. 219-234. McGraw-Hill, 1999.

18. W. J. Shyr, B. W. Wang, T. J. Su and T.L. Kang, "Evolutionary Approach to Multiobjective Problems using Adaptive Memetic Algorithm", Proceedings of the first international congress on autonomous intelligent systems (ICAIS 2002), pp. 7-11, Feb. 2002.

19. T. White and F. Oppacher, "Adaptive Crossover Using Automata", Proceedings of Third Conference Parallel Problem Solving from Nature (Lecture Notes in Computer Science, vol.866), Y. Davidor, H. P. Schwefel and R. Manner, Eds. New York: Springer-Verlag, pp. 229-238, 1994.