Effective System Identification Using Fused Network and DE Based Training Scheme

Transcription

1 International Journal of Soft Comuting and Engineering (IJSCE) ISSN: 3-37, Volume-3, Issue-3, Jul 3 Effective Sstem Identification Using Fused Network and DE Based Training Scheme Saikat Singha Ro, Joshri Das, Susovan Mondal Abstract Adative direct modeling or sstem identification finds extensive alications in telecommunication, control sstem, instrumentation, ower sstem engineering and geohsics. If the lants or sstems are nonlinear, dnamic, single-inut single-outut (SISO), the identification task becomes more difficult. The dnamic sstem identification task is basicall a model estimation rocess of caturing the dnamics of the sstem using the measured data. The Functional Link Artificial Neural Network (FLANN) is a single neuron single laer network first roosed b Pao. The structure of the FLANN is simle as it reresents a flat net with no hidden laers. Therefore the comutation and learning algorithm used in the architecture is straight forward. In the resent investigation the identification roblem is erformed on three standard benchmark nonlinear dnamic series-arallel models using Differential Evolution (DE) for training the weights of FLANN structure. The erformance of the roosed FLANN-DE identification model is comared with FLANN-Genetic Algorithm and FLANN-Back Proagation method. Index Terms Differential Evolution, FLANN, Genetic Algorithm, Sstem Identification. I. INTRODUCTION Identification of a nonlinear dnamic lant is a maor area in engineering toda. Sstem identification is widel used in a numerous alications like biological rocesses [], control sstem [], signal rocessing [3] and communication engineering []. Manractical sstems used in rocess control, robotics and autonomous sstem are nonlinear and dnamic in nature. To find a erfect model of these te of lants is a challenging task. There are certain classical arameterized models such as Winner-Hamarstein [5], Voltera Series [] and Polnomial identification model [7-8] which offer a reasonable recision, but the roblem with these methods is that the involve lot of comutational comlexit. Subsequentl, man neural network based models using multi-laer ercetion (MLP), radial basis function (RBF) and recurrent neural network. have been roosed for nonlinear sstem identification roblem. For basic neural network generall back roagation (BP) is used as an adative algorithm, to rovide better accurac. Earlier Nerandra and Parthasarath (99) [9] have emloed the multilaer ercetron (MLP) networks for effective identification and control of dnamic sstems like truck-backer-uer roblem []. Manuscrit received Jul, 3 Saikat Singha Ro, Electronics & Communication Engg.,CITM Boinch Hooghl, NIT Durgaore, India. Joshri Das, Radio Phsics, Universit of Calcutta, India. Susovan Mondal, Electronics & Communication Engg.,SIEM, Siligur India. However, the maor disadvantage of earlier methods is that, the emlo derivative based learning algorithm such as back roagation algorithm (BP), to train the sstem arameters which at times lead to local minima thereb leading to incorrect estimation. On the other hand the functional link artificial neural network (FLANN) is basicall a single laer structure in which nonlinear maing of the inut is achieved b exanding them with nonlinear functions. The genetic algorithm (GA) is one of the most oular oulation based stochastic search algorithm, insired b Darwin's theor of survival and is being used as a ver useful otimization technique in man fields.[-3]. In recent ast a romising variant of GA namel, the differential evolution (DE) has been roosed b Storn and Price [], which is also a oulation, based stochastic otimization [5]. The DE has roven to be suerior to other otimization algorithms [-9], in terms of convergence seed and robustness. It has also been used for man diverse alications such as digital filter design [], electromagnetics [], ower sstem [-3] and designing of arra antenna []. The literature surve reveals that the identification models need further imrovement in terms of achieving erformance accurac and architectural simlicit. These two issues have been addressed in this aer. Firstl a single laer nonlinear architecture incororating nonlinear maing of the inuts have been introduced as the back bone of the model. Secondl the feed forward as well as feedback arameters are roosed to be udated more accuratel with DE based learning rule. The aer has been organized into sections. In section a brief introduction of nonlinear identification scheme is resented. A low comlexit nonlinear architecture which serves as the backbone of the model is dealt in section 3. It also outlines the fundamental of DE algorithm and its variants which are used for training the weights of the model. Section rovides evolutionar algorithm like GA and DE. Section 5 rovides GA and DE based nonlinear sstem identification. Final section rovides simulation and results. II. NONLINEAR DYNAMIC SYSTEM IDENTIFICATION Sstem Identification is defined as the roblem of determining a mathematical model satisfing a set of inut-outut data. Once a sstem has been identified, its outut can be redicted for a given inut. Fig. shows an identification model of nonlinear dnamic lant. Where are inut to both the lant and the model and and ^( are the desired and estimated oututs at k th instant resectivel. The obective of the identification task is to minimize the error e( recursivel,, such that ^( aroaches the desired lant outut when same inut is alied to both the lant and the model. For mathematical evaluation, three tes of single-inut single-outut (SISO) lants [9] are described in difference equations ( to (3) are considered. 5

2 Effective Sstem Identification Using Fused Network and DE Based Training Scheme Each inut undergoes an nonlinear exansion and then alied to an adative linear combiner whose weights are udated b using adative algorithm. In [] trigonometric exansion has been roosed, because it has ielded better erformance for most of the alications. Accordingl in the roosed model sine and cosine exansions have been adoted. The exanded vector V( of is written as follows: Fig. Block diagram of nonlinear sstem identification Te-I: ( Te-: n ( a (k ) g[,k,...k m ] i ( f[(k-,(k ),...(k n ] b i) i () Te-3 (3) ( f[ (k-,(k ),...(k n)] m i i Where, and ( are the inut and outut of the SISO lant resectivel at the k th time instant under the condition that m n. Here a i (i n- and a i (i m- are the arameters of the feed forward and feedback aths of the lant. In addition f(.) and g(.) reresent the nonlinear function associated with the outut. The error signal obtained b the difference between lant and model oututs as well as the outut information are used b a suitable learning algorithms to train the weights of the model so that the squared error value rogressivel decreases to a minimum value as iteration roceeds. When the squared error attains a lowest value, training is stoed and the adative structure corresonding to the last weight vector reresents the desired identification model. III. DEVELOPMENT OF A NOVEL NONLINEAR IDENTIFICATION SCHEME Figure shows a single laered nonlinear structure roosed b Pao, which is caable of forming comlex decision regions b generating nonlinear decision boundaries [5]. In this structure, the nonlinear adative architecture inut dimension is increased b nonlinearl maing the inut atterns b using trigonometric functions. For nonlinear dnamic sstem identification, a similar structure has been roosed in [] in which the weights of the model are udated using a steeest decent algorithm. In order to identif dnamic lants a series-arallel scheme is emloed during training hase [9] where the feedback is taken from the lant outut instead of the model. A structure of a FLANN is shown in Fig.. m a k i) g[,k,...k m i V(=[,sin{π},cos{π}.sin{nπ},cos{nπ}] () = [v (,v (.v n (] T (5) If n numbers of sine and cosine exansions of inut samles are made and the first term is an unit inut then after exansion the total number of terms become N=n+There are a total of (n + numbers of terms in the inut vector. The weight vector related to the k th inut vector defined in () is given as: h( = [h (, h (, h (,. h n+ (] T () Hence the estimated outut of the identification model is comuted as: v(. h( (7) IV. EVOLUTIONARY ALGORITHMS A. Genetic Algorithm (GA) Genetic algorithm is a art of evolutionar comuting. GA was first introduced b John Holland and was later develoed b Goldberg and De Jong [7]. The Algorithm begins with an initial set of solutions (reresented b chromosomes) which are called as oulation. Solutions from one oulation are taken and used to form a new oulation. This is motivated b a hoe, that the new oulation will be better than the older one. Solutions which are then selected to form new solutions (offsring) are selected according to their fitness - the more suitable the are the more chances that the will reroduce. This is reeated until some condition (for examle number of oulations or imrovement of the best solution) is satisfied. Ideall, there are five hases in a GA rogram: initialization, selection, crossover, mutation and elimination. Flow grah for Simle Genetic Algorithm Fig. Structure of FLANN model

3 International Journal of Soft Comuting and Engineering (IJSCE) ISSN: 3-37, Volume-3, Issue-3, Jul 3 GA Oerators: Deending uon the alication, man individual solutions are created randoml to form an initial oulation, covering the entire range of ossible solutions (this is called as search sace). Each oint in the search sace reresents one ossible solution marked b its value (fitness). The crossover and mutation are the most imortant arts of the genetic algorithm which hels the algorithm to be traed in local minima. The erformance is influenced mainl b these two oerators. Crossover: In crossover recombination between two arent chromosomes is done to roduce offsring that contain some arts of both arents genetic material. A robabilit term, P c, is set to determine the oeration rate. Generall the robabilit of crossover is high. This is a determining factor that distinguishes the GA from all other algorithms. Mutation: Mutation oeration introduces variations into the chromosomes. This is a rocess of making a good chromosome bad and vice versa in terms of its fitness. This variation can be global or local. The oeration occurs occasionall (usuall with small robabilit P m ) but it randoml alters the value of a articular string osition. Each bit of a bit string is relaced b a randoml generated bit if a robabilit test is assed. Within a secific robabilit, certain digits are altered from either to or to in binar encoding. Selection: Finall the fitness (cost function) of original arents, offsring (children after crossover of selected arents) and mutated offsring are calculated. Again the best chromosomes are selected from the entire ools which are then treated as the arents of the next generation. The entire rocess continues till the global otimum is reached. B. Differential Evolution: Differential Evolution (DE) is a global otimization algorithm. It is used frequentl used in the field of numerical otimization roblem because it adats an encoding scheme with real valued number, instead of using binar encoding as was the case in GA. In DE, initiall some vectors which are ossible solution within a D-dimensional search sace are randoml created much like GA, then evolved over a time, to exlore the entire search area, thereb locating the minimum of obective function. The initial oulation is denoted b NP which is reresented as X (G), (i=,, (NP-) and ( =,, D) where i is the oulation, is the number of arameters and G is the generation to which the oulation belongs. STEPS IN DE: Initialization: The uer and lower bound of each arameter is to be secified before oulation initialization. Once initialization bounds have been secified, a random number generator assigns each arameter of ever vector a value from within the rescribed range. For an examle (G=) the value of a th arameter of an i th vector is x, () ) rand (,.( b, i, U, L L (8) Where U and L are uer and lower bound, for range notification. Mutation: After initialization DE mutates unlike GA where first crossover is done after initialization In mutation the difference of two randoml selected vectors are multilied b a constant factor and then added with a randoml selected vector from the oulation i.e. in DE a differential mutant oerator is used. Equation (9) shows how to combine three different, randoml chosen vectors to create a mutant vector; V (G+: ( G x ( G) F.( x ( G) x ( )) (9) v r, r, r3, G This te of mutation is called as de/rand/. There are certain other formats of creating the mutant vector. DE mutation strategies like de/rand/, de/best/, de/best/ and de/current to best/ which are as described follows: ( ( V (G + = X (G) + F.(X (G) + X (G) - X (G) - X (G)) best, r, r, r3, r, () V (G + = X (G) +.(X (G) - X (G)) F.( X (G) - X (G)) best, r, r, (3) The scale factor, F is a ositive real number which controls the rate at which the oulation evolves. While there is no uer limit on F, effective values are seldom greater than. In our simulation we used de/best/ mutation strateg. Crossover: Now trail vector U (G+ is created using crossover oerator: u V (G + = X (G) + F.(X (G) + X (G) - X (G) - X (G)) r5, r, r, r3, r, V (G + = X (G) best, ( G v x ( G if rand (, ( G) if rand (, CR or CR or () The crossover robabilit, C r [,], controls the fraction of arameter values that are coied from the mutant. In crossover if the value of the randoml generated number is less than C r then the trial arameter is inherited from the mutant, V, otherwise it is coied from x. Selection: If the obective function value of the trial vector, U, has an equal or lower than that of its target vector, X, it relaces the target vector in the next generation; otherwise, the target retains its lace in the oulation for at least one generation. x ( G u x ( G) if ( G) F.( X (G) - X (G)) r, r3, f(u otherwise f(x V. GA AND DE BASED NONLINEAR SYSTEM IDENTIFICATION A. GA based Nonlinear Sstem Identification: (5) Sstem Identification on a nonlinear dnamic sstem using FLANN as structure and GA as udate algorithm is carried out according to these following stages: Ste : Initialization of Parameter. N= Initial oulation. P m = Mutation robabilit. S= Selection rate. ) rand ) rand 7

4 Effective Sstem Identification Using Fused Network and DE Based Training Scheme Ste : n uniforml distributed random signals over the interval [-, ] are generated and alied to the actual nonlinear dnamic sstem and to the adative model simultaneousl. This serves as the inut to both the sstem and the adative model. In the resent investigation a series arallel identification model is used. Ste 3: The lant s outut serves as the desired outut. The estimated outut is obtained from adative model b using equation (7). Ste : Each of the desired outut is comared with the corresonding estimated outut and thus n numbers of errors roduced. Ste 5: For each i th weight vector the mean square error (MSE) is calculated b using the following fitness function: MSE( i) n i e ( n, i) / n () Ste : Random oulation of n chromosomes (suitable solutions for the roblem) is then generated. Ste 7: The fitness of each chromosome in the oulation is evaluated. Ste 8: New oulation is then created b reeating following stes until the new oulation is comlete. Ste 9: Two arent chromosomes are selected from the initial oulation according to their fitness (the better fitness, the bigger chance to be selected). Ste : With a crossover robabilit, the arents are crossed over to form new offsring (children). If no crossover is erformed, offsring is the exact relica of the arents. Ste : With a mutation robabilit new offsring at each locus (osition in chromosome) are mutated. New offsring are then laced in the new oulation. Ste : After each iteration minimum of MSE (MMSE) is calculated which shows the learning behavior of the adative model. Ste 3: Use newl generated oulation for a further run of the algorithm. If the end condition is satisfied then sto the rocess and return the best solution in current oulation. B. DE based Nonlinear Sstem Identification: Ste : Initialize the arameter used in DE: N = Select the total number of oulation F = Select the scale factor which controls the rate at which the oulation evolves. CR = Initialize it with some constant value, which selects whether the new oulation is coied from the trial vector or from the target vector. D = number of arameters of the FLANN model is to be otimized. G = number of generations. N = number of inut samles. Ste : n uniforml distributed random signals over the interval [-, ] are again generated and are alied to both the actual nonlinear dnamic sstem and to the adative model simultaneousl as we did in GA also. Here again the same series arallel identification scheme is used. Ste 3: The lant s outut serves as the desired outut and estimated outut is obtained from adative model using equation (7). Ste : Each of the desired outut is comared with the corresonding estimated outut and n numbers of errors are roduced. Ste 5: The mean square error (MSE) is calculated for each i th weight vector b using fitness function described in equation (). Ste : Three random vectors are selected from the initial oulation and a mutant vector is obtained b using equation (. Ste 7: Then it is checked whether the vector elements are within the search range or not. If it is not within the search range then bring it into secified search range. Ste 8: Generate a random number and comare this with Crossover Ratio (CR), initiall selected. Then using equation () obtains the trail vector. Ste 9: The estimated outut is obtained from the adative model b using this newl generated trail vectors. n numbers of errors are obtained b comaring the estimated outut with the desired outut. The MSE is then calculated from equation (). Ste : According to equation (5) oulation for next generation are selected from the trail vector or from the target vector and new oulation is created for next generation. Ste : After each iteration minimum of MSE (MMSE) is calculated which shows the learning behavior of the adative model. Ste : Using the new generation the stes from to are reeated. If the end condition is satisfied then sto the rocess and return the best solution in the current oulation. VI. SIMULATION AND RESULTS For nonlinear dnamic lants described b difference equation in (, () & (3), extensive simulation studies have been carried out. In this investigation a series-arallel model is used along with DE for training the weights of FLANN structure. The erformance of the roosed FLANN-DE identification model is then comared with FLANN-GA and FLANN-BP methods. In FLANN-BP model an uniforml distributed random signal over the interval [-, ] is used as inut, and 5, iterations are carried out for training. The testing is analzed barallel scheme. The inut to the identified model is given as (7) Normalized mean square error (NMSE) [8] is used, for comarison of two models. s NMSE [ (8) ( ( ] s k Where σ is the variance of desired signal and s is the testing samle. A. Identification of SISO dnamic sstems Examle : In this examle, the lant to be identified is of model- te and is reresented b the difference equation [9] as follows: (9) Where unknown nonlinear function g (.) are given b NL-: sin / 5).8sin / 5) g (x).3(.sin( x) For k 5.sin / 5).( k.3sin(3 x) g[ ] For k > 5.sin(5 x) () 8

5 Oututs Oututs Oututs Oututs Oututs Oututs International Journal of Soft Comuting and Engineering (IJSCE) ISSN: 3-37, Volume-3, Issue-3, Jul 3 NL-: 3 g.x.x 3.x. (x) 5 3.x.8x.x.x NL-3: 3. 3(x).5sin ( x).cos( x) x. g 3 ( () To identif the lant a series-arallel model is used which is described b following difference equation (8) N[] is FLANN-BP, FLANN-GA or FLANN-DE model. The FLANN inut is exanded to ten terms for NL- () and eleven terms for NL- ( and NL-3 () resectivel. In FLANN-GA model training is done for 5 iterations. The mutation robabilit (P m ) and selection rate (S) are chosen to be.5 and.5 resectivel. In DE, CR=.5, F=.5, number of generations = 5 and DE/best/ scheme is used for mutation. Both the convergence arameter µ and the momentum factor η are chosen to be. for FLANN-BP. The results of identification of (9) with nonlinear function (), ( and () are shown in Fig.3, Fig. and Fig.5 resectivel (a) FLANN-BP (exansion - -.3(.( k (a) FLANN-GA (exansion N[ ] (a) FLANN-DE (exansion Fig.3 Comarison of outut resonse of examle- using nonlinearit defined in () (a) FLANN-BP (exansion (b) FLANN-GA (exansion (c) FLANN-DE (exansion Fig. Comarison of outut resonse of examle- using nonlinearit defined in ( 9

6 Oututs Oututs Oututs Oututs Oututs Oututs Effective Sstem Identification Using Fused Network and DE Based Training Scheme (a) FLANN-BP (exansion (b) FLANN-GA (exansion FLANN inuts are exanded to 9 terms using trigonometric exansion. The resonse of the examle is shown in Fig.. From these results it is evident that FLANN-DE method gives accurate identification of the resent sstem. From these result it is observed that FLANN-DE identification model gives better result than FLANN-GA and FLANN-BP model. From table-i it is also evident that FLANN-DE aroach gives lower NMSE than the other identification model (a) FLANN-BP (exansion 9) (c) FLANN-DE (exansion Fig.5 Comarison of outut resonse of examle- using nonlinearit defined in () Examle : In this examle the lant to be identified is of model- te [9] and is reresented b the difference equation: (3) f [ (, ] The unknown nonlinear function f(.) is given b ((k -(( -.5)(( -.) f((x), (k -). ( To identif the model a series-arallel model is used (k N( ( () (5) Here value of µ and η are set as.5 and. resectivel for FLANN-BP. All the arameters in FLANN-GA and FLANN-DE models are same as used in examle-. The ) (b) FLANN-GA (exansion 9) (c) FLANN-DE (exansion 9) Fig. Comarison of outut resonse of examle- Examle 3: In this case the lant is of model-3 te [9] and reresent b the difference equation: () f [ ( ] g[ ]

7 Oututs Mean Square Error (MSE) Oututs Mean Square Error (MSE) Oututs International Journal of Soft Comuting and Engineering (IJSCE) ISSN: 3-37, Volume-3, Issue-3, Jul 3 Where f( ) and g() is nonlinear function and is given b ( 3) f() and (7) g( x) x.8)( x The identification model of equation () is as follows: (8) (9) Where N and N is FLANN-BP, FLANN-GA or FLANN-DE model. N and N contain 7 and 5 exansion resectivel for FLANN-BP, FLANN-GA and FLANN-DE models. The arameters for GA and DE are retained same as was in examle-. For BP, convergence and momentum arameter is chosen as.. The result of identification is shown in Fig.7 where it is observed that FLANN-DE model shows better result than other two identification models ) ( k N[ ( ] N[ ] (a) FLANN-BP (exansion ) (b) FLANN-GA (exansion ) This is the comarison table of three identification model for three nonlinear dnamic sstems with resect no NMSE defined in (8). Examle Exansions NMSE in db FLANN- BP FLANN- GA FLANN-D E Ex-with () Ex- with ( Ex- with () Ex Ex Table-I: Comarison of NMSE of different examles Further, we have also investigated on the convergence attern of various variants of DEs. The various variants of Des are described in equation (, (, () and (3). For examle- the convergence of various variants of DEs is lotted in figure-8. Similarl, in figure-9 and figure- the convergences of various DEs are lotted for examle- and examle-3 resectivel. From the convergence grahs (Fig.8, Fig.9 and Fig. we conclude that for examle- and examle- DE/best/ erforms best, but for examle-3 DE/current to best/ shows better results DErand DErand DEbest DEbest DE current to best Iteration Fig. 8: Comarison of different DE strategies for examle DE/rand/ DE/rand/ DE/best/ DE/best/ DE/current to best/ (c) FLANN-DE (exansion ) Fig.7 Comarison of outut resonse of examle Iteration Fig. 9: Comarison of different DE strategies for examle-

8 Mean Square Error (MSE) Effective Sstem Identification Using Fused Network and DE Based Training Scheme.8... DE/best/ DE/best/ DE/rand/ DE/rand/ DE/current to best 8 8 Iteration Fig. : Comarison of different DE strategies for examle-3 VII. CONCLUSION In the resent investigation, the identification roblem is erformed on three standard benchmark nonlinear dnamic series-arallel models. From the simulation stud it is evident that FLANN-DE rovides accurate identification for nonlinear dnamic models. When comared to FLANN-GA and FLANN-BP the FLANN-DE identification model gives better results. From table-i it is also evident that FLANN-DE aroach gives lower NMSE than the other two identification models. From the convergence grahs (Fig.8, Fig.9 and Fig. we can conclude that for examle- and examle- DE/best/ erforms well but for examle-3 DE/current to best/ shows better result. REFERENCES [] Y. Xie, B. Guo, L. Xu, J. L P. Stoica, Multistatic adative microwave imaging for earl breast cancer detection, IEEE Trans. Biomed. Eng. 53 (8) () [] S. Chen, S.A. Billings, Reresentation of non-linear sstems: the NARMAX model, Int. J. Control 9 (989) 3 3 [3] M. Adrad, A. Belouchran Estimation of multi comonent olnomial hase signals iminging on a multisensor arra using state-sace modeling, IEEE Trans. Signal Process. 55 ( (7) 3 5. [] H. Huiberts, H. Nimeier, R. Willems, Sstem identification in communication with chaotic sstems, IEEE Trans. Circuits Sst. I 7 () () [5] F. Dinga, T. Chenb, Identification of Hammerstein nonlinear ARMAX sstems, Automatica (5) [] M. Schetzmen, The Voltera and Winner Theories on Nonlinear Sstems, Wile, New York, 98. [7] E. Hernandez, Y. Arkun, Control of nonlinear sstems using olnomial ARMA models, AICHE J. 39 (3) (993). [8] T.T. Lee, J.T. Jeng, The Chebshev olnomial-based unified model neural networks for functional aroximation, IEEE Trans. Sst. Man Cbern. B 8 (998) [9] Narendra, K. S., & Parthasarath, K. Identification and control of dnamical sstems using neural networks, IEEE Transactions on Neural Networks, vol. no.,. 7, Mar. 99. [] Nguen, D. H., & Widrow, B. Neural networks for self-learning control sstem. International Journal of Control, vol. 5, no.,. 39 5, 99. [] M. Srinivas, L. M. Patnaik, Genetic Algorithm: A Surve, IEEE comuter, vol. 7, no.,. 7-, 99. [] D. B. Fogel, An Introduction to Simulated Evolutionar Otimization, IEEE Trans. On SMC., vol., no.,. [3] W. Atmar, Notes on the Simulation of Evolution, IEEE Trans. On SMC., vol., no.,. 3-7, 99. [] R. Storn and K. Price, Differential evolution A simle and efficient heuristic for global otimization over continuous saces, Journal of Global Otimization, vol.,.3-359, 997. [5] Vavak, F., Fogart, T. and Jukes, K A genetic algorithm with variable range of local search for tracking changing environments. In Proceedings of the th Conference on Parallel Problem Solving from Nature, 99. [] K. Price, R. M. Storn, and J. A. Laminen, Differential Evolution: A Practical Aroach to Global Otimization (Natural Comuting Series), st ed. New York: Sringer, 5, ISBN: [7] J. Vesterstroem and R. Thomsen, A comarative stud of differential evolution, article swarm otimization, and evolutionar algorithms on numerical benchmark roblems, Proc. Congr. Evol. Comut., vol., ,. [8] J. Andre, P. Siarr, and T. Dognon, An imrovement of the standard genetic algorithm fighting remature convergence in continuous otimization, Advance in Engineering Software 3,. 9,. [9] O. Hrstka and A. Ku cerová, Imrovement of real coded genetic algorithm based on differential oerators reventing remature convergence, Advance in Engineering Software 35,. 37,. [] R.Storn, Differential evolution design for an IIR-filter with requirements for magnitude and grou dela. Technical Reort TR-95-, International Comuter Science Institute, Berkele, CA 995. [] Qing, A.: Electromagnetic inverse scattering of multile erfectl conducting clinders b differential evolution strateg with individuals in grous (GDES). IEEE Trans. Antennas Proagate. 5(5), 3 9 (). [] Lakshminarasimman, L., Subramanian, S.: Hdrothermal otimal ower flow using modified hbrid differential evolution. Caledonian J. Engg. 3(, 8 (7a) [3] Lakshminarasimman, L., Subramanian, S.: Short-term scheduling of hdrothermal ower sstem with cascaded reservoirs b using modified differential evolution. IEE Proc. Gener. Transm. Distrib. 53(), 93 7 () [] Yang, S., Gan, Y.B., Qing, A, Sideband suression in time-modulated linear arras b the differential evolution algorithm, IEEE Antennas Wireless Proagate. Lett., ,. [5] Y.H. Pao, S. M. Phillis and D. J. Sobaic, Neural-net comuting and intelligent control sstems. Int. J. Conr., vol. 5, no.,.3-89, 99. [] Patra, J. C., Pal, R. N., Chatter B. N., & Panda, G. Identification of nonlinear dnamic sstems using functional link artificial neural networks, IEEE Transactions in Sstems Man and Cbernetics-Part B: Cbernetics, vol.9 no.,. 5, 999. [7] D.E Goldbareg, Genetic algorithms in search, otimization, and Machine learning. Reading, M A: Addison-Wesle, 989. [8] Gershenfeld, N. A., & Weigend, A. S., The future of time series: Learning and understanding. Time series rediction: Forecasting the future and ast. Reading, MA: Addison-Wesle, 993. SAIKAT SINGHA ROY did his Bachelors in Phsics in. Subsequentl, he did his M.Sc in Electronic Science in 8, from Vidasagar Universit and M.Tech in Communication Engg.in, from KIIT Universit. He is currentl the Head of the Deartment of Electronics & Communication Engg., CITM Boinch Hooghl, India. His research interests include Soft Comuting, Evolutionar Comutation and Pattern Recognition. JOYSHRI DAS did her Bachelors in Electronics & Communication Engg. in 7. Subsequentl, she did her M.Tech in Mechatronics in, from BESU, Sibur. She is currentl a facult of Electronics & Communication Engg., CITM Boinch Hooghl, India. Her research interests include Soft Comuting, Digital Signal Processing and Pattern Recognition. SUSOVAN MONDAL did his Bachelors in Electronics in. Subsequentl, he did his M.Sc in Electronic Science in 8, from Vidasagar Universit and M.Tech in Communication Engg.in, from KIIT Universit. He is currentl a facult of Electronics & Communication Engg., of SIEM, Siligur India.