APPLICATION OF RBF NEURAL NETWORK IMPROVED BY PSO ALGORITHM IN FAULT DIAGNOSIS

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1 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: APPLICATION OF RBF NEURAL NETWORK IMPROVED BY PSO ALGORITHM IN FAULT DIAGNOSIS 1 LIN CUI CAIYIN WANG 1 BAOSHENG YANG 1 School of Informaton Engneerng Suzhou Unversty Suzhou Anhu Chna School of Mechancal Electrc and Engneerng Suzhou Unversty Suzhou Anhu Chna ABSTRACT The current fault dagnoss methods based on conventonal BP neural networ and RBF neural networ exst long tranng tme slow convergence speed and low judgment accuracy rate and so on. In order to mprove the ablty of fault dagnoss ths paper puts forward a nd of fault dagnoss method based on RBF Neural Networ mproved by PSO algorthm. By usng partcle swarm algorthm s heurstc global optmzaton ablty the connecton weght values of RBF neural networ are optmzed. And then combned wth RBF neural networ s nonlnear processng ablty transformer fault samples are traned and tested. The expermental results show that compared wth conventonal fault dagnoss methods based on BP neural networ and RBF neural networ the method based on RBF Neural Networ mproved by PSO algorthm can effectvely avod the problems of RBF neural networ s nstablty RBF neural networ easly fallng nto local mnma and low correct dagnoss rate whch can effectvely mprove the convergence speed and the effcency of fault dagnoss. Keywords: Partcle Swarm Optmzaton Algorthm RBF Neural Networ BP Neural Networ Transformer Fault Dagnoss 1. INTRODUCTION Nowadays wth the ncreasng complexty of control system structure the fault dagnoss of nonlnear system has become a hot and dffcult problem n today's felds of fault dagnoss; transformer fault dagnoss s one of them. Because neural networ has the ablty of good self-learnng parallelsm strong fault tolerance and generalzaton ablty wthout needng a precse mathematcal model a set of nonlnear mappngs can be well acheved. Thus neural networs are wdely used n fault dagnoss. At present the two types of feed-forward neural networ Bacpropagaton (BP) neural networ and Radal Bass Functon (RBF) neural networ are wdely used n fault dagnoss. But tradtonal BP neural networ and ts mproved method have the shortcomngs of local optmal solutons slow tranng speed and low effcency and so on whch lmt the scope of applcaton of BP neural networ [1]. RBF neural networ can solve these problems. RBF neural networ has a hgher computng speed t can globally approxmate to a nonlnear functon wth arbtrary precson whch has been wdely used n many felds. However n practcal applcaton of fault dagnoss the output weght values center value and wdth of the hdden unt of RBF neural networ have a large mpact on ts performance. And parameters optmzaton algorthms of RBF neural networ gradent descent algorthm and genetc algorthm are not partcularly desrable n parameter optmzaton results []. Partcle Swarm Optmzaton (PSO) can be appled to solve the parameters optmzaton problem of RBF neural networ. PSO algorthm s a new fast optmzaton method whch has fast convergence rate hgh robustness and strong global search capablty and s easy to mplement etc [3]. PSO s used to optmze the RBF neural networ s connecton weght values whch not only can play the generalzaton ablty of RBF neural networ greatly but also can mprove the convergence speed and learnng ablty of RBF neural networ. In ths paper we propose the transformer fault dagnoss method based on RBF neural networ mproved by PSO algorthm whch maes full use of heurstcs and global optmzaton ablty of PSO algorthm. The total content percentage of ol dssoluton characterstcs gas n power transformers s regarded as RBF neural networ s nput. Output and nput varance of RBF neural networ are regarded as ftness functons. Through contnuous teratons the optmal soluton s fnally got whch s regarded as the nput and output layer connecton weghts and thresholds of RBF neural 68

2 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: networ. Compared wth BP neural networ and RBF neural networ the experments show that our proposed method can optmze the weghts and thresholds of RBF neural networ and can avod fallng nto local mnmal and nstablty whch can greatly mprove the learnng effcency of RBF neural networ.. PARTICLE SWARM OPTIMIZATION ALGORITHM Partcle swarm optmzaton (PSO) algorthm s a swarm ntellgence optmzaton algorthm ntroduced by Amercan psychologst James Kennedy and electrcal engneer Russell Eberhart n 1995[4].The basc dea of PSO algorthm stems from smulaton of the behavor of brds predaton and PSO s an optmzaton algorthm whch utlzes the cooperaton and competton of the groups partcles to produce the optmal soluton. When solvng optmzaton problems PSO algorthm regards the soluton of each problem as search space of a brd called a partcle. Each partcle has a ftness value determned by the optmzed functon and has a velocty to decde ts flyng drecton and dstance. Partcles follow the current optmal partcle for searchng n the soluton space. PSO algorthm frst ntalzes a group of random partcles (random soluton) and then fnds the optmal soluton by teraton. Durng each of teraton partcles update ther own by tracng the two extremums. The frst extremum s the optmal soluton found by the partcle tself whch s regarded as ts ndvdual best poston; another extremum s the optmal soluton found by entre swarm whch s noted as the global best poston [5]. The mathematcal model of PSO algorthm s descrbed as followngs: Suppose that the partcle populaton sze s N the goal search space s D- dmensonal. The poston vector of the -th partcle n D-dmensonal space x = ( x x x x ) each x s 1 D represents a potental feasble soluton of search space. When puttng x nto the target functon ts ftness value can be calculated whch can be used to judge whether the partcle s good or not. The flght speed of the -th partcle s represented as a vector v = ( v 1 v v vd ). The ndvdual best poston searched out by PSO s P = ( P P P P ) and the global 1 D best poston searched out by the entre partcle swarm s Q = ( Q 1 Q Q QD ). When fndng out two best values P and Q each partcle updates ts own speed and locaton accordng to the followng formulas. Iteratve formula s as follows: P t + 1 xt + 1 f( xt + 1 ) < f( Pt ) = Pt else (1) v = t 1 ωv + t cr 1 1 ( P t xt ) + cr ( Q + t xt ) () x = x + v (3) t + 1 t t + 1 Where c 1 s a cogntve acceleraton factor to adjust the step length of flght drecton of ndvdual optmal partcle c s a socal acceleraton factor whch s used to adjust the step length of flght drecton of the global optmal partcle. r 1 and r are two random numbers between zero and one and addng randomness maes search space be enlarged. vt and x t respectvely denote the speed and poston of the - th partcle of the -dmensonal n the t-th teraton Pt and Q t respectvely denote the ndvdual and global best poston of the -th partcle of - dmensonal space n the t-th teraton. ω s the nerta factor whch can control the search speed and mae partcles converge to local mnma qucly and then get the fnal soluton through local search. The updated formula of nerta factor ω s as follows: ω = ω ( ω ω ) t/ T (4) max max mn max 3. STRUCTURE ANALYSIS OF RBF NEURAL NETWORK In 1998 Broomhead and so on ntroduced Radal Bass Functon (RBF) neural networ. RBF neural networ s a feed-forward and bac-propagaton neural networ ncludng an nput layer a hdden layer and an output layer [6]. The networ structure s shown n Fgure 1. Nodes of the nput layer smply pass nput sgnals to the hdden layer the hdden layer neurons produce nonlnear mappng by usng radal bass functon and output layer neurons execute lnear weghted combnaton to the output of the hdden layer. 69

3 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: x 1 x x n Input Layer h 1 W h m Hdden Layer Output Layer Fgure 1: The Structure Of RBF Neural Networ y 1 y y q As shown n Fg 1 X = [ x1 x x ] T n s an n- dmensonal nput vector H = [ h1 h h ] T m s a radal bass drecton vector of RBF networ whch represents the output of the hdden layer unt and usually s expressed by usng Gaussan functon whch s gven by: X C h ( x) = exp = 1 m (5) b Where C represents the center of the -th bass functon b represents the wdth of the -th bass functon and b s a number greater than zero s the Eucldean norm m represents the number of nodes of the hdden layer. W = [ w1 w w ] T m s a weght vector of RBF networ. The output of RBF neural networ s lnear combnaton of the output of the hdden layer nodes whch s expressed as: y( x) = Wh( x) (6) = 1 q Where = 1 q. q s the number of nodes of the output layer. W represents the connecton weght values between the -th hdden layer nodes and the -th output nodes. Two categores of parameters need to be determned n RBF neural networ [7]: the frst category parameters are the center C the wdth b and the number of centers n of radcal bass functon; another category parameters are connecton weght values between the output layer and the hdden layer. After the center C the wdth b and the number of centers n of radcal bass functon are determned we can obtan the connecton weght values between the output layer and the hdden layer by usng the least squares method. Therefore determnng C b and n of radcal bass functon s the ey to establsh neural networ. RBF 4. STEPS OF PSO OPTIMIZING RBF NEURAL NETWORK Now we understand that RBF neural networ's performance manly depends on the center and the wdth of radcal bass functon of the hdden layer and the weght values of the output layer. Tradtonal RBF neural networ learnng strategy has sgnfcant drawbacs whch only fnds the optmal soluton n local space to determne the networ structure parameters. If these parameters are set ncorrectly t would cause declne n the approachng accuracy and even produce networ dvergence [8]. PSO algorthm has fast convergence speed strong global search capablty and does not requre gradent nformaton and so on whch can mprove convergence speed and stablty of RBF neural networ. Therefore n ths paper we utlze PSO algorthm to optmze the tradtonal RBF neural networ learnng strategy. The learnng process based on RBF neural networ mproved by PSO s descrbed as followngs: (1) Pretreatment the transformer's orgnal fault data sample. The collected raw data are dvded nto two parts tranng set and test set. Tranng set s used to create a fault model; test set s used to verfy the valdty of the model. () Utlze RBF neural networ to learn the tranng set. Durng the learnng process usng PSO to optmze parameter the parameter optmzaton process s as follows: (a) Intalze partcle swarm and RBF neural networ. The populaton sze N search space dmenson D and acceleraton coeffcents c 1 and c of partcle swarm should be determned. Accordng to the formula () (3) and (4) partcle velocty v 1 poston x 1 and nerta factor ω are also ntalzed. The maxmum value of speed and the maxmum value of poston are set to meet Vmax = Xmax. The mnmum error and the maxmum number of teratons T are also decded. RBF neural networ should also be ntalzed ncludng the numbers of nput and output and the number of centers of radcal bass functon. The center C the wdth b and the number of centers nodes n of radcal bass functon are combned nto a partcle. 70

4 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: (b) Select the ndvdual best poston of each partcle P and the global best poston of partcle swarm Q. Indvdual ftness value of each partcle s calculated accordng to the formulas (1) and (3).The nertal factor ω s updated accordng to the formula (4). Accordng to the formula () and (3) speed and poston are also updated. Judgng whether the partcle velocty and poston exceed the maxmum value f exceed the maxmum value the partcle velocty and poston should be adjusted. (c) Judge whether to arrve at the maxmum number of teratons or meet the requrements of the mnmum error f t s the teraton should be stopped. The global optmal values are regarded as weghts and thresholds of RBF neural networ otherwse return to (b). (d) The decoded value of the best poston experenced by partcle swarm s looed upon as the structural parameters of RBF neural networ then tranng samples are traned and ther mean square error on tranng set are calculated out. (e) Evaluate search poston of each partcle accordng to the mean square error to fnd the optmal parameters and establsh the optmal model of RBF neural networ. (3) Utlze the establshed RBF neural networ model to execute fault dagnoss to the test set and lastly obtan dagnoss results. Specfc learnng process s shown n Fgure. 5. SIMULATION VERIFICATION 5.1 Expermental Prncple Consultng the relevant references[9]-[10] we now that accordng to the cause of faults and the extent of the damage of transformers the common transformer faults can be dvded nto fve types that are normal low-md temperature overheatng (low temperature overheatng md temperature overheatng) hgh temperature overheatng low energy dscharge and hgh energy dscharge. When varous transformers faults happen H CH 4 C H 6 C H 4 and C H n transformer ol share of dfferent ngredents thus we can determne what nd of fault occurs accordng to the gases decomposton n transformer ol. 5. Expermental Data and Parameters To verfy the effectveness of our proposed method based on RBF neural networ mproved by PSO algorthm (PSO-RBF) we adopted fault samples of Reference [11] as the expermental data set. Among 150 fault data samples the top 100 were used for tranng; the last 50 were used to test. Tranng samples were processed and the processng results are shown n Table 1. Input varables X ( = 1 5) respectvely represent the percentage of the total gas content occuped by the content of H CH 4 C H 6 C H 4 and C H. The output fault types Y ( = 1 5)respectvely denote normal low-md temperature overheatng hgh temperature overheatng low energy dscharge and hgh energy dscharge. As can be seen from Table 1 there s a complex nonlnear relatonshp between the composton of gases dssolved n transformer ol and fault types. Table 1 : The Orgnal Fault Samples No. X 1 X X 3 X 4 X 5 Y 1 Y Y 3 Y 4 Y Fg : Flow Chart Of Establshng The Optmal RBF Neural Networ Model 5.3 Smulaton Results and Analyss Under the Wndows XP operatng system usng Matlab 007 toolbox PSO algorthm was used to tran RBF neural networ wth tranng sample. 71

5 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: Frstly RBF neural networ model was ntalzed the number of nput varables 1 and the number of output fault types are both 5 the number of centers of radcal bass functon n s equals to 10. The populaton sze of Partcle Swarm N s equals to 30 the number of parameters to be optmzed D= n+ n+ n+ = D s search space dmensons the acceleraton coeffcent c 1 = c =.0 the nerta factor s 0.71 the speed and poston of the maxmum value were set to meet Vmax = X and the maxmum number of max teratons were set to T = 000. Tranng results are shown n Fgure 3. Fg 3: Tranng Error Curve Of PSO-RBF Neural Networ To verfy the effectveness of our proposed PSO- RBF algorthm adoptng the same fault samples we respectvely traned and tested the conventonal RBF neural networ and BP neural networ. Tranng results are shown n Fgure 4 and Fgure 5. Fg 4: Tranng Error Curve Of RBF Neural Networ Fg 5: Tranng Error Curve Of BP Neural Networ As can be seen from Fgure 3 Fgure 4 and Fgure 5 PSO-RBF neural networ has a faster convergence speed than tradtonal RBF neural networ and BP neural networ. Because each tranng result was unstable we respectvely too tranng 100 tmes and then calculated average convergence steps for the three methods. The tranng and test results of the three algorthms are as shown n Table. Table : Results Of Tranng And Test Algorthm Average convergence steps Convergence success rate Correct rate PSO-RBF % 96% RBF % 94% BP % 86% As can be seen from Table the average convergence step of PSO-RBF neural networ s 1156 whle the average convergence step of RBF neural networ s 184 and the average convergence step of BP neural networ s 043 PSO-RBF neural networ has the smallest average convergence steps. Convergence success rate of PSO-RBF was also much more greatly mproved than convergence success rates of RBF neural networ and BP neural networ whch effectvely mproved RBF networ s convergence speed and stablty. In the fault dagnoss results of PSO-RBF neural networ there only appeared to be a wrong judgment and a case not n full complance wth the model n addton smulaton results bascally conformed to the actual faults and the correct rate arrved at 96%. RBF neural networ model judged wrongly once two cases does not fully meet the actual fault types; the correct rate s 94%. BP networ model judged wrongly three tmes four cases does not fully meet the actual fault types and the correct rate s only 86%. The expermental 7

6 Journal of Theoretcal and Appled Informaton Technology JATIT & LLS. All rghts reserved. ISSN: E-ISSN: results show that our proposed PSO- RBF model has a hgher convergence rate and a hgher fault dagnoss accuracy to fault dagnoss of power transformers. 6. CONCLUSION Ths paper taes full advantage of PSO algorthm to optmze the center value and wdth of RBF neural networ and weght values from the hdden layer to the output layer. The optmzed neural networ was used for transformer fault dagnoss. Smulaton results show that compared wth the other two fault dagnoss methods based on conventonal RBF neural networ and BP neural networ RBF neural networ mproved by PSO algorthm obtans faster convergence speed and hgher convergence success rate and the correct rate of transformer fault dagnoss s effectvely mproved and the effect s very obvous. ACKNOWLEDGEMENTS Ths wor was supported by Project of Anhu Provnce Natural Scence Foundaton of Chna (No Q64) and Ordnary Project of Anhu Provnce Colleges and Unverstes Natural Scence Foundaton of Chna (No.KJ011B173) and Open Project of Intellgent Informaton Processng Lab at Suzhou Unversty of Chna (No.01YKF36). REFERENCES: [1] G.L. Wang J.H. Wu S.F. Yn L.Q. Yu J. Wang Comparson between BP neural networ and multple lnear regresson method Proceedngs of the Frst Internatonal Conference on Informaton Computng and Applcatons (Page: Year of Publcaton:010 ISBN: ). [] D.J. Du K. L M.R. Fe A fast mult-output RBF neural networ constructon method Neurocomputng Vol. 73 No pp [3] H. Modares A. Alf M.N. Sstan Parameter estmaton of blnear systems based on an adaptve partcle swarm optmzaton Engneerng Applcatons of Artfcal Intellgence Vol. 3 No pp [4] S. Solomon P. Thulasraman R. Thulasram Collaboratve mult-swarm PSO for tas matchng usng graphcs processng unts Proceedngs of the 13th Annual Conference on Genetc and Evolutonary Computaton(Page: Year of Publcaton:011 ISBN: ). [5] A.W. Mohemmed M. Zhang W. N. Browne Partcle swarm optmsaton for outler detecton Proceedngs of the 1th Annual Conference on Genetc and Evolutonary Computaton (Page:83-84 Year of Publcaton:010 ISBN: ). [6] O.P. Sangwan P.K. Bhata Y.Sngh Radal bass functon neural networ based approach to test oracle ACM SIGSOFT Software Engneerng Notes Vol. 36 No pp [7] H.G. Han Q.L. Chen J.F. Qao An effcent self-organzng RBF neural networ for water qualty predcton Neural Networs Vol. 4 No pp [8] Z.F. Chen P.D. Qan Z.F. Chen Applcaton of PSO-RBF neural networ n networ ntruson detecton Proceedngs of the 3rd Internatonal Conference on Intellgent nformaton Technology Applcaton(Page: Year of Publcaton:009 ISBN: ). [9] J.P. Sh W.G. Tong D.L. Wang Desgn of the Transformer Fault Dagnoss Expert System Based on Fuzzy Reasonng Proceedngs of the 009 Internatonal Forum on Computer Scence-Technology and Applcatons (Page: Year of Publcaton: 009 ISBN: ). [10] A. Shntemrov W. Tang Q.H. Wu Power transformer fault classfcaton based on dssolved gas analyss by mplementng bootstrap and genetc programmng IEEE Transactons on Systems Man and Cybernetcs Part C: Applcatons and Revews Vol. 39 No pp [11] L. L Y.P. N J.Y. Sun Research of Transformer Fault Dagnoss Based On Improved Partcle Swarm Algorthm Control and Instruments n Chemcal Industry Vol. 37 No pp