BP Neural Network based on PSO Algorithm for Temperature Characteristics of Gas Nanosensor

Transcription

1 2318 JOURNAL OF COMPUTERS, VOL. 7, NO. 9, SEPTEMBER 2012 BP Neural Network based on PSO Algorthm for Temperature Characterstcs of Gas Nanosensor Weguo Zhao Center of Educaton Technology, Hebe Unversty of Engneerng, Handan , Chna Emal: Abstract To comprehensvely understand the characterstcs of gas nanosensor between temperature and senstvty, ths paper has developed a Backward Propagaton (BP) neural network based on Partcle Swarm Optmzaton (PSO), whch s appled to fttng the temperature-senstvty characterstc of the S n O 2 gas nanosensor mxed wth benzene. The smulaton results show the PSO can well optmze the structure of the BP network, and the fttng accuracy of the temperature of nanosensor usng the acqured BP model s mproved greatly and the optmzed BP network has better generalzaton performance than the tradtonal BP network, and the acqured curve s both smooth and accurate, so the study shows that BP-PSO neural network s effectve for fttng the temperature characterstcs of gas nanosensor. Index Terms gas nanosensor, temperature characterstcs, neural network, PSO I. INTRODUCTION Wth the development of the electronc and communcaton technque, sensor technque has been mproved greatly and sensor has become an ndspensable equpment, whch has found wdespread applcatons n ndustry, agrculture, transportaton and so on. As one of the most mportant branches of sensor, nanosensor has been under research by many nsttutons and a great number of researchers for as long as ten years. A nanosensor s a sensor bult on the atomc scale based n measurements of nanometers, whch are any bologcal, chemcal, or surgcal sensory ponts used to convey nformaton about nanopartcles to the macroscopc world. Ther use manly nclude varous medcnal purposes and as gateways to buldng other nanoproducts, such as computer chps that work at the nanoscale and nanorobots [1, 2]. Presently, there have been a number of advances n the research and development of nanosensor for a number of dfferent applcatons. Some of the major applcatons are the medcal feld, natonal securty, aerospace, ntegrated crcuts, and many more. Along wth many dfferent applcatons for nanosensor, there are also many dfferent types of nanosensor, and a number of ways to manufacture them [3]. Nanotechnology offers the Manuscrpt receved Sept. 10, 2011; revsed Oct. 17, 2011; accepted Oct. 28, Project number: and E promse of mproved gas sensors wth low-power consumpton, fast response tme whch wll enable portablty for a wde range of applcatons. Indeed, nanostructured materals such as nanotubes and nanowres have been shown to be sutable for sensng varous gases [4]. Gas nanosensor s manly used for testng gas densty and humdty [5], currently, the majorty of nanosensors are made of nano S n O 2 flm, whch s mxed wth dfferent heavy metal partcles, t greatly enhance ts freedom and flexblty. In recent years, many nanosensor researches and applcatons show that gas nanosensor has varous advantages such as good stablty, hgh senstvty, fast responsblty, and hgh accuracy and so on. But the senstvty of gas nanosensor s very senstve to the temperature of envronments tested, so senstvty s consdered as a mpartment parameter for gas nanosensor and the measurement system smulaton [6, 7]. There exsts a nonlnear relatonshp between temperature and senstvty n gas nanosensor, but many applcatons was also based on a lnear computaton, whch resulted n bg nonlnear error. So, to elmnate or compensate the nonlnear error and have a thorough understandng of the relaton between temperature and senstvty, there are some fttng models establshed based on test data. Lu Hayan [8] proposed the comparson of the cubc polynomal method and the splne polynomal fttng n least square method for gas nanosensor, the smulaton results show the accuracy of the cubc polynomal method s better then that of the splne polynomal fttng n least square method, and ts fttng curve s smooth wthout any break n connectons; ZENG Zhezhao [7] ntroduced the neural network algorthm wth Fourer bass functons for fttng the temperature characterstcs of gas nanosensor, the experment nvolved nferrng that the method s both smooth and accurate. In recent decades, as a good nonlnear model, Artfcal Neural Network (ANN) s wdely appled to many complex nonlnear questons, and the BP neural network s one of the wdest network types, whch has a powerful capablty to generalze the nonlnear relatonshp between nput and desred output, but the tradtonal BP network can trap nto local mnmum and has nherent searchng rate slowly when tranng. Guo Wenxan[9] proposed BP neural network model based on PSO was do: /jcp

2 JOURNAL OF COMPUTERS, VOL. 7, NO. 9, SEPTEMBER appled to predct rver temperature of the Yangtze Rver, the study proved that PSO-BP neural network model was effectve n rver temperature predcton. Wang Png [10] establshed an mproved algorthm called PSO-BP, the new algorthm fully shows the ablty of nonlnear approach of multlayer feedforward network, mproves the performance of ANN, and provdes a favorable bass for further on-lne applcaton of a comprehensve model, t s appled to mechancal property predcton of strp model, nferrng excellent performance. So, to overcome the shortcomngs, n ths paper, a combnaton of Partcle Swarm Optmzaton s used to tran and optmze the BP network structure ncludng ts weghts and thresholds, t can overcome the over-fttng problem and the local mnma problem of the BP neural network, and then the establshed BP network s appled to fttng the relatonshp between temperature and senstvty n the SnO 2 gas nanosensor, the smulaton results show the fttng curve s accurate and the BP network based on PSO s practcal and effectve. II. BP NEURAL NETWORK As s a type of complex system, artfcal neural network s made up of plenty of nerve cells, whch can smulate the way that human deals wth the problem, parallel process nformaton and make nonlnear transformaton. Artfcal neural network handlng nformaton frst s tran to neural network, then composes lnear functons and gan ft weght, fnally completes the nonlnear processng about varety nformaton. Under the stuaton of loosng of sample and parameters drftng, t can also guarantee the stable output. Ths characterstc of artfcal neural network has been successfully used n many felds, ncludng pattern recognton, mage processng, ntellgent control, optmal calculaton, artfcal ntellgence and so on [11]. Back propagaton was proposed by generalzng the Wdrow-Hoff learnng rule to multple layer network and nonlnear dfferentable transfer functon. Input vectors and correspondng target vectors are used to tran a network untl t can approxmate a functon, assocate nput vectors wth specfc output vectors, or classfy nput vectors n an approprate way as defned n ths study. The back propagaton algorthm conssts of two paths; forward path and backward path. Forward path contan creatng a feed forward network, ntalzng weght, smulaton and tranng the network. The network weghts and bases are updated n backward path [12]. A typcal three layers BP neural network wth 4 nputs s shown n Fg. 1 In general, the mplementaton of the tranng algorthm makes use of the followed sgmod as the output functon of each node whose value s n (0, 1), 1 f( x) = (1) 1 + e x The error margn of the actual output Y of the BP network and expectaton output T s: n 1 2 E = ( y t) (2) 2 = 1 Fgure 1. Structure of BP neural network When we tran a neural network wth a gradent and descent method based on back propagaton [13] the network s provded wth a set of tranng samples along wth ther target outputs. One by one, each sample s placed nto the nputs of the neural network. The resultng outputs are then compared to the target values and an error s calculated for each node, startng wth nodes n the output layer and propagatng backward toward nodes n the nput layer. The error at an output node, wth respect to ts target t and output o, s δ = o& ( t o) (3) The error at hdden node, wth respect to each of ts downstream connectons j, s δ = o& δ (4) w j j ε Downstream() Each weght w j between nodes and j s adjusted based on a learnng constant η, the calculated error δ j at the target node j and the output x of the source node. Δw = η δ x (5) j III. PSO ALGORITHM PSO s a method for performng numercal optmzaton wthout explct knowledge of the gradent of the problem to be optmzed [14, 15]. PSO s bascally developed through smulaton of brd flockng and fsh schoolng n two-dmenson space whch s based on a smple concept, so the computaton tme s short and requres few memores, and then t was orgnally developed for nonlnear optmzaton problems wth contnuous varables so that t s easly expanded to treat a problem wth dscrete varables. The poston of each ndvdual (agent) s represented by XY axs poston and also the velocty s expressed by vx (the velocty of X axs) and vy (the velocty of Y axs). Modfcaton of the agent poston s realzed by the poston and velocty nformaton. An optmzaton technque based on the above concept can be descrbed as follows: namely, brd flockng optmzes a certan objectve functon. Each agent knows j j

3 2320 JOURNAL OF COMPUTERS, VOL. 7, NO. 9, SEPTEMBER 2012 ts best value so far (pbest) and ts XY poston. Moreover, each agent knows the best value so far n the group (gbest) among pbests. Each agent tres to modfy ts poston usng the followng nformaton: the current postons (x,y), the current veloctes (vx,vy), the dstance between the current poston, pbest and gbest. Ths modfcaton can be represented by the concept of velocty. Velocty of each agent can be modfed by the followng equaton: v + = wv + c rand ( pbest x ) + c rand gbest x k 1 k k 1 k 2 ( ) where, k v : velocty of agent at teraton k, w : nerta weght, c j : weght factor, rand : random number between 0 and 1, x k : current poston of agent at teraton k, pbest : pbest of agent. Usng the above equaton, a certan velocty, whch gradually gets close to pbest and gbest can be calculated. The current poston (searchng pont n the soluton space) can be modfed by the followng equaton: x = x + v. (7) k + 1 k k + 1 VI. BP NETWORK BASED ON PSO BP network has excellent characterstcs of nonlnear approxmaton and has been wdely used n many felds, but t has the dsadvantages of nherent slowly searchng rate and partally leadng to mnmum. To mprove the performance of BP network, we use PSO to optmze all weghts and thresholds n BP network. So, we adopt the global searchng for the optmum weghts and thresholds nstead of BP tself, the method wll mprove the soluton of results and ncrease the convergence speed of the BP network, the flowchart of the BP based on PSO s shown n Fg. 2 and the procedure s summarzed as follows: Step 1: Normalze the tranng samples and test samples nto [-1, 1]. Step 2: Defne the network structure of BP network accordng to the nput samples and the output samples. Step 3: Intalze parameters m, w, c 1, c 2, θ, where: m: number of populaton, w: nerta weght, c : weght factor, θ: parameter of dentfcaton (coeffcent of nonlnear rectfcaton equaton), the velocty and poston of each partcle are ntalzed randomly. Step 4: Each partcle s velocty s updated accordng to (6) and each partcle s poston s updated accordng to (7). Step 5: Each partcle s ftness s evaluated. The Mean square Error (MSE) of BP neural network s used as the ftness functon to gude the partcle populaton for searchng for the optmum soluton, we use all the tranng samples to calculate n forward propagaton for 6) each partcle, so as to generate the tranng error of partcles wth tranng samples. Step 6: The personal best poston pbest and and the global best poston gbest are updated. Step 7: If the maxmum of the teraton s acheved or the optmum soluton s acqured, then the algorthm s stopped, else return to Step 4. Fgure 2. Normalze tranng samples Defne the network structure of BP network Update poston and velocty of each partcle accordng to equaton (6) (4) and (7) (5) Evaluate each partcle s ftness accordng to the MSE Return the optmal soluton value Calculate the total force n dfferent drectons of each of agent Update the personal best poston and the global best poston No Termnaton s satsfed? Yes The flowchart of the BP network based on PSO V EXPERIMENT AND RESULTS We put S n O 2 gas nanosensor wth mxed wth dfferent concentraton of benzene nto a testng equpment whose gas densty and pressure s constant, then the temperature s changed every 10 and the senstvty of nanosensor s recorded. The expermental results between temperature and senstvty are lst n [8]. In ths paper, the BP network based on PSO s appled to ft the temperature characterstcs of gas nanosensor [16], frstly, we need to determne the nvolved parameters, whch s gven as follows [9]:

4 JOURNAL OF COMPUTERS, VOL. 7, NO. 9, SEPTEMBER a = (8) km ( 1) b= x + k 1 (9) Where x s set to 2 constantly, k s the number of neurons of output layer, s the number neurons of nput layer, m s the sze of the tranng samples, and the number of the neurons of the hdden layer h s searched n range [a, b], so the number of parameters to be optmzed by the PSO n the BP network s h+h+h k+k. Then, the PSO algorthm we used s the standard global verson wth nerta weght, the populaton szes the partcles s set at 50, the maxmum teraton s 100, the acceleraton factors c1 and c2 are both 2.0, a decayng nerta weght w startng at 0.9 and endng at 0.2 s used. For the comparson, the standard BP network and the BP network based PSO are both appled to the temperature characterstcs of gas nanosensor, the tranng parameters are set as follows: learnng rate s 0.02, and Momentum constant s 0.9, the weghts and bases are ntalzed randomly. The two methods are traned wth the same tranng samples, and the same test samples are used too n testng. The 30 senstvty values correspondng to dfferent temperatures are used as a dataset as shown n Table 1, of whch 25 samples are as tranng samples, the remanng 5 samples randomly selected as test samples as valdaton data. We use the tranng samples to tran the BP network based on PSO, the fnal number of the hdden layer s 5, so the BP structure of the two methods s Fg. 3 and Fg. 4 demonstrate the convergence process usng the two methods respectvely when tranng, Fg. 5 and Fg. 6 show the fttng results for the two methods, Table 2 summarzes the tranng results of the two methods usng the tranng samples. It can be seen that the BP optmzed usng PSO acheve the optmal error at the teraton of 26 and the MSE s , whle the BP network acheve the optmal error at the epoch of 802 and the MSE s It s clear that the BP network based on PSO requres fewer tranng tme and has faster convergence speed than the BP network, moreover, the tranng accuracy of the former s better than that of the latter. So, we has establshed a good predcton model based on the BP optmzed usng PSO, whch s appled to predct the Senstvty of nanosensor correspondng to the desred temperature. MSE MSE Epochs Fgure 3. Convergence process of BP network Iteratons Fgure 4. Convergence of BP network based on PSO TABLE I. THE PERFORMANCE COMPARISON OF TWO METHODS Method Epoch(Iteraton) Tranng error(mse) BP BP based on PSO Fgure 5. Fttng result of BP network

5 2322 JOURNAL OF COMPUTERS, VOL. 7, NO. 9, SEPTEMBER 2012 Fgure 8. Predcted value versus actual for BP-PSO Fgure 6. Fttng result of BP based on PSO The predcton results of the remanng 5 samples usng the two methods are depcted n Fg. 7 and Fg. 8 respectvely, they show the predcton value of the BP network based on PSO s nearer to the dagonal lne nferrng ts hgher predcton accuracy than that of t counterpart, Fg. 9 llustrates the comparson of relatve error of the test samples for the two method, t s obvous that the relatve error of most of the test samples usng the BP-PSO s smaller than that usng the BP network except for the ffth test sample, the average relatve error of BP network s and the average relatve error of BP- PSO s only , t proves that the proposed method has a better predcton ablty than ts counterpart. We can see that the BP-PSO has a better generalzaton performance, whether ts convergence speed or ts predcton ablty, ths results shows the fact that the SPO has a good generalzaton performance and global searchng for the optmum, t can refne the optmal parameters of the BP network structure, whch can better reflect the nonlnear relatonshp between the temperature and the senstvty of nanosensor. Relatve error Fgure 9. 0 BP BP-PSO Temperature/ Comparson of relatve error for two methods IV. CONCLUSIONS In ths paper, we have proposed a BP neural network model whose struct s optmzed usng the PSO, and t s appled to fttng the temperature characterstcs of the S n O 2 gas nanosensor mxed wth benzene. The smulaton results show the PSO can well refne the structure of BP neural network, the proposed method has greater mprovement n both accuracy and convergence speed for the tradtonal BP neural network, so t provde a practcal and effectve method for gas nanosensr. Our future research s to nvestgate the fttng model based on onlne and apply t to gas nanosensor. Fgure 7. Predcted value versus actual value for BP network ACKNOWLEDGEMENTS Ths work s supported by the Scence and Technology Research Project of Unversty of Hebe Provnce No , and the Natural Scence Foundaton of Hebe Provnce of Chna No. E REFERENCES [1] Foster LE, "Medcal Nanotechnology: Scence, Innovaton, and Opportunty", Upper Saddle Rver: Pearson Educaton, [2] [3] html

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