Grain Moisture Sensor Data Fusion Based on Improved Radial Basis Function Neural Network

Transcription

1 Gran Mosture Sensor Data Fuson Based on Improved Radal Bass Functon Neural Network Lu Yang, Gang Wu, Yuyao Song, and Lanlan Dong 1 College of Engneerng, Chna Agrcultural Unversty, Bejng,100083, Chna zhjunr@gmal.com,{yanglu,maozhhua}@cau.edu.cn 2 Department of Research & Development Bejng Bey Innovaton Vacuum Technology CO. Ltd Bejng, , Chna Donglanlan2005@126.com Abstract. Dffculty was known to get satsfactory measurement effect on precson n capactve gran s mosture measurement due to many nfluencng factors, such as temperature, speces, compacton and so on. The data confuson method of Radal Bass Functon (RBF) nerve network s adopted. Wth mproved orthogonal optmal method, the RBF nerve network s weght factors can be obtaned. Ths method can avod artfcally selected the number of hdden unts, whch can cause low learn precson or over learn. Tests showed that the mproved RBF network algorthm reduces the network structure, greatly enhances the learnng speed of calculaton. By usng of the mproved RBF nerve network, the precson for wheat s mosture measurement has been mproved. Keywords: Radal Bass Functon Never Network, mosture measurement, k-means clusterng, hdden layer neuron. 1 Introducton There are some methods for gran mosture measurement, e.g. resstance measurng, capactance measurng, measurng wth Infrared Radaton, mcro wave, neutron spectrum, NMR, etc [1~3]. The advantages of low cost, hgh sensblty, wde dynamc range and smplcty for real tme measurng make the capactve mosture meter as one of the common method used for gran mosture measurement. The Delectrc Constant (DC) of dry gran s 2~5, whle the DC for pure water s 81. As the mosture n the tested sample grows, the DC value also grows. Ths s the bass for Capactve Mosture Meter (CMM) measurng [4]. Dfferent type of gran has dfferent DC. The CMM measurng s affected by sample s temperature, category and compactness. The conventonal way of measurng the capactve mosture only measures the capactor value to get the mosture level, whch s not accurate. Temperature compensaton for the mosture measurng s actually to solve the accuracy problem by mult-sensor nformaton fuson. D. L and Y. Chen (Eds.): CCTA 2012, Part II, IFIP AICT 393, pp , IFIP Internatonal Federaton for Informaton Processng 2013

2 100 L. Yang et al. There are a number of methods for such data fuson appled n ndustral technology, e.g. Mult-dmensonal Regresson Analyss, Bayesan Dervaton, Artfcal Neural Network, D-S Theory and Fuzzy Set Theory. It s as mportant academcally as t s practcally to get the best data fuson based on dfferent models. In recent years, the BP Neural Network has been used for lnearzaton or temperature compensaton for measured data. Same as the other forward network algorthms, BP Neural Network algorthm can be trapped by local optmum. In late 80 s last century, J. Mody [5] and C. Darken [6] proposed the Radal Bass Functon (RBF) Neural Network [7~9]. RBF Network has a character called optmal approxmaton, whch wll avod local optmum trap durng network establshng. Ths makes RBF a more effectve and fast respondng neural network, wth a strong nonlnear processng capablty. It s presented here the mathematcal model for RBF Neural Network appled on gran mosture measurng. 2 Structure of RBF Neural Network for Gran Mosture Measurng 2.1 Structure of Neural Network There are a few major factors affectng the measurng accuracy of gran mosture: the ambent temperature, the testng frequency and the compactness of the gran. Ths model composes by nput layer, hdden layer and output layer. The nput layer has 3 neurons, the hdden layer has I neurons, the output layer has one neuron. The neural network topology s show n Fgure 1. ϕ 1 ϕ ϕ I Fg. 1. RBF network structure of mosture measurement system

3 Gran Mosture Sensor Data Fuson Mathematcs Model The nput vector s = [ x, x, x ] X ; x1, x2, x3 are temperature, frequency and compactness. The output vector s Y = y, y s gran mosture. RBF network hdden layer output (the th node): ( ) u = ϕ X t. (1) In the sentence, RBF functon (ϕ ) s Gauss functon, t s the centre of th hdden node, s Eucldean Norm. From the mathematcal model, t s known that: y = wu θ. (2) In the sentence, w s the th connecton weght between the th output u and the system output y, θ s respectvely the neurons threshold of output. W, as a Vector wth I dmensons, s gven by weghts matrx composed of output connecton weghts: [ w w w w ] W = 1, 2, I. (3) To get RBF network for a measurng system, whch has N groups of nputs and outputs, can be descrbed n mathematcal model as: to get the optmum weghts matrx W so as to acheve mnmum error between output of RBF network and the expected output of the samples. The target functon s: 1 1 mn B = dk Y = ( d y ). (4) 2 2 N 2 2 k k k k = 1 Y k s kth output vector of RBF network, tranng samples. d k s kth expected output vector of 3 Tranng Algorthm of RBF Neural Network There are 2 stages for ths algorthm. Stage 1 s to determne the centre of the radal prmary functon for the hdden layer; stage 2 s the get the optmum weghts matrx from nonlnear programmng model. The method that the centre s chose randomly, selected by self-organzaton and K-means clusterng algorthm are methods that determne the centre of the radal prmary functon. Comparng to the other methods,

4 102 L. Yang et al. K-means clusterng algorthm has a advantage that t can reduce the sample space by automatcally classfyng the sample space to k classes, automatcally gettng the centre of the radal prmary functon for every class. The stage 2 of K-means clusterng algorthm get the weght vector by Orthogonal Least Squares (OLS), but small k may lead to bad accuracy; bg k wll lead to bad accuracy and complex network. The mproved RBF network OLS algorthm s proposed to solve ths problem n the text. 3.1 Conventonal RBF Network Algorthm Three parameters are needed to be computed and learned: center vector n bass functon, varance vector and weght value matrx. 1) Calculatng the Centre Vector n the Bass Functon: K-means clusterng algorthm can calculate the centre vector n the bass functon as follows: Frst, ntalzng cluster centre. Select I dfferent samples randomly from tranng samples set as the centre vector t (0),( = 1,2,, I) accordng to experence, and make the teraton step n=0. Second, nput tranng samples X k randomly. Thrd, fnd the clusterng centre ( ) k another word, makng ( ) = arg mn ( n) k k X that has mnmum dstance wth k X. In X X t ( = 1,2,, I) (5) In the sentence, t ( n) s th centre vector of nth teraton bass functon. Fourth, adjust the centre vector of bass functon accordng to the follow method. [ ] t( n) + η Xk ( n) t( n) =( Xk ) t ( n + 1) = t ( n) other In the sentence, η s a step and 0<η <1. At last, judge whether all tranng samples are learned and dstrbuton don t change. If so, calculaton s over, or makng n= n+ 1, turnng to second step. Fnal t ( = 1,2,, I) s the fnal th centre vector of the bass functon. 2) Calculatng the Varance: The approxmate formula that calculate the varance s as follow when Gaussan functon s selected as RBF functon: D σ1 = σ2 = = σ = 2I (6) max I (7)

5 Gran Mosture Sensor Data Fuson 103 In the sentence, I s the number of hdden node, and D max s maxmum dstance between centres selected. 3) Calculatng the weght vector: OLS and Gvens OLS are the general methods to calculatng the weght vector W. 3.2 Improved RBF Network OLS Algrthm Structural optmzaton n network s a dffcult. The general structure has large numbers of hdden nodes and leads to over-learn. The general orthogonal method s the tradtonal Gram-Schmdt whch has roundng error. The hdden network structure s optmzed wth the mproved method n the artcle. I egenvectors are obtaned by K-mean clusterng [10]. Suppose the output testng samples column vector s: The hdden layer output vector s: d = [,,, ]. (8) d1 d2 d I T = u1, u2,, u I U. (9) The expected output vector can be expressed by hdden layer functon output vector: d = UW + E. (10) In the sentence, E s error vector. Make U as orthogonal trangular factorzaton wth Gram-Schmdt orthogonal algorthm [11]: U = QR. (11) The elements n upper trangular matrx R are computed n row but not n lne n mproved Gram-Schmdt method whch lead to lower roundng error. For detals, vewng q 1 as the result of u 1, at the same tme u2,, ui mnus the parallel component of u 1 n advanced: R11 = u11, q1 = u1 / R11 T (1) R1j = qu 1 j, uj = uj q1r1j 2 j I After the computaton, u (1), (1),, (1) 2 u3 ui are orthogonal wth q 1.. (12)

6 104 L. Yang et al. Then, Ortho-normalzed (1) (1) (1) u 2 : u3,, ui mnus the parallel component of (1) u 2 : (1) (1) R22 = u22, q2 = u2 / R22 T (1) (2) (1) R2 j = qu 2 j, uj = uj q2r2 j 3 j I (13) q, q. Repeatng the steps, the orthogonal (2) (2) Thus, u3,, ui are orthogonal wth 1 2 matrx Q and upper trangular matrx R are obtaned. The structure network s optmzed wth mproved Gram-Schmdt method and detal solvng process s desgned n the artcle. The mproved optmzed network structure s obtaned by sentence (10): I T 2 T d d g + E E. (14) = 1 In the sentence, I = 1 g 2 = T GG T G = ( g, g..., g,..., g ) = RW Q d 1 2 I Suppose the compresson rato s: 2 T [ ] / 1 err = g d d I. (15) Above result show that as the roundng error s lower n the mproved Gram-Schmdt, the numbers of the hdden layer nodes can be computed precsely. The computaton amount s decreased and over learned problem s avoded. 4 Data Analyss and Processng Comparng experments have been done to verfy the functon of the mproved RBF algorthm[13~14] n ths artcle, whch s supposed to acheve hgher mosture detectng accuracy. BP network, tradtonal RBF network and mproved RBF methods are used to compare for data fuson process. 300 groups of wheat samples are prepared for the experments. Among whch, 250 samples are used for learnng algorthm, and 50 groups are used for measurng. 4.1 Compare the Measurng Results Wth the Method of Improved RBF to That Wth Method Wthout Data-fuson Process Testng values and standard values of the two methods are lsted n the Table 1 and 2.

7 Gran Mosture Sensor Data Fuson 105 Table 1. Compare the Standard Values to the Results Processed wthout Data Fuson No. y (%) d (%) Error (%) No y (%) d (%) Error (%) Table 2. Compare the Standard Values to the Results Processed By Improved RBF Neural Network No. y (%) d (%) Error (%) No y (%) d (%) Error (%) The Tables show that wth the method wthout data-fuson, the error s ±5.0%. Wth the method of mproved RBF, the error s reduced to ±1.9%. 4.2 Compare the Measurng Results wth the Method of Improved RBF to That wth BP Network Method Fgure 2 shows the compared curves of the measurng result usng two methods. The sold lne and dotted lne show respectvely the measurng error made by the mproved RBF method, and that made by BP network method[15~16]. The maxmum error and mnmum error s respectvely ±1.9% and ±0.2% when measurng wth the mproved RBF method. The maxmum error and mnmum error s respectvely ±4.0% and ±0.3% when measurng wth the BP network method. 4.3 Compare the Measurng Results wth the Method of Improved RBF to That wth Regular RBF Method Computatonal scales for these two methods are compared wth the same ntal condtons. The ntal condtons are: three nput varables and one output varable wth 300 learnng samples. The conventonal algorthm takes the same feature

8 106 L. Yang et al. Fg. 2. Comparson of measure results between textual algorthms to BP neural network algorthms samples as one group by clusterng algorthm, reducng the hdden nodes from 250 to 164. The mproved Gram-Schmdt method[17~18] s used to solve network weght and confrm the numbers of the hdden nodes automatcally, reducng the hdden nodes to 56. Fgure 3 shows the compared curves of the measurng result usng two methods. The sold lne and dotted lne show respectvely the measurng error made by the mproved RBF method and regular RBF method. The maxmum error range error s respectvely ±1.9% and ±3.1% when measurng wth the mproved RBF method and regular RBF method. Fg. 3. Comparson of measure results between textual algorthms to RBF network algorthms

9 Gran Mosture Sensor Data Fuson Concluson The data fuson method of RBF neural network s adopted n ths study. Wth mproved orthogonal-optmzng method, the study shows, whle the RBF nerve network's weghng factors are obtaned, the number of hdden unts can be acqured. Ths method can avod too few nerve elements that wll result has been approved for ts advantages over the ordnary methods wth laboratory tests on gran of wheat, rce, corn, etc[19~20]. References 1. Teng, Z., et al.: Study of New Instrument for Quck Measurng Mosture Content of Cereals. Journal of HuNan Unversty Nayural Scences 26(3), (1999) 2. Cheng, W., et al.: An On-lne Measurement and Montorng System of Gran Mosturedurng Dryng Process. Transactons of the Chnese Socety of Agrcultural Machnery 31(2), (2000) 3. Yuan, Z., et al.: Fast Neutron Water-Content Mater. Nuclear Electroncs & DetectonTechnology 19(1) (1999) 4. Zha, B., Chen, Q.: Data Processng of Mosture Content Measurement Based on Data Fuson. Journal of Laonng Instute of Technology 26(3), (2006) 5. Hardy, R.: Multquadrc Equatons of Topography and Other Irregualr Sufaces. Journal of Geophyscs Research, (1987) 6. Harder, R., Desmaras, R.: Interpolaton usng surface splnes. J. Arcraft. 9, (1972) 7. Moody, J., Darken, C.: Fast learnng n networks of locally-turned processng unts. Neural Computaton 1(2), (1989) 8. Yan, P., Zhang, C.: Artfcal Neural Networks and Evolutonary Computng. Tsnghua Unversty Press, BeJng (2002) 9. Bllngs, S., Zheng, G.L.: Radal bass functon network confguraton usng genetc algorthms. Neural Networks 8(6), (1995) 10. Lu, J.: Study on RBF Neural Network Improvement and ts Applcaton. Lanzhou Unversty, Lanzhou (2008) 11. Huan, Y., D, C., Zhu, S.: Matrx Theory and ts Applcaton. Unversty of Scence and Technology of Chna Press, HeFe (2005) 12. Zhu, C., Zhao, X.: RBF algorthm and ts Applcaton n Mult-Reach Water Qualty Smulaton. College of Urban Constructon Hebe Unversty of Engneerng Handan (2009) 13. Wang, X., La, H.: An Improved RBF Algorthm for Text Classfcaton. Communcaton Technology 44(12), (2011) 14. L, B., La, X.: An Improved GGAP-RBF Algorthm and Its Applcaton to Functon Approxmaton 20(2), (2007) 15. Qu, C., Zuo, X., Wang, C., Wu, J.: A BP neural network based nformaton fuson method for urban traffc speed estmaton, School of Computer. Bejng Unvemty of Posts and Telecommuncatons 8(1), (2010) 16. Fu, Q., L, G., Wang, Z.: Method of Chaotc Predcton Based on Wavelet BP Network and Its Applcaton. Journal of System s Scence and Informaton 6(1), (2008)

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