Neural Network Linearization of Pressure Force Sensor Transfer Characteristic

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1 Acta Polytechnica Hungarica Vol., No., 006 Neural Network Linearization of Preure Force Senor Tranfer Characteritic Jozef Vojtko, Irena Kováčová, Ladilav Madaráz, Dobrolav Kováč Faculty of Electrical Engineering and Informatic, Technical Univerity of Košice, Letná 9, Košice, Slovak Republic Abtract: The paper deal with an elatomagnetic enor of preure force and neural network deign in order to achieve linear enor output. There are decribed baic propertie of uch enor and it equivalent electrical cheme. The feeding and evaluating circuit were deigned in order to obtain the optimal working condition. Keyword: meaurement, elatomagnetic enor, neural network, non-linearity, hyterei Introduction Elatomagnetic enor have become more widepread owing to their extenive ue in indutrial and civil automation. However, deigning low-cot and accurate enor till require great theoretical and experimental effort to material engineer. But thi tak can be olved by advanced electronic technique for automatic calibration, linearization and error compenation. Baic Propertie of Elatomagnetic Senor The elatomagnetic enor [EMS] of a preure force that utilize the Villary phenomena principle, which conit of the fact that if a ferromagnetic body i ubjected to mechanical tre, it form i changed and conequently it permeability i changed, too []. Villary principle i baed on equation: M p w = H H, ϑ p,ϑ () 5

2 J. Vojtko et al. Neural Network Linearization of Preure Force Senor Tranfer Characteritic where M i magnetic polarization, p i general preure, w i relative deformation, H i intenity of magnetic field, ϑ i ambient temperature. We can tate magnetotriction coefficient in aturation for cubic crytal hown in Fig. by following equation: λ = h + α i β i h ( αα ββ + αα ββ + α α β β )+ i= h4 + α i β i A h 5 ( αα α ββ + α α α β β + αα α ββ )+ i= + h A if: K < 0 for example Ni () + h A if: K 0 for example Fe > = α α + α α + α α, α, α, β, β, β where A, K i firt aniotropic contant, ( α ) ( ) are coine function of angle created by vector of magnetic field and magnetotriction in aturation tate, h h5 are magnetotriction parameter which were tated experimentally. According to Fig., we can tate α i = coϕ i and βi = coγ i. Alo we are able to implify the above mentioned equation by the fact that parameter h and h have few time greater value than ret parameter o the ret parameter can be negligible. [xyz] [] y b γ ϕ ϕ [abc] [ ½ 0] [000] ϕ γ x a γ z c Figure Single cubic crytal The reulting magnetotriction in direction <00> and <> will be given a: 6

3 Acta Polytechnica Hungarica Vol., No., 006 = λ00 α i β i i= + λ αα ββ + αα ββ + α α β β () λ ( ) Next relation decribe dependency between magnetic induction and magnetic intenity: B = ( μ + Δμ)H (4) where Δ μ repreent the increment of permeability caued by acting of external preure force. The next relation can be obtained by comparing of increment of magnetic and elatomagnetic energie: ΔμH = σλ m where λ m repreent a magnetotriction coefficient. It i defined like: M λ m = λ (6) M It generally hold that: M B = (7) M B By utilizing of the lat two equation we can obtain the final dependence for permeability increment caued by the acting of external preure force []: μ σλ Δ μ = (8) B For permeability increment calculation we can utilize oftware calculator hown in Fig.. Since the permeability determine the magnetic field in a ferromagnetic body, o the magnetic field i alo changed and we could meaure it change by change of the induced electric voltage. On the bae of the above mentioned one can ee that the preductor can be decribed a a tranformer in which the mutual inductance between the primary and econdary winding i changed proportionally to the acting tre or to the preure, but only in the cae if magnetizing current I m i contant and output current I i negligible. (5) 7

4 J. Vojtko et al. Neural Network Linearization of Preure Force Senor Tranfer Characteritic Figure Intelligent calculator The elatomagnetic enor equivalent electrical cheme i hown in Fig.. R L I p I /p L.p R.p U R U L I m U L U R U p U m L m R m p. U Figure Elatomagnetic enor equivalent electrical cheme The change of the output voltage value can be calculated by following equation: ΔU = 4 π f N N p I p ( r r ) r r π r ln r h π λ μ B 8 fn F = r h N p I p B πr λ μ r ln F r (9) 8

5 Acta Polytechnica Hungarica Vol., No., 006 Thi equation correpond with practical manufacturing of elatomagnetic enor in Fig. 4 []. Propertie of the ferromagnetic material have a ignificant influence on enor enitivity, mainly: aturation magnetotriction coefficient λ, permeability of material μ and aturation intrinic induction B (for 6 4 elatomagnetic enor EMS-00kN: λ =.5 0, μ = H/m, B =.8T ). a) b) Figure 4 Sketche of elatomagnetic enor a) compoed enor EMS-00kN, b) detail of heet element 9

6 J. Vojtko et al. Neural Network Linearization of Preure Force Senor Tranfer Characteritic The decribed circuit fully correpond to the tranformer. In thi cae, the relation between magnetic intenity and magnetic induction i given by nonlinear hyterei curve. The maximum ueful ignal i obtained if output current I i reduced to the minimum and if the influence of primary current I p effective value i eliminated. In thi cae, the magnetizing voltage U m correpond to the maximum output voltage U for given operating point which i depending on the primary current I p value and the acting force. Such a way can be reduced the power of the feeding ource. A Deign of the Feeding and Evaluating Circuit The feeding circuit mut fulfill baic condition which conit in the current feeding requet, becaue only in thi cae, the change of acting preure force on the elatomagnetic enor core will be repreented by the change of output econdary voltage U [4]. An example of uch feeding ource realization i hown in Fig. 5. Such a way i imply poible to ecure realization of the harmonic contant current ource by tep down line voltage tranformer with mall output power. +Ucc Line Voltage ~ Step Down Tranformer u iref R R ip Q + iout iin OA - Q -Ucc F ~ Output Signal Elatomagnetic Senor Figure 5 An example of the optimal feeding ource For econd requet fulfilling, which i concerning to the econdary winding current I minimum value we mut to ecure a high a poible input impedance of evaluating circuit. A imple and uitable output evaluating ubcircuit can be realized by OA a it i hown in Fig. 6. 0

7 Acta Polytechnica Hungarica Vol., No., 006 +U cc input OA + -U cc output Figure 6 An example of output ubcircuit connection with high impedance 4 Neural Network Deign The neural network (NN) i expected to eliminate tranformer nonlinearity. However, NN output hould be linear and expreed by equation of traight line. In order to achieve thi aim, everal NN model were deigned. The difference between linear output and the real enor output are hown in the Fig. 7. The characteritic ΔU i i gained from output enor voltage U = f(f) (if force F wa increaing from 0 kn to 00 kn characteritic upward) and characteritic ΔU d i gained from U = f(f) (if force F wa decreaing from 00 kn to 0 kn characteritic downward). It can be expreed by next equation: ΔU ΔU = U (0) i U lin = U () d U lin Figure 7 Difference between the linear and the real enor output

8 J. Vojtko et al. Neural Network Linearization of Preure Force Senor Tranfer Characteritic The NN tak i to reduce the deviation between U, U and linear regreion of enor output U lin. Finally, the difference ΔU i and ΔU d will be limited. The mot common artificial neural network, called multilayer feed-forward neural network (FFNN) wa ued for thi purpoe [5]. Conception of FFNN with one-unit time delay i hown in Fig. 8. Figure 8 The conception of NN The enor output i at the ame time the NN input. However, in thi propoal the two NN input neuron are ued. The both are directly connected to enor via ADC converter, but the econd one i time delayed. A decreaing of enor error i expected by uing thi NN connection. 5 Training Proce The topology of NN conit of 0 neuron in hidden layer, which eem to be the mot convenient according to computing peed and accuracy. There were training cycle ued. Like a learning algorithm the backpropagation wa ued and it offer an effective approach to the computation of the gradient [6], in Fig. 9. The learning parameter α, which pecifie the tep width of the gradient decent, wa changed in the wide range (ee Fig. 0). Here i the SSE (um of quare error) dependence on training cycle. A we can ee, the training proce with higher learning parameter achieve maller SSE at the contant number of training cycle. If α parameter wa more than, the um quare error (SSE) of training et wa decreaed rapidly (the NN repond to trained data wa good), but SSE error of tet et wa increaed (the NN repond to untrained data wa bad) over-trained NN.

9 Acta Polytechnica Hungarica Vol., No., 006 Figure 9 The training proce Figure 0 The training proce with different α parameter The output of NN wa ocillated at larger α parameter, o the tability of NN wa not guaranteed. Advantage of higher NN learning rate wa the decreaing of training cycle and at the ame time the decreaing of SSE error of training et, but big diadvantage were: over-trained NN, bad generalization, ocillation of NN and intability of NN. Concluion Such contruction of elatomagnetic preure force enor i predetermined for hard field condition and aggreive corroding media. It output ignal i even 000 time greater a ignal of reitance tranducer and thi fact enable to implify feeding and data evaluation. Such enor are alo le enitive againt extremit electromagnetic interference. A general contruction of thee enor

10 J. Vojtko et al. Neural Network Linearization of Preure Force Senor Tranfer Characteritic can be realized with maller cot and dimenion. The neural network imulator SNNS v4. wa ued for imulation of deigned NN. The NN hould have decreaed the enor error and it output hould have been a linear function. Fig. how the difference between teted data U tet and linear regreion U lin (ΔU tet = U tet - U lin ), and difference between NN model data U NN and U lin (ΔU NN = U NN - U lin ). Figure Difference between teted data, NN output and linear regreion The nonlinearity of enor output wa δ S = 4,4% (for teted data δ S =,69%). The nonlinearity of deigned model wa δ NN =,5% in comparion with a claical FFNN model (without one-unit time delay) where the nonlinearity wa δ NN =,5%. The finally, the deigned model of error correction of elatomagnetic enor by uing FFNN (with one-unit time delay) achieve quantitatively lower linearity error in comparion with real enor output. Acknowledgement The author gratefully acknowledge the contribution of Slovak Grant Agency a project No./076/00 and Intitutional project No. 44 of Faculty of Electrical Engineering and Informatic, Technical Univerity of Košice. Reference [] M. Mojžiš et al.: Propertie of 00 kn Force Senor. Journal of Electrical Engineering, Vol. 50, No. -4, 999 pp [] M. Peťko: Obtainment of Prime Magnetia-tion Work Value and Magnetiation Work Value by Uing Approximate Function. In Proceeding of the II Doctoral conference, TU FEI Košice, 00, pp [] M. Mojžiš, M. Orendáč, J. Vojtko: Preure Force Senor. In Proceeding of the II Internal cientific conference, TU FEI Košice, 00, pp

11 Acta Polytechnica Hungarica Vol., No., 006 [4] D. Kováč: Feeding and Evaluating Circuit for an Elatomagnetic Senor. Journal of Electrical Engineering, Vol. 50, No. 7-8, 999, pp [5] S. Haykin: Neural Network (A Comprehenive Foundation). Macmillan College Publihing Company Inc., ISBN , 994 [6] M. Kuczmann, A. Ivanyi: A new neural-network-baed calar hyterei model. IEEE Tranaction on Magnetic, Vol. 8, 00, pp [7] V. Kvanička, Ľ. Beňušková, J. Popíchal, I. Farkaš, P. Tiňo, V. Kráľ: Introduction to neural network theory (Úvod do teórie neurónových ietí, in Slovak), Iri Publiher, Bratilava, 997 [8] A. Zell et al.: SNNS Uer Manual, verion 4.. Univerity of Stuttgart, Intitute for Parallel and Ditributed High Performance Sytem; Univerity of Tübingen, Since 989 5