FAULT PROGNOSTICS AND RELIABILITY ESTIMATION OF DC MOTOR USING TIME SERIES ANALYSIS BASED ON DEGRADATION DATA

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1 FAULT PROGNOSTICS AND RELIABILITY ESTIMATION OF DC MOTOR USING TIME SERIES ANALYSIS BASED ON DEGRADATION DATA LI WANG, HUIYAN ZHANG, HONG XUE School of Compuer and Informaion Engineering, Beijing Technology and Business Universiy, Beijing 00048, China ABSTRACT This paper presens a mehod of faul prognosics and reliabiliy esimaion for DC moor using ime series modeling procedure based on DC moor performance degradaion daa. DC moor performance degradaion daa are reaed as a ime series daa and sochasic process are uilized o describe he degradaion process for predicing long-erm rend. A degradaion es is processed for DC moor unil hey failed and he degradaion daa are colleced for faul prognosics and reliabiliy esimaion. Degradaion pah of DC moors are prediced using ime series analysis based on shor ime period degradaion daa. A comparison beween he prediced failure ime and he real failure ime of DC moors is processed and he resuls show ha he faul prognosics and reliabiliy esimaion of DC moors using ime series analysis is effecive. Keywords: Faul Prognosics, Reliabiliy Esimaion, DC Moor, Time Series, Degradaion Daa INTRODUCTION Faul prognosics and reliabiliy esimaion echnology is used o predic he probable failure ime of a produc while operaing o help people decide wheher o fix or replace he produc before is failure. I acuires he main performance indexes variaions wih ime of a produc, processes real-ime daa analysis and presens a lifeime predicion of he produc. Much work has been down in faul prognosics and reliabiliy esimaion mehods, which are proposed including arificial inelligence, fuzzy logic, neural nework and grey heory [-3]. For mos kinds of mechanical and elecrical producs, such as DC moor, he main performance index of he producs degrades wih ime and i will lead o he failure of he produc if i passes a specified hreshold. Hence, if he degradaion pah of he performance of he produc is prediced, he failure ime of he produc could be esimaed. In recen years, many scholars have made grea success for faul prognosics and reliabiliy esimaion of DC moor. However, mos researchers have focused on he use of inelligen mehods, which exis some shorage, such as ha hey only emphasis he fiing abiliy of model and ake lile consideraion of he reasoning abiliy and predicion abiliy of model. Time series analysis is a mehod o esablish a sochasic model for ime series daa based on is propery, and uilizes he sochasic model o predic he long erm rend. As he degradaion daa of producs are random variables arranged in emporal order which could be reaed as ime series daa, ime series mehod is applicable o predicion he long-erm degradaion rend. 2 TIME SERIES ANALYSIS OF DEGRADATION DATA The sochasic analysis of degradaion daa using ime series analysis is based on he following hypoheses: () The performance of he produc degrades monoonously; (2) The failure mechanism of produc remains he same during he degradaion process. In a degradaion es, performance degradaion daa is usually eually spaced and is variance is homogeneous for a fixed sampling freuency. And he degradaion daa is nonsaionary according o he firs hypohesis. 2. Degradaion Daa Decomposiion Le Y denoe he performance degradaion measuremen a ime. Based on Cramer Decomposiion Theorem, any ime series {Y} can 568

2 be decomposed ino wo componens: deerminisic componen and saionary random componen. Hence, Y could be expressed as, Y = T + S + ξ, =,2, L () Where T is he rend componen and S is he seasonal componen, boh of which are deerminisic componens. ξ is residual componen and i is he saionary random componen. 2.2 Trend Componen Modeling The rend componen T is exraced from performance degradaion daa using regression model, T = cf () + c2, =, 2, L (2) Where f() is a specified regression funcion which fis he degradaion rend of he daa well, c and c2 are regression parameers which could be esimaed by performance degradaion daa. 2.3 Seasonal Componen Modeling Exrac he season componen S, which is modeled by Hidden Periodiciy (HP) regression model, S = Aj cos ( ωj+ φj), =, 2, L (3) j = 0 Where < ω < ω2l < ω π. 2.4 Residual Componen Modeling The residual componen ξ is modeled by auoregressive (AR) model, p ξ = ϕ ξ + ε, =, 2, L, j j j= ε = 0, ε 2 = σ, ( ) Var( ) ( ε ε ) E Cov, = 0, i i (4) As he saionary random series {ξ} and ime series {Y} are dependen, i is needed o separae he esimaion of he parameers in S and ξ wih he esimaion of parameers in T. Hence, HP regression model of season componen S and AR model of residual componen ξ are combined ino X using Auo Regression-Hidden Periodiciy (ARHP) model o esimae he parameers. Se, X = S + ξ, =,2, L (5) Subsiue E.(3) and E.(4) o E.(5), i is expressed as, p ϕ cos( ω φ ) ε (6) X = X + A + + j j j j j j= j= E.(6) is an ARHP model. Hence, he performance degradaion measuremen Y is obained as, Y = T + X, =,2, L (7) E. (7) is a Regression-Auo Regression (RAR) model []. 3 FAILURE TIME PREDICTIONS AND RELIABILITY ESTIMATION 3. Failure Time Predicions In pracice, faul or failure occurs ofen as produc performance level achieves a specified hreshold which is denoed as D. Produc failure ime is ime scale from he beginning of operaing o he firs achieving. In his paper, failure ime is obained by predicion of degradaion daa. Y f = inf : = D; 0 (8) y0 3.2 Reliabiliy Esimaion The failure ime predicion is assumed o obey a cerain locaion-scale disribuion as deermined by a Pearson chi-suare Goodness of Fi Tes. The esimae of he locaion and scale parameers of he failure ime disribuion are obained by MLE. This paper denoes failure ime predicion of i h produc as f (), when oal number of producs is m, and hen i he predicion of he maximum likelihood funcion for he failure ime disribuion is L Here, β ( µ, σ ) m (, β ) ( β ) f f () i T = (9) i= =, T means ranspose of marix. This paper denoes failure ime disribuion as F(), reliabiliy of produc is esimaed by R () = F () (0) Here, µ, σ are mean value and variance of failure ime disribuion. 4 DC MOTOR DEGRADATION TESTING 4. Dc Moor Failure Mechanism Analyses DC moor srucure principle is shown as Figure. From Figure, he DC moor consiss of elecric brush, commuaor, coil winding and ferrie magne. 569

3 Figure Dc Moor Srucure Principle In pracice, mos DC moor failure mechanism is elecric brush and commuaor wear. I leads o DC moor degradaion. Figure 2 shows he failure mechanism. Figure 3 Degradaion Tesing Sie The consrucion of he degradaion esing sysem is shown in Figure 4, Figure 2 Dc Moor Failure Mechanism 4.2 Degradaion Tesing Sysem Design A degradaion esing sysem for DC moors is buil o obain degradaion daa of hem and predic failure ime of DC moors based on shor ime period degradaion daa and compare hem wih he real failure ime recorded o verify he faul prognosics and reliabiliy esimaion mehod based on ime series analysis. The degradaion esing sie is shown in Figure 3, Figure 4 Degradaion Tesing Sysem Consrucion The degradaion sysem consiss of PC, daa acuisiion board, I/O connecor, DC moor, resisor and power. The power supplies volage o moor and resisor which are series conneced, he I/O connecor acuires he volage over he resisor and sends i o PC hrough daa acuisiion board. The PC records he volage of he resisor in a specified freuency. The oupu volage is defined as he volage over he moor, and i is given as, Voupu = Vpower R () resisor Vpower Rresisor + Rmoor As he moor degrading, he resisance of he moor is increasing, and i would resul in he decreasing curren in he circui, hence, he volage over he resisor is decreasing, and he oupu volage is increasing. Therefore, he oupu volage could reflec he performance sae of he moor. 570

4 The design volage of he moor is 3v. The resisance of he resisor is ohm. Hence, for a moor wih he resisance of 29 ohm, when i is operaing, he oupu volage should be an increasing value from 4.83v based on E.() and when he moor fails, he volage over he resisor is around zero and he oupu volage is around power volage, which is 5v, as a resul of circui inerferences. 5 DEGRADATION TESTING DATA ANALYSIS A degradaion esing is processed for DC moors and he degradaion daa of 4 moors are uilized o verify he ime series analysis mehod. The PC records he volage over he resisor every hundred minues. The degradaion pah of moors are preprocessed by iniial value processing for eliminaing influence of heir iniial value difference and normalizing he failure crierion, which are shown in Figure 5, Figure 6 The Esimaion Of Trend Componen HP regression model of season componen S and AR model of residual componen ξ are combined ino X using ARHP model, and he performance degradaion measuremen Y is obained by RAR model. Then, he predicion of degradaion measuremen Y is shown in Figure 7, Figure 5 Preprocessed Degradaion Pah Of DC Moors 5. Faul Prognosic Faul prognosic for DC moors using ime series analysis is processed as follows. The rend componen T is se as a power form as i fis he degradaion pah well, c2 T,,2, = c + c3 = L (2) The esimaions of parameer c, c2 and c3 are obained by regression analysis using degradaion daa. The esimaion of rend componen T is shown in Figure 6, Figure 7 The Esimaion Of Season Componen The predicion of failure ime and he real failure ime of each moor is shown in Figure 8, Figure 8 Failure Time Predicion And Real Failure Time 5.2 Reliabiliy Esimaion Reliabiliy of DC moor is esimaed by R () = Φ ln µ / σ (3) {[ ] } 57

5 Here, µ, σ are mean value and variance of lognormal disribuion. The prediced reliabiliy and real reliabiliy of DC moor are all showed in Figure 9 for compare. Technology and Business Universiy under grans QNJJ REFRENCES: Figure 9 The Prediced Reliabiliy And The Real Reliabiliy The saisic daa of real reliabiliy and prediced reliabiliy is shown in Table, Saisic Daa Real reliabiliy Prediced relilabiliy TABLE : Reliabiliy Saisic Daa Log mean Log variance Median failure ime hours hours From Table, i is obvious ha he predicion of reliabiliy curve is very near and jus before he real reliabiliy curve of DC moor. 6 CONCLUSIONS This paper presens a mehod of faul prognosics and reliabiliy esimaion for DC moor using ime series modeling procedure based on DC moor performance degradaion daa. I describes he performance degradaion measure of DC moor by Regression-Auo Regression model. A degradaion es of DC moors is processed and he degradaion daa are uilized o predic he failure ime and reliabiliy of DC moors. The resuls show ha faul prognosics and reliabiliy esimaion by he proposed mehod is very near he real reliabiliy of DC moor. ACKNOWLEDGEMENTS This research is suppored by he Research Foundaion for Youh Scholars of Beijing [] Vicor Chan, William Q. Meeker, Time Series Modeling of Degradaion Due o Oudoor Weahering, Communicaions in Saisics - Theory and Mehods, 37:3, , [2] Bachmann, S. M., Using he Exising Specral Cluer Filer Wih he Nonuniformly Spaced Time Series Daa in Weaher Radar, IEEE Geoscience and Remoe Sensing Leers, Vol. 5, No. 3, July [3] Wang, L., Li, X. and Jiang, T., SLD Consan-Sress ADT Daa Analysis based on Time Series Mehod, he Proceedings of he 8h Inernaional Conference on Reliabiliy, Mainainabiliy and Safey, Chengdu, China, July 2-25, [4] Wang Li, Li Xiaoyang, Jiang Tongmin, CSADT Life Predicion based on DAD using Time Series Mehod, Proceedings of Annual Reliabiliy and Mainainabiliy Symposium (RAMS20), 20. [5] Wang Li, Li Xiaoyang, Wan Bo, Sep-Sress ADT Daa Esimaion based on Time Series Mehod, Proceedings of Annual Reliabiliy and Mainainabiliy Symposium (RAMS200), 200. [6] Wang, J., Zhang, T., Degradaion predicion mehod by use of auoregressive algorihm, IEEE Transacions Indusrial Technology, 2-24, Page(s):-6, April [7] Bo Wan, Jun Yao, New Approach o Esimaing he Consan-sress Acceleraed Life Tes, 9h Inernaional Conference on Engineering Srucural Inegriy Assessmen (ESIA9), Beijing, China, 2007 [8] Zaiwen Liu, Xiaoyi Wang, Lifeng Cui. Research on Waer Bloom Predicion Based on Leas Suares Suppor Vecor Machine World Congress on Compuer Science and Informaion Engineering, 2008 [9] John P. Rooney., Sorage Reliabiliy, Proc Ann. Reliabiliy & Mainainabiliy Symp., 989, pp [0] Michael Pech, Abhiji Dasgupa. Physics-Of-Failure, An Approach o Reliable Produc Developmen, IEEE Inegraed Reliabiliy Workshop, 995, pp. -4. [] Serdobolskii, Mulivariae Saisical Analysis, Springer,