A model-based prognostics method for fatigue crack growth in fuselage panels
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摘要
This paper proposes a model-based prognostics method that couples the Extended Kalman Filter(EKF) and a new developed linearization method. The proposed prognostics method is developed in the context of fatigue crack propagation in fuselage panels where the model parameters are unknown and the crack propagation is affected by different types of uncertainties. The coupled method is composed of two steps. The first step employs EKF to estimate the unknown model parameters and the current damage state. In the second step, the proposed efficient linearization method is applied to compute analytically the statistical distribution of the damage evolution path in some future time. A numerical case study is implemented to evaluate the performance of the proposed method. The results show that the coupled EKF-linearization method provides satisfactory results: the EKF algorithm well identifies the model parameters, and the linearization method gives comparable prediction results to Monte Carlo(MC) method while leading to very significant computational cost saving. The proposed prognostics method for fatigue crack growth can be used for developing predictive maintenance strategy for an aircraft fleet, in which case, the computational cost saving is significantly meaningful.
This paper proposes a model-based prognostics method that couples the Extended Kalman Filter(EKF) and a new developed linearization method. The proposed prognostics method is developed in the context of fatigue crack propagation in fuselage panels where the model parameters are unknown and the crack propagation is affected by different types of uncertainties. The coupled method is composed of two steps. The first step employs EKF to estimate the unknown model parameters and the current damage state. In the second step, the proposed efficient linearization method is applied to compute analytically the statistical distribution of the damage evolution path in some future time. A numerical case study is implemented to evaluate the performance of the proposed method. The results show that the coupled EKF-linearization method provides satisfactory results: the EKF algorithm well identifies the model parameters, and the linearization method gives comparable prediction results to Monte Carlo(MC) method while leading to very significant computational cost saving. The proposed prognostics method for fatigue crack growth can be used for developing predictive maintenance strategy for an aircraft fleet, in which case, the computational cost saving is significantly meaningful.
This paper proposes a model-based prognostics method that couples the Extended Kalman Filter(EKF) and a new developed linearization method. The proposed prognostics method is developed in the context of fatigue crack propagation in fuselage panels where the model parameters are unknown and the crack propagation is affected by different types of uncertainties. The coupled method is composed of two steps. The first step employs EKF to estimate the unknown model parameters and the current damage state. In the second step, the proposed efficient linearization method is applied to compute analytically the statistical distribution of the damage evolution path in some future time. A numerical case study is implemented to evaluate the performance of the proposed method. The results show that the coupled EKF-linearization method provides satisfactory results: the EKF algorithm well identifies the model parameters, and the linearization method gives comparable prediction results to Monte Carlo(MC) method while leading to very significant computational cost saving. The proposed prognostics method for fatigue crack growth can be used for developing predictive maintenance strategy for an aircraft fleet, in which case, the computational cost saving is significantly meaningful.
引文
1.Mar éJ-C,Fu J.Review on signal-by-wire and power-by-wire actuation for more electric aircraft.Chin J Aeronaut 2017;30(3):857-70.
2.Schijve J.Fatigue damage in aircraft structures,not wanted,but tolerated?Int J Fatigue 2009;31(6):998-1011.
3.Liu J,Zhang M,Zuo H,Xie J.Remaining useful life prognostics for aeroengine based on superstatistics and information fusion Chin J Aeronaut 2014;27(5):1086-96.
4.Hu C,Zhou Z,Zhang J,Si X.A survey on life prediction of equipment.Chin J Aeronaut 2015;28(1):25-33.
5.Li Q,Gao Z,Tang D,Li B.Remaining useful life estimation for deteriorating systems with time-varying operational conditions and condition-specific failure zones.Chin J Aeronaut 2016;29(3):662-74.
6.Wang X,Lin S,Wang S,He Z,Zhang C.Remaining useful life prediction based on the Wiener process for an aviation axial piston pump.Chin J Aeronaut 2016;29(3):779-88.
7.Papalexopoulos AD,Hesterberg TC.A regression-based approach to short-term system load forecasting.IEEE Trans Power Syst1990;5(4):1535-47.
8.Chen Y,Dong G,Han J,Wah BW,Wang J.Chapter 29-Multidimensional regression analysis of time-series data streams VLDB’02:Proceedings of the 28th international conference on very large databases.San Francisco:Morgan Kaufmann;2002.p.323-34.
9.Brahim-Belhouari S,Bermak A.Gaussian process for nonstationary time series prediction.Comput Stat Data Anal 2004;47(4):705-12.
10.Zhu L,Wang Y,Fan Q.MODWT-ARMA model for time series prediction.Appl Math Model 2014;38(5):1859-65.
11.Peter Carden E,Brownjohn JMW.ARMA modelled time-series classification for structural health monitoring of civil infrastructure.Mech Syst Signal Proc 2008;22(2):295-314.
12.Qin M,Li Z,Du Z.Red tide time series forecasting by combining ARIMA and deep belief network.Knowl-Based Syst2017;125:39-52.
13.Zhang GP.Time series forecasting using a hybrid ARIMA and neural network model.Neurocomputing 2003;50:159-75.
14.Wang L,Zeng Y,Chen T.Back propagation neural network with adaptive differential evolution algorithm for time series forecasting.Expert Syst Appl 2015;42(2):855-63.
15.Aizenberg I,Sheremetov L,Villa-Vargas L,Martinez-Mun?oz JMultilayer neural network with multi-valued neurons in time series forecasting of oil production.Neurocomputing 2016;175980-9.
16.Chen T-T,Lee S-J.A weighted LS-SVM based learning system for time series forecasting.Inf Sci 2015;299:99-116.
17.Zhang F,Deb C,Lee SE,Yang J,Shah KW.Time series forecasting for building energy consumption using weighted support vector regression with differential evolution optimization technique.Energy Build 2016;126:94-103.
18.Cagcag Yolcu O,Yolcu U,Egrioglu E,Aladag CH.High order fuzzy time series forecasting method based on an intersection operation.Appl Math Model 2016;40(19):8750-65.
19.Yang X,Yu F,Pedrycz W.Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system.Int J Approx Reason 2017;81:1-27.
20.Deb C,Zhang F,Yang J,Lee SE,Shah KW.A review on time series forecasting techniques for building energy consumption.Renew Sustain Energy Rev 2017;74:902-24.
21.Rezvanizaniani SM,Liu Z,Chen Y,Lee J.Review and recent advances in battery health monitoring and prognostics technologies for Electric Vehicle(EV)safety and mobility.J Power Sources2014;256:110-24.
22.Hu Y,Baraldi P,Maio FD,Zio E.Online performance assessment method for a model-based prognostic approach.IEEE Trans Reliab 2016;65(2):718-35.
23.Pugno N,Ciavarella M,Cornetti P,Carpinteri A.A generalized Paris’law for fatigue crack growth.J Mech Phys Solids 2006;54(7):1333-49.
24.Paris P.A critical analysis of crack propagation laws.J Basic Eng1963;85(4):528-33.
25.Molent L,Barter SA.A comparison of crack growth behaviour in several full-scale airframe fatigue tests.Int J Fatigue 2007;29(6):1090-9.
26.Karandikar JM,Kim NH,Schmitz TL.Prediction of remaining useful life for fatigue-damaged structures using Bayesian CI.Eng Fract Mech 2012;96:588-605.
27.Gobbato M,Kosmatka JB,Conte JP.A recursive Bayesian approach for fatigue damage prognosis:An experimental validation at the reliability component level.Mech Syst Signal Proc2014;45(2):448-67.
28.Branco R,Antunes FV,Martins Ferreira JA,Silva JM.Determination of Paris law constants with a reverse engineering technique.Eng Fail Anal 2009;16(2):631-8.
29.Kumar P.Elements of fracture mechanics.New York:Mc GrawHill Education;2009.
30.Anderon TL.Fracture mechanics:Fundamentals and applications.Boca Raton:CRC Press;2005.
31.Kim NH,An D,Choi JH.Prognostics and health management of engineering systems.Amsterdam:Springer;2017.
32.Durbin J,Kppoman SJ.Time series analysis by state space methods.Oxford:Oxford University Press;2012.
33.Sun J,Zuo H,Wang W,Pecht MG.Prognostics uncertainty reduction by fusing on-line monitoring data based on a statespace-based degradation model.Mech Syst Signal Proc 2014;45(2):396-407.
34.Sun J,Zuo H,Wang W,Pecht MG.Application of a state space modeling technique to system prognostics based on a health index for condition-based maintenance.Mech Syst Signal Proc2012;28:585-96.
35.Hu Y,Baraldi P,Di Maio F,Zio E.A particle filtering and kernel smoothing-based approach for new design component prognostics.Reliab Eng Syst Saf 2015;134:19-31.
36.My?tyri E,Pulkkinen U,Simola K.Application of stochastic filtering for lifetime prediction.Reliab Eng Syst Saf 2006;91(2):200-8.
37.Wang Y,Binaud N,Gogu C,Bes C,Fu J.Determination of Paris’law constants and crack length evolution via extended and unscented Kalman filter:An application to aircraft fuselage panels.Mech Syst Signal Proc 2016;80:262-81.
38.Singleton RK,Strangas EG,Aviyente S.Extended Kalman filtering for remaining-useful-life estimation of bearings.IEEETrans Ind Electron 2015;62(3):1781-90.
39.Bressel M,Hilairet M,Hissel D,Ould Bouamama B.Extended Kalman filter for prognostic of proton exchange membrane fuel cell.Appl Energy 2016;164:220-7.
40.Xu X,Chen N.A state-space-based prognostics model for lithiumion battery degradation.Reliab Eng Syst Saf 2017;159:47-57.
41.Baptista M,Henriques EMP,de Medeiros IP,Malere JPNascimento CL,Prendinger H.Remaining useful life estimation in aeronautics:combining data-driven and Kalman filtering Reliab Eng Syst Saf 2018.Available from:https://doi.org/101016/j.ress.2018.01.017.
42.Zhang H,Zhao Y.The performance comparison and analysis of extended Kalman filters for GPS/DR navigation.Optik 2011;122(9):777-81.
43.Rice J.Mathematical statistics and data analysis.Riviera:Duxbury Press;2006.
44.Wang Y,Gogu C,Binaud N,Bes C.Predicting remaining usefu ife by fusing SHM data based on extended Kalman filter Proceedings of the 25th European safety and reliability conference2015 Sep 7-10;Zurich,Switzerland.2015.p.2489-96.
45.Grewal MS,Andrews AP.Kalman filtering:Theory and practice with MATLAB.Hoboken:John Wiley&Sons;2014.
46.Cortie MB,Garrett GG.On the correlation between the C and m in the Paris equation for fatigue crack propagation.Eng Fract Mech 1988;30(1):49-58.
47.Benson JP,Edmonds DV.The relationship between the parameters C and m of Paris’law for fatigue crack growth in a low-alloy steel.Scripta Mater Scripta Metallurgica 1978;12(7):645-7.
48.Bi_li_r ?G.The relationship between the parameters C and n of Paris’law for fatigue crack growth in a SAE 1010 steel.Eng Fract Mech 1990;36(2):361-4.
49.Pattabhiraman S,Gogu C,Kim NH,Haftka RT,Bes C.Skipping unnecessary structural airframe maintenance using an on-board structural health monitoring system.Proc Inst Mech Eng Part O-JRisk Reliab 2012;226(5):549-60.
2.Schijve J.Fatigue damage in aircraft structures,not wanted,but tolerated?Int J Fatigue 2009;31(6):998-1011.
3.Liu J,Zhang M,Zuo H,Xie J.Remaining useful life prognostics for aeroengine based on superstatistics and information fusion Chin J Aeronaut 2014;27(5):1086-96.
4.Hu C,Zhou Z,Zhang J,Si X.A survey on life prediction of equipment.Chin J Aeronaut 2015;28(1):25-33.
5.Li Q,Gao Z,Tang D,Li B.Remaining useful life estimation for deteriorating systems with time-varying operational conditions and condition-specific failure zones.Chin J Aeronaut 2016;29(3):662-74.
6.Wang X,Lin S,Wang S,He Z,Zhang C.Remaining useful life prediction based on the Wiener process for an aviation axial piston pump.Chin J Aeronaut 2016;29(3):779-88.
7.Papalexopoulos AD,Hesterberg TC.A regression-based approach to short-term system load forecasting.IEEE Trans Power Syst1990;5(4):1535-47.
8.Chen Y,Dong G,Han J,Wah BW,Wang J.Chapter 29-Multidimensional regression analysis of time-series data streams VLDB’02:Proceedings of the 28th international conference on very large databases.San Francisco:Morgan Kaufmann;2002.p.323-34.
9.Brahim-Belhouari S,Bermak A.Gaussian process for nonstationary time series prediction.Comput Stat Data Anal 2004;47(4):705-12.
10.Zhu L,Wang Y,Fan Q.MODWT-ARMA model for time series prediction.Appl Math Model 2014;38(5):1859-65.
11.Peter Carden E,Brownjohn JMW.ARMA modelled time-series classification for structural health monitoring of civil infrastructure.Mech Syst Signal Proc 2008;22(2):295-314.
12.Qin M,Li Z,Du Z.Red tide time series forecasting by combining ARIMA and deep belief network.Knowl-Based Syst2017;125:39-52.
13.Zhang GP.Time series forecasting using a hybrid ARIMA and neural network model.Neurocomputing 2003;50:159-75.
14.Wang L,Zeng Y,Chen T.Back propagation neural network with adaptive differential evolution algorithm for time series forecasting.Expert Syst Appl 2015;42(2):855-63.
15.Aizenberg I,Sheremetov L,Villa-Vargas L,Martinez-Mun?oz JMultilayer neural network with multi-valued neurons in time series forecasting of oil production.Neurocomputing 2016;175980-9.
16.Chen T-T,Lee S-J.A weighted LS-SVM based learning system for time series forecasting.Inf Sci 2015;299:99-116.
17.Zhang F,Deb C,Lee SE,Yang J,Shah KW.Time series forecasting for building energy consumption using weighted support vector regression with differential evolution optimization technique.Energy Build 2016;126:94-103.
18.Cagcag Yolcu O,Yolcu U,Egrioglu E,Aladag CH.High order fuzzy time series forecasting method based on an intersection operation.Appl Math Model 2016;40(19):8750-65.
19.Yang X,Yu F,Pedrycz W.Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system.Int J Approx Reason 2017;81:1-27.
20.Deb C,Zhang F,Yang J,Lee SE,Shah KW.A review on time series forecasting techniques for building energy consumption.Renew Sustain Energy Rev 2017;74:902-24.
21.Rezvanizaniani SM,Liu Z,Chen Y,Lee J.Review and recent advances in battery health monitoring and prognostics technologies for Electric Vehicle(EV)safety and mobility.J Power Sources2014;256:110-24.
22.Hu Y,Baraldi P,Maio FD,Zio E.Online performance assessment method for a model-based prognostic approach.IEEE Trans Reliab 2016;65(2):718-35.
23.Pugno N,Ciavarella M,Cornetti P,Carpinteri A.A generalized Paris’law for fatigue crack growth.J Mech Phys Solids 2006;54(7):1333-49.
24.Paris P.A critical analysis of crack propagation laws.J Basic Eng1963;85(4):528-33.
25.Molent L,Barter SA.A comparison of crack growth behaviour in several full-scale airframe fatigue tests.Int J Fatigue 2007;29(6):1090-9.
26.Karandikar JM,Kim NH,Schmitz TL.Prediction of remaining useful life for fatigue-damaged structures using Bayesian CI.Eng Fract Mech 2012;96:588-605.
27.Gobbato M,Kosmatka JB,Conte JP.A recursive Bayesian approach for fatigue damage prognosis:An experimental validation at the reliability component level.Mech Syst Signal Proc2014;45(2):448-67.
28.Branco R,Antunes FV,Martins Ferreira JA,Silva JM.Determination of Paris law constants with a reverse engineering technique.Eng Fail Anal 2009;16(2):631-8.
29.Kumar P.Elements of fracture mechanics.New York:Mc GrawHill Education;2009.
30.Anderon TL.Fracture mechanics:Fundamentals and applications.Boca Raton:CRC Press;2005.
31.Kim NH,An D,Choi JH.Prognostics and health management of engineering systems.Amsterdam:Springer;2017.
32.Durbin J,Kppoman SJ.Time series analysis by state space methods.Oxford:Oxford University Press;2012.
33.Sun J,Zuo H,Wang W,Pecht MG.Prognostics uncertainty reduction by fusing on-line monitoring data based on a statespace-based degradation model.Mech Syst Signal Proc 2014;45(2):396-407.
34.Sun J,Zuo H,Wang W,Pecht MG.Application of a state space modeling technique to system prognostics based on a health index for condition-based maintenance.Mech Syst Signal Proc2012;28:585-96.
35.Hu Y,Baraldi P,Di Maio F,Zio E.A particle filtering and kernel smoothing-based approach for new design component prognostics.Reliab Eng Syst Saf 2015;134:19-31.
36.My?tyri E,Pulkkinen U,Simola K.Application of stochastic filtering for lifetime prediction.Reliab Eng Syst Saf 2006;91(2):200-8.
37.Wang Y,Binaud N,Gogu C,Bes C,Fu J.Determination of Paris’law constants and crack length evolution via extended and unscented Kalman filter:An application to aircraft fuselage panels.Mech Syst Signal Proc 2016;80:262-81.
38.Singleton RK,Strangas EG,Aviyente S.Extended Kalman filtering for remaining-useful-life estimation of bearings.IEEETrans Ind Electron 2015;62(3):1781-90.
39.Bressel M,Hilairet M,Hissel D,Ould Bouamama B.Extended Kalman filter for prognostic of proton exchange membrane fuel cell.Appl Energy 2016;164:220-7.
40.Xu X,Chen N.A state-space-based prognostics model for lithiumion battery degradation.Reliab Eng Syst Saf 2017;159:47-57.
41.Baptista M,Henriques EMP,de Medeiros IP,Malere JPNascimento CL,Prendinger H.Remaining useful life estimation in aeronautics:combining data-driven and Kalman filtering Reliab Eng Syst Saf 2018.Available from:https://doi.org/101016/j.ress.2018.01.017.
42.Zhang H,Zhao Y.The performance comparison and analysis of extended Kalman filters for GPS/DR navigation.Optik 2011;122(9):777-81.
43.Rice J.Mathematical statistics and data analysis.Riviera:Duxbury Press;2006.
44.Wang Y,Gogu C,Binaud N,Bes C.Predicting remaining usefu ife by fusing SHM data based on extended Kalman filter Proceedings of the 25th European safety and reliability conference2015 Sep 7-10;Zurich,Switzerland.2015.p.2489-96.
45.Grewal MS,Andrews AP.Kalman filtering:Theory and practice with MATLAB.Hoboken:John Wiley&Sons;2014.
46.Cortie MB,Garrett GG.On the correlation between the C and m in the Paris equation for fatigue crack propagation.Eng Fract Mech 1988;30(1):49-58.
47.Benson JP,Edmonds DV.The relationship between the parameters C and m of Paris’law for fatigue crack growth in a low-alloy steel.Scripta Mater Scripta Metallurgica 1978;12(7):645-7.
48.Bi_li_r ?G.The relationship between the parameters C and n of Paris’law for fatigue crack growth in a SAE 1010 steel.Eng Fract Mech 1990;36(2):361-4.
49.Pattabhiraman S,Gogu C,Kim NH,Haftka RT,Bes C.Skipping unnecessary structural airframe maintenance using an on-board structural health monitoring system.Proc Inst Mech Eng Part O-JRisk Reliab 2012;226(5):549-60.