An algorithm for estimating the effect of maintenance on aggregated covariates with application to railway switch point machines

• Autorzy: Babishin Vladimir , Taghipour Sharareh

Identyfikatory

DOI

10.17531/ein.2019.4.11

Warianty tytułu

PL

Algorytm do oceny wpływu konserwacji na zagregowane zmienne towarzyszącei jego zastosowanie w odniesieniu do kolejowych napędów zwrotnicowych

• Języki publikacji: EN

Abstrakty

EN

We propose an algorithm for estimating the effectiveness of maintenance on both age and health of a system. One of the main contributions is the concept of virtual health of the device. It is assumed that failures follow a nonhomogeneous Poisson process (NHPP) and covariates follow the proportional hazards model (PHM). In particular, the effect of maintenance on device’s age is estimated using the Weibull hazard function, while the effect on device’s health and covariates associated with condition-based monitoring (CBM) is estimated using the Cox hazard function. We show that the maintenance effect on the health indicator (HI) and the virtual HI can be expressed in terms of the Kalman filter concepts. The HI is calculated from Mahalanobis distance between the current and the baseline condition monitoring data. The effect of maintenance on both age and health is also estimated. The algorithm is applied to the case of railway point machines. Preventive and corrective types of maintenance are modelled as different maintenance effect parameters. Using condition monitoring data, the HI is calculated as a scaled Mahalanobis distance. We derive reliability and likelihood functions and find the least squares estimates (LSE) of all relevant parameters, maintenance effect estimates on time and HI, as well as the remaining useful life (RUL).

PL

W artykule zaproponowano algorytm służący do szacowania skuteczności utrzymania ruchu w odniesieniu do wieku i stanu technicznego (kondycji) systemu. Główny wkład proponowanej metody stanowi koncepcja wirtualnego stanu urządzenia. Metoda zakłada, że uszkodzenia można zamodelować za pomocą niejednorodnego procesu Poissona, a zmienne towarzyszące za pomocą modelu proporcjonalnego hazardu. Mówiąc precyzyjniej, wpływ konserwacji na wiek urządzenia szacuje się z wykorzystaniem funkcji hazardu Weibulla, natomiast wpływ na stan urządzenia i zmienne towarzyszące związane z monitorowaniem stanu ocenia się stosując funkcję hazardu Coxa. W artykule pokazujemy, że wpływ konserwacji na wskaźnik stanu i wskaźnik stanu wirtualnego można wyrazić w kategoriach filtra Kalmana. Wskaźnik stanu oblicza się na podstawie odległości Mahalanobisa między bieżącymi a początkowymi danymi z monitorowania stanu. Ocenia się także wpływ utrzymania na wiek i kondycję systemu. Proponowany algorytm zastosowano w odniesieniu do napędów zwrotnicowych. Zapobiegawcze i naprawcze typy konserwacji zamodelowano jako różne parametry utrzymania ruchu. Korzystając z danych z monitorowania stanu, obliczono wskaźnik stanu jako skalowaną odległość Mahalanobisa. Wyprowadzono funkcje niezawodności i wiarygodności oraz obliczono metodą najmniejszych kwadratów szacunkowe wielkości wszystkich istotnych parametrów, a także szacunkowy wpływ konserwacji na wskaźniki czasu i stanu technicznego oraz pozostały okres użytkowania (RUL).

Słowa kluczowe

EN

virtual health indicator; virtual age; maintenance effectiveness; preventive and corrective maintenance; Cox-Weibull hazard function; proportional hazards model

PL

wirtualny wskaźnik stanu technicznego; wiek wirtualny; skuteczność konserwacji; konserwacja zapobiegawcza i korygująca; funkcja hazardu Coxa–Weibulla; model proporcjonalnego hazardu

• Wydawca: Polskie Naukowo-Techniczne Towarzystwo Eksploatacyjne
• Czasopismo: Eksploatacja i Niezawodność
• Rocznik: 2019
• Tom: Vol. 21, no. 4
• Strony: 619--630
• Opis fizyczny: Bibliogr. 46 poz., rys., tab.

Twórcy

autor

Babishin Vladimir

• Department of Mechanical and Industrial Engineering Ryerson University 350 Victoria Street Toronto, Ontario, M5B 2K3, Canada

autor

Taghipour Sharareh

• Department of Mechanical and Industrial Engineering Ryerson University 350 Victoria Street Toronto, Ontario, M5B 2K3, Canada

Bibliografia

• 1. Ardakani HD, Lucas C, Siegel D, Chang S, Dersin P, Bonnet B, Lee J. PHM for Railway System - a Case Study on the Health Assessment of Point Machines. Proceedings of the Prognostics and Health Management (PHM) IEEE Conference 2012 : 74-79, https://doi.org/10.1109/ICPHM.2012.6299533.
• 2. Atamuradov V, Medjaher K, Dersin P, Lamoureux B, Zerhouni N. Prognostics and Health Management for Maintenance Practitioners - Review, Implementation and Tools Evaluation. International Journal of Prognostics and Health Management 2017; 8 (Special Issue on Railways & Mass Transportation): 1-31.
• 3. Babishin V, Hajipour Y, Taghipour S. Optimisation of Non-Periodic Inspection and Maintenance for Multicomponent Systems. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2018; 20(2): 327-342, https://doi.org/10.17531/ein.2018.2.20.
• 4. Babishin V, Taghipour S. Joint Maintenance and Inspection Optimization of a k-out-of-n System. In: Proceedings of the Annual Reliability and Maintainability Symposium (RAMS) 2016: 1-6, https://doi.org/10.1109/RAMS.2016.7448039.
• 5. Babishin V, Taghipour S. Joint Optimal Maintenance and Inspection for a k-out-of-n System. International Journal of Advanced Manufacturing Technology 2016;87 (5-8): 1739-1749, https://doi.org/10.1007/s00170-016-8570-z.
• 6. Babishin V, Taghipour S. Maintenance Effectiveness Estimation with Applications to Railway Industry. In: Proceedings of the Annual Reliability and Maintainability Symposium (RAMS) 2019, https://doi.org/10.1109/RAMS.2019.8769273.
• 7. Babishin V, Taghipour S. Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements. Applied Mathematical Modelling 2016; 40 (23-24): 10480-10505, https://doi.org/10.1016/j.apm.2016.07.019.
• 8. Bendell A, Wightman DW, Walker EV. Applying Proportional Hazards Modelling in Reliability. Reliability Engineering and System Safety 1991; 34: 35-53, https://doi.org/10.1016/0951-8320(91)90098-R.
• 9. Brown M, Proschan F. Imperfect repair. Journal of Applied Probability 1983; 20: 851-859, https://doi.org/10.2307/3213596.
• 10. Cha JH, Finkelstein M. Optimal Long-Run Imperfect Maintenance With Asymptotic Virtual Age. IEEE Transactions on Reliability 2016; 65(1): 187-196, https://doi.org/10.1109/TR.2015.2451612.
• 11. Chan JK, Shaw L. Modelling repairable systems with failure rates that depend on age and maintenance. IEEE T Reliab. 1993; 42: 566-570, https://doi.org/10.1109/24.273583.
• 12. Chen Y, Meng X, Chen S. Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks. Mathematical Problems in Engineering 2014, https://doi.org/10.1155/2014/507846.
• 13. Conn A, Deleris L, Hosking J, Thorstensen T. A simulation model for improving the maintenance of high cost systems, with application to offshore oil installation. Quality and Reliability Engineering International 2010; 26: 733-748, https://doi.org/10.1002/qre.1136.
• 14. Corman F, Kraijema S, Godjevac M, Lodewijks G. Optimizing preventive maintenance policy: A data-driven application for a light rail braking system. Proc IMechE Part O: J Risk and Reliability 2017; 231(5): 534-545, https://doi.org/10.1177/1748006X17712662.
• 15. Cox DR. Regression models and life-tables. New York: Springer; 1992, https://doi.org/10.1007/978-1-4612-4380-9_37.
• 16. Dagpunar J. Some properties and computational results for a general repair process. Naval Research Logistics 1998; 45: 391-405, https://doi.org/10.1002/(SICI)1520-6750(199806)45:4<391::AID-NAV5>3.0.CO;2-0.
• 17. Doyen L, Gaudoin O. Classes of imperfect repair models based on reduction of failure intensity or virtual age. Rel Eng and Sys Safety 2004;84: 45-56, https://doi.org/10.1016/S0951-8320(03)00173-X.
• 18. Doyen L, Gaudoin O. Imperfect maintenance in a generalized competing risks framework. Journal of Applied Probability 2006; 43: 825-839, https://doi.org/10.1239/jap/1158784949.
• 19. Fuqing Y, Kumar U. A General Imperfect Repair Model Considering Time-Dependent Repair Effectiveness. IEEE Transactions on Reliability 2012; 61(1): 95-100, https://doi.org/10.1109/TR.2011.2182222
• 20. Galar D, Gustafson A, Tormos B, Berges L. Maintenance Decision Making Based on Different Types of Data Fusion. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2012; 14(2): 135-144.
• 21. Grimble MJ. Robust Industrial Control: Optimal Design Approach for Polynomial Systems. New Jersey: Prentice Hall; 1994.
• 22. Heng A, Tan ACC, Mathew J, Montgomery N, Banjevic D, Jardine AKS. Intelligent condition-based prediction of machinery reliability.Mechanical Systems and Signal Processing 2009; 23: 1600-1614, https://doi.org/10.1016/j.ymssp.2008.12.006.
• 23. Hu J, Jiang Z, Liao H. Preventive maintenance of a single machine system working under piecewise constant operating condition. Reliability Engineering and System Safety 2017; 168: 105-115, https://doi.org/10.1016/j.ress.2017.05.014.
• 24. Innotrack. Deliverable 1.4.8 - Overall Cost Reduction. Project Report. Gothenburg, Sweden: Chalmers University of Technology 2009. TIP5-CT-2006-031415.
• 25. Kallen M. Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes. Rel Eng and Sys Safety 2011; 96: 636-641, https://doi.org/10.1016/j.ress.2010.12.005.
• 26. Kalman RE. A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering 1960; 82(35): 35-45, https://doi.org/10.1115/1.3662552.
• 27. Kijima M. Some results for repairable systems with general repair. Journal of Applied Probability 1989; 26: 89-102, https://doi.org/10.2307/3214319.
• 28. Kijima M, Nakagawa T. Replacement policies of a shock model with imperfect maintenance. Eur J Oper Res. 1992; 57: 100-110, https://doi.org/10.1016/0377-2217(92)90309-W.
• 29. Kumar S, Vichare NM, Dolev E, Pecht M. A health indicator method for degradation detection of electronic products. Microelectronics Reliability 2012; 52: 439-445, https://doi.org/10.1016/j.microrel.2011.09.030.
• 30. Letot C, Dersin P, Pugnaloni M, Dehombreux P, Fleurquin G, Douziech C, La-Cascia P. A Data Driven Degradation-Based Model for the Maintenance of Turnouts: a Case Study. IFAC-PapersOnLine 2015: 958-963, https://doi.org/10.1016/j.ifacol.2015.09.650.
• 31. Levenberg K. A Method for the Solution of Certain Non-Linear Problems in Least Squares. Applied Mathematics Quarterly 1944; 2: 164-168, https://doi.org/10.1090/qam/10666.
• 32. Lim TJ, Lie CH. Analysis of system reliability with dependent repair modes. IEEE Transactions on Reliability 2000; 49(2): 153-162, https://doi.org/10.1109/24.877332.
• 33. Malik M. Reliable preventive maintenance scheduling. AIIE Transactions 1979; 11: 221-228, https://doi.org/10.1080/05695557908974463.
• 34. Marquardt D. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. SIAM Journal on Applied Mathematics 1963; 11(2):431-441, https://doi.org/10.1137/0111030.
• 35. Martorell S, Sanchez A, Serradell V. Age-dependent reliability model considering effects of maintenance and working conditions. Reliability Engineering and System Safety 1999; 64(1): 19-31, https://doi.org/10.1016/S0951-8320(98)00050-7.
• 36. Nasr A, Gasmi S, Sayadi M. Estimation of the parameters for a complex repairable system with preventive and corrective maintenance. In: IEEE Proc, International Conference on Electrical Engineering and Software Applications (ICEESA) 2013: 1-6, https://doi.org/10.1109/ICEESA.2013.6578455.
• 37. Pham H, Wang H. Imperfect maintenance. Eur J Oper Res. 1996; 94: 425-438, https://doi.org/10.1016/S0377-2217(96)00099-9.
• 38. Pulcini G. Mechanical Reliability and Maintenance Models. In: H P, editor. Handbook of Reliability Engineering. London: Springer-Verlag 2003: 317-348, https://doi.org/10.1007/1-85233-841-5_18.
• 39. Said U, Taghipour S. Modeling Failure Process and Quantifying the Effects of Multiple Types of Preventive Maintenance for a Repairable System. Quality and Reliability Engineering International 2016; 33(5): 1149-1161, https://doi.org/10.1002/qre.2088.
• 40. Syamsundar A, Muralidharan K, Naikan V. General repair models for maintained systems. Sri Lankan Journal of Applied Statistics 2012; 12(1): 117-143, https://doi.org/10.4038/sljastats.v12i0.4971.
• 41. Syamsundar A, Naikan VNA. Imperfect repair proportional intensity models for maintained systems. IEEE transactions on Reliability 2011; 60(4): 782-787, https://doi.org/10.1109/TR.2011.2161110.
• 42. Uematsu K, Nishida T. One unit system with a failure rate depending upon the degree of repair. Math. Japonica 1987; 32: 685-691, https://doi.org/10.1016/0026-2714(87)90015-1.
• 43. Wang Y, Cotofana S. A novel virtual age reliability model for time-to-failure prediction. Integrated Reliability Workshop Final Report (IRW). IEEE; 2010, https://doi.org/10.1109/IIRW.2010.5706498.
• 44. Wu S, Zuo MJ. Linear and nonlinear preventive maintenance models. IEEE T Reliab. 2010; 59(1): 242-249, https://doi.org/10.1109/TR.2010.2041972.
• 45. Yu P, Song J, Cassady C. Parameter estimation for a repairable system under imperfect maintenance. In: Proceedings of the Annual Reliability and Maintainability Symposium 2008: 428-433.
• 46. Zhou X, Xi L, Lee J. Reliability-centred predictive maintenance scheduling for a continuously monitor system subject to degradation. Reliab Eng Syst Safety 2007; 92(4): 530-534, https://doi.org/10.1016/j.ress.2006.01.006.