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Similarity-based residual life prediction method based on dynamic time scale and local similarity search

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Abstract

Residual useful life (RUL) prediction is the core of prognostics and health management. Similarity-based residual life prediction (SbRLP) is vital in RUL prediction due to its independence from degradation modeling, as well as high accuracy and robustness in prediction. However, researchers typically adopt a fixed time scale and global similarity search to perform similarity measurement, leading to considerable prediction errors and prolonged prediction times. Hence, a novel SbRLP method based on a dynamic time scale and local similarity search is proposed herein. First, the monitoring variables are reduced using the variable selection method based on multilayer information overlap. Next, the health states of reference samples are divided into five states using the K-means algorithm and the health states of the operating sample are recognized using the L-KNN algorithm. Further, dynamic time scales of the operating and reference samples are determined based on their length proportions of degradation trajectory at different prediction times. The local similarity search intervals of reference samples are obtained based on their health state levels. Next, the RULs of the operating sample are predicted using the local similarity search intervals and dynamic time scales. Finally, the effectiveness and superiority of the enhanced SbRLP are demonstrated using the commercial modular aero-propulsion system simulation dataset. The results reveal that the enhanced SbRLP yields a more accurate and efficient prediction of RUL in comparison with alternative methods.

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Abbreviations

RUL:

Residual useful life

PHM:

Prognostics and health management

DTW:

Dynamic time warping

SOMM:

Self-organizing map models

SVDD:

Support vector data descriptions

LSTM:

Long short-term memory

PCA:

Principal component analysis

HPC:

High-pressure compressor

LPT:

Low-pressure turbine

RMSE:

Root-mean-square error

L-KNN:

KNN algorithm fused with LSTM

SbRLP:

Similarity-based residual life prediction

DCNN:

Deep convolutional neural network

SVM:

Support vector machines

CHSMM:

Continuous hidden semi-Markov models

KNN:

K-nearest neighbors

C-MAPSS:

Commercial modular aero-propulsion system simulation

LPC:

Low-pressure compressor

HPT:

High-pressure turbine

MAE:

Mean absolute error

Score:

Score function

\(rr_{ab}\) :

Person correlation of variables \(a\) and \(b\)

\(pp_{ab}\) :

\(A - 2\)-Order partial correlation of variables \(a\) and \(b\)

\({\text{SIO}}_{a}\) :

Univariate information overlap of variable \(a\)

\(R_{a}\) :

Person correlation between variable \(a\) and the monitoring time

\(X_{{{\text{r}}i}} \left( {q \cdot \Delta t} \right)\) :

Value of reference sample \(i\) at sampling point \(q\)

\(\psi_{{{\text{r}}i}}^{k} \left( {q \cdot \Delta t} \right)\) :

Weight of the \(k\) th nearest neighbor sample of \(X_{ri} \left( {q \cdot \Delta t} \right)\)

\(H_{{\text{o}}}^{p}\) :

Time scale of the operating sample at time \(p \cdot \Delta t\)

\(w_{d}\) :

Importance of variable \(d\)

\(K_{{{\text{r}}i}}^{5} \cdot \Delta t\) :

Failure time of the \(i\) th reference sample

\({\text{HS}}_{g}\) :

Best health state in \({\text{HD}}_{{{\text{op}}}}\)

\({\text{Sim}}\left( {p,H_{{\text{o}}}^{p} ,i,H_{{{\text{r}}i}}^{p} ,q} \right)\) :

Similarity between sequences \(Y_{{{\text{op}}}}\) and \(Y_{{{\text{r}}i}}^{p}\)

\({\text{SSI}}_{{{\text{r}}i}}^{p}\) :

Local similarity search interval of the \(i\) th reference sample at time \(p \cdot \Delta t\)

\({\text{ARL}}_{ri} (p)\) :

Actual RUL of the \(i\) th reference sample

\(x_{{{\text{r}}i}}^{d} \left( {q \cdot \Delta t} \right)\) :

Value of variable \(d\) of reference sample \(i\) at sampling point \(q\)

\(cc_{ab}\) :

One element in the inverse matrix of the correlation matrix \(\left( {rr_{ab} } \right)_{A \times A}\)

\({\text{TIO}}_{A}\) :

Overall information overlap of \(A\) monitoring variables

\({\text{MSA}}_{a} \left( A \right)\) :

Correlation between variable \(a\) and other \(A - 1\) variables

\(d_{{{\text{r}}i}}^{k} \left( {q \cdot \Delta t} \right)\) :

Euclidean distance between \(X_{{{\text{r}}i}} \left( {q \cdot \Delta t} \right)\) and its \(k\) th nearest neighbor sample

\(y_{{\text{o}}} \left( p \right)\) :

Health index of the operating sample at time \(p \cdot \Delta t\)

\(X_{{\text{o}}} \left( {p \cdot \Delta t} \right)\) :

Value of the operating sample at sampling point \(p\)

\(Y_{{{\text{op}}}}\) :

Similarity measurement sequence of the operating sample at time \(p \cdot \Delta t\)

\(H_{{{\text{r}}i}}^{p}\) :

Time scale of the \(i\) th reference sample

\({\text{EM}}_{{\text{o}}}\) :

Expected lifetime of the operating sample

\({\text{HS}}_{l}\) :

Worst one health state in \({\text{HD}}_{{{\text{op}}}}\)

\(Y_{{{\text{r}}i}}^{p}\) :

Similarity measurement sequence of reference sample \(i\) at time \(p \cdot \Delta t\)

\(N_{{{\text{r}}i}} \left( p \right)\) :

Similarity sampling point of the \(i\) th reference sample corresponding to the similarity \(S_{o \leftrightarrow ri} (p)\)

\({\text{PRL}}_{{\text{o}}} \left( p \right)\) :

RUL of the operating sample at time \(p \cdot \Delta t\)

\(x_{{\text{o}}}^{d} \left( {q \cdot \Delta t} \right)\) :

Value of variable \(d\) of the operating sample at sampling point \(q\)

References

  1. Ma B, Yan S, Wang X, Chen J, Zheng C (2020) Similarity-based failure threshold determination for system residual life prediction. Eksploat Niezawodn 22(3):520–529

    Google Scholar 

  2. Kong X, Yang J, Li L (2021) Remaining useful life prediction for degrading systems with random shocks considering measurement uncertainty. J Manuf Syst 61:782–798

    Google Scholar 

  3. Ding P, Liu X, Li H, Huang Z, Zhang K, Shao L, Abedinia O (2021) Useful life prediction based on wavelet packet decomposition and two-dimensional convolutional neural network for lithium-ion batteries. Renew Sust Energ Rev 148:111287

    Google Scholar 

  4. Lyu Y, Zhang Q, Chen A, Wen Z (2023) Interval prediction of remaining useful life based on convolutional auto-encode and lower upper bound estimation. Eksploat Niezawodn 25(2):1–10

    Google Scholar 

  5. Lyu Y, Jiang Y, Zhang Q, Chen C (2021) Remaining useful life prediction with insufficient degradation data based on deep learning approach. Eksploat Niezawodn 23(4):745–756

    Google Scholar 

  6. Cubillo A, Perinpanayagam S, Esperon-Miguez MA (2016) Review of physics-based models in prognostics: Application to gears and bearings of rotating machinery. Adv Mech Eng 8(8):1687814016664660

    Google Scholar 

  7. Chan KS, Enright MP, Moody JP, Hocking B, Fitch SH (2012) Life prediction for turbo propulsion systems under dwell fatigue conditions. J Eng Gas Turbine Power 134:122501

    Google Scholar 

  8. Lei Y, Li N, Guo L, Li N, Yan T, Lin J (2018) Machinery health prognostics: a systematic review from data acquisition to RUL prediction. Mech Syst Signal Pr 104:799–834

    Google Scholar 

  9. Su C, Chen H, Wen Z (2021) Prediction of remaining useful life for lithium-ion battery with multiple health indicators. Eksploat Niezawodn 23(1):176–183

    Google Scholar 

  10. Wang Z, Chen Y, Cai Z, Wang L (2020) Methods for predicting the remaining useful life of equipment in consideration of the random failure threshold. J Syst Eng Electron 31(2):415–431

    Google Scholar 

  11. Qian Y, Yan R, Gao RX (2017) A multi-time scale approach to remaining useful life prediction in rolling bearing. Mech Syst Signal Pr 83:549–567

    Google Scholar 

  12. Liu J, Djurdjanovic D, Ni J, Casoetto N, Lee J (2007) Similarity based method for manufacturing process performance prediction and diagnosis. Comput Ind 58(6):558–566

    Google Scholar 

  13. Yu W, Kim IY, Mechefske C (2020) An improved similarity-based prognostic algorithm for RUL estimation using an RNN autoencoder scheme. Reliab Eng Syst Safe 199:106926

    Google Scholar 

  14. Wang H, Chen J, Qu J, Ni G (2020) A new approach for safety life prediction of industrial rolling bearing based on state recognition and similarity analysis. Safety Sci 122:104530

    Google Scholar 

  15. You MY, Meng G (2013) Toward effective utilization of similarity based residual life prediction methods: Weight allocation, prediction robustness, and prediction uncertainty. P I Mech Eng E-J Pro 227(E1):74–84

    Google Scholar 

  16. You MY, Meng GA (2011) generalized similarity measure for similarity-based residual life prediction. P I Mech Eng E-J Pro 225(3):151–160

    Google Scholar 

  17. Zhang Q, Tse PWT, Wan X, Xu G (2015) Remaining useful life estimation for mechanical systems based on similarity of phase space trajectory. Expert Syst Appl 42(5):2353–2360

    Google Scholar 

  18. Zhao HL, Chen TM (2022) Engine life prediction based on two-scale similarity. J Propul Tech 43:355–362

    Google Scholar 

  19. Liang Z, Gao J, Jiang H (2019) A maintenance support framework based on dynamic reliability and remaining useful life. Measurement 147:106835

    Google Scholar 

  20. Zio E, Di Maio F (2010) A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system. Reliab Eng Syst Safe 95(1):49–57

    Google Scholar 

  21. Chen YX, Rao Y, Cai ZY, Wang ZZ (2021) Remaining useful lifetime prediction and economic reserve strategy of equipment components based on improved similarity. Syst Eng Electron 43(09):2688–2696

    Google Scholar 

  22. Gu MY, Chen YL (2019) Two improvements of similarity-based residual life prediction methods. J intel Manuf 30(1):303–315

    Google Scholar 

  23. Qi LI, Gao ZB, Li SY, Li BA (2016) Similarity-based remaining useful life prediction method under varying operational conditions. J Beijing Univ Aeronaut Astronaut 42(06):1236–1243

    Google Scholar 

  24. Gu MY, Ge JQ (2022) An improved similarity-based residual life prediction method based on the dynamic variable combination. Sadhana-Acad P Eng S 47(3):1–13

    MathSciNet  Google Scholar 

  25. Hou M, Pi D, Li B (2020) Similarity-based deep learning approach for remaining useful life prediction. Measurement 159:107788

    Google Scholar 

  26. Li G, Huang Q, Mao Y, Chai Y (2022) A deep learning method on remaining useful life estimation based on linear regression model and greed matching strategy. In: Sixth international conference on electromechanical control technology and transportation (ICECTT 2021). Vol 12081, pp 1069–1076

  27. Wang T, Yu J, Siegel D (2008) A similarity-based prognostics approach for remaining useful life estimation of engineered systems. In: 2008 international conference on prognostics and health management (PHM), pp 53–56

  28. Tavenard R, Amsaleg L (2015) Improving the efficiency of traditional DTW accelerators. Knowl Inf Syst 42(1):215–243

    Google Scholar 

  29. Deng M, Li ZL, Chen XY (2007) Extended Hausdorff distance for spatial objects in GIS. Int J Geogr Inf Sci 21(4):459–475

    Google Scholar 

  30. Tong X, Liang D, Jin Y (2014) A linear road object matching method for conflation based on optimization and logistic regression. Int J Geogr Inf Sci 28(4):824–846

    Google Scholar 

  31. Gu MY, Ge J (2022) Method for residual useful life prediction based on compound similarity. J Mech Sci Technol 36(12):5959–5969

    Google Scholar 

  32. Zhang BS, Zhang L, Zhang B (2020) Equipment health classification model based on failure risk scale. Syst Eng Electron 42(2):489–496

    Google Scholar 

  33. Nakamura T, Nagai T, Mochihashi D, Kobayashi I, Asoh H, Kaneko M (2017) Segmenting continuous motions with hidden semi-markov models and gaussian processes. Front Neurorobotics 11:67

    Google Scholar 

  34. Kim HE, Tan AC, Mathew J, Choi BK (2012) Bearing fault prognosis based on health state probability estimation. Expert Syst Appl 39(5):5200–5213

    Google Scholar 

  35. Cerrada M, Sánchez RV, Li C, Pacheco F, Cabrera D, de Oliveira JV, Vásquez RE (2018) A review on data-driven fault severity assessment in rolling bearings. Mech Syst Signal Pr 99:169–196

    Google Scholar 

  36. Pan YN, Chen J, Guo L (2009) Robust bearing performance degradation assessment method based on improved wavelet packet-support vector data description. Mech Syst Signal Pr 23(3):669–681

    Google Scholar 

  37. Chen XG, Fan YJ, Ma ZP (2023) Aging state discrimination of oil-paper insulation primitive Raman spectroscopy based on integrated enhanced KNN. Laser Optoelectron P. https://kns.cnki.net/kcms2/detail/31.1690.TN.20230714.0950.044.html

  38. Liu Y, Hu X, Zhang W (2019) Remaining useful life prediction based on health index similarity. Reliab Eng Syst Safe 185:502–510

    Google Scholar 

  39. Benkedjouh T, Medjaher K, Zerhouni N (2013) Remaining useful life estimation based on nonlinear feature reduction and support vector regression. Eng Appl Artif Intel 26(7):1751–1760

    Google Scholar 

  40. Yan J, Koc M, Lee J (2004) A prognostic algorithm for machine performance assessment and its application. Prod Plan Control 15(8):796–801

    Google Scholar 

  41. Guo L, Lei Y, Li N, Xing SB (2017) Deep convolution feature learning for health indicator construction of bearings. In: 2017 Prognostics and system health management conference (PHM). pp 318–323.

  42. Chen HH (2022) Method of screening evaluation indicators based on anti-image correlation matrix. Chin J Manag Sci 30(11):149–158

    Google Scholar 

  43. Destrero A, Mosci S, Mol CD (2009) Feature selection for high dimensional data. Comput Manag Sci 6(1):25–40

    MathSciNet  Google Scholar 

  44. Wu WL, Zhou XL (2019) Establishment and application of the evaluation system of inclusive green growth performance in China. Chin J Manag Sci 27(9):183–194

    Google Scholar 

  45. Liu Z, Zuo MJ, Qin Y (2015) Remaining useful life prediction of rolling element bearings based on health state assessment. P I Mech Eng C-J Mec 230(2):314–330

    Google Scholar 

  46. Gu MY, Ge JQ (2023) Research on health state assessment and prediction for complex equipment based on the improved FMECA and GM (1,1). Int J Syst Assur Eng 14:523–538

    Google Scholar 

  47. You MY, Meng G (2013) A framework of similarity-based residual life prediction approaches using degradation histories with failure, preventive maintenance, and suspension events. IEEE T Reliab 62(1):127–135

    Google Scholar 

Download references

Funding

The paper is financially supported by the Science and technology planning project of Zhejiang provincial market supervision administration (Project number: ZD2024005); open foundation of the key laboratory of intelligent robot for operation and maintenance of Zhejiang Province (Project number: SZKF-2022-R05); National Natural Science Foundation of China (Project number: 52175257); National key R&D plan project (Project number: 2021YFC3340400); and Key R&D project of Zhejiang Province (Project number: 2021C01053).

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Authors and Affiliations

  1. College of Quality and Standardization Engineering, China Jiliang University, Hangzhou, China

    Meng Yao Gu, Zhi Xi Dai & Xin Sheng Xu

  2. Postdoctoral Research Station of Zhejiang Institute of Product Quality and Safety Sciences, Hangzhou, 310018, China

    Meng Yao Gu

  3. College of Mechanical Engineering, Zhejiang University, Hangzhou, 310018, China

    Meng Yao Gu

  4. Zhejiang Key Laboratory of Intelligent Operation and Maintenance Robot, Hangzhou Shenhao Technology Co., Ltd, Hangzhou, China

    Hai Teng Wu

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  1. Meng Yao Gu
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Correspondence to Meng Yao Gu or Zhi Xi Dai.

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Gu, M.Y., Dai, Z.X., Wu, H.T. et al. Similarity-based residual life prediction method based on dynamic time scale and local similarity search. J Braz. Soc. Mech. Sci. Eng. 46, 276 (2024). https://doi.org/10.1007/s40430-024-04857-3

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