{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T02:49:20Z","timestamp":1775962160224,"version":"3.50.1"},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T00:00:00Z","timestamp":1687651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T00:00:00Z","timestamp":1687651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"NTNU Norwegian University of Science and Technology"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Syst Assur Eng Manag"],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Deterioration modelling and remaining useful life (RUL) prediction of roller bearings is critical to ensure a safe, reliable, and efficient operation of rotating machinery. RUL prediction models in model-based approaches are often based on constant failure threshold and time-domain features for bearings\u2019 failure prognosis. Due to nonlinearity of the acceleration signals, noises, and measurement errors, the time-domain features used as condition indicators are unable to track bearings\u2019 degradation successfully and they are mostly utilized for fault diagnosis, especially in the fault classification field using machine learning algorithms. This paper proposes an adaptive RUL prediction framework with a stochastic failure threshold which comprises of two main phases of feature extraction and RUL prediction using laboratory-acquired accelerated life test data obtained from contaminated bearings. The first phase is to decompose the empirical input signals into different frequency bands using some time\u2013frequency transformation functions and extract several condition indicators for the second phase. The second phase is based on a stochastic Wiener process while the key parameters of the model are updated iteratively using a Bayesian approach, and RUL at different degradation datapoints is computed numerically. The experimental results showed the good performance of the developed framework. Some factors affecting RUL prediction such as the length of bearing samples, and degradation mechanism are highlighted in the result. The results of this paper can be further used for an effective maintenance optimization, determining an optimal maintenance alarm threshold, improving the reliability and safety of rotating machinery, and reducing the downtime cost.<\/jats:p>","DOI":"10.1007\/s13198-023-01979-0","type":"journal-article","created":{"date-parts":[[2023,6,25]],"date-time":"2023-06-25T17:01:36Z","timestamp":1687712496000},"page":"1756-1777","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adaptive remaining useful life prediction framework with stochastic failure threshold for experimental bearings with different lifetimes under contaminated condition"],"prefix":"10.1007","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6340-5038","authenticated-orcid":false,"given":"Bahareh","family":"Tajiani","sequence":"first","affiliation":[]},{"given":"J\u00f8rn","family":"Vatn","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,25]]},"reference":[{"issue":"April","key":"1979_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/J.RESS.2018.02.003","volume":"184","author":"W Ahmad","year":"2019","unstructured":"Ahmad W, Khan SA, Islam MMM, Kim JM (2019) A reliable technique for remaining useful life estimation of rolling element bearings using dynamic regression models. Reliab Eng Syst Saf 184(April):67\u201376. https:\/\/doi.org\/10.1016\/J.RESS.2018.02.003","journal-title":"Reliab Eng Syst Saf"},{"issue":"4","key":"1979_CR2","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/S13198-013-0195-0\/FIGURES\/1","volume":"5","author":"F Ahmadzadeh","year":"2014","unstructured":"Ahmadzadeh F, Lundberg J (2014) Remaining useful life estimation: review. Int J Syst Assur Eng Manag 5(4):461\u2013474. https:\/\/doi.org\/10.1007\/S13198-013-0195-0\/FIGURES\/1","journal-title":"Int J Syst Assur Eng Manag"},{"key":"1979_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-016-0459-6","author":"N Bessous","year":"2016","unstructured":"Bessous N, Zouzou SE, Bentrah W, Sbaa S, Sahraoui M (2016) Diagnosis of bearing defects in induction motors using discrete wavelet transform. Int J Syst Assur Eng Manag. https:\/\/doi.org\/10.1007\/s13198-016-0459-6","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"3","key":"1979_CR4","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1007\/S13198-013-0151-Z\/FIGURES\/6","volume":"5","author":"A Bhattacharya","year":"2014","unstructured":"Bhattacharya A, Dan PK (2014) Recent trend in condition monitoring for equipment fault diagnosis. Int J Syst Assur Eng Manag 5(3):230\u2013244. https:\/\/doi.org\/10.1007\/S13198-013-0151-Z\/FIGURES\/6","journal-title":"Int J Syst Assur Eng Manag"},{"key":"1979_CR5","doi-asserted-by":"publisher","unstructured":"Boashash B, Touati S, Flandrin P, Hlawatsch F, Taub\u00f6ck G, Oliveira PM, Barroso V et al (2016) Advanced time-frequency signal and system analysis. In: Boashash B (ed) Time-frequency signal analysis and processing: a comprehensive reference. Elsevier Inc., pp 141\u2013236. https:\/\/doi.org\/10.1016\/B978-0-12-398499-9.00004-2","DOI":"10.1016\/B978-0-12-398499-9.00004-2"},{"issue":"3","key":"1979_CR6","doi-asserted-by":"publisher","first-page":"156","DOI":"10.22266\/ijies2019.0630.17","volume":"12","author":"T Boukra","year":"2019","unstructured":"Boukra T, Bensafia Y, Khettab K (2019) Contribution in enhancing the remaining useful life prediction in abrupt failures: bearing case. Int J Intell Eng Syst 12(3):156\u2013165. https:\/\/doi.org\/10.22266\/ijies2019.0630.17","journal-title":"Int J Intell Eng Syst"},{"key":"1979_CR7","doi-asserted-by":"publisher","DOI":"10.3390\/machines5040021","author":"W Caesarendra","year":"2017","unstructured":"Caesarendra W, Tjahjowidodo T (2017) A review of feature extraction methods in vibration-based condition monitoring and its application for degradation trend estimation of low-speed slew bearing. Machines. https:\/\/doi.org\/10.3390\/machines5040021","journal-title":"Machines"},{"issue":"April","key":"1979_CR8","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/J.RENENE.2015.12.010","volume":"89","author":"J Chen","year":"2016","unstructured":"Chen J, Pan J, Li Z, Zi Y, Chen X (2016) Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals. Renew Energy 89(April):80\u201392. https:\/\/doi.org\/10.1016\/J.RENENE.2015.12.010","journal-title":"Renew Energy"},{"issue":"90","key":"1979_CR9","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","volume":"19","author":"JW Cooley","year":"1965","unstructured":"Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex Fourier series. Math Comput 19(90):297\u2013301. https:\/\/doi.org\/10.1090\/S0025-5718-1965-0178586-1","journal-title":"Math Comput"},{"key":"1979_CR10","doi-asserted-by":"crossref","unstructured":"Cowles MK (2013) Applied Bayesian statistics: with R and OpenBUGS examples, vol 232. https:\/\/books.google.com\/books\/about\/Applied_Bayesian_Statistics.html?id=iVxDAAAAQBAJ","DOI":"10.1007\/978-1-4614-5696-4"},{"issue":"3","key":"1979_CR11","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/S13198-019-00813-W","volume":"10","author":"MA Farsi","year":"2019","unstructured":"Farsi MA, Masood Hosseini S (2019) Statistical distributions comparison for remaining useful life prediction of components via ANN. Int J Syst Assur Eng Manag 10(3):429\u2013436. https:\/\/doi.org\/10.1007\/S13198-019-00813-W","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"4","key":"1979_CR12","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1007\/S13198-016-0509-0\/FIGURES\/12","volume":"7","author":"V Fornl\u00f6f","year":"2016","unstructured":"Fornl\u00f6f V, Galar D, Syberfeldt A, Almgren T (2016) RUL estimation and maintenance optimization for aircraft engines: a system of system approach. Int J Syst Assur Eng Manag 7(4):450\u2013461. https:\/\/doi.org\/10.1007\/S13198-016-0509-0\/FIGURES\/12","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"1","key":"1979_CR13","doi-asserted-by":"publisher","first-page":"182","DOI":"10.3390\/S21010182","volume":"21","author":"T Gao","year":"2020","unstructured":"Gao T, Li Y, Huang X, Wang C (2020) Data-driven method for predicting remaining useful life of bearing based on Bayesian theory. Sensors 21(1):182. https:\/\/doi.org\/10.3390\/S21010182","journal-title":"Sensors"},{"issue":"May","key":"1979_CR14","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.neucom.2017.02.045","volume":"240","author":"L Guo","year":"2017","unstructured":"Guo L, Li N, Jia F, Lei Y, Lin J (2017) A recurrent neural network based health indicator for remaining useful life prediction of bearings. Neurocomputing 240(May):98\u2013109. https:\/\/doi.org\/10.1016\/j.neucom.2017.02.045","journal-title":"Neurocomputing"},{"issue":"1971","key":"1979_CR15","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1098\/RSPA.1998.0193","volume":"454","author":"NE Huang","year":"1998","unstructured":"Huang NE, Shen Z, Long SR, Wu MC, Snin HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A Math Phys Eng Sci 454(1971):903\u2013995. https:\/\/doi.org\/10.1098\/RSPA.1998.0193","journal-title":"Proc R Soc A Math Phys Eng Sci"},{"key":"1979_CR16","doi-asserted-by":"publisher","unstructured":"Huang NE (2005) Introduction to the Hilbert\u2013Huang transform and its related mathematical problems. 1\u201326. World Scientific Publishing Co. https:\/\/doi.org\/10.1142\/9789812703347_0001","DOI":"10.1142\/9789812703347_0001"},{"issue":"April","key":"1979_CR17","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/J.RESS.2018.02.010","volume":"184","author":"J Jiao","year":"2019","unstructured":"Jiao J, Zhao M, Lin J, Liang K (2019) Hierarchical discriminating sparse coding for weak fault feature extraction of rolling bearings. Reliab Eng Syst Saf 184(April):41\u201354. https:\/\/doi.org\/10.1016\/J.RESS.2018.02.010","journal-title":"Reliab Eng Syst Saf"},{"issue":"2","key":"1979_CR18","doi-asserted-by":"publisher","first-page":"6128","DOI":"10.1016\/J.MATPR.2017.12.219","volume":"5","author":"S Kumar","year":"2018","unstructured":"Kumar S, Goyal D, Dang RK, Dhami SS, Pabla BS (2018) Condition based maintenance of bearings and gears for fault detection: a review. Mater Today Proc 5(2):6128\u20136137. https:\/\/doi.org\/10.1016\/J.MATPR.2017.12.219","journal-title":"Mater Today Proc"},{"issue":"1","key":"1979_CR19","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/S13198-021-01282-W\/FIGURES\/13","volume":"13","author":"V Kumar","year":"2022","unstructured":"Kumar V, Parida MK, Albert SK (2022) The state-of-the-art methodologies for quality analysis of arc welding process using weld data acquisition and analysis techniques. Int J Syst Assur Eng Manag 13(1):34\u201356. https:\/\/doi.org\/10.1007\/S13198-021-01282-W\/FIGURES\/13","journal-title":"Int J Syst Assur Eng Manag"},{"key":"1979_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/S13198-020-01039-X\/FIGURES\/14","author":"W Laala","year":"2020","unstructured":"Laala W, Guedidi A, Guettaf A (2020) Bearing faults classification based on wavelet transform and artificial neural network. Int J Syst Assur Eng Manag. https:\/\/doi.org\/10.1007\/S13198-020-01039-X\/FIGURES\/14","journal-title":"Int J Syst Assur Eng Manag"},{"key":"1979_CR21","doi-asserted-by":"publisher","unstructured":"Lall P, Lowe R, Goebel K (2013) Prognostic health monitoring for a micro-coil spring interconnect subjected to drop impacts. In: PHM 2013\u20142013 IEEE international conference on prognostics and health management, conference proceedings. https:\/\/doi.org\/10.1109\/ICPHM.2013.6621458","DOI":"10.1109\/ICPHM.2013.6621458"},{"key":"1979_CR22","doi-asserted-by":"publisher","first-page":"106628","DOI":"10.1016\/J.RESS.2019.106628","volume":"195","author":"D Lee","year":"2020","unstructured":"Lee D, Choi D (2020) Analysis of the reliability of a starter-generator using a dynamic Bayesian network. Reliab Eng Syst Saf 195:106628. https:\/\/doi.org\/10.1016\/J.RESS.2019.106628","journal-title":"Reliab Eng Syst Saf"},{"key":"1979_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2012.09.015","author":"Y Lei","year":"2012","unstructured":"Lei Y, Lin J, He Z, Zuo MJ (2012) A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mech Syst Signal Process. https:\/\/doi.org\/10.1016\/j.ymssp.2012.09.015","journal-title":"Mech Syst Signal Process"},{"issue":"April","key":"1979_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/J.RESS.2017.11.021","volume":"172","author":"X Li","year":"2018","unstructured":"Li X, Ding Q, Sun JQ (2018a) Remaining useful life estimation in prognostics using deep convolution neural networks. Reliab Eng Syst Saf 172(April):1\u201311. https:\/\/doi.org\/10.1016\/J.RESS.2017.11.021","journal-title":"Reliab Eng Syst Saf"},{"issue":"12","key":"1979_CR25","doi-asserted-by":"publisher","first-page":"7762","DOI":"10.1109\/TIE.2015.2455055","volume":"62","author":"N Li","year":"2015","unstructured":"Li N, Lei Y, Lin J, Ding SX (2015) An improved exponential model for predicting remaining useful life of rolling element bearings. IEEE Trans Ind Electron 62(12):7762\u20137773. https:\/\/doi.org\/10.1109\/TIE.2015.2455055","journal-title":"IEEE Trans Ind Electron"},{"key":"1979_CR26","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2018.11.011","author":"X Li","year":"2018","unstructured":"Li X, Zhang W, Ding Q (2018b) Deep learning-based remaining useful life estimation of bearings using multi-scale feature extraction. Reliab Eng Syst Saf. https:\/\/doi.org\/10.1016\/j.ress.2018.11.011","journal-title":"Reliab Eng Syst Saf"},{"issue":"July","key":"1979_CR27","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/J.ASOC.2016.03.013","volume":"44","author":"L Liao","year":"2016","unstructured":"Liao L, K\u00f6ttig F (2016) A hybrid framework combining data-driven and model-based methods for system remaining useful life prediction. Appl Soft Comput 44(July):191\u2013199. https:\/\/doi.org\/10.1016\/J.ASOC.2016.03.013","journal-title":"Appl Soft Comput"},{"issue":"1","key":"1979_CR28","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1006\/JSVI.2000.2864","volume":"234","author":"J Lin","year":"2000","unstructured":"Lin J, Qu L (2000) Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis. J Sound Vib 234(1):135\u2013148. https:\/\/doi.org\/10.1006\/JSVI.2000.2864","journal-title":"J Sound Vib"},{"issue":"February","key":"1979_CR29","doi-asserted-by":"publisher","first-page":"108182","DOI":"10.1016\/J.RESS.2021.108182","volume":"218","author":"S Liu","year":"2022","unstructured":"Liu S, Fan L (2022) An adaptive prediction approach for rolling bearing remaining useful life based on multistage model with three-source variability. Reliab Eng Syst Saf 218(February):108182. https:\/\/doi.org\/10.1016\/J.RESS.2021.108182","journal-title":"Reliab Eng Syst Saf"},{"issue":"October","key":"1979_CR30","doi-asserted-by":"publisher","first-page":"107646","DOI":"10.1016\/J.RESS.2021.107646","volume":"214","author":"J Liu","year":"2021","unstructured":"Liu J, Pan C, Lei F, Hu D, Zuo H (2021) Fault prediction of bearings based on LSTM and statistical process analysis. Reliab Eng Syst Saf 214(October):107646. https:\/\/doi.org\/10.1016\/J.RESS.2021.107646","journal-title":"Reliab Eng Syst Saf"},{"key":"1979_CR31","doi-asserted-by":"crossref","unstructured":"Liu J, Vatn J, Pedersen VGB, Yin S, Tajiani B (2022) A comparison study for bearing remaining useful life prediction by using standard stochastic approach and digital twin. https:\/\/www.researchgate.net\/publication\/363346096_A_comparison_study_for_bearing_remaining_useful_life_prediction_by_using_standard_stochastic_approach_and_digital_twin","DOI":"10.1504\/IJRS.2023.134275"},{"issue":"14","key":"1979_CR32","doi-asserted-by":"publisher","first-page":"2705","DOI":"10.3390\/EN12142705","volume":"12","author":"R Narayanan","year":"2019","unstructured":"Narayanan R, Halawa E, Jain S (2019) Remaining useful life prediction of rolling element bearings using supervised machine learning. Energies 12(14):2705. https:\/\/doi.org\/10.3390\/EN12142705","journal-title":"Energies"},{"key":"1979_CR33","unstructured":"Nectoux P, Gouriveau R, Medjaher K, Ramasso E, Chebel-Morello B, Zerhouni N, Varnier C et al (2012) PRONOSTIA: an experimental platform for bearings accelerated degradation tests, pp 1\u20138. https:\/\/hal.archives-ouvertes.fr\/hal-00719503"},{"issue":"August","key":"1979_CR34","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/J.RESS.2019.03.018","volume":"188","author":"KTP Nguyen","year":"2019","unstructured":"Nguyen KTP, Medjaher K (2019) A new dynamic predictive maintenance framework using deep learning for failure prognostics. Reliab Eng Syst Saf 188(August):251\u2013262. https:\/\/doi.org\/10.1016\/J.RESS.2019.03.018","journal-title":"Reliab Eng Syst Saf"},{"issue":"October","key":"1979_CR35","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/J.APM.2017.05.049","volume":"50","author":"D Pan","year":"2017","unstructured":"Pan D, Liu JB, Huang F, Cao J, Alsaedi A (2017) A Wiener process model with truncated normal distribution for reliability analysis. Appl Math Model 50(October):333\u2013346. https:\/\/doi.org\/10.1016\/J.APM.2017.05.049","journal-title":"Appl Math Model"},{"key":"1979_CR36","doi-asserted-by":"publisher","unstructured":"Peng W, Coit DW (2007) Reliability and degradation modeling with random or uncertain failure threshold. In: 2007 proceedings\u2014annual reliability and maintainability symposium, RAMS, pp 392\u201397. https:\/\/doi.org\/10.1109\/RAMS.2007.328107","DOI":"10.1109\/RAMS.2007.328107"},{"key":"1979_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/S13198-021-01407-1\/TABLES\/7","author":"KN Ravikumar","year":"2021","unstructured":"Ravikumar KN, Aralikatti SS, Kumar H, Kumar GN, Gangadharan KV (2021) Fault diagnosis of antifriction bearing in internal combustion engine gearbox using data mining techniques. Int J Syst Assur Eng Manag. https:\/\/doi.org\/10.1007\/S13198-021-01407-1\/TABLES\/7","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"4","key":"1979_CR38","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1190\/1.1441816","volume":"5","author":"NH Ricker","year":"1940","unstructured":"Ricker NH (1940) The form and nature of seismic waves and the structure of seismograms. Geophysics 5(4):348\u2013366. https:\/\/doi.org\/10.1190\/1.1441816","journal-title":"Geophysics"},{"key":"1979_CR39","unstructured":"Rudin C (2019) Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature.Com. https:\/\/www.nature.com\/articles\/s42256-019-0048-x?fbclid=IwAR3156gP-ntoAyw2sHTXo0Z8H9p-2wBKe5jqitsMCdft7xA0P766QvSthFs&ref=https:\/\/githubhelp.com"},{"key":"1979_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-017-0573-0","author":"F Salehpour-Oskouei","year":"2017","unstructured":"Salehpour-Oskouei F, Pourgol-Mohammad M (2017) Risk assessment of sensor failures in a condition monitoring process; degradation-based failure probability determination. Int J Syst Assur Eng Manag. https:\/\/doi.org\/10.1007\/s13198-017-0573-0","journal-title":"Int J Syst Assur Eng Manag"},{"key":"1979_CR41","doi-asserted-by":"publisher","DOI":"10.36001\/IJPHM.2010.V1I1.1336","author":"A Saxena","year":"2010","unstructured":"Saxena A, Celaya J, Saha B, Saha S, Goebel K (2010) Metrics for offline evaluation of prognostic performance. Int J Progn Health Manag. https:\/\/doi.org\/10.36001\/IJPHM.2010.V1I1.1336","journal-title":"Int J Progn Health Manag"},{"issue":"2","key":"1979_CR42","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1109\/TASE.2013.2260740","volume":"11","author":"XS Si","year":"2014","unstructured":"Si XS, Zhou D (2014) A generalized result for degradation model-based reliability estimation. IEEE Trans Autom Sci Eng 11(2):632\u2013637. https:\/\/doi.org\/10.1109\/TASE.2013.2260740","journal-title":"IEEE Trans Autom Sci Eng"},{"issue":"3","key":"1979_CR43","doi-asserted-by":"publisher","first-page":"1781","DOI":"10.1109\/TIE.2014.2336616","volume":"62","author":"RK Singleton","year":"2015","unstructured":"Singleton RK, Strangas EG, Aviyente S (2015) Extended Kalman filtering for remaining-useful-life estimation of bearings. IEEE Trans Ind Electron 62(3):1781\u20131790. https:\/\/doi.org\/10.1109\/TIE.2014.2336616","journal-title":"IEEE Trans Ind Electron"},{"issue":"9","key":"1979_CR44","doi-asserted-by":"publisher","first-page":"2230","DOI":"10.1007\/S11771-016-3281-Z","volume":"23","author":"S-J Tang","year":"2016","unstructured":"Tang S-J, Yu C-Q, Feng Y-B, Xie J, Gao Q-H, Si X-S (2016) Remaining useful life estimation based on wiener degradation processes with random failure threshold. J Cent South Univ 23(9):2230\u20132241. https:\/\/doi.org\/10.1007\/S11771-016-3281-Z","journal-title":"J Cent South Univ"},{"issue":"5","key":"1979_CR45","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/S13198-021-01190-Z\/FIGURES\/6","volume":"12","author":"NM Thoppil","year":"2021","unstructured":"Thoppil NM, Vasu V, Rao CSP (2021) Health indicator construction and remaining useful life estimation for mechanical systems using vibration signal prognostics. Int J Syst Assur Eng Manag 12(5):1001\u20131010. https:\/\/doi.org\/10.1007\/S13198-021-01190-Z\/FIGURES\/6","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"3","key":"1979_CR46","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1142\/S1793536910000549","volume":"2","author":"G Wang","year":"2010","unstructured":"Wang G, Chen XY, Qiao FL, Zhaohua Wu, Huang NE (2010) On intrinsic mode function. Adv Adapt Data Anal 2(3):277\u2013293. https:\/\/doi.org\/10.1142\/S1793536910000549","journal-title":"Adv Adapt Data Anal"},{"key":"1979_CR47","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/198362","author":"F Wang","year":"2014","unstructured":"Wang F, Chen S, Sun J, Yan D, Wang L, Zhang L (2014a) Time-frequency fault feature extraction for rolling bearing based on the tensor manifold method. Math Probl Eng. https:\/\/doi.org\/10.1155\/2014\/198362","journal-title":"Math Probl Eng"},{"issue":"2","key":"1979_CR48","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1002\/QRE.1489","volume":"30","author":"X Wang","year":"2014","unstructured":"Wang X, Jiang P, Guo Bo, Cheng Z (2014b) Real-time reliability evaluation with a general wiener process-based degradation model. Qual Reliab Eng Int 30(2):205\u2013220. https:\/\/doi.org\/10.1002\/QRE.1489","journal-title":"Qual Reliab Eng Int"},{"issue":"June","key":"1979_CR49","doi-asserted-by":"publisher","first-page":"107504","DOI":"10.1016\/J.RESS.2021.107504","volume":"210","author":"H Wang","year":"2021","unstructured":"Wang H, Liao H, Ma X, Bao R (2021) Remaining useful life prediction and optimal maintenance time determination for a single unit using isotonic regression and gamma process model. Reliab Eng Syst Saf 210(June):107504. https:\/\/doi.org\/10.1016\/J.RESS.2021.107504","journal-title":"Reliab Eng Syst Saf"},{"key":"1979_CR50","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/4068431","author":"J Wen","year":"2018","unstructured":"Wen J, Gao H, Zhang J (2018a) Bearing remaining useful life prediction based on a nonlinear wiener process model. Shock Vib. https:\/\/doi.org\/10.1155\/2018\/4068431","journal-title":"Shock Vib"},{"issue":"August","key":"1979_CR51","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/J.RESS.2018.04.005","volume":"176","author":"Y Wen","year":"2018","unstructured":"Wen Y, Wu J, Das D, Tseng TLB (2018b) Degradation modeling and rul prediction using wiener process subject to multiple change points and unit heterogeneity. Reliab Eng Syst Saf 176(August):113\u2013124. https:\/\/doi.org\/10.1016\/J.RESS.2018.04.005","journal-title":"Reliab Eng Syst Saf"},{"key":"1979_CR52","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/8927937","author":"B Wu","year":"2017","unstructured":"Wu B, Li W, Qiu MQ (2017) Remaining useful life prediction of bearing with vibration signals based on a novel indicator. Shock Vib. https:\/\/doi.org\/10.1155\/2017\/8927937","journal-title":"Shock Vib"},{"issue":"6","key":"1979_CR53","doi-asserted-by":"publisher","first-page":"3703","DOI":"10.1109\/TII.2018.2868687","volume":"15","author":"M Xia","year":"2019","unstructured":"Xia M, Li T, Shu T, Wan J, De Silva CW, Wang Z (2019) A two-stage approach for the remaining useful life prediction of bearings using deep neural networks. IEEE Trans Ind Inform 15(6):3703\u20133711. https:\/\/doi.org\/10.1109\/TII.2018.2868687","journal-title":"IEEE Trans Ind Inform"},{"issue":"August","key":"1979_CR54","doi-asserted-by":"publisher","first-page":"107638","DOI":"10.1016\/J.RESS.2021.107638","volume":"212","author":"T Yan","year":"2021","unstructured":"Yan T, Lei Y, Li N, Wang B, Wang W (2021) Degradation modeling and remaining useful life prediction for dependent competing failure processes. Reliab Eng Syst Saf 212(August):107638. https:\/\/doi.org\/10.1016\/J.RESS.2021.107638","journal-title":"Reliab Eng Syst Saf"},{"key":"1979_CR55","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.isatra.2021.03.045","volume":"121","author":"C Yang","year":"2022","unstructured":"Yang C, Ma J, Wang X, Li X, Li Z, Luo T (2022) A novel based-performance degradation indicator RUL prediction model and its application in rolling bearing. ISA Trans 121:349\u2013364. https:\/\/doi.org\/10.1016\/j.isatra.2021.03.045","journal-title":"ISA Trans"},{"key":"1979_CR56","unstructured":"Yuan MJ, Wang MK, Welte TM (2019) Twin Exponential degradation model for online remaining useful life prediction"},{"issue":"3","key":"1979_CR57","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1016\/J.EJOR.2018.02.033","volume":"271","author":"Z Zhang","year":"2018","unstructured":"Zhang Z, Si X, Changhua Hu, Lei Y (2018) Degradation data analysis and remaining useful life estimation: a review on Wiener-process-based methods. Eur J Oper Res 271(3):775\u2013796. https:\/\/doi.org\/10.1016\/J.EJOR.2018.02.033","journal-title":"Eur J Oper Res"},{"issue":"3","key":"1979_CR58","doi-asserted-by":"publisher","first-page":"53","DOI":"10.3390\/SCI2030053","volume":"2","author":"J Zhang","year":"2020","unstructured":"Zhang J, Soangra R, Lockhart TE (2020) A comparison of denoising methods in onset determination in medial gastrocnemius muscle activations during stance. Sci 2(3):53. https:\/\/doi.org\/10.3390\/SCI2030053","journal-title":"Sci"},{"issue":"6","key":"1979_CR59","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1007\/s10845-012-0657-2","volume":"24","author":"Z Zhang","year":"2013","unstructured":"Zhang Z, Wang Yi, Wang K (2013) Fault diagnosis and prognosis using wavelet packet decomposition, Fourier transform and artificial neural network. J Intell Manuf 24(6):1213\u20131227. https:\/\/doi.org\/10.1007\/s10845-012-0657-2","journal-title":"J Intell Manuf"},{"key":"1979_CR60","doi-asserted-by":"publisher","DOI":"10.1007\/s13198-019-00818-5","author":"X Zhang","year":"2019","unstructured":"Zhang X, Zhao J, Ni X, Sun F, Ge H (2019) Fault diagnosis for gearbox based on EMD-MOMEDA. Int J Syst Assur Eng Manag. https:\/\/doi.org\/10.1007\/s13198-019-00818-5","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"4","key":"1979_CR61","doi-asserted-by":"publisher","first-page":"3208","DOI":"10.1109\/TIE.2018.2844856","volume":"66","author":"J Zhu","year":"2019","unstructured":"Zhu J, Chen N, Peng W (2019) Estimation of bearing remaining useful life based on multiscale convolutional neural network. IEEE Trans Ind Electron 66(4):3208\u20133216. https:\/\/doi.org\/10.1109\/TIE.2018.2844856","journal-title":"IEEE Trans Ind Electron"}],"container-title":["International Journal of System Assurance Engineering and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-023-01979-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13198-023-01979-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-023-01979-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T19:19:28Z","timestamp":1702667968000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13198-023-01979-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,25]]},"references-count":61,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["1979"],"URL":"https:\/\/doi.org\/10.1007\/s13198-023-01979-0","relation":{},"ISSN":["0975-6809","0976-4348"],"issn-type":[{"value":"0975-6809","type":"print"},{"value":"0976-4348","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,25]]},"assertion":[{"value":"11 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"We, the authors of this manuscript have no conflicts of interest to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"We, the authors ensure that no human or animal participation is involved in this research.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human participants and\/or animals"}},{"value":"We haven\u2019t used human participation or other personal information, informed consent is not required.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed conssent"}}]}}