Time-Invariant Learning and History-Based Inference for Survival Models in Predictive Maintenance
- 1Department of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, No. 1 International University Park Road, Shenzhen 518172, China
- 2Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Vorobjovy Gory, Moscow 119899, Russia
Abstract
This study addresses failure prediction for continuously monitored equipment using time-invariant (TI) survival models, which describe each object by a single state, or time-varying (TV) models, which use sequences of observed states. Monitoring data form TV observation chains, yet many classical and machine learning TV models use these chains only during training and, at inference, rely on the latest observation, discarding the accumulated degradation history. This paper proposes two methods intended to address this gap. The first samples individual observations from TV chains, augmenting each with the time remaining until the outcome, so that classical models can be trained on TV data. The second aggregates predictions made at different time points into a single survival curve using geometric, ordinal, and time-distance weighting schemes. On the Backblaze hard-drive dataset, statistical and machine learning survival models are compared under two training scenarios, a single observation versus sampled TV chains, and two inference scenarios, the latest observation versus the aggregated history, evaluated in terms of ranking quality, survival function approximation, and time-dependent discrimination. TV training based on sampled observations was associated with improved performance of the machine learning ensembles across the reported metrics. The classical Cox proportional hazards model did not benefit from the sampled TV training, since its survival function approximation and ranking quality slightly decreased, while the time-varying Cox model improved mainly in time-dependent discrimination. Among the evaluated methods, GBSA and RSF provided the strongest overall empirical performance on the reported metrics. Aggregation was generally associated with lower IBS and higher IAUC, although the effect was not monotonic across all models and aggregation depths. The gains were concentrated in the statistical models and were marginal for the machine learning ensembles, except for RSF under TV training. In this exploratory comparison with the aggregation configuration selected by the test metric, geometric weighting performed best for IBS and IAUC, whereas time-distance weighting better retained ranking quality.
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BibTeX
@article{vasilev2026timeinvariant,
title = {{Time-Invariant Learning and History-Based Inference for Survival Models in Predictive Maintenance}},
author = {Iulii Vasilev and Mark Goverdovskiy and Mikhail Petrovskiy and Igor Mashechkin},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14213944},
url = {https://www.mdpi.com/2227-7390/14/21/3944},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Time-Invariant Learning and History-Based Inference for Survival Models in Predictive Maintenance
AU - Iulii Vasilev
AU - Mark Goverdovskiy
AU - Mikhail Petrovskiy
AU - Igor Mashechkin
PY - 2026
DA - 2026/10/29
JO - Mathematics
DO - 10.3390/math14213944
UR - https://www.mdpi.com/2227-7390/14/21/3944
AB - This study addresses failure prediction for continuously monitored equipment using time-invariant (TI) survival models, which describe each object by a single state, or time-varying (TV) models, which use sequences of observed states. Monitoring data form TV observation chains, yet many classical and machine learning TV models use these chains only during training and, at inference, rely on the latest observation, discarding the accumulated degradation history. This paper proposes two methods intended to address this gap. The first samples individual observations from TV chains, augmenting each with the time remaining until the outcome, so that classical models can be trained on TV data. The second aggregates predictions made at different time points into a single survival curve using geometric, ordinal, and time-distance weighting schemes. On the Backblaze hard-drive dataset, statistical and machine learning survival models are compared under two training scenarios, a single observation versus sampled TV chains, and two inference scenarios, the latest observation versus the aggregated history, evaluated in terms of ranking quality, survival function approximation, and time-dependent discrimination. TV training based on sampled observations was associated with improved performance of the machine learning ensembles across the reported metrics. The classical Cox proportional hazards model did not benefit from the sampled TV training, since its survival function approximation and ranking quality slightly decreased, while the time-varying Cox model improved mainly in time-dependent discrimination. Among the evaluated methods, GBSA and RSF provided the strongest overall empirical performance on the reported metrics. Aggregation was generally associated with lower IBS and higher IAUC, although the effect was not monotonic across all models and aggregation depths. The gains were concentrated in the statistical models and were marginal for the machine learning ensembles, except for RSF under TV training. In this exploratory comparison with the aggregation configuration selected by the test metric, geometric weighting performed best for IBS and IAUC, whereas time-distance weighting better retained ranking quality.
SN - 2227-7390
ER -