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Evidential Domain Adaptation for Remaining Useful Life Prediction with Incomplete Degradation

Yubo Hou, Mohamed Ragab, Yucheng Wang, Min Wu, Abdulla Alseiari, Chee-Keong Kwoh, Xiaoli Li, Zhenghua Chen

arXiv:2603.15687v1cs.LGcs.AI

TL;DR

Incomplete target-domain degradation trajectories make RUL domain adaptation difficult because global alignment can mismatch degradation stages and feature matching may not capture differing patterns. EviAdapt segments domains by degradation stage and aligns evidential uncertainty across corresponding stages. Across reported experiments, it outperforms existing methods, with average improvements of 16%, 42%, and 2% on C-MAPSS, N-CMAPSS, and PHM2010, respectively.

  • Problem

    Incomplete target domains lack late degradation stages, while global alignment and direct feature matching can misalign domains in cross-domain RUL prediction.

  • Method

    EviAdapt segments source and target data by degradation rate, aligns corresponding degradation stages, and aligns their uncertainty using evidential learning.

  • Results

    Average improvements of 16%, 42%, and 2% are reported on C-MAPSS, N-CMAPSS, and PHM2010, respectively, over state-of-the-art methods.

  • Takeaways & Limitations

    Stage-wise uncertainty alignment provides the paper’s supported approach for addressing incomplete-target cross-domain RUL prediction.

Abstract

from arXiv · show

Accurate Remaining Useful Life (RUL) prediction without labeled target domain data is a critical challenge, and domain adaptation (DA) has been widely adopted to address it by transferring knowledge from a labeled source domain to an unlabeled target domain. Despite its success, existing DA methods struggle significantly when faced with incomplete degradation trajectories in the target domain, particularly due to the absence of late degradation stages. This missing data introduces a key extrapolation challenge. When applied to such incomplete RUL prediction tasks, current DA methods encounter two primary limitations. First, most DA approaches primarily focus on global alignment, which can misaligns late degradation stage in the source domain with early degradation stage in the target domain. Second, due to varying operating conditions in RUL prediction, degradation patterns may differ even within the same degradation stage, resulting in different learned features. As a result, even if degradation stages are partially aligned, simple feature matching cannot fully align two domains. To overcome these limitations, we propose a novel evidential adaptation approach called EviAdapt, which leverages evidential learning to enhance domain adaptation. The method first segments the source and target domain data into distinct degradation stages based on degradation rate, enabling stage-wise alignment that ensures samples from corresponding stages are accurately matched. To address the second limitation, we introduce an evidential uncertainty alignment technique that estimates uncertainty using evidential learning and aligns the uncertainty across matched stages.

I. INTRODUCTION

RUL domain adaptation is needed because operating-condition shifts and incomplete target degradation trajectories make labeled target data costly and global alignment unreliable. EviAdapt addresses these issues through degradation-stage alignment and evidential uncertainty alignment, with experiments reporting strong cross-domain performance.

  • RUL prediction supports maintenance decisions, reliability, cost reduction, safety, and operational performance in industrial systems.
  • Operating-condition shifts degrade data-driven RUL models, while collecting labeled target-domain data and retraining are impractical and costly.
  • Incomplete target domains often lack late degradation data, causing global alignment to mismatch degradation stages across domains.
  • EviAdapt segments source and target data by degradation rate and aligns samples within corresponding degradation stages.
  • EviAdapt aligns uncertainty levels between corresponding degradation stages rather than directly matching features, using evidential learning.
  • Experiments on C-MAPSS, N-CMAPSS, and PHM2010 report that EviAdapt significantly outperforms existing state-of-the-art cross-domain RUL methods.

II. RELATED WORKS

Related work covers metric-based and adversarial domain adaptation, incomplete-data methods, and uncertainty estimation. These approaches motivate EviAdapt’s stage-aware uncertainty alignment for incomplete target-domain RUL prediction.

  • UDA for RUL prediction transfers knowledge from labeled source domains to unlabeled target domains by minimizing domain discrepancy.
  • Metric-based methods learn invariant features through constraints such as MMD and covariance-shift minimization.
  • Adversarial methods use domain discriminators and adversarial training to learn domain-invariant representations.
  • Incomplete-target methods use consistency regularization, generated full-cycle data, or degradation-level fusion, but may overlook stage characteristics or lack generalizability.
  • Existing domain adaptation methods also ignore uncertainty when learning domain distributions.
  • Evidential learning estimates uncertainty with a single deterministic model, while existing regression approaches may rely on restrictive Gaussian assumptions.

III. METHODOLOGY

EviAdapt pretrains a source encoder and evidential RUL predictor, then represents predictive uncertainty with Normal-Inverse-Gamma distributions for adaptation. The predictor is trained using likelihood and tilted losses, with RUL estimated from predicted γ values.

  • The problem formulation transfers knowledge from labeled source samples to unlabeled target samples for target-domain RUL prediction.
  • EviAdapt uses source encoder ES, target encoder ET, and shared predictor R as its three main components.
  • The source encoder extracts features, while the predictor estimates RUL quantiles and uncertainty from those features.
  • The evidential predictor uses a Normal-Inverse-Gamma prior over Gaussian likelihood parameters and produces a Student-t predictive distribution.
  • Training minimizes negative log-likelihood and uses tilted loss to regularize evidence assigned to prediction errors.
  • RUL is estimated by averaging the predicted γ values across quantiles.

D. Stage Segmentation

EviAdapt aligns uncertainty rather than features, but performs this alignment stage-wise because global uncertainty alignment can be suboptimal for incomplete target trajectories.

  • EviAdapt aligns uncertainty between source and target domains instead of directly aligning features to align conditional distributions.
  • Global uncertainty alignment can be suboptimal when the target domain contains incomplete degradation data.
  • The method addresses this issue through stage segmentation before alignment.

1) Identifying Source Degradation Stages:

Source data are divided into sluggish, moderate, and accelerated degradation stages using health-index evolution and labeled lifecycle ranges.

  • Source data are categorized into three degradation stages using available RUL labels and a health index formed from key sensor readings.
  • The sluggish stage spans 0–33% of the lifecycle and has a relatively low degradation rate.
  • The moderate stage spans 33–85% and represents an accelerating degradation rate before the high-failure-risk phase.
  • The accelerated stage spans 85–100%, where degradation increases significantly and failure risk rises steeply.
  • For a 120-cycle engine, the three stages correspond to cycles 0–40, 40–102, and 102–120, respectively.

2) Identifying Target Degradation Stages:

Because target labels are unavailable and degradation stages may be missing, target data are pseudo-labeled with the pretrained source model and aligned using evidential distributions for corresponding stages.

  • The incomplete target domain is segmented using pseudo labels generated by the pretrained source model.
  • Incomplete target trajectories may omit parts of the moderate and fully accelerated degradation stages, motivating a two-stage target classification.
  • The stage-wise evidential alignment loss aligns uncertainty levels between corresponding source and target degradation stages rather than directly matching features.
  • The loss takes parameters of source and target Normal-Inverse-Gamma evidential distributions as inputs, with a kernel measuring their distance.

F. Overall Objective

EviAdapt fine-tunes a target encoder for RUL estimation by combining source pretraining, degradation-stage segmentation, and stage-wise evidential uncertainty alignment.

  • Overall Objective: The algorithm pretrains a source encoder and predictor using labeled source data before adapting the target encoder.The source encoder ES and predictor R are pretrained on (XS, yS).
  • Overall Objective: Stage-wise evidential alignment matches uncertainty levels between corresponding source and target degradation stages.The stage-wise evidential alignment loss uses source and target evidential distributions to train the target encoder.
  • Overall Objective: The trained target encoder is then used to predict RUL in the target domain.
  • Overall Objective: It estimates target RUL and segments source and target data into degradation stages based on degradation rates.Target stages are formed from estimated target RUL, while source stages use labeled source RUL.

IV. EXPERIMENTS

The experiments evaluate EviAdapt on three benchmark datasets using common LSTM-based feature extraction and RUL-oriented evaluation metrics.

  • Data Preparation: The study evaluates methods on the C-MAPSS, N-CMAPSS, and PHM2010 benchmark datasets.These datasets cover turbofan-engine and cutting-tool degradation settings.
  • Data Preparation: C-MAPSS experiments simulate incomplete target data by removing the final 40% of target training run-to-failure trajectories.
  • Experimental Setting: Experiments are repeated five times and averaged, with the same LSTM feature extractor used for the proposed and baseline methods.Dataset-specific layer counts and hidden-state sizes are selected, with Adam and a target-encoder learning rate of 5e-5.
  • Experimental Setting: RMSE measures equal errors across early and late RUL predictions, while Score penalizes late RUL prediction errors more severely.The estimated and true RUL values are denoted by byi and yi in the RMSE definition.

C. Comparison with State-of-the-Art Methods

EviAdapt outperforms benchmark adaptation methods across cross-domain scenarios on C-MAPSS, N-CMAPSS, and PHM2010, with the strongest reported gains on N-CMAPSS.

  • C. Comparison with State-of-the-Art Methods: On C-MAPSS, EviAdapt achieves the best RMSE results in 8 scenarios and the best Score results in 9 of 12 scenarios.Its average performance improves by over 5% in RMSE and 16% in Score versus the second-best method.
  • C. Comparison with State-of-the-Art Methods: On N-CMAPSS, EviAdapt achieves the best performance across all six scenarios for both RMSE and Score.Average performance improves by over 30% in RMSE and 42% in Score compared with the second-best method.
  • C. Comparison with State-of-the-Art Methods: On PHM2010, EviAdapt achieves the best RMSE performance in 3 of 6 cross-domain wear-depth prediction scenarios.Average RMSE performance improves by over 2% compared with the second-best method.
  • C. Comparison with State-of-the-Art Methods: The reported results are consistent with EviAdapt’s intended alignment of uncertainty within corresponding degradation stages.

D. Ablation Study

The ablation study compares global versus same-stage alignment and feature versus uncertainty alignment in EviAdapt. Same-stage and uncertainty-based alignment produce the strongest comparative results.

  • Ablation design: The ablation varies alignment scope between global alignment and same degradation stage alignment.Global alignment considers the entire dataset, whereas same-stage alignment focuses on data within the same degradation stage.
  • Results: 65% improvement in average Score is reported for uncertainty alignment over feature alignment.
  • Results: 67% maximum improvement in average Score is reported for same degradation stage alignment over global alignment.

E. Sensitivity Analysis

The sensitivity analysis shows that quantile choices affect EviAdapt differently across domain transfers, while feature visualizations show closer source-target distributions after adaptation. The paper also reports broad gains across three benchmark datasets and identifies source-free adaptation as future work.

  • Quantile sensitivity: Quantile [0.25, 0.5] achieves the best reported performance for DS01→DS02 in RMSE and Score.For DS02→DS01 and DS02→DS03, the same quantile set achieves the best reported Score.
  • Quantile sensitivity: The impact of quantile values varies with the source and target domains.The paper attributes this variation to different quantile sets capturing different domain information.
  • Feature distribution: After adaptation, source and target latent feature distributions are closely aligned in the DS01→DS03 visualization.Before adaptation, many source samples are far from the target distribution.
  • Overall results: 16%, 42%, and 2% average improvements are reported on C-MAPSS, N-CMAPSS, and PHM2010, respectively.
  • Future work: Future work targets source-free domain adaptation to reduce dependence on fully labeled source domains and address source-data privacy constraints.
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