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

cs.LGMar 15, 2026

Evidential Domain Adaptation for Remaining Useful Life Prediction with Incomplete Degradation

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

Organizations: Institute for Infocomm Research (I2R), Agency for Science, Technology and Research (A*STAR), Singapore. · School of Computer Science and Engineering, Nanyang Technological University, Singapore. · Propulsion and Space Research Center, Technology Innovation Institute, UAE.

Abstract

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.

Figures & tables

Fig. 1 : Comparison of existing solutions and the proposed solution and the proposed solution for incomplete degradation domain adaptation in RUL prediction. (a) Under global alignment, early degradation in the target domain may be incorrectly aligned with late stage degradation in the source domain. (b) The patterns of the two domains may differ in the early stage, where the source domain experiences steady degradation, while the target domain degrades rapidly.

Fig. 2 : An overview of our proposed EviAdapt approach. EviAdapt comprises three main components: source encoder $E_{S}$ , target encoder $E_{T}$ and shared predictor $R$ . $E_{S}$ and $R$ are pretrained to learn the RUL distribution and its uncertainty of the source domain using evidential learning. During adaptation, source and target data are segmented into different degradation stages. Eventually, $E_{T}$ is trained to align the uncertainty of the same degradation stages between the source and target domains.

Notation	Definition
$X_{S}/X_{T}$	source/target data
$y_{S}$	source RUL label
$N_{S}/N_{T}$	number of source/target samples
$f_{S}/f_{T}$	source/target features
$E_{S}/E_{T}$	source/target encoder
$R$	predictor

TABLE I : List of notations.

Fig. 3 : Three degradation stages categorized by the health index.

Dataset	C-MAPSS				N-CMAPSS			PHM2010
Sub-dataset	FD001	FD002	FD003	FD004	DS01	DS02	DS03	C1	C4	C6
# Engine units for training	100	260	100	249	6	6	9	NA
# Engine units for testing	100	259	100	248	4	3	6	NA
# Complete Training samples	17731	48558	21220	56815	4881	5237	5532	69176	70270	69054
# Incomplete Training samples	9438	24607	11893	29434	2918	3131	3302	42162	41505	41432
# Testing samples	100	259	100	248	2717	1240	4225	28108	27671	27622

TABLE II : Details of benchmark datasets.

Parameter	C-MAPSS	N-CMAPSS	PHM2010
# of Layers	5	1	5
# of Hidden Size	32	64	32
Dropout	0.5	0.1	0.1

TABLE III : Parameter setting for the LSTM feature extractor.

Methods	F1 $\rightarrow$ F2	F1 $\rightarrow$ F3	F1 $\rightarrow$ F4	F2 $\rightarrow$ F1	F2 $\rightarrow$ F3	F2 $\rightarrow$ F4	F3 $\rightarrow$ F1	F3 $\rightarrow$ F2	F3 $\rightarrow$ F4	F4 $\rightarrow$ F1	F4 $\rightarrow$ F2	F4 $\rightarrow$ F3	Avg.
Source-RMSE	55.35	60.52	55.98	52.29	53.60	54.86	41.94	44.37	40.57	46.09	51.46	49.10	50.51
DDC	40.00	40.06	43.98	38.83	48.24	43.06	41.55	40.65	43.68	40.51	39.61	38.16	41.53
Deep Coral	36.90	41.75	45.21	35.88	41.16	43.85	36.16	37.08	37.78	36.11	36.80	35.96	38.72
ADARUL	44.73	54.37	36.93	48.41	48.84	49.38	34.19	36.19	39.98	28.05	33.76	37.43	41.02
CADA	45.24	54.57	38.73	49.60	49.07	48.74	41.23	39.41	40.55	32.22	39.65	38.17	43.10
Cons DANN	28.52	34.65	29.95	22.86	28.77	29.63	21.02	24.32	27.44	21.21	25.40	23.67	26.45

TABLE IV : Comparison of the proposed EviAdapt against benchmark approaches on C-MAPSS (RMSE). Note that F1 is short for FD001, and F1

\rightarrow

F2 refers to the scenario where FD001 is the source domain and FD002 is the target domain. Bold indicates the best result, and underline indicates the second-best result.

Methods	F1 $\rightarrow$ F2	F1 $\rightarrow$ F3	F1 $\rightarrow$ F4	F2 $\rightarrow$ F1	F2 $\rightarrow$ F3	F2 $\rightarrow$ F4	F3 $\rightarrow$ F1	F3 $\rightarrow$ F2	F3 $\rightarrow$ F4	F4 $\rightarrow$ F1	F4 $\rightarrow$ F2	F4 $\rightarrow$ F3	Avg.
Source-RMSE	75683	46833	72564	16834	23400	67866	6740	25030	19995	11831	46169	13971	35576
DDC	22208	6368	21318	4930	6514	16958	6140	22422	21397	5939	23050	4238	13457
Deep Coral	11782	6723	18697	2986	6802	16098	3001	11538	9907	3033	11495	3416	8790
ADARUL	36618	27370	19401	11467	15171	44955	3862	16706	19380	3207	8913	6032	17757
CADA	37815	27805	24187	13201	15690	47750	6676	22293	19964	4907	13183	6560	20003
Cons DANN	5817	4614	7028	1164	2017	5948	1076	6019	5811	947	4529	1343	3859

TABLE V : Comparison of the proposed EviAdapt against benchmark approaches on C-MAPSS (Score). Note that F1 is short for FD001, and F1

\rightarrow

F2 refers to the scenario where FD001 is the source domain and FD002 is the target domain. Bold indicates the best result, and underline indicates the second-best result.

Methods	DS01 $\rightarrow$ DS02	DS01 $\rightarrow$ DS03	DS02 $\rightarrow$ DS01	DS02 $\rightarrow$ DS03	DS03 $\rightarrow$ DS01	DS03 $\rightarrow$ DS02	Avg.
Source-RMSE	21.89	28.23	33.29	25.64	40.37	26.50	29.32
DDC	19.23	21.12	21.05	15.86	24.75	17.78	19.96
Deep Coral	14.06	15.75	21.34	16.37	24.42	16.21	18.03
ADARUL	9.97	13.50	17.51	14.20	14.07	9.18	13.07
CADA	10.05	14.12	16.07	13.14	18.88	12.90	14.19
Cons DANN	10.03	11.91	16.52	12.96	17.48	10.25	13.19

TABLE VI : Comparison of the proposed EviAdapt against benchmark approaches on N-CMAPSS (RMSE). Bold indicates the best result, and underline indicates the second-best result.

Methods	DS01 $\rightarrow$ DS02	DS01 $\rightarrow$ DS03	DS02 $\rightarrow$ DS01	DS02 $\rightarrow$ DS03	DS03 $\rightarrow$ DS01	DS03 $\rightarrow$ DS02	Avg.
Source-RMSE	7202	58571	62615	49246	118257	11480	51228
DDC	5767	28992	16178	14566	24616	5325	15908
Deep Coral	2880	13444	17037	15810	22697	3804	12613
ADARUL	1579	11370	11924	11135	5908	1441	7226
CADA	1632	12260	8568	9814	13335	2459	8011
Cons DANN	1715	8216	9634	9675	10183	1783	6868

TABLE VII : Comparison of the proposed EviAdapt against benchmark approaches on N-CMAPSS (Score). Bold indicates the best result, and underline indicates the second-best result.

Methods	C1 $\rightarrow$ C4	C1 $\rightarrow$ C6	C4 $\rightarrow$ C1	C4 $\rightarrow$ C6	C6 $\rightarrow$ C1	C6 $\rightarrow$ C4	Avg.
Source-RMSE	0.209	0.111	0.311	0.201	0.280	0.312	0.237
DDC	0.176	0.272	0.223	0.340	0.127	0.170	0.218
Deep Coral	0.175	0.194	0.155	0.150	0.116	0.169	0.160
ADARUL	0.216	0.114	0.313	0.202	0.300	0.323	0.245
CADA	0.209	0.111	0.311	0.201	0.280	0.312	0.237
Cons DANN	0.173	0.106	0.109	0.118	0.112	0.233	0.142

TABLE VIII : Comparison of the proposed EviAdapt against benchmark approaches on PHM2010 (RMSE). Bold indicates the best result, and underline indicates the second-best result.

Alignment Scope	Alignment Type	F1 $\rightarrow$ F2	F1 $\rightarrow$ F3	F1 $\rightarrow$ F4	F2 $\rightarrow$ F1	F2 $\rightarrow$ F3	F2 $\rightarrow$ F4	F3 $\rightarrow$ F1	F3 $\rightarrow$ F2	F3 $\rightarrow$ F4	F4 $\rightarrow$ F1	F4 $\rightarrow$ F2	F4 $\rightarrow$ F3	Avg.
$G$	$Fea$	25.47	27.47	34.36	26.11	34.98	36.39	26.87	32.80	33.67	25.42	26.74	25.00	29.61
$G$	$Unc$	29.61	32.91	36.00	23.81	31.53	31.50	24.35	24.72	26.45	23.08	24.12	23.83	27.66
$S$	$Unc$	29.95	31.13	33.72	21.64	26.03	28.83	19.19	19.92	28.53	23.67	18.59	20.58	25.00

TABLE IX : Ablation study for the proposed EviAdapt on C-MAPSS (RMSE).

Alignment Scope	Alignment Type	F1 $\rightarrow$ F2	F1 $\rightarrow$ F3	F1 $\rightarrow$ F4	F2 $\rightarrow$ F1	F2 $\rightarrow$ F3	F2 $\rightarrow$ F4	F3 $\rightarrow$ F1	F3 $\rightarrow$ F2	F3 $\rightarrow$ F4	F4 $\rightarrow$ F1	F4 $\rightarrow$ F2	F4 $\rightarrow$ F3	Avg.
$G$	$Fea$	3953	2344	35593	7522	11296	59736	27492	94580	80814	3577	8686	2317	28159
$G$	$Unc$	6224	2246	8268	3832	7880	29588	6345	26558	15633	891	2608	1093	9264
$S$	$Unc$	4976	2435	7456	908	1404	5227	1178	3974	5146	1361	3980	809	3238

TABLE X : Ablation study for the proposed EviAdapt on C-MAPSS (Score).

Fig. 4 : The sensitivity analysis for different set of quantile values on N-CMAPSS (RMSE).

Fig. 5 : The sensitivity analysis for different set of quantile values on N-CMAPSS (Score).

Fig. 6 : Feature distribution analysis. Up: before adaptation. Down: after adaptation.

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Remaining useful life estimation predicts how long machines, batteries, and other assets can operate before failure or end of life.

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Jul 26, 2026J/K move · Enter open · S save

Generalization bounds and sample complexity for remaining useful life prediction from complete degradation trajectories

Huy Hoang Le, Kim-Anh Nguyen

R&D Department, PowerMore Ltd., Da Nang 550000, Vietnam · Faculty of Electrical Engineering, University of Science and Technology, The University of Danang, Da Nang 550000, Vietnam

RUL Estimation Sample Complexity Physics-Informed ML Statistical Learning Theory

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Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as

O(B^{2}\sqrt{p/n})

, where

p

is the model complexity and

n

the number of trajectories, and a minimax lower bound proves that the

Θ(p/n)

rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal

O(p/n)

rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias

-

variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2

-

3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.

Abstract

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