Rethinking Remaining Useful Life Prediction with Scarce Time Series Data: Regression under Indirect Supervision

TL;DR

This work tackles RUL prediction under severe data scarcity with indirect supervision by introducing parameterized static regression, which uses pointwise covariates and a parametrical rectification to capture temporal effects without interpolation. AER and ResGUR-based posterior estimators are trained with a novel identical-batch training strategy and a regression-plus-reconstruction loss, while PR rectifies predictions at inference by fitting a parametric labeling function (linear or Weibull-based). The approach demonstrates competitive or superior performance on CMAPSS and N-CMAPSS benchmarks under simulated scarcity, with ablations showing the value of non-linear labeling, reconstruction loss, and batch sampling size. The method offers a scalable, interpolation-free path for reliable RUL estimation in data-scarce industrial settings and provides practical guidance for choosing labeling functions and training configurations.

Abstract

Supervised time series prediction relies on directly measured target variables, but real-world use cases such as predicting remaining useful life (RUL) involve indirect supervision, where the target variable is labeled as a function of another dependent variable. Trending temporal regression techniques rely on sequential time series inputs to capture temporal patterns, requiring interpolation when dealing with sparsely and irregularly sampled covariates along the timeline. However, interpolation can introduce significant biases, particularly with highly scarce data. In this paper, we address the RUL prediction problem with data scarcity as time series regression under indirect supervision. We introduce a unified framework called parameterized static regression, which takes single data points as inputs for regression of target values, inherently handling data scarcity without requiring interpolation. The time dependency under indirect supervision is captured via a parametrical rectification (PR) process, approximating a parametric function during inference with historical posteriori estimates, following the same underlying distribution used for labeling during training. Additionally, we propose a novel batch training technique for tasks in indirect supervision to prevent overfitting and enhance efficiency. We evaluate our model on public benchmarks for RUL prediction with simulated data scarcity. Our method demonstrates competitive performance in prediction accuracy when dealing with highly scarce time series data.

Figures (5)

• Figure 1: Illustration of different types of multivariate time series data. They are categorized and defined in this paper based on their sampling frequency, $i.e.$, scarcity.
• Figure 2: Proposed batch training technique and static regression models for posterior estimation. (a) Batch training technique under indirect supervision conducts data sampling from each $\mathcal{D}_i$ at a time with $|\mathcal{B}_i| =\min(M_i,B)$. (b) Posterior estimation with $\mathbf{x}^i_{t,s}$ using an AER / ResGUR model and $\hat{y}^{i}_{t,s}$ as outputs (reconstructed $\hat{\mathbf{x}}^i_{t,s}$ also as outputs with AER).
• Figure 3: Prediction performance (RMSE$_{\,i}$) on CMAPSS with simulated data scarcity in both train and test sets. The Posteriori Estimates are outputs from ResGUR and AER, with the Predictions rectified through the PR process.
• Figure 4: Prediction performance ($\text{RMSE}_{\,i,t}$) on mean N-CMAPSS with (a) simulated scarcity and (b) example demonstrations under 70% scarcity similated.
• Figure 5: Prediction performance on DS02 with varying sample size, $i.e.$, $B$, during (a) training and (b) testing stages.