小样本下绝缘纸聚合度预测的近红外光谱模型传递方法

Near-infrared spectroscopy (NIRS) technology serves as a novel method for non-destructive evaluation of the degree of polymerization (DP) in insulating paper. However, variations across NIR instruments significantly limit the applicability of trained evaluation models to new devices, hindering the widespread adoption of spectral analysis. For oil-immersed insulating paper (a liquid-impregnated solid material), conventional calibration transfer methods based on transfer functions are ineffective, making label-free calibration transfer under small-sample conditions an urgent challenge. In this paper, we propose a low-rank & sparse multi-task learning (LSMTL) method that employs a trace norm constraint to enforce a low-rank structure on the weight matrix for extracting shared feature representations across tasks, while preserving task-specific outlier features via an L2,1 norm sparse constraint enhance small-sample modeling performance. We established a multi-task database containing 1 200 spectral data collected from 4 spectrometers, developed the LSMTL framework for NIR quantitative analysis modeling, and systematically investigated its hyperparameter sensitivity and performance advantages. Results demonstrate that: the trace norm regularizer enforces low-rank structure on multi-task weight matrices, increasing similarity among low-rank weight vectors l across tasks; the L2, 1 norm decouples tasks to preserve sparse weights s with specificity, enabling joint optimization of task correlations and feature preservation; the low-rank penalty a controls task coupling intensity (higher a strengthens l consistency), while the sparse penalty β governs s sparsity (higher β reduces s contribution to w); optimal a/β values follow an inverse relationship with slave instrument sample size-fewer samples require stronger penalties. Experimental results on our dataset show that LSMTL outperforms three labeled transfer methods (DS, PDS, CCA) and four label-free methods (TrAdaBoost, Transfer CNN, Mu-PLS, MTL-Trace), achieving optimal test performance with 30 samples (RMSE=97.3, R2 =0.72, MAPE=10.2%). The method demonstrates particular advantages in small-sample settings, underscoring its strong potential for NIRS-based DP evaluation.