【摘要】 近红外光谱用于绝缘纸聚合度测定是一种新方法，但近红外仪器间的差异会导致训练过的评估模型在新仪器上的适用性显著降低，制约了它的推广应用。对于油浸绝缘纸这类液浸固体物质，同一样品多次采集的光谱呈现显著分散性，导致基于主从机光谱转移矩阵的有标模型传递方法应用效果不佳，如何实现小样本下的无标模型传递是亟待解决的问题。提出了一种基于正则化多任务学习的近红外光谱仪无标模型传递方法（LSMTL）,利用迹范数约束权重矩阵的低秩结构，挖掘多任务间相似的特征表示，同时通过L_{2, 1}范数的稀疏约束最大程度保留各任务的离群特征，提升小样本任务的建模效果。建立了包含4台光谱仪、 1 200条光谱数据的多任务数据库，提出了用于建立近红外光谱定量分析模型的LSMTL算法框架，并系统考察了LSMTL的超参数敏感性和性能优势。结果表明，迹范数正则项通过约束多任务权重矩阵使其形成低秩结构，增加了各任务的低秩权重向量l的相似性，实现了多任务间的权重耦合。L_{2, 1}范数约束下各任务间是解耦的，使得任务的稀疏权重s具有特异性，两种范数共同作用实现了各任务的关联性挖掘和特性保留。低秩惩罚系数α影响了任务间的耦合程度，α越大，各任务的低秩权重l越趋于一致，稀疏惩罚系数β则影响了各任务非耦合权重s的稀疏性，β越大，s绝对值越小，对w的贡献越少。α与β的取值取决于从机样本数量，从机样本数越少，施加的惩罚应越强。自建数据集测试结果表明，相比三种有标模型传递（DS、 PDS、 CCA）及四种无标模型传递（TrAdaBoost、 Transfer CNN、 Mu-PLS、 MTL-Trace）,提出的LSMTL方法在30个建模样本情况下测试集性能最优，RMSE=97.3、R²=0.72、 MAPE=10.2%,尤其在小样本建模时展现出很强的应用潜力。更多还原

【Abstract】 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 L_2,1 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 L_{2, 1} norm decouples tasks to preserve sparse weights s with specificity, enabling joint optimization of task correlations and feature preservation; the low-rank penalty α controls task coupling intensity（higher α strengthens l consistency）, while the sparse penalty β governs s sparsity（higher β reduces s contribution to w）; optimal α/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.更多还原