基于物理先验残差网络的茶叶轻元素极小样本XRF定量分析

Physics-Guided Residual Networks for Small-Sample XRF Quantification of Light Elements in Tea

摘要: 能量色散X射线荧光光谱(EDXRF)在农产品无损检测中具有重要应用前景，但茶叶等轻基体中轻元素(如Al、S、Ca)的定量分析常受制于强烈的基体效应(吸收–增强效应)。此外，在极小样本量条件下，常规数据驱动模型在处理高维光谱数据时面临严重的“维数灾难”与过拟合风险。为破解这一难题，本文提出了一种基于物理先验残差网络(Physics-Guided Residual Network, PGRN)的小样本定量分析方法。该架构采用两阶段融合策略：第一阶段，基于X射线物理先验知识，提取目标元素的净峰面积构建单变量物理底座(Physical Baseline)，为模型提供基础的物理鲁棒性，有效规避小样本下的模型失效；第二阶段，结合标准正态变量变换(SNV)与稀疏机器学习算法(Lasso/ElasticNet)，在包含相邻干扰元素的特定光谱感兴趣区(ROI)内，针对性地学习并补偿物理模型无法解释的基体效应残差。实验结果表明，与传统物理定量方法相比，PGRN实现了预测精度的显著提升。以受基体效应影响严重的硫(S)元素为例，其交叉验证决定系数(R²)从0.567显著提升至0.831，交叉验证均方根误差(RMSECV)大幅下降。该方法有效打破了小样本光谱分析的过拟合困境，为复杂基体下的高精度XRF定量分析提供了一种兼具数据驱动精度与物理可解释性的白盒新范式。

Abstract: Energy-dispersive X-ray fluorescence (EDXRF) spectrometry holds significant potential for the non-destructive testing of agricultural products. However, the quantitative analysis of light elements (e.g., Al, S, Ca) in light matrices such as tea leaves is frequently constrained by intense matrix effects (absorption-enhancement). Furthermore, under extremely small sample conditions, conventional data-driven models face the severe “curse of dimensionality” and high risks of overfitting when processing high-dimensional spectral data. To address this dilemma, a novel quantitative analysis method based on a Physics-Guided Residual Network (PGRN) is proposed. The architecture adopts a two-stage fusion strategy. In the first stage, guided by X-ray physical prior knowledge, a univariate physical baseline is established by extracting the net peak area of the target element, providing fundamental physical robustness. In the second stage, by combining Standard Normal Variate (SNV) transformation with the sparse Lasso machine learning algorithm, the matrix effect residuals are specifically extracted and compensated within targeted spectral regions of interest (ROIs) encompassing adjacent interfering elements. Experimental results demonstrate that PGRN achieves a significant improvement in prediction accuracy. Taking sulfur S, which is severely affected by matrix effects, as an example, the cross-validation coefficient of determination (R²) was significantly improved from 0.567 to 0.831, with a substantial decrease in RMSECV. This method effectively overcomes the overfitting bottleneck in small-sample spectral analysis, providing a novel white-box paradigm that integrates data-driven accuracy with physical interpretability for high-precision XRF quantification in complex matrices.