Beyond Beer-Lambert Linear Regression: Multi-Layer Modeling for Wide-Range Concentration Quantification Using Ultraviolet-visible Spectroscopy

Abstract

Ultraviolet–visible (UV-Vis) spectroscopy is widely used for chemical quantification due to its simplicity and low cost; however, accurate concentration prediction becomes challenging when target concentrations span wide ranges, where the global linearity assumption of the Beer-Lambert law often breaks down. To address this limitation, we propose a multi-layer modeling framework that exploits local linearity rather than relying on a single global model. Two approaches, dynamical-layer regression and classified-layer regression, are both integrated with principal component regression and partial least squares. The framework is evaluated using UV-Vis spectra of nickel sulfate and cobalt sulfate solutions across concentrations ranging from 10⁻⁶ to 0.9 mol L⁻¹, as well as mixed-solution scenarios. The proposed methods consistently outperform conventional single-layer linear models and global nonlinear models, achieving up to a 50% reduction in root mean squared error and R² values exceeding 0.99 for single-solute datasets. These results demonstrate that the proposed framework provides a robust and effective solution for wide-range concentration prediction in spectroscopic analysis.