Sibono Leonardo, Tronci Stefania, Hedegaard Martin Aage Barsøe, Errico Massimiliano, Grosso Massimiliano
Dipartimento di Ingegneria Meccanica, Chimica e dei Materiali, Università degli Studi di Cagliari, Via Marengo 2, 09123, Cagliari, Italy.
Department of Green Technology, University of Southern Denmark, Campusvej 55, 5230, Odense, Denmark.
Anal Bioanal Chem. 2025 Jun 26. doi: 10.1007/s00216-025-05965-2.
The rennet-induced coagulation of reconstituted skimmed milk powder was investigated in this work. An analysis of Raman spectra, coupled with rheological measurements and multivariate statistical analysis, was conducted in order to develop a mathematical model for describing the dynamic behavior of milk constituents involved in coagulation. The first principal component from Raman data was used to describe the κ-casein concentration evolution, while the second principal component served to estimate the number of cross-linking sites, of which consumption generates the permanent cross-links, which were assumed to be proportional to the elastic modulus. Three levels of temperature and two levels of rennet concentration were explored. A system of three ordinary differential equations (ODEs) was proposed and analytically integrated to predict the temporal evolution of the first two principal components from Raman spectra and the elastic modulus, which is the parameter of interest in the industrial applications. An activation function was employed to activate/deactivate the generation term of the elastic modulus, as a result of gelation occurring after a delay period. Pseudo-kinetic constant of aggregation and lag time resulted in depending on both temperature and rennet concentration. A test sample was used to validate the prediction capability of the model, which resulted in high prediction performances (R = 0.9992). Afterwards, the calibrated model was coupled with a Kalman filter algorithm to provide a real-time monitoring procedure for the in-line estimation of the elastic modulus.
本研究对凝乳酶诱导的复原脱脂奶粉的凝固过程进行了研究。结合流变学测量和多元统计分析对拉曼光谱进行了分析，以建立一个数学模型来描述参与凝固过程的牛奶成分的动态行为。拉曼数据的第一主成分用于描述κ-酪蛋白浓度的变化，而第二主成分用于估计交联位点的数量，交联位点的消耗会产生永久性交联，假定其与弹性模量成正比。研究了三个温度水平和两个凝乳酶浓度水平。提出了一个由三个常微分方程（ODE）组成的系统，并进行了解析积分，以预测拉曼光谱的前两个主成分和弹性模量随时间的变化，弹性模量是工业应用中的关键参数。由于在延迟期后发生凝胶化，采用了一个激活函数来激活/停用弹性模量的生成项。聚集的伪动力学常数和滞后时间取决于温度和凝乳酶浓度。使用一个测试样品来验证模型的预测能力，结果显示预测性能很高（R = 0.9992）。之后，将校准后的模型与卡尔曼滤波算法相结合，以提供一种用于在线估计弹性模量的实时监测程序。
