Petersen Nanna, Stocks Stuart, Gernaey Krist V
Department of Chemical Engineering, Technical University of Denmark, Building 229, DK-2800 Kgs. Lyngby, Denmark.
Biotechnol Bioeng. 2008 May 1;100(1):61-71. doi: 10.1002/bit.21732.
The main purpose of this article is to demonstrate that principal component analysis (PCA) and partial least squares regression (PLSR) can be used to extract information from particle size distribution data and predict rheological properties. Samples from commercially relevant Aspergillus oryzae fermentations conducted in 550 L pilot scale tanks were characterized with respect to particle size distribution, biomass concentration, and rheological properties. The rheological properties were described using the Herschel-Bulkley model. Estimation of all three parameters in the Herschel-Bulkley model (yield stress (tau(y)), consistency index (K), and flow behavior index (n)) resulted in a large standard deviation of the parameter estimates. The flow behavior index was not found to be correlated with any of the other measured variables and previous studies have suggested a constant value of the flow behavior index in filamentous fermentations. It was therefore chosen to fix this parameter to the average value thereby decreasing the standard deviation of the estimates of the remaining rheological parameters significantly. Using a PLSR model, a reasonable prediction of apparent viscosity (micro(app)), yield stress (tau(y)), and consistency index (K), could be made from the size distributions, biomass concentration, and process information. This provides a predictive method with a high predictive power for the rheology of fermentation broth, and with the advantages over previous models that tau(y) and K can be predicted as well as micro(app). Validation on an independent test set yielded a root mean square error of 1.21 Pa for tau(y), 0.209 Pa s(n) for K, and 0.0288 Pa s for micro(app), corresponding to R(2) = 0.95, R(2) = 0.94, and R(2) = 0.95 respectively.
本文的主要目的是证明主成分分析（PCA）和偏最小二乘回归（PLSR）可用于从粒度分布数据中提取信息并预测流变性质。对在550升中试规模罐中进行的具有商业相关性的米曲霉发酵样品，就粒度分布、生物量浓度和流变性质进行了表征。使用赫谢尔-布克利模型描述流变性质。对赫谢尔-布克利模型中的所有三个参数（屈服应力（τ(y)）、稠度指数（K）和流动行为指数（n））进行估计时，参数估计的标准偏差很大。未发现流动行为指数与任何其他测量变量相关，并且先前的研究表明丝状发酵中流动行为指数为恒定值。因此选择将该参数固定为平均值，从而显著降低其余流变参数估计的标准偏差。使用PLSR模型，可以根据粒度分布、生物量浓度和过程信息对表观粘度（μ(app)）、屈服应力（τ(y)）和稠度指数（K）做出合理预测。这为发酵液的流变学提供了一种具有高预测能力的预测方法，并且相对于先前的模型具有优势，即τ(y)和K以及μ(app)都可以被预测。在独立测试集上进行验证时，屈服应力（τ(y)）的均方根误差为1.21 Pa，稠度指数（K）为0.209 Pa·s(n)，表观粘度（μ(app)）为0.0288 Pa·s，分别对应R(2) = 0.95、R(2) = 0.94和R(2) = 0.95。
