Determination of the Concentration of Propionic Acid in an Aqueous Solution by POD-GP Model and Spectroscopy

Abstract

Biorefining and biorefineries are the future of industry and energy. It is still a long way to complete its implementation, but small biorefineries focused mainly on the production of fuels and energy are more and more frequent in rural areas and large areas located near big cities in which, in addition to fuels and energy, various organic substances of high market value are also produced. In order to optimize biogas production and to control methane fermentation processes, fast and accurate identification of carboxylic acid concentrations, including propionic acid as a precursor to acetic acid, is needed. In this study, a process quality control method was developed to evaluate the propionic acid content of an aqueous solution from the fermentation mass. The proposed methodology is based on near infrared spectroscopy with multivariate analysis and stochastic metamodeling with a denoising procedure based on proper orthogonal decomposition (POD). The proposed methodology uses the Bayesian theory, which provides additional information on the magnitude of the correlation between state and control variables. The calibration model was, therefore, constructed by using Gaussian Processes (GP) to predict propionic acid content in the aqueous solution using an NIR-Vis spectrophotometer. The design of the calibration model was based on absorbance spectra and calculation data from selected wavelength ranges from 305 nm to 2210 nm. Measurement data were first denoised and truncated to build a fast and reliable metamodel for precise identification of the acid content of an aqueous solution at a concentration from 0 to 5.66%. The mean estimation error generated by the metamodel does not exceed 0.7%.

Estimation of the Edge Crush Resistance of Corrugated Board Using Artificial Intelligence

“…The Gaussian process is fully defined by the mean function µ such that is the mean of and the covariance/kernel function such that is the covariance between the value of the function at , and the value of the function at , . Without going into details, because there are many textbooks and books on this subject, in recent scientific papers, one can also find details of their implementation [ 61 , 64 ]; the most important thing from the point of view of regression accuracy is the proper selection of kernel functions and proper training of hyperparameters.…”

“…It is possible to find the unknown parameters using any optimization procedure. In the literature, one can find methods, in which a searching for the most probable set is performed by maximizing the log likelihood function [ 61 , 64 ] using any gradient-based optimization algorithms, e.g., a first-order batch Levenberg–Marquardt algorithm already presented in the previous section.…”

“…Among the numerous applications of ANN one can mention a few, e.g., medical diagnosis [ 60 , 61 ], image recognition [ 62 ], economics [ 63 ], biosystem engineering [ 64 ] or automobile guidance systems [ 65 ]. ANN is also utilized in the paper industry.…”

Application of Artificial Neural Networks to Numerical Homogenization of the Precast Hollow-Core Concrete Slabs

“…Another example could be the paper of Staszak et al [13], in which it was shown that the precast concrete slabs reinforced with spatial linear trusses may be efficiently homogenized to one effective layer of a representative shell element. On the other hand, the computational time (ii) can be reduced by using soft computing methods such as the artificial neural network (ANN) algorithms [14][15][16][17][18] or metamodeling [19,20]. This usually requires a significant computational effort, which is incurred before the solution of the target computational problem is needed, but it allows one to obtain a solution with an acceptably small error in a fraction of a second when the actual problem occurs.…”

Robust Estimation of the Chronological Age of Children and Adolescents Using Tooth Geometry Indicators and POD-GP

“…The present work is an extension of the work presented by Zaborowicz [ 29 ]. New elements that are additionally included here are: (a) automatic sensitivity analysis of all 21 indices to see which of them carry more information; (b) the use of data compression techniques based on the Proper Orthogonal Decomposition (POD) [ 30 , 31 , 32 , 33 ], which allows not only the reduction of the size of the input vector but also the denoising of the data, thereby reducing the risk of overfitting the model; (c) the use of Gaussian processes (GP) [ 34 , 35 ], which allows results and their uncertainty to be obtained. This model is trained once-for-all and can later be used as a ready-made tool for in situ identification of the dental age of new patients.…”