Mathematical Modelling of Batch Distillation Columns: A Comparative Analysis of Non-Linear and Fuzzy Models

Distillation is the process most commonly used in industry to separate chemical mixtures; its applications range from cosmetic and pharmaceutical to petrochemical industries. The equipment required to perform the distillation process is known as distillation column. Since initial investment and maintenance costs for distillation columns are very high it is necessary to have an appropriate mathematical model that allows improving the comprehension of the column dynamics, especially its thermal behaviour, in order to enhance the control and safety of the process. This chapter presents a general panorama of the mathematical modelling of distillation columns, having as a specific case of study the comparison of a space-state non-linear model and a Takagi-Sugeno fuzzy model for a batch distillation column using a binary mixture (Ethanol-Water)

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation Columns

In this chapter, the analysis and design of a fuzzy observer based on a Takagi-Sugeno model of a batch distillation column are presented. The observer estimates the molar compositions and temperatures of the light component in the distillation column considering a binary mixture. This estimation aims to allow monitoring the physical variables in the process to improve the quality of the distillated product as well as to detect failures that could affect the system performance. The Takagi-Sugeno fuzzy model is based on eight linear subsystems determined by three premise variables: the opening percentage of the reflux valve and the liquid molar composition of the light element of the binary mixture in the boiler and in the condenser. The stability analysis and the observer gains are obtained by linear matrix inequalities (LMIs). The observer is validated by MATLAB® simulations using real data obtained from a distillation column to verify the observer’s convergence and analyze its response under system disturbances

Real-Time Tracking and Detection of Cervical Cancer Precursor Cells: Leveraging SIFT Descriptors in Mobile Video Sequences for Enhanced Early Diagnosis

Cervical cancer ranks among the leading causes of mortality in women worldwide, underscoring the critical need for early detection to ensure patient survival. While the Pap smear test is widely used, its effectiveness is hampered by the inherent subjectivity of cytological analysis, impacting its sensitivity and specificity. This study introduces an innovative methodology for detecting and tracking precursor cervical cancer cells using SIFT descriptors in video sequences captured with mobile devices. More than one hundred digital images were analyzed from Papanicolaou smears provided by the State Public Health Laboratory of Michoacán, Mexico, along with over 1800 unique examples of cervical cancer precursor cells. SIFT descriptors enabled real-time correspondence of precursor cells, yielding results demonstrating 98.34% accuracy, 98.3% precision, 98.2% recovery rate, and an F-measure of 98.05%. These methods were meticulously optimized for real-time analysis, showcasing significant potential to enhance the accuracy and efficiency of the Pap smear test in early cervical cancer detection

Image processing for AFB segmentation in bacilloscopies of pulmonary tuberculosis diagnosis.

Image segmentation applied to medical image analysis is still a critical and important task. Although there exist several segmentation algorithms that have been widely studied in literature, these are subject to segmentation problems such as over- and under-segmentation as well as non-closed edges. In this paper, a simple method that combines well-known segmentation algorithms is presented. This method is applied to detect acid-fast bacilli (AFB) in bacilloscopies used to diagnose pulmonary tuberculosis (TB). This diagnosis can be performed through different tests, and the most used worldwide is smear microscopy because of its low cost and effectiveness. This diagnosis technique is based on the analysis and counting of the bacilli in the bacilloscopy observed under an optical microscope. The proposed method is used to segment the bacilli in digital images from bacilloscopies processed using Ziehl-Neelsen (ZN) staining. The proposed method is fast, has a low computational cost and good efficiency compared to other methods. The bacilli image segmentation is performed by image processing and analysis techniques, probability concepts and classifiers. In this work, a Bayesian classifier based on a Gaussian mixture model (GMM) is used. The segmentations' results are validated by using the Jaccard index, which indicates the efficiency of the classifier

Comparison between mathematical methods to estimate blood glucose levels from ECG signals

Diabetes mellitus, known as diabetes, is a chronic disease that affects the control of blood glucose concentration levels, it is a disease that mostly affects adults (type 2 diabetes), but it can also occur in children (type 1 or childhood diabetes), as well as in pregnant women (gestational diabetes). Diabetes is one of the diseases with the highest prevalence and high mortality worldwide. Diabetes has no cure, but continuous monitoring to maintain blood glucose levels in normal ranges reduces the possibility of suffering from gastrointestinal problems, vision loss, limb amputations (such as diabetic foot) and damage to vital organs such as the heart and kidneys, among other associated complications. This article compares the results in glucose estimation by using a linear, quadratic and cubic regression considering the electrical characteristics generated in the cardiac conduction (HR, HRV, T-wave peak, and QT interval) recorded on a single-lead electrocardiogram (VII), used as a non-invasive blood glucose estimation model. The best estimate was obtained using a cubic regression. The validation was performed using the Clarke grid having 77.78 % of data in the A zone and 22.22 % in the B zone and a Pearson correlation value of 0.94103 in the cubic regression