Open-Circuit Fault-Tolerant Strategy for Interleaved Boost Converters via Filippov Method

Interleaved converters use an increased number of power electronics switches; this may subsequently affect their reliability. However, this is an opportunity to develop fault-tolerant strategies to improve their reliability and to ensure continuity of service. This is why we herein propose, for the first time, a mathematical function to simultaneously model the healthy and faulty conditions of each switch, thus enabling a unique model of the system. This model is then used in an original fault-tolerant strategy based upon the peak current control with slope compensation. This method not only extends the stable range of the load variation but also ensures the stability in faulty conditions. Finally, the simulation results validate its effectiveness and confirm the theoretical analysis.

Kinetic Energy Dose as a Unified Metric for Comparing Ball Mills in the Mechanocatalytic Depolymerization of Lignocellulose

Mechanochemistry utilizes mechanical forces to activate chemical bonds. It offers environmentally benign routes for both (bio) organic and inorganic syntheses. However, direct comparison of mechanochemistry results is often very challenging. In mechanochemical synthetic protocols, ball mill setup (mechanical design and grinding vessel geometry) in addition to experimental parameters (milling frequency, duration, ball count and size) vary broadly. This fact poses a severe issue to further progress in this exciting research area because ball mill setup and experimental parameters govern how much kinetic energy is transferred to a chemical reaction. In this work, we address the challenge of comparing mechanochemical reaction results by taking the energy dose provided by ball mills as a unified metric into account. In this quest, we applied kinematic modeling to two ball mills functioning under distinct working principles to express the energy dose as a mathematical function of the experimental parameters. By examining the effect of energy dose on the extent of the mechanocatalytic depolymerization (MCD) of lignocellulosic biomass (beechwood), we found linear correlations between yield of water-soluble products (WSP) and energy dose for both ball mills. Interestingly, when a substrate layer is formed on the grinding jar wall and/or grinding medium, a weak non-linear correlation between water-soluble products yield and energy dose is identified. We demonstrate that the chemical reaction’s best utilization of kinetic energy is achieved in the linear regime, which presents improved WSP yields for given energy doses. In the broader context, the current analysis outlines the usefulness of the energy dose as a unified metric in mechanochemistry to further the understanding of reaction results obtained from different ball mills operating under varied experimental conditions.

Age dynamics of the need for outpatient medical care for conditions that determine the basic value of the need in women with the diseases of the circulatory system

INTRODUCTION: The results obtained from the analysis of age dynamics are insufficient for development a program of reducing morbidity and, ultimately, mortality, since a need of medical care already indicates a problem; so prevention and screening programs should surpass the emergence of these problems. AIM: To analyze the age dynamics of the need for outpatient medical care for conditions that determine the basic value of the need in women with diseases of the circulatory system. MATERIALS AND METHODS: We used data on 780,000 visits during one year to medical organizations that provide medical care on an outpatient basis. We studied the probability of an episode and the dynamics of the frequency of episodes depending on age in six five-year age groups: 31 to 35 years, 36 to 40 years, 41 to 45 years, 46 to 50 years, 51 to 55 years, and 56 to 60 years. The dynamics of the frequency of episodes was modeled by a mathematical function with the largest value of the approximation coefficient. The dynamics of the frequency of episodes was modeled by a mathematical function with the largest value of the approximation coefficient. RESULTS: The dynamics of the need for outpatient medical care for hypertensive diseases [Diseases characterized by high blood pressure] (I10 – I15), ischemic heart diseases (I20 – I25) and vascular diseases of the brain (I60 – I69) is characterized by an increasing trend in demand indicators throughout the studied age period. The greatest increase in indicators is observed in the age groups of 31–40 years for ischemic heart diseases and vascular diseases of the brain and 41–50 years for hypertensive conditions. The greatest increase in demand is observed for coronary heart diseases (I20 – I25). The total amount of resources required increases more than 350 times over the 30-year age period, despite the stable value of the average duration of treatment. The increase in the total amount of resources required for vascular diseases of the brain is 30 times. The lowest growth gradient is registered in relation to hypertensive conditions (10-fold growth). As a critical age period, it is most appropriate to consider the age of a woman under 35 years. CONCLUSION: Mathematical modeling is optimally performed using power functions for hypertensive conditions and vascular diseases of the brain and exponential functions for ischemic heart diseases. All the proposed models are characterized by high approximation coefficients.

Application of Wigner Distribution Function for THz Propagation Analysis

The construction of a transmission line (TL) for a wide tunable broad-spectrum THz radiation source is not a simple task. We present here a platform for the future use of designs of the TL through our homemade simulations. The TL is designed to be a component of the construction of an innovative accelerator at the Schlesinger Family Center for Compact Accelerators, Radiation Sources and Applications (FEL). We developed a three-dimensional space-frequency tool for the analysis of a radiation pulse. The total electromagnetic (EM) field on the edge of the source is represented in the frequency domain in terms of cavity eigenmodes. However, any pulse can be used regardless of its mathematical function, which is the key point of this work. The only requirement is the existence of the original pulse. This EM field is converted to geometric-optical ray representation through the Wigner transform at any desired resolution. Wigner’s representation allows us to describe the dynamics of field evolution in future propagation, which allows us to determine an initial design of the TL. Representation of the EM field by rays gives access to the ray tracing method and future processing, operating in the linear and non-linear regimes. This allows for fast work with graphics cards and parallel processing, providing great flexibility and serving as future preparation that enables us to apply advanced libraries such as machine learning. The platform is used to study the phase-amplitude and spectral characteristics of multimode radiation generation in a free-electron laser (FEL) operating in various operational parameters.

Multi-objective optimization of a geothermal steam turbine combined with reverse osmosis and multi-effect desalination for sustainable freshwater production

A novel geothermal desalination system is proposed and optimized in terms of maximizing the exergy efficiency and minimizing the total cost rate of the system. The system includes a geothermal steam turbine with a flash chamber, a reverse osmosis unit and a multi-effect distillation system. First, exergy and economic analyses of the system are performed using Engineering Equation Software. Then, an artificial neural network is used to develop a mathematical function linking input design variables and objective functions for this system. Finally, a multi-objective optimization is carried out using a genetic algorithm to determine the optimum solutions. The Utopian method is used to select the favorable solution from the optimal solutions in the Pareto frontier. Also, the distributions of the values of design variables within their allowable ranges are investigated. It is found that the optimum exergy efficiency and total cost rate of the geothermal desalination system are 29.6% and 3410 $/h, respectively. Increasing the seawater salinity and decreasing the intake geothermal water temperature results in an improvement in both exergy efficiency and total cost rate of the system, while variations in the flash pressure and turbine outlet pressure lead to a conflict between the exergy efficiency and total cost rate of the geothermal desalination system over the range of their variations.

Auditing and Debugging Deep Learning Models via Flip Points: Individual-Level and Group-Level Analysis

Deep learning models have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Nevertheless, they are consistently utilized in many applications, consequential to humans’ lives, usually because of their better performance. Therefore, there is a great need for computational methods that can explain, audit, and debug such models. Here, we use flip points to accomplish these goals for deep learning classifiers used in social applications. A trained deep learning classifier is a mathematical function that maps inputs to classes. By way of training, the function partitions its domain and assigns a class to each of the partitions. Partitions are defined by the decision boundaries which are expected to be geometrically complex. This complexity is usually what makes deep learning models powerful classifiers. Flip points are points on those boundaries and, therefore, the key to understanding and changing the functional behavior of models. We use advanced numerical optimization techniques and state-of-the-art methods in numerical linear algebra, such as rank determination and reduced-order models to compute and analyze them. The resulting insight into the decision boundaries of a deep model can clearly explain the model’s output on the individual level, via an explanation report that is understandable by non-experts. We also develop a procedure to understand and audit model behavior towards groups of people. We show that examining decision boundaries of models in certain subspaces can reveal hidden biases that are not easily detectable. Flip points can also be used as synthetic data to alter the decision boundaries of a model and improve their functional behaviors. We demonstrate our methods by investigating several models trained on standard datasets used in social applications of machine learning. We also identify the features that are most responsible for particular classifications and misclassifications. Finally, we discuss the implications of our auditing procedure in the public policy domain.

Considering Existing Factors That May Cause Radiation Hormesis at <100 mSv and Obey the Linear No-Threshold Theory at ≥100 mSv

The linear no-threshold (LNT) theory describes the linear relationship between a radiation dose and its effects. However, whether the linear relationship is maintained at low radiation doses has yet to be determined. Many previous studies support the radiation hormesis theory, which states that radiation has beneficial effects on health. In this viewpoint, we propose a mathematical function fitted to a model consistent with both the LNT at ≥100 mSv and radiation hormesis theories at <100 mSv, and the model requires a factor whose amount or activity takes a mountain-like shape versus the radiation dose and have one maximum value at 40.9 mSv. We searched a wide range of factors with these features based on searches on PubMed, and then evaluated whether these factors were suitable candidates consistent with both the LNT and radiation hormesis theories. Our consideration indicated that these factors did not completely follow the equation suggested at this time. Of course, other theories do not deny that these factors are involved in hormesis. However, based on our theory, still unknown factors may be involved in radiation hormesis, and then such unknown factors which are activated at <100 mSv should be searched.

Analysis of the most common methods for determining the stability of energy systems

Problem. There are many methods for determining the stability of the energy system. In normal operating condition (normal rated mode), the power system must reliably ensure the consumption of electricity of normalized quality. However, in addition to the normal state, there are emergency and transient states caused by various transients. This is due to the fact that the energy system is constantly changing its parameters. Such changes are determined by variations in the amount of power produced and consumed, as well as the changes in system configuration. Goal. The goal is studying the possibilities of various methods of determining the power systems stability and drawing up the general algorithm of actions for maintenance of their stability. Methodology. When determining the stability of energy systems by the Lyapunov method, two methods can be used: the direct method and the first approximation method. Lyapunov direct method refers to differential methods. To conclude about the stability of the system we do not find a general or particular solution of differential equations, but with their help we find a mathematical function, the complete derivative of which over time allows to obtain a conclusion about the stability of the system. Results. Many methods can be used to determine whether a sustainable energy system is stable or not. The most common are the Lyapunov methods and the Moiseev method. It is determined that the direct Lyapunov method refers to differential methods. The application of the direct Lyapunov method for energy problems is limited. Currently, it can be used only for some individual cases. The method of the first approximation (Lyapunov first method) has received wider application in the solution of power problems. When applying this method, which belongs to the group of methods of full integration, the right-hand sides of the equations are decomposed into power series. Originality. It is determined that one of the perspective directions of increasing the efficiency of the mathematical device work is using the methods of the second order in modeling and optimization of operating modes of electric power systems. This allows you to increase the speed and reliability of the convergence of iterative processes. Practical value. Based on the analysis of various existing methods for solving the problems of stability of energy systems, an algorithm of actions is proposed and developed, which will help to solve the problem of stability in practice.

Mathematical function data model analysis and synthesis system based on short-term human movement

The paper proposes a data model analysis algorithm for human motion function based on short-term behaviour. The algorithm uses a functional data analysis (FDA) method to perform Fourier fitting on the motion data and extract the fitted approximate single period data. Finally, the algorithm depicts the internal change in the motion in the low-dimensional space. The study found that the characteristic motion data obtained by the algorithm has smooth characteristics, and the relevant case analysis also verifies the algorithm's effectiveness.

Human gait modelling and tracking based on motion functionalisation

This paper proposes a mathematical function movement model based on the gait movement of the human body and, in particular, on the trajectory of the limbs during human movement. The article systematically measures and experimentally deals with the trajectory of the limbs of 40 students in the walking movement. The linear high-order polynomial fitting method eliminates the motion error. Simultaneously, the linear relationship least square method is used to obtain the expression of the limb motion function. Finally, the mathematical model of the limb motion trajectory is obtained. It is verified through experiments that the model proposed in the thesis can calculate the law of limb movement and movement parameters of any person under normal walking movement. This research has high research value for human movement rehabilitation and the design of wearable equipment.