Practical Calculations Research Articles

Experimental and numerical study on axial compression behavior of slender CFST columns with localized pitting corrosion damage

In order to investigate the axial compression behavior of slender circular concrete-filled steel tubes (CFSTs) with localized pitting corrosion damage, an experimental and numerical study was performed in this paper. In the experimental study, mechanically drilled cylindrical pits were employed to simulate localized pitting corrosion damage. Seven specimens were tested, with six specimens containing corrosion pits located at mid-height and one intact specimen. The experimental results showed that the localized pitting corrosion damage degraded the axial compression behavior of the specimens. Numerical models were developed and validated by the experimental results and used to consider the random characteristics of corrosion pits. A parametric analysis was then performed based on the validated numerical models. It was revealed that the ultimate strength of CFST was influenced by the location and dimensions of the pitting corrosion. Considering the random nature of localized pitting corrosion damage located at the midheight, practical calculation models for predicting the ultimate strength of CFSTs were put forward based on the methods provided in existing codes. On account of the obtained data pool, the predictions were verified against the results from the tests and parametric analysis. In addition, considering the random locations of the pitting region on the surface of the member, a method based on the controlling section was proposed to determine whether the corrosion should be considered and to calculate the ultimate strength.

Evaluating Health Care Professionals' Readiness for e-Health Adoption in the Context of the COVID-19 Pandemic: A Georgian Perspective.

Background: The COVID-19 pandemic has accelerated the adoption of Electronic health (e-Health), leveraging technologies such as telemedicine, electronic health records, artificial intelligence, and patient engagement platforms. This transformation underscores e-Health's role in providing efficient, patient-centered care. Our study explores health care professionals' readiness for these technologies, emphasizing the need for tailored education in this evolving landscape. Methods: In our study, conducted between February and March 2023, we administered a questionnaire-based survey to 500 staff members (82.4% female, 17.6% male) aged 25-70 from medical universities in Tbilisi, Georgia. The structured questionnaire covered topics such as computer literacy, telemedicine awareness, patient data security, and ethical considerations. We employed SPSS v21.0 for data analysis, encompassing descriptive statistics and thematic analysis of open-ended responses. Results: Our study included 500 participants categorized into five age groups. Notably, 31% considered themselves computer "experts," while 69% rated their skills as "intermediate" or "advanced." Furthermore, 85% used computers professionally, with 33% having practical computer training. Interestingly, 59% expressed interest in information technology training. Regarding e-Health, 15% believed it involves remote communication between health care professionals and patients, while 42% considered it "correct," and 37% "might be correct." Concerning its application in managing patients, opinions varied. In terms of e-Health's integration into Georgia's health care, responses ranged. Regarding patient data safety, participants exhibited diverse views. Finally, opinions on the necessity of informed consent for e-Health applications varied among participants. Conclusions: Our study explores health care professionals' readiness for e-Health adoption during the COVID-19 pandemic. It reveals varying computer literacy levels, a willingness to learn, differing views on e-Health applications, and mixed opinions on its integration into Georgian health care. These findings emphasize the need for clear e-Health terminology, education, tailored approaches, and a focus on data privacy and informed consent. Overall, e-Health's transformative role in modern health care is underscored.

Semi‐Quantum Secure Multiparty Summation and its Applications to Anonymous Auction and Ranking

AbstractSemi‐quantum secure summation allows multiple parties with limited quantum capabilities to perform collective calculations under the premise of protecting privacy. However, current approaches are confined to low‐dimensional quantum states as information carriers and are restricted to scenarios involving two or three parties. This limitation hinders their universality and ability to fulfill the requirements of practical secure multiparty computations. To address these challenges, a novel semi‐quantum secure multiparty summation (SQSMS) protocol is proposed based on high‐dimensional entangled states and single‐particle states. The protocol leverages the entanglement correlation to guarantee the security of the transmission, enabling resistance against various potential attacks. Then, by utilizing the IBM Qiskit platform, corresponding quantum circuits and simulation results are presented to validate the feasibility and correctness of the protocol. Furthermore, building upon the foundation of the SQSMS protocol, semi‐quantum anonymous auction and anonymous ranking protocols are further constructed. Compared with previous approaches, the designed protocols cater to the requirements of their respective counterparts. Consequently, the approach may have broad applications in semi‐quantum secure multiparty computation scenarios.

Quantile Regression in Survival Analysis: Comparing Check-Based Modeling and the Minimum Distance Approach

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates.
 Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation.
 Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation.
 Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.
 

Comparative analysis of calculations in thin-walled structure design

This article focuses on reproducing normative calculation conditions through numerical methods and comparing these with outcomes obtained using specialized software for structural engineers. We analyse the basis of normative critical forces and stress values, including conditions of fixity, types of structures, and materials, and how these are represented in practical calculations and numerical modelling. The investigation is intended to enhance understanding between normative assumptions and their practical application in design, offering valuable guidelines for refining calculation methods.

The Problem of the Reliability of Bending Models for Composite Plates of Medium Thickness

Most refined bending models of medium-thick plates, which consider transverse shear and partial compression deformations, differ little. However, despite a significant increase in the order of the governing differential equations, the results obtained from their equations give mainly a small increase in accuracy compared to the existing theories. On the other hand, such an increase in the order of the constructed systems of differential equations requires a significant increase in the effort required to solve them, complicates their physical interpretation, and narrows the range of people who can use them, primarily engineers and designers. Therefore, developing a plate-bending model that incorporates all the above factors and is on par with previously applied theories regarding the complexity of the calculation equations remains relevant. For example, most of the applied theories that do not consider transverse compression cannot be used to solve problems of contact interaction with rigid and elastic dies and bases because it is impossible to satisfy the conditions at the contact boundary of the outer surface of the plate, as well as the boundary conditions at the edges of the plate. Therefore, to provide guaranteed accuracy of the results, some researchers of these problems have introduced such a concept as “energy consistency” between the functions of representation of the displacement vector components, their number, the order of equations, and the number of boundary conditions. The authors, based on the developed version of the model of orthotropic plates of medium thickness, investigate the problem of taking into account the so-called “energy consistency” effect of the bending model, depending on the order of the design equations and the number of boundary conditions, as well as its usefulness and disadvantages in practical calculations. The equations of equilibrium in displacements and expressions for stresses in terms of force and moment forces are recorded. For rectangular and circular plates of medium thickness, test problems are solved, and the numerical data are compared with those obtained using spatial problems of elasticity theory, as well as the refined Timoshenko and Reissner theories. An analysis of the obtained results is provided.

ОБГРУНТУВАННЯ ПОКАЗНИКА ЕФЕКТИВНОСТІ РОБОТИ ЗАГОНУ ЗАБЕЗПЕЧЕННЯ РУХУ КОЛОН ПІД ЧАС МАРШУ

The article shows the necessity of improving the system of task performance by the detachment of ensuring the movement of columns during the march. The successful performance of combat tasks by units and units of the Armed Forces of the Armed Forces of Ukraine is not possible without comprehensive support, in particular, without such an important type of operational (combat) support as engineering, which is organized for the purpose of timely and covert deployment of troops (forces), conducting maneuvers by them, creating the necessary conditions for the successful performance of assigned tasks, increasing the level of protection of troops (forces) and objects from the enemy's means of destruction, assigning losses to the enemy and complicating his actions. The engineering support of combat operations of units is inextricably linked with the implementation of a certain management procedure, the development of options for working out the received tasks and the purposeful use of engineering units. One of the important tasks of combat engineering support is the preparation and maintenance of troop (force) movement routes. Preparation and maintenance of troop movement routes (forces) is carried out in all types of combat operations, on the march and in the deployment of troops in place. The existing indicators for evaluating the level of efficiency of the use of machines do not allow for a generalized assessment of the level of effectiveness of tasks performed by the detachment ensuring the movement of columns during the march. Therefore, there was a need to obtain a dependency for evaluating the effectiveness of tasks performed by the unit to ensure the movement of columns during the march. In order to determine the efficiency of the convoy movement support unit, it is proposed to use the coefficient of performance of tasks by the column movement support unit during the march. Dependencies for evaluating the effectiveness of tasks performed by the squad to ensure the movement of columns during the march allow you to determine the influence of various factors on the efficiency indicator and outline ways to meet the specified requirements for modern models of engineering machines. A practical calculation was carried out.

Використання цифрових інструментів у соціальній роботі з молоддю

The article analyzes contemporary application of digital tools in social work practice with young people. Given the subject of study, the concept of “digital tools” is interpreted as software, applications or electronic platforms used to solve certain tasks of social work. With consideration of statistics regarding Internet penetration level in early 2024 in Ukraine, the use of offline, online and mixed digital tools in social work with young people is justified. Possible ways of computer, console and mobile games implementation in social work practice with young people are presented. The example of a computer game, which was designed and developed directly for social work is given. The differences between digital tools that involve the “immersion” of users into virtual and augmented reality are revealed. Examples of VR- and AR-applications already used in social work practice are provided. Major areas of application of tools for organizing online-communication and interaction are revealed. The most widespread social media platforms in Ukraine are determined as of early 2024. Key areas of using social media in social work practice with youth are outlined. The possibilities of integrating Artificial Intelligence tools into the social work practice with young people are delineated, examples of such AI-instruments are given. The article also indicates that digital tools are often used in addition to traditional offline interaction with the clients. The main advantages of digital tools implementation in social work practice with young people, as well as the key emerging challenges related to social work digitalization are identified.

Dynamics of acoustically-induced droplet instability

The advancement of the theory of droplet stability in the acoustic field is of significant value in improving ultrasonic atomization and ultrasonic levitation technology. In this work, in order to reveal the detailed mechanism of acoustic droplet instability and give the instability criterion for easy application, the dynamics of droplet instability in standing wave acoustic field (19.8 kHz) is studied by combining practical experiment, theoretical derivation and numerical calculation. The acoustic instability of the droplet occurring near the wave nodes is mainly manifested in two typical modes: disk instability and edge-sharpening instability. The appearance of these two instability modes depends on the relative magnitude of the standing wave field strength. Specifically, with the gradual enhancement of the intensity of the standing wave field, the instability mode of the droplet will gradually change from disc instability to edge-sharpened instability.The droplets show obvious self-accelerating expansion in the equatorial plane in the instability process. The positive feedback between the droplet aspect ratio and the negative pressure of acoustic radiation at the equator of the droplet is the reason for the above self-accelerating behavior. The theoretical results obtained through deduction indicate that the amplitude of the negative acoustic radiation pressure at the droplet equator is proportional to the square of the droplet aspect ratio. The surface tension of the droplet is the main factor hindering its deformation, while the acoustic radiation suction at the equator is the main factor driving the deformation of the droplet. Based on this, the force equilibrium equation of the droplet interface is established, and the dimensionless criterion of acoustic droplet instability, i.e. the acoustic Weber number <i>We</i><sub>a</sub>, is derived. When <i>We</i><sub>a</sub>≤1, the droplet interface stays in equilibrium, and when <i>We</i><sub>a</sub> >1, the equatorial acoustic suction is larger than the surface tension, and the droplet instability occurs, and the average error between the experimental results and the theoretical results is only 9%.

Frontiers of Artificial Intelligence Versus Generative, Explainable and Quantum Technologies: An Overview

Generative AI can produce content that is similar to human ingenuity, revolutionizing a number of industries with lifelike outputs like music and images. Misinformation and intellectual property rights give rise to ethical concerns. Notwithstanding these difficulties, generative AI has the potential to spur additional innovation in a variety of sectors, subject to moral issues. The goal of explainable AI (XAI) is to improve AI systems’ accountability and transparency, which is essential for their inclusion into industries like banking and healthcare. However, in order to effectively explain complicated AI systems, strong XAI techniques are required. Quantum artificial intelligence (QAI) promises improvements in cryptography and optimization by using quantum physics to speed up AI systems. However, there are still difficulties in creating practical quantum computers and improving quantum AI algorithms. The present overview provides new insights into developing a platform to explore AI in various arenas of life sciences and technologies and social up-gradation.

Parallel optimization approaches for scattering source term and angle merging in MOC high-order anisotropic computation on GPUs

The introduction of high-order anisotropic scattering and thousand-group calculations significantly increases the computational workload of the MOC method, posing difficulties for practical parallel computation on GPUs. In this paper, a GPU-based MOC algorithm is optimized, focusing on the performance optimization of the kernel function that merges high-order anisotropic angular flux density into scalar flux density moments, as well as the optimization of the scattering source term calculation method in thousand-group calculations. Two parallel algorithms based on azimuthal and polar angles are proposed for high-order anisotropic scattering. For the thousand-group calculation, a data structure is designed according to the physical characteristics of the anisotropic scattering matrix, and then two optimization algorithms are proposed from the perspectives of memory access and parallelism. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is more advantageous. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is found to be more advantageous. Based on a self-designed fast reactor fuel lattice, it is concluded that the parallelism-oriented calculation method for the thousand-group anisotropic scattering source term is more efficient. Finally, the Roofline model is used to analyze the advantages of the algorithm.

MATHEMATICAL MODEL OF OSHTEС MODERNIZATION WHEN SELECTING SWITCH GEAR EQUIPMENT

In this work, engineering calculations and selection of equipment were performed based on the calculation of short circuits during the modernization of the Osh Thermal Power Plant. Two feasible options for the structural diagram of a thermal power plant are considered. To solve the problem, the following was completed: drawing up technically possible options for a structural diagram and reasoned selection of the best suitable one, taking into account reliability; assessment of new structural schemes of thermal power plants using calculations and comparisons based on technical and economic indicators; the values ​​of the supertransient current in places of short circuit, the shock current and its effective values ​​are determined; selection of new equipment based on short circuit current values. As a result, the circuit breaker was tested for thermal and dynamic resistance to short circuit currents; checking the circuit breaker for breaking and closing capacity. Work was carried out to study methods of practical calculation and develop a mathematical model of the electromechanical transient process using the example of calculating short circuits during the modernization of thermal power plants.

The study of the criterion of the marginal and dynamic equilibrium of the riverbed

The article analyzes the results of theoretical and experimental studies on the stability criterion of Rusle from non-cohesive soils, and notes their advantages and disadvantages. A significant influence of the average slope and transport sediment flow on head losses was revealed. An assessment was made of the shape of the channel of the limiting and dynamic equilibrium of the channel laid in easily eroded soils - justified for considering the parameters of molasses. A number of empirical substitutabilities are given A number of empirical substitutabilities are given w0=f(d) and i=f(H⁄d), constructed based on hydrometrological data of Central Asian water basins, which can be used for practical calculation of watercourses. An improved method has been proposed that allows the design of river structures taking into account the criterion of equilibrium of fine sand sediment grains.

CONCENTRATION OF THE UKRAINIAN BANKING SYSTEM: PROBLEMS AND PROSPECTS

The article examines the relevance of the issue of concentration of the banking system of Ukraine and identifies the main prospects for reducing the share of the state in the banking services market. The period from 2009-2022 inclusive was chosen for analysis and evaluation, which made it possible to identify the main trends and factors that influenced the growth and decline of such concentration indices as Herfindahl–Hirschman Index and CR in terms of the following indicators: assets, corporate loans, retail deposits, authorised capital, commission income, and interest income. The obtained calculations helped to determine the level of concentration of the domestic banking system. The purpose of the article is to allocate scientific approaches and carry out practical calculations to determine the degree of concentration of the banking system and to determine the need for its deconcentration. The results of the analysis demonstrate the growing scientific interest of both domestic and foreign economic schools in the problem of concentration in the banking system. However, it is worth noting that the peak of publication activity was observed in 2018-2020, with the top three countries being the United States of America, the United Kingdom, and Malaysia. The results of the calculations showed that the number of banks in Ukraine does not have a significant impact on the level of concentration. With a fairly large number of banks in 2013, namely 180 institutions, there was a sharp increase in concentration, but a larger share of the market was controlled by private capital, but since 2017, a larger share of the banking sector has been owned by the state. The author notes that the concentration of market power by state-owned banks has led to the emergence of a monopoly, but transformational measures to reduce the concentration of the banking system should be carried out taking into account the existing financial and economic feasibility. Of course, there is a risk of ineffective management decisions by bank management, but it is the largest state-owned banks that demonstrate the sustainability and profitability of their activities.

PLASTIC DEFORMATION WITH OPEN STITCHING. STITCHING ON BACKING RING AND HOLLOW STITCHING

A theoretical analysis of the types of firmware on the backing ring and hollow stitching has been carried out. Formulas for practical calculations of these types of firmware are obtained.

How to discriminate wood of CITES-listed tree species from their look-alikes: using an attention mechanism with the ResNet model on an enhanced macroscopic image dataset.

Global illegal trade in timbers is a major cause of the loss of tree species diversity. The Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) has been developed to combat the illegal international timber trade. Its implementation relies on accurate wood identification techniques for field screening. However, meeting the demand for timber field screening at the species level using the traditional wood identification method depending on wood anatomy is complicated, time-consuming, and challenging for enforcement officials who did not major in wood science. This study constructed a CITES-28 macroscopic image dataset, including 9,437 original images of 279 xylarium wood specimens from 14 CITES-listed commonly traded tree species and 14 look-alike species. We evaluated a suitable wood image preprocessing method and developed a highly effective computer vision classification model, SE-ResNet, on the enhanced image dataset. The model incorporated attention mechanism modules [squeeze-and-excitation networks (SENet)] into a convolutional neural network (ResNet) to identify 28 wood species. The results showed that the SE-ResNet model achieved a remarkable 99.65% accuracy. Additionally, image cropping and rotation were proven effective image preprocessing methods for data enhancement. This study also conducted real-world identification using images of new specimens from the timber market to test the model and achieved 82.3% accuracy. This study presents a convolutional neural network model coupled with the SENet module to discriminate CITES-listed species with their look-alikes and investigates a standard guideline for enhancing wood transverse image data, providing a practical computer vision method tool to protect endangered tree species and highlighting its substantial potential for CITES implementation.

INTERDISCIPLINARY APPROACH TO TEACHING GRAPHIC DESIGN FOR FUTURE TEACHERS OF LABOR EDUCATION IN THE CONTEXT OF IT EDUCATION

This article examines the importance of effectively integrating graphic design into computer science education, emphasizing the need for integrative curricula. It is emphasized that such an approach requires taking into account the specifics of both disciplines and contributes to the formation of a comprehensive understanding of the subject, the development of professional competencies, and the training of specialists capable of meeting the requirements of modern society. In the context of the rapid development of digital technologies, the article emphasizes the relevance of the integration of graphic design into IT education. The practical aspects of such integration are considered, including the usage of innovative technical tools, programs, and teaching methods aimed at improving the quality of education.
 Special attention is paid to project-oriented learning, which allows students to implement practical tasks, developing both graphic and computer skills. Examples are given of how students can be involved in the development of websites, mobile applications, and multimedia projects, using knowledge from both fields. Emphasis is also placed on the importance of software tools such as Adobe Photoshop, and Illustrator for graphic design and programming languages and environments for web development, enabling students to acquire the necessary technical skills for their future careers.
 Special attention is paid to the role of integration in qualified teacher training capable of working effectively in a high-tech, information-oriented society. Specific examples of courses and projects that demonstrate the implementation of an interdisciplinary approach in education are provided, as well as recommendations for further improvement of educational programs are developed. The analysis emphasizes the potential and importance of integrated teaching of graphic design and informatics for the training of future teachers, aimed at their professional development and improvement of the educational process in general.

Comprehensive Fatigue Analysis and Practical Design Methodology for Weld Toes in the Sphere of Welded Hollow Spherical Joints in Grid Structures

This paper addresses the issue of fatigue in grid structures, a topic of interest in engineering and academia. The goal is to establish a practical fatigue design calculation method for weld toes in welded hollow spherical joints (WHSJs). The study focuses on commonly used steel tube-WHSJs in grid structures, conducting 25 constant amplitude and four variable amplitude fatigue tests on tube–sphere joints (TSJs) to derive corresponding S-N curves. Using ANSYS, the hot spot stress concentration coefficient Kh at the weld toes in 22 TSJs was calculated, resulting in a numerical solution for Kh ranging from 2.0550 to 4.8600. Based on this, fatigue design methods were established using nominal stress amplitude and hot spot stress amplitude as fundamental parameters. Within a fatigue design reference period of two million cycles, the allowable nominal stress amplitude for TSJs is 22 N/mm2, and the allowable hot spot stress amplitude is 66 N/mm2. The study also conducted macroscopic and microscopic analyses on fatigue fractures of TSJs, revealing that the weld toe in the sphere of TSJs is the primary site for fatigue crack initiation. This research provides practical calculation methods for fatigue design in WHSJ grid structures, contributing to their broader application.

CALCULATION OF POWER TRANSFORMER INDUCTANCE MATRIX

Practical calculations of electric equipment and electric networks are performed using equivalent circuits. Without taking into account saturation phenomena, electromagnetic processes in a power transformer are described by a system of linear equations, which can be represented in matrix form. The transformer inductance matrix contains self and mutual winding inductances, whose values for one phase are determined directly from the passport data containing the results of no-load and short circuit experiments. Mutual inductances between phases depending on the type and size of the magnetic core are not usually given in the transformer documentation. It does not allow to simulate the operating modes that differ from the steady state with uniform phase load.
 
 The purpose of the work is to develop an algorithm for calculating elements of the power transformer inductance matrix according to its passport data and magnetic circuit parameters.
 
 The scientific novelty lies in use of information about magnetic circuit type and size to determine elements of the inductance matrix.
 
 Materials and methods. Methods of linear electric and magnetic circuit theory are used in the work.
 
 Results. The proposed algorithm for calculation of power transformer inductance matrix includes three stages: calculation of self and mutual inductances for one phase; construction of an equivalent circuit for a magnetic circuit and calculation of magnetic fluxes in order to take into account the mutual influence of windings on various phases; assembly of the inductance matrix of three-phase transformer. A method is proposed for constructing the transformer inductance matrix with an arbitrary type of magnetic circuit, phases and windings quantity. The method involves preliminary calculation of the coefficient matrix that characterizes the magnetic circuit and depends mainly on its type and, to a less, on the ratio of geometric dimensions in rods and yokes. The coefficient matrix can be calculated in advance and used to determine the inductance matrix of a wide range of transformers.
 
 Conclusions. 1. The passport data of the transformer do not allow to model transformer operation at unbalanced load validly. 2. An algorithm for determining the inductance matrix of transformers has been developed. 3. A method for compilation of a transformer inductance matrix with an arbitrary type of magnetic circuit, the number of phases and windings is introduced. The practical significance of the algorithm is determined by the simplicity of algorithmizing, as well as by the possibility of using it in computer simulation of electrical circuits with transformers, for example, using the modified nodal analysis method.

Fast evaluation of generalized associated linear equations (GALEs) for nonlinear systems characterization and compensation

Nonlinear Output Frequency Response Functions (NOFRFs), which are a one-dimensional extension of the linear Frequency Response Function (FRF) to nonlinear cases, have been introduced for nonlinear system characterization and compensation. The evaluation of NOFRFs is accomplished by solving a series of linear difference or differential equations, known as Generalized Associated Linear Equations (GALEs). However, the derivation of GALEs often includes numerous recursive and symbolic calculations, posing significant challenges in both practical applications and computer programming. In the present study, a fast-computing algorithm, based on combinatorial calculations as opposed to recursive and symbolic calculations, is proposed for fast evaluation of GALEs. This allows for the evaluation of NOFRFs in a more streamlined and straightforward manner. The applications of the proposed fast-computing algorithm for nonlinear system characterization and compensation are demonstrated through several case studies including a High Power Amplifier (HPA) and a Duffing system. The results of the case studies show the effectiveness of applying the GALEs and NOFRFs for system design and safety control across a wide range of engineering applications.