An Uncertainty-Aware Continual Learning Framework for Fault Diagnosis of Rotating Machinery With Homogeneous-Heterogeneous Faults
Jipu Li, Ke Yue, Zhuyun Chen
et al.
The demand for disruption-free fault diagnosis of mechanical equipment under a constantly changing operation environment poses a great challenge to the deployment of data-driven diagnosis models in practice. Extant continual learning-based diagnosis models suffer from consuming a large number of labeled samples to be trained for adapting to new diagnostic tasks and failing to account for the diagnosis of heterogeneous fault types across different machines. In this paper, we use a representative mechanical equipment - rotating machinery – as an example and develop an uncertainty-aware continual learning framework (UACLF) to provide a unified interface for fault diagnosis of rotating machinery under various dynamic scenarios: class continual scenario, domain continual scenario, and both. The proposed UACLF takes a three-step to tackle fault diagnosis of rotating machinery with homogeneous-heterogeneous faults under dynamic environments. In the first step, an inter-class classification loss function and an intra-class discrimination loss function are devised to extract informative feature representations from the raw vibration signal for fault classification. Next, an uncertainty-aware pseudo labeling mechanism is developed to select unlabeled fault samples that we are able to assign pseudo labels confidently, thus expanding the training samples for faults arising in the new environment. Thirdly, an adaptive prototypical feedback mechanism is used to enhance the decision boundary of fault classification and diminish the model misclassification rate. Experimental results on three datasets suggest that the proposed UACLF outperforms several alternatives in the literature on fault diagnosis of rotating machinery across various working conditions and different machines. Note to Practitioners—This paper presents a continual fault diagnosis methodology for mechanical equipment under various working conditions across different machines with homogeneous-heterogeneous faults. On the application side, the proposed UACLF can be applied to facilitate diagnosis across a broad range of complex industrial equipment, including aerospace, automobile transmission, and wind turbines, among others. With the uncertainty-aware pseudo labeling, the proposed framework is empowered to select the samples in the new phase that we are able to reliably assign their labels. Hence, it can effectively improve mechanical equipment fault classification accuracy in the case that only a small portion of labeled fault samples is available. When training the model, given the model architecture, fault samples collected from multiple accelerometers are fed into the developed model. Four different loss functions, supervision loss, inter-class classification loss, intra-class discrimination loss, and uncertainty estimation loss, are employed to train the diagnostic model. Experiments conducted on three different laboratory datasets have demonstrated the effectiveness of the proposed framework, but have not been tested in the practical industrial applications. We will consider testing the proposed UACLF in an actual plant in future research.
7 sitasi
en
Computer Science
High-Efficiency and Low-Defect Removal Mechanism of Silicon Carbide Using Center-Inlet Computer-Controlled Polishing
Pengli Lei, Baojian Ji, Jing Hou
et al.
Reaction-bonded silicon carbide (RB-SiC) is the preferred material for space optical systems because of its low density and high specific stiffness. However, its hardness and multi-component properties lead to low efficiency and pit defects during the polishing process, making the fabrication of RB-SiC a significant challenge. This study proposes a high-efficiency and low-defect fabrication method for RB-SiC using center-inlet computer-controlled polishing (CCP). We first investigated the polishing efficiency and surface quality achieved with center-inlet and non-center-inlet liquids. The results show that the defect density under non-center-inlet conditions was positively correlated with process parameters, while fewer defects and higher efficiency could be achieved under center-inlet conditions. Additionally, the efficient removal and defect suppression mechanisms under the center-inlet condition were revealed based on machining force, heat, and defect characterization. Under center-inlet conditions, the friction coefficient is larger and stable, resulting in high removal efficiency. The macro–micro coupled analysis results show that pit defects are generated through the combined action of force and heat, which leads to the thermo-mechanical degradation and shedding of SiC particles due to the temperature increase in the machining zone. The results demonstrate that center-inlet CCP not only ensures sufficient abrasion at the polishing interface to achieve high removal efficiency but also significantly suppresses the processing heat, thereby resulting in a low-defect surface.
Mechanical engineering and machinery
A formal theory on problem space as a semantic world model in systems engineering
Mayuranath SureshKumar, Hanumanthrao Kannan
Classic problem-space theory models problem solving as a navigation through a structured space of states, operators, goals, and constraints. Systems Engineering (SE) employs analogous constructs (functional analysis, operational analysis, scenarios, trade studies), yet still lacks a rigorous systems-theoretic representation of the problem space itself. In current practice, reasoning often proceeds directly from stakeholder goals to prescriptive artifacts. This makes foundational assumptions about the operational environment, admissible interactions, and contextual conditions implicit or prematurely embedded in architectures or requirements. This paper addresses that gap by formalizing the problem space as an explicit semantic world model containing theoretical constructs that are defined prior to requirements and solution commitments. These constructs along with the developed axioms, theorems and corollary establish a rigorous criterion for unambiguous boundary semantics, context-dependent interaction traceability to successful stakeholder goal satisfaction, and sufficiency of problem-space specification over which disciplined reasoning can occur independent of solution design. It offers a clear distinction between what is true of the problem domain and what is chosen as a solution. The paper concludes by discussing the significance of the theory on practitioners and provides a dialogue-based hypothetical case study between a stakeholder and an engineer, demonstrating how the theory guides problem framing before designing any prescriptive artifacts.
Enhancing Predictive Maintenance in Industrial Machinery: A Hybrid Approach Combining Vibration Analysis and Computer Vision
Luis A. Ayala, Luis F. Quiroz, Axel Herrera-Cabrera
An Incremental Learning Framework for Mechanical Fault Diagnosis With Bi-Level Multiscale Convolutional Attention
Zhen Jia, Zhenbao Liu, Guoyu Yao
et al.
Fault diagnosis for rotating machinery is important for optimizing productivity and enhancing safety. However, in practical engineering, data-driven methods are not only challenged by the problem of insufficient fault data, but also often cannot achieve continuous learning and online diagnosis of newly emerging fault types in constantly changing operating environments. To address these issues, this article proposed a continuous few-shot incremental learning method based on bi-level multiscale convolutional attention (BMCA) mechanism. First, infrared thermal imaging data are used as input signals, and a variational encoder (VAE) synthesis replay bank is constructed to automatically replenish and retain the most representative samples for relearning. Next, a cross-channel dynamic spatial (CCDS) convolutional attention mechanism is proposed to achieve a dynamic allocation of attention weights in both channel and spatial feature dimensions. Finally, the update scale of the model is constrained by the designed focus-knowledge distillation (FKD) loss function, and the weights of the small samples as well as the loss contribution of the hard-to-categorize samples are dynamically adjusted. The experimental results of bearing data based on infrared thermal imaging show that the diagnostic accuracy of this method can still reach 96.68% under the condition of small samples, and the incremental learning strategy effectively alleviates the negative effects of catastrophic forgetting and insufficient samples.
6 sitasi
en
Computer Science
The application of 3D printing in mechanical manufacturing
Junrui Ma
In modern society, with the continuous development of science and technology, 3D printing technology has become a hot technology in the field of machinery manufacturing. 3D printing can improve production efficiency, and can accurately produce three-dimensional products that can be directly applied to the mechanical parts that need to be manufactured. This article will introduce the basic principles of 3D and its advantages, but also introduce the application of 3D printing, focusing on the application of 3D printing in the construction field using cement-based materials, while printing some key components in the automotive field, fiber composite materials in the aviation field is also a development direction. This article also looks for some obvious problems with 3D printing, especially the performance of 3D printed products, as well as the cost-related issues of 3D printing, for these problems, the paper gives solutions and future directions. 3D printing will have an important position in the future, and will be widely used in the field of mechanical manufacturing and production, which has great significance
Mechanical fault diagnosis of small sample based on frequency-guided multiscale CNN model
Jingya Yang, Limei Yan
The study of advanced rotating machinery fault diagnosis technology is of great significance to improve the safety and reliability of equipment operation. Training samples are difficult to obtain in engineering practice, leading to weak generalization and low diagnostic accuracy of deep learning-based fault diagnosis methods. To solve the problem of insufficient small sample data to support the training of traditional intelligent diagnostic methods, a small sample fault diagnosis method based on frequency-guided multi-scale convolutional neural network (CNN) model is proposed in this paper. The model consists of multi-scale feature extraction (MFE), dual convolution fusion (DCF), frequency guided feature fusion (FGFF) module, and kolmogorov–arnold networks fully connected (KAN-FC) module. The MFE can comprehensively extract original fault signal features even with small sample data; the DCF effectively integrates the attention weight relationships between channels and spatial dimensions; and the FGFF integrates features extracted from multiple branches to build the feature network relationship. Additionally, the KAN is introduced as the fully connected layer of the model, which can better adapt to the differences in small data samples under various working conditions. When the proportion of the small sample training set is 0.3, the G-mean value on the Case Western Reserve University dataset is 99.89%, and the G-mean value on the Paderborn University (PU) dataset is 100%, which is approximately 0.59%–9.69% higher than that of other models. Through comparative verification, it is demonstrated that the proposed model outperforms existing models in small sample fault diagnosis and has strong generalization performance.
The 3D tooth model segmentation method based on GAC+PointMLP network
Jianjun Chen, Liyuan Zheng, Huilai Zou
et al.
Precise segmentation of individual teeth from digital three-dimensional (3D) tooth models is critical in computer-assisted orthodontic surgery. This study explores the application of Point Multi-Layer Perceptron (PointMLP) in processing 3D tooth models and introduces an innovative integration of the Graph Attentional Convolution (GAC) Layer with a graph attention mechanism. By incorporating the GAC Layer into PointMLP, the model can focus on key local regions in the 3D tooth model and dynamically adjust the attention applied to these areas. This enhanced attention mechanism allows the model to better capture subtle surface structures, facilitating the accurate extraction of valuable local features. Compared to other traditional segmentation algorithms, the proposed method shows improvements of 1.1, 2.04, 1.06, 2.2, and 1.8 percentage points in Overall Accuracy (OA), Sensitivity (SEN), Positive Predictive Value (PPV), and Intersection Over Union (IoU), respectively. At the same number of training epochs, our method outperforms both GAC and PointMLP in segmentation performance.
Control engineering systems. Automatic machinery (General), Systems engineering
AI for Requirements Engineering: Industry adoption and Practitioner perspectives
Lekshmi Murali Rani, Richard Berntsson Svensson, Robert Feldt
The integration of AI for Requirements Engineering (RE) presents significant benefits but also poses real challenges. Although RE is fundamental to software engineering, limited research has examined AI adoption in RE. We surveyed 55 software practitioners to map AI usage across four RE phases: Elicitation, Analysis, Specification, and Validation, and four approaches for decision making: human-only decisions, AI validation, Human AI Collaboration (HAIC), and full AI automation. Participants also shared their perceptions, challenges, and opportunities when applying AI for RE tasks. Our data show that 58.2% of respondents already use AI in RE, and 69.1% view its impact as positive or very positive. HAIC dominates practice, accounting for 54.4% of all RE techniques, while full AI automation remains minimal at 5.4%. Passive AI validation (4.4 to 6.2%) lags even further behind, indicating that practitioners value AI's active support over passive oversight. These findings suggest that AI is most effective when positioned as a collaborative partner rather than a replacement for human expertise. It also highlights the need for RE-specific HAIC frameworks along with robust and responsible AI governance as AI adoption in RE grows.
Teaching Empirical Research Methods in Software Engineering: An Editorial Introduction
Daniel Mendez, Paris Avgeriou, Marcos Kalinowski
et al.
Empirical Software Engineering has received much attention in recent years and became a de-facto standard for scientific practice in Software Engineering. However, while extensive guidelines are nowadays available for designing, conducting, reporting, and reviewing empirical studies, similar attention has not yet been paid to teaching empirical software engineering. Closing this gap is the scope of this edited book. In the following editorial introduction, we, the editors, set the foundation by laying out the larger context of the discipline for a positioning of the remainder of this book.
GLUE: Generative Latent Unification of Expertise-Informed Engineering Models
Tim Aebersold, Soheyl Massoudi, Mark D. Fuge
Engineering complex systems (aircraft, buildings, vehicles) requires accounting for geometric and performance couplings across subsystems. As generative models proliferate for specialized domains (wings, structures, engines), a key research gap is how to coordinate frozen, pre-trained submodels to generate full-system designs that are feasible, diverse, and high-performing. We introduce Generative Latent Unification of Expertise-Informed Engineering Models (GLUE), which orchestrates pre-trained, frozen subsystem generators while enforcing system-level feasibility, optimality, and diversity. We propose and benchmark (i) data-driven GLUE models trained on pre-generated system-level designs and (ii) a data-free GLUE model trained online on a differentiable geometry layer. On a UAV design problem with five coupling constraints, we find that data-driven approaches yield diverse, high-performing designs but require large datasets to satisfy constraints reliably. The data-free approach is competitive with Bayesian optimization and gradient-based optimization in performance and feasibility while training a full generative model in only 10 min on a RTX 4090 GPU, requiring more than two orders of magnitude fewer geometry evaluations and FLOPs than the data-driven method. Ablations focused on data-free training show that subsystem output continuity affects coordination, and equality constraints can trigger mode collapse unless mitigated. By integrating unmodified, domain-informed submodels into a modular generative workflow, this work provides a viable path for scaling generative design to complex, real-world engineering systems.
An Exploratory Study on the Engineering of Security Features
Kevin Hermann, Sven Peldszus, Jan-Philipp Steghöfer
et al.
Software security is of utmost importance for most software systems. Developers must systematically select, plan, design, implement, and especially, maintain and evolve security features -- functionalities to mitigate attacks or protect personal data such as cryptography or access control -- to ensure the security of their software. Although security features are usually available in libraries, integrating security features requires writing and maintaining additional security-critical code. While there have been studies on the use of such libraries, surprisingly little is known about how developers engineer security features, how they select what security features to implement and which ones may require custom implementation, and the implications for maintenance. As a result, we currently rely on assumptions that are largely based on common sense or individual examples. However, to provide them with effective solutions, researchers need hard empirical data to understand what practitioners need and how they view security -- data that we currently lack. To fill this gap, we contribute an exploratory study with 26 knowledgeable industrial participants. We study how security features of software systems are selected and engineered in practice, what their code-level characteristics are, and what challenges practitioners face. Based on the empirical data gathered, we provide insights into engineering practices and validate four common assumptions.
Mechanical Vibration on Rotor Balancing
T. P
This project investigates the principles, methodologies, and practical applications of rotor balancing, with a specific focus on the impact of unbalanced forces that lead to mechanical vibrations in rotating systems. Rotor balancing is a fundamental process in the operation and maintenance of machinery and rotating equipment. It plays a critical role in ensuring smooth operation by minimizing the vibrations caused by uneven mass distribution during rotation. Unbalanced rotors, if left uncorrected, can result in a wide range of issues such as excessive wear and tear, increased operational noise, premature mechanical failure, and significant energy losses. In mechanical systems, rotors are vital components found in numerous machines including electric motors, centrifugal pumps, turbines, compressors, and generators. Any imbalance in these rotating elements can disrupt operational stability, affect product quality in manufacturing systems, and even pose safety hazards in industrial environments. This project emphasizes the importance of early detection and precise correction of rotor imbalances as a key factor in preventive maintenance programs. The study covers the foundational concepts of vibration theory, providing an in-depth understanding of the sources, types, and effects of rotor imbalance. Imbalances are generally categorized as static (single-plane imbalance), dynamic (multi-plane imbalance), or a combination of both. The project further explores the science behind the forces generated by these imbalances and how they affect machinery behavior under operational loads. Various methods and techniques of rotor balancing are examined, including both static and dynamic balancing procedures. The project discusses traditional as well as modern balancing techniques, highlighting the role of advanced diagnostic instruments such as vibration analyzers, accelerometers, and balancing machines. The procedures for field balancing and shop balancing are also compared, offering insight into the most effective practices depending on the operational context. The overall objective of this project is to provide a comprehensive and practical understanding of rotor dynamics and the influence of vibration on the performance, efficiency, and longevity of machinery. By adopting effective rotor balancing techniques, industries can reduce unplanned downtime, enhance system performance, lower maintenance costs, and increase the overall reliability and safety of their equipment. The outcomes and findings of this study are intended to serve as a technical guide for engineers, maintenance personnel, and technicians working in sectors such as manufacturing, power generation, aviation, and mechanical services, where rotor balancing is essential. Ensuring proper rotor balance not only extends equipment life but also contributes to sustainable engineering practices through optimized energy usage and reduced mechanical failures. Key Words: Rotor Balancing, Vibration Analysis, Static Balancing, Dynamic Balancing, Rotor Dynamics, Unbalanced Forces, Machinery Maintenance
A Brief Analysis of Electromagnetic Principles in Mechanical Design
Rui Yin
Mechanical design is a crucial branch of engineering technology that focuses on the conception, development, and optimization of mechanical systems. This field encompasses a wide range of activities, from the initial design ideas to the final implementation of complex machinery. One of the innovative aspects of mechanical design is the application of electromagnetic phenomena, which offers valuable insights and references for improving various mechanical systems. This paper utilizes a literature review approach to delve into the application of electromagnetic principles within mechanical design. It explains the fundamental concepts of these principles and assesses their significant roles, particularly in areas such as electromagnetic drive, electromagnetic braking, and electromagnetic induction. By presenting practical examples, the paper highlights the importance and vast potential of integrating electromagnetic principles into modern mechanical design. Ultimately, this study aims to foster technological advancements in mechanical design, streamline the design process, and effectively solve real-world engineering challenges
A review: the application of generative adversarial network for mechanical fault diagnosis
Weiqing Liao, Ke Yang, Wenlong Fu
et al.
Mechanical fault diagnosis is crucial for ensuring the normal operation of mechanical equipment. With the rapid development of deep learning technology, the methods based on big data-driven provide a new perspective for the fault diagnosis of machinery. However, mechanical equipment operates in the normal condition most of the time, resulting in the collected data being imbalanced, which affects the performance of mechanical fault diagnosis. As a new approach for generating data, generative adversarial network (GAN) can effectively address the issues of limited data and imbalanced data in practical engineering applications. This paper provides a comprehensive review of GAN for mechanical fault diagnosis. Firstly, the development of GAN-based mechanical fault diagnosis, the basic theory of GAN and various GAN variants (GANs) are briefly introduced. Subsequently, GANs are summarized and categorized from the perspective of labels and models, and the corresponding applications are outlined. Lastly, the limitations of current research, future challenges, future trends and selecting the GAN in the practical application are discussed.
Harnessing Bayesian Deep Learning to Tackle Unseen and Uncertain Scenarios in Diagnosis of Machinery Systems
Zhou Kai, Qianyu Zhou, Jiong Tang
Direct inverse analysis of faults in machinery systems such as gears using first principle is intrinsically difficult, owing to the multiple time- and length-scales involved in vibration modeling. As such, data-driven approaches have been the mainstream whereas supervised trainings are deemed effective. Nevertheless, existing techniques often fall short in their ability to generalize from discrete data labels to the continuous spectrum of possible faults which is further compounded by various uncertainties. This research proposes an interpretability-enhanced deep learning framework that incorporates Bayesian principles, effectively transforming convolutional neural networks into dynamic predictive models and significantly amplifying their generalizability with more accessible insights of the model's reasoning processes. Our approach is distinguished by a novel implementation of Bayesian inference, enabling the navigation of the probabilistic nuances of gear fault severities. By integrating variational inference into the deep learning architecture, we present a methodology that excels in leveraging limited data labels to reveal insights into both observed and unobserved fault conditions. This approach improves the model's capacity for uncertainty estimation and probabilistic generalization. Experimental validation on a lab-scale gear setup demonstrated the framework's superior performance, achieving nearly 100% accuracy in classifying known fault conditions, even in the presence of significant noise, and maintaining 96.15% accuracy when dealing with unseen fault severities. These results underscore the method's capability in discovering implicit relations between known and unseen faults, facilitating extended fault diagnosis, and effectively managing large degrees of measurement uncertainties.
Research on Fault Prediction and Health Management System of Railway Tunnel Drilling and Blasting Construction Machinery Based on Machine Learning
Jinshuo Zhang
: During the construction of railway tunnel by drilling and blasting method, the machinery and equipment run in the harsh environment of high load, high dust and high humidity for a long time, and the equipment fails frequently, which seriously affects the construction progress and safety. Traditional methods of periodic maintenance and passive fault repair have been difficult to meet the needs of modern tunnel engineering. This paper presents a machine learning method to predict and manage the fault of railway tunnel construction machinery and equipment by drilling and blasting method. The system collects equipment operation data in real time through sensors, preprocesses it by means of data cleaning, feature extraction, etc., and performs fault prediction and health status assessment through decision tree and other machine learning algorithms. This paper describes the system architecture design, data processing flow, model selection and training methods. The system can predict potential mechanical failures in advance, reduce unplanned downtime, and improve equipment reliability and overall efficiency of tunnel construction. The fault prediction system aided by machine learning can not only reduce the failure rate of equipment, but also provide accurate health assessment and early warning mechanism, which has a wide range of engineering applications.
Model for dimensioning borehole heat exchanger applied to mixed-integer-linear-problem (MILP) energy system optimization
Tobias Blanke, Holger Born, Bernd Döring
et al.
Abstract This paper introduces three novel approaches to size geothermal energy piles in a MILP, offering fresh perspectives and potential solutions. The research overlooks MILP models that incorporate the sizing of a geothermal borefield. Therefore, this paper presents a new model utilizing a g-function model to regulate the power limits. Geothermal energy is an essential renewable source, particularly for heating and cooling. Complex energy systems, with their diverse sources of heating and cooling and intricate interactions, are crucial for a climate-neutral energy system. This work significantly contributes to the integration of geothermal energy as a vital energy source into the modelling of such complex systems. Borehole heat exchangers help generate heat in low-temperature energy systems. However, optimizing these exchangers using mixed-integer-linear programming (MILP), which only allows for linear equations, is complex. The current research only uses R-C, reservoir, or g-function models for pre-sized borefields. As a result, borehole heat exchangers are often represented by linear factors such as 50 W/m for extraction or injection limits. A breakthrough in the accuracy of borehole heat exchanger sizing has been achieved with the development of a new model, which has been rigorously compared to two simpler models. The geothermal system was configured for three energy systems with varying ground and bore field parameters. The results were then compared with existing geothermal system tools. The new model provides more accurate depth sizing with an error of less than 5 % compared to simpler models with an error higher than 50 %, although it requires more calculation time. The new model can lead to more accurate borefield sizing in MILP applications to optimize energy systems. This new model is especially beneficial for large-scale projects that are highly dependent on borefield size.
Renewable energy sources, Geology
Investigation of Liquid Collagen Ink for Three-Dimensional Printing
Colten L. Snider, Chris J. Glover, David A. Grant
et al.
Three-dimensional printing provides more versatility in the fabrication of scaffold materials for hard and soft tissue replacement, but a critical component is the ink. The ink solution should be biocompatible, stable, and able to maintain scaffold shape, size, and function once printed. This paper describes the development of a collagen ink that remains in a liquid pre-fibrillized state prior to printing. The liquid stability occurs due to the incorporation of ethylenediaminetetraacetic acid (EDTA) during dialysis of the collagen. Collagen inks were 3D-printed using two different printers. The resulting scaffolds were further processed using two different chemical crosslinkers, 1-Ethyl-3-[3-dimethylaminopropyl]carbodiimide hydrochloride)/N-hydroxysuccinimide (EDC/NHS) and genipin; gold nanoparticles were conjugated to the scaffolds. The 3D-printed scaffolds were characterized to determine their extrudability, stability, amount of AuNP conjugated, and overall biocompatibility via cell culture studies using fibroblast cells and stroma cells. The results demonstrated that the liquid collagen ink was amendable to 3D printing and was able to maintain its 3D shape. The scaffolds could be conjugated with gold nanoparticles and demonstrated enhanced biocompatibility. It was concluded that the liquid collagen ink is a good candidate material for the 3D printing of tissue scaffolds.
Mechanical engineering and machinery
Development of the Theoretical Approach Based on Matrix Theory for Analyzing the State of Information Security Systems
Bobok I.I., Kobozeva A.A.
. The widespread introduction of information technologies into all spheres of society, the crea-tion of a significant amount of confidential and critical data in digital form leads to an increase in the priority of information security tasks everywhere, including in the energy sector, which relates to the critical infrastructure of any state. The purpose of the work is to develop the men-tioned approach to ensure the possibility of increasing the efficiency of information security methods based on it. The goal was achieved through a detailed study of disturbances in the val-ues of formal parameters that uniquely determine the matrix that is assigned to the information security system under conditions of active attacks (disturbances) on the system. Singular num-bers and singular vectors of the matrix are considered as such parameters. The most important result of the work is the substantiation of the existence and establishment of interconnected re-gions of stabilization of disturbances of singular numbers and singular vectors of the system ma-trix, while the region of stabilization of singular numbers corresponds to the region of monoto-nous decrease in their disturbances with increasing numbers, while the stabilization of singular vectors corresponds to the region in which their disturbances are comparable with 90 degrees. It is shown that the stabilization process is determined by the mathematical properties of the pa-rameters under consideration. The significance of the obtained result lies in the possibility of using it to improve various information security systems that were built or studied using a gen-eral approach to analyzing their state, both theoretically and practically. The work provides ex-amples of such use.
Electrical engineering. Electronics. Nuclear engineering, Production of electric energy or power. Powerplants. Central stations