Modeling Of Complex Objects Research Articles

Masked contrastive graph representation learning for age estimation

Age estimation of face images is a crucial task with various practical applications in areas such as video surveillance and Internet access control. While deep learning-based age estimation methods like Convolutional Neural Networks (CNN), Multilayer Perceptrons (MLP), and Transformers have shown remarkable performance, they have limitations when modeling complex or irregular objects, and often contain redundant information. Although existing graph neural networks (GNNs) can alleviate this issue, they only considers the structural information of the image and ignores the semantic features, thus the feature representation capability of graph nodes is limited. To address these issues, this paper proposes a novel Masked Contrastive Graph Representation Learning (MCGRL) method for accurate age estimation of face images. Our approach leverages CNN to extract semantic features of the image, which are then partitioned into patches that serve as nodes in the graph. We use a masked graph convolutional network (GCN) to derive image-based node representations that capture rich structural information. Finally, we incorporate multiple losses to explore the complementary relationship between structural information and semantic features, which improves the feature representation capability of GCN. Experimental results on real-world face image datasets demonstrate the superiority of our proposed method over other state-of-the-art age estimation approaches. Our code is available at https://github.com/yuntaoshou/MCGRL

Thermal response function method: A method for predicting the transient surface temperature of black-box objects

In engineering practice, thermal analysis of objects with unknown internal structure and/or thermophysical properties, and uncertainties in contact thermal resistances, is very challenging and even impossible using the traditional approach of direct solving the heat transfer equation. In this work, a thermal response function method (TRFM) is proposed for predicting the transient surface temperature of ‘black-box’ objects (i.e., unknown internal structure and thermophysical properties). The method relies on an introduced measurable quantity called thermal response function, which characterizes the thermal response characteristics of an object. Using the measured thermal response functions as input parameters, the transient temperature distribution on the surface of a black-box object under arbitrary external heat flux boundary condition can be predicted through linear superposition. Proof-of-concept simulations and experiments are conducted to demonstrate the feasibility and effectiveness of the TRFM method. The predicted surface temperature distribution under various external heat fluxes using TRFM agree well with the reference results. The results show that the TRFM is very promising as a solution of the challenging problem of predicting the transient surface temperature of black-box objects, with potential application for thermal imaging modeling of complex objects.

Математическое моделирование мягкого экзоскелета из магнитно-реологических модулей с интеллектуальным управлением

The article considers a fundamentally new generation of soft exoskeletons based on magnetic rheological modules. A model of an exoskeleton link with adjustable rigidity is proposed, for which a system of differential equations of motion is compiled. A model of an exoskeleton for human lower extremities, composed of modules with magnetic rheological fluid, has been developed. The problems of kinematics and dynamics that arise when controlling the movement of an exoskeleton are presented. A block diagram of an algorithm for controlling the movement of an exoskeleton has been developed, solving control problems taking into account neural network methods. A qualitative study by analytical methods of the proposed mathematical model of an exoskeleton with links with adjustable stiffness is carried out. The use of regulation of the rigidity of the links of the exoskeleton modules in the necessary way will make it possible to create devices that are comfortable for the user, both from the physiological and psychological points of view. Soft exoskeletons will be in demand in many industries and medicine. The use of electromagnetic actuators, which, as a rule, have smaller dimensions and energy consumption, an almost instantaneous response speed in comparison with pneumatic drives, hydraulic drives and electric drives, is promising and technically, energetically, environmentally, economically more acceptable. Under the action of electric or magnetic fields, the stiffness of electroelastic and magneto-rheological materials can change by more than an order of magnitude. This makes it possible to create exoskeleton links with adjustable stiffness. Regulation of the rigidity of the elements of the exoskeleton modules in real time is a complex control task. Therefore, exoskeleton motion control requires the development of adaptive type algorithms based on a neuro-fuzzy approach, using information received from feedback. Neural network algorithms for self-learning in the process of functioning are a logically expedient part of a soft bionic exoskeleton. Also, as a necessary component of the exoskeleton, along with the actuator part, a sensor system is needed with sensitive sensors for the user’s neuromuscular impulses and various sensors for position, speed, acceleration, force, moment of force of the exoskeleton. A comprehensive study of scientific and technical problems of the functioning of the model of the magnetic-rheological medium, exoskeleton modules and their compilation into a single multi-link structure, its movement using the technology of modern mathematical modeling was carried out. The construction of neuro-fuzzy control systems for soft exoskeletons is described as part of the development of new mathematical methods for modeling complex technical objects using modern mechatronics and cyborgics.

Acceleration of computations in modelling of processes in complex objects and systems

The development of methods of parallelization of computing processes, which involve the decomposition of the computational domain, is an urgent task in the modeling of complex objects and systems. Complex objects and systems can contain a large number of elements and interactions. Decomposition allows you to break down a system into simpler subsystems, which simplifies the analysis and management of complexity. By dividing the calculation area of the part, it is possible to perform parallel calculations, which increases the efficiency of calculations and reduces simulation time. Domain decomposition makes it easy to scale the model to work with larger or more detailed systems. With the right choice of decomposition methods, the accuracy of the simulation can be improved, since different parts of the system may have different levels of detail and require appropriate methods of additional analysis. Decomposition allows the simulation to be distributed between different participants or devices, which is relevant for distributed systems or collaborative work on a project. In this work, mathematical models are built, which consist in the construction of iterative procedures for "stitching" several areas into a single whole. The models provide for different complexity of calculation domains, which makes it possible to perform different decomposition approaches, in particular, both overlapping and non-overlapping domain decomposition. The obtained mathematical models of subject domain decomposition can be applied to objects and systems that have different geometric complexity. Domain decomposition models that do not use overlap contain different iterative methods of "stitching" on a common boundary depending on the types of boundary conditions (a condition of the first kind is a Dirichlet condition, or a condition of the second year is a Neumann condition), and domain decomposition models with an overlap of two or more areas consist of the minimization problem for constructing the iterative condition of "stitching" areas. It should be noted that the obtained models will work effectively on all applied tasks that describe the dynamic behavior of objects and their systems, but the high degree of efficiency of one model may be lower than the corresponding the degree of effectiveness of another model, since each task is individual. Keywords: mathematical modelling, decomposition of the computational domain, parallelization, optimization, complex objects and systems.

Random Sampling Method of Large-Scale Graph Data Classification

Graph data appears in broad real-world applications in modelling complex objects in big data. Effective analysis of graph data provides a deeper understanding of the data in data mining tasks, including classification, clustering, prediction, and recommendation systems. Mining a large number of graphs becomes a challenging task because state-of-the-art methods are not scalable due to the memory limit. To address this issue, we propose a novel approximate random sampling method for large-scale graph data classification. In this approach, we applied a representation method to encode each graph as a record of a vector string and a set of graphs as a set of N records in a file. Then, we partition the set of records into disjoint subsets of data blocks, making each data block a random sample of the data file. After that, we randomly select a subset of data blocks, each being a random sample of the graph dataset, and compute the different graph property distributions. Since the data blocks in this model are much smaller than the entire data set, it is more efficient to analyze them on a standalone small machine, and multiple data blocks can be analyzed on multiple nodes of the cluster in parallel. Finally, we classified the graphs of data blocks using the SVM algorithm. In experimental evaluation, our proposed method outperformed state-of-the-art graph kernels on graph classification datasets in terms of accuracy.

Features of learning three-dimensional modeling and visualization in Autodesk 3Ds Max

The article describes the trends in the development of three-dimensional modeling in the modern world. The main areas of human activity that actively use the possibilities of three-dimensional graphics are indicated. An analysis of the latest research on this topic in the field of architectural design has been carried out. The main advantages of computer design in Autodesk 3Ds Max are identified and argued. One of the main directions in computer design is architectural visualization, which includes both the creation of a 3D model and obtaining the final realistic image of the object. Autodesk 3Ds Max is the most versatile software product that allows architects to actively use the available wide range of tools and functions of the program when creating realistic visualization of architectural and design projects. The main stages of studying the 3Ds Max program are defined, which allow to simplify and speed up the educational and working process of modeling and visualization of architectural projects. Given the wide range of tools and functions, 3Ds Max requires a special approach to learning it. Learning three-dimensional graphics based on Autodesk 3Ds Max should include familiarization with the program interface, study of basic modeling techniques, practical exercises for modeling simple and complex objects, and work on creating a model and visualization of an architectural or design project. Mastering all these components allows the user to understand the principles of working with three-dimensional graphics, optimize and speed up the work process of creating an architectural visualization according to a specific design. Three-dimensional modeling and visualization is a promising direction of modern computer design. Optimizing the learning and workflow of visualization will help create high-quality and highly realistic images of architecture and design, as well as better develop the field of architecture as a whole.

FAILURE MODEL OF NON-RESTORABLE COMPLEX TECHNICAL OBJECT OF MILITARY EQUIPMENT

Maintenance (MT) is a necessary component the process of operating a complex technical object of military equipment, intended for long-term operation in wartime and harsh operating conditions. The volume, content and timing of maintenance must be completely determined by the reliability properties of the object, conditions and modes of its use. Effective implementation of any maintenance operation is possible only if the design of the object provides special means for this purpose (for measuring the defining parameters) and ensures the accessibility and convenience of performing the operation. Complex technical objects in modern society are extremely important. Such objects belong to the class of restored objects long-term repeated use. They are usually expensive and require significant operating costs. To ensure the required level of failure-free operation during their operation, maintenance is usually carried out, the essence of which is the timely preventive replacement of elements that are in a pre-failure state, which is very important for military equipment. A characteristic feature of complex technical objects for special purposes (military equipment) is the presence in their composition of a large number (tens, hundreds of thousands) different types of components that have different levels of reliability, different patterns of their wear and aging processes. This feature requires a more subtle approach to organizing and planning maintenance during operation (of military equipment). The above statements fully justify the conclusion about need to determine the main characteristics of the maintenance system in early stages of its design, when it is still possible to make changes to design of the object. In this work, a model of failure-free operation non-repairable complex technical object of military equipment is developed. The work also confirms the general idea that data obtained fully confirm the assumption that a maintenance strategy that is not restored is more preferable in the case of unreliable (inaccurate) information about the reliability indicators of elements of a military equipment object.

РАЗВИТИЕ ИНСТРУМЕНТОВ ОЦЕНКИ РЕЗЕРВОВ ПРОПУСКНОЙ СПОСОБНОСТИ ЖЕЛЕЗНОДОРОЖНЫХ УЧАСТКОВ НА БАЗЕ СОЗДАНИЯ ЦИФРОВОГО ДВОЙНИКА И ПРИМЕНЕНИЯ ИСКУССТВЕННОЙ НЕЙРОННОЙ СЕТИ

The article proposes the development of artificial intelligence technologies and the development of specialized research tools for ways to enhance the capacity of the direction based on the creation of a digital twin of a real railway section of the North Caucasus Railway with heavy freight and passenger traffic in the direction of the ports of the Azov-Black Sea basin and resorts in Southern Russia. The task of intelligent (neural network) control of the transportation process is actualized, the problems of modeling complex objects are disclosed and the subtasks of conducting an experiment on the choice of control actions for operational capacity increase on a railway section are formed.

System Principles of Innovative Development Management of the Region

Further development of the clarification of the objectives of the construction and use of system mathematical models in the formation and implementation of programs of innovative development of regions was achieved: clarification of how the conceptual apparatus is used (conducting a study of the semantics of the concept of innovative development and its components); problem analysis of innovative development of regions (complex analysis of the institutional environment of functioning); conducting economic-mathematical system analysis (taking into account the relationship between subsystems from the point of view of integrity); system modeling (evaluation of goals and means - resources); assessment of risks and determination of measures for their elimination or smoothing (continuous control and analysis of implementation and, if necessary, taking appropriate measures); application of a system of criteria for evaluating the effectiveness of management of innovative development at both the macro and meso levels with the possibility of timely adaptation to the economic situation (development and use of an innovative lever in the form of resource multipliers and their evaluation, based on the systemic interaction of all resources). The analysis of approaches in the management of innovative development of the country and its regions, in the form in which they are used at present, allows us to conclude that they are insufficiently effective for the implementation of measures proposed by state programs. A fundamentally new approach and concept is needed for the processes of forming and implementing programs, as well as for the very development of strategic program documents, necessary changes in management, initially focused on performance, with the help of clearly, mathematically based, formulated tasks, goals and management criteria. The system of managing the innovative development of the region should ensure the formation of optimal programs of regional development, which will allow for their preliminary assessment, analysis, tracking of possible scenarios of development of events and trends during implementation, correction of previously formed programs, using the capabilities of modern technologies. The study of the peculiarities of the development of regions in terms of innovative activity requires, first of all, a systematic study of the semantics of the concept of innovative development and its components. system modeling of complex objects takes into account all existing direct, reverse, cross connections, while management is implemented using information and communication processes and connections of the circuit covering all other circuits. "Management of regional development, in particular, innovative development", implies the existence of management objects and subjects, the developed model also includes management of the formation of operating conditions. Until now, system modeling is widely used in solving management tasks as a methodological approach for formalizing management goals and criteria, researching the mechanisms of functioning of system objects.

Application of the Finite Element Method in Modeling Biological Systems in Traumatology and Orthopedics

Surgical treatment of fractures of the proximal femur is a problem due to the lack of a uniform treatment strategy. Of particular importance is the analysis of the processes occurring in bone tissue during the healing of fractures under dynamic conditions, especially the analysis of mechanical stresses. The finite element method is an effective method for mathematical modeling of complex objects and describing the stress-strain states of these objects. In order to improve the results of treatment of fractures of the proximal femur and pelvic bones, mathematical modeling was carried out using the finite element method of a pertrochanteric femur fracture under conditions of fixation with a dynamic pin and a pelvic fracture under various conditions of its submersible fixation

Transformation of Mathematical Model for Complex Object in Form of Interval Difference Equations to a Differential Equation

Mathematical models of complex objects in the form of interval difference equations are built on the basis of the obtained experimental interval data within the limits of the inductive approach. At the same time, interpretation of physical properties of the object on the base of such model is complex enough. A method of transformation of a mathematical model in the form of interval differential equations was proposed in the article. The proposed method is based on the formulas for representing the values of the function at the node of the difference grid in the Taylor series in the neighborhood of the base node, as well as the differential representation of the derivatives in the same neighborhood. The developed approach creates opportunities for the identification of interval models of complex objects based on the analysis of interval data with further interpretation of the physical properties of the modeled object according to the classical scheme.

Visualization of multidimensional areas of solutions to mathematical models of complex objects

The visualization of mathematical models of multidimensional objects implicitly defined as surfaces F (X) = 0 is performed using two- and three-dimensional projections obtained by rotating and shifting coordinates. In the new coordinates, the model has the form y = f(x) where one of the variables is dependent (this is the direction of design), and the rest make up the vector of independent variables. A new model is often more convenient than the original one, but not all design directions adequately reflect its properties since it is possible to transfer projections of several points of the original surface into one (gluing). For some directions (directions of ambiguity), the projection may consist of points with several preimages (corresponding to the ambiguity of the function f). In this case, the projection is divided into the area of ambiguity and the area of unambiguity. For other directions (directions of uniqueness), the entire projection is the domain of uniqueness. The paper investigates the evolution of design directions and areas of ambiguity and unambiguity in projections of complex objects. A criterion for choosing the direction of unambiguity is proposed in which all points of the model remain different, i.e., multiplicity visually disappears (“hidden multiplicity”). Examples of applying the criterion to models of objects of various geometries are given.

Visualization of multidimensional areas of solutions to mathematical models of complex objects

Visualization of mathematical models of multidimensional objects implicitly defined as a surface F (X) = 0 is performed using two- and three-dimensional projections obtained by rotating and shifting coordinates. In the new coordinates, the model has the form y = f(x) where one of the variables is dependent (this is the direction of design), and the rest make up the vector of independent variables. A new model is often more convenient than the original one, but not all design directions adequately reflect its properties since it is possible to transfer projections of several points of the original surface into one (gluing). For some directions (directions of ambiguity), the projection may consist of points with several preimages (corresponds to the ambiguity of the function f). In this case, the projection is divided into the area of ambiguity and the area of unambiguity. For other directions (directions of uniqueness), the entire projection is the domain of uniqueness. The paper investigates the evolution of design directions and areas of ambiguity and unambiguity of projections of complex objects. A criterion for choosing the direction of unambiguity is proposed in which all points of the model remain different, i.e., multiplicity visually disappears (“hidden multiplicity”). Examples of applying the criterion for models of objects of various geometries are given.

НЕЧІТКІ МНОЖИНИ ТИПУ-2 В ЗАДАЧАХ МОДЕЛЮВАННЯ ТА ОЦІНЮВАННЯ СТАНІВ КРИТИЧНИХ СИСТЕМ З НЕДОВИЗНАЧЕНИМИ ВХІДНИМИ ДАНИМИ ТА ВИКОРИСТАННЯМ ЕКСПЕРТІВ

A method of type-2 fuzzy sets implementation for critical systems’ modeling and state assessment tasks with uncertain input data is proposed. It is shown that the basis for solving the modeling task is designing of a fuzzy logic system with interval membership functions of type-2. The paper presents the task of further developing the process of estimating the interval output of a fuzzy system with experts involvement. An approach based on fuzzy sets is proposed for solving the task of critical systems’ modeling and states assessment. Using the example of energy grid systems, where a high degree of uncertainty is present, it is shown that the main factors that influence the appearance of uncertainty in the initial data set of such systems are caused by the lack of sufficient information in the open print and the high variability of threats under the influence of the growing pace of digitalization of business processes. An analysis of expert evaluations of the interval output of fuzzy systems based on examples of modeling complex objects in various fields of application is given. The first example demonstrates the results of modeling in the field of natural sciences with uncertain initial data for assessing the prospects of an artesian well, where the final assessment is made by an expert. The second example demonstrates the implementation of the interval fuzzy model in the task of social orientation, where the problem of recruiting personnel in social groups from the point of view of professional suitability is modeled. The third task refers to modeling in the field of medical diagnosis of diseases of the endocrine system. Evaluation by experts of the results of interval fuzzy modeling in this field makes it possible to determine the state of a person's disease for endocrine pathology and prescribe timely treatment. The given examples of evaluating the interval output of a fuzzy system, taking into account the opinion of experts, confirm the possibilities for making decisions that are adequate for the subject area in the conditions of uncertain input data. Prospects for the application of the proposed models for the problems of cyber security of critical systems are given.

Problems of constructing logical-linguistic models of complex management dynamic objects

Objective. The aim of the study is to solve the problems of constructing logicallinguistic (fuzzy) models for controlling the trajectory movement of complex dynamic objects.Method. To build logical-linguistic (fuzzy) control models, theories of fuzzy sets and algorithms of L. Zadeh were used.Result. The process of constructing logical-linguistic (fuzzy) models for controlling the trajectory movement of complex dynamic objects using the theory of fuzzy sets and fuzzy algorithms is given. A marine mobile object (MMO) operating in an uncertain environment was used as a control object in the work. It is shown that logical-linguistic (fuzzy) MPO control models can be built taking into account the rich practical experience of a navigator who does not have special knowledge, expressed by them in a qualitative form for building fuzzy control models.Conclusion. Logicallinguistic control models make it possible to ensure the movement of a marine moving object along a given trajectory with a quality of the controlled process sufficient for practical purposes under conditions of various external disturbances and drift of the parameters of the controlled object. The use of fuzzy control algorithms can significantly reduce the cost of computer time compared to the optimal search algorithm with an acceptable deterioration in the quality of the process and ensure the implementation of the control process in real time.

WORLD AND DOMESTIC EXPERIENCE IN THE FIELD OF BUILDING INFORMATION MODELING

New approaches to engineering activities in the field of construction require intensive development of information modeling technologies, which are based on models of individual or complex objects with the principles of 3D-modeling, parameterization and automatic creation of documentation for their full life cycle. In a large number of Western countries information modeling technologies has become an integral part of the engineering design process so far, while in the CIS countries in general, and in the Republic of Belarus in particular, there is a noticeable lag in this area. At the same time, one of the main reasons for this tendency in the Republic of Belarus is the lack of national standards for information modeling. Nevertheless, in recent years these technologies has attracting increasing interest in industry and government support, and therefore the use of experience in the field of information design regulation and the application of BIM technologies in the construction industry for the development of national standards is an important and promising area of research. This article discusses the regulatory documents in the field of BIM design developed by the leading countries in this area, the main trends in the development of the national BIM standard, as well as possible scenarios for the information modeling introduction in the construction industry of the Republic of Belarus.

ОНТОЛОГІЯ ЯК ПРОГРАМНА НАДБУДОВА ДО СИСТЕМИ ДЛЯ МАТЕМАТИЧНОГО МОДЕЛЮВАННЯ НА ОСНОВІ ІНТЕРВАЛЬНИХ ДАНИХ

The article considers an important scientific problem of developing methods and means of constructing discrete models of complex objects in the form of interval difference equations based on a combination of ontological approach and analysis of interval data to expand the scope and conditions of application of models. impetus for the development of applied research in the fields of national defense, environmental protection, medicine and other areas, where the necessary component of the decision support system are mathematical models of objects with distributed parameters. The essence of the approach to mathematical modeling based on interval analysis is characterized, the main feature of which is the multiple estimation of the parameters of the input-output model, built on the results of experiments in which the output variables are obtained in interval form. The main research results presented in the article are: description of the approach to the use of mathematical modeling ontology based on interval data for software development and use, in order to expand the scope and conditions of application of models while ensuring its given prognostic properties; a step-by-step scheme of the process of developing an onto-controlled software system of mathematical modeling based on interval analysis is proposed; the scheme of the process of realization, use and updating of the considered ontological model of the subject area of mathematical modeling on the basis of interval data is offered. The peculiarity of the approaches proposed in this article is that they can be implemented as a software add-on to applied systems of mathematical modeling based on interval analysis. The combination of approaches based on interval analysis and ontological representation of the subject area provides increased efficiency of computational procedures for identifying models of complex objects, as well as the adaptive use of different models for different subject areas in decision support systems.

Information system for creating a generalized model of complex technical objects

Creation of complex technical objects (CTO, such as science-intensive engineering objects, which are characterized by the number of elements and connections equal to 106 and more) – a process containing long subprocesses, complex objects, models, and based on available standards and information technology (IT). It is known from practice that CTO models are created with the help of information systems - components of CALS and PLM-solutions. This process have the following shortcomings: models at different stages of creation of CTO are not completely interconnected; CTO modeling takes place using different components of IT CALS and PLM-solutions, which creates constant difficulties in data conversion and leads to partial or complete loss of model data; there is no automated communication with other CTO models.
 A generalized model of complex technical objects is proposed, which based on using the theoretical-multiple approach allows to establish an information connection between the models of the process of creating complex technical objects. The information system of creation of the generalized model of difficult technical objects that allowed automating process of processing and construction of models is developed; to supplement the technology of parallel PLM design and components of information technologies CALS and PLM-solutions for the task of creating models of complex technical objects.

IMPLEMENTATION OF A FINITE ELEMENT CLASS LIBRARY USING GENERALIZED PROGRAMMING

Context. For computer modeling of complex objects and phenomena of various nature, in practice, the numerical finite element method is often used. Its software implementation (especially for the study of new classes of problems) is a rather laborious process. The high cost of software development makes the development of new approaches to improving the efficiency of programming and maintenance (including the addition of new functions) urgent. Objective. The aim of the work is to create a new effective architecture of programs for finite element analysis of problems in mathematical physics, which makes it easy to expand their functionality to solve new classes of problems. Method. A method for developing programs for finite element analysis using generalized programming is proposed, which makes it possible to significantly simplify the architecture of the software and make it more convenient for maintenance and modification by separating algorithms and data structures. A new architecture of classes that implement finite element calculation is proposed, which makes it possible to easily expand the functionality of programs by adding new types of finite elements, methods for solving systems of linear algebraic equations, parallel computations, etc. Results. The proposed approach was implemented in software as a class library in C ++. A number of computational experiments have been carried out, which have confirmed its efficiency in solving practical problems. Conclusions. The developed approach can be used both to create general-purpose finite element analysis systems with an open architecture, and to implement specialized software packages focused on solving specific classes of problems (fracture mechanics, elastomers, contact interaction, etc.).

Modeling of Bank Credit Risk Management Using the Cost Risk Model

This article deals with the issue of managing bank credit risk using a cost risk model. Modeling of bank credit risk management was proposed based on neural-cell technologies, which expand the possibilities of modeling complex objects and processes and provide high reliability of credit risk determination. The purpose of the article is to improve and develop methodical support and practical recommendations for reducing the level of risk based on the value-at-risk (VaR) methodology and its subsequent combination with methods of fuzzy programming and symbiotic methodical support. The model makes it possible to create decision support subsystems for nonperforming loan management based on the neuro-fuzzy approach. For this paper, economic and mathematical tools (based on the VaR methodology) were used, which made it possible to analyze and forecast the dynamics of overdue payment; assess the quality of the credit portfolio of the bank; determine possible trends in bank development. A scientific and practical approach is taken to assess and forecast the degree of credit problematicity by qualitative criteria using a mathematical model based on a fuzzy technology, which can forecast the increased risk of loan default at an early stage in the process of monitoring the loan portfolio and model forecasting changes in the degree of credit problematicity on change of indicators. A methodology is proposed for the analysis and forecasting of indicators of troubled loan debt, which should be implemented as software and included in the decision support system during the process of monitoring the risk of the bank’s credit portfolio.