In modern industrial settings, one of the primary challenges is ensuring uninterrupted equipment operation while minimizing production downtime. The aim of this research was to develop a digital twin capable of real-time assessment of equipment failure probability based on incoming sensor data. A Bayesian approach was employed as the methodological foundation: the model sequentially updates the prior probability of failure using new data obtained from sensors. The prototype was implemented in the R programming language, which enabled effective visualization of dynamic changes in failure probability. A simulation of sensor data was conducted to demonstrate how the posterior probability of equipment failure evolves at each stage. The model exhibited adaptability to changing operational conditions while maintaining high accuracy in risk assessment. The developed digital twin has proven effective as a tool for assessing the technical condition of the equipment. The use of a Bayesian framework ensures model flexibility and facilitates its integration into monitoring systems for predictive analytics. The proposed solution offers substantial practical value for enterprises pursuing the digitalization of production processes and the implementation of intelligent maintenance systems. The developed prototype can be integrated into existing monitoring infrastructure, enabling timely detection of failure indicators, reducing repair costs, and improving equipment reliability.

The rapid expansion of small and medium enterprise (SME) lending has intensified the need for accurate and interpretable credit risk forecasting. Financial institutions must anticipate potential business loan delinquency to maintain portfolio stability and meet regulatory standards. This study proposes an interpretable multi-model framework that integrates statistical (correlation screening and ordinary least squares regression), probabilistic (Gaussian Naïve Bayes), and classical time-series (SARIMA) methods to balance explanatory insight and predictive accuracy in delinquency forecasting. Ordinary least squares regression is used to quantify the direction and strength of each driver and yields statistically significant coefficients (β ≈ 1.336 for the overdue 15+ days bucket, p < 10⁻²²). The Naïve Bayes classifier provides a probabilistic early-warning signal with an out-of-sample accuracy of 55%, precision of 43%, recall of 75%, and ROC AUC of 0.371. Finally, a seasonal ARIMA model fitted on the selected regressors achieves a mean absolute percentage error (MAPE) of 7.6% and an out-of-sample R² of 0.49, demonstrating competitive forecasting performance while maintaining interpretability. The results show that the framework offers actionable insights for risk managers by identifying key risk drivers, providing probabilistic alarms, and generating calibrated point forecasts. The proposed approach contributes to the development of intelligent and explainable forecasting and control systems for modern financial institutions.

This study aims to develop a digital twin model based on Bayesian methods for accurate and adaptive failure prediction in complex engineering systems operating under uncertainty. To achieve this, the research employs Bayesian networks that model probabilistic relationships among sensor data such as temperature, pressure, vibration, and humidity enabling real-time updates and robust predictions. The methodology involves training and testing the model on real-world industrial datasets, where it demonstrated superior performance. Experimental results revealed that the proposed model achieved an accuracy of 91%, which is 16% higher than traditional approaches, and also outperformed others in terms of F1-score and ROC-AUC. These findings highlight the strength of Bayesian inference in handling incomplete or noisy data and maintaining high interpretability. The study concludes that integrating Bayesian models into digital twins enhances their adaptability and reliability for critical systems. In practical terms, the developed approach can significantly improve predictive maintenance, reduce operational risks, and support real-time decision-making in industrial environments. Furthermore, the integration of this solution with Internet of Things (IoT) and Industrial IoT (IIoT) technologies is identified as a promising direction for future research, aimed at creating intelligent, self-updating monitoring systems.

В данной работе исследуется синергетический потенциал байесовской теоремы и YOLOv8 в области классификации электрических цепей. Интеграция этих методологий свидетельствует о значительном повышении точности прогнозирования, особенно в сценариях с ограниченной доступностью наборов данных. Объединяя байесовские принципы с надежностью YOLOv8, наше исследование преодолевает проблемы, связанные с недостаточным количеством обучающих данных, представляя новый подход, который значительно повышает точность идентификации компонентов схемы. Результаты этого исследования позиционируют объединение байесовской теоремы и YOLOv8 как надежное решение, особенно полезное для совершенствования моделей классификации в средах с ограниченными ресурсами. Этот гибридный подход не только устраняет ограничения, связанные с нехваткой данных, но и демонстрирует свою эффективность в составлении более надежных и точных прогнозов. Тонкое понимание неопределенностей, обеспечиваемое байесовскими принципами, дополняет эффективность YOLOv8, делая комбинированную модель устойчивой перед лицом проблем. В заключение, наше исследование вносит свой вклад в развивающийся ландшафт классификации электрических цепей, представляя комплексное решение, которое процветает в сценариях с ограниченным набором данных. Эта новая интеграция не только повышает точность, но и обещает изменить парадигму интеллектуальных систем в полевых условиях, предлагая более надежный и детальный подход к классификации схем в реальных условиях с ограниченными ресурсами.

This study investigates evidence propagation in Bayesian networks with complex topologies, aiming to improve inference efficiency beyond the limitations of traditional singly connected (polytree) structures. An iterative inference algorithm is developed that leverages structural properties such as d-separation and the Markov blanket. The proposed method partitions networks into modular components and iteratively propagates evidence through them. The algorithm is tested on Bayesian networks with multiply connected graphs, using both forward and backward propagation phases to ensure convergence. The findings demonstrate that the method significantly reduces computational complexity while maintaining high accuracy. By localizing computations and employing iterative updates, the algorithm achieves efficient convergence even in the presence of multiple cycles and conflicting pieces of evidence. Experimental results confirm the robustness of the proposed approach. The iterative propagation algorithm enhances the applicability of Bayesian networks to real-world scenarios involving high-dimensional and interconnected variables, overcoming the limitations of standard methods and enabling scalable, accurate probabilistic reasoning. The algorithm has practical implications for decision support systems, medical diagnostics, and intelligent data processing, where real-time inference in complex network structures is essential.

The rapid expansion of small and medium enterprise (SME) lending has intensified the need for accurate and interpretable credit risk forecasting. Financial institutions must an-ticipate potential business loan delinquency to maintain portfolio stability and meet reg-ulatory standards. This study proposes a multi-model analytical framework that inte-grates statistical, probabilistic, and machine learning methods—Linear Regression, Naïve Bayes, and NeuralProphet—to improve both interpretability and predictive accuracy in delinquency forecasting. Linear Regression is employed to identify key macroeconomic and portfolio-level variables that influence default behavior, providing transparent and explainable insights with statistically significant coefficients. The Naïve Bayes model in-troduces a probabilistic layer to assess the likelihood of delinquency escalation under var-ying business conditions. Finally, the NeuralProphet model performs nonlinear time-series forecasting using the selected regressors and achieves an R² of 0.89 with a mean absolute percentage error of 8.5 percent, while residuals remain approximately normally distributed according to the Shapiro–Wilk test. The results show that the pro-posed multi-stage framework effectively combines interpretability and predictive perfor-mance, supporting explainable, data-driven decision-making in SME credit risk manage-ment. The approach contributes to the development of intelligent forecasting and control systems for modern financial institutions.