Technological objects and processes are often characterized by fuzzy initial information necessary for developing their models and optimization. The purpose of the study is to develop a method for synthesizing linguistic models of fuzzy described objects and a heuristic method for solving the multicriteria optimization problem in a fuzzy environment. Based on the expert assessments and logical rules of conditional inference, a method for synthesizing linguistic models was developed for describing processes with fuzzy input and output parameters. To solve the problem of multicriteria optimization, a heuristic method based on the modification and combination of various optimality principles is proposed. Coking reactor models were developed by modifying the successive regression inclusion method and the least squares method. Linguistic models of the delayed coking process were developed in the Fuzzy Logic Toolbox, allowing to evaluate the coke quality depending on the temperature and pressure of coking reactors. Using the proposed heuristic method, the problem of two-criteria optimization of the delayed coking process with fuzzy constraints is solved. The results confirm the advantages of the proposed fuzzy approach compared with the well-known approaches. Unlike them, the proposed method allows making adequate decisions in a fuzzy environment by maximizing the use of available fuzzy information.

A leading cause of accidents during the landing phase of a flight lies in a considerable altitude loss by an aircraft as a result of the impact of a microburst of wind. One of the significant factors focuses primarily on the need to simultaneously satisfy various requirements regarding conditions of environmental disturbances and a wide range of systemic changes. The paper presents an algorithm for synthesizing an optimal controller that solves the mixed H2/H∞ control problem for the stabilization of aircraft in glide-path landing mode in the presence of uncertainty. Firstly, the principles of multi-criteria optimization are presented, and the mixed H2/H∞ problem is interpreted as the synthesis of a system with optimal quadratic performance, subject to its readiness to operate with the worst disturbance. Then, the ensuing section expounds upon the mathematical depiction of the vertical trajectory of aircraft, duly considering the perturbations imposed by wind phenomena. Subsequently, the effectiveness of mixed H2/H∞ control is confirmed compared to autonomous H2 or H∞ regulators through simulation outcomes acquired from the created system. Optimization based on a hybrid (mixed) criterion allowed combining the strengths of locally optimal systems based only on H2 or H∞ theory.

The paper considers the main ways of describing the process that characterizes the arrival of packets to a multiservice node of a telecommunications network. The features of the process under consideration are best represented by the cumulative distribution function A(t). It determines the distribution of the interval size between the moments of arrival of neighboring packets to the multiservice node. These intervals are random values. If it is not possible to perform measurements that allow the choosing of the A(t) function, then the distribution law of random variables is selected based on reasonable assumptions. For telephone switching nodes, the Poisson flow hypothesis was used, which is often similar to the symmetric distribution of the number of calls at time interval t. The results of traffic measurements for multiservice switching nodes showed that the studied distribution is inherently asymmetric. This paper mainly considers the possibility of choosing the A(t) function based on the measurement results presented in a form of the histogram a(t), which contains a series of values. This histogram allows us to obtain the desired distribution as a stepwise function by integration of the a(t). Practical interest is associated with the possibility of reducing the number of readings used to assess the A(t) function. The methods used by some authors are based on the application of arbitrarily chosen functions A(t) with so-called heavy tails. The proposed approach is based on real distributions defined at a finite time interval. As a result of this research, a methodology has been developed to accurately describe the process of packet arrival at the input of the multiservice node. The proposed methodology is based on analytical methods. It guarantees error minimization when investigating the probabilistic characteristics of a switching node in a multiservice network.

Multi-parametric industrial time-series forecasting is important for predictive monitoring, soft sensing, and decision support in complex process industries. This study proposes a process-informed hybrid ARX-residual deep sequence architecture for short-horizon multi-output forecasting of fluid catalytic cracking unit (FCCU) product yields. The model combines a frozen linear ARX branch with causal temporal convolution, a three-layer GRU, causal self-attention, additive attention pooling, residual gating, and a consistency-regularized multi-output objective. Experiments were performed on an open simulated FCCU benchmark containing 20,160 one-minute observations from seven normal and disturbed operating scenarios. The leakage-controlled pipeline uses scenario-wise chronological splitting, train-only median imputation and standardization, exclusion of fault-timing metadata and direct algebraic target components, and 30 min causal windows for five-minute-ahead forecasting. Across ten prespecified random seeds, the proposed model achieved a historical-test RMSE of 0.022809 $\pm$ 0.000116, compared with 0.022751 for ARX-like Ridge. Dependence-aware statistical analyses did not establish a consistent statistical advantage for either model across the evaluated runs. Rolling-origin evaluation likewise showed similar point accuracy, while leave-one-scenario-out evaluation revealed severe extrapolation failure for the unseen pressure-drop scenario. The results support the reproducibility of the proposed architecture and the importance of the ARX-based dynamic structure, but they do not establish the statistical superiority of the full deep residual architecture. Independent industrial data or newly prespecified simulation trajectories are required for confirmatory external validation.

В статье рассмотрена история появления и развития цифровых двойников, привлекающих при стальное внимание исследователей и пользователей. Было показано, что, в отличие от большого числа альтернативных определений, термин «цифровой двойник» содержательно раскрывает суть и разнообразие форм указанных инструментов, выявлена роль ЦД как неотъемлемого виртуального компонента киберфизической системы (КФС), отражающего в цифре свойства и поведение ее физического компонента (оригинала) на протяжении различных этапов его жизненного цикла. Рассмотрены базовые технологии построения и сопровождения цифровых двойников (ЦД) с учетом широкого разнообразия задач автоматизации технологических производств, решаемых с помощью ЦД. Сравниваются подходы к построению моделей технологических объектов – фундаментальное моделирование, моделирование на основе данных и гибридное моделирование.

This work is devoted to the study and solution of the problems of modeling complex objects on the example of the atmospheric block of the primary oil refining unit, associated with the deficit and fuzziness of the necessary initial information. Since many real technological objects of oil refining and other industries are often characterized by a deficit and fuzziness of the necessary information for their study, modeling, and optimization, this work allows solving an urgent scientific and practical problem. An effective method has been proposed that allows, based on a system approach, expert assessment methods, theories of fuzzy sets, and available information of various natures to develop hybrid models of complex objects in conditions of deficiency and fuzzy initial information. Based on the proposed hybrid method and available statistical and fuzzy information, effective hybrid models of atmospheric block columns of the primary oil refining unit were developed. In this case, statistical models were developed based on experimental and statistical data. With crisp input, mode parameters, and fuzzy output parameters, atmospheric block fuzzy models based on the proposed method, determining the quality of the manufactured products, were developed. Moreover, with the fuzzy input, mode, and output parameters of the atmospheric block columns, linguistic models based on the methods of expert assessments, logical rules of conditional inference, and the proposed method, assessing the quality of the produced gasoline, were developed. The linguistic models developed in Fuzzy Logic Toolbox allow for the assessment of the quality of gasoline from the atmospheric block depending on the content of chloride salts and the mass fraction of sulfur in the raw material. The results obtained using the proposed modeling method show their advantages in comparison with known modeling methods.