This work continues exploratory research aimed at improving methods using isolines of key navigation parameters traditionally applied in coastal navigation. The previously proposed idea of combining isolines for a single landmark base based on measured bearings and distances has been extended to multiple landmark bases, with tracking of four landmarks considered the basic option. Assuming the presence of irregular and regular measurement errors, regular errors are first compensated by transitioning to differential isolines in a general form. Next, the isolines or position line equations are presented in a reduced standard form and then solved using the least squares method. To compare different solutions, the accuracy of the obtained fixed position is estimated by the radial error. It is shown that regular errors are compensated when position lines are presented in a reduced standard form, but their reduction also allows compensating residual effects caused by the computational procedure. The most important findings of the research are visualized, and the main expressions are practically applied in the software of modern navigation systems. Simulation has shown that the radial error of the fixed vessel position, calculated from 26 reduced position lines presented in the standard form for four landmarks, is nearly twice less than the requirement for GNSS systems. Formalization of the proposed methods in state-of-the-art navigation systems and autonomous vessels will allow solving navigation information processing problems in coastal navigation at a new qualitative level.

A depth-based method for determining vessel longitude using a neural network is proposed. The input of the network is a vector containing depth values measured at a certain spatial interval using an echo sounder. The output of the network is the longitude corresponding to the position of the last sounding. The network has several hidden layers, varying from one to ten layers. The hidden neurons use hyperbolic tangent activation functions, while the single neuron of the output layer employs a linear activation function. Algorithms for training data generation, network training, and testing are defined. Together, they form the basis for creating a neural network-based system for vessel longitude prediction, implemented in the Python programming language. The TensorFlow library is used for working with neural networks. An official electronic navigational chart is chosen as the source of bathymetric data. Based on the extracted sounding layer, a regular grid is formed, where depth values at the grid nodes are calculated using linear interpolation. The procedure for forming training and test data includes pseudorandom variations of sea level, which may result from both real fluctuations and measurement errors. For the test set, the accuracy of the network is acceptable for navigation, and the results depend on the number of hidden layers. The best accuracy, in terms of minimal maximum absolute longitude prediction error, is achieved with the network having the greatest number of hidden layers. It is also noted that it is necessary to test the developed neural networkbased system using vessel motion modelling.

The study evaluates the effectiveness of integrating specialized transshipment equipment for handling railway rolling stock in the rear area of the marine terminal and during the loading of bulk cargo into the technological chains for processing large-capacity containers. It is noted that the problem requires a comparative assessment of operational characteristics and preliminary calculations of the performance of loading and unloading machines at the cargo fronts where they are employed. The technological process for handling fertilizers in large-capacity containers is proposed to be considered as two subsystems differing in work rhythm: ensuring transfer of cargo between the railway and the accumulation warehouse, as well as delivery for loading by internal terminal transport. To develop proposals for the optimal use of the selected type of transshipment equipment at the work fronts, a comparative analysis of the terminal’s “bottlenecks,” identified in the presented mathematical model, can be performed. It is emphasized that the proposed technology for handling bulk cargo at a sea container terminal differs from the traditional scheme for handling large-capacity containers in that the container is used only at the stage of fertilizer delivery to the ship. After the container is emptied, it must be transported through the terminal warehouse to the packing point at the manufacturing plant. Since the two processing subsystems identified in the course of the study at the marine fertilizer terminal in bulk containers require the creation of a different number of service channels for cargo flows, this case provides a classic example of solving a problem of a multi-channel queuing system with waiting, in order to calculate the number of unloading, loading, and reloading positions at each identified work front. The paper concludes that the reliability of assessing the capabilities of the terminal’s transshipment equipment will make it possible to organize a queuing system without waiting, i. e., with a given service intensity.

This article discusses the requirements for the main operating systems of an automatic tugboat designed to perform escort, mooring, and unmooring operations for vessels in port waters. The relevance of the work stems from the need to increase the safety and efficiency of port operations through the introduction of autonomous technologies. The architectural and structural features of the automatic tugboat, which ensure high maneuverability and operational reliability, are presented. Particular attention is paid to the key functional systems: the automatic navigation system and the situational awareness system. Mathematical models and algorithms are proposed for analyzing the navigation situation, adjusting routes, ensuring safe separation from other vessels, as well as methods for integrating data from various information sources (high-precision navigation systems, AIS, radar, log) using the Kalman filter. Requirements for the propulsion system with azimuth thrusters, the power supply system with redundancy, the rigid coupling system (including magnetic devices), and the emergency towing system are also described. The study results aim to create a safe, reliable, and highly automated automatic tugboat capable of effectively interacting with the environment and performing complex maneuvers in confined conditions.

The topic of this paper is a qualitative study of navigational isosurfaces to establish the practicality of polynomial approximation for a class of differentiable functions with minimized “smoothness.” When solving problems of restoring the scalar field of navigation parameters, it is certainly important to form an initial correct judgment about the isogeometric proximity between the approximate and approximating functions, provided specific information is given about the differential properties of the synthesized navigation isosurface. It is assumed that the structure of the graphical model of the object under study and the characteristics of function approximation theory should be consistent with each other when forming a unified information approach. As a concrete illustrative example, a study of the differential properties of a formalized representation of an astronavigational isosurface — with geometric interpretation in the form of computer screenshots obtained as a result of the work of a compiled software module — has been performed. An assumption is made regarding the realistic possibility of choosing the optimal approximate navigation function based on visualization of the “smoothness” of a navigation function of any dimension in accordance with Schoenberg’s hypothesis about the relationship between minimum curvature and maximum smoothness of an algebraic line. The search for a solution to the problem of graphical transformation of break points of an abstract isoline, formalized in strict mathematical terms as a special case of a navigational isosurface, is determined. The developed methodology is proposed for effective verification of the reliability of big geospatial data. The prospective importance of proper mathematical processing of marine spatial data from geographic information systems is emphasized as a priority in providing consumers with reliable information for practical purposes. The relevance of the need to conduct a qualitative study of navigational isosurfaces to successfully approximate them from the unified standpoint of spline function theory coincides with the prediction of the emergence of complex hypothetical isolines, which are expected to be studied during the evolution of technical means of navigation.

The implementation of the smart port concept through the phased introduction of various interconnected systems is an important element in the development of autonomous navigation. One such component may be a system for providing autonomous piloting and mooring of vessels in a seaport, whose tasks include remote control of automated tugboats for cargo vessel piloting as well as monitoring the autonomous operation of the tugboats. However, the operation of such systems is not permissible without the supervision of properly trained personnel. Such personnel must ensure and monitor the safety of piloting and escorting operations for sea and river vessels, monitor, control and manage automatic tugboats in various operating modes, perform their technical maintenance and repair, as well as maintenance of other equipment for autonomous piloting and mooring, fulfil the operational procedures of the remote-control center, and communicate with other services. The authors conclude that it is necessary to develop, systematize and subsequently establish regulatory and legal requirements for the process and outcome of professional training of the external tug master, automated tug operator, remote control center administrator, remote control system engineer, pilot, service engineer at the base/terminal of automatic tugs, and service system engineer supporting the maintenance facility for automatic tugboats. The results obtained in this work can serve as a basis for further research, as well as for setting requirements for the professional training, qualifications, and experience of personnel for autonomous vessel piloting and mooring systems.

This article addresses issues related to the duration of accident-free operation of Volgoneft-type tankers, project No. 1577, provided that high-quality repairs and modernization are carried out. The relevance of the study is due to the accident that occurred on December 15, 2024, in the Kerch Strait, where two vessels of this project (Volgoneft-212 and Volgoneft-239) were wrecked, leading to an environmental disaster caused by fuel oil spill. The paper examines possible causes of the accident, including failure to comply with requirements of the Russian classification society (RS), overloading, and lack of high-quality hull repairs. The article considers the hypothesis that the reliability of vessel operation is determined not by their age, but by their technical condition, which is ensured by the shipowner through regular inspections combined with high-quality hull repair. The article presents the results of strength calculations for tanker hulls carried out in 2019–2024 and provides data on modernization, including the replacement of structures with high-strength steel (RS D32 with a yield strength of 315 MPa), raising of the second bottom, and relocation of bulkheads in the cargo area according to MAKO requirements. The design features of the vessels, their classification restrictions, and the influence of residual deformations, such as overall residual buckling, on the probability of hull fracture are analyzed. Special attention is given to hazardous sections in the cargo tank area, where fractures occurred in the wrecked vessels. To increase reliability, it is proposed to reinforce the hulls with additional strips at the most weakened connections (deck covering or bottom plating), which is an economically efficient solution. The conclusion is made that, subject to compliance with the Russian classification society’s requirements for regular technical inspections and an individual approach to repairs, Volgoneft-type tankers can continue safe and effective operation despite their average age of 48 years in 2025. The results show that modernized tankers have sufficient strength reserve for safe operation within the RCS classes (“XM-PR 2.5” or “XM-SP 3.5”).

The paper studies changes in water resistance to the motion of a high-speed passenger catamaran due to changes in trim and draft. The trim can vary within small limits both during design by changing the arrangement of masses and during operation due to ballasting or the movement of passengers. The draft can also change during the design process due to changes in equipment or inaccuracies in determining the masses, and during project modernization — for example, for operation in another area. During operation, the draft depends on the vessel’s load. Through such variations, it is possible to provide the vessel with better seaworthiness and operational qualities. One way to improve such qualities can be to reduce water resistance to the vessel’s motion, as this can reduce the load on the main engines, decrease fuel consumption, and increase achievable speed. This paper presents the results of a study of the vessel’s trim parameters on the residual resistance coefficient. The tests were carried out in the towing tank at the Admiral Makarov State University of Maritime and Inland Shipping. The paper presents experimentally obtained curves of residual resistance coefficients for four specified values of static trim. The displacement was kept constant and corresponded to the full load of the vessel, and the model’s center of gravity position was changed by transferring ballast. The studies were performed for the case of a landing with maximum operational trim by the stern (the static trim angle was –0.7 degrees, the running trim angle at maximum speed was about –2 degrees), for the case in which the running trim was close to zero (the static trim angle was 1.4 degrees), and for two intermediate variants. The tests were conducted in calm deep water for Froude numbers from 0.41 to 0.82, corresponding to full-scale vessel speeds from 14 to 28 knots. It was shown that the effect of trim on resistance depends on speed. At Froude numbers of 0.40 to 0.55 (full-scale vessel speed of 14–19 knots), trim by the stern increases resistance. At higher speeds, with increasing trim, the value of the residual resistance coefficient decreases, while with increasing speed, the positive effect of trim also increases. The effect of increasing draft on the value of residual resistance with constant trim is also estimated. At low speeds, increasing draft increases the residual resistance coefficient; with increasing draft, this effect decreases. Thus, some trim by the stern allows reducing the value of towing resistance when moving at high speeds in calm deep water.

This paper is devoted to the analysis of the structural and hydrostatic characteristics of container ships in the context of their changes in longitudinal waves. It is noted that the structural and hydrostatic characteristics of container ships have their own specifics, due, in particular, to the economic optimization of container transportation, and directly affect the behavior of the ship in waves. These specifics should be considered by navigators when calculating and monitoring stability during the voyage. It is emphasized that the hydrostatic characteristics of a ship in waves are constantly changing, and their consideration is a difficult task. Currently, no practical solution to this problem has been proposed. The passage of a wave along the hull of a ship assumes that different parts of it will have different draughts at different times. Based on this, this paper examines the variation and dependence of ship characteristics for different draughts. The waterline area and its completeness coefficients are considered as one of the most important parameters. To calculate them in waves, a technique is proposed, which consists in dividing the waterline into sections and determining the area of each section, taking into account its completeness coefficient, depending on the draught. Calculations performed using the characteristics of existing container ships of different tonnages have shown the dependencies and relations between such structural and hydrostatic characteristics of container ships as hull shape, relations between linear dimensions, draught, block coefficient and waterline area coefficient. It is noted that further research based on the results obtained in this work can form the basis for the development of a methodology for considering the parameters of a container ship in waves, suitable for use by navigators in practice. This will certainly contribute to improving the safety of operation of container ships.

The problems associated with mutual flows of electric energy between several alternating current diesel generators during their parallel operation are considered. It is noted that of electrical energy in some cases leads to emergency situations, reduces the efficiency of operation of units and their reliability. Fluctuations in operating parameters cause voltage pulsations, reduce unit efficiency, limit the use of full power, have a negative psychophysiological effect on personnel, and lead to increased wear of rotation speed controllers units. At the same time, if we present the phenomena occurring in the system of parallel diesel generators in a simplified manner, we can provide a scientific understanding of the essence of the processes and develop practical recommendations for ensuring the quality of the energy generated. A mathematical model of two parallel diesel generators is presented, from which it follows that the exchange oscillations are of a single-node form, the node of which is located in the middle of a conditional flexible shaft in the form of an electrical connection connecting the diesel generators. With a significant swing in the amplitude of oscillations, their frequency in various load modes is 2 to 5 Hz. It is close to the frequency of the disturbing forces caused by the working processes in the diesel engine. In a simplified torsion system for parallel operation of a group of diesel generators on a powerful electric network, each unit should be considered as a single-mass torsion system. The natural frequency of a single-node oscillation form has one node in the zone of conditional electrical connection between generators. Resonance oscillations in the system arise due to an unstable working process as a result of unstable operation of the fuel equipment from cycle to cycle. This leads to an increased flow of electrical energy between parallel diesel generators. This phenomenon is usually accompanied by a decrease in the efficiency of the installation as a whole.

The results of calculations of relative atomization characteristics for diesel distillate and low-viscosity marine fuel are presented. The analysis shows that, compared to diesel fuel, the atomization of low-viscosity marine fuel is characterized by greater non-uniformity and increased droplet size. This slows the combustion process and shifts heat generation to the expansion line. As a result, converting a diesel engine to low-viscosity marine fuel leads to increased specific consumption, exhaust gas temperature, and harmful emissions. To improve the operational properties of low-quality fuels, a method of preliminary treatment using a high-voltage electric charge was developed and implemented. Results of trial tests of a diesel engine running on modified fuel are presented. Based on the calculations and investigation of spray parameters, factors contributing to reduced efficiency of marine diesel engines when using heavy fuels were identified. A method for increasing energy efficiency and reducing the negative environmental impact of marine diesel engines operating on low-cost, low-quality fuel was proposed. This approach is both economically justified and environmentally efficient for improving the performance of marine diesel engines running on poor-quality heavy fuels and can be recommended for widespread use in the shipping industry.

The purpose of this work is to implement intelligent algorithms for the synthesis of control systems for electric drives of power supply systems at water transport facilities using artificial neural networks. The use of such intelligent algorithms will make it possible to carry out in practice the digital transformation of hardware units of regulators (controllers) in control systems for various objects, including electric drives, into mathematical algorithms based on neural network controllers. Such controllers, for example, those using a reference model, are more preferable when controlling nonlinear objects, since the neural networks on which they are based are nonlinear. In view of this, the scope of their application has been significantly expanded in the further development of methods for computer monitoring and parametric identification of ship and shore power supply management models, as well as the analysis and forecasting of energy efficiency indicators of their operating modes. The procedure for synthesizing a neural network regulator built on the basis of a reference model to stabilize the angular velocity of a DC motor is considered, aiming to compensate for oscillations occurring in the drive control loop. Using a PID tuner, the parameters of the PID controller were determined, significantly affecting control quality and allowing it, together with a typical first-order astatic link, to perform the function of a reference regulator for training the neural network controller. It is shown that the selected parameters of the neural model of the controlled object and the neural network reference regulator made it possible to significantly improve the quality of the transient process and eliminate oscillations in the DC motor drive control. The indicators and characteristics of the training quality of the neural network regulator and the neural model of the object with the selected training parameters are presented. An algorithm for training the neural model of the controlled object and the neural network regulator based on the dynamic nature of the backpropagation of error deviations of output signal values from reference ones in a multilayer neural network is proposed, with the purpose of correction through introducing adjustments to the values of synaptic weight coefficients. The algorithm can be applied in control systems for electric drives of unmanned objects, including aircraft, waterborne, and land-based systems in inland water transport.

This study is devoted to one aspect of designing automated control systems for water transport facilities, such as logistics centers, container terminals, ports, ship repair yards, shipping companies, and lock navigation channels on regulated inland waterways. The problem of developing a methodology for the quantitative design assessment of the structural complexity of software under development is considered, since this complexity is a significant factor in assessing its reliability, and increasing complexity inevitably leads to various types of vulnerabilities in program code. A set of factors on which structural complexity depends is defined. A corresponding set of terms is introduced to designate these factors assuming the use of a modular development principle: module call spectrum, module alternative spectrum, module depth, module cyclicity, weighted module depth, weighted module cyclicity. The expediency of transitioning to the corresponding dimensionless indicators is justified. Building on the previously formulated multiplicative method of aggregating a general system integral indicator from a set of partial indicators, a final formula for the design indicator of structural complexity of automated control system software is provided, and a method for including it in the design assessment of the overall reliability of the control loop is proposed. A metric for vector evaluation of differences in structural complexity among alternative software products is introduced.