The purpose of the work is to improve the efficiency of solving optimal design problems for hinge-rod structures (HRS) intended for operation in aggressive technological environments, specifically by refining the correction function method and ensuring its accuracy control. The scientific novelty of the obtained results lies in the further development of the correction function method for solving the durability problem of corroding structures, which, unlike the existing method, is controlled by accuracy and provides more precise solutions. In addition, a method for determining significant factors in the durability problem of corroding structures is proposed for the first time, based on an artificial neural network (ANN) optimized using the Optimal Brain Surgeon method. The first chapter examines the problem of optimal design of a corroding HRS and identifies the main issues associated with its solution, such as the discrete nature of the problem and the need to model the impact of the aggressive environment on the structure when calculating the constraint function. Key models are considered, distinguishing the problem statement for aggressive environments from classical ones: the model of geometric damage accumulation in the structure in the form of a system of differential equations (SDE) and the model of the corroding cross-section of a structural element. It is established that increasing the efficiency of the solution through optimizat ion methods is not feasible; however, improving efficiency at the stage of constraint function calculation, specifically solving the PDCS, is possible. A review of existing methods for solving PDCS is conducted, providing essential information about the methods, analyzing their advantages and disadvantages, and assessing their accuracy control. The choice of the correction function method for solving PDCS as the basis of the dissertation research is substantiated. The second chapter explores the correction function method for solving CSD. The form of the correction function and methods for its construction through approximation are determined. The architecture of the ANN and the main properties of the ANN used for approximating the correction function are presented. It is established that separate ANNs are required for different types of loads and rod cross-sections. An analysis of the polynomial degree impact on the accuracy of approximating the axial force dependence on time is conducted. The analysis showed that a third-degree polynomial is sufficient for satisfactory accuracy in solving PDCS. The use of the Optimal Brain Surgeon (OBS) method for a justified selection of significant ANN parameters is proposed. Applying the OBS method reduced the number of ANN input parameters without significant loss of accuracy, with the number of ANN neurons decreased by nearly threefold. A method for generating a training sample for the ANN is described, including stages for obtaining reference and approximate numerical solutions for calculating correction function values. In the third chapter, a modification of the correction function method for solving PDCS is presented, refining the original method. Alternative input data sets for the ANN were considered, increasing information on axial forces over time. The proposed refinement showed an average error reduction of 43.5% and 9.7% compared to the original method. The author's modification eliminates the need for preliminary approximation of axial forces before applying the correction function, positively affecting computational complexity. For the refined method, accuracy control was established by determining the relationship between the mathematical expectation of the target metric and the parameters of the numerical solution. This finds a balance between computational complexity and required accuracy, which is crucial in optimal design problems for structures with many elements. In evaluating the models, the dependence of ANN output on random initial weight coefficients was considered, enhancing the reliability of the results. The fourth chapter solves the practical problem of optimal design for a corroding HRS with the author's proposed correction function modifications. A statically indeterminate 15-rod HRS was considered as the model structure, with the problem solved in two formulations differing in the number of varied parameters. The genetic algorithm with the penalty function method was applied to solve the problem. Comparison with other authors' results and other approaches showed that the author's proposed correction function method modification has the lowest computational complexity.
