Vol 25, No 3 (2024)

A method for synthesizing μ robust stable linear minimax extrapolator of a stationary random process under conditions of interval uncertainty of the parameters of the measured signal is presented. A robust and stable minimax extrapolation is shown in a constructive form of μ, both in terms of the result and the solution. The theorems of determinization and reduction on the existence and uniqueness of a consistent interval saddle point in the problem of extrapolation with small indistinct interval deviations in the right parts of the restrictions on the spectral power density of the perturbation of the measured signal in the form of a consistent interval Lagrange function are formulated and proved. In a constructive form, a 4-step algorithm is proposed for determinizing the search for the optimum of an imperfectly defined functional of the variance of the estimation error to find the optimum of the same name for two fully defined (deterministic) functionals. This approach, unlike others (for example, probabilistic), always ensures the existence of a stable result and solution of a single optimum in the problem of interval minimax extrapolation due to regularization by a small parameter with a derivative of the eigenfunction of a singularly perturbed integro-differential equation of the first order with an integral operator of the Voltaire type of the second kind, defined by a symmetric, closed real the core. Unlike classical forecasting and estimation methods, the proposed method allows us to obtain guaranteed interval-stable robust estimates of the state with some deviations of the actual probabilistic characteristics of the initial data from the hypothetical ones.

This study investigates patterns of land displacement in Kern County, California, using Sentinel-1 satellite imagery and the Interferometric Synthetic Aperture Radar (InSAR) technique. A time-series analysis was performed to examine the temporal evolution of land displacement using the Small Baseline Subset (SBAS-InSAR) approach. The LicSAR (Comet Portal) and Liscbas toolbox were employed to analyze Sentinel-1 satellite data collected between 2014 and 2022. For the ascending orbit, the observation period spanned approximately 6.6 years, encompassing 256 images and 1,499 interferograms. The descending orbit covered around 7 years, with a network of 266 images and 954 interferograms. The data were decomposed into ascending and descending paths to identify both vertical and horizontal displacement patterns. An accuracy evaluation was conducted using 85 GPS stations in central California, revealing an RMSE of 1.89 and an R -squared value of 0.9 for the horizontal direction, and an RMSE of 2.4 with an R -squared value of 0.94 for the vertical direction, indicating a high level of accuracy. These results demonstrate the effectiveness of InSAR in capturing detailed land displacement patterns. This study also discusses the advantages and limitations of using InSAR for tracking land deformation and provides recommendations for future research.

The negative consequences of the peak selection of network products (electricity, water, gas, and other resources, including time distribution in computer programs) force the supplier to introduce tariff-based time payments. Thus, the question arises as to whether the consumer’s payment can indeed be minimized at a specific mode of product consumption if there is a system of its accumulation, that is, capacitor or storage, which replenishes or consumes its reserves at times of low and high tariff prices. To achieve this objective, it is necessary to make optimal use of accumulator resources, which can be drawn upon during periods of high tariffs and replenished when the need for them is less urgent and tariffs are lower. To achieve this, an appropriate mathematical problem is formulated (for the purposes of concretization, relating to the question of minimizing the payment for electricity consumption) that considers the operational characteristics of the storage and the different modes of energy consumption. This mathematical problem for the minimum can be solved using standard linear programming. The results of the numerical calculations of payments for a particular enterprise both without storage and with the use of capacitor are presented. The gain in payment was approximately 20 per cent.

Despite the widespread introduction of 3D printing in machine-building industries within the framework of Industry 4.0, the quality of manufactured products currently requires regulation and improvement. To reduce the volume of defects and increase the fault tolerance of the product, improve the condition of the workplace, work convenience, accounting for finished products and other important factors of the high-quality production cycle, there are a sufficient number of methods and practices used in many fields (automotive, mechanical engineering, energy, etc.). One of these methods is DMAIC, which involves the introduction of the 6 sigma method into the technological sphere of additive manufacturing product quality management in order to improve its quality at these enterprises. The “define-measure-analyze-improve-control” cycle is used by the author in the context of this study to analyze the possible optimization of production procedures at additive manufacturing enterprises by selective laser melting (SLM). The analysis of production practices and suggestions for improving the quality of manufactured products, based on the DMAIC, method, will improve the current additive manufacturing processes at large technological enterprises and will be able to positively affect the quality characteristics of products. With the help of a technological approach based on the DFSS cycle, through the application of each step sequentially, an effective change in the positive side of quality as the production process itself is possible: the manufacturing accuracy increases at each stage, the process is modernized with each new cycle, based on previous results; as well as finished products: the number of defects decreases, the mechanical characteristics of products improve.

The article discusses various methods for creating decision support systems to determine the technical appearance and design characteristics of multi-apartment residential buildings at the pre-construction stage. To solve this problem, structural optimization is used, which includes determining the number of elevators, the height of the building and the number of floors, orienting the building to the cardinal directions, determining the parameters of engineering communications and the investment attractiveness of new housing. The advantages and disadvantages of machine learning methods and various types of logical inference in expert systems for determining the technical appearance and design characteristics of multiapartment residential buildings are analyzed. A comparative analysis of the various approaches has led to the conclusion that the tools of expert systems based on fuzzy logic are the most advisable. This paper presents an overview of the fundamental principles underlying the operation of fuzzy expert systems. It also offers a critical assessment of their potential for universal applicability and versatility in addressing design challenges related to construction projects.