title: ÐÐ¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð´ÐµÑÐ°Ð»ÐµÐ¹ Ð¿ÑÐ¸ ÑÐ±Ð¾ÑÐºÐµ Ð°Ð²Ð¸Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Optimization of the positioning of parts during the assembly of aircraft structures
Creators: name: ÐÐµÐ»ÑÐ´ÐµÐ², ÐÐ¸ÑÐ¸Ð»Ð»
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÑÐ±Ð¾ÑÐºÐ° Ð°Ð²Ð¸Ð°ÑÐ¸Ð¾Ð½Ð½ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹
ÐºÐ¾Ð½ÑÐ°ÐºÑÐ½Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ°
Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ
Ð¿Ð¾ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÐ½ÑÐ¹ ÑÐ¿ÑÑÐº
ÑÑÑÑÐ¾Ð³Ð°ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
aircraft assembly
contact problem
optimization
coordinate descent
surrogate modeling

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð° Ð·Ð°Ð´Ð°ÑÐ° Ð¼Ð¸Ð½Ð¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸, Ð·Ð°Ð²Ð¸ÑÑÑÐµÐ³Ð¾ Ð¾Ñ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ ÐºÑÑÐ»Ð° ÑÐ°Ð¼Ð¾Ð»ÑÑÐ° Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾ ÐµÐ³Ð¾ ÑÑÐ·ÐµÐ»ÑÐ¶Ð°. Ð§ÐµÑÐµÐ· ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²ÐºÑ ÐºÐ¾Ð½ÑÐ°ÐºÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð² ÑÐµÑÐ¼Ð¸Ð½Ð°Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð° Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð° Ð²Ð·Ð°Ð¸Ð¼Ð¾ÑÐ²ÑÐ·Ñ Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð´ÐµÑÐ°Ð»ÐµÐ¹ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¸ Ð¸ Ð·Ð°Ð·Ð¾ÑÐ° Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÐ¾ÐµÐ´Ð¸Ð½ÐµÐ½Ð¸Ñ. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð½ÑÑ Ð³ÑÐ°ÑÐ¸ÐºÐ¾Ð², ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð» Ð±ÑÐ» Ð¾ÑÐµÐ½ÑÐ½ ÐºÐ°Ðº ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½ÑÐ¹ Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½Ð¾. ÐÐ°Ðº ÑÐ»ÐµÐ´ÑÑÐ²Ð¸Ðµ, Ð´Ð»Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸, Ð¿Ð¾Ð¼Ð¸Ð¼Ð¾ Ð¼ÐµÑÐ¾Ð´Ð° Ð¿Ð¾ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÑÐºÐ°, Ð±ÑÐ»Ð¾ Ð·Ð°Ð´ÐµÐ¹ÑÑÐ²Ð¾Ð²Ð°Ð½Ð¾ ÑÑÑÑÐ¾Ð³Ð°ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° ÑÑÑÐ¾Ð¸Ð»Ð°ÑÑ ÐºÐ²Ð°Ð´ÑÐ¸ÐºÐ° Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐ¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¾Ð², ÑÐ¾ÑÐºÐ° Ð¾Ð¿ÑÐ¸Ð¼ÑÐ¼Ð° ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð½Ð°ÑÐ¾Ð´Ð¸Ð»Ð°ÑÑ Ð½ÐµÐ¿Ð¾ÑÑÐµÐ´ÑÑÐ²ÐµÐ½Ð½Ð¾. ÐÐ¾ÑÐ»Ðµ Ð²ÑÐ±Ð¾ÑÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ Ð½ÐµÑÐºÐ¾Ð»ÑÐºÐ¸Ñ ÐµÑ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¹, Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°Ð±Ð¾ÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð². ÐÐ¿Ð¸ÑÐ°ÑÑÑ Ð½Ð° ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ, Ð±ÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´ Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð², ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¿Ð¾Ð»ÐµÐ·Ð½Ñ Ð² Ð°Ð²Ð¸Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ Ð¿ÑÐ¾Ð¼ÑÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð·Ð°Ð¼ÐµÐ´Ð»ÐµÐ½Ð¸Ñ ÑÑÑÐ°Ð»Ð¾ÑÑÐ½Ð¾Ð³Ð¾ Ð¸Ð·Ð½Ð°ÑÐ¸Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ñ ÑÑÐ¾ÐºÐ° ÑÐºÑÐ¿Ð»ÑÐ°ÑÐ°ÑÐ¸Ð¸ Ð²Ð¾Ð·Ð´ÑÑÐ½ÑÑ ÑÑÐ´Ð¾Ð².
description: In the given work, the task of minimizing the deformation energy functional, depending on the initial position of the aircraft wing relative to its fuselage, is formulated. Through the formulation of the contact problem in terms of quadratic programming, the relationship between the initial position of the structural parts and the gap in the junction area was shown. Based on the constructed graphs, the functional was evaluated as quadratic globally. As a result, surrogate modeling was used to optimize the energy functional, in addition to the coordinate descent method. Based on the calculated values of the functional, a quadric was constructed using the least squares method, the optimum point of which was located directly. After selecting the model and several of its variations, a comparative analysis of the results of the methods was carried out. Based on the results, it was concluded that the proposed algorithms are applicable, which can be useful in the aviation industry to slow fatigue wear and increase the service life of aircraft.