title: Ð ÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð² Ð·Ð°Ð´Ð°ÑÐµ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ð¿Ð¾ Ð´Ð°Ð½Ð½ÑÐ¼ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑ Ð´Ð»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ ÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾ÑÑÐ¸ Ð² ÑÐ¸Ð»ÑÐ½Ð¾Ð¼ ÑÐ¼ÑÑÐ»Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Regularization in the problem of building a regression on data with interval uncertainty to achieve consistency in the strong sense
Creators: name: ÐÑÑÐ½Ð¾ÑÐ¾Ð², ÐÐ¼Ð¸ÑÑÐ¸Ð¹
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: 2022
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð½Ð°Ð»Ð¸Ð·
ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð°Ñ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ°
Ð·Ð°Ð´Ð°ÑÐ° Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸
Ð¼ÐµÑÐ¾Ð´ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸
classical interval arithmetic
optimization problem
interval regression model
uncertainty variation method

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð² ÑÐ°Ð¼ÐºÐ°Ñ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ Ð¾Ð±ÑÐµÐºÑÑ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¸ Ð¸ Ð¸Ñ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð°, Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐµ Ð´Ð»Ñ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ð½Ð° ÑÐ·ÑÐºÐµ Octave Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÑÐ°Ð½Ð´Ð°ÑÑÐ½ÑÑ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ¾Ð², Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾ÑÐºÑÑÑÐ¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ kinterval. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°ÐµÐ¼ÑÐµ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ:ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑ Ð²ÑÐ¾Ð´Ð½ÑÑ Ð°ÑÐ³ÑÐ¼ÐµÐ½ÑÐ¾Ð². ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñ Ñ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼ (Ð·Ð°Ð¿Ð°Ð·Ð´ÑÐ²Ð°Ð½Ð¸ÐµÐ¼) Ð²Ð¾ Ð²ÑÐ¾Ð´Ð½Ð¾Ð¼ Ð°ÑÐ³ÑÐ¼ÐµÐ½ÑÐµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð´Ð»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ ÑÐµÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ. ÐÐµÑÐ²Ð°Ñ Ð·Ð°Ð´Ð°ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐ¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ°Ð³Ð¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»Ñ, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð²Ð°Ð»Ð° Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»Ñ Ð¾Ñ Ð¿Ð¾ÑÑÑÐ¿Ð°ÑÑÐµÐ³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÑÑÑÐµÐ³Ð¾ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ ÑÐµÐ»ÑÑ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð² ÑÐ¾ÑÐºÐ°Ñ Ð½ÐµÐ¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð°. ÐÐ°Ð½Ð½ÑÐ¼Ð¸, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐ¼Ð¸ Ð²Ð¾ Ð²ÑÐ¾ÑÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµ, ÑÐ²Ð»ÑÑÑÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑ Ð´Ð²ÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² â ÐºÐ°Ð»Ð¸Ð±ÑÐ¾Ð²Ð¾ÑÐ½Ð¾Ð³Ð¾ Ð¸ Ð½Ð°ÑÑÑÐ°Ð¸Ð²Ð°ÐµÐ¼Ð¾Ð³Ð¾. ÐÐ°ÑÑÑÐ°Ð¸Ð²Ð°ÐµÐ¼ÑÐ¹ Ð´Ð°ÑÑÐ¸Ðº Ð¾ÑÐ»Ð¸ÑÐ°ÐµÑÑÑ Ð¾Ñ ÐºÐ°Ð»Ð¸Ð±ÑÐ¾Ð²Ð¾ÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ¼, ÑÑÐ¾ Ð²ÑÐ´Ð°ÑÑ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð½ÑÐµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÑÐµÐ°Ð»ÑÐ½ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑ Ð² ÑÐ°Ð¼ÐºÐ°Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð´Ð»Ð¸Ð½Ñ Ð¸ÑÑÐ¾ÑÐ¸Ð¸, Ð½Ðµ Ð¸Ð·Ð²ÐµÑÑÐ½Ð¾Ð¹ Ð½Ð°Ð¼. ÐÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ Ð¿Ð¾ÑÑÑÐ¾Ð¸ÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð´Ð»Ð¸Ð½Ñ Ð¸ÑÑÐ¾ÑÐ¸Ð¸ Ð±ÑÐ´ÐµÑ Ð²ÑÐ´Ð°Ð²Ð°ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ ÑÑÐ¾Ð¶Ð¸Ðµ Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÐ¼Ð¸ Ð½Ð°ÑÑÑÐ°Ð¸Ð²Ð°ÐµÐ¼Ð¾Ð³Ð¾.
description: This work is devoted to the construction of interval regression models using linear programming methods within classical interval arithmetic. The main objects of interval arithmetic and their properties necessary for research are considered. The work was done in the Octave language using standard tools, as well as the open library "kinterval". Tasks solved in the course of work: 1. Building a linear regression model for problems with interval uncertainty of input arguments. 2. Building a linear regression model for problems with integration (delay) in the input argument. The work for each task uses real data. The first task is devoted to the construction of a regression model that describes the operation of a stepper motor, specifically, the dependence of the position of a motor shaft on the incoming control action of the system in order to predict the state of the system at points of an incomplete step. The data used in the second task are temperature measurements of two sensors - calibration and Ñustomizable. Customizable sensor differs from a calibration sensor in that it gives the averaged values of real temperature measurements within of history an unknown length. It is necessary to build a model that, for the obtained value of the history length, will produce temperature values similar to the values of the Ñustomizable sensor.