Numerical Differentiation in the Measurement Model

Loktionov, A. P.

doi:10.1007/s11018-019-01677-z

Cited by 2 publications

(4 citation statements)

References 8 publications

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“…Оценивание повышения точности определения начальных параметров оптимизацией числа узлов аппроксимации В рассмотренных частных примерах модели измерений и обработки данных получены формулы (12), (19), (24) с оптимальным количеством узлов сетки аппроксимации N опт < N max = n + 1, не выполняется исследованное в работе [37] Координаты узлов аппроксимации в моделях 3d 0 d 1 M, 3d 0 d 1 P, 4d 0 d 1 MP на рис. 3, а также в модели 1M на рис.…”

Section: результаты и их обсуждениеunclassified

“…Координаты узлов аппроксимации в модели 5d 0 d 1 MPq на рис. 3 получены в работе [37]. Координаты узлов аппроксимации в моделях 3d 0 d 1 q, 4d 0 d 1 Mq, 4d 0 d 1 Pq на рис.…”

Section: результаты и их обсуждениеunclassified

“…47 с. решения обратных задач на основе методов численного дифференцирования, полиномиальной аппроксимации, линейной лагранжевой интерполяции, а также проведения регуляризации и редукции измерений. В публикациях [26][27][28][29][30][31][32][33][34][35][36][37] исследовано применение сеточного метода с использованием шага сетки аппроксимации в качестве параметра регуляризации, констант Лебега для выбора оптимального распределения узлов сетки, а также алгоритмов вычисления производных. В работе [37]…”

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“…В публикациях [26][27][28][29][30][31][32][33][34][35][36][37] исследовано применение сеточного метода с использованием шага сетки аппроксимации в качестве параметра регуляризации, констант Лебега для выбора оптимального распределения узлов сетки, а также алгоритмов вычисления производных. В работе [37]…”

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Information and Measurement System for Monitoring Beams in Building Structures

Loktionov

2022

Proceedings of the SWSU

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Purpose of research. The development of a method and algorithm for reducing measurements of beam identification parameters in an information and measurement system for monitoring building structures with measurement of deflections and recovery of actual values of beam initial parameters and external load when solving the inverse Cauchy problem.Methods. The solution of the problem is carried out through formulating the transverse bending of the beam according to the Euler – Bernoulli theory using the method of regularization and reduction of measurements by solving the inverse Cauchy problem by means of linear Lagrangian approximation in the procedure of numerical differentiation of the beam deflection function. A methodology is formulated for identifying insignificant beam identification parameters by comparing the deflection of the beam caused by the parameter under study with the sensitivity threshold of measuring instruments. In this case, the modification of the state space of identification parameters with a decrease in its dimension is simulated.Results. The working capability of the formulated experimental calculation method is confirmed by numerical experiment with a load on the beam in the form of a bending moment, concentrated and (or) constant distributed load. It has been established that when identifying insignificant initial parameters and loads acting on the beam, the reduction of measurements increases the accuracy of restoring the beam identification parameters.Conclusion. The developed methodology can be used to improve the accuracy of inspection methods of construction facilities at the stage of experimental and theoretical research.

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Information and Measurement System for Monitoring Beams in Building Structures

Loktionov

2022

Proceedings of the SWSU

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Measuring-polynomial processing of input data of a computer system

Loktionov,

Vatutin

2024

Proceedings of the SWSU

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Purpose of research. The purpose of this study is to solve the problem of restoring the external load on the rack– and-beam structural system and to assess the impact on the accuracy of solving the problem of the error of noisy deflections – constructive input data of the computing system.Methods. The main scientific methods used in this study are methods of modeling and identification of boundary conditions, the grid method of regularization of solving inverse incorrect problems. Measurement reduction and approximation methods, methods for evaluating the quality of input data processing, regularization and approximation algorithms using the Lebesgue grid function, and numerical methods are also used.Results. The main result of this work is two theorems about the external load on a rack-and-beam structural system. The existence and uniqueness of the solution is proved. Also, the results are the formulas of Lagrange multipliers in linear Lagrangian approximation and the optimal plan of coordinates of the nodes of the approximation grid for the equation of deflections of the beam of the fourth and fifth degree with Chebyshev alternance. An assessment of the quality of the approximation of the external load on the rack-and-beam structure by the values of the target parameters was carried out.Conclusion. This article proposes a method for restoring the external load on a rack-and-beam structure using the results of solving the inverse Cauchy problem for the equation of deflections of a beam with minimizing the influence of the error of noisy input data.

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Numerical Differentiation in the Measurement Model

Cited by 2 publications

References 8 publications

Information and Measurement System for Monitoring Beams in Building Structures

Information and Measurement System for Monitoring Beams in Building Structures

Measuring-polynomial processing of input data of a computer system

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