Approximation methods for the actual trajectory of load carried by overhead crane to the required one: A comparative analysis

Корытов, М. С.; Щербаков, С. В.; Shershneva, E. O.; Breus, I.V.

doi:10.5937/jsscm1602045k

Cited by 3 publications

(1 citation statement)

References 4 publications

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“…To improve the efficiency of information and measurement systems (IMS), methods for approximation of functions and numerical differentiation are being improved (Cheney and Kincaid 2013, Chekushkin et al 2015, Korytov et al 2016, Loktionov 2017a). These methods in technical applications are used in solving inverse problems to calculate the non-measurable parameters of the force element of the mechanical structure and the initial conditions that can depend on the external load (Loktionov 2007, Loktionov 2017b.…”

Section: Introductionmentioning

confidence: 99%

Information Measuring System of Numerical Differentiation for the Analysis of Elements of Mechanical Structures

Loktionov¹

2018

JSSCM

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In this paper, the theory of the Lagrange polynomial approximation of a directly non-measurable characteristic of an element of a mechanical structure by means of an information-measuring system of numerical differentiation is refined. It is shown how to obtain the maximal accuracy of approximation on the basis of the theory of inverse problems and the method of reduction of measurements. For a cantilever beam loaded with concentrated force at its free end, a method has been developed for the experimental and calculated determination of the bending moment at the fixed end of the beam. The basis of the method is the procedure for the optimal placement of sensors and transformation of sensor output signals, if the length of the beam and the initial parameters of the elastic line (lateral displacement and the angle of rotation on the support) are not accurate.

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Section: Introductionmentioning

confidence: 99%

Information Measuring System of Numerical Differentiation for the Analysis of Elements of Mechanical Structures

Loktionov¹

2018

JSSCM

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Numerical Differentiation in the Measurement Model

Loktionov

2019

Meas Tech

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Chebyshev Alternance when Approximating Initial Conditions of the Inverse Cauchy Problem

Loktionov

2022

Proceedings of the SWSU

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Purpose of research. The work is devoted to a range of questions related to Cauchy problem on the segment of real axis with the application of the inverse Cauchy problem, in which real constants are initial conditions which are optimally restored according to experimental or tabular values of the solution of the differential equation. The object of the study is an information-measuring system, in which approximate values of initial conditions are calculated from discrete function values of Cauchy problem solving.Methods. The following problems are solved for this purpose: parameters of measuring section placement on the investigated object and approximation grid on measuring section are developed. Characteristics of recovery accuracy of initial conditions of the task are formulated.Results. An experimental-calculated method of determining initial conditions in the inverse Cauchy problem is proposed. It is based on the concept of objective function of regularization of the problem. Task regularization parameter in the form of minimum value by Lebesgue function is proposed.Conclusion. The reaction of uniformly approximating method of the initial conditions of the inverse Cauchy problem to the deviation of the approximation grid coordinates nodes from the coordinates of Chebyshev alternance was described. Graphs of method reaction to deviation of grid pitch from optimal pitch are given.

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Approximation methods for the actual trajectory of load carried by overhead crane to the required one: A comparative analysis

Cited by 3 publications

References 4 publications

Information Measuring System of Numerical Differentiation for the Analysis of Elements of Mechanical Structures

Information Measuring System of Numerical Differentiation for the Analysis of Elements of Mechanical Structures

Numerical Differentiation in the Measurement Model

Chebyshev Alternance when Approximating Initial Conditions of the Inverse Cauchy Problem

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