基于功能空间理论的系统诊断参数集定义

Q3 Mathematics
V. Senchenkov, D. Absalyamov, D. Avsyukevich
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引用次数: 1

摘要

本文考虑了复杂技术系统的一组诊断参数形成的方法和数学装置的发展,其内容包括使用泛函空间理论处理系统输出过程的轨迹。输出变量的轨迹被认为是勒贝格可测函数。它确保了一种统一的方法来获得诊断参数,而不管这些变量的物理性质和它们的一组跳变(轨迹的有限不连续)。它充分考虑到结构的复杂性、系统运行的各种物理原理和算法。在轨迹集上定义了可测方形勒贝格可积函数的因子空间结构(空间)。这些空间的性质允许将轨迹分解为相互正交方向的可数集合,并以收敛级数的形式表示它们。一组诊断参数的选择作为一个有序序列的分解系数的轨迹成傅立叶级数的部分和被证实。给出了用正交勒让德基将轨迹分解为傅立叶级数的部分和时,与初始变量相比改进的系统诊断参数集的形成过程。提出了一种确定该集合幂的数值方法。揭示了从系统振动过程中获取诊断信息的新途径。在振动轨迹集上定义了连续平方黎曼可积函数(空间)的空间结构。由于它们是上述因子空间中的子空间,因此振动轨迹变换的一般方法基础保持不变。然而,选择诊断参数的算法组件变得更加具体和可观察。通过实现一个用正交三角基分解振动轨迹的数值过程来证明这一点,振动轨迹包含在空间中。给出了振动过程实验研究结果的处理方法,并在此基础上对系统某控制点的诊断参数子集进行了设置。本文的材料是对获取复杂系统技术条件信息理论的贡献。所提出的发展的应用价值是它们用于自动诊断工具的合成算法支持的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Definition of Set of diagnostic Parameters of System based on the Functional Spaces Theory
The development of methodical and mathematical apparatus for formation of a set of diagnostic parameters of complex technical systems, the content of which consists of processing the trajectories of the output processes of the system using the theory of functional spaces, is  considered in this paper. The trajectories of the output variables are considered as Lebesgue measurable functions. It ensures a unified approach to obtaining diagnostic parameters regardless  a physical nature of these variables and a set of their jump-like changes (finite discontinuities of trajectories). It adequately takes into account a complexity of the construction, a variety of physical principles and algorithms of systems operation. A structure of factor-spaces of measurable square Lebesgue integrable functions, ( spaces) is defined on sets of trajectories. The properties of these spaces allow to decompose the trajectories by the countable set of mutually orthogonal directions and represent them in the form of a convergent series. The choice of a set of diagnostic parameters as an ordered sequence of coefficients of decomposition of trajectories into partial sums of Fourier series is substantiated. The procedure of formation of a set of diagnostic parameters of the system, improved in comparison with the initial variants, when the trajectory is decomposed into a partial sum of Fourier series by an orthonormal Legendre basis, is presented. A method for the numerical determination of the power of such a set is proposed. New aspects of obtaining diagnostic information from the vibration processes of the system are revealed. A structure of spaces of continuous square Riemann integrable functions ( spaces) is defined on the sets of vibrotrajectories. Since they are subspaces in the afore mentioned factor-spaces, the general methodological bases for the transformation of vibrotrajectories remain unchanged. However, the algorithmic component of the choice of diagnostic parameters becomes more specific and observable. It is demonstrated by implementing a numerical procedure for decomposing vibrotrajectories by an orthogonal trigonometric basis, which is contained in spaces. The processing of the results of experimental studies of the vibration process and the setting on this basis of a subset of diagnostic parameters in one of the control points of the system is provided. The materials of the article are a contribution to the theory of obtaining information about the technical condition of complex systems. The applied value of the proposed development is a possibility of their use for the synthesis of algorithmic support of automated diagnostic tools.
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
发文量
0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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