基于有限马尔可夫链嵌入法的智慧路灯系统联合Signature计算

doi:10.12005/orms.2023.0288

摘要/Abstract

摘要： 智慧路灯是现代化建设背景下的重要基础设施载体,集照明设备和传感设备于一体,并且可以根据实际应用的场景布放各种功能模块。城市管理部门需要根据不同路段的车道类型,选择适合的路灯型号和铺设方式。为了描述路段上由智慧路灯构成的可靠性系统的结构特性,本文构建了共用部件的线形n中取连续k型冗余系统模型,并针对这类系统给出了基于有限马尔可夫链嵌入法的联合Signature计算方法。和基于定义的方法相比,该方法有统一的表达式,不仅提高了计算效率,还降低了计算的复杂度。最后,本文通过算例演示了该方法的运算效率,并讨论了其可能的应用与改进。

关键词: 联合Signature, n中取连续k型系统, 有限马尔可夫链嵌入法, 智慧路灯

Abstract: With the development of science and technology, equipment systems gradually present the characteristics of large-scale and complicated, which greatly increases the system failure risk, and the system reliability problem begins to attract people's attention. As a public infrastructure carrier integrating lighting equipment and sensing equipment, smart street lights can collect road data in real time and monitor road conditions through various sensors, and they can also manage vehicle flow in real time through lighting equipment, which is of great significance to the planning and construction of smart cities in China. Smart street lights can deploy different lighting modules and sensing modules according to the actual application scenario to achieve different functions such as lighting, advertising (LED screen), broadcasting (sound column), Wi-Fi, monitoring and alarm, and these modules may have different demand amounts and coverage. The city management department needs to choose the appropriate street light type and laying method according to the lane type of different road segments.
In recent years, there have been numerous studies on smart street light systems at home and abroad, including system hardware and software design and implementation, energy saving strategies and control algorithms, related technical means and empirical research and so on. At present, researchers have realized the importance of reliability in the study of smart street light systems, but there is still a large gap in the system modeling and analysis based on reliability. In fact, for a smart street light system on a certain road segment, in order to study the related reliability problems, it can be regarded as several linear consecutive-k-out-of-n type redundant systems sharing components. In order to better characterize the structural properties of such systems, this paper presents a computational method for joint signature of two linear consecutive-k-out-of-n type redundant systems sharing components based on the finite Markov chain imbedding approach (FMCIA). This method can be used for reliability analysis and structural comparison of such systems, and will provide theoretical basis for management decision-making of road planning.
Signature theory is an important tool for describing system structure in reliability theory. The proposing of signature measures overcomes the difficulty of characterizing the structure of large complex systems, and provides a way to compare system structures through stochastic orders. Computation of measures has always been a hot and difficult problem in the signature field. Existing methods include definition method, path/cut set method, reliability method, binary decision diagram method, generating function method, Markov process method and module decomposition method and so on. Each method has its advantages, disadvantages and application scopes. Among them, the reliability method uses the one-one relationship between signature and system reliability to transform the signature computational problem into a reliability computational problem, and its computational efficiency depends on efficiency of the reliability computational method. For the linear consecutive-k-out-of-n redundant systems sharing components studied in this paper, if traditional definition method is applied to computing their joint signature, the process of system state change needs to be considered under n! different orderings of component failures, which makes computational efficiency very low for large n. Therefore, this paper presents a computational method of the joint signature based on the FMCIA. The idea of this method is to obtain the joint reliability function of the system by using the FMCIA, and then calculate the joint signature according to the relationship between the joint signature and the joint reliability function.
The FMCIA is a method to transform the reliability problem into finite-state Markov chain. With outstanding advantages in system reliability computation and unified analytical expression, this method is widely used in reliability computation, especially in the reliability computation of linear/circular consecutive-k-out-of-n type redundant systems and its derivative systems. In recent years, in addition to the common k-out-of-n: F/G systems and (m-) consecutive-k-out-of-n: F/G systems (with sparse d), this method has also been used to calculate the reliability of many other consecutive-k-out-of-n type redundant systems. When n is very large, this method can also simplify the computation by eigenvalue decomposition, which makes it more efficient in computing the reliability measures.
To sum up, this paper studies the reliability problems of smart street light systems by using a model of linear consecutive-k-out-of-n systems sharing components, and presents a new method to calculate the joint signature based on the FMCIA. The main contributions of this paper are as follows: On the one hand, for the smart street light systems composed of lighting equipment and sensing equipment, a model of a linear consecutive-k₁-out-of-n system and a consecutive-k₂-out-of-n system that share components are established, which shortens the distance between the actual demand for reliability analysis of smart street light systems and relevant reliability theories; On the other hand, a computational method based on the finite Markov chain imbedding approach is proposed to solve the computational problem of the joint signature for these redundant system models, which is more efficient than the traditional definition method. This method effectively reduces the computational complexity and provides a more applicable theoretical tool for the computation of the joint signature. Its possible applications include such systems,but are not limited to them and they can be widely used in the system reliability analysis in fields like wireless communication, pipeline transportation, quality control, pattern recognition and many others in the future.

Key words: joint signature, consecutive-k-out-of-n type system, finite Markov chain imbedding approach(FMCIA), smart street light

中图分类号:

O213.2

易鹤, 李想, 路靖雯. 基于有限马尔可夫链嵌入法的智慧路灯系统联合Signature计算[J]. 运筹与管理, 2023, 32(9): 79-85.

YI He, LI Xiang, LU Jingwen. Computation of Joint Signature for A Smart Street Light System Based on Finite Markov Chain Imbedding Approach[J]. Operations Research and Management Science, 2023, 32(9): 79-85.

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