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Research on basic theory of space fault network and system fault evolution process

  • Tie-jun CuiEmail author
  • Sha-sha Li
Deep Learning for Big Data Analytics
  • 31 Downloads

Abstract

To describe the system fault evolution process, the space fault network theory is proposed. Space fault network theory is the third stage of space fault tree theory. The paper introduces the basic research results of space fault network. The basic ideas, basic definitions and corresponding physical meanings of space fault network are discussed. The properties, structure and space fault tree transformation method of space fault network are further studied. The characteristics of the system fault evolution process and its four elements are discussed. The representation methods of space fault network for system fault evolution process are presented. The transformation methods of the general space fault network and multidirectional ring space fault network into space fault tree are given and studied. In particular, the classification and characteristics of unidirectional ring space fault network are studied in detail. Based on the system fault evolution process of the example, we conducted a qualitative analysis, and a space fault network is established and transformed. At the same time, a quantitative analysis is carried out according to the derivation process of the transformation of multidirectional ring space fault network. The results show that the space fault network can effectively describe and analyze the system fault evolution process. This paper has solved some basic problems of system fault evolution process, but more complicated situations need further research.

Keywords

Safety system engineering System reliability Space fault network System fault evolution 

Abbreviations

SFN

Space fault network

SFEP

System fault evolution process

FEP

Fault evolution process

SFT

Space fault tree

GSFN

General space fault network

MRSFN

Multidirectional ring space fault network

URSFN

Unidirectional ring space fault network

EE

Edge event

PE

Process event

TE

Target event

EP, means PEO, including FP and FPD

Event probability

PEO

Probability of event occurrence

FP/FPD

Fault probability/fault probability distribution

TP

Transfer probability

MS

Model span

MW

Model width

MRSFN with URSFN

Multidirectional ring space fault network with the unidirectional ring space fault network

NRURSFN

No relationship URSFN

ORURSFN

Or relationship URSFN

ARURSFN

And relationship URSFN

MRURSFN

Mixed relationship URSFN

CE

Cause event

RE

Result event

TFEP

Target fault evolution process

OFEP

Order fault evolution process

UFEP

Unit fault evolution process

IFEP

Incremental fault evolution process

DFEP

Decrement fault evolution process

List of symbols

\(W = (V,L,R,B,B)\)

System of space fault network

\(v_{i}\)

Node

\(V = \{ v_{1} ,\,v_{2} , \ldots ,v_{I} \}\)

Node set of the network

pi

Fault probability/fault probability distribution

\(l_{j}\)

Connect

\(L = \{ l_{1} ,\,l_{2} , \ldots ,l_{J} \}\)

Connect set of the network

c

Cause event

r

Result event

ef

Route

E = {e1,e2,…,eF}

Route set of the network

pcr

Transfer probability

\(r_{o}\)

Span

\(R = \{ r_{1} ,\,r_{2} , \ldots ,r_{O} \}\)

Span set of the network

\(b_{m}\)

Width

\(B = \{ b_{1} ,\,b_{2} , \ldots ,b_{M} \}\)

Width set of the network

B

Boolean algebra system

k

Number of fault cycles

\(\eta\)

Target event

δ

Event set of cyclic structure

ii

The iith event in δ

ζ

Connect set in δ

jj

The jjth transfer probability inδ

xk

Value of influencing factors

dk

Symbols of factors

N

Order of system fault evolution process

\(W_{\text{fault}}\)

System fault evolution process

O = {o1, o2…, oI,}

Object set

S = {s1, s2,…, sII,}

State set

X = {x1, x2,…,xM}

Factor set

W = (O, S, L, X)

System of space fault network

X1

The first element in the example

X2

The second elements in the example

Notes

Acknowledgements

The authors wish to thank all his friends for their valuable critics, comments and assistances on this paper. This study was partially supported by the grants (Grant Nos. 51704141, 2017YFC1503102) from the Natural Science Foundation of China.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Safety Science and EngineeringLiaoning Technical UniversityFuxinChina
  2. 2.Tunnel & Underground Structure Engineering Center of LiaoningDalian Jiaotong UniversityDalianChina
  3. 3.School of Business AdministrationLiaoning Technical UniversityHuludaoChina

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