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

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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.

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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

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

System of space fault network

\(v_{i}\) :

Node

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

Node set of the network

p i :

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

e f :

Route

E = {e1,e2,…,eF}:

Route set of the network

p c→r :

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

x k :

Value of influencing factors

d k :

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

X 1 :

The first element in the example

X 2 :

The second elements in the example

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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.

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Authors and Affiliations

  1. College of Safety Science and Engineering, Liaoning Technical University, Fuxin, 123000, Liaoning, China

    Tie-jun Cui

  2. Tunnel & Underground Structure Engineering Center of Liaoning, Dalian Jiaotong University, Dalian, 116028, Liaoning, China

    Tie-jun Cui

  3. School of Business Administration, Liaoning Technical University, Huludao, 125105, Liaoning, China

    Sha-sha Li

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  1. Tie-jun Cui
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Correspondence to Tie-jun Cui.

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Cui, Tj., Li, Ss. Research on basic theory of space fault network and system fault evolution process. Neural Comput & Applic 32, 1725–1744 (2020). https://doi.org/10.1007/s00521-019-04247-0

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