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


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.


Safety system engineering System reliability Space fault network System fault evolution 



Space fault network


System fault evolution process


Fault evolution process


Space fault tree


General space fault network


Multidirectional ring space fault network


Unidirectional ring space fault network


Edge event


Process event


Target event

EP, means PEO, including FP and FPD

Event probability


Probability of event occurrence


Fault probability/fault probability distribution


Transfer probability


Model span


Model width


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


No relationship URSFN


Or relationship URSFN


And relationship URSFN


Mixed relationship URSFN


Cause event


Result event


Target fault evolution process


Order fault evolution process


Unit fault evolution process


Incremental fault evolution process


Decrement fault evolution process

List of symbols

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

System of space fault network



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

Node set of the network


Fault probability/fault probability distribution



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

Connect set of the network


Cause event


Result event



E = {e1,e2,…,eF}

Route set of the network


Transfer probability



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

Span set of the network



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

Width set of the network


Boolean algebra system


Number of fault cycles


Target event


Event set of cyclic structure


The iith event in δ


Connect set in δ


The jjth transfer probability inδ


Value of influencing factors


Symbols of factors


Order of system fault evolution process


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


The first element in the example


The second elements in the example



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.


  1. 1.
    Qiu J, Zhang M (2018) Research on the evolution of knowledge system under different trust environments in OKC. Oper Res Manag Sci 27(3):175–183Google Scholar
  2. 2.
    Ren C, Zhai G, Li S-S, Chen W, Wu Y (2016) Systematic evolution of economic growth in China’s national autonomous areas. Explor Econ Probl 10:121–129Google Scholar
  3. 3.
    Sun B, Xu X, Yao H (2016) Study on the evolution of innovation ecosystem based on the framework of multi-level perspectives. Stud Sci Sci 34(8):1244–1254Google Scholar
  4. 4.
    Liu X, Sun Z, Sun Q (2016) Urban traffic system evolution based on logistic model. J Chongqing Jiaotong Univ (Natl Sci) 35(1):156–161Google Scholar
  5. 5.
    Jihong W, Chunmei C, Xianrui S (2015) A research on the enterprise system evolution based on the mutation theory. Sci Res Manag 36(S1):279–282Google Scholar
  6. 6.
    Barafort B, Shrestha A, Cortina S, Renault A (2018) A software artefact to support standard-based process assessment: evolution of the TIPA framework in a design science research project. Comput Stand Interfaces. Google Scholar
  7. 7.
    Zylbersztajn D (2017) Agribusiness systems analysis: origin, evolution and research perspectives. Revista de Administrao 52(1):114–117CrossRefGoogle Scholar
  8. 8.
    Fuxjager MJ, Schuppe ER (2018) Androgenic signaling systems and their role in behavioral evolution. J Steroid Biochem Mol Biol. Google Scholar
  9. 9.
    Getir S, Grunske L, van Hoorn A et al (2018) Supporting semi-automatic co-evolution of architecture and fault tree models. J Syst Softw 142:115–135CrossRefGoogle Scholar
  10. 10.
    Harkat M-F, Mansouri M, Nounou M et al (2019) Fault detection of uncertain nonlinear process using interval-valued data-driven approach. Chem Eng Sci. Google Scholar
  11. 11.
    Germán-Salló Z, Strnad G (2018) Signal processing methods in fault detection in manufacturing systems. Procedia Manuf 22:613–620CrossRefGoogle Scholar
  12. 12.
    Delpha C, Diallo D, Al Samrout H et al (2018) Multiple incipient fault diagnosis in three-phase electrical systems using multivariate statistical signal processing. Eng Appl Artif Intell 73:68–79CrossRefGoogle Scholar
  13. 13.
    Shahnazari H, Mhaskar P, House JM et al (2019) Modeling and fault diagnosis design for HVAC systems using recurrent neural networks. Comput Chem Eng 126:189–203CrossRefGoogle Scholar
  14. 14.
    Shahnazari H, Mhaskar P (2018) Distributed fault diagnosis for networked nonlinear uncertain systems. Comput Chem Eng 115:22–33CrossRefzbMATHGoogle Scholar
  15. 15.
    Wang R, Edgar TF, Baldea M et al (2018) A geometric method for batch data visualization, process monitoring and fault detection. J Process Control 67:197–205CrossRefGoogle Scholar
  16. 16.
    Calderon-Mendoza E, Schweitzer P, Weber S (2019) Kalman filter and a fuzzy logic processor for series arcing fault detection in a home electrical network. Int J Electr Power Energy Syst 107:251–263CrossRefGoogle Scholar
  17. 17.
    Zhang Y, Wang Z, Ma L et al (2019) Annulus-event-based fault detection, isolation and estimation for multirate time-varying systems: applications to a three-tank system. J Process Control 75:48–58CrossRefGoogle Scholar
  18. 18.
    Sonoda D, de Souza ACZ, da Silveira PM (2018) Fault identification based on artificial immunological systems. Electr Power Syst Res 156:24–34CrossRefGoogle Scholar
  19. 19.
    Sánchez-Fernández A, Baldán FJ, Sainz-Palmero GI et al (2018) Fault detection based on time series modeling and multivariate statistical process control. Chemom Intell Lab Syst 182:57–69CrossRefGoogle Scholar
  20. 20.
    Sakthivel R, Joby M, Wang C et al (2018) Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults. Appl Math Comput 332:425–436MathSciNetGoogle Scholar
  21. 21.
    Leung AC-S, Sum PF, Ho K (2011) The effect of weight fault on associative networks. Neural Comput Appl 20(1):113–121CrossRefGoogle Scholar
  22. 22.
    Yari M, Bagherpour R, Jamali S, Shamsi R (2016) Development of a novel flyrock distance prediction model using BPNN for providing blasting operation safety. Neural Comput Appl 27(3):699–706CrossRefGoogle Scholar
  23. 23.
    Cui T-J, Ma Y-D (2013) Research on multi-dimensional space fault tree construction and application. China Saf Sci J 23(4):32–37Google Scholar
  24. 24.
    Cui T-J, Li S-S (2018) Deep learning of system reliability under multi-factor influence based on space fault tree. Neural Comput Appl. Google Scholar
  25. 25.
    Cui T-J, Li S-S (2018) Study on the construction and application of discrete space fault tree modified by fuzzy structured element. Clust Comput. Google Scholar
  26. 26.
    Cui T-J, Wang P-Z, Ma Y-D (2016) Inward analysis of system factor structure in 01 space fault tree. Syst Eng Theory Pract 36(8):2152–2160Google Scholar
  27. 27.
    Cui T-J, Li S-S (2017) Study on the relationship between system reliability and influencing factors under big data and multi-factors. Clust Comput. Google Scholar
  28. 28.
    Li S-S, Cui T-J, Liu J (2017) Study on the construction and application of cloudization space fault tree. Clust Comput. Google Scholar
  29. 29.
    Cui T-J, Wang P-Z, Li S-S (2017) The function structure analysis theory based on the factor space and space fault tree. Clust Comput 20(2):1387–1398CrossRefGoogle Scholar
  30. 30.
    Li S-S, Cui T-J, Liu J (2018) Research on the clustering analysis and similarity in factor space. Int J Comput Syst Sci Eng 33(5):397–404Google Scholar
  31. 31.
    Cui T-J, Li S-S, Zhu B-Y (2019) Construction space fault network and recognition network structure characteristic. Appl Res Comput 36(8):1–5Google Scholar
  32. 32.
    Cui T-J, Li S-S, Zhu B-Y (2018) Multidirectional ring network structure with one-way ring and its fault probability calculation. China Saf Sci J 28(7):19–24Google Scholar

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

Personalised recommendations