Finite Degradation Structures · Finite degradation structures (FDSs) Operations on FDSs...

Finite Degradation Structures A Unified Framework of Combinatorial Models in Probabilistic Risk/Safety Assessment

PhD candidate: Liu YangSupervisor: Professor Antoine RauzyCo-Supervisor: Associate Professor Cecilia Haskins

Public PhD defense

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

1

www.ntnu.no

Outline

PhD Defense – June 2nd 2020, NTNU

2

Introduction

Background and motivation

Overview of PhD work

Main contributions

Theoretical development

Computer-based implementation

Interesting applications

Conclusion

Background and motivation 3

❑ Reliability and safety analysis aims at evaluating whether the system is reliable or safe

enough to operate.

❑ To evaluate the reliability and safety of a system, we need indicators:

• Scenarios: in what situation the system may fail

• Probabilities: how probable the system may fail

❑ To obtain the indicators, we need to design models:

• Combinatorial models (Fault trees and related formalisms like HiP-HOPS [Papadopoulos 2011],

multistate system approaches [Levitin 2003, Zaitseva 2013], ...)

• State/transition models (Markov chains, Petri nets, Guarded Transition Systems [Rauzy 2008], ...)

Introduction

• Background and motivation

• Overview of PhD work

Main contributions

Conclusion

Papadopoulos, Y., Walker, M., Parker, D., Rüde, E., Hamann, R., Uhlig, A., ... & Lien, R. (2011). Engineering failure analysis and design optimisation with

HiP-HOPS. Engineering Failure Analysis, 18(2), 590-608.

Lisnianski, A., & Levitin, G. (2003). Multi-state system reliability: assessment, optimization and applications (Vol. 6).

Zaitseva, E., & Levashenko, V. (2013). Multiple-valued logic mathematical approaches for multi-state system reliability analysis. Journal of Applied

Logic, 11(3), 350-362.

Rauzy, A. B. (2008). Guarded transition systems: a new states/events formalism for reliability studies. Proceedings of the Institution of Mechanical Engineers,

Part O: Journal of Risk and Reliability, 222(4), 495-505.


Most relevant and most probable ones leading to

the failure of the system

Background and motivation 4

Combinatorial models• Boolean formalisms

• Multistate systems

Scenarios

that cause the failure of system

that don’t cause the failure of system

Minimal failure scenarios

Non-minimal failure scenarios

(showing the least situations that the system fails)Cut sets

Path sets

Minimal cutsets

Failure scenarios

Non-failure scenarios

?

Fault tree analysis, ...

Extended fault trees

Multivalued logic appraoches

Multivalued decision diagrams

Universal generation functions

...

Existing tools

Introduction



Main contributions

Conclusion


Overview of PhD work 5

Introduction



Main contributions

Conclusion

Finite Degradation

Structures

(FDSs)

A unified framework of combinatorial models

1

2

3

• Finite degradation structures (FDSs)

• Operations of FDSs

• Reliability/safety modeling by FDSs

• Assessment of models and accessible results

• Data structure: extended decision diagrams

• Algorithms of calculating indicators

• Modeling language: FDS-ML (textual language)

• Software: LatticeX

• Safety instrumented systems

• Railway signal systems

• Modeling of epistemic uncertainty

• Interface between MBSE and MBSA


Theoretical development

Computer-based

implementation


Theoretical development 6

Introduction

Main contributions

• Theoretical development

Illustrative example

Finite degradation structures (FDSs)

Operations on FDSs

Reliability modeling using FDSs

Accessible results

• Computer-based implementation

• Interesting applications

Modeling of epistemic uncertainty

FDSs as interface between MBSA

and MBSE

Conclusion

Algebraic foundation

Modeling framework


Illustrative example 7

Safety Instrumented System (multistate)

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

According to the standard IEC 61508,

the components of SIS may fail into

different failure modes:

Extracted from ISO/TR12489



Problems

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

• In IEC 61508, the combination of different failure modes are ignored, because its occurrence

probability is often low.

• But, low probability scenarios may be critical to system’s reliability and safety.

• Some interesting scenarios are also ignored:

o This channel is failed-

dangerously.

o By the alarm, you “detect”,

to some extent, the failure of valve.



Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Propose a modeling framework, called Finite Degradation Structures (FDSs), to support the

modeling and the calculations for multistate systems.

ModelsScenarios

Probabilistic indicatorsSystem

Modeling CalculationIndicators

Finite Degradation Structures

(FDSs)

Multistate Multistate Multistate

Critical scenarios:

• Minimal scenarios

• Maximal scenarios

Our solution


Finite degradation structures (FDSs) 10

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Formal definitionFDS

Assign a probability measure 𝑝

𝑝 𝐹𝑑𝑢, 𝑡 = 𝑓𝐹𝑑𝑢 𝑡, … ∈ 0,1

𝑝 𝐹𝑠, 𝑡 = 𝑓𝐹𝑠 𝑡, … ∈ 0,1

𝑝 𝐹𝑑𝑑, 𝑡 = 𝑓𝐹𝑑𝑑 𝑡, … ∈ 0,1

𝑝 𝑊, 𝑡 = 𝑓𝑤 𝑡, … ∈ 0,1

Finite degradation structures (FDSs) 11

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Formal definitionFDS


Operations on FDSs 12

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

▪ Operations are used to describe the

relation between components, i.e. how

the failure of components may lead to

failure of the system.

▪ The operations on FDSs are defined as

surjective mappings:


Monoidal product

⨂

Achieve the composition

of the state spaces of different components.

Cartesian product of sets

Product order

Product measure

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion



Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

=

Domain (product FDS)

(Discrete surjective mapping)

Codomain (FDS)

Monoidal productMonoidal product

⨂

Achieve the composition

of the state spaces of different components.

operation



Operations for safety instrumented system

Notations(Operator and variables)

Truth tables(valuation of the operation) (Hasse diagram)

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


Minimal & maximal scenarios (local)

Minimalstate combinations

of reaching an undesired state

Maximalstate combinations

of staying in an acceptable state

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


Reliability modeling using FDSs 17

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Modeling framework



SyntaxWell-formed formulas

Boolean equations

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Finite degradation

model

SemanticsOperations on FDSs



Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Finite Degradation Model(Expression tree)

𝑆𝑦𝑠𝑡𝑒𝑚

𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

⟺


20Accessible results

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Probabilistic

indicators

State probability:

Scenarios

Set of scenarios:

Minimal & maximal scenarios:

Conditional probability:

Conditional scenarios:

Sensitivity:


Accessible results 21



𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Scenarios

Degradation orders can propagate bottom-up

through the operations in the model.

Probabilistic indicators

Probabilities can propagate bottom-up through the

operations in the model.

Inputs

FDSs equipped with probability distributions at

component level.


Inputs


component level.




𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Scenarios










𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

C_s: a set of conditions that limit the valuation of

certain state variables.

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


Inputs


component level.




𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion




Scenarios







𝑆𝐶1

𝑆𝐶2

𝐺𝑆

𝐺𝑉

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

Scenarios

▪ Maximal scenarios of 𝑆𝑦𝑠𝑡𝑒𝑚 = 𝑊

▪ Minimal scenarios of 𝑆𝑦𝑠𝑡𝑒𝑚 = 𝐹𝑑𝑑

The combination of

different failure

modes appears in

minimal scenarios.


Computer-based implementation 26

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


Computer-based implementation 27

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

FDS-ML: textual modeling language for designing finite degradation models

LatticeX: a small tool developed in Python to perform the required calculations


Yang, L., & Rauzy, A. (2019, October). FDS-ML: A New Modeling Formalism for Probabilistic Risk and Safety Analyses. In International Symposium on

Model-Based Safety and Assessment (pp. 78-92). Springer, Cham.

Interesting applications 28

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


Epistemic uncertainty:

The state of component/system becomes

uncertain due to the lack of detections.


29

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion


FDSs as interface between MBSA and MBSE

MBSE (Model-Based Systems Engineering)

MBSA (Model-Based Safety Assessment)

Synchronize

▪ Structural behavior (hierarchical decomposition)▪ Functional behavior (states and mappings)


Yang, L., Rauzy, A., & Haskins, C. (2018, October). Finite degradation structures: a formal framework to support the interface between MBSE and MBSA. In 2018

IEEE International Systems Engineering Symposium (ISSE) (pp. 1-6). IEEE.

Conclusion 30

Introduction

Main contributions




Operations on FDSs


Accessible results





and MBSE

Conclusion

❑ We propose a modeling framework, called finite degradation structures

(FDSs), seen as the unified framework of reliability combinatorial models for

both Boolean and multistate systems.

❑ The most highlighted part of FDSs is the extension of the notion of minimal

cut/path sets into multistate systems, i.e. as minimal/maximal scenarios.

Future works:

• Completing the theoretical framework, including the calculation of importance

measures for multistate systems [Zaitseva 2012], the coherency problems, etc.

• Enlarging the modeling library

• Improving the efficiency of the calculation algorithms [Rauzy 2019]

• Upgrading the software LatticeX

Zaitseva, E. (2012). Importance analysis of a multi-state system based on multiple-valued logic methods. In Recent Advances in System

Reliability (pp. 113-134). Springer, London.

Rauzy, A., & Yang, L. (2019). Decision Diagram Algorithms to Extract Minimal Cutsets of Finite Degradation Models. Information, 10(12), 368.


Thanks.


Academic publications 31

1. Reliability modeling using finite degradation structures (Conference paper)

Liu Yang and Antoine Rauzy

3rd International Conference on System Reliability and Safety (ICSRS 2018),

Barcelona, November 2018

2. Finite degradation structures: a formal framework to

support the interface between MBSE and MBSA(Conference paper)

Liu Yang, Antoine Rauzy and Cecilia Haskins

2018 IEEE International Systems Engineering Symposium (ISSE), Rome, October

2018

3. Reliability assessment of phased-mission systems with

AltaRica 3.0(Conference paper)

Michel Batteux, Tatiana Prosvirnova, Antoine Rauzy and Liu Yang

29th European Safety and Reliability Conference (ESREL 2019), Hanover,

September 2019

4. Finite degradation analysis of multiple safety instrumented

systems(Conference paper)

Liu Yang, Antoine Rauzy and Mary Ann Lundteigen

29th European Safety and Reliability Conference (ESREL 2019), Hanover,

September 2019

5. FDS-ML: a new modeling formalism for probabilistic risk

and safety analyses(Conference paper)


6th International Symposium on Model-Based Safety and Assessment (IMBSA

2019), Thessaloniki, October 2019

6. Model synthesis using Boolean expression diagrams(Journal paper)


Reliability Engineering & System Safety, 2019.

7. Finite degradation structuresAntoine Rauzy and Liu Yang

Journal of Applied Logic, November 2019.

8. Decision diagram algorithms to extract minimal cutsets

of finite degradation modelsAntoine Rauzy and Liu Yang

Information, November 2019.

9. Epistemic space of degradation processesLiu Yang and Antoine Rauzy

Under review by Journal of Applied Non-Classical Logics, submitted in July

2019.

Finite Degradation Structures · Finite degradation structures (FDSs) Operations on FDSs...

Documents

Transcript of Finite Degradation Structures · Finite degradation structures (FDSs) Operations on FDSs...