1 Public PhD defense Finite Degradation Structures A Unified Framework of Combinatorial Models in Probabilistic Risk/Safety Assessment PhD candidate: Liu Yang Supervisor: Professor Antoine Rauzy Co-Supervisor: Associate Professor Cecilia Haskins PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Outline 2 Introduction Background and motivation Overview of PhD work Main contributions Theoretical development Computer-based implementation Interesting applications Conclusion PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Background and motivation 3 Introduction ❑ Reliability and safety analysis aims at evaluating whether the system is reliable or safe • Background and motivation enough to operate. • Overview of PhD work Main contributions ❑ To evaluate the reliability and safety of a system, we need indicators : Conclusion • 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], ...) 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. PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Background and motivation 4 Introduction • Background and motivation • Overview of PhD work • Boolean formalisms Combinatorial models Main contributions • Multistate systems Conclusion Non-minimal failure scenarios that cause the failure of system Minimal failure scenarios Cut sets Scenarios (showing the least situations that the system fails) Failure scenarios Fault tree analysis, ... Most relevant and most probable ones leading to the failure of the system Existing tools Extended fault trees that don’t cause the Multivalued logic appraoches Minimal cutsets Multivalued decision diagrams failure of system Universal generation functions ? ... Path sets Non-failure scenarios PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Overview of PhD work 5 Introduction • Background and motivation • Overview of PhD work • Finite degradation structures (FDSs) 1 • Theoretical development Operations of FDSs Main contributions • Reliability/safety modeling by FDSs • Assessment of models and accessible results Conclusion Finite Degradation Structures • Data structure: extended decision diagrams Computer-based 2 • Algorithms of calculating indicators (FDSs) implementation • Modeling language: FDS-ML (textual language) • A unified framework of Software: LatticeX combinatorial models • Safety instrumented systems 3 Interesting applications • Railway signal systems • Modeling of epistemic uncertainty • Interface between MBSE and MBSA PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Theoretical development 6 Introduction Main contributions Algebraic foundation • Theoretical development Illustrative example Finite degradation structures (FDSs) Modeling framework 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 PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Illustrative example 7 Introduction Main contributions Safety Instrumented System (multistate) • Theoretical development Illustrative example Finite degradation structures (FDSs) Operations on FDSs According to the standard IEC 61508, Reliability modeling using FDSs the components of SIS may fail into Accessible results different failure modes : • Computer-based implementation • Interesting applications Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE Conclusion Extracted from ISO/TR12489 PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Illustrative example 8 Introduction Problems Main contributions • Theoretical development • In IEC 61508, the combination of different failure modes are ignored , because its occurrence Illustrative example probability is often low . Finite degradation structures (FDSs) Operations on FDSs • But, low probability scenarios may be critical to system’s reliability and safety. Reliability modeling using FDSs • Accessible results Some interesting scenarios are also ignored: • Computer-based implementation • Interesting applications Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE o This channel is failed- dangerously. Conclusion By the alarm, you “detect”, o to some extent, the failure of valve. PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Illustrative example 9 Introduction Main contributions Our solution • Theoretical development Illustrative example Finite degradation structures (FDSs) Propose a modeling framework, called Finite Degradation Structures (FDSs), to support the Operations on FDSs modeling and the calculations for multistate systems. Reliability modeling using FDSs Accessible results • Computer-based implementation • Interesting applications Multistate Multistate Multistate Modeling of epistemic uncertainty FDSs as interface between MBSA Modeling Calculation Probabilistic indicators and MBSE System Models Indicators Scenarios Conclusion Critical scenarios: Finite Degradation Structures • Minimal scenarios (FDSs) • Maximal scenarios PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Finite degradation structures (FDSs) 10 Introduction Main contributions Formal definition • Theoretical development FDS Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results • Computer-based implementation • Interesting applications Modeling of epistemic uncertainty Assign a probability measure 𝑞 FDSs as interface between MBSA and MBSE 𝑞 𝐺𝑒𝑣, 𝑢 = 𝑔 𝐺𝑒𝑣 𝑢, … ∈ 0,1 Conclusion 𝑞 𝐺𝑡, 𝑢 = 𝑔 𝐺𝑡 𝑢, … ∈ 0,1 𝑞 𝐺𝑒𝑒, 𝑢 = 𝑔 𝐺𝑒𝑒 𝑢, … ∈ 0,1 𝑞 𝑋, 𝑢 = 𝑔 𝑥 𝑢, … ∈ 0,1
Finite degradation structures (FDSs) 11 Introduction Main contributions Formal definition • Theoretical development FDS 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 PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Operations on FDSs 12 Introduction Main contributions • Theoretical development ▪ Operations are used to describe the Illustrative example relation between components, i.e. how Finite degradation structures (FDSs) the failure of components may lead to Operations on FDSs Reliability modeling using FDSs failure of the system. Accessible results ▪ The operations on FDSs are defined as • Computer-based implementation • Interesting applications surjective mappings : Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE Conclusion
Operations on FDSs 13 Introduction Monoidal product 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 Achieve the composition and MBSE Cartesian product of sets of the state spaces of different components. Conclusion Product order Product measure PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Operations on FDSs 14 Introduction Monoidal product Monoidal product Main contributions • Theoretical development Illustrative example Finite degradation structures (FDSs) Operations on FDSs operation Reliability modeling using FDSs = Accessible results ⨂ • Computer-based implementation • Interesting applications (Discrete surjective mapping) Modeling of epistemic uncertainty FDSs as interface between MBSA Achieve the composition and MBSE Domain (product FDS) Codomain (FDS) of the state spaces of different components. Conclusion PhD Defense – June 2 nd 2020, NTNU www.ntnu.no
Operations on FDSs 15 Introduction Operations for safety instrumented system 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 Notations Truth tables (Operator and variables) (valuation of the operation) (Hasse diagram)
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