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SMT-based Analysis of Reli liability Architectures Alessandro - - PowerPoint PPT Presentation

Sep 15, 2022 274 likes •912 views

SMT-based Analysis of Reli liability Architectures Alessandro Cimatti Fondazione Bruno Kessler, Trento, Italy Joint work with Marco Bozzano and Cristian Mattarei Safety Critical Systems a system whose safety cannot be shown solely by test,

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SMT-based Analysis of Reli liability Architectures

Alessandro Cimatti

Fondazione Bruno Kessler, Trento, Italy

Joint work with Marco Bozzano and Cristian Mattarei

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Safety Critical Systems

“a system whose safety cannot be shown solely by test, whose logic is difficult to comprehend without the aid of analytical tools… …and that might directly or indirectly contribute to put human lives at risk, damage the environment, or cause big economical losses” [SAE ARP4754]

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Power system: …in a perfect world

Engine +

  • 3
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Power system: …in real world

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Reliability Improvement

  • How to improve reliability?
  • Redundancy is one of the fundamental solutions
  • Multiple replicas of components
  • Can act as backup
  • Adopted in many critical system design such as:
  • Computer and communication systems
  • Electric power transmission and distribution system
  • Rail and Road transportation systems
  • Water, Oil and Gas distribution
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SLIDE 6

A classification of Redundancy

  • Hot stand-by: redundant components are powered

and completely functional at the same time

  • Warm stand-by: redundant components are in an

idle state, and they become functional only when it is necessary

  • Cold stand-by: similar to warm stand-by, but

redundant components are turned off rather than being idle

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Our goal

  • Given a selected form of redundancy, what are its

features?

  • How to quantify reliability?
  • In practice, many forms of redundancy are possible
  • Which one is best?
  • Currently, this is a manual process!
  • In this talk:
  • SMT-based analysis of redundancy architectures
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SLIDE 8

Outline

  • Architectural Design in Critical Systems
  • Redundant Systems
  • Reliability Analysis
  • Automated Approaches
  • EUF modeling and Fault Tree Analysis
  • Efficient Analysis via Predicate Abstraction
  • Conclusion

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  • Increase reliability for critical design
  • Usage of redundant scheme (e.g. Triple Modular Redundancy)
  • Hard to analyze and optimize system reliability

Nominal architecture Redundant architecture

Redundant systems definition: TMR

[Abraham74]

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Triple Modular Redundancy: Possible Patterns

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1 voter 2 voters 3 voters

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TMR: Linear Structures

M M M V

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TMR: Linear Structures

M M M V M M M V

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TMR: Linear Structures

M M M V M M M V M M M V M M M V

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TMR: Linear Structures

M M M V M M M V M M M V M M M V M M M V M M M V V M M M V V V M M M V

>

?

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TMR: Linear Structures

M M M V M M M V M M M V M M M V M M M V M M M V V M M M V V V M M M V M M M V V M M M V V M M M V M M M V V V M M M V V V M M M V V V M M M V V V M M M V V V

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SLIDE 16

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Triple Redundant Module comparison (1 voter)

Reliability analysis: manual approach

[Hamamatsu10]

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Reliability analysis: manual approach

  • Manual approach to reliability computation:
  • Slow, expensive and error prone
  • Limited expressiveness
  • Support only for linear structures
  • no general approach also for Tree- and DAG-shaped
  • Needs space discretization
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SLIDE 18

Outline

  • Architectural Design in Critical Systems
  • Redundant Systems
  • Reliability Analysis
  • Automated Approaches
  • EUF modeling and Fault Tree Analysis
  • Efficient Analysis via Predicate Abstraction
  • Conclusion

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Automated Analysis of Reliability Architecture

  • 1. Model the extended system with uninterpreted

functions

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Modeling of the extended system

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Modeling of the extended system

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Automated Analysis of Reliability Architecture

  • 1. Model the extended system with uninterpreted

functions

  • 2. Perform Fault Tree Analysis

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SAT-Based Fault Tree Analysis

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SAT-Based Fault Tree Analysis

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Fault Tree Analysis: equivalence check

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Fault Tree Analysis: equivalence check

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Automated Analysis of Reliability Architecture

  • 1. Model the extended system with uninterpreted

functions

  • 2. Perform Fault Tree Analysis
  • 3. Extract Reliability Function, from BDD

representation of Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Reliability Function Extraction

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BDD representation of the Fault Tree

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Automated Analysis of Reliability Architecture

  • 1. Model the extended system with uninterpreted

functions

  • 2. Perform Fault Tree Analysis
  • 3. Extract Reliability Function, from BDD

representation of Fault Tree

  • 4. Evaluate the results with analytical tools

(Octave/Matlab)

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Triple Redundant Module comparison (1 voter)

e d c b a

1-Rv 1-Rm

Automated Analysis of Reliability Architecture

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Uniform probability analysis

1 voter patterns comparison (2D) 1 voter patterns comparison (3D)

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Uniform probability analysis

1 vs 2 voters comparison (2D) 1 vs 2 voters comparison (3D)

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Uniform probability analysis

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Not uniform probability analysis

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Automated Analysis of Reliability Architectures

  • Full automated technique for the Analysis of

Reliability Architecture

  • Symbolic technique
  • generates the closed form of Reliability function
  • Allows for the reusability of analysis results
  • generation of Reliability Functions Libraries
  • Useful to explore the design space
  • Bottleneck:
  • the AllSMT computation is monolithic
  • Hard to deal with big systems (> 10 stages)
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Outline

  • Architectural Design in Critical Systems
  • Redundant Systems
  • Reliability Analysis
  • Automated Approaches
  • EUF modeling and Fault Tree Analysis
  • Efficient Analysis via Predicate Abstraction
  • Conclusion

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Counter-Example Guided Abstraction-Refinement (CEGAR)

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P0 P1 not P1 01 00 10 11 P2 not P2 000 010 011 001 100 101 Ψ0(X) Ψ1(X) Ψ2(X) I(X) R(X, X') State vars X Abstract State vars P AI (P) AR(P,P') not P0

Predicate abstraction

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CEGAR with Predicate abstraction

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Computing Abstractions

  • Given concrete model CI(X), CR(X, X')
  • Given set of predicates Ψi(X)

each associated to abstract variable Pi

  • Obtain the corresponding abstract model
  • AR(P, P') is defined by

∃ X X'.(CR(X, X') ⋀ ⋀i Pi ↔ Ψi(X) ⋀ ⋀i Pi' ↔ Ψi(X') )

  • Existential quantification as AllSMT
  • SMT solver extended to generate all satisfying

assignment

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Modular Abstraction for Safety Assessment

  • Compose the whole system using the abstraction of

each single module

  • Preserve the cut-set generation i.e. provide the

same results by means of modular abstract state space

  • Generate a pure Boolean model, and abstract SMT

formulas

  • Compute the results via BDD based engine with

known variable ordering

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Combinatorial System: Generic Component

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Combinatorial System: Abstractor and Concretizer

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Combinatorial System: Sequential composition

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Combinatorial System: Parallel Composition

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Combinatorial System: Reduction and Parallel Equivalence

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Combinatorial System: Modular Abstraction Equivalence

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Modular Abstraction

Boolean Data

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… …

Modular Abstraction

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… = = … … … V = =

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Modular Abstraction

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Experimental Evaluation: Concrete vs Abstraction

  • Redundant network description:
  • Linear TMR structures with 1, 2 and 3 voters. Single

(triplicated) input and output ports

  • Tree and DAG like structures randomly generated with 1,

2 and 3 voters; 1, 2 and 3 (triplicated) input ports; single (Tree) or double (DAG) output ports

  • Fault Tree Analysis with equivalence check:

perfect vs redundant (and faulty) circuit

  • Engines detail
  • MathSAT5 (EUF) for concrete case
  • NuSMV3 with BDD-based engine for modular

abstraction

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DAG like example with 60 modules

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Concrete vs Abstraction: linear

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Concrete vs Abstraction: Tree and DAG (< 15 modules)

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Abstraction: Tree and DAG

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Outline

  • Architectural Design in Critical Systems
  • Redundant Systems
  • Reliability Analysis
  • Manual Reliability techniques
  • Automated Approaches
  • EUF modeling and Fault Tree Analysis
  • Efficient Analysis via Predicate Abstraction
  • Conclusion

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Conclusion

  • Automated technique for the analysis of reliability

architectures

  • Management of linear, Tree and DAG like structures
  • Efficient analysis of large systems (> 140 modules)

via predicate abstraction

  • Take-away
  • SMT view crucial to devise novel solutions!
  • Efficiency does not come for free…

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Thanks for your attention!