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Semi-Markov processes for calculating the safety of autonomous vehicles
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Semi-Markov processer för beräkning av säkerheten hos autonoma fordon (Swedish)
Abstract [en]

Several manufacturers of road vehicles today are working on developing autonomous vehicles. One subject that is often up for discussion when it comes to integrating autonomous road vehicles into the infrastructure is the safety aspect. There is in the context no common view of how safety should be quantified. As a contribution to this discussion we propose describing each potential hazardous event of a vehicle as a Semi-Markov Process (SMP). A reliability-based method for using the semi-Markov representation to calculate the probability of a hazardous event to occur is presented. The method simplifies the expression for the reliability using the Laplace-Stieltjes transform and calculates the transform of the reliability exactly. Numerical inversion algorithms are then applied to approximate the reliability up to a desired error tolerance. The method is validated using alternative techniques and is thereafter applied to a system for automated steering based on a real example from the industry. A desired evolution of the method is to involve a framework for how to represent each hazardous event as a SMP.

Abstract [sv]

Flertalet tillverkare av vägfordon jobbar idag på att utveckla autonoma fordon. Ett ämne ofta på agendan i diskussionen om att integrera autonoma fordon på vägarna är säkerhet. Det finns i sammanhanget ingen klar bild över hur säkerhet ska kvantifieras. Som ett bidrag till denna diskussion föreslås här att beskriva varje potentiellt farlig situation av ett fordon som en Semi-Markov process (SMP). En metod presenteras för att via beräkning av funktionssäkerheten nyttja semi-Markov representationen för att beräkna sannolikheten för att en farlig situation ska uppstå. Metoden nyttjar Laplace-Stieltjes transformen för att förenkla uttrycket för funktionssäkerheten och beräknar transformen av funktionssäkerheten exakt. Numeriska algoritmer för den inversa transformen appliceras sedan för att beräkna funktionssäkerheten upp till en viss feltolerans. Metoden valideras genom alternativa tekniker och appliceras sedan på ett system för autonom styrning baserat på ett riktigt exempel från industrin. En fördelaktig utveckling av metoden som presenteras här skulle vara att involvera ett ramverk för hur varje potentiellt farlig situation ska representeras som en SMP.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:078
Keywords [en]
Semi-Markov process, functional safety, autonomous vehicle, hazardous event, Stieltjes convolution, reliability, Laplace-Stieltjes transform, Euler algorithm, Talbot algorithm
Keywords [sv]
Semi-Markov process, funktionell säkerhet, autonoma fordon, farlig situation, Stieltjes faltning, funktionssäkerhet, Laplace-Stieltjes transform, Eulers algoritm, Talbots algoritm
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-252331OAI: oai:DiVA.org:kth-252331DiVA, id: diva2:1320087
External cooperation
Scania CV AB
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2019-06-04 Created: 2019-06-04 Last updated: 2019-06-04Bibliographically approved

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