Efficient Splitting of Test and Simulation Cases for the Verification of Highly Automated Driving Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11093)


We address the question of feasibility of tests to verify highly automated driving functions by optimizing the trade-off between virtual tests for verifying safety properties and physical tests for validating the models used for such verification. We follow a quantitative approach based on a probabilistic treatment of the different quantities in question. That is, we quantify the accuracy of a model in terms of its probabilistic prediction ability. Similarly, we quantify the compliance of a system with its requirements in terms of the probability of satisfying these requirements. Depending on the costs of an individual virtual and physical test we are then able to calculate an optimal trade-off between physical and virtual tests, yet guaranteeing a probability of satisfying all requirements.


Verification Simulation Highly automated driving Statistical verification Testing Advanced driver assistant systems Optimal trade-off 



This study was partially supported and financed by Opel Automobile within the context of PEGASUS (Project for the Establishment of Generally Accepted quality criteria, tools and methods as well as Scenarios and Situations for the release of highly-automated driving functions), a project funded by the German Federal Ministry for Economic Affairs and Energy.


  1. 1.
    Winner, H.: Quo vadis, FAS? In: Winner, H., Hakuli, S., Lotz, F., Singer, C. (eds.) Handbuch Fahrerassistenzsysteme. ATZ/MTZ-Fachbuch, pp. 1167–1186. Springer, Wiesbaden (2015). Scholar
  2. 2.
    Kalra, N., Paddock, S.M.: Driving to safety: How many miles of driving would it take to demonstrate autonomous vehicle reliability? RAND Corp. 94, 182–193 (2016)Google Scholar
  3. 3.
    Stellet, J.E., Zofka, M.R., Schumacher, J., Schamm, T., Niewels, F., Zollner, J.M.: Testing of advanced driver assistance towards automated driving: a survey and taxonomy on existing approaches and open questions. In: 2015 IEEE 18th International Conference on Intelligent Transportation Systems (ITSC), pp. 1455–1462. IEEE (2015)Google Scholar
  4. 4.
    Hallerbach, S., Eberle, U., Köster, F.: Absicherungs- und Bewertungsmethoden für kooperative hochautomatisierte Fahrzeuge. In: AAET 2017, Braunschweig (2017) 369Google Scholar
  5. 5.
    Hakuli, S., Krug, M.: Virtuelle integration. In: Winner, H., Hakuli, S., Lotz, F., Singer, C. (eds.) Handbuch Fahrerassistenzsysteme. A, pp. 125–138. Springer, Wiesbaden (2015). Scholar
  6. 6.
    Nentwig, M.: Untersuchungen zur Anwendung von computergenerierten Kamerabildern für die Entwicklung und den Test von Fahrerassistenzsystemen. Ph.D. thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg (2014)Google Scholar
  7. 7.
    Mauritz, M., Rausch, A., Schaefer, I.: Dependable ADAS by combining design time testing and runtime monitoring. In: 10th International Symposium on Formal Methods, FORMS/FORMAT 2014, pp. 28–37 (2014)Google Scholar
  8. 8.
    Schuldt, F., Menzel, T., Maurer, M.: Eine Methode für die Zuordnung von Testfällen für automatisierte Fahrfunktionen auf X-in-the-Loop Verfahren im modularen virtuellen Testbaukasten. In: 10. Workshop Fahrerassistenzsysteme, p. 171 (2015)Google Scholar
  9. 9.
    Clopper, C.J., Pearson, E.S.: The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26(4), 404–413 (1934)CrossRefGoogle Scholar
  10. 10.
    Ammersbach, C., Winner, H.: Functional decomposition: an approach to reduce the approval effort for highly automated driving. In: 8. Tagung Fahrerassistenz (2017)Google Scholar
  11. 11.
    Hallerbach, S., Xia, Y., Eberle, U., Koester, F.: Simulation-based identification of critical scenarios for cooperative and automated vehicles. In: SAE International WCX World Congress Experience, April 2018Google Scholar
  12. 12.
    Giles, M.B.: Multi-level Monte Carlo path simulation. Oper. Res. 56(3), 607–617 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.OFFIS - Institut für InformatikOldenburgGermany
  2. 2.Opel Automobile GmbHRüsselsheim am MainGermany

Personalised recommendations