Functional decomposition—A contribution to overcome the parameter space explosion during validation of highly automated driving

Amersbach, Christian; Winner, Hermann · 2019 · Crossref

DOI: 10.1080/15389588.2019.1624732

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Summary

This study addresses the "parameter space explosion" that hinders the validation of highly automated driving (HAD) systems, specifically SAE Level 3 "Autobahn-Chauffeur" functions. Current statistical validation methods require billions of test kilometers, which is practically infeasible. While scenario-based testing offers an alternative, it suffers from an exponential increase in required test cases due to the multitude of influence parameters and their discretization steps. The authors propose functional decomposition as a method to reduce this validation effort by testing individual functional layers of the driving system rather than the complete system as a whole. The researchers quantified the potential reduction in test suite sizes by analyzing an exemplary set of nine logical scenarios, including the "Swiss scenario" and eight scenarios from the PEGASUS project. They modeled the parameter space using a five-layered decomposition of the driving function (perception, classification, prediction, planning, and execution). Due to a lack of empirical failure data for HAD, the study assumed required test coverage levels based on failure-triggering fault interaction (FTFI) numbers from other domains, estimating that 3-wise coverage represents the best case and 10-wise coverage the worst case. The analysis compared the size of test suites required for testing the complete system against those required for particular testing of decomposed layers, utilizing systematic test case generation strategies. The results demonstrate that functional decomposition significantly reduces the size of required test suites. By isolating functional layers, the study identified three main reduction effects: the parameter space for a single layer is smaller than that of the complete system; less complex subsystems require lower test coverage; and perception-related parameters can be aggregated across similar scenarios. Consequently, the combination of these effects reduced the test suite size by a factor of 20 for 10-wise coverage and by a factor of 130 for 3-wise coverage. This corresponds to a 95–99% reduction in the number of concrete scenarios required compared to scenario-based testing of the complete system. For instance, the absolute number of test cases for 3-wise coverage dropped from approximately 6.8 million to 50,000. The authors conclude that functional decomposition is a valuable contribution to overcoming the parameter space explosion in HAD validation. While the resulting parameter space remains large, the significant reduction in test suite size makes validation more feasible. However, the study acknowledges limitations, noting that the findings are based on assumptions regarding discretization steps and test coverage due to the absence of empirical HAD failure data. The authors emphasize that further studies are needed to validate these findings with practical implementations and to confirm that independent testing of functional layers can fully replace complete system testing without compromising fault detection potential.

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