AIB 2013-20: Time-Continuous Behaviour Comparison Based on Abstract Models

[Thomas Ströder]

The following technical report is available from
http://aib.informatik.rwth-aachen.de:

Time-Continuous Behaviour Comparison Based on Abstract Models
Jacob Palczynski
AIB 2013-20

Model-based approaches in the development of embedded software become
more and more widely spread. In these approaches, different models of
one target system are the central elements. Re- cently, a growing number
of algorithms and functionality of embedded software are designed using
such model-based approaches, a prominent one is Rapid Control
Prototyping. Its main advantage is the possibility to develop
functionality of both controlling embedded software and controlled
system in one modelling environment. Additionally, the developer can
simulate the whole system and improve its performance, debug algorithms,
etc. in early development stage. Important test phases are Software in
the Loop and Hardware in the Loop. In this work, we discuss two problems
that may occur during these phases.

The first question is: Taking into account the continuous
characteristics of system variables, how can we safeguard a consistent
evolution of the development artefacts? To deal with this problem, test
results are compared in order to safeguard a consistent evolution of the
development artefacts. Since different artefacts were tested at
different stages of the development under different conditions, we
cannot expect that the results of each test case to be exactly equal,
but at most similar. This similarity check of continuous systems is
addressed in this work.

The methodology presented here is based on behavioural black-box models
of our system in the time domain on different levels of abstraction. A
behaviour is represented by the input and output signals of a system and
their interrelationship. On each level of abstraction, a system's model
is put up by a set of behaviours, each of which consists of input
signals and the according output signals created by the system. The
description of the signals themselves varies strongly, depending on the
level of abstraction.

For the comparison of two systems or artefacts, we have to introduce a
similarity relation with respect to an abstract model. Two systems are
similar with respect to an abstract model A, when their behaviours
conform to this abstract model A. The central question is how we can
find properties in measured signal data. To find a characteristic
property in a set of measured signal data, we compute the cross
correlation of the interpolated measured data and a template signal. By
this, we find on which time interval of the measured data one property
potentially occurs. Repeating this for all properties yields all
occurrences of the properties in the system's abstract behaviour model.
In the end, we know that these systems conform the abstract model and
therefore are similar with respect to the abstract model.

The second problem we address is: How can we analyse correctly test
results obtained from real time test devices that do not have certified
clocks? The motivation here are possible differences in sample timing
due to not exactly working hardware timers. Due to this, a drift occurs
in the sampled data which leads to distorted signals and seemingly wrong
timings of events. We compare such a signal to one obtained with a
certified device by searching for certain properties, and obtaining the
points in time of the occurrences. Using these time information, we can
estimate the difference of the sample times, i.e. the drift. For the
search for properties based we use the cross correlation approach
already used for regression tests.