AGIAS Generalised Interval Arithmetic Simulator (AGIAS) is a specialised simulator which
uses affine arithmetic to model parameter variations. It uses a specialised root-finding
algorithm to simulate analogue circuits with parameter variations in one single simulation
run. This is a significant speed-up compared to the multiple runs needed by industrialised
solutions such as Monte-Carlo (MC) or Worst-Case Analysis (WCA). Currently, AGIAS
can simulate analogue circuits only under very specific conditions. In many cases, circuits
can only be simulated for certain operating points. If the circuits is to be evaluated in other
operating points, the solver becomes numerically unstable and simulation fails. In these
cases, interval widths approach infinity.
Behavioural modelling of analogue circuits was introduced by researchers working around
limitations of simulators. Most early approaches require expert knowledge and insight into
the circuit which is modelled. In recent years, Machine Learning techniques for automatic
generation of behavioural models have made their way into the field. This thesis combines
Machine Learning techniques with affine arithmetic to include the effects of parameter
variations into models.
Support Vector Machines (SVMs) train two sets of parameters: one slope parameter
and one offset parameter. These parameters are replaced by affine forms. Using these two
parameters allows affine SVMs to model effects of parameter variations with varying widths.
Training requires additional information about maximum and minimum values in addition to
the nominal values in the data set. Based on these changes, affine ε Support Vector Machine
(ε̂SVR) and ν Support Vector Machine (ν̂SVR) algorithms for regression are presented. To
train the affine parameters directly and profit from the Sequential Minimal Optimisation
algorithm (SMO)’s selectivity, the SMO is extended to handle the new, larger optimisation
problems.
The new affine SVMs are tested on analogue circuits that have been chosen based on
whether they could be simulated with AGIAS and how strongly non-linear their characteristic
function is.
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