In the industry frequently the question about an appropriate process control arises.
Due to the rising complexity it is usually impossible, but at least time consuming, to develop
a mathematical accurate model. A self-adaptive model-based controler is therefore of special
interest.An important subject, which was part of the research interests of project part C1 of the special
research center 396, is an efficient inference algorithm to evaluate dynamic hybrid bayesian networks. It was
studied whether the inference algorithm for discrete dynamic Bayesian networks, called interface algorithm,
published by K. Murphy in his PhD-thesis is also applicable for hybrid dynamic Bayesian networks. The expected
advantage of this algorithm is that the run-time, depending on the number of time-slices, raises only linear,
whereas the application of an exact inference algorithm requires exponential time.
When the interface algorithm is applied to hybrid dynamic Bayesian network the computation of a correct
mean and variance is no longer guaranteed, as the strong marginalisation, resulting in a correct marginal distribution,
is replaced by weak marginalisation. During weak marginalisation a mixture of Gaussians is replaced by a mixture
of Gaussians with less mixture components. In the overall inference process it is therefors no longer possible to
guarantee an exact mean and variance.
The second emphasis of project-part C1 is the development of models for manufacturing processes,
particularly finding a suitable structure of a Bayesian model. Regarding the parameters of a hybrid
Bayesnetzes, it gets ovious that each parameter can be mapped to a special configuration of
the discrete parents. If the data are collected by an experimental design it has to be guaranteed that
for each set of discrete nodes {X1, ..., Xn}, being parent of another node, all possible settings
x1, ..., xn are part of the experimental design in order to train all parameter.
These findings were used in the development of an experimental design for injection moulding.
When several factors are recognized as important at the same time, i.e. only when a special relation
guarantees an optimal result, a hidden node, representing these factors, is added to the Bayesian network.
Of course the experimental design and the gathered data have also an influence of the automatic structure
learning. If the data are gathered during production, the factors might look as if they were correlated,
because only special settings lead to an acceptable result. On the other hand the input parameters should
be modeled as independent, because they can usually changed independently. That is no edges should connect
the nodes representing input parameters.