8.5. Conclusions and Comparison of the Different
this chapter, a growing neural network algorithm for building non-uniform
neural networks was applied to the refrigerant data set. The algorithms showed
improved calibrations compared with the common non-optimized neural network.
Yet, the variable selection and the topology of the networks were only partly
reproducible. Thus, similar to the genetic algorithms a parallel framework and
additionally a loop-based framework were introduced to improve the
reproducibility and to improve the calibration quality further.
loop-based framework showed the best generalization ability of all multivariate
data analysis methods introduced and applied in this work as it allows building
non-uniform neural networks of any arbitrary size and topology exploiting a
data set limited in size to a maximum extent. The predictions of the external
validation data showed impressively low rel. RMSE of 1.50% for R22 and 2.37%
for R134a, which are only slightly higher than the standard deviations of the
sensor signals of reproduced measurements. The loop-based framework needs a lot
computing power (2 weeks for each analyte of the refrigerant data set using an
up-to-date personal computer) and is hardly suited for parallel computing
hardware as it is a loop based approach and not a parallel approach.
reproducible variable selection is important, both, the parallel growing network
framework introduced in this chapter and the genetic algorithm framework introduced
in the previous chapter are a good choice, whereby the
latter scales better with an increasing number of variables, but shows a slightly
worse generalization ability. Both parallel frameworks showed improved calibrations
compared with the common neural networks. Both frameworks are well suited for
parallel computer hardware rendering both methods ideally suited for computer
single run growing neural network algorithm is a good choice for data sets with
not too many variables to find an optimized non-uniform network topology
without the danger of overfitting (about 3 hours computing time for each
analyte of the refrigerant data set). Different single runs of the growing
neural network all showed better calibrations than the non-optimized neural
single runs of genetic algorithms are frequently reported in literature, this
method has been proven to be inferior compared with the different new
algorithms and frameworks introduced in this work. Though being the fastest
methods for a successful variable selection (about 1 hour for refrigerant data
set), the instability of the variable selection and the resulting diversity of
the quality of calibration and of prediction render single runs genetic
algorithms rather useless for most applications.
it may be said, that the growing neural networks and all three frameworks introduced
in this work performed better than the common non-optimized neural networks.
Among these new methods introduced in this work, no general recommendation for
a specific method can be given as the method of choice for the optimization
of neural networks depends on the needs of the user and on the data set.
Comparison of the rel. RMSE of the calibration and validation data in % for
the growing neural network approaches and the non-optimized neural networks.
Addtionally the number of adjustable parameters used by the networks are listed.