![](bg3.png)
parameter is large and as a Gauss–Newton algorithm
when this parameter is small. The use of a robust
criterion allows to avoid the influence of outliers and
provides a regularization effect in order to prevent
overfitting. An important issue in neural network
design is the determination of its structure. To
determine it, two approaches can be used. The first
one is constructive, where the hidden neurons are
added one after the other (Ma and Khorasani 2004).
The second approach exploits a structure with too
many initial hidden neurons, and then prunes the
least significant ones (Setiono and Leow 2000,
Engelbrecht 2001). We focus on the pruning
approach that allows a simultaneous selection of the
input neurons and the number of hidden neurons.
The pruning phase is performed in two steps. First,
the Engelbrecht algorithm is used which allows to
quickly simplify the structure and second, the
Setiono and Leow algorithm is used which is slower
but also more efficient (Thomas
et al. 2013).
3 ONLINE ADAPTATION OF THE
MODEL
3.1 Generalities
Ideally, the data collected during the
experimentation phase should describe all the states
of the system to model. However, it is sometimes
not feasible due to the high number of potential
situations the system could encounter. Indeed, in our
case data collected are different depending on the
seasons, the yearly weather, changes in user’s habits
and so on. Technically, it would thus be highly
difficult to obtain an exhaustive data set. As a result,
our approach consists in two phases: first, a learning
phase is achieved based on a data set obtained via a
relatively short experimentation phase (in our case, 1
month, see section 4.1) to construct a first “specific”
NN model. Then, a relearning is launched if and
only if a significant difference (called “drift”)
between the system behavior and its corresponding
NN model is detected.
In many case, a drift may appear between the model
constructed and the system studied. This drift may
be due to two main reasons. The first one concerns
the evolution of input parameters. With a learning
approach, the obtained model is valid only on the
learned domain. The model is able to provide a valid
solution only in this concerned domain.
The second reason concerns the uncontrolled
modification of the machine or environment
behavior. Indeed, A change of a parameter
(voluntarily or not, measured or not) which is not an
input of the model, can affect the behavior of the
machine. In this case, this parameter should be part
of the model inputs but, as it was considered
constant for the duration of the learning step, it was
not retained as such. Due to this change, which may
even be unknown to operators and users, the model
will therefore provide results out of step with reality.
To take into account these problems, a relearning
on new data is needed. There are two practical ways
to implement learning in neural networks: batch
training and on-line training. Whenever a new data
is received, batch learning uses this new data
together with the past data to perform a retraining.
But this approach is time consuming. The on-line
approach uses only new data to adapt the model.
However, this approach suffers from slow training
error convergence as a large number of training data
may be required (Liang
et al. 2006). Moreover,
different works have shown that on-line training
strategy does not converge to the optimal weights
(Heskes and Wiegerinck 1996, Nakama 2009).
We thus propose here another approach where a
batch learning is performed periodically when a drift
between the model and the system occurs, in order
to synchronize the model with the reality.
Because this synchronization is time consuming, the
synchronization frequency must be optimized.
Rather than consider a resynchronization frequency
in response to events (arrival of new information
from one of the connected devices, solicitation by an
operator…) or a periodically one (every hour,
week…), it is better to rely on statistical findings.
Among the 7 basic tools for quality control, control
charts, also known as Shewhart charts or process-
behavior charts (Shewhart 1931), are interesting
Statistical Process Control (SPC) tools useful for our
proposed system.
3.2 Control Charts
Control charts are particularly relevant to the
dynamic quality control with the use of time-series
(Tague 2004). They can determine statistically if a
variation is no longer under control. Indeed, it is
known that even when a process is under control
there is approximately a 0.27% probability of a point
exceeding a 3σ control limit (Pareto). These few
isolated points should not trigger synchronization.
But the detection of too many points above this limit
may underlines the presence of a special cause, even
if it is not yet known.
The Combination of a neural network with the
NCTA2014-InternationalConferenceonNeuralComputationTheoryandApplications
174