ANEXO RELATIVO A LOS CONCEPTOS FUNDAMENTALES UTILIZADOS POR ESTE TEXTO REFUNDIDO

This section first briefly describes the second real-world production facility that we used for demonstrating our approach, the so-called Lemgo Model Factory. Then, the models learned for a component of this facility using the HyBUTLA algorithm are presented. Such models are used for executing the anomaly detection experiments, which are presented in Section 8.3.

8.2.1 Plant Description

The Lemgo Model Factory (LMF) is the exemplary hybrid production system at the Institute Industrial IT in Lemgo, Germany. It represents a small plant for storing, transporting, processing and packing bulk materials, such as corn. It is made of several modules, namely: the storage system, transportation system, weighting station, bottle- filling mechanism, material-processing facility, product packing system, bearing robot, and lid robot. These modules consist of a number of components, such as distributed PLCs, industrial networks (using e.g. the PROFINET protocol [PM08]), conveyor belts, and a popping machine. These components are already identified by the manually created parallelism model, which is explained in Subsection 2.1.1. The plant comprises around 250 measurable discrete and continuous signals. We show one part of the plant’s interior in Figure 8.1.

The component of the LMF that we modeled using our HyBUTLA algorithm is the popping machine. It consists of one container, the fan and the heater. First, the corn is delivered to the container and then the heater and fan are activated. The fan blows the hot air inside the container and creates popcorn as a result.

Logs made during described production cycle represent one learning example of the popping machine. They comprise the time stamp and the logs of: six discrete binary control signals, five continuous input signals and one continuous output signal.

8.2 Learning Behavior Models for the Lemgo Model Factory 119

Fig. 8.1 One part of the Lemgo Model Factory.

This signal is the active power of the popping machine heater. Figure 8.2 shows its typical time diagram. The normal measurement range of this signal is 150–3250 W. This information (expert knowledge) is important for the ANODA algorithm, which can detect significant deviations of this signal from the lower or upper bound of the measurement range. The data sampling rate at the popping machine is 1 Hz. For learning models, we had logs of 12 production cycles at our disposal, which are by experts identified as normal (i.e. recorded during normal operating conditions in the plant). Logs of the additional 13th cycle are used as a test example for the anomaly detection experiments given in the following section. In the average, the example length is 191 samples (i.e. the average production cycle lasts around three minutes).

0 50 100 150 200 250 300 350 400 0 500 1000 1500 2000 2500 Time (s) A ct iv e p ow er (W)

120 8 Real-World Plants

8.2.2 Models Learned with the HyBUTLA Algorithm

In our papers cited at the beginning of this chapter, we have published several case studies conducted at LMF and gave properties of various models learned using the HyBUTLA algorithm. In all those cases, an interesting trade-off was observed that we want to present and explain here. To that aim, we first give properties and learning times of several popping machine models identified by our algorithm. The general goal was to learn the smallest possible model, with the highest possible accuracy of approximating the continuous output signal.

The properties of the Prefix Tree Acceptor (PTA) and two specific learned behavior models are given in Table 8.2. We denoted the first learned model by Amin. It is the

smallest model identified by the HyBUTLA algorithm without the application of the additional splitting step (model obtained for α = 0.25, see the expression (6.3)). The split function (see Subsection 6.5.2) was applied to this model and resulted in the second model denoted by Asplit. For these three models (i.e. PTA, Amin and Asplit)

Table 8.2 gives: their number of states, the size reduction (in relation to the PTA size), the average model coefficient of determination achieved using the multiple linear regression with linear terms (MLR − LT R2), and total learning times.

Table 8.2 Properties of learned behavior models and their learning times. Automaton Properties _{PTA A} minAsplit #states 52 7 24 Size reduction (%) 0 86.5 53.9 MLR-LTR2_{(%) 78.3 75.1 93.5} MLR-LT time (s) 3.4 7.1 185.3

It can be seen that by merging the PTA states a very small model Aminis obtained

with only seven states. Thus, the reduction of the PTA size obtained by merging its states is over 86%. By applying the splitting step, this size reduction has unfortunately decreased, but the MLR-LT R2_{of the final A}

splitmodel has increased by around

18% in the absolute value comparing to Amin. It is interesting that this final model

has higher MLR-LT R2_{even than the PTA itself.}

Table 8.2 presents only three specific learned models. However, during the splitting step a number of models with different sizes and coefficients of determination were created. We have summarized their main properties and showed them graphically in Figure 8.3. Three aforementioned models are denoted at the bottom of the figure. This figure illustrates the existing trade-off between the model size reduction and the accuracy of approximating the continuous output signal. It demonstrates the benefit that our split function has brought to the HyBUTLA algorithm. Depending on the application area, the flexibility now exists to select a model with the appropriate size-accuracy ratio. Furthermore, the model with the R2of over 93% (Asplit) is in

this example learned using the simple MLR-LT method for regression. This approach is several times faster than our previous approach without the split function, where continuous output signals had to be learned with neural networks in order to achieve high R2_{values [VKBNM11a].}

8.3 Anomaly Detection Experiments 121