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Sensitivity analysis

By doing instantaneous or consecutive predictions under small changes made in the process parameter space we can investigate the leverage effects of the parameter changes. This is crucial for two reasons. Firstly, random variation causes small perturbations in the process parameters. This kind of noise is always present in a production process. Secondly, one can make improvements in the process by changing standard operating procedures in a directions that result in products of better quality.

Figure 5.8: The leverage effect

In the Figure 5.8 the mechanism behind the tool is shown. A small change along one of the coordinates in the measurement space is made. The new vector of all components is mapped to the SOM. If the best-matching unit changes, the values of that unit are shown to the user. The interpretation of this is that the the small change in one of the measurement space axes caused the other values to change. In the Figure 5.8 the component value on the axis pointing upward decreased a little caused by the small increase in the measurement on the axis pointing to the right. The third component remained the same.

A software tool was developed to help in the mentioned goals. In the Figure 5.9 the different functions of the tool are described.

Figure 5.9: Functions of the tool program

One can perform all the parts needed to train a SOM from pre-processed data. First, data is read to the program. With the aid of the tool, the training process of the Self-Organizing Map can be handled. Instead of training a SOM, one can also load in a SOM and also save a SOM for later inspection and use.

This representation is used in giving instantaneous predictions under small changes made by the user. This reveals the leverage effects in a given operation point under small changes. It must be remembered that same changes can have different effects in different operations points.

The parameters settings are controlled by the user. The user has the choice of locking one or several parameters, thus limiting the operating point to a certain location in the measurement space. The tool updates only those components which are not locked. If no parameters are locked, the shown values are the direct copies of the values in the codebook vector.

As the user changes one of the parameters, the best-matching unit is constantly searched for. If the best-matching unit changes, all the other parameter settings are changed according to the values in that particular codebook vector. This corresponds to a kind of a projection from the parameter space to the SOM codebook vectors.

The user can then investigate the leverage effects caused by the small parameter changes. In this way, the operator can ``play-along'' with the process and learn about the dynamic behavior of the process.

Figure 5.10: The interface of the tool for analyzing the leverage effects

The graphical interface of the leverage analyzer tool is illustrated in Figure 5.10. A static picture of the tool does not reveal much of its function or the purpose, but hands-on experience has proven it useful.

Besides the prediction, a measure of reliability is shown. The measure of reliability used is the quantization error between the codebook vector and the input vector set by the user. Locking parameters can have negative side-effects: we can drift away from the surface defined by the SOM. The quantization error provides a way to detect this.

No commitment is made to which parameters are independent and which are independent parameters. Naturally, one is interested in finding a combination of raw material characteristics and process parameter setting that produce the best possible quality, but one could as well predict best possible incoming raw material given the quality characteristics of the end product and the process parameter settings.

next up previous contents
Next: Using SOM and local Up: Using SOM as a Previous: Predicting quality parameters

Jaakko Hollmen
Fri Mar 8 13:44:32 EET 1996