II. Decision support

Design methods: academic | industrial | simultaneous

Known problems: target mixture | components to be used

For the decision support design two probabilistic mixtures are required – one representing the given system (identified from system data) and another corresponding to a required target (user ideal).
The identified mixture can be static (approximating data distribution) or dynamic (modeling system behavior). The target mixture is considered mostly to be static with a single component. Three design methods are elaborated, all based on minimization of the Kullback-Leibrer divergence which measures the difference between two probability distributions.

1. Academic design method

   Principle of the method is simple: component weights of the identified mixture are changed in order to make the resulting advisory mixture as similar to the target as possible.
   In most practical cases a single component is selected, i.e. its weight is set to 1 while weights of the others are zeros. The principle of the method and influence of target mixture parameters are depicted on section Gallery II.
   The advice based on academic design sounds: operate the process so that process data correspond to the selected components. It means for multimodal processes to prefer a specific mode or to keep the process in the neighborhood of a given working point.
   Utilization of the method is considerably limited because it is not known how to reach the required mode – that is the reason for the term academic design.

2. Industrial design method

   For the industrial design part of the data channels (mostly denoted as system inputs) are considered as directly manipulable by an operator. Result of the design recommends setpoints for these inputs without changing weights of the advisory mixture in comparison with the identified one. It corresponds to the situation met commonly in industry – proportion of particular process modes is given and it is impossible or not known how to change it.

   Principally, the design corresponds to the optimal controller design.

3. Simultaneous design method

   Simultaneous design combines both principles: selects mixture components by changing their weights and recommends setpoints for inputs. The method is supposed to be better than a sequential application of the academic and industrial designs despite its significant sensitivity to parameters of the target mixture.

   A simple comparative example can be found in Gallery II.

Known problems

1. Target mixture definition

   It would be advantageous to be able to define the target without any reference to the state and properties of the system (in other words without any reference to parameters of the identified mixture). In some measure, such approach can be applied for the academic design. Generally, parameters of the identified mixture must be taken into consideration seriously to obtain reasonable results. There exist several “tricks” and empirical rules for construction of the target mixture. Nevertheless, an all-purpose solution is still to be found. Another research topic is a more complex multicomponent target mixture.

2. Time dependency of components weights

   Components weight of the dynamic mixture estimate how particular components (particular models) participate on approximation of all data used for identification. However with changing modes of the system in time, component weights should be changed to model the system by a subset of appropriate models only. Rules for recalculation of weights based on actual data exist but must be further elaborated.