(757b) Multi-Scale Identification

Many processes are of multiple scale, in fact if one looks at the details all of them are purely due to the nature of matter. If we are interested to identify process models, we often want to capture more than one scale independently implying that we want to split the analysis into a slow and a fast process in a hierarchical manner. So if we start at a large time scale, we split the world into three domains: a constant part, modelled as thermodyanmic reservoirs, a dynamic part, and an event-dynamic part, latter representing instant changes in the state on the small scale. The split is relative anddirectly  related to the chosen granularity of the process model. Changing the scale, the split can be done again on the next lower granularity. Here, what was the event-dynamic part on the larger scale is split again moving the event-dynamic boundary to a smaller time scale, whilst the upper one will be in the part that was the event-dynamic or dynamic domain on the larger granular model. The overall procedure is thus hierarchical. On any scale, when we perform the analysis, the split is always into three parts.

Often the interest is focusing on the split of the dynamic / event-dynamic part into two separate section. Identification experiments are performed, which will usually excite both domains. Splitting the identification into two dynamic regions is then the task.

We use wavelets for solving this problem, thereby utilising the unique properties of wavelts of acting as frequency filters whilst being local in the time domain. We demonstrate the procedure on a nominal plant with two separate time constant to which we fit two models from the same data, namely a fast model that does not meet the steady state conditions and a slower one that does cover the low frequency range of the plant.