Building Optimal Multiresolution Soft Sensors for Continuous Processes

Data-driven models used in soft sensor applications are expected to capture the dominant relationships between the different process variables and the outputs, while accounting for their high-dimensional, dynamic, and multiresolution character. While the first two characteristics are often addressed, the multiresolution aspect is usually disregarded and confused with a multirate scenario: multi resolution occurs when variables have different levels of granularity, because of, for instance, automatic averaging operations over certain time windows; on the other hand, a multirate structure is caused by the existence of different sampling rates, but the granularity of the recorded values is the same. This has two major and immediate implications. First, current methods are unable to handle variables with different resolutions in a consistent and rigorous way, since they tacitly assume that data represent instant observations and not averages over time windows. Second, even if data is available at a single-resolution (i.e., all variables with the same granularity), it is not guaranteed that the native resolution of the predictors is the most appropriate for modeling. Therefore, soft sensor development must address not only the selection of the best set of predictors to be included in the model, but also the optimum resolution to adopt for each predictor. In this work, two novel multiresolution frameworks for soft sensor development are proposed (MRSS-SC and MRSS-DC) that actively introduce multiresolution into the data by searching for the best granularity for each variable. The performance of these methodologies is comparatively assessed against current single-resolution counterparts. The optimized multiresolution soft sensors are bounded to be at least as good as their single-resolution versions, and the results confirm that they almost always perform substantially better.