Merging Parameter Estimation and Classification Using LASSO

Soft sensing is a way to indirectly obtain information of signals for which direct sensing is difficult or prohibitively expensive. It may not a priori be evident which sensors provide useful information about the target signal. There may be sensors irrelevant for the estimation as well as sensors for which the information is very poor. It is often required that the soft sensor should cover a wide range of operating points. This means that some sensors may be useful in certain operating conditions while irrelevant in others, while others may have no bearing on the target signal whatsoever. However, this type of structural information is typically not available but has to be deduced from data. A further compounding issue is that multiple operating conditions may be described by the same model, but which ones is not known in advance either. In this contribution, we provide a systematic method to construct a soft sensor that can deal with these issues. While the different models can be used, we adopt the multi-input single output finite impulse response models since they are linear in the parameters. We propose a single estimation criterion, where the objectives are encoded in terms of model fit, model sparsity (reducing the number of different models), and model parameter coefficient sparsity (to exclude irrelevant sensors). A post-processing model clustering step is also included. As proof of concept, the method is tested on field test datasets from a prototype vehicle.