As mentioned previously, inferential measurement systems are usually developed using 'data-based' methodologies. That is, the model used to infer primary outputs are usually developed using data collected from the process. Whilst this make the strategy somewhat generic, the performances of the resulting inferential measurement models are influenced significantly by the quality of the data used to generate them. In developing any type of models models using historical plant data, we must always remember the adage: rubbish in, rubbish out.

As the flow chart on the left shows, the first and most important thing to do is to rid the data of spurious/errant points or outliers. These can have significant impact on the model structure selection and estimator testing stages of the development cycle. Next, noise in the data should be attentuated as much as possible. Here we advocate the use of low phase shift filters (filters that have the least time-lags on the processed signals). This is because the inferential estimator has to provide compensation for measurement delays.

If after noise filtering, the processed signals lags the raw data significantly, then the predictive capabilities of the estimator will be reduced. On very noisy systems, this loss of  predictive capabilities can be very pronounced. An algorithm that we have found to give good phase characteristics and yet is easy to understand and implement is the Brown's Exponential Smoother. This algorithm is quite commonly used in time-series forecasting applications.

As an example, consider the simulated red noisy signal in the following graph.

The blue plot is the original noise free sequence. Application of a first order low-pass filter gives rise to the following filtered signal:

Notice that while the level of noise has been removed significantly, the filtered signal lags the real signal quite considerable. Application of a minimum phase lag filter, on the other hand, yields the following performance:

Here, the overall degree of noise attenuation is just as good if not better, and the lag between filtered signal and the true underlying one is quite acceptable. Details of the algorithm that gave this performance can be found in:

Tham, M.T. and Parr, A. (1994). 'Succeed at online data validation and reconstruction'. Chemical Engineering Progress, May, 46-56.

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