(585f) Noise Covariance Estimation for an Air Separation Plant

Noise is ubiquitous in systems engineering. Therefore, process models often consist of a deterministic part describing the underlying physics and a stochastic part describing the noises affecting a system. Identifying the noise model is important because it is necessary in order to build an optimal state estimator for a system. Two assumptions are common in modeling noises:

1) There are two distinct types of noise: process noise and measurement noise.
2) Noises can be modeled as zero-mean Gaussian random variables.

Under these assumptions, the task of identifying the noise model reduces to identifying the process and measurement noise covariance matrices.

Given the deterministic part of a system model, there are several methods to estimate noise covariances from process data. Maximum likelihood estimation (MLE), often using the expectation maximization (EM) algorithm, is perhaps the most common. The major drawback of this approach is that the objective function of the MLE problem scales with the amount of data being processed and it can quickly become intractable. A more recent approach is the autocovariance least-squares (ALS) algorithm. The ALS problem is generally easier to solve than the MLE problem, but yields solutions that lack the clear statistical interpretation of the MLE approach.

In this work we present a case study using a model from an industrial air separation plant. We investigate the relevance and utility of noise identification in chemical engineering systems and the issues that arise when using these methods with industrial models.