Interaction Analysis of Multivariate Control Systems Under Bayesian Framework

Detection and quantification of interactions between the loops of a multivariable system are of interest for different purposes, such as control system design, optimization, fault diagnosis, and performance assessment. This paper proposes a new method for interaction analysis based on decomposing the estimated transfer function between variables in the form of impulse response coefficients. The method not only provides an estimation of the direct (feedback and interaction free) transfer function between the variables, but also provides a measure of strength of all the indirect paths connecting variables together individually. The advantage of the method is that it provides a complete picture of the different paths through which variables can influence each other along with an estimation of the energy transferred through each path independently. The analysis is performed by estimating structural vector autoregressive models under Bayesian framework. Bayesian approach provides certain advantages in terms of dealing with high dimensional variables and overparameterization problem. An appropriate design of the prior probability for the model parameters also better ensures convergence to a physically interpretable model. A procedure to design the prior distribution for the model parameters is presented in this paper.