Condition monitoring for the quadruple water tank system using H-infinity Kalman Filtering

Abstract

The problem of statistical fault diagnosis for the quadruple watertanks system is examined. The solution of the fault diagnosis problem for the dynamic model of the four-water tanks system is a non-trivial case, due to nonlinearities and the system’s multivariable structure. In the article’s approach, the system’s dynamic model undergoes first approximate linearization around a temporary operating point which is recomputed at each sampling period. The linearization procedure relies on Taylor series expansion and on the computation of the Jacobian matrices of the state-space description of the system. The H-infinity Kalman Filter is used as a robust state estimator for the approximately linearized model of the quadruple water tanks system. By comparing the outputs of the H-infinity Kalman Filter against the outputs measured from the real water tanks system the residuals sequence is generated. It is concluded that the sum of the squares of the residuals’ vectors, being weighted by the inverse of the associated covariance matrix, stands for a stochastic variable that follows the χ2 distribution. As a consequence, a statistical method for condition monitoring of the quadruple water tanks system is drawn, by using the properties of the χ2 distribution and the related confidence intervals. Actually, normal functioning can be ensured as long as the value of the aforementioned stochastic variable stays within the previously noted confidence intervals. On the other side, one can infer the malfunctioning of the quadruple water tanks system with a high level of certainty (e.g. of the order of 96% to 98%), when these confidence intervals are exceeded. The article’s method allows also for fault isolation, that is for identifying the specific component of the quadruple water tanks system that has been subject to fault or cyber-attack.