The complexity of industrial systems and the mathematical models to describe them increases. In many cases, point sensors are no longer sufficient to provide controllers and monitoring instruments with the information necessary for operation. The need for other types of information, such as audio and video, has grown. These are examples of information-rich signals for which suitable applications range in a broad spectrum from micro-electromechanical systems and bio-medical engineering to paper making and steel production.
Recursive parameter estimation algorithms are employed to identify parameters in a mathematical model from measurements of input and output signals. For accurate parameter estimation, the input signal must be persistently exciting, i.e. such that important features of the modelled system are reflected in the output over a sufficient period of time.
The Stenlund-Gustafsson (SG) algorithm, a Kalman filter based method for recursive parameter estimation in linear regression models, that does not diverge under lack of excitation, is studied. The stationary properties of the algorithm and the corresponding Riccati equation are formulated in terms of the excitation space spanned by the regressor vectors.
Furthermore, it is shown that the Riccati equation of the studied algorithm can be solved element-wise. Convergence estimates for the elements of the solution to the Riccati equation are provided, directly relating convergence rate to the signal-to-noise ratio in the regression model. An element-wise form of the parameter update equation is also given, where the connection to specific elements of the solution to the Riccati equation is apparent.
The SG-algorithm is employed for two applications with audio signals. One is in an acoustic echo cancellation setting where its performance is shown to match that of other well-known estimation techniques, such as the normalized least mean squares and the Kalman filter. When the input is not sufficiently exciting, the studied method performs best of all considered schemes.
The other application is the Linz-Donawitz (LD) steel converter. The converter consists of a vessel with molten metal and foam is produced to facilitate chemical reactions. A common problem, usually referred to as slopping, arises when the foam rises above the limits of the vessel and overflows. A warning system is designed, based on the SG-algorithm and change detection methods, to give alarms before slopping occurs. A black-box model relates different sensor values of which one is the microphone signal picked up in the area above the converter. The system detected slopping correctly in 80% of the blows in field studies at SSAB Oxelösund.
A practical example of a vision-based system is provided by cavity form estimation in a water model of the steel bath. The water model is captured from the side by a video camera. The images together with a non-linear model are used to estimate important process parameters, related to the heat and mass transport in the LD-converter.