Adaptive Filter Based On Lyapunov Stability Theory: Application to On-line Bit-Rock Interaction Surveillance

AbstractAn adaptive algorithm based on Lyapunov Stability Theory (LST) is developed in this paper. This algorithm is obtained from Recursive Least Square (RLS) approach. Indeed, it is well-known that performances of RLS based methods depend mainly on the difficult choice of the forgetting factor. For this reason, we propose to make the forgetting factor variable by using gradient descent method (GD) where the learning rate is adaptive through LST. The developed strategy represents an extension of the existing variable forgetting factor obtained by adopting the GD method. The advantage of the proposed algorithm besides the stability provided lies in the good performances given in terms of tracking ability of time varying parameters. Particularly, these kinds of approaches are very useful in the context of faults diagnosis in order to detect faults which might occur at their earliest possible stage. The efficiency of the proposed approach is first highlighted by using simulated data; secondly they are emphasized, for faults diagnosis purpose, thanks to experimental data obtained from an oilfield drilling process that is considered as a case study.