Recursive least mean dual p-power solution to the generalization of evolving fuzzy system under multiple noises

Online neuro-fuzzy model learning of dynamic systems with measurement noise

“…The generalised total least squares method can also be used for modelling single-input single-output systems [48] and multi-input single-output systems [43] with noisy inputs and outputs, but they are not for NF model updating. The generalised total least squares algorithm is extended in [21] for training an NF model with partial input signals corrupted by noise and also in [19] considering multiple types of noises. However, the method in [21] needs prior knowledge of the noise variances, while the method in [19] assumes that the noise distribution is known, which restricts their online application.…”

“…The generalised total least squares algorithm is extended in [21] for training an NF model with partial input signals corrupted by noise and also in [19] considering multiple types of noises. However, the method in [21] needs prior knowledge of the noise variances, while the method in [19] assumes that the noise distribution is known, which restricts their online application. Lughofer [31] proposes a recursive weighted total least squares method for estimating NF model parameters with noisy input data without requiring prior knowledge of the noise variances or distribution.…”

“…However, their work needs an extra algorithm called Incremental Polynomial Kalman Smoother for recursively estimating the noise covariance matrix, which improves the design complexity. Moreover, all the existing methods [19,21,31,40] do not consider more complex systems with time-varying dynamics and changing operational conditions. Therefore, there is a need for new algorithms to update the NF model parameters for complex nonlinear systems based on noisy data, without requiring a prior knowledge or complex design for dealing with the noise.…”

“…To overcome the above limitations in the existing methods, this paper presents a novel NF model learning method. Compared to the state-of-the-art methods [19,21,31,40], the main contributions of this paper are summarised as follows:…”

“…(1) An online NF modelling strategy is developed for multi-input single-output dynamic systems based on noisy data. The strategy addresses modelling of nonlinear systems with time-varying dynamics and changing operational conditions, which is not studied in [19,21,31,40]. The proposed method is directly applicable for multi-input multi-output systems by presenting them using a set of multiinput single-output models.…”