Adaptive modelling with tunable RBF network using multi-innovation RLS algorithm assisted by swarm intelligence

In this paper, we propose a new on-line learning algorithm for the non-linear system identification: the swarm intelligence aided multi-innovation recursive least squares (SI-MRLS) algorithm. The SI-MRLS algorithm applies the particle swarm optimization (PSO) to construct a flexible radial basis function (RBF) model so that both the model structure and output weights can be adapted. By replacing an insignificant RBF node with a new one based on the increment of error variance criterion at every iteration, the model remains at a limited size. The multi-innovation RLS algorithm is used to update the RBF output weights which are known to have better accuracy than the classic RLS. The proposed method can produces a parsimonious model with good performance. Simulation result are also shown to verify the SI-MRLS algorithm.

An implicit pole-assignment self-tuning regulator

A new self-tuning implicit pole-assignment algorithm is presented which, through the use of a pole compression factor and different RLS model and control structures, overcomes stability and convergence problems encountered in previously available algorithms. Computational requirements of the technique are much reduced when compared to explicit pole-assignment schemes, whereas the inherent robustness of the strategy is retained.

Return periods of losses associated with European windstorm series in a changing climate

Possible future changes of clustering and return periods (RPs) of European storm series with high potential losses are quantified. Historical storm series are identified using 40 winters of reanalysis. Time series of top events (1, 2 or 5 year return levels (RLs)) are used to assess RPs of storm series both empirically and theoretically. Additionally, 800 winters of general circulation model simulations for present (1960–2000) and future (2060–2100) climate conditions are investigated. Clustering is identified for most countries, and estimated RPs are similar for reanalysis and present day simulations. Future changes of RPs are estimated for fixed RLs and fixed loss index thresholds. For the former, shorter RPs are found for Western Europe, but changes are small and spatially heterogeneous. For the latter, which combines the effects of clustering and event ranking shifts, shorter RPs are found everywhere except for Mediterranean countries. These changes are generally not statistically significant between recent and future climate. However, the RPs for the fixed loss index approach are mostly beyond the range of pre-industrial natural climate variability. This is not true for fixed RLs. The quantification of losses associated with storm series permits a more adequate windstorm risk assessment in a changing climate.

Zero attracting recursive least squares algorithms

The l1-norm sparsity constraint is a widely used technique for constructing sparse models. In this contribution, two zero-attracting recursive least squares algorithms, referred to as ZA-RLS-I and ZA-RLS-II, are derived by employing the l1-norm of parameter vector constraint to facilitate the model sparsity. In order to achieve a closed-form solution, the l1-norm of the parameter vector is approximated by an adaptively weighted l2-norm, in which the weighting factors are set as the inversion of the associated l1-norm of parameter estimates that are readily available in the adaptive learning environment. ZA-RLS-II is computationally more efficient than ZA-RLS-I by exploiting the known results from linear algebra as well as the sparsity of the system. The proposed algorithms are proven to converge, and adaptive sparse channel estimation is used to demonstrate the effectiveness of the proposed approach.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.