13,939 research outputs found
On the smoothness of nonlinear system identification
We shed new light on the \textit{smoothness} of optimization problems arising
in prediction error parameter estimation of linear and nonlinear systems. We
show that for regions of the parameter space where the model is not
contractive, the Lipschitz constant and -smoothness of the objective
function might blow up exponentially with the simulation length, making it hard
to numerically find minima within those regions or, even, to escape from them.
In addition to providing theoretical understanding of this problem, this paper
also proposes the use of multiple shooting as a viable solution. The proposed
method minimizes the error between a prediction model and the observed values.
Rather than running the prediction model over the entire dataset, multiple
shooting splits the data into smaller subsets and runs the prediction model
over each subset, making the simulation length a design parameter and making it
possible to solve problems that would be infeasible using a standard approach.
The equivalence to the original problem is obtained by including constraints in
the optimization. The new method is illustrated by estimating the parameters of
nonlinear systems with chaotic or unstable behavior, as well as neural
networks. We also present a comparative analysis of the proposed method with
multi-step-ahead prediction error minimization
A new class of wavelet networks for nonlinear system identification
A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions
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Behavioural pattern identification and prediction in intelligent environments
In this paper, the application of soft computing techniques in prediction of an occupant's behaviour in an inhabited intelligent environment is addressed. In this research, daily activities of elderly people who live in their own homes suffering from dementia are studied. Occupancy sensors are used to extract the movement patterns of the occupant. The occupancy data is then converted into temporal sequences of activities which are eventually used to predict the occupant behaviour. To build the prediction model, different dynamic recurrent neural networks are investigated. Recurrent neural networks have shown a great ability in finding the temporal relationships of input patterns. The experimental results show that non-linear autoregressive network with exogenous inputs model correctly extracts the long term prediction patterns of the occupant and outperformed the Elman network. The results presented here are validated using data generated from a simulator and real environments
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