NARMAXNon-Linear Auto-Regressive Moving Average with Exogeneous Input
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After the learning and fitting processes of network, the acquired network is then applied for prediction of time delay system [10,11] based on the NARMAX model.
NARMAX model is widely used in system identification and prediction [12,13]:
It can be noted in (1) that the multidimension inputs of NARMAX model include the past [n.sub.y] system outputs and [n.sub.u] system inputs.
For the NARMAX model based on neural network, we need to establish suitable inputs for the model [18].
He describes several nonlinear system identification methods, but focuses particularly on nonlinear autoregressive moving average model with exogenous inputs (NARMAX) methods.
The common nonlinear dynamic system is described as a form of NARMAX model as follows:
U model is a special structure form of NARMAX model, which not only has a simple structure but also can be widely applied to many nonlinear systems.
Long, "A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term," ISA Transactions, vol.
It has been well proven that the applications of autoregressive models like nonlinear autoregressive (NAR), nonlinear autoregressive with exogenous input (NARX), or nonlinear autoregressive moving average with exogenous input (NARMAX) are capable of predicting the time-series data with high fidelity.
Exceptions include a series of interesting results such as the work of [23], where the authors make a study of the possible use of SVM for system identification, in particular for parameter estimation in discrete-time linear models and model structure identification for nonlinear models, more specifically Nonlinear Auto-Regressive Moving Average with eXogeneous Input (NARMAX) models.