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A hybrid model, which is composed of an autoregressive moving-average (ARMA) filter and a feedforward neural network (FNN), is proposed to increase prediction accuracy and to reduce learning time for the estimation of thermal deformations in a machine tool. The ARMA filter is used to yield state variables which establish the relationship between the present and past states of thermal deformations for the reservation of the influences of past temperatures and deformation. Otherwise, the quantity of FNN inputs is very vast because of the data needed for the non-linear system. These state variables, which are estimated by past measured temperatures and past estimated deformation, serve as inputs of the FNN. The algorithms of this hybrid model are presented and verified by the experimental results; also, the prediction accuracy is compared with the ARMA and FNN independently for the same learning iterations.

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