TY - JOUR
T1 - Modelling and prediction of machining errors using ARMAX and NARMAX structures
AU - Fung, Eric H K
AU - Wong, Y. K.
AU - Ho, H. F.
AU - Mignolet, Marc
N1 - Funding Information:
The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU5151/97E). The authors would like to thank the reviewers for their useful comments.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2003/8
Y1 - 2003/8
N2 - Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.
AB - Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.
KW - ARMAX and NARMAX models
KW - Forecasting
KW - Machine error compensation
KW - Neural networks
KW - Recursive extended least square
KW - Recursive parameter estimation
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U2 - 10.1016/S0307-904X(03)00071-4
DO - 10.1016/S0307-904X(03)00071-4
M3 - Article
AN - SCOPUS:0042342397
VL - 27
SP - 611
EP - 627
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
SN - 0307-904X
IS - 8
ER -