A hybrid of nonlinear autoregressive model with exogenous input and autoregressive moving average model for long-term machine state forecasting

Hong Thom Pham, V.T. Tran, Bo-Suk Yang

Research output: Contribution to journalArticleAcademicpeer-review

40 Citations (Scopus)


This paper presents an improvement of hybrid of nonlinear autoregressive with exogenous input (NARX) model and autoregressive moving average (ARMA) model for long-term machine state forecasting based on vibration data. In this study, vibration data is considered as a combination of two components which are deterministic data and error. The deterministic component may describe the degradation index of machine, whilst the error component can depict the appearance of uncertain parts. An improved hybrid forecasting model, namely NARX–ARMA model, is carried out to obtain the forecasting results in which NARX network model which is suitable for nonlinear issue is used to forecast the deterministic component and ARMA model are used to predict the error component due to appropriate capability in linear prediction. The final forecasting results are the sum of the results obtained from these single models. The performance of the NARX–ARMA model is then evaluated by using the data of low methane compressor acquired from condition monitoring routine. In order to corroborate the advances of the proposed method, a comparative study of the forecasting results obtained from NARX–ARMA model and traditional models is also carried out. The comparative results show that NARX–ARMA model is outstanding and could be used as a potential tool to machine state forecasting.
Original languageEnglish
Pages (from-to)3310-3317
JournalExpert systems with applications
Issue number4
Publication statusPublished - 2010
Externally publishedYes



  • Autoregressive moving average (ARMA)
  • Nonlinear autoregressive with exogenous input (NARX)
  • Long-term prediction
  • Machine state forecasting

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