### Abstract

Auto Regressive Integrated Moving Average (ARIMA) is a broad class of time series models, and it has been achieved using the statistical differencing approach. It is normally being performed using the computational method. Thus, it is useful to choose the suitable model from a possibly large selection of the available ARIMA formulations. The ARIMA approach was then analysed with the presence of stationary behaviour in a nonstationary data. For the purpose of the random data analysis, a nonstationary data that exhibiting a random behaviour was used. This random data was measured in the unit of microstrain on the lower suspension arm or a car travelling on a country road surface. With this engineering unit, hence, the data is known as a variable amplitude fatigue loading. Experimentally, the data was collected for 225 seconds at the sampling rate of 200 Hz, which gave 45,000 discrete data points. Using the computational analysis by means of statistical software package, the ARIMA parameters were estimated by the application of the data smoothing technique in order to reduce the random variation of the fatigue data. Therefore, the significant ARIMA parameters were established and being applied in the study of the variation in nonstationary data. For this paper, finally, it is suggested that the ARIMA method provided a good platform to analyse fatigue random data, especially in the scope of the durability research.

Original language | English |
---|---|

Pages (from-to) | 59-66 |

Number of pages | 8 |

Journal | WSEAS Transactions on Mathematics |

Volume | 7 |

Issue number | 2 |

Publication status | Published - Feb 2008 |

### Fingerprint

### Keywords

- ARIMA
- Fatigue
- Nonstationary data
- Statistical analysis
- Statistics

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Computational Mathematics
- Computer Science (miscellaneous)

### Cite this

*WSEAS Transactions on Mathematics*,

*7*(2), 59-66.

**Statistical analysis of a nonstationary fatigue data using the ARIMA approach.** / Abdullah, Shahrum; Ibrahim, M. D.; Zaharim, Azami; Mohd Nopiah, Zulkifli.

Research output: Contribution to journal › Article

*WSEAS Transactions on Mathematics*, vol. 7, no. 2, pp. 59-66.

}

TY - JOUR

T1 - Statistical analysis of a nonstationary fatigue data using the ARIMA approach

AU - Abdullah, Shahrum

AU - Ibrahim, M. D.

AU - Zaharim, Azami

AU - Mohd Nopiah, Zulkifli

PY - 2008/2

Y1 - 2008/2

N2 - Auto Regressive Integrated Moving Average (ARIMA) is a broad class of time series models, and it has been achieved using the statistical differencing approach. It is normally being performed using the computational method. Thus, it is useful to choose the suitable model from a possibly large selection of the available ARIMA formulations. The ARIMA approach was then analysed with the presence of stationary behaviour in a nonstationary data. For the purpose of the random data analysis, a nonstationary data that exhibiting a random behaviour was used. This random data was measured in the unit of microstrain on the lower suspension arm or a car travelling on a country road surface. With this engineering unit, hence, the data is known as a variable amplitude fatigue loading. Experimentally, the data was collected for 225 seconds at the sampling rate of 200 Hz, which gave 45,000 discrete data points. Using the computational analysis by means of statistical software package, the ARIMA parameters were estimated by the application of the data smoothing technique in order to reduce the random variation of the fatigue data. Therefore, the significant ARIMA parameters were established and being applied in the study of the variation in nonstationary data. For this paper, finally, it is suggested that the ARIMA method provided a good platform to analyse fatigue random data, especially in the scope of the durability research.

AB - Auto Regressive Integrated Moving Average (ARIMA) is a broad class of time series models, and it has been achieved using the statistical differencing approach. It is normally being performed using the computational method. Thus, it is useful to choose the suitable model from a possibly large selection of the available ARIMA formulations. The ARIMA approach was then analysed with the presence of stationary behaviour in a nonstationary data. For the purpose of the random data analysis, a nonstationary data that exhibiting a random behaviour was used. This random data was measured in the unit of microstrain on the lower suspension arm or a car travelling on a country road surface. With this engineering unit, hence, the data is known as a variable amplitude fatigue loading. Experimentally, the data was collected for 225 seconds at the sampling rate of 200 Hz, which gave 45,000 discrete data points. Using the computational analysis by means of statistical software package, the ARIMA parameters were estimated by the application of the data smoothing technique in order to reduce the random variation of the fatigue data. Therefore, the significant ARIMA parameters were established and being applied in the study of the variation in nonstationary data. For this paper, finally, it is suggested that the ARIMA method provided a good platform to analyse fatigue random data, especially in the scope of the durability research.

KW - ARIMA

KW - Fatigue

KW - Nonstationary data

KW - Statistical analysis

KW - Statistics

UR - http://www.scopus.com/inward/record.url?scp=48849105125&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48849105125&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:48849105125

VL - 7

SP - 59

EP - 66

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

IS - 2

ER -