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Realization of the real-time time domain averaging method using the Kalman filter

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Abstract

Time Domain Averaging (TDA) is a traditional (though powerful) method of extracting periodic signals from a composite signal, based on averaging signal sections of the period chosen. The TDA method has been widely used for the condition monitoring of rotating machinery as a pre-process. However, the averaging process requires the measured data to be recorded, and thus may not be easily implemented as a real-time (or on-line) processor. This paper presents an alternative method of performing the TDA that can easily be realized as a real-time averaging processor by using the Kalman filter. The suggested method has another advantage over the traditional TDA method, which is to monitor the variance reduction continuously as the averaging process evolves. This may help to determine whether the averaging is further needed or not. The method is verified by using both simulated data and a measured signal.

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Abbreviations

A :

matrix of the state model

H :

matrix of the measurement function

K k :

Kalman gain matrix

P k :

error covariance matrix

Q :

process noise covariance matrix

R :

measurement noise covariance matrix

v k :

process noise vector

w k :

measurement noise vector

x k :

state vector at the k-th state

f p :

Fundamental frequency

M :

Number of segments

N :

number of elements in each segment

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Authors and Affiliations

  1. Department of Mechanical & Automotive Engineering, Andong National University, 388, Songcheon-dong, Andong, South Korea, 760-749

    Kihong Shin

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  1. Kihong Shin
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Correspondence to Kihong Shin.

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Shin, K. Realization of the real-time time domain averaging method using the Kalman filter. Int. J. Precis. Eng. Manuf. 12, 413–418 (2011). https://doi.org/10.1007/s12541-011-0053-4

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  • DOI: https://doi.org/10.1007/s12541-011-0053-4

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