Abstract

The stability of a fiber optic gyroscope (FOG) in measurement while drilling (MWD) could vary with time because of changing temperature, high vibration, and sudden power failure. The dynamic Allan variance (DAVAR) is a sliding version of the Allan variance. It is a practical tool that could represent the non-stationary behavior of the gyroscope signal. Since the normal DAVAR takes too long to deal with long time series, a fast DAVAR algorithm has been developed to accelerate the computation speed. However, both the normal DAVAR algorithm and the fast algorithm become invalid for discontinuous time series. What is worse, the FOG-based MWD underground often keeps working for several days; the gyro data collected aboveground is not only very time-consuming, but also sometimes discontinuous in the timeline. In this article, on the basis of the fast algorithm for DAVAR, we make a further advance in the fast algorithm (improved fast DAVAR) to extend the fast DAVAR to discontinuous time series. The improved fast DAVAR and the normal DAVAR are used to responsively characterize two sets of simulation data. The simulation results show that when the length of the time series is short, the improved fast DAVAR saves 78.93% of calculation time. When the length of the time series is long ( samples), the improved fast DAVAR reduces calculation time by 97.09%. Another set of simulation data with missing data is characterized by the improved fast DAVAR. Its simulation results prove that the improved fast DAVAR could successfully deal with discontinuous data. In the end, a vibration experiment with FOGs-based MWD has been implemented to validate the good performance of the improved fast DAVAR. The results of the experience testify that the improved fast DAVAR not only shortens computation time, but could also analyze discontinuous time series.

Highlights

  • Gyroscopes are sensors that are appropriate for a wide variety of applications in the inertial navigation scope

  • Both the normal dynamic Allan variance (DAVAR) algorithm and the fast algorithm become invalid for discontinuous time series

  • The results prove that the improved fast DAVAR is correct

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Summary

Introduction

Gyroscopes are sensors that are appropriate for a wide variety of applications in the inertial navigation scope. The output signal of the gyroscopes in the MWD system would be interrupted due to error in the mud pulse communication or sudden power outages In this case, both the classical DAVAR and the fast DAVAR algorithms are unable to deal with discontinuous time series. In order to deal with the discontinuous gyroscope data, a further improvement is made on the basis of the fast DAVAR.

Structure of the FOG-Based MWD
Allan Variance
Different noise terms appear in in different regions of
Computation Process of Dynamic Allan Variance
Fast Dynamic Allan Variance
Extension to Discontinuous Time Series
Models and Simulations
Experiments
Findings
Conclusions

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