6.0 Conclusions
The following conclusions may be drawn from our study.
- The linear least square error method (LLS) and 2D interpolation method
exhibit lower mean relative error (-4.2% and +1.2%) compared to that
of the test dataset before calibration (-8.3%). Either modeling
approaches was able to improve accuracy (indicated by the improvement
in systematic error) but not the precision (indicated by the standard
deviation of relative errors, which is associate with the distribution
patterns of random errors).
- Three types of Gaussian Naïve Bayes modeling approaches were tested.
The best result has succeeded to reduce the standard deviation value
of relative error from ±20.3% (of test data) to ±8.0 %. However, the
reduction is achieved at the cost of increased mean relative error
from -8.3% (of test data) to – 9.5% (after data cleaning). Results
also show the Gaussian Naïve Bayes method is useful to improve random
errors, but not the systematic errors.
- Since different types of errors may coexist in the same data set (such
as systematic errors and random errors), we show that use of multiple
modeling approaches can successfully reduce both types of errors. When
the 2D interpolation method was applied to the test data using the
Gaussian Naïve Bayes algorithm, the mean relative errors were reduced
from -8.3% (of test dataset) to -0.6% (after data cleaning), and
standard deviation of the relative errors was reduced from ±20.3% to
±13.7%.
- These results proved that multiple machine learning models can be
trained to evaluate the sampled data from flow meter, thus
re-calibrating both the systematic errors and random errors.
- Our study shows a high accuracy ultrasonic flow meter with systematic
errors less than 1% for oil and gas multiphase application is
possible with the aid of artificial intelligence technology.