Engineering Optimization

45Case Study 10: Data Reconciliation

45.1 Description and Analysis

Values of data from online sensors are corrupted by sensor drift, which could be due to ambient conditions (temperature, humidity, etc.), dust accumulation, element wear, corrosion, cumulative vibration damage, etc. It could also be that the sensor was not perfectly calibrated, which leads to incorrect values. These aspects mean that the value is biased, is in error, and has a systematic error.

Further, measurements don’t occur just once; instead, process sensors are sampled once each minute, or second, or whatever the sampling interval. This produces a sequence of biased values.

Further, the sensors report a noisy value. The value with the systematic error is also confounded with random perturbations on each sampling, which can arise from turbulence, mechanical vibrations, electromagnetic interference, imperfect mixing, etc. This is termed random error. (These temporal perturbations about the nominal value might not be independent or Gaussian. There are often autocorrelation and non‐Gaussian drivers. This exercise will not consider those cases.)

Random error can be reduced by averaging sequential data. However, even if the random error could be eliminated, the systematic bias remains. Data reconciliation is a procedure to use online data to estimate the systematic errors of the same online data. In data reconciliation the correction is based on redundant measurements (but not at the same location) and a model. ...