(672a) Sensor Fusion with Irregular Sampling and Varying Measurement Delays

In multi-sensor fusion, several sources of information are combined in order to increase the estimation quality for the quantity of interest. This activity finds many applications from tactical missile defense to self-driving cars and the estimation of variables difficult to measure such as concentrations in chemical processes (Gao & Harris 2002, Kumar et al. 2007, Safari et al. 2014). In these situations, it is common to resource to laboratory analysis that provide more accurate measurements, but usually at slower sampling rates and with significant delays. Therefore, soft sensors and online analyzers are often introduced in the process to provide more frequent and updated measurements (Fatehi & Huang 2017).

Since Bar-Shalom & Campo (1986) introduced track-to-track fusion (TTF), several methods have been proposed based on the use of Kalman filter (KF) for sensor fusion. TTF makes use of a KF to track each sensor and fuses the sensors’ state estimates into a new state estimate using a static linear estimation equation (Chen et al. 2003). Gao & Harris (2002) reviewed measurement fusion processes and proposed a modified track-to-track fusion (MTF). However, these methodologies rely on first-principle models and do not capitalize on prior knowledge about the relative quality of the sensors. Therefore, in this work we present a KF based sensor fusion scheme that integrates data collected from a dynamic soft sensor, an online analyzer and a laboratory analyzer. Fusion occurs in the absence of a first-principle model and accommodates a less reliable (but more frequent) online analyzer recurring to laboratory measurements. This scheme has the capability for managing asynchronous sampling rates and detecting faulty measurements while reducing false alarms and missed identifications.

Two fusion schemes are proposed and outlined: a more classic tracked Bayesian fusion scheme (TBF) and a novel modification of the track-to-track algorithm, designated bias-corrected track-to-track fusion (BCTTF). When comparing these two schemes, the new BCTTF has shown to be better in terms of prediction performance and alarm identification sensitivity. This algorithm produces also a less noisy signal. The analysis of the figures of merit leads us to recommend the use of BCTTF as a fusion algorithm under multi-rate sensor fusion conditions.

The presented case study arises from a real world chemical plant and comprises two trayed distillation columns for product purification in a Dow production facility. Process measurements include pressures, temperatures and flow rates across the columns, as well as, reflux ratio and online analyzer readings from upstream reactors. Quality variables regard the concentrations of impurity components, say A and B. These are sampled every hour by an online analyzer and a soft sensor. Furthermore, every 12 hours a laboratory sample is grabbed for analysis (Lu & Chiang 2018). By applying the BCTTF algorithm and analyzing the results, we could confirm its good performance and infer that the laboratory sampling rate can be reduced to 1 sample every 48 hours without significant loss of prediction power. This allows for a meaningful cost reduction in laboratory material and hours of work. Finally, an Emergency Laboratory Sampling Plan is outlined to cope with possible faults that may put the online analyzer out of service and to have better control over the process during an abnormal operation time period.

References

Bar-Shalom Y, Campo L. The effect of the common process noise on the two-sensor fused-track covariance. IEEE Transactions on Aerospace and Electronic Systems. 1986;22:803-805.

Chen H, Kirubarajan T, Bar-Shalom Y. Performance limits of track-to-track fusion vs. centralized estimation: Theory and application. IEEE Transactions on Aerospace and Electronic Systems. 2003;39:386-398.

Fatehi A, Huang B. Kalman filtering approach to multi-rate information fusion in the presence of irregular sampling rate and variable measurement delay. Journal of Process Control. 2017;53:15-25.

Gao J, Harris C. Some remarks on Kalman filters for the multisensor fusion. Information Fusion. 2002;3:191-201.

Kumar M, Garg DP, Zachery RA. A method for judicious fusion of inconsistent multiple sensor data. IEEE Sensors Journal. 2007;7:723-733.

Lu B, Chiang L. Semi-supervised online soft sensor maintenance experiences in the chemical industry. Journal of Process Control. 2018;67:23-34.

Safari S, Shabani F, Simon D. Multirate multisensor data fusion for linear systems using Kalman filters and a neural network. Aerospace Science and Technology. 2014;39:465-471.