Ask Russ Rhinehart - How does One Calibrate First-Principles Models?

Russ' Response:

Calibrate means to adjust coefficient values. In process instruments calibration usually means to adjust the zero and span knobs to convert the sensor response to the measurement (for instance conductivity to concentration, or millivolt to temperature). For process simulators, calibration means adjusting model coefficients to best fit the model to data – to create the Digital Twin.

Why is model coefficient adjustment needed? Our models are not perfect. For instance, models for flow pressure losses in piping systems are based on the ideal Bernoulli squared velocity and a sum of loss factors. Realities, however, make true values different from the book values. Coefficient adjustment may be needed to better fit the ideal model to reality.

The choice of which model coefficient is to be adjusted should be compatible with the following principles:

1. The model coefficient must represent a process feature of uncertain value. (If the value could be known, adjustment would not be needed.)
2. The model coefficient value must have a significant impact on the modeled input-output relation. (If it has an inconsequential impact, there is no justification to adjust it.)
3. Each coefficient to be adjusted needs at least one independent response variable.

Some coefficients will relate to transient responses only. Such as a valve or in-tank mixing time-constant or a transport delay. Some coefficients will relate to steady state responses such as catalyst efficiency, or heat exchanger fouling. If you want to adjust coefficients related to transient conditions, then your data needs to include transient data. On the other hand, you can use transient data to adjust coefficients related to steady state conditions.

In any case, the data should have significant input changes so that the output response is large relative to measurement noise level and drifts due to unmeasured variables.

An extended version of this pod with details and examples can be accessed under the MODELING/SIMULATION Menu on my web site, www.r3eda.com. For more information on this topic email Russ Rhinehart at [email protected].