M6: Introduction to STAN and data reconciliation

Question 1

What are the priciples behind data reconciliation / flow adjustment?

Answer 1

Flows and their uncertainties are adjusted by making use of the mass balance principle.

Find best estimate for the variable X. The difference between the measured value of X and the best estimate is called the residuals. In data reconcilliation the goal is to minimize the residuals by using different methods. We have used the least square method (Gauss method).

Question 2

Mention 4 different methods to minimize the residuals:

Answer 2

• minimize sum of residuals
• minimize largest residual
• minimize sum of the squared abs. residuals
• minimize sum of squared relative residuals

Question 3

List the two benefits of data reconciliation:

Answer 3

1. Adjusted flows are consistent with mass balance principle
2. Reconciliation provides information about
   • -> possible systematic errors (e.g., missing flows)
   • -> accuracy of results
   • -> propagation of uncertainties (measurement errors)
   • -> how to optimize measurement strategy

Question 4

Motivation of using data reconcilliation.

Answer 4

1. Computation capacity for complex MFA
2. All flows have uncertainties
   The case on slide 14 using a geometric solution makes two important assumptions that limit its application:
   –> All flows are measured
   –> All flows are constant without uncertainties
   Not realistic for many MFA applications.
3. Not all flows have information

Question 5

What are the take away messages from the lecture about data reconcilliation?

Answer 5

• Data reconciliation does not provide the true values
–> only best estimates for a balanced system

• Data reconciliation only works for random errors
–> if the system is not understood correctly (systematic errors) data reconciliation may even worsen the flow values!!!