Uncertainty propagation system and method

• US 20040260526A1
• Filed: 07/15/2004
• Published: 12/23/2004
• Est. Priority Date: 06/06/2001
• Status: Active Grant

• Current Assignee: Callaghan Innovation
• Original Assignee: Industrial Research Limited
• Inventors: Hall, Blair Durham, Willink, Robin Daniel
• Granted Patent: US 7,130,761 B2
• Time in Patent Office: Days
• US Class Current: 703/12
• CPC Class Codes: G01R 22/00 Arrangements for measuring time integral of electric power or current, e.g. electricity meters
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

The invention provides a method of calculating uncertainty in the system represented as two or more modules comprising the steps of passing uncertainty information from each module to at least one further module; and calculating uncertainty in the measurement result from the information exchanged between the modules. The invention also provides a method of propagating uncertainty in a measurement system and also provides related systems for calculating uncertainty and propagating uncertainty.

Claims

1. An uncertainty calculation system represented as a plurality of connected modules:

wherein each module is associated with a set of inputs, one output and one function, in which the function is configured to determine the value of the output from the value of each input to the module (module-input) and

to determine the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input); and

wherein one module has an output that represents a measurement result and in which the contributions to the uncertainty are combined to determine the uncertainty in the measurement result.

2. A system as claimed in claim 1 wherein the values of input quantities and output quantities and measurement result are scalars.

3. A system as claimed in claim 2 wherein:

for each specific module the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of a system-input is determined as the sum of terms for each input to the module;

each term being the partial derivative of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input.

4. A system as claimed in claim 3 wherein the method further comprises the step of calculating the uncertainty in the measurement result as the standard deviation of the statistical distribution associated with the measurement result.

5. A system as claimed in claim 1 wherein the values of input quantities and output quantities and measurement results are vectors.

6. A system as claimed in claim 5 wherein:

for each specific module the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of a system-input is determined as the sum of terms for each input to the module;

each term being the Jacobian matrix of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input.

7. A system as claimed in claim 6 wherein the method further comprises the step of calculating the uncertainty in the measurement result as the variance-covariance matrix of the multidimensional statistical distribution associated with the measurement result.

8. An uncertainty calculation system comprising:

two or more modules representing a measurement system;

each with the ability to pass uncertainty information to at least one further module; and

a calculating component configured to calculate uncertainty in the measurement system from the information passed between the modules.

9. A system as claimed in claim 8 wherein the system enables information exchange between modules, and the calculating component is configured to combine the uncertainty associated with each of the inputs to the system to calculate the uncertainty in the measurement result.

10. A system as claimed in claim 8 or claim 9 wherein the two or more modules represent a decomposition of a model of the measurement system.

11. A system as claimed in any one of claims 8 to 10 claim 8 further configured to calculate a measurement result from the information passed between the modules.

12. A method of calculating uncertainty in the measurement result of a measurement system represented as a plurality of connected modules, the method comprising the steps of:

associating each module with a set of inputs, one output and one function;

using the function to determine the value of the output from the value of each input to the module (module-input);

using the function to determine the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of any input to the system (system-input); and

generating an output that represents a measurement result in which the contributions to the uncertainty are combined to determine the uncertainty and the measurement result.

13. A method of calculating uncertainty as claimed in claim 12 wherein the values of input quantities and output quantities and measurement results are scalars.

14. A method of calculating uncertainty as claimed in claim 13 further comprising the step of determining, for each specific module, the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of a system-input as the sum of terms for each input to the module, each term being the partial derivative of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input.

15. A method of calculating uncertainty as claimed in claim 14 further comprising the step of calculating the uncertainty in the measurement result as the standard deviation of the statistical distribution associated with the measurement result.

16. A method of calculating uncertainty as claimed in claim 12 wherein the values of input quantities and output quantities and measurement results are vectors.

17. A method of calculating uncertainty as claimed in claim 16 further comprising the step of determining, for each specific module, the contribution to the uncertainty in the value of the output arising from the uncertainty in the value of a system-input as the sum of terms for each input to the module, each term being the Jacobian matrix of the module function with respect to that module-input multiplied by the contribution to the uncertainty in the value of that module-input arising from the uncertainty in the value of that system-input.

18. A method of calculating uncertainty as claimed in claim 17 further comprising the step of calculating the uncertainty in the measurement result as the variance-covariance matrix of the multidimensional statistical distribution associated with the measurement result.