Empirical modeling with globally enforced general constraints

Patent metadata

Field	Value
Publication number	US-2016018795-A1
Application number	US-201514868022-A
Country	US
Kind code	A1
Filing date	Sep 28, 2015
Priority date	Nov 6, 2012
Publication date	Jan 21, 2016
Grant date	—

Abstract

In certain embodiments, a method includes formulating an optimization problem to determine a plurality of model parameters of a system to be modeled. The method also includes solving the optimization problem to define an empirical model of the system. The method further includes training the empirical model using training data. The empirical model is constrained via general constraints relating to first-principles information and process knowledge of the system.

First claim

1 . A system comprising:
a controller configured to control operation of the system based at least in part on an empirical model subject, wherein the empirical model is configured to model operation of the system, the empirical model comprises a model parameter, and the controller is configured to:
determine an operational parameter of the system; and
automatically determine an empirical model based at least in part on the operational parameter by:
formulating an optimization problem comprising an objective function and a general constraint on the model parameter, the operational parameter, or both, wherein the objective function is configured to describe a relationship between the model parameter and the operational parameter;
randomly selecting a first vector in a model space upon which the empirical model is defined; and
solving the optimization problem to define the empirical model subject to the general constraints by determining the model parameter such that the general constraint is enforced at the first vector.

2 . The system of claim 1 , wherein the controller is configured to determine a first asymptotic behavior of the system and to determine the empirical model such that the empirical model comprises a second asymptotic behavior that conforms with the first asymptotic behavior.

3 . The system of claim 1 , wherein the controller is configured to:
select a second vector in the model space; and solve the optimization problem to define the empirical model subject to the general constraints by determining the model parameter such that the general constraint is enforced at the first vector and the second vector.

4 . The system of claim 3 , wherein the controller is configured to select the second vector based at least in part on an assigned probability value.

5 . The system of claim 1 , wherein:
the general constraint is configured to be expressed as a Taylor series expansion; and the controller is configured to solve the optimization problem such that each term of the Taylor series expansion is enforced at the first vector.

6 . The system of claim 1 , wherein the general constraint comprises first-principles information, process knowledge, or both.

7 . The system of claim 1 , wherein the first vector comprises the operational parameter.

8 . The system of claim 1 , wherein the controller is configured to select the first vector such that the general constraint is enforced across an entire model space.

9 . The system of claim 1 , wherein the system comprises a manufacturing plant, an oil refinery, a chemical plant, a power generation facility, or any combination thereof.

10 . A tangible, non-transitory, computer-readable medium comprising instructions configured to be executable by a control circuit of a controller, wherein the instructions comprise instructions to:
instruct, using the control circuit, a system to operate by processing inputs; determine, using the control circuit, operational data sets during operation of the system, wherein the operational data sets comprise sensor data, actuator data, the processing inputs, or any combination thereof; select, using the control circuit, a first subset of the operational data sets as training operational data sets and a second subset of the operational data sets as testing operational data sets; automatically determine, using the control circuit, an empirical model configured to model operation of subject to general constraints on parameters of the empirical model, operation of the system, or both by solving an optimization problem based on the training operational data sets; validate, using the control circuit, the empirical model based on the testing operational data sets; and control, using the control circuit, subsequent operation of the system based at least in part on the empirical model after validated.

11 . The computer-readable medium of claim 10 , wherein the instructions to determine the empirical model comprise instructions to:
formulate the optimization problem used to determine the parameters of the empirical model, wherein the instructions comprise instructions to:
determine an objective function describing relationship between the parameters of the empirical model and the operation of the system; and
determine the general constraints on the parameters of the empirical model, the operation of the system, or both; and
solve the optimization problem to define the empirical model subject to the general constraints, wherein the instructions comprise instructions to:
randomly select a plurality of vectors in a model space upon which the empirical model is defined; and
determine the parameters of the empirical model by solving the optimization problem such that the general constraints are enforced at each of the plurality of vectors.

12 . The computer-readable medium of claim 11 , wherein the instructions to determine the objective function comprise instructions to determine a weighting coefficient in the objective function corresponding with each of the general constraints.

13 . The computer-readable medium of claim 10 , comprising instructions to determine a first asymptotic behavior of the system;
wherein the instructions to determine empirical model comprise instructions to determine the empirical model with a second asymptotic behavior that conforms with the first asymptotic behavior.

14 . The computer-readable medium of claim 10 , comprising instructions to assign a probability value to each of the operational data sets;
wherein the instruction to select the first subset and the second subset comprises instructions to:
select the first subset based at least in part on the probability value assigned to each of the operational data sets; and
select the second subset based at least in part on the probability value assigned to each of the operational data sets.

15 . A method comprising:
controlling, using a controller, operation of a system based at least in part on an empirical model configured to model operation of the system; determining, using the controller, operational data sets during operation of the system, wherein the operational data sets comprise sensor data, actuator data, inputs to the system, or any combination thereof; automatically adapting, using the controller, the empirical model subject to general constraints on parameters of the empirical model, operation of the system, or both by solving an optimization problem based on the operational data sets; and controlling, using the controller, subsequent operation of the system based at least in part on the empirical model after adaptation.

16 . The method of claim 15 , wherein automatically adapting the empirical model comprises:
formulating the optimization problem used to determine the parameters of the empirical model, wherein formulating the optimization problem comprises:
determining an objective function describing relationship between the parameters of the empirical model and the operation of the system; and
determining the general constraints on the parameters of the empirical model, the operation of the system, or both; and
solving the optimization problem to define the empirical model subject to the general constraints, wherein solving the optimization problem comprises:
randomly selecting a plurality of vectors in a model space upon which the empirical model is defined; and
determining the parameters of the empirical model by solving the optimization problem such that the general constraints are enforced at each of the plurality of vectors.

17 . The method of cl

Assignees

• Rockwell Automation Tech Inc

Inventors

• Sayyar-Rodsari Bijan
• Hartman Eric Jon
• Schweiger Carl Anthony

Classifications

• G06N20/00 Primary

  Machine learning · CPC title

• G06F17/10

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• G06N3/02

  Neural networks · CPC title

• G05B13/041 Primary

  in which a variable is automatically adjusted to optimise the performance · CPC title

• G06N3/048

  Activation functions · CPC title