CA2414707A1 - Computer method and apparatus for constraining a non-linear approximator of an empirical process - Google Patents

Computer method and apparatus for constraining a non-linear approximator of an empirical process Download PDF

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CA2414707A1
CA2414707A1 CA002414707A CA2414707A CA2414707A1 CA 2414707 A1 CA2414707 A1 CA 2414707A1 CA 002414707 A CA002414707 A CA 002414707A CA 2414707 A CA2414707 A CA 2414707A CA 2414707 A1 CA2414707 A1 CA 2414707A1
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linear
initial
network model
linear network
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CA2414707C (en
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Paul Turner
John P. Guiver
Brian Lines
S. Steven Treiber
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Aspentech Corp
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric

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  • Engineering & Computer Science (AREA)
  • Artificial Intelligence (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Automation & Control Theory (AREA)
  • General Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Software Systems (AREA)
  • Medical Informatics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Feedback Control In General (AREA)
  • Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
  • Error Detection And Correction (AREA)
  • Control By Computers (AREA)

Abstract

A constrained non-linear approximator for empirical process control is disclosed. The approximator contains the behavior of the derivative of a subject empriical model without adversely affexting the ability of the model to represent generic non-linear relationships. There are threee stages to developing the constrained non-linear approximator. The first stage is the specification of the general shape of the gain trajectory or base non-linear function which is specified graphically, algebraically or generaiclly and is used as the basis for transfer functions used in the second stage. The second stage of the invention is the interconnection of the transfer functions to allow non-linear approxiamtion. The final stage of the invention is the constrained optimization of the model coefficients such that the general shape of the input/output mappings (and their corresponding derivatives) are conserved.

Claims (24)

1. A method for modeling a non-linear empirical process, comprising the steps of:
creating an initial model generally corresponding to the non-linear empirical process to be modeled, the initial model having an initial input and an initial output;
constructing a non-linear network model based on the initial model, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output; and optimizing the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model.
2. The method of Claim 1, wherein the step of creating the initial model includes specifying a general shape of a gain trajectory for the non-linear empirical process.
3. The method of Claim 1, wherein the step of creating the initial model includes specifying a non-linear transfer function suitable for use in approximating the non-linear empirical process.
4. The method of Claim 3, wherein the non-linear network includes interconnected transformation elements and the step of constructing the non-linear network includes incorporating the non-linear transfer function into at least one transformation element.
5. The method of Claim 4, wherein the step of optimizing the non-linear model includes setting constraints by taking a bounded derivative of the non-linear transfer function.
6. The method of Claim 5, wherein the non-linear transfer function includes the log of a hyperbolic cosine function.
7. The method of Claim 1, wherein the non-linear network model is based on a layered network architecture having a feedforward network of nodes with input/output relationships to each other, the feedforward network having transformation elements; each transformation element having a non-linear transfer function, a weighted input coefficient and a weighted output coefficient; and the step of optimizing the non-linear network model includes constraining the global behavior of the non-linear network model to a monotonic transformation based on the initial input by pairing the weighted input and output coefficients for each transformation element in a complementary manner to provide the monotonic transformation.
8. The method of Claim 1, wherein the step of optimizing the non-linear network model comprises adjusting the optimizing based on information provided by an advisory model that represents another model of the non-linear empirical process that is different from the initial model, the non-linear network model, and the optimized model.
9. The method of Claim 8, wherein the advisory model is a first principles model of the non-linear empirical process.
10. The method of Claim 1, wherein the non-linear empirical process is part of a greater process, and the method further includes the step of deploying the optimized model in a controller that controls the greater process.
11. A computer apparatus for modeling a non-linear empirical process, comprising:
a model creator for creating an initial model generally corresponding to the non-linear empirical process to be modeled, the initial model having an initial input and an initial output;

a model constructor coupled to the model creator for constructing a non-linear network model based on the initial model, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output; and an optimizer coupled to the model constructor for optimizing the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model.
12. The computer apparatus of Claim 11, wherein the model creator specifies a general shape of a gain trajectory for the non-linear empirical process.
13. The computer apparatus of Claim 11, wherein the model creator specifies a non-linear transfer function suitable for use in approximating the non-linear empirical process.
14. The computer apparatus of Claim 13, wherein the non-linear network includes interconnected transformation elements and the model constructor incorporates the non-linear transfer function into at least one transformation element.
15. The computer apparatus of Claim 14, wherein the optimizer sets constraints by taking a bounded derivative of the non-linear transfer function.
16. The computer apparatus of Claim 15, wherein the non-linear transfer function includes the log of a hyperbolic cosine function.
17. The computer apparatus of Claim 11, wherein the model constructor constructs the non-linear network model based on a layered network architecture having a feedforward network of nodes with input/output relationships to each other, the feedforward network having transformation elements, each transformation element having a non-linear transfer function, a weighted input coefficient and a weighted output coefficient; and the optimizer constrains the global behavior of the non-linear network model to a monotonic transformation based on the initial input by pairing the weighted input and output coefficients for each transformation element in a complementary manner to provide the monotonic transformation.
18. The computer apparatus of Claim 11, further comprising an advisory model that represents another model of the non-linear empirical process that is different from the initial model, the non-linear network model, and the optimized model; and wherein the optimizer adjusts the optimizing based on information provided by the advisory model.
19. The computer apparatus of Claim 18, wherein the advisory model is a first principles model of the non-linear empirical process.
20. The computer apparatus of Claim 11, wherein the non-linear empirical process is part of a greater process managed by a controller coupled to the optimizer, and the optimizer communicates the optimized model to the controller for deployment in the controller.
21. A computer program product that includes a computer usable medium having computer program instructions stored thereon for modeling a non-linear empirical process, such that the computer program instructions, when performed by a digital processor, cause the digital processor to:
create an initial model generally corresponding to the non-linear empirical process to be modeled, the initial model having an initial input and an initial output;
construct a non-linear network model based on the initial model, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output; and optimize the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model.
22. A method for modeling a polymer process; comprising the steps of:
specifying a base non-linear function for an initial model generally corresponding to the polymer process to be modeled, the initial model including an initial input and an initial output and the base non-linear function including a log of a hyperbolic cosine function;
constructing a non-linear network model based on the initial model and including the base non-linear function, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output; and optimizing the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model by setting constraints based on taking a bounded derivative of the base non-linear function.
23. A computer apparatus for modeling a polymer process; comprising:
a model creator for specifying a base non-linear function for an initial model generally corresponding to the polymer process to be modeled, the initial model including an initial input and an initial output and the base non-linear function including a log of a hyperbolic cosine function;
a model constructor coupled to the model creator for constructing a non-linear network model based on the initial model and including the base non-linear function, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output; and an optimizer coupled to the model constructor for optimizing the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model by setting constraints based on taking a bounded derivative of the base non-linear function.
24. A computer program product that includes a computer usable medium having computer program instructions stored thereon for modeling a polymer process, such that the computer program instructions, when performed by a digital processor, cause the digital processor to:

specify a base non-linear function for an initial model generally corresponding to the polymer process to be modeled, the initial model including an initial input and an initial output and the base non-linear function including a log of a hyperbolic cosine function;
construct a non-linear network model based on the initial model and including the base non-linear function, the non-linear network model having multiple inputs based on the initial input and a global behavior for the non-linear network model as a whole that conforms generally to the initial output;
and optimize the non-linear network model based on empirical inputs to produce an optimized model by constraining the global behavior of the non-linear network model by setting constraints based on taking a bounded derivative of the base non-linear function.
CA2414707A 2000-06-29 2001-06-27 Computer method and apparatus for constraining a non-linear approximator of an empirical process Expired - Fee Related CA2414707C (en)

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US60/214,875 2000-06-29
PCT/US2001/020218 WO2002003152A2 (en) 2000-06-29 2001-06-27 Computer method and apparatus for constraining a non-linear approximator of an empirical process

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