Computer method and apparatus for constraining a non-linear approximator of an empirical process
First Claim
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.
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Accused Products
Abstract
A constrained non-linear approximator for empirical process control is disclosed. The approximator constrains the behavior of the derivative of a subject empirical model without adversely affecting the ability of the model to represent generic non-linear relationships. There are three 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 generically 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 approximation. 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.
88 Citations
24 Claims
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1. A method for modeling a non-linear empirical process, comprising the steps of:
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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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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11. A computer apparatus for modeling a non-linear empirical process, comprising:
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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. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20)
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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:
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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.
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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.
- comprising the steps of;
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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.
- comprising;
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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:
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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.
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Specification