Method for steady-state identification based upon identified dynamics
First Claim
1. A method for training a steady-state non-linear model of a plant, comprising the steps of:
- generating an input set of historical training data representative of the historical operation of the plant and having input data u(t) and output data y(t);
identifying a linear dynamic model of the plant representing the dynamics of the plant for a given output variable of the plant;
pre-filtering the historical input data through the dynamic model to impress the dynamics of the plant as defined by the linear dynamic model on the input data u(t); and
training a non-linear model of the plant with the pre-filtered input data u(t) to provide a stored representation of the steady-state operation in the non-linear model associated with the given output variable.
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Abstract
A method for modeling a steady-state network in the absence of steady-state historical data. A steady-state neural network can be tied by impressing the dynamics of the system onto the input data during the training operation by first determining the dynamics in a local region of the input space, this providing a set of dynamic training data. This dynamic training data is then utilized to train a dynamic model, gain thereof then set equal to unity such that the dynamic model is now valid over the entire input space. This is a linear model, and the historical data over the entire input space is then processed through this model prior to input to the neural network during training thereof to remove the dynamic component from the data, leaving the steady-state component for the purpose of training. This provides a valid model in the presence of historical data that has a large content of dynamic behavior. A single dynamic model is required for each output variable in a multi-input multi-output steady-state model such that for each output there is a separate dynamic model required for pre-filtering. They are combined in a single network made up of multiple individual steady-state models for each output. The dynamic model can be identified utilizing a weighting factor for the gain to force the dynamic gain of the dynamic model to the steady-state gain by weighting the difference thereof during optimization of the dynamic model. The steady-state model is optimized utilizing gain constraints during the optimization procedure such that the gain of the network is prevented from exceeding the gain constraints.
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Citations
36 Claims
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1. A method for training a steady-state non-linear model of a plant, comprising the steps of:
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generating an input set of historical training data representative of the historical operation of the plant and having input data u(t) and output data y(t); identifying a linear dynamic model of the plant representing the dynamics of the plant for a given output variable of the plant; pre-filtering the historical input data through the dynamic model to impress the dynamics of the plant as defined by the linear dynamic model on the input data u(t); and training a non-linear model of the plant with the pre-filtered input data u(t) to provide a stored representation of the steady-state operation in the non-linear model associated with the given output variable. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method for training a steady-state, non-linear model of a plant having multiple input variables and multiple output variables, comprised of the steps of:
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generating an input of historical training data representative of the historical operations of the plant and having input data u(t) and output data y(t); identifying a plurality of linear dynamic models, one for each output variable of the plant, each of which represents the dynamics of the plant for the given output variables of the plant; pre-filtering the historical input data for each of the input variables through each of the dynamic models to impress the dynamics of the plant for the associated output variable with the associated dynamic model on the input data u(t); and training a plurality of non-linear models in the plant, each non-linear model associated with one of the output variables, and each of the non-linear models filtered with the pre-filtered input data u(t) for the associated output variable to provide a stored representation of the steady-state operation of each of the output variables in the associated non-linear model. - View Dependent Claims (10)
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11. A method for training a steady-state model, the model having an input and an output and a mapping layer for mapping the input to the output through a stored representation of a plant, comprising:
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providing a training data set having a set of input data u(t) and target output data y(t) representative of the operation of a plant; training the model with a predetermined training algorithm; and constraining the training algorithm to maintain the sensitivity of the output with respect to the input substantially within user defined bounds. - View Dependent Claims (12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
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22. A method for developing a linear dynamic model of a plant, comprising the steps of:
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creating a linear model for predicting a dynamic response y(t) from an input u(t) and having a dynamic gain kd, which linear model can define the dynamic response of the plant; generating a training data set of dynamic input data ud (t) and output data yd (t); providing a user defined sensitivity value representing the sensitivity of the output of the plant with respect to the input of the plant at steady-state; training the linear model on the training data set with a predetermined training algorithm; and constraining the training algorithm with a scaled level of the difference between the dynamic gain and the user defined sensitivity such that an error generated with the training algorithm will increase as the difference between the dynamic gain and the user defined sensitivity increases. - View Dependent Claims (23, 24, 25, 26, 27, 28, 29, 30, 31)
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32. A method for determining the dead-time d between an input variable u(t) to a plant and an output variable y(t) from the plant, comprising the steps of:
- providing a historical data set of input variables u(t) for a given output variable y(t);
defining a minimum dead-time di,min and a maximum dead-time di,max; varying the value of di from di,min to di,max for each input variable ui (t-di); determining the strength of the statistical relationship between the input variable u(t) and the output variable y(t) for each value of i as di varies from dimin to dimax ; and select the value of j for di as the di value having the strongest statistical relationship for the given input variable. - View Dependent Claims (33, 34, 35, 36)
- providing a historical data set of input variables u(t) for a given output variable y(t);
Specification