Apparatus and method for modeling relationships between signals
First Claim
Patent Images
1. A method, comprising:
- electronically receiving a projection associated with a first signal and a second signal, the first and second signals associated with a control system, the second signal comprising a first portion associated with the first signal and a second portion not associated with the first signal, the projection comprising an upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal;
electronically identifying model parameters using at least a portion of the projection; and
electronically generating and storing a model associated with the model parameters, the model associating the first signal and the first portion of the second signal;
wherein identifying the model parameters comprises;
identifying one or more pole candidates using one or more first defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more pole candidates; and
identifying one or more model candidates using one or more second defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more model candidates; and
wherein each of the one or more second defined areas represents a backward column Hankel matrix centered along one of multiple diagonals of the upper triangular matrix, and wherein identifying the one or more model candidates comprises rewriting each backward column Hankel matrix as a forward column Hankel matrix.
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Abstract
A projection is associated with a first signal and a second signal. The second signal includes a first portion associated with the first signal and a second portion not associated with the first signal. The projection at least substantially separates the first portion of the second signal from the second portion of the second signal. One or more parameters of a model are identified using at least a portion of the projection. The model associates the first signal and the first portion of the second signal.
62 Citations
23 Claims
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1. A method, comprising:
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electronically receiving a projection associated with a first signal and a second signal, the first and second signals associated with a control system, the second signal comprising a first portion associated with the first signal and a second portion not associated with the first signal, the projection comprising an upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; electronically identifying model parameters using at least a portion of the projection; and electronically generating and storing a model associated with the model parameters, the model associating the first signal and the first portion of the second signal; wherein identifying the model parameters comprises; identifying one or more pole candidates using one or more first defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more pole candidates; and identifying one or more model candidates using one or more second defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more model candidates; and wherein each of the one or more second defined areas represents a backward column Hankel matrix centered along one of multiple diagonals of the upper triangular matrix, and wherein identifying the one or more model candidates comprises rewriting each backward column Hankel matrix as a forward column Hankel matrix. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A method, comprising:
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electronically receiving a projection associated with a first signal and a second signal, the first and second signals associated with a control system, the second signal comprising a first portion associated with the first signal and a second portion not associated with the first signal, the projection comprising a first upper triangular matrix, having two diagonals that divide the upper triangular matrix into four sections, a first of the diagonals starting at an upper left corner of the upper triangular matrix and traveling down and right in the upper triangular matrix, a second of the diagonals starting at a lower left corner of the upper triangular matrix and traveling up and right in the upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; electronically identifying one or more model parameters using at least a portion of the projection; and electronically generating and storing a model associated with the one or more model parameters, the model associating the first signal and the first portion of the second signal; wherein identifying the one or more model parameters comprises; identifying one or more model parameters for each of multiple defined areas in the first upper triangular matrix, the defined areas located in a single one of the sections of the upper triangular matrix; selecting the one or more model parameters associated with a specific one of the defined areas in the first upper triangular matrix; and wherein selecting the one or more model parameters associated with the specific one of the defined areas in the first upper triangular matrix comprises; for each defined area in the first upper triangular matrix, generating a matrix comprising a forward column Hankel matrix based on a prediction error, the prediction error associated with the one or more model parameters that are associated with that defined area; for each generated matrix, performing canonical QR-decomposition on the matrix to form a second upper triangular matrix, each second upper triangular matrix having an upper right portion denoted RE3; for each second upper triangular matrix, identifying a value for ∥
RE3∥
22; andselecting the one or more model parameters associated with the defined area having the second upper triangular matrix with a smallest value for ∥
RE3∥
22.
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11. An apparatus, comprising:
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at least one input receiving a first signal and a second signal associated with a control system, the second signal comprising a first portion associated with the first signal and a second portion not associated with the first signal; and at least one processor; generating a projection associated with the first and second signals and identifying model parameters using at least a portion of the projection, the projection comprising an upper triangular matrix having two diagonals that divide the upper triangular matrix into four sections, a first of the diagonals starting at an upper left corner of the upper triangular matrix and traveling down and right in the upper triangular matrix, a second of the diagonals starting at a lower left corner of the upper triangular matrix and traveling up and right in the upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; and generating and storing a model associated with the model parameters, the model associating the first signal and the first portion of the second signal; wherein the at least one processor identifies the model parameters by; identifying one or more pole candidates using one or more first defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more pole candidates, the one or more first defined areas located in a single one of the sections of the upper triangular matrix; and identifying one or more model candidates using one or more second defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more model candidates; and wherein each of the one or more second defined areas represents a matrix centered along one of the diagonals of the upper triangular matrix. - View Dependent Claims (12, 13, 14, 15, 16)
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17. An apparatus, comprising:
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at least one input receiving a first signal and a second signal associated with a control system, the second signal comprising a first portion associated with the first signal and a second portion not associated with the first signal; and at least one processor; generating a projection associated with the first and second signals and identifying one or more model parameters using at least a portion of the projection, the projection comprising a first upper triangular matrix, having two diagonals that divide the upper triangular matrix into four sections, a first of the diagonals starting at an upper left corner of the upper triangular matrix and traveling down and right in the upper triangular matrix, a second of the diagonals starting at a lower left corner of the upper triangular matrix and traveling up and right in the upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; and generating and storing a model associated with the one or more model parameters, the model associating the first signal and the first portion of the second signal; wherein the at least one processor identifies the one or more model parameters by; identifying one or more model parameters for each of multiple defined areas in the first upper triangular matrix, the defined areas located in a single one of the sections of the upper triangular matrix; and selecting the one or more model parameters associated with a specific one of the defined areas in the first upper triangular matrix; and wherein the at least one processor selects the one or more model parameters associated with the specific one of the defined areas in the first upper triangular matrix by; for each defined area in the first upper triangular matrix, generating a matrix comprising a forward column Hankel matrix based on a prediction error, the prediction error associated with the one or more model parameters that are associated with that defined area; for each generated matrix, performing canonical QR-decomposition on the matrix to form a second upper triangular matrix, each second upper triangular matrix having an upper right portion denoted RE3; for each second upper triangular matrix, identifying a value for ∥
RE3∥
22; andselecting the one or more model parameters associated with the defined area having the second upper triangular matrix with a smallest value for ∥
RE3∥
22.
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18. A computer readable medium embodying a computer program, the computer program comprising:
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computer readable program code that receives a projection associated with a first signal and a second signal, the first and second signals associated with a control system the second signal comprising a first portion associated with the first signal and a second portion associated with at least one disturbance, the projection comprising an upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; computer readable program code that identifies model parameters using at least a portion of the projection; and computer readable program code that generates and stores a model associated with the model parameters, the model associating the first signal and the first portion of the second signal; wherein the computer readable program code that identifies the model parameters comprises; computer readable program code that identifies one or more pole candidates using one or more first defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more pole candidates; and computer readable program code that identifies one or more model candidates using one or more second defined areas in the upper triangular matrix, the model parameters comprising at least one of the one or more model candidates; and wherein each of the one or more second defined areas represents a backward column Hankel matrix centered along one of multiple diagonals of the upper triangular matrix, and wherein the computer readable program code that identifies the one or more model candidates comprises computer readable program code that rewrites each backward column Hankel matrix as a forward column Hankel matrix. - View Dependent Claims (19, 20, 21, 22)
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23. A computer program readable medium embodying a computer program, the computer program comprising:
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computer readable program code that receives a projection associated with a first signal and a second signal, the first and second signals associated with a control system the second signal comprising a first portion associated with the first signal and a second portion associated with at least one disturbance, the projection comprising a first upper triangular matrix, having two diagonals that divide the upper triangular matrix into four sections, a first of the diagonals starting at an upper left corner of the upper triangular matrix and traveling down and right in the upper triangular matrix, a second of the diagonals starting at a lower left corner of the upper triangular matrix and traveling up and right in the upper triangular matrix, the projection at least partially isolating the first portion of the second signal from the second portion of the second signal; computer readable program code that identifies one or more model parameters using at least a portion of the projection; and computer readable program code that generates and stores a model associated with the one or more model parameters, the model associating the first signal and the first portion of the second signal; wherein the computer readable program code that identifies the one or more model parameters comprises; computer readable program code that identifies one or more model parameters for each of multiple defined areas in the first upper triangular matrix, the defined areas located in a single one of the sections of the upper triangular matrix; and computer readable program code that selects the one or more model parameters associated with a specific one of the defined areas in the first upper triangular matrix; and wherein the computer readable program code that selects the one or more model parameters associated with the specific one of the defined areas comprises; computer readable program code that, for each defined area in the first upper triangular matrix, generates a matrix comprising a forward column Hankel matrix based on a prediction error, the prediction error associated with the one or more model parameters that are associated with that defined area; computer readable program code that, for each generated matrix, performs canonical QR-decomposition on the matrix to form a second upper triangular matrix, each second upper triangular matrix having an upper right portion denoted RE3; computer readable program code that, for each second upper triangular matrix, identifies a value for ∥
RE3∥
22; andcomputer readable program code that selects the one or more model parameters associated with the defined area having the second upper triangular matrix with a smallest value for ∥
RE3∥
22.
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Specification