Method and apparatus for dynamical system analysis
First Claim
1. A method for estimating and updating parameters which characterize the state of a dynamical system subject to one or more disturbances comprising the steps ofobtaining one or more first signals related in time or amplitude to the disturbances, sensing the system at one or more locations to obtain sensed signals indicative of the dynamical state of the system, generating predicted parameters from previously estimated parameters, generating a synthesized signal as a weighted sum of products of said first signals and said predicted parameters, and adjusting the predicted parameters according to an error signal which is the difference between the synthesized signal and the sensed signal to obtain new estimated parameters.
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Abstract
A method and apparatus are provided for simultaneously characterizing the disturbance of a dynamical system and the dynamic response model of the system. The disturbance is characterized by a sum of reference signals weighted by disturbance parameters. The dynamic response model is similarly characterized by a set of response parameters, which model the relationship between a set of test signals and the response to these test signals. The disturbance parameters and the response parameters are estimated jointly to provide a characterization of the dynamical system. This estimation is achieved by sensing the system at one or more locations to obtain a sensed signal, obtaining reference signals related to the disturbances, synthesizing an estimate of the sensed signal from the reference signals, the test signals, the disturbance parameters and the response parameters, and jointly adjusting the disturbance parameters and the response parameters according to the difference between the synthesized signal and the sensed signal. The characterization may be incorporated in systems or methods for control or monitoring of dynamical systems.
34 Citations
45 Claims
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1. A method for estimating and updating parameters which characterize the state of a dynamical system subject to one or more disturbances comprising the steps of
obtaining one or more first signals related in time or amplitude to the disturbances, sensing the system at one or more locations to obtain sensed signals indicative of the dynamical state of the system, generating predicted parameters from previously estimated parameters, generating a synthesized signal as a weighted sum of products of said first signals and said predicted parameters, and adjusting the predicted parameters according to an error signal which is the difference between the synthesized signal and the sensed signal to obtain new estimated parameters.
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19. A method for controlling the state of a dynamical system subject to one or more disturbances, where the state is characterized by a set of parameters, comprising the steps of
selecting initial values for the estimated parameters and then repeating the steps of sensing the system at one or more locations to obtain sensed signals indicative of the state of the system, obtaining one or more first signals related in time or amplitude to the disturbances, generating predicted parameters from said previously estimated parameters, generating a synthesized signal as a weighted sum of the first signals and the predicted parameters, adjusting the predicted parameters according to an error signal which is the difference between the synthesized signal and the sensed signal to obtain new estimated parameters, generating a control signal dependent upon the estimated parameters, and supplying said control signal to an actuator so as to generate controlled disturbances in said dynamic system and thereby control the state of said system.
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24. A system for analyzing the state of a dynamical system subject to one or more disturbances, in which the state of the system includes the disturbance of the system and the disturbance is characterized by a set of disturbance parameters, comprising:
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sensors at one or more locations producing sensed signals, reference signal generating means for generating reference signals related to said disturbances, disturbance signal synthesizer means for combining said reference signals with the set of disturbance parameters to produce a synthesized disturbance signal, signal subtraction means for producing an error signal corresponding to the difference between said sensed signal and said synthesized signal, and disturbance parameter adjustment means for adjusting said parameters in response to said error signal. - View Dependent Claims (25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39)
where m is the index of the disturbance, k is a harmonic number, bk,m are disturbance parameters and φ
m(n) is a signal which phase related to the mth disturbance source at sample n, and in which the state of the system is characterized by the complex amplitudes Bk,m=b2k,m+i.b2k+1,m.
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26. A system as in claim 24 in which the disturbance at sample n is synthesized as
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m = 0 M - 1 ∑ k = 0 K b k m x m ( n - k ) , ( 90 ) where m is the index of the reference signal, k is a parameter index, bkm are disturbance parameters and xm(n) is the mth reference signal at sample n.
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27. A system as in claim 26 in which said disturbance parameter adjustment means operates according to a time domain algorithm in which the adjustment to the disturbance parameters is proportional to the product of the error signal and a gain, said gain being dependent upon the reference signals.
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28. A system as in claim 26 in which said disturbance parameter adjustment means operates according to a frequency domain algorithm in which the Fourier transform of the adjustment to the disturbance parameters is proportional to the product of the Fourier transform of the error signal and the complex conjugate of the Fourier transform of the reference signal.
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29. A system as in claim 24, in which the state of the system includes the dynamic response of the system and the dynamic response is characterized by a set of response parameters, said system further including:
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test signal generating means for generating test signals, actuator means responsive to said test signals for generating controlled disturbances in said dynamical system response signal synthesizer means for combining said test signals with a set of response parameters to produce a synthesized response signal, response parameter adjustment means for adjusting said response parameters in accordance with said error signal, wherein said error signal corresponds to the said sensed signal minus said synthesized disturbance signal and minus said synthesized response signal.
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30. A system as in claim 29 in which said response parameter adjustment means operates according to a time domain algorithm in which the adjustment to the response parameters is proportional to the product of the error signal and a gain, said gain being dependent upon the test signals.
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31. A system as in claim 29 in which said response parameter adjustment means operates according to a frequency domain algorithm in which the Fourier transform of the adjustment to the response parameters is proportional to the product of the Fourier transform of the error signal and the complex conjugate of the Fourier transform of the reference signal.
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32. A system as in claim 29 in which said dynamical system is a machine and including
machinery monitoring means for monitoring the time variations in said disturbance parameters and said response parameters, wherein said machinery monitoring means periodically monitors said parameters so as to determine the condition of the machine. -
33. A system as in claim 24 in which said dynamical system is a machine and including
machinery monitoring means for monitoring the time variations in said disturbance parameters and periodically comparing said parameters with those expected from known operating or fault conditions so as to determine the condition of the machine. -
34. A system as in claim 33 in which said machinery monitoring means also monitors said error signal.
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35. A system as in claim 33 in which said machinery monitoring means also monitors said synthesized disturbance signal.
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36. A system as in claim 24 and including signal compression means which is responsive to said disturbance parameters and produces a compressed data signal.
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37. A system as in claim 36 and including transmission means for transmitting said compressed data signal to a remote location for further processing or analysis.
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38. A system as in claim 36 and including storage means for storing said compressed data signal.
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39. A system as in claim 36 in which said signal compression means is also responsive to said reference signals, or to a signal from which said reference signals are derived.
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40. A system for controlling the state of a dynamical system subject to one or more disturbances in which the state of the system includes the disturbance of the system, characterized by a set of disturbance parameters and also includes the dynamic response of the system, characterized by a set of response parameters, comprising
sensor means at one or more locations producing sensed signals indicative of the state of said dynamical system, reference signal generating means for generating reference signals related to said disturbances, disturbance signal synthesizer means for combining said reference signals with a set of disturbance parameters to produce a synthesized disturbance signal, test signal generating means for generating test signals, response signal synthesizer means for combining said test signals with a set of response parameters to produce a synthesized response signal, signal subtraction means for producing an error signal corresponding to said sensed signal minus said synthesized disturbance signal and minus said synthesized response signal, disturbance parameter adjustment means for adjusting said disturbance parameters in response to said error signal, response parameter adjustment means for adjusting said response parameters in response to said error signal, controller means responsive to said response parameters and said reference signals and generating a control signal, and actuator means responsive to said control signal for generating controlled disturbances in said dynamical system, thereby controlling the state of said system.
Specification