Method and apparatus for characterizing the unknown state of a physical system
First Claim
1. A machine implemented method for characterizing an unknown state of a physical system with reference to like physical systems in a known state comprising the steps of:
- obtaining with suitable detecting means a time-varying data signal characteristic of a state of interest from each of a large plurality of physical systems in the known state which are similar to the physical system being characterized;
subjecting each of said time-varying data signals to a non-linear coordinate transformation comprising taking a normalized first intergral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said intergral, and converting said difference to polar coordinates;
constructing a standard signature template representative of the known state from a composite of said transformed data signals, said standard signature template including a primary signature comprising a closed multi-dimensional region within said polar coordinate system having an inner boundary and an outer boundary, and a secondary signature comprising at least one isocline disposed within said region;
plotting said standard signature template using plotting means;
obtaining with said suitable measuring means at least one time-varying data signal characteristic of said state of interest from the physical system being characterized;
subjecting said at least one time-varying data signal to said non-linear coordinate transformation to obtain at least one response signature representative of the unknown state;
plotting said at least one response signature over said standard signature template using said plotting means;
determining whether the system being characterized is in the known state by comparing said at least one response signature plot to the standard signature template by determining whether said at least one response signature plot lies wholly within said closed multi-dimensional region, and whether said at least one response signature plot crosses any of said isoclines situated within said closed multi-dimensional region;
indicating the physical system being characterized as being in the known state if said at least one response signature plot lies wholly within said closed multi-dimensional region and does not cross any of said isoclines situated within said closed region, and if the system being characterized is not in the known state,evaluating the relative degree of departure of the system being characterized from the known state.
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Abstract
A method and an apparatus are disclosed for characterizing the unknown state of a physical system having a time varying history, the characterization being made with reference to a known state of like physical systems. A response signature representative of the unknown system state is compared to a standard signature representative of the known system state. The standard signature includes a primary signature comprising a multi-dimensional region within a pre-defined, transformed coordinate system having an inner and outer boundary, and a secondary signature comprising at least one, but preferably two or more isoclines situated within the bounded region. If the response signature lies wholly within the bounded region and does not cross any of the region'"'"'s isoclines, the system being characterized is deemed to be in the known state. Conversely, if both of these criteria are not satisfied the relative degree of departure of the system in the unknown state from the known system state is predicted using one or more point functions representative of the system being characterized.
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Citations
29 Claims
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1. A machine implemented method for characterizing an unknown state of a physical system with reference to like physical systems in a known state comprising the steps of:
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obtaining with suitable detecting means a time-varying data signal characteristic of a state of interest from each of a large plurality of physical systems in the known state which are similar to the physical system being characterized; subjecting each of said time-varying data signals to a non-linear coordinate transformation comprising taking a normalized first intergral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said intergral, and converting said difference to polar coordinates; constructing a standard signature template representative of the known state from a composite of said transformed data signals, said standard signature template including a primary signature comprising a closed multi-dimensional region within said polar coordinate system having an inner boundary and an outer boundary, and a secondary signature comprising at least one isocline disposed within said region; plotting said standard signature template using plotting means; obtaining with said suitable measuring means at least one time-varying data signal characteristic of said state of interest from the physical system being characterized; subjecting said at least one time-varying data signal to said non-linear coordinate transformation to obtain at least one response signature representative of the unknown state; plotting said at least one response signature over said standard signature template using said plotting means; determining whether the system being characterized is in the known state by comparing said at least one response signature plot to the standard signature template by determining whether said at least one response signature plot lies wholly within said closed multi-dimensional region, and whether said at least one response signature plot crosses any of said isoclines situated within said closed multi-dimensional region; indicating the physical system being characterized as being in the known state if said at least one response signature plot lies wholly within said closed multi-dimensional region and does not cross any of said isoclines situated within said closed region, and if the system being characterized is not in the known state, evaluating the relative degree of departure of the system being characterized from the known state. - View Dependent Claims (2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16)
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7. A machine implemented method for characterizing an unknown state of a physical system with reference to like physical systems in a known state comprising the steps of:
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obtaining with suitable detecting means a time-varying data signal characteristic of a state of interest from each of a large plurality of physical systems in the known state which are similar to the physical system being characterized; subjecting each of said time-varying data signals to a non-linear coordinate transformation comprising taking a normalized first intergral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said intergral, and converting said difference to polar coordinates; constructing a standard signature template representative of the known state from a composite of said plurality of transformed data signals, said standard signature template including a primary signature comprising a closed two-dimensional region within a pre-defined coordinate system having an inner boundary and an outer boundary, and a secondary signature comprising a plurality of substantially parallel isoclines situated within said closed two-dimensional region; plotting said standard signature template using two dimensional plotting means; obtaining at least one time-varying data signal characteristic of said state of interest from the physical system being characterized; subjecting said at least one time-varying data signal to said non-linear coordinate transformation to obtain at least one response signature representative of the unknown state; plotting said at least one response signature over said standard signature template using said two dimensional plotting means; comparing said at least one response signature plot to the standard signature template to determine whether said at least one response signature plot lies wholly within said two dimensional closed region or crosses any of said isoclines situated within said two dimensional closed region; assigning said at least one response signature plot either a predetermined negative weighted value if said at least one response signature plot is wholly within said closed two dimensional region and does not cross any of said isoclines, a pre-determined positive weighted value if said at least one response signature plot lies wholly or partially outside said closed two dimensional region or crosses any of said isoclines, or a zero weighted value if the positioning of said at least one response signature plot with respect to said closed two dimensional region and said isoclines is indeterminate; obtaining a time-varying data signal characteristic of said state of interest from each of a large plurality of physical systems not in the known state which are similar to the physical system being characterized; subjecting each of said time-varying data signals obtained from said physical systems not in the known state to said non-linear coordinate transformation; measuring a plurality of geometric features of each of said time-varying data signals obtained from said physical systems in the known state and of said non-linear transformations of said known state data signals; calculating and plotting a plurality of point function coordinates representative of systems in the known state utilizing a plurality of pre-defined point functions and said geometric feature measurements obtained from said physical systems in the known state; measuring said plurality of geometric features of each of said time-varying data signals obtained from said physical systems not in the known state and of said non-linear transformations of said data signals not in the known state; calculating and plotting a plurality of point function coordinates representative of systems not in the known state utilizing said plurality of pre-defined point functions and said geometric feature measurements obtained from said physical systems not in the known state; measuring said plurality of predetermined geometric features of said at least one time-varying data signal obtained from said physical system being characterized and of said non-linear transformation of said at least one data signal; calculating a plurality of point function coordinates representative of the system being characterized utilizing said plurality of pre-defined point functions and said geometric feature measurements obtained from said physical system being characterized; comparing said point function coordinates for said system being characterized with said point function coordinates for said systems in the known state, and for said systems not in the known state; assigning each of said point functions for said system being characterized a pre-determined negative weighted value if said coordinates calculated with said point function fall within said plot of said point functions for systems in the known state, a pre-determined positive weighted value if said coordinates calculated with said point function fall within said plot of said point functions for systems not in the known state, or by a weighting factor of zero if said coordinates calculated by said point function fall in neither of said plots; summing said response signature and said point function weighted values to obtain a number; and comparing said number to a pre-determined cut-off value to determine if the system being characterized is in the known state. - View Dependent Claims (8)
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17. An apparatus for characterizing the unknown state of a physical system with reference to like physical systems in a known state comprising:
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means for measuring a plurality of time-varying data signals characteristic of a state of interest from a plurality of physical systems in the known state, and at least one time-varying data signal characteristic of said state of interest from the physical system in the unknown state; means for calculating a non-linear coordinate transformation of said plurality of time-varying data signals obtained from said physical systems in the known state to form a standard signature template representative of the known state, said non-linear coordinate transformation comprising taking a normalized first integral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said integral, and converting said difference to polar coordinates, said standard signature template including a primary signature comprising a closed multi-dimensional region within a polar coordinate system having an inner boundary and an outer boundary and a secondary signature comprising a plurality of substantially parallel isoclines disposed within said region; means for calculating said non-linear coordinate transformation for said at least one time-varying data signal obtained from said physical system in the unknown state to form at least one response signature plot representative of the unknown state; means for plotting said standard signature template and for plotting said at least one response signature plot over said standard signature template; means for comparing said at least one response signature plot to said standard signature template to determine whether the system in the unknown state is in the known state, said comparing means comprising means for determining whether said at least one response signature plot lies wholly within said closed two dimensional region or crosses any of said isoclines situated within said closed two dimensional region; means for indicating said unknown system as being in the known state if said at least one response signature plot lies wholly within said closed two dimensional region and does not cross any of said isoclines situated within said closed region; and means for evaluating the relative degree of departure from the known state if the system in the unknown state is not in the known state. - View Dependent Claims (18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29)
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Specification