Mathematical model useful for determining and calibrating output of a linear sensor
First Claim
1. A method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model, the method comprising:
- analyzing a statistically significant number of linear sensors to obtain a first operating profile for each sensor at a first operating condition, T1;
analyzing the statistically significant number of linear sensors to obtain a second operating profile for each sensor at a second operating condition, T2;
optionally confirming that each operating profile obtained represents a linear relationship between sensor input and sensor output using reciprocal slopes of output-input lines;
optionally confirming that operating profiles developed over a continuum of operating conditions represent a linear relationship using reciprocal slopes of each operating profile;
individually testing a linear sensor to obtain at least four data points, wherein the four data points correspond to test data obtained based on a first and second input at each of the first and second operating conditions and are represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22);
developing a theoretical prediction of the output model from the four data points and relaying the theoretical prediction of the output model to an electronic component, wherein the theoretical prediction of the output model for determining output at a given operating condition, T, and based on a given input, I, is developed in accordance with the following mathematical equation;
Output=O0+I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21);
b2=(I12−
I22)/(O12−
O22); and
O0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2;
comparing accuracy of the relationship between the theoretical prediction of the output model for the first operating condition to sensor output in the first operating profile for the first operating condition corresponding to the given input; and
comparing accuracy of the relationship between the theoretical prediction of the output model for the second operating condition to sensor output in the second operating profile for the second operating condition corresponding to the given input.
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Abstract
The present invention relates to a method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model. The method comprises steps of: analyzing a statistically significant number of linear sensors to obtain operating profiles at two or more operating conditions; individually testing a linear sensor to obtain at least four data points; developing a theoretical prediction of the output model for each operating condition from the four data points; and comparing accuracy of the relationship between the theoretical prediction of the output model to sensor output in the operating profile corresponding to a given input for the same operating condition. Also disclosed are calibration algorithms associated therewith, as well as mechatronic units and further assemblies therefrom.
48 Citations
23 Claims
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1. A method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model, the method comprising:
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analyzing a statistically significant number of linear sensors to obtain a first operating profile for each sensor at a first operating condition, T1; analyzing the statistically significant number of linear sensors to obtain a second operating profile for each sensor at a second operating condition, T2; optionally confirming that each operating profile obtained represents a linear relationship between sensor input and sensor output using reciprocal slopes of output-input lines; optionally confirming that operating profiles developed over a continuum of operating conditions represent a linear relationship using reciprocal slopes of each operating profile; individually testing a linear sensor to obtain at least four data points, wherein the four data points correspond to test data obtained based on a first and second input at each of the first and second operating conditions and are represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22);developing a theoretical prediction of the output model from the four data points and relaying the theoretical prediction of the output model to an electronic component, wherein the theoretical prediction of the output model for determining output at a given operating condition, T, and based on a given input, I, is developed in accordance with the following mathematical equation;
Output=O0+I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21);b2=(I12−
I22)/(O12−
O22); andO0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2;comparing accuracy of the relationship between the theoretical prediction of the output model for the first operating condition to sensor output in the first operating profile for the first operating condition corresponding to the given input; and comparing accuracy of the relationship between the theoretical prediction of the output model for the second operating condition to sensor output in the second operating profile for the second operating condition corresponding to the given input. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9)
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10. A calibration algorithm generating a calibration curve for a linear sensor upon input of four data points,
wherein the calibration algorithm is electronically stored within a memory; -
wherein the four data points correspond to test data obtained from the linear sensor based on a first and second sensor input at each of the first and second operating conditions, the four data points individually being represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22); andwherein the calibration algorithm determines output of a linear sensor at a given operating condition, T, based on a given input, I, and wherein the algorithm conforms to the following mathematical equation;
Output=O0+I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21);b2=(I12−
I22)/(O12−
O22); andO0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2wherein the output of the linear sensor determined from the calibration algorithm is relayed to an electronic component. - View Dependent Claims (11, 12, 13, 14, 15, 16, 17, 18, 19, 20)
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21. A method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model, the method comprising:
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optionally analyzing a statistically significant number of linear sensors to obtain a first operating profile for each sensor at a first operating condition, T1; optionally analyzing the statistically significant number of linear sensors to obtain a second operating profile for each sensor at a second operating condition, T2; optionally confirming that each operating profile obtained represents a linear relationship between sensor input and sensor output using reciprocal slopes of output-input lines; optionally confirming that operating profiles developed over a continuum of operating conditions represent a linear relationship using reciprocal slopes of each operating profile; individually testing a linear sensor to obtain at least four data points, wherein the four data points correspond to test data obtained based on a first and second input at each of the first and second operating conditions and are represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22);developing a theoretical prediction of the output model from the four data points and relaying the theoretical prediction of the output model to an electronic component, wherein the theoretical prediction of the output model for determining output at a given operating condition, T, and based on a given input, I, is developed in accordance with the following mathematical equation;
Output=O0+I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21);b2=(I12−
I22)/(O12−
O22); andO0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2;optionally comparing accuracy of the relationship between the theoretical prediction of the output model for the first operating condition to sensor output in the first operating profile for the first operating condition corresponding to the given input; and optionally comparing accuracy of the relationship between the theoretical prediction of the output model for the second operating condition to sensor output in the second operating profile for the second operating condition corresponding to the given input.
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22. A method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model, the method comprising:
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obtaining a first operating profile for each sensor at a first operating condition, T1; obtaining a second operating profile for each sensor at a second operating condition, T2; optionally confirming that each operating profile obtained represents a linear relationship between sensor input and sensor output using reciprocal slopes of output-input lines; optionally confirming that operating profiles developed over a continuum of operating conditions represent a linear relationship using reciprocal slopes of each operating profile; individually testing a linear sensor to obtain at least four data points, wherein the four data points correspond to test data obtained based on a first and second input at each of the first and second operating conditions and are represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22);developing a theoretical prediction of the output model from the four data points and relaying the theoretical prediction of the output model to an electronic component, wherein the theoretical prediction of the output model for determining output at a given operating condition, T, and based on a given input, I, is developed in accordance with the following mathematical equation;
Output=O0I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21);b2=(I12−
I22)/(O12−
O22); andO0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2;comparing accuracy of the relationship between the theoretical prediction of the output model for the first operating condition to sensor output in the first operating profile for the first operating condition corresponding to the given input; and comparing accuracy of the relationship between the theoretical prediction of the output model for the second operating condition to sensor output in the second operating profile for the second operating condition corresponding to the given input.
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23. A method of analyzing accuracy of linear sensor output based on a theoretical prediction of the output model, the method comprising:
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optionally obtaining a first operating profile for each sensor at a first operating condition, T1; optionally obtaining a second operating profile for each sensor at a second operating condition, T2; optionally confirming that each operating profile obtained represents a linear relationship between sensor input and sensor output using reciprocal slopes of output-input lines; optionally confirming that operating profiles developed over a continuum of operating conditions represent a linear relationship using reciprocal slopes of each operating profile; individually testing a linear sensor to obtain at least four data points, wherein the four data points correspond to test data obtained based on a first and second input at each of the first and second operating conditions and are represented as follows;
(I11, O11), (I21, O21), (I12, O12), and (I22, O22);developing a theoretical prediction of the output model from the four data points and relaying the theoretical prediction of the output model to an electronic component, wherein the theoretical prediction of the output model for determining output at a given operating condition, T, and based on a given input, I, is developed in accordance with the following mathematical equation;
Output=O0+I/b,
wherein b=b1+[(b1−
b2)/(T1−
T2)](T−
T1), where b1=(I11−
I21)/(O11−
O21),b2=(I12−
I22)/(O12−
O22); andO0=(O01+O02)/2, where O01=O11−
I11/b1 and O02=O12−
I12/b2;optionally comparing accuracy of the relationship between the theoretical prediction of the output model for the first operating condition to sensor output in the first operating profile for the first operating condition corresponding to the given input; and optionally comparing accuracy of the relationship between the theoretical prediction of the output model for the second operating condition to sensor output in the second operating profile for the second operating condition corresponding to the given input.
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Specification