Sensor signal solving method based on inverse function polynomial interpolation, sensor and storage medium

Abstract

This application provides a sensor signal calculation method based on inverse function polynomial interpolation, including the steps of: in the measured physical quantity x Selecting non-equidistant interpolation position parameters within the normalized interval t i Output the corresponding measured physical quantity x i The signal is then converted by the sensor to obtain an electrical signal. y i ,Will x i and y i Form the interpolation point set {( x i ,y i After that, positive function polynomial interpolation is performed; calculations are then performed on the electrical signal. y The interpolation independent variable points of the corresponding inverse function; the equation is solved using numerical calculation methods. y' i = f ( x The solution obtained x' i and y' i Form the inverse function interpolation point set {( y' i , x' i Then construct the polynomial to obtain the inverse function: x = f ‑1 After (y), the coefficients are rearranged into a power-law form and stored in the sensor's non-volatile memory. Using this method, the sensor can directly calculate the value of the measured physical quantity from the electrical signal. This method is simple, fast, computationally efficient, resource-saving, and produces a more accurate sensor output signal. This application also provides a sensor and storage medium employing the above calculation method.

Description

Technical Field

[0001] This invention belongs to the field of sensor signal processing technology, specifically relating to a sensor signal calculation method based on inverse function polynomial interpolation, as well as a sensor and storage medium using this method. Background Technology

[0002] In various measurement systems, sensors (such as pressure, temperature, and displacement sensors) measure the physical quantity to be measured. x Converted into electrical signals y ， Its input-output characteristics are usually determined by nonlinear functions. y = f ( x Description. Since sensor signals are generally predominantly linear, therefore, f ( x It is often approximated as a polynomial. 。

[0003] Traditional high-precision calibration methods typically employ high-order polynomials for positive characteristics. f ( x Fitting 。 In sensor calibration systems, polynomial interpolation techniques (such as Lagrange interpolation) are often used to obtain the required values. f ( x ) 。 During real-time calculation at the measurement site, for the electrical signal output by each sensor... y ， Equations are often solved using iterative numerical methods (such as Newton's method). f ( x ) =y In order to obtain the measured physical quantity x value 。 However, this method has significant drawbacks: (1) large computational load, low efficiency, and poor real-time performance; (2) high resource consumption; and (3) convergence depends on the selection of the initial value for iteration. Meanwhile, in polynomial interpolation techniques, the traditional method uses equal-interval sampling. This method causes fluctuations in data near the zero and full-scale points, potentially leading to the "Runge phenomenon," resulting in poor accuracy of measurement data near the zero point and significantly reducing the signal's fidelity. Summary of the Invention

[0004] This application provides a sensor signal calculation method based on inverse function polynomial interpolation, as well as a sensor and storage medium. The sensor can directly calculate the value of the measured physical quantity through electrical signals, which is simple, fast, has low computational load, high efficiency, low resource consumption, and can make the sensor output signal more accurate.

[0005] Firstly, this application provides a sensor signal calculation method based on inverse function polynomial interpolation, including the following steps: S1 The physical quantity to be measured x Normalize to the [0,1] interval, and select N non-equally spaced interpolation position parameters within this interval. t i ( i= 0, 1, ..., N-1), to obtain the point set { t 0 ,t 1 ,…,t N-1},in, t 0=0, corresponding to the zero point of the sensor. t N-1 =1, corresponding to the full-scale point of the sensor; S2 controls the standard source of the output physical quantity, causing it to conform to the interpolation position parameters. t i The determined non-equal interval distribution outputs N measured physical quantities x i ,in x i = t i ,Will x i The input is to the sensor, and after the sensor conversion, N quantities are obtained that are related to the measured physical quantity. x i Corresponding electrical signal y i ( i =0,1,…,N-1); S3 will x i and y i Form the interpolation point set {( x i , y i Based on this point set, a Lagrange interpolation polynomial is constructed to obtain the positive function relationship. Rearranged into exponentiation form: = f ( x )= k 0+ k 1 y 1 + ... + k N-1 y N-1 ,in k 0, k 1,..., k N-1 These are the coefficients of the combined polynomial; S4 will use the N electrical signals y i The maximum value in is denoted as y max ， The minimum value is denoted as y min According to the interpolation position parameters t i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i + y min ; S5 for each y' i The equations are solved using numerical methods. y' i = f ( x ), to obtain the solution x' i; Afterwards, x' i and y' i Form the inverse function interpolation point set { ( y' i , x' i )}; then based on the inverse function interpolation point set {( y' i , x' i Constructing the Lagrange polynomial yields the inverse function: Rearranged into exponentiation form: x=f -1 (y)= a 0+ a 1 y 1 + ... + a N-1 y N-1 ,in a 0, a 1,..., a N-1 These are the coefficients of the combined polynomial; S6. Transform the polynomial x=f -1 The coefficients in (y) { a 0, a 1, …, a N-1Stored in the sensor's non-volatile memory.

[0006] Secondly, this application provides a sensor applicable to the aforementioned sensor signal processing method based on inverse function polynomial interpolation, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. The memory stores the inverse function interpolation polynomial x=f obtained by the aforementioned method. -1 The coefficient of (y) { a 0, a 1, …, a N-1 When the processor executes the computer program, it bases its decisions on the electrical signals output by the sensors. y Value, substitute into the polynomial x= = a 0+ a 1 y 1 + ... + a N-1 y N-1 The measured physical quantity can be directly calculated. x The value of .

[0007] Thirdly, this application provides a computer-readable storage medium storing a computer program configured to be executed by a processor to perform data processing of the sensor.

[0008] This application has the following technical effects: (1) The solution method provided in this application, in the sampling signal of the sensor y Solve into the measured physical quantity x In the calibration system, polynomial interpolation is used to obtain the inverse function f. -1 (y) can be used to measure the physical quantity being measured. x The solution is simplified to a simple evaluation, with all steps completed before the sensor leaves the factory. Once the sensor product is manufactured, the measured physical quantity is already stored. x The coefficients of the inverse function polynomial can be determined on-site by simply measuring the electrical signal output by the sensor. y Value, substitute into the polynomial x= = a 0+ a 1 y 1 + ... + a N-1 y N-1 In this way, the measured physical quantity can be directly calculated. xCompared with existing technologies, the solution method of this application is simple, fast, has a small computational load, and is highly efficient. It can be implemented on a host computer and is also easy to process in the sensor, thus improving the real-time performance of sensor products.

[0009] (2) This application eliminates the need to store the iterative algorithm code and derivative polynomial required by the iterative numerical calculation method in the sensor after it leaves the factory, thus reducing resource consumption.

[0010] (3) The solution method provided in this application uses non-equal interval interpolation position parameters, which can make the sampling points densely distributed near the zero point and full scale point in the range. This can fundamentally avoid the Runge oscillation phenomenon of the interpolation signal, ensure the stable convergence of the interpolation, significantly improve the measurement accuracy near the full scale point and zero point, fundamentally ensure the stability and uniform convergence of high-order interpolation, and achieve higher fitting accuracy and smaller error. It can deeply restore the original signal collected by the sensor, enabling the sensor to obtain more accurate measurement values, thereby improving the sensor accuracy.

[0011] (4) The solution method provided in this application supports global high-order interpolation and is easy to implement. Attached Figure Description

[0012] Figure 1 This is a flowchart of the sensor signal calculation method based on inverse function polynomial interpolation provided in this application; Figure 2 This is a schematic diagram of a sensor embodiment provided in this application. Detailed Implementation

[0013] In the following description, specific technical features are set forth for illustrative purposes and not for limitation, and are intended to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may be implemented in other embodiments without these specific technical features. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted to avoid unnecessary detail that could obscure the description of this application.

[0014] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements, etc., but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements and / or a collection thereof.

[0015] Currently, in order to improve the accuracy of sensors during the manufacturing process, they are usually calibrated before leaving the factory. The calibration phase is performed in a controlled laboratory or at a calibration station on the production line, and its purpose is to establish the functional relationship with high confidence. y=f ( xThe data is then written into the sensor to provide an accurate conversion benchmark for field measurements after the product leaves the factory.

[0016] The physical link of the calibration system is: "Standard source (controllable) → Measured physical quantity". x →Sensor→ Output electrical signal y "This means generating the measured physical quantity through a precisely controllable standard source." x (Such as standard sources for non-electrical physical quantities such as pressure, temperature, flow rate, and displacement), the physical quantity to be measured x The input is converted into an electrical signal by the sensor. y .

[0017] In the above process, it is necessary to control the physical quantities first. x Then convert the output from the sensor. y However, in existing technologies, standard sources do not output electrical signals. y The sensor is also unable to transmit electrical signals. y The physical quantity is then taken as input, transformed, and output. x .

[0018] This application first defines the physical quantity to be measured. x Define a normalization interval, and select N non-equally spaced interpolation position parameters within this interval. t i Control the standard source of the sensor calibration system to make it conform to the interpolated position parameters with non-equidistant intervals. t i Output and t i Equal measured physical quantities x i ， Converted into electrical signals by the sensor y i Then, the positive function is obtained first through Lagrange polynomial interpolation. y=f ( x Then, numerical calculation methods were used to calculate each... y i corresponding x i The value is used to obtain the inverse function interpolation point set {( y' i , x' i )}, then use the interpolation point set {( y' i , x' i Construct the inverse Lagrange interpolation polynomial x=f with non-equal intervals. -1 (y), so as long as an electrical signal is obtained y The sensor can directly calculate and convert the measured physical quantity.x The value of .

[0019] See Figure 1 The sensor signal calculation method based on inverse function polynomial interpolation provided in this application includes the following steps: S1 The physical quantity to be measured x Normalized to the interval [0,1], N non-equally spaced interpolation position parameters are selected within this interval. t i ( i= 0, 1, ..., N-1), to obtain the point set { t 0 ,t 1 ,…,t N-1},in, t 0=0, corresponding to the zero point of the sensor. t N-1 =1, corresponding to the full-scale point of the sensor.

[0020] The sensors referred to in this application include, but are not limited to, pressure sensors, displacement sensors, image sensors, speed sensors, strain sensors, temperature sensors, and humidity sensors.

[0021] Measured physical quantity x Non-electrical information such as force, distance, temperature, light, sound, and chemical composition.

[0022] The non-equidistant interpolation position parameters of this application t i The following formula can be used to determine the density of sensors near their zero and full-scale points:

[0023] Among them, when i When =0, t 0 = 0; when i= N At 1 o'clock, t N 1 = 1.

[0024] Alternatively, the following formula can be used to determine it:

[0025] Among them, when i When =0, t 0 = 0; when i= N At 1 o'clock, t N 1 = 1.

[0026] Alternatively, the following formula can be used to determine it:

[0027] Based on the above calculation formula, the measured physical quantity can be obtained. x The set of interpolated position parameter points with non-equal intervals in the interval [0,1] { t 0, t 1,…, t N-1 These non-equally spaced interpolated position parameters t i The dense distribution of the sensor near the zero and full-scale points can fundamentally avoid the oscillation phenomenon of the interpolation signal, ensure stable convergence of the interpolation, significantly improve the measurement accuracy near the full-scale and zero points, and ensure high fidelity of the signal. S2 controls the standard source of the output physical quantity, causing it to conform to the interpolation position parameters. t i The determined non-equal interval distribution outputs N measured physical quantities x i ， in x i = t i ,Will x i The input is processed by the sensor, and after conversion, N quantities related to the measured physical quantity can be obtained. x i Corresponding electrical signal y i ( i =0,1,…,N-1).

[0028] Based on the fact that existing calibration equipment cannot achieve precise control y i And measured x i However, it can be controlled precisely. x i And measured y i ， This step is based on the obtained non-uniformly spaced interpolation position parameters. t i Precise control of the standard source ensures that the physical quantities output by the standard source are... x i The value is equal to t i ， Then x i The input sensor is converted to obtain N corresponding electrical signals. y i ( i=0,1,…,N-1), used for subsequent positive function interpolation, and thus as a prerequisite for inverse function interpolation.

[0029] S3 will x i and y i Form the interpolation point set {( x i , y i Based on this point set, a Lagrange interpolation polynomial is constructed to obtain the positive function relationship. .

[0030] The fully expanded form of this positive function is:

[0031] Combining like terms in the above Lagrange interpolation polynomials, we can simplify them into the following formula: x The power-law form, Right now: y = f ( x )= k 0+ k 1 y 1 + ... + k N-1 y N-1 , in k 0, k 1,..., k N-1 These are the coefficients of the combined polynomial.

[0032] S4 will generate N electrical signals y i The maximum value in is denoted as y max ， The minimum value is denoted as y min Then the sensor's electrical signal y The range is [ y min ，y max Then, based on the interpolation position parameters... t i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i+ y min .

[0033] S5 for each y' i The equations are solved using numerical methods. y' i = f ( x Solve for the measured physical quantity. x' Then the solution obtained x' i and y' i Form the inverse function interpolation point set { ( y' i , x' i )}, and then based on the above inverse function interpolation point set { ( y' i , x' i By constructing the Lagrange polynomial, we can obtain the inverse function polynomial: ; The fully expanded form of the inverse function is:

[0034] Expanding the Lagrange interpolation polynomial of the inverse function and combining like terms, we can simplify it to: y The exponentiation form, i.e., x = f -1 (y)= a 0+ a 1 y 1 + ... + a N-1 y N-1 ， in a 0, a 1,..., a N-1 These are the coefficients of the combined polynomial.

[0035] As long as the electrical signal is acquired y Substituting this into the polynomial, we can directly obtain... x The value, that is, according to the above inverse function polynomial, is obtained through an electrical signal. y The measured physical quantity can be obtained directly. x The value of .

[0036] In this step, numerical calculation method is used to solve the equation. y' i = f( x In this process, Newton's iteration method or other numerical calculation methods can be used.

[0037] S6. Transform the polynomial x=f -1 The coefficient of (y) { a 0, a 1, …, a N-1 Stored in the sensor's non-volatile memory.

[0038] Before the sensor product leaves the factory, x=f has already been stored at the calibration station. -1 The coefficient of (y) can be used for field measurement immediately after leaving the factory. During measurement, the electrical signal output by the sensor at the field can be used as a reference. y The value is substituted into the inverse polynomial x=f -1 In (y), the measured physical quantity can be directly calculated. x The value of . Thus, during on-site measurement, there is no need to use complex iterative numerical calculation methods to calculate the positive function. y = f ( x Solve to obtain x The value can be directly obtained using the polynomial x=f -1 (y) can be used to calculate the measured physical quantity. x The value of is used to avoid complex calculations.

[0039] The following describes in detail the sensor signal direct calculation method based on inverse function polynomial interpolation of this application with reference to application examples.

[0040] Example 1: Taking a certain pressure sensor as an example, the measured physical quantity x Pressure value, measuring range t ∈[0,1]MPa, output voltage signal y (mV).

[0041] S1 sets the physical quantity to be measured. x Given a pressure range [0,1], take interpolation position parameter points N=7 at non-equal intervals within this range. Calculate the interpolation position parameters within this range using the following formula. t i :

[0042] in, i When =0, t 0 = 0; i= At 6 o'clock, t 6 = 1. The obtained interpolation position parameters t i The point set is:

[0043] As can be seen, the above point set is densely distributed near the endpoints, which is beneficial to the high fidelity of the signal.

[0044] S2, based on the above point set, controls the standard pressure source to conform to the interpolated position parameters. t i The determined non-equal interval distribution outputs N measured physical quantities (pressure). x i ， Will x i The input sensor converts the signal into a voltage signal. y i The point set is: {0, 0.55003, 2.05216, 4.1013, 6.1441, 7.63426, 8.1784} S3 will x i and y i Form the interpolation point set {( x i , y i )}:

[0045] The above interpolation point set {( x i , y i Construct the Lagrange interpolation polynomial for the positive function. y = f ( x ), and organized into x The power form: y = f ( x =8.21186 x -0.0161274 x 2 +0.0436519 x 3 -0.153734 x 4 +0.13484 x 5 -0.0420859 x 6 .

[0046] S4 Based on interpolation position parameterst i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i + y min .

[0047] y' i =（y max - y min ）t i + y min (i=0,1,…,6) Known y max =8.1784, y min =0, according to the above y' i The calculation formula yields the voltage signal. y' i The point set is: {0,0.54785,2.0446,4.0892,6.1338,7.63055,8.1784}.

[0048] S5 is based on each of the above. y' i Solve the equation using Newton's iterative method y' i = f ( x ),That x' i The solution set is: {0,0.066722,0.24908,0.49852,0.74874,0.93256,1} Will x' i and y' i Form the inverse function interpolation point set { ( y' i , x' i Construct the Lagrange interpolation polynomial x=f for the inverse function (i=0,1,…,6). -1 (y), and organize them into y The power form: x=f -1(y)=0.121775 y +0.0000293756 y 2 -9.78293*10 -6 y 3 +4.17078*10 -6 y 4 -4.44788*10 -7 y 5 +1.69645*10 -8 y 6 .

[0049] In the formula y Indicates voltage signal, f -1 ( y () indicates pressure value x As long as the voltage signal is obtained... y Substituting this into the polynomial, the measured physical quantity (pressure) can be directly obtained. x The value of .

[0050] S6 will f -1 The coefficients of (y) are {0, 0.121775, 0.0000293756, -9.78293 × 10⁻⁶}. -6 4.17078×10 -6 -4.44788×10 -7 1.69645×10 -8 The data is stored in the sensor's non-volatile memory. At this point, the sensor's calibration work before leaving the factory is complete.

[0051] Comparative testing: Four electrical signal values, 0.5, 2.5, 4.5, and 6.5, all in mV (millivolts), were used. The measured physical quantity (pressure) was obtained by applying Newton's iteration method and the sensor signal calculation method of this application, respectively. x The values ​​are shown in the table below:

[0052] The data in the comparison table shows that the data obtained by the two methods are consistent in the last 6 decimal places, indicating that the solution algorithm proposed in this application is entirely feasible to replace Newton's iteration method.

[0053] Example 2: Taking a certain flow sensor as an example, the measured physical quantity x The value is the flow rate, and the range is t∈[0,1]m. 3 / s, output voltage signal y (mV).

[0054] S1 Set the physical quantity to be measured x The flow rate range is [0,1]. Within this range, non-equal interval interpolation point N=5 is selected. t 0=0, t 4=1, t i =(2 i -1) / 2(N-2) i =1,2,3) The obtained interpolation position parameters t i The point set is: .

[0055] The above point set is also densely distributed near the endpoints, which is beneficial to the high fidelity of the signal.

[0056] S2, based on the above point set, controls the standard flow source to follow the interpolated position parameters. t i The determined non-equal interval distribution outputs N measured physical quantities (flow rates). x i ， Corresponding to x i The input sensor converts the signal into a voltage signal. y i The point set is: {0.3611, 1.67769, 4.2674, 6.78609, 8.0157} S3 will x i and y i Form the interpolation point set {( x i , y i )}: {(0, 0.3611), (1 / 6, 1.67769), (3 / 6, 4.2674), (5 / 6, 6.78609), (1, 8.0157)}.

[0057] The above interpolation point set {( x i , y i Construct the Lagrange interpolation polynomial for the positive function. y = f ( x ), and organized into xThe power form: f ( x = 0.3611 + 7.9354 x -0.1976 x 2 -0.1088 x 3 +0.0256 x 4 .

[0058] S4 based on interpolation position parameters t i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i + y min .

[0059] y' i =（y max - y min ）t i + y min (i=0,1,…,4) Known y max =8.0157, y min =0.3611, according to the above y' i The calculation formula yields the voltage signal. y' i The point set is: {0.3611,1.63687,4.1884,6.73993,8.0157}.

[0060] S5 is based on each of the above. y' i Solve the equation using Newton's iterative method y' i = f ( x' i ),That x' i The solution set is: {0,0.16147,0.48970,0.82713,1}.

[0061] Willx' i and y' i Form the inverse function interpolation point set { ( y' i , x' i Construct the Lagrange interpolation polynomial x=f for the inverse function (i=0,1,…,4). -1 (y), and organize them into y The power form: x=f -1 (y) = -0.045456 + 0.125748 y +0.000359124 y 2 +0.0000313621 y 3 -4.19159*10 -7 y 4 .

[0062] In the formula y Indicates voltage signal, f -1 ( y ) represents the flow rate value x As long as the voltage signal is obtained... y Substituting this into the polynomial, the measured physical quantity (flow rate) can be directly obtained. x The value of .

[0063] S5 will f -1 The coefficients of (y) are {-0.045456, 0.125748, 0.000359124, 0.0000313621, -4.19159*10}. -7 The data is stored in the sensor's non-volatile memory. At this point, the sensor's calibration work before leaving the factory is complete.

[0064] Comparative testing: Four electrical signal values, 0.5, 2.5, 4.5, and 6.5, all in mV (millivolts), were used. The measured physical quantity (flow rate) was obtained by applying Newton's iteration method and the solution method of this application, respectively. x The values ​​are shown in the table below:

[0065] The data in the table shows that the data obtained by both methods are consistent in the last five decimal places, indicating that the solution algorithm of this application is entirely feasible as a replacement for Newton's iteration method. Since this embodiment only has five sampling points, the number of identical decimal places is one less than in Embodiment 1, which is normal. If more sampling points are used, the solution algorithm of this application will be even closer to Newton's iteration method.

[0066] Example 3: Taking a certain displacement sensor as an example, the measured physical quantity x Displacement value, range t ∈[0,1] meters, output voltage signal y (mV).

[0067] S1 sets the physical quantity to be measured x Given the displacement range [0,1], take non-equally spaced interpolation position parameter points N=7 within this range, and calculate the interpolation position parameters within this range using the following formula. t i : ( i =0,1,…,6) in, i When =0, t 0 = 0; when i= At 6 o'clock, t 6=1, The obtained interpolation position parameters t i The point set is: {0,0.09903,0.27748,0.5,0.72252,0.90097,1} As can be seen, the above point set is also densely distributed near the endpoints, which is beneficial to the high fidelity of the signal.

[0068] S2 Based on the above point set, control the standard displacement source to make it conform to the interpolated position parameters. t i The determined non-equal interval distribution outputs N measured physical quantities (displacements). x i ， Corresponding to x i The input sensor converts the signal into a voltage signal. y i The point set is: {0.00005,0.8079,2.2629,4.07435,5.8810,7.3251,8.1245}.

[0069] S3 will xi and y i Form the interpolation point set {( x i , y i )}: {(0, 0.00005); (0.09903, 0.8079); (0.27748, 2.2629); (0.5, 4.07435); (0.72252, 5.8810); (0.90097, 7.3251); (1, 8.1245);} The above interpolation point set {( x i , y i Construct the Lagrange interpolation polynomial for the positive function. y = f ( x ), and organized into x The power form: f ( x = 0.00005 + 8.15849 x +0.00145565 x 2 -0.0678452 x 3 +0.0840228 x 4 -0.0813582 x 5 +0.0296872 x 6 .

[0070] S4 based on interpolation position parameters t i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i + y min . y' i =（y max - y min ）t i + y min(i=0,1,…,6).

[0071] Known y max =8.1245, y min =0.00005, according to the above y' i The calculation formula yields the voltage signal. y' i The point set is: {0.00005,0.804623,2.25441,4.06228,5.87014,7.31993,8.1245}.

[0072] S5 is based on each of the above. y' i Solve the equation using Newton's iterative method y' i = f ( x ),That x' i The solution set is: {0,0.0986233,0.2764378,0.4985150,0.7211805,0.90032854,1} Will x' i and y' i Form the inverse function interpolation point set { ( y' i , x' i Construct the Lagrange interpolation polynomial x=f for the inverse function (i=0,1,…,6). -1 (y), and organize them into y The power form: x=f -1 (y) = -6.12859 * 10 -6 +0.122572 y -3.03445*10 -6 y 2 +0.0000155631 y 3 -2.39697*10 -6 y 4 +2.87192*10 -7 y 5 -1.28569*10 -8 y6 In the formula y Indicates an electrical signal. f -1 ( y () represents the displacement value. As long as the electrical signal is acquired... y Substituting this into the polynomial, we can directly obtain the measured physical quantity (displacement). x The value of .

[0073] S6 will f -1 The coefficient of (y) is -6.12859 × 10 -6 , 0.122572, -3.03445×10 -6 , 0.0000155631, -2.39697×10 -6 2.87192×10 -7 -1.28569×10 -8 The data is stored in the sensor's non-volatile memory. At this point, the sensor's calibration work before leaving the factory is complete.

[0074] Comparative testing: Four electrical signal values, 0.5, 2.5, 4.5, and 6.5, all in mV (millivolts), were used. The measured physical quantity (displacement) was obtained by applying Newton's iteration method and the solution method of this application, respectively. x The values ​​are shown in the table below:

[0075] The data in the table shows that the data obtained by the two methods are consistent in the last six decimal places, indicating that the solution algorithm proposed in this application is entirely feasible as a replacement for Newton's iteration method.

[0076] Based on the above-mentioned direct sensor signal calculation method based on inverse function polynomial interpolation, this application also provides a sensor, such as... Figure 2 As shown, the sensor includes: a processor 1, a memory 2, and a computer program 3 stored in the memory 2 and capable of running the above-described method on the processor 1, wherein the memory 2 stores the inverse function interpolation polynomial x=f in the above-described method. -1 The coefficient of (y) { a 0, a 1, …, a N-1 The sensor is calibrated before leaving the factory. During field measurement, processor 1 executes computer program 3 based on the electrical signal output by the sensor. y Value, substitute into the polynomial x= = a 0+ a 1 y 1 +... + a N-1 y N-1 In this way, the measured physical quantity can be directly calculated. x The value of .

[0077] The sensor includes, but is not limited to, processor 1 and memory 2. Those skilled in the art will understand that... Figure 2 This is merely an example of a sensor and does not constitute a limitation on the sensor. It may include more or fewer components than illustrated, or combine certain components, or use different components.

[0078] The processor 1 can be a central processing unit, or other general-purpose processors, digital signal processors, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0079] The memory 2 can be an internal storage unit of the sensor, such as a chip, hard disk or memory, or it can be an internal storage unit or / and external storage device equipped on the sensor.

[0080] This application also provides a computer-readable storage medium, including a memory, a processor, and a computer program stored in the memory and executable on the processor, for storing computer programs or instructions so that the processor can read and execute them to complete sensor data processing.

[0081] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A sensor signal resolving method based on inverse function polynomial interpolation, characterized by, Including the following steps: S1 measured physical quantity x normalized to the interval [0, 1], in which interval N non-equally spaced interpolation position parameters are selected t i i= 0, 1, …, N-1), a point set { t 0 ,t 1 ,…,t N-1} is obtained, wherein, t 0=0, corresponding to the zero point of the sensor, t N-1 =1, corresponding to the full-scale point of the sensor;​ S2 controls the standard source of the output physical quantity to follow the interpolation position parameter t i The determined non-equidistantly distributed output N measured physical quantities x i wherein x i = t i , the x i input sensor, after sensor conversion, obtains N corresponding electrical signals with the measured physical quantities x i corresponding electrical signals y i ( i =0,1,…,N-1). S3 will x i and y i Form the interpolation point set {( x i , y i Based on this point set, a Lagrange interpolation polynomial is constructed to obtain the positive function relationship. Rearranged into exponentiation form: = k 0+ k 1 y 1 + ... + k N-1 y N-1 （1） in k 0, k 1,..., k N-1 These are the coefficients of the combined polynomial; S4 will use the N electrical signals y i The maximum value in is denoted as y max ， The minimum value is denoted as y min According to the interpolation position parameters t i Calculate the independent variable points of the inverse function interpolation y' i =（y max - y min ）t i + y min ; S5 for each y' i The equations are solved using numerical methods. y' i = f ( x ), to obtain the solution x' i Afterwards, x' i and y' i Form the inverse function interpolation point set { ( y' i , x' i )}; then based on the inverse function interpolation point set {( y' i , x' i Constructing the Lagrange polynomial yields the inverse function: Rearranged into exponentiation form: x=f -1 (y)= a 0+ a 1 y 1 + ... + a N-1 y N-1 ， (2) in a 0, a 1,..., a N-1 These are the coefficients of the combined polynomial; S6. Transform the polynomial x=f -1 The coefficients in (y) { a 0, a 1, …, a N-1 Stored in the sensor's non-volatile memory.

2. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1, wherein the non-equal interval interpolation position parameters t i The sensors are densely packed near their zero and full-scale points.

3. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1 or 2, characterized in that, The interpolation position parameters for non-equidistant intervals are determined using the following formula. t i : （3） Among them, when i When =0, t 0 = 0; when i= N At 1 o'clock, t N 1 = 1.

4. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1 or 2, characterized in that, The interpolation position parameters for non-equidistant intervals are determined using the following formula. t i : （4） Among them, when i When =0, t 0 = 0; when i= N At 1 o'clock, t N 1 = 1.

5. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1 or 2, characterized in that, The interpolation position parameters for non-equidistant intervals are determined using the following formula. t i : （5）。 6. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1, characterized in that, In step S3, the positive function y = f ( x The expansion of ) is: 。 7. The sensor signal calculation method based on inverse function polynomial interpolation according to claim 1, characterized in that, In the S5 step, the inverse function x = f -1 The expansion of (y) is 。 8. A sensor, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The memory stores the inverse function interpolation polynomial x=f obtained by the method according to any one of claims 1-7. -1 The coefficient of (y) { a 0, a 1, …, a N-1 }; When the processor executes the computer program, it bases its decisions on the electrical signals output by the sensor. y Value, substitute into the polynomial x= = a 0+ a 1 y 1 + ... + a N-1 y N-1 The measured physical quantity can be directly calculated. x The value of .

9. A computer-readable storage medium storing a computer program, characterized in that, The computer program is configured to be executed by a processor to perform data processing on the sensor of claim 8.

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