Method for sensing underwater two-dimensional direct-current flow field by using tubular IPMC sensor
By dividing the outer surface electrode of the tubular IPMC sensor into four sub-electrodes and fitting the calibration curve using the least squares method, the challenge of IPMC sensor in DC flow velocity perception is solved, and the ability of two-dimensional DC flow field perception is realized.
Patent Information
- Application Number
- CN202411922311.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-25
- Publication Date
- 2025-03-25
- Estimated Expiration
- 2044-12-25
AI Technical Summary
Existing IPMC sensors have challenges in DC flow velocity perception and lack effective algorithms and models to describe the correspondence between sensor output and input.
Using a tubular IPMC sensor, the outer surface electrode is divided into four sub-electrodes and the calibration curve is fitted using the least squares method to describe the relationship between the sensor output signal changes with the flow rate, thereby realizing two-dimensional DC flow field perception.
The two-dimensional isotropic sensing capability of a single IPMC sensor has been realized, and the shortcomings of IPMC DC flow rate sensors in the prior art are overcome, which is of great significance to promoting the development of intelligent flexible materials and underwater perception technology.
Abstract
Description
Technical Field
[0001] The present invention relates to the field of sensor sensing technology, and in particular to a method for sensing an underwater two-dimensional direct current flow field by using a tubular IPMC sensor. Background Art
[0002] IPMC (Ionic Polymer Metal Composites) is a representative ionic EAP (Electro Active Polymer, EAP) smart material. The structure of IPMC is composed of "electrode-ion exchange membrane-electrode", and its shape is just like "sandwich bread". The ion exchange membrane in the middle layer is usually Nafion membrane from DuPont, USA, which contains hydrophobic polymer chains, mobile cations and a certain amount of solvent. The precious metal electrodes on both sides of the ion exchange membrane (common ones are palladium, platinum, gold, etc.) are mostly prepared by surface plating process.
[0003] IPMC sensors have the characteristics of soft texture, fast response, simple structure, high sensitivity, strong plasticity, and the ability to operate in complex underwater environments. They can be used to sense and measure underwater flow velocity, and therefore have great application potential in underwater robots, energy collection, environmental monitoring, marine resource development and other fields.
[0004] Existing methods of using IPMC sensors for flow velocity sensing are mostly based on the design of flow velocity sensors based on sheet IPMC materials. Therefore, the sensing ability of a single sensor is one-dimensional. Even if they are assembled into sensor devices with multi-dimensional sensing capabilities, it is difficult to simultaneously meet measurement requirements such as miniaturization, compact structure, high stability, and simple calculation algorithms.
[0005] Flow velocity sensing requires, on the one hand, the sensor device to convert the measured physical quantity into a measurable electrical signal, and on the other hand, it also requires the design and derivation of algorithms and models that match the physical characteristics of the sensor, and the provision of calculation formulas to quantitatively describe the corresponding relationship between the sensor output and input. Currently, many researchers have done a lot of work on the design of the sensor device itself, but there is relatively little work on the related matching algorithms and models.
[0006] In addition, due to the properties of the IPMC material itself, if the IPMC sensor remains in a fixed bending deformation state after being bent by force, it will not generate a sensing signal. The sensing signal will only be generated during the dynamic process of bending and recovery. In other words, the IPMC material is naturally unresponsive to external DC excitation. Therefore, there are still huge challenges and difficulties in using IPMC sensors to sense DC underwater excitation. Summary of the invention
[0007] To solve the above problems, the present invention provides a method for sensing an underwater two-dimensional DC flow field using a tubular IPMC sensor, comprising the following steps: Step 1: Use Nafion tube to process tubular IPMC, divide its outer surface electrode into four sub-electrodes along the axial direction, and use the inner surface electrode as a common ground line; the four sub-electrodes are sub-electrode p1, sub-electrode p2, sub-electrode p3, and sub-electrode p4 in the radial direction, wherein sub-electrode p1 and sub-electrode p3, and sub-electrode p2 and sub-electrode p4 are symmetrical along the axis; Step 2: Convert the current output of each sub-electrode into a measurable bipolar voltage signal, namely u1(t), u2(t), u3(t), and u4(t), where t represents the time variable; Step 3: Conduct a characterization experiment on the underwater 3D DC flow field perception of the tubular IPMC sensor, calibrate the zero-point noise u10(t), u20(t), u30(t), and u40(t) of the four-way sensor signal in a static water environment, and calibrate the sensor signals u1(t,v,n), u2(t,v,n), u3(t,v,n), and u4(t,v,n) of each sub-electrode facing the water flow direction under different laminar flow velocities, where the scalar v represents the flow velocity, and the positive integer n represents the number of the sub-electrode n facing the water flow direction, and the value range of n is 1~4; Step 4: For each sub-electrode facing the water flow direction, a calibration curve is fitted by the least square method to describe the corresponding relationship between the four-way output signals of the tubular IPMC sensor and the laminar flow velocity. The horizontal axis variable of the calibration curve is the flow velocity v, and the vertical axis variable is the corrected mean value of the sensor signal of the sub-electrode minus the corrected mean value of the sensor signal of the sub-electrode symmetrical to the sub-electrode; Step 5: Use the tubular IPMC sensor to sense the underwater two-dimensional DC flow field: obtain the one-dimensional DC flow velocity information vx in the x direction through u1(t), u3(t), and the calibration curve, and obtain the one-dimensional DC flow velocity information vy in the y direction through u2(t), u4(t), and the calibration curve.
[0008] Further, in step 1, the method for processing tubular IPMC using Nafion tube is: Step 1.1: Use Nafion tube to process into tubular IPMC; Step 1.2: Divide the outer surface electrode into four mutually insulated equal parts along the axial direction of the tubular IPMC to form four sub-electrodes, and an insulating isolation zone is provided between adjacent sub-electrodes. The outer surface metal deposition at the isolation zone position is removed to achieve an insulating effect; Step 1.3: Connect a wire to the entire inner surface electrode as a common ground wire, and connect each of the four sub-electrodes with a wire as a signal wire. Each signal wire and the common ground wire constitute a sensing signal output of the sensor; Step 1.4: The tubular IPMC is encapsulated in a film capsule and placed in a water bath for a predetermined period of time and then taken out, and the tubular IPMC has moisture inside; Step 1.5: Use gelatin resin material to perform biomimetic encapsulation on the tubular IPMC.
[0009] Furthermore, after step 1.4, a thin film coating is formed on the surface of the tubular IPMC, and the thickness of the thin film coating is between 20 microns and 50 microns.
[0010] Furthermore, the positions where the inner surface electrode, the outer surface sub-electrode and the corresponding wires are connected are located at the same height position of the tube body.
[0011] Furthermore, in step three, the tubular IPMC sensor is located at a depth of at least 10 cm below the water surface, with its axis perpendicular to the water surface.
[0012] Furthermore, in step three, the duration of the collected sensor signal is at least 10 seconds, and the sampling frequency is at least 1000 Hz.
[0013] Furthermore, in step 4, according to the amount of data obtained in the characterization experiment, the calibration curve can be fitted as a straight line or a parabola; or piecewise fitted as a combination of different curves.
[0014] Furthermore, in step 4, the calculation method of the corrected mean is: the mean of the sub-electrode sensor signal minus the mean of the zero-point noise of the sub-electrode sensor signal.
[0015] Furthermore, in step five, the axis of the tubular IPMC sensor is perpendicular to the plane formed by the x-direction and the y-direction, the axis and the x-direction form a first plane, the first plane intersects with the surfaces of the sub-electrode p1 and the sub-electrode p3 at the axial midline, the axis and the y-direction form a second plane, the second plane intersects with the surfaces of the sub-electrode p2 and the sub-electrode p4 at their axial midlines; when the water flows along the x-direction, the sub-electrode p3 faces the water flow direction, and when the water flows along the y-direction, the sub-electrode p4 faces the water flow direction.
[0016] Furthermore, in step 5, the method for obtaining the value of vx is as follows: pre-setting the time window length, calculating the corrected mean value of u1(t) minus the corrected mean value of u3(t), and finding the corresponding horizontal axis coordinate point in the calibration curves of the sub-electrode p1 and the sub-electrode p3 according to the calculation result; The value of vy is obtained by calculating the corrected mean value of u2(t) minus the corrected mean value of u4(t), and finding the corresponding horizontal axis coordinate point in the calibration curves of sub-electrode p2 and sub-electrode p4 based on the calculation result, which is the value of vy.
[0017] The beneficial effects of the present invention are: The present invention overcomes the shortcomings of the prior art and utilizes a tubular symmetrical structure to realize the direct two-dimensional isotropic sensing capability of a single IPMC sensor. From the perspective of energy, the DC flow velocity sensing characteristics of the sensor are quantitatively calibrated and described to solve the problem of the lack of effective algorithms and models in the existing IPMC DC flow velocity sensors. This is of great significance for promoting the application of intelligent flexible materials and the development of underwater sensing technology. DETAILED DESCRIPTION
[0018] Before introducing the present invention, a method for preparing an underwater two-dimensional sensing IPMC sensor is first described.
[0019] The preparation method of the underwater two-dimensional sensing IPMC sensor includes the following steps: Step 1.1: Select a Nafion tube and process it into a tubular IPMC.
[0020] The specific processing steps include Step 1~Step 5: Step 1. In the pretreatment stage: Boil the Perma Pure Nafion drying tube (model: TT-110) in 2wt% dilute hydrochloric acid for 1 hour, and then heat it in deionized water for 1 hour to remove impurities and allow the Nafion tube to bend freely.
[0021] Step 2. In the ion adsorption stage: immerse the Nafion tube in a solution of tetraammineplatinum chloride (molecular formula: [Pt(NH3)4]Cl2), and the platinum ions in the platinum complex solution are exchanged with the cations in the Nafion.
[0022] Step 3. In the first chemical plating stage: clean the Nafion tube with deionized water, put it into a 5 wt% sodium borohydride (molecular formula: NaBH4) solution, use a heated magnetic stirrer to increase the temperature of the solution, and add 1 ml of sodium borohydride solution every 15 minutes. Through the reduction reaction, platinum electrodes are formed on the inner and outer surfaces of the Nafion tube.
[0023] Step 4. In the secondary chemical plating stage: In order to precipitate more platinum ions, repeat the acid treatment from Step 1 to Step 3 to the reduction reaction step to complete the secondary deposition of platinum and enhance the conductivity of the platinum electrode.
[0024] Step 5. In the replacement reaction stage: After the reduction reaction is completed, the Nafion tube is cleaned and then placed in dilute hydrochloric acid and boiled in a constant temperature water bath to allow the cations in the Nafion tube to exchange with the hydrogen ions in the hydrochloric acid.
[0025] It should be noted that the electrodes at both ends of the cross section of the tubular IPMC need to be removed to prevent the inner and outer surface electrodes from short-circuiting with each other.
[0026] Step 1.2: Make the sub-electrodes on the outer surface. The specific method is: remove the surface electrode to make an isolation zone, divide the outer electrode into four mutually insulated equal parts along the axial direction of the tubular IPMC, and form four uniform and symmetrical sub-electrodes on the outer surface. It should be noted that, while ensuring sufficient insulation between adjacent sub-electrodes, the width of the isolation zone should be as thin as possible, and the depth of the isolation zone should be as shallow as possible, so as to minimize the impact of this step on the overall material properties and mechanical properties of the tubular IPMC.
[0027] When manufacturing sub-electrodes, a mold can be made using a 3D printing method, and the tubular IPMC can be placed and fixed in the mold. The mold acts as a mask, covering the sub-electrode part while exposing the isolation zone part to be processed, thereby ensuring that the division of the sub-electrode is uniform and symmetrical.
[0028] Step 1.3: Make a common ground wire. Lead a wire to connect the entire inner surface electrode as a common ground wire, lead 4 wires to connect the 4 sub-electrodes on the outer surface as 4 signal wires, each signal line and the common ground wire constitute a sensor signal output of the sensor; in this step, the connection method between the wire and the electrode can be welding or bonding, or other methods that can ensure long-term good conductivity.
[0029] The four signal lines of the sub-electrodes on the outer surface can also be combined in pairs to form multi-channel sensing signal outputs.
[0030] Step 1.4: Film encapsulation. The tubular IPMC connected with the wires is encapsulated with a polymer film encapsulation by vacuum physical vapor deposition, and then placed in a high temperature (the high temperature is generally 60-80 degrees Celsius) water bath for a period of time and then taken out to lock sufficient water molecules inside the tubular IPMC encapsulated by the film encapsulation. The polymer material used for encapsulation can form a thin film coating on the surface of the tubular IPMC through the process of vacuum physical vapor deposition.
[0031] After depositing the thin film, the temperature and duration of the water bath are determined based on the thickness of the film. The thicker the film, the higher the water bath temperature and the longer the immersion time required.
[0032] The thickness of the thin film coating is between 20 microns and 50 microns, which can ensure that the coating has extremely low permeability to water molecules at room temperature, and the permeability of the coating to water molecules will be greatly improved in a high-temperature water bath. The polymer material includes but is not limited to Parylene.
[0033] In this embodiment, the film thickness is 25 microns, the temperature of the high-temperature water bath is 80 degrees Celsius, and it is taken out after immersion for 48 hours. Changing the thickness of the film capsule packaging, the temperature of the high-temperature water bath, and the length of the immersion time will directly change the number of water molecules that enter the tubular IPMC through osmosis, thereby affecting the sensing characteristics of the tubular IPMC.
[0034] Step 1.5: Bionic packaging. The above-processed tubular IPMC is subjected to bionic packaging of the colloidal resin material by injection molding, which plays a role in amplifying water flow excitation. The mold is made by 3D printing or machining, and the tubular IPMC after step 4 is placed and fixed in the center of the mold; the colloidal resin material used for bionic packaging can wrap the tubular IPMC and fill the space inside the tube through the injection molding process, forming the packaging shape of the bionic bullet shell as a whole, and the axis of the packaging shell coincides with the axis of the tubular IPMC, and the main cross-sectional radius is larger than the outer radius of the tubular IPMC. Preferably, the difference between the two radii is about 1-3 mm. In this embodiment, the main cross-sectional radius is about two millimeters larger than the outer radius of the tubular IPMC. The colloidal resin material includes but is not limited to polydimethylsiloxane (PDMS).
[0035] Step 1.6: Use 3D printing to make the base of the tubular IPMC processed above, and the axial direction of the tubular IPMC is perpendicular to the plane of the base.
[0036] The method of the present invention will be further described below.
[0037] Step 1: According to the above content, use Nafion tube to process tubular IPMC, and divide its outer surface electrode into four sub-electrodes that are insulated from each other and orthogonally symmetrically distributed along the axial direction, and form four sensing signal outputs with the inner surface electrode respectively. The inner surface electrode serves as a common ground wire, and the four sub-electrodes are numbered p1, p2, p3, and p4 in sequence along the radial direction, wherein sub-electrode p1 and sub-electrode p3, sub-electrode p2 and sub-electrode p4 are symmetrical along the axis, and sub-electrode p1 is adjacent to sub-electrode p2 and sub-electrode p4 respectively.
[0038] Step 2: Use a signal conditioning circuit based on photoelectric coupling and a signal amplification circuit based on an operational amplifier to convert the current output of each sensing signal into a measurable bipolar voltage signal u1(t), u2(t), u3(t), and u4(t), which correspond to sub-electrode p1, sub-electrode p2, sub-electrode p3, and sub-electrode p4, respectively. The t in the voltage signal represents the time variable.
[0039] The signal conditioning circuit and the signal amplification circuit include an RC low-pass filter circuit based on a resistor-capacitor combination, the low-pass cutoff frequency of which is set to 20 Hz, and the output range of the bipolar voltage signal is between positive and negative 5 volts.
[0040] Step 3: Conduct a characterization experiment on underwater 3D DC flow field perception of the tubular IPMC sensor in an experimental environment that can provide stable laminar flow. Calibrate the zero-point noise u10(t), u20(t), u30(t), and u40(t) of the four sensor signals in a static water environment. Calibrate the sensor signals u1(t,v,n), u2(t,v,n), u3(t,v,n), and u4(t,v,n) of each sub-electrode facing the water flow direction under different laminar flow rates, where the scalar v represents the flow velocity, and the positive integer n represents the number of the sub-electrode pn facing the water flow direction. The value of n is 1, 2, 3, or 4.
[0041] A circulating water tank is used to build an experimental environment that can provide a stable laminar flow. The water flow rate of the circulating water tank can be adjusted, and multiple honeycomb filters are set in the water tank to reduce the occurrence of turbulence. A third-party flow velocity sensing device is used to obtain the actual value of the flow velocity as a reference value for calibration, including but not limited to the use of impeller water flow Hall sensor and Doppler flow meter.
[0042] The tubular IPMC sensor should be placed at least 10 cm below the water surface, with its axis perpendicular to the water surface, and the plane formed by its axis and the water flow direction intersects with the sub-electrode surface facing the water flow direction at the midline of the sub-electrode axis, and the plane also intersects with the sub-electrode surface facing the water flow direction at the midline of the sub-electrode axis. It should be noted that it is preferred to collect the sensing signal after the experimental environment reaches a steady state, the signal duration is at least 10 seconds, and the sampling frequency is above 1000 Hz.
[0043] Step 4: Based on the data in the characterization experiment, for the case where each sub-electrode faces the water flow direction, a calibration curve is fitted using the least squares method to describe the corresponding relationship between the changes in the four-way output signals of the tubular IPMC sensor as the laminar flow velocity changes. The horizontal axis variable of the calibration curve is the flow velocity v, and the vertical axis variable is the corrected mean value of the sensor signal of the sub-electrode minus the corrected mean value of the sensor signal of the sub-electrode symmetrical to the sub-electrode.
[0044] The corrected mean refers to the mean of the sub-electrode sensing signal minus the mean of the zero-point noise of the sub-electrode sensing signal.
[0045] Step 5: When using the tubular IPMC sensor to sense the underwater two-dimensional DC flow field, first obtain the one-dimensional DC flow velocity information vx in the x-direction through u1(t) and u3(t) and the aforementioned calibration curve, and synchronously obtain the one-dimensional DC flow velocity information vy in the y-direction through u2(t) and u4(t) and the aforementioned calibration curve. The x-direction and y-direction are orthogonal to each other, and the vx and vy together realize the two-dimensional DC flow field perception.
[0046] The length of the sensor signal acquisition time window needs to be set in advance. The longer the time window, the worse the real-time performance of the calculated flow rate information and the smaller the error; the shorter the time window, the better the real-time performance, but the higher the error. After experiments, the time window of this embodiment is set to 5 seconds, which can better balance the real-time and error requirements. The axis of the tubular IPMC sensor is perpendicular to the plane formed by the x-direction and the y-direction. The plane formed by the axis and the x-direction intersects with the surfaces of the sub-electrodes p1 and p3 at their axial midline. The plane formed by the axis and the y-direction intersects with the surfaces of the sub-electrodes p2 and p4 at their axial midline. When the water flows along the x-direction, p3 faces the direction of the water flow. When the water flows along the y-direction, p4 faces the direction of the water flow.
[0047] Calculate the corrected mean value of u1(t) minus the corrected mean value of u3(t), and find the corresponding horizontal axis coordinate point in the calibration curves of p1 and p3 based on the calculation result, which is the value of vx; calculate the corrected mean value of u2(t) minus the corrected mean value of u4(t), and find the corresponding horizontal axis coordinate point in the calibration curves of p2 and p4 based on the calculation result, which is the value of vy.
Claims
1. A method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor, characterized in that: The method comprises the following steps: Step 1: Use Nafion tube to process tubular IPMC, divide its outer surface electrode into four sub-electrodes along the axial direction, and use the inner surface electrode as a common ground line; the four sub-electrodes are sub-electrode p1, sub-electrode p2, sub-electrode p3, and sub-electrode p4 in the radial direction, wherein sub-electrode p1 and sub-electrode p3, and sub-electrode p2 and sub-electrode p4 are symmetrical along the axis; Step 2: Convert the current output of each sub-electrode into a measurable bipolar voltage signal, namely u1(t), u2(t), u3(t), and u4(t), where t represents the time variable; Step 3: Conduct a characterization experiment on the underwater 3D DC flow field perception of the tubular IPMC sensor, calibrate the zero-point noise u10(t), u20(t), u30(t), and u40(t) of the four-way sensor signal in a static water environment, and calibrate the sensor signals u1(t,v,n), u2(t,v,n), u3(t,v,n), and u4(t,v,n) of each sub-electrode facing the water flow direction under different laminar flow velocities, where the scalar v represents the flow velocity, and the positive integer n represents the number of the sub-electrode n facing the water flow direction, and the value range of n is 1~4; Step 4: For each sub-electrode facing the water flow direction, a calibration curve is fitted by the least square method to describe the corresponding relationship between the four-way output signals of the tubular IPMC sensor and the laminar flow velocity. The horizontal axis variable of the calibration curve is the flow velocity v, and the vertical axis variable is the corrected mean value of the sensor signal of the sub-electrode minus the corrected mean value of the sensor signal of the sub-electrode symmetrical to the sub-electrode; Step 5: Use the tubular IPMC sensor to sense the underwater two-dimensional DC flow field: obtain the one-dimensional DC flow velocity information vx in the x direction through u1(t), u3(t), and the calibration curve, and obtain the one-dimensional DC flow velocity information vy in the y direction through u2(t), u4(t), and the calibration curve.
2. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 1, characterized in that: In step 1, the method of processing tubular IPMC using Nafion tube is as follows: Step 1.1: Use Nafion tube to process into tubular IPMC; Step 1.2: Divide the outer surface electrode into four mutually insulated equal parts along the axial direction of the tubular IPMC to form four sub-electrodes, and an insulating isolation zone is provided between adjacent sub-electrodes; Step 1.3: Connect a wire to the entire inner surface electrode as a common ground wire, and connect each of the four sub-electrodes with a wire as a signal wire. Each signal wire and the common ground wire constitute a sensing signal output of the sensor; Step 1.4: The tubular IPMC is encapsulated in a film capsule and placed in a water bath for a predetermined period of time and then taken out, and the tubular IPMC has moisture inside; Step 1.5: Use gelatin resin material to perform biomimetic encapsulation on the tubular IPMC.
3. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2, characterized in that: After step 1.4, a thin film coating is formed on the surface of the tubular IPMC, and the thickness of the thin film coating is between 20 microns and 50 microns.
4. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: The positions where the inner surface electrode, the outer surface sub-electrode and the corresponding wires are connected are located at the same height position of the tube body.
5. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In step three, the tubular IPMC sensor is located at a depth of at least 10 cm below the water surface, with its axis perpendicular to the water surface.
6. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In the step three, the duration of the collected sensor signal is at least 10 seconds, and the sampling frequency is at least 1000 Hz.
7. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In step 4, according to the amount of data obtained in the characterization experiment, the calibration curve can be fitted as a straight line or a parabola; or piecewise fitted as a combination of different curves.
8. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In the step 4, the calculation method of the corrected mean value is: the mean value of the sub-electrode sensor signal minus the mean value of the zero-point noise of the sub-electrode sensor signal.
9. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In step five, the axis of the tubular IPMC sensor is perpendicular to the plane formed by the x-direction and the y-direction. The axis and the x-direction form a first plane, which intersects the surfaces of the sub-electrode p1 and the sub-electrode p3 at the axial midline. The axis and the y-direction form a second plane, which intersects the surfaces of the sub-electrode p2 and the sub-electrode p4 at their axial midlines. When the water flows along the x-direction, the sub-electrode p3 faces the water flow direction, and when the water flows along the y-direction, the sub-electrode p4 faces the water flow direction.
10. The method for sensing underwater two-dimensional DC flow field using a tubular IPMC sensor according to claim 2 or 3, characterized in that: In step 5, the vx value is obtained by presetting the time window length, calculating the corrected mean value of u1(t) minus the corrected mean value of u3(t), and finding the corresponding horizontal axis coordinate point in the calibration curves of sub-electrode p1 and sub-electrode p3 according to the calculation result; The value of vy is obtained by calculating the corrected mean value of u2(t) minus the corrected mean value of u4(t), and finding the corresponding horizontal axis coordinate point in the calibration curves of sub-electrode p2 and sub-electrode p4 based on the calculation result, which is the value of vy.
Citation Information
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