A method for evaluating the scope of PSP pressure calibration data based on double-frame images

Abstract

This application provides a method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images, belonging to the field of aero-engine technology. The method includes: building a test system; setting timing control rules to control the camera to expose twice for each switch of the light source probe, obtaining two fluorescence images of the experimental specimen; based on the timing control rules, acquiring two fluorescence images at normal pressure as reference images, and two images under no-light conditions as background images; acquiring two fluorescence images at each standard pressure point as experimental images; calculating the light intensity ratio and the average light intensity ratio based on the reference image, background image, and experimental images; plotting the relationship curve between each standard pressure point and the corresponding average light intensity ratio as calibration data; calculating the overlap ratio of light intensity ratios between two adjacent standard pressure points, statistically analyzing the standard pressure range where the overlap ratio is zero, and setting this as the applicable range of the calibration data for pressure measurement in the current test system. This scheme improves the accuracy of pressure measurement.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and in particular to a method for evaluating the applicability of PSP pressure calibration data based on dual-frame images. Background Technology

[0002] To address the technical challenge of accurately measuring the pressure distribution and aerodynamic loads acting on engine blades during rotation using conventional pressure measurement techniques, Pressure Sensitive Paint (PSP) technology is widely adopted internationally. This technology utilizes the oxygen quenching principle of photoluminescence, where fluorescence intensity gradually decreases as the concentration of oxygen molecules in the environment increases. By quantitatively detecting the light intensity distribution of the fluorescent coating, the pressure distribution on the model surface can be measured.

[0003] This technology is currently one of the most advanced non-contact pressure testing technologies in the world and is considered one of the most promising testing technologies of the 21st century. Compared with traditional discrete point measurement technology, non-contact pressure-sensitive paint pressure measurement technology breaks through the limitations of spatial resolution of the measurement area, and eliminates the need for complex pressure point design and processing of the model, significantly improving data density, shortening the experimental cycle, and reducing experimental costs.

[0004] It has the advantage of non-contact and rapid acquisition of continuous pressure distribution on the model surface under steady or unsteady flow conditions, making it suitable for non-contact measurement of surface pressure when engine blades are rotating. The obtained experimental data can be used as a basis for verifying and confirming the calculation results of numerical simulation methods.

[0005] The currently commonly used single-frame intensity method for PSP surface pressure measurement is easily affected by camera and light source instability, which introduces measurement errors. Summary of the Invention

[0006] In view of this, embodiments of this application provide a method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images, which at least partially solves the problem in the prior art that PSP surface pressure measurement is easily affected by the instability of camera and light source, leading to measurement errors.

[0007] This application provides a method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images, including:

[0008] A test system was built, which included a light source probe, a light source controller, a timing controller, a camera, and an acquisition and processing system connected in sequence. The timing control rules of the timing controller were set to control the camera to expose twice for each time the light source probe was switched on and off, so as to obtain two fluorescence images of the experimental specimen with grayscale differences. Based on the timing control rules, the acquisition and processing system acquires two fluorescence images from the camera under normal pressure as reference images, and acquires two images from the camera under no-light conditions as background images. The surface of the experimental specimen was placed under a series of standard pressure points, and the acquisition and processing system acquired two fluorescence images corresponding to each standard pressure point as experimental images. For each standard pressure point, based on the reference image, background image, and the experimental image corresponding to that standard pressure point, calculate the light intensity ratio and the average light intensity ratio of the experimental specimen at that standard pressure point; plot the relationship curve between each standard pressure point and the corresponding average light intensity ratio, and use this relationship curve as calibration data; Based on the light intensity ratio corresponding to two adjacent standard pressure points, the overlap ratio is calculated, and the standard pressure range when the overlap ratio is zero is statistically analyzed. The standard pressure range is then set as the applicable range for pressure measurement of the calibration data in the current test system.

[0009] According to a specific implementation of an embodiment of this application, the step of setting the timing control rules of the timing controller includes: The timing controller generates two square wave signals, including a first signal and a second signal. The first signal is output to the light source controller to control the light source to turn on and off, and the second signal is output to the camera to control the camera to acquire images. Within one cycle, one square wave signal of the first signal corresponds to two square wave signals of the second signal. When the first signal is at a high level, the light source is turned on; when the first signal is at a low level, the light source is turned off. When the second signal is at a high level, the camera begins exposure. The time interval between the two square wave signals of the second signal is greater than or equal to the camera's sampling interval. When the first signal is at a high level, the camera begins exposure and captures the first image. When the first signal drops from a high level to a low level, the camera captures the second image.

[0010] According to a specific implementation of an embodiment of this application, the step of the camera acquiring a second image when the first signal drops from a high level to a low level includes: The rising edge of the second square wave signal of the second signal is earlier than the falling edge of the square wave signal of the first signal, and the falling edge of the second square wave signal of the second signal is later than the falling edge of the square wave signal of the first signal.

[0011] According to a specific implementation of an embodiment of this application, the step of calculating the light intensity ratio and the average light intensity ratio of the experimental specimen at the standard pressure point based on the reference image, the background image, and the experimental image corresponding to the standard pressure point includes: Based on the experimental images, the region of interest in the images is obtained; Using the reference image as a reference, the experimental images corresponding to different standard pressure points are registered to the same coordinate system; For each standard pressure point, based on the reference image, background image, and registered experimental image, the light intensity ratio of each data point in the region of interest is calculated, and the average light intensity ratio of all data points in the region of interest is calculated to obtain the average light intensity ratio.

[0012] According to a specific implementation of this application, the formula for calculating the light intensity ratio is: , Where IR is the light intensity ratio, and I 1_exp The light intensity I of the data point in the first image of the experimental image corresponding to each standard pressure point. 2_exp The light intensity I at the data point of the second image in the experimental image corresponding to each standard pressure point. 1_dark I represents the light intensity of the data points in the first image of the background image. 2_dark I represents the light intensity of the data points in the second image within the background image. 1_ref The light intensity is the data point of the first image in the reference image, and k is the adjustment coefficient, with a value ranging from 0.1 to 10.

[0013] According to a specific implementation of an embodiment of this application, the method further includes: The value of k is adjusted according to the coating on the surface of the test piece and the light source, so as to minimize the calibration error or maximize the applicability of the calibration data to pressure measurement in the current testing system.

[0014] According to a specific implementation of an embodiment of this application, the method further includes: For the light intensity ratio data at each standard pressure point, percentiles are calculated to remove abnormal noise, and the minimum and maximum light intensity ratios of all data points within the region of interest at each standard pressure point are calculated.

[0015] According to a specific implementation of an embodiment of this application, the formula for calculating the overlap ratio is as follows: , Where overlapRatio is the overlap ratio, min is the minimum value, max is the maximum value, Mi is the maximum light intensity ratio of all data points in the region of interest under the i-th standard pressure point, Mi+1 is the maximum light intensity ratio of all data points in the region of interest under the (i+1)-th standard pressure point, Ni is the minimum light intensity ratio of all data points in the region of interest under the i-th standard pressure point, and Ni+1 is the minimum light intensity ratio of all data points in the region of interest under the (i+1)-th standard pressure point.

[0016] According to a specific implementation of an embodiment of this application, the method further includes: The reference image, background image, and experimental image corresponding to each standard pressure point were preprocessed to remove random noise.

[0017] Beneficial effects: The PSP pressure measurement calibration data applicability evaluation method based on dual-frame images in this application overcomes the susceptibility of traditional single-frame intensity methods to interference from factors such as light source and camera instability. By reasonably setting the timing between the light source and the camera, dual-frame images are acquired when the light source is on and off. The light intensity ratio is calculated according to a specific formula to obtain calibration data of standard pressure and light intensity ratio. Combined with the calibration data, the measured pressure can be calculated by back-calculating from the light intensity data, thus improving the accuracy of PSP surface steady-state pressure measurement. Furthermore, the applicability of the calibration data can be evaluated by calculating the overlap ratio of light intensity ratios under different standard pressures within the ROI (Region of Interest). This can serve as a general evaluation standard for PSP measurement technology, assessing the measurement performance of PSP coatings, systems, and processing procedures. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of a test system according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a square wave signal of a timing controller according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a pressure measurement calibration system according to an embodiment of the present invention. Detailed Implementation

[0020] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0021] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0023] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0024] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0025] In one embodiment, a method for evaluating the applicability of PSP pressure calibration data based on dual-frame images is provided, including: Step 1: Build the test system, referring to... Figure 1 The testing system includes a light source probe, a light source controller, a timing controller, a camera, and an acquisition and processing system connected in sequence. The timing control rules of the timing controller are set to control the camera to expose twice for each time the light source probe is switched on and off, so as to obtain two fluorescence images of the experimental specimen with grayscale differences. Specifically, while ensuring that the experimental specimen fills the entire field of view of the camera as much as possible, the camera, light source probe, light source controller, timing controller, and acquisition and processing system are set up. The timing controller parameters are set according to the aforementioned timing control rules and debugged to ensure that the light source emission and camera acquisition meet the requirements. Figure 2 The timing control requirements are shown below; Step 2: Based on the timing control rules, the acquisition and processing system acquires two fluorescence images of the camera under normal pressure as reference images, and acquires two images of the camera under no-light conditions as background images. Step 3: Place the surface of the experimental piece under a series of standard pressure points, and the acquisition and processing system acquires two fluorescence images corresponding to each standard pressure point as experimental images. Specifically, the calibration device can provide a series of standard pressures, so that the surface of the calibration sample is under the corresponding standard pressure. The standard pressure value is set, and the acquisition and processing system acquires multiple fluorescence images from the camera under different standard pressure conditions as experimental images. Step 4: For each standard pressure point, based on the reference image, background image, and the experimental image corresponding to that standard pressure point, calculate the light intensity ratio and average light intensity ratio of the experimental specimen at that standard pressure point; plot the relationship curve between each standard pressure point and the corresponding average light intensity ratio, and use this relationship curve as calibration data. Step 5: Based on the light intensity ratio corresponding to two adjacent standard pressure points, calculate the overlap ratio, and statistically analyze the standard pressure range when the overlap ratio is zero. Set the standard pressure range as the applicable range for pressure measurement of the calibration data in the current test system.

[0026] In practice, the surface of the experimental specimen is coated with a pressure-sensitive coating. A light source probe and its controller generate a continuous laser of a specific wavelength (e.g., 405nm) to illuminate the pressure-sensitive coating (PSP) on the specimen surface. Upon excitation, the PSP produces fluorescence of a specific wavelength (e.g., 650nm), and the fluorescence image is captured by a camera. By designing a reasonable two-frame timing sequence, two frames of images are acquired: one during light source excitation and one after (including coating luminescence lifetime information). These images are then processed to remove noise from the system itself (camera, light source, etc.), improving measurement accuracy. By calculating the light intensity ratio overlap ratio under different standard pressures within the ROI region, the applicability of the calibration data is evaluated. Specifically, the pressure range with a zero overlap ratio represents the accurately measurable pressure range for this group of PSP coatings within the current measurement system layout and ROI region.

[0027] In this embodiment, two camera exposures are triggered by a single light source illumination, directly obtaining two dual-frame images under the same pressure state. Grayscale difference data for calculation can be obtained without additional adjustment of test conditions. Compared to the traditional single-frame acquisition method, the evaluation of the applicable range of calibration data can be completed without multiple repeated calibration experiments, simplifying the operation process and reducing the interference of environmental fluctuations on the calibration results. The overlap ratio is calculated directly based on the light intensity ratio of adjacent standard pressure points, which can intuitively reflect the distinguishability of light intensity signals under different pressure points. When the overlap ratio is not zero, it indicates that there is observable overlap in the light intensity signals of adjacent pressure points. At this time, the uncertainty of the pressure measurement result will increase significantly. Therefore, the pressure range with a zero overlap ratio can accurately reflect the actual applicable range of the current calibration data under this test system.

[0028] In one embodiment, refer to Figure 2 The timing control rules for the timing controller include: The timing controller generates two square wave signals, including a first signal and a second signal. The first signal is output to the light source controller to control the light source to turn on and off, and the second signal is output to the camera to control the camera to acquire images. Within one cycle, one square wave signal of the first signal corresponds to two square wave signals of the second signal. When the first signal is at a high level, the light source is turned on; when the first signal is at a low level, the light source is turned off. When the second signal is at a high level, the camera begins exposure. The time interval between the two square wave signals of the second signal is greater than or equal to the camera's sampling interval. When the first signal is at a high level, the camera begins exposure and acquires the first image (I1). When the first signal drops from a high level to a low level, the camera acquires the second image (I2). The first image (I1) and the second image (I2) should have a difference in grayscale.

[0029] Furthermore, the step of the camera capturing a second image when the first signal drops from a high level to a low level includes: The rising edge of the second square wave signal of the second signal is earlier than the falling edge of the square wave signal of the first signal, and the falling edge of the second square wave signal of the second signal is later than the falling edge of the square wave signal of the first signal.

[0030] In one embodiment, calculating the light intensity ratio and average light intensity ratio of the experimental specimen at the standard pressure point based on the reference image, the background image, and the experimental image corresponding to the standard pressure point includes: Based on the experimental image (one experimental image can be randomly selected), obtain the region of interest of the image; Using the reference image as a benchmark, the experimental images corresponding to different standard pressure points are registered to the same coordinate system to reduce image jitter caused by field vibration. For each standard pressure point, based on the reference image, background image, and registered experimental image, the light intensity ratio of each data point in the region of interest is calculated, and the average light intensity ratio of all data points in the region of interest is calculated to obtain the average light intensity ratio.

[0031] Furthermore, the formula for calculating the light intensity ratio is: (1), Where IR is the light intensity ratio, and I 1_exp The light intensity I of the data point in the first image of the experimental image corresponding to each standard pressure point. 2_exp The light intensity I at the data point of the second image in the experimental image corresponding to each standard pressure point. 1_dark I represents the light intensity of the data points in the first image of the background image. 2_dark I represents the light intensity of the data points in the second image within the background image. 1_ref The light intensity is the data point of the first image in the reference image, and k is the adjustment coefficient, with a value ranging from 0.1 to 10.

[0032] In practice, PSP pressure measurement calibration based on dual-frame images involves obtaining the relationship curve between known pressure and light intensity ratio, i.e., the calibration data. (Refer to...) Figure 3 The calibration device provides standard pressure to the experimental specimen. Following the same test layout and hardware settings as the experimental conditions (i.e., excitation wavelength and timing signal), the camera acquires PSP fluorescence images at different standard pressure points. The light intensity ratio is calculated according to a specific formula (1), and the average light intensity ratio within the ROI region on the experimental specimen surface is obtained. The curve showing the relationship between this average light intensity ratio and the standard pressure is the calibration data. The acquisition and processing system acquires fluorescence images from the camera at normal pressure as reference images (I...). 1_ref and I 2_ref I 2_ref (As for the light intensity of the data points in the second image in the reference image), the image of the camera under no light is acquired as the background image (I). 1_dark and I 2_dark ), and collected fluorescence images under the corresponding experimental conditions as experimental images (I 1_exp and I 2_exp ).

[0033] During pressure calibration, the applicability of the calibration data can be assessed by calculating the overlap ratio of light intensity ratio under different standard pressures within the ROI area. That is, the pressure range with an overlap ratio of 0 is the pressure range that the PSP coating can be accurately measured within the current measurement system layout and ROI area. The overlap ratio is calculated as follows: for each standard pressure light intensity ratio data, the percentile is calculated to remove abnormal noise, and the average light intensity ratio, minimum light intensity ratio, and maximum light intensity ratio are calculated; for the minimum and maximum light intensity ratios of adjacent standard pressure points, the overlap ratio is calculated according to formula (2).

[0034] Furthermore, the method also includes: The value of k is adjusted according to the coating on the surface of the test piece and the light source, so as to minimize the calibration error or maximize the applicability of the calibration data to pressure measurement in the current testing system.

[0035] Furthermore, the method also includes: For the light intensity ratio data at each standard pressure point, percentiles are calculated to remove abnormal noise, and the minimum and maximum light intensity ratios of all data points within the region of interest at each standard pressure point are calculated.

[0036] Furthermore, the formula for calculating the overlap ratio is as follows: (2), Where overlapRatio is the overlap ratio, min is the minimum value, max is the maximum value, Mi is the maximum light intensity ratio of all data points in the region of interest under the i-th standard pressure point, Mi+1 is the maximum light intensity ratio of all data points in the region of interest under the (i+1)-th standard pressure point, Ni is the minimum light intensity ratio of all data points in the region of interest under the i-th standard pressure point, and Ni+1 is the minimum light intensity ratio of all data points in the region of interest under the (i+1)-th standard pressure point.

[0037] Furthermore, the method also includes: Preprocess the reference image, background image, and experimental image corresponding to each standard pressure point separately (e.g., average multiple images) to remove random noise from the images.

[0038] The embodiments provided by this invention overcome the susceptibility of traditional single-frame intensity methods to interference from factors such as unstable light sources and cameras. By rationally setting the timing between the light source and the camera, two-frame images are acquired when the light source is on and off. The light intensity ratio is calculated according to a specific formula to obtain calibration data of the standard pressure and light intensity ratio. Combined with the calibration data, the measured pressure can be calculated by inversely from the light intensity data, thus improving the accuracy of steady-state pressure measurement on the PSP surface. Furthermore, by calculating the overlap ratio of light intensity ratios under different standard pressures within the ROI (Region of Interest), the applicability of the calibration data can be evaluated. This can serve as a general evaluation standard for PSP measurement technology, assessing the measurement performance of PSP coatings, systems, and processing procedures.

[0039] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images, characterized in that, include: A test system was built, which included a light source probe, a light source controller, a timing controller, a camera, and an acquisition and processing system connected in sequence. The timing control rules of the timing controller were set to control the camera to expose twice for each time the light source probe was switched on and off, so as to obtain two fluorescence images of the experimental specimen with grayscale differences. Based on the timing control rules, the acquisition and processing system acquires two fluorescence images from the camera under normal pressure as reference images, and acquires two images from the camera under no-light conditions as background images. The surface of the experimental specimen was placed under a series of standard pressure points, and the acquisition and processing system acquired two fluorescence images corresponding to each standard pressure point as experimental images. For each standard pressure point, based on the reference image, background image, and the experimental image corresponding to that standard pressure point, calculate the light intensity ratio and the average light intensity ratio of the experimental specimen at that standard pressure point; plot the relationship curve between each standard pressure point and the corresponding average light intensity ratio, and use this relationship curve as calibration data; Based on the light intensity ratio corresponding to two adjacent standard pressure points, the overlap ratio is calculated, the standard pressure range when the overlap ratio is zero is statistically analyzed, and the standard pressure range is set as the applicable range for pressure measurement of the calibration data in the current test system. The timing control rules for setting the timing controller include: The timing controller generates two square wave signals, including a first signal and a second signal. The first signal is output to the light source controller to control the light source to turn on and off, and the second signal is output to the camera to control the camera to acquire images. Within one cycle, one square wave signal of the first signal corresponds to two square wave signals of the second signal. When the first signal is high, the light source is turned on; when the first signal is low, the light source is turned off. When the second signal is high, the camera begins exposure. The time interval between the two square wave signals of the second signal is greater than or equal to the camera's sampling interval. When the first signal is high, the camera begins exposure and captures the first image; when the first signal drops from high to low, the camera captures the second image. The process of the camera capturing a second image when the first signal drops from a high level to a low level includes: The rising edge of the second square wave signal of the second signal is earlier than the falling edge of the square wave signal of the first signal, and the falling edge of the second square wave signal of the second signal is later than the falling edge of the square wave signal of the first signal.

2. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 1, characterized in that, The calculation of the light intensity ratio and average light intensity ratio of the experimental specimen at the standard pressure point, based on the reference image, background image, and experimental image corresponding to the standard pressure point, includes: Based on the experimental images, the region of interest in the images is obtained; Using the reference image as a reference, the experimental images corresponding to different standard pressure points are registered to the same coordinate system; For each standard pressure point, based on the reference image, background image, and registered experimental image, the light intensity ratio of each data point in the region of interest is calculated, and the average light intensity ratio of all data points in the region of interest is calculated to obtain the average light intensity ratio.

3. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 2, characterized in that, The formula for calculating the light intensity ratio is: ， Where IR is the light intensity ratio, and I 1_exp The light intensity I of the data point in the first image of the experimental image corresponding to each standard pressure point. 2_exp The light intensity I at the data point of the second image in the experimental image corresponding to each standard pressure point. 1_dark I represents the light intensity of the data points in the first image of the background image. 2_dark I represents the light intensity of the data points in the second image within the background image. 1_ref The light intensity is the data point of the first image in the reference image, and k is the adjustment coefficient, with a value ranging from 0.1 to 10.

4. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 3, characterized in that, The method further includes: The value of k is adjusted according to the coating on the surface of the test piece and the light source to minimize the calibration error or maximize the applicability of the calibration data to pressure measurement in the current testing system.

5. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 2, characterized in that, The method further includes: For the light intensity ratio data at each standard pressure point, percentiles are calculated to remove abnormal noise, and the minimum and maximum light intensity ratios of all data points within the region of interest at each standard pressure point are calculated.

6. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 5, characterized in that, The formula for calculating the overlap ratio is: ， Where overlapRatio is the overlap ratio, min is the minimum value, max is the maximum value, and M is the maximum value. i M represents the maximum light intensity ratio of all data points within the region of interest at the i-th standard pressure point. i+1 N represents the maximum light intensity ratio of all data points within the region of interest at the (i+1)th standard pressure point. i N represents the minimum light intensity ratio of all data points within the region of interest at the i-th standard pressure point. i+1 It represents the minimum light intensity ratio of all data points within the region of interest under the (i+1)th standard pressure point.

7. The method for evaluating the applicability of PSP pressure measurement calibration data based on dual-frame images according to claim 1, characterized in that, The method further includes: The reference image, background image, and experimental image corresponding to each standard pressure point were preprocessed to remove random noise.

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