Multi-mode-based intelligent reading method for single-pointer meter of transformer substation

Abstract

The invention discloses a multi-mode-based intelligent reading method for a single-pointer meter of a transformer substation. According to the method, the dial image information and the text information in the preset point position template of the camera are subjected to multi-modal matching, so that deep fusion of the image and the text information is realized. Through the multi-mode combination, the position of the image can be corrected, the quality of the recognized image can be improved, the influence caused by image distortion, insufficient light and inaccurate focusing can be reduced, and the feature matching precision can be compared and enhanced, so that the dial plate recognition process is optimized. The fusion processing significantly improves the accuracy and reliability of the reading of the single-pointer meter, and provides a more stable basis for subsequent data analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular to a multi-modal-based intelligent reading method for a single-pointer meter in a substation. Background Art

[0002] In the context of smart grids, the informatization and automation of power systems have become the focus. As a key node for power transmission and distribution, the monitoring of equipment status and energy consumption is particularly important for substations. Among them, single-pointer meters play a vital role in monitoring equipment operating parameters such as current, voltage, and oil level. By obtaining the readings of single-pointer meters in real time, managers can efficiently grasp the working status of equipment, detect abnormalities in time, and ensure the stability and safety of power grid operation. This automated monitoring method not only improves the efficiency of equipment management, but also provides reliable data support for efficient and intelligent power operation and maintenance. In addition to the power industry, single-pointer meters are also widely used in the monitoring of other industrial equipment. For industrial scenarios that require real-time understanding of equipment status, such as manufacturing, petrochemical industry, and automated production lines, the monitoring method based on intelligent readings can significantly improve the stability and safety of production, reduce the need for manual inspections, and optimize the efficiency of industrial management.

[0003] Single pointer meters are usually used to monitor the current, voltage or power of key equipment such as oil level meters and ammeters. Through the automatic reading system, substations can be unattended and remotely monitored, significantly improving the level of intelligent power grid management. Traditional manual reading methods are inefficient and prone to errors, especially in high-risk environments such as substations. Frequent manual operations may also bring safety hazards.

[0004] The existing single-pointer meter intelligent reading technology solution mainly relies on image processing, machine vision and deep learning algorithms to achieve efficient and automated data collection through automatic recognition of pointer meters. The solution involves multiple key steps, including image acquisition, image preprocessing, pointer detection, angle reading and error correction, to ensure the accuracy and reliability of data.

[0005] First, the system uses a high-resolution camera to capture images of the meter to ensure image clarity and detail. To obtain stable readings, the camera is usually fixed directly above the meter to prevent angle deviation from affecting image quality. In low-light environments, the image acquisition system also uses fill light measures to reduce the interference of ambient light on the image. The captured images undergo pre-processing steps such as grayscale, denoising, and contrast enhancement to improve the recognizability of the pointer and scale, thereby ensuring that subsequent algorithms can accurately recognize them.

[0006] Secondly, a deep learning-based target detection algorithm (such as YOLO, FCOS, etc.) is used to locate the dial area, and the dial is further accurately segmented through edge detection and other technologies to eliminate background interference. This process can effectively improve the accuracy and reliability of pointer detection. Then, the system identifies the pointer position through feature extraction and angle calculation methods, and calculates the pointer angle using geometric principles or neural network-based regression algorithms. Traditional methods usually rely on feature point analysis and triangulation, while deep learning regression algorithms can effectively reduce reading errors when the amount of data is large, improving the overall reading accuracy. The obtained pointer angle will be mapped to the dial scale range to accurately calculate the meter reading. After that, the reading results are transmitted to the remote monitoring center in real time through the data transmission system, so that managers can keep track of the equipment's operating status at any time. Current intelligent reading solutions usually integrate real-time monitoring and alarm systems. When it is detected that the equipment operating parameters exceed the set threshold, the system will immediately trigger an alarm to notify the relevant operation and maintenance personnel to achieve unattended automated monitoring.

[0007] The single-pointer meter intelligent reading method based on deep learning algorithms and traditional image processing technology can read the dial pointer reading efficiently and automatically, greatly improving the efficiency of data collection. However, this method has high requirements for the image clarity captured by the camera. When the image is blurred, the accuracy and reliability of the reading are often significantly affected, which may lead to misreading or missed reading, thus affecting the monitoring and management of the equipment. In addition, deep learning models usually require a large amount of training data and high computing resources, especially when processing complex images and real-time data. This requirement makes it difficult for some edge devices or low-power systems to achieve efficient image processing and reading functions. Therefore, how to reduce the requirements for image clarity and reduce the consumption of computing resources has become a key issue that needs to be solved urgently.

[0008] Furthermore, the existing single-pointer meter intelligent reading method collects images by setting the camera position, so the collected images are often clearer. However, changes in ambient light and camera shooting position offset still affect the quality of the captured images. Fluctuations in lighting conditions may cause the image to be overexposed or too dark, thereby affecting the visibility of the pointer and scale, and thus reducing the recognition accuracy.

[0009] Therefore, the prior art has defects and needs to be improved. Summary of the invention

[0010] The technical problem to be solved by the present invention is: to provide a multi-modal intelligent reading method for a single-pointer meter in a substation. When the image captured by the camera is offset or affected by light, the image is corrected and optimized to improve the image quality, thereby improving the accuracy of the meter reading.

[0011] The technical solution of the present invention is as follows: a multi-modal-based intelligent reading method for a single-pointer meter in a substation is provided, comprising the following steps.

[0012] S1: preset camera positions are set in the substation. Each preset position is configured with template prior information. The template prior information records text information of the preset position, including: image of the recognition area, point image, dial type, and image path.

[0013] S2: After obtaining the image captured by the camera at the preset point, the target detection model is applied to identify the position of the dial in the image captured by the camera.

[0014] S3: capture an image of the dial area in the image, match the image with the point image of the template prior information of the preset point, and align the dial image.

[0015] S4: Use the target detection model, instance segmentation model, and OCR detection model to detect the scale digital information on the dial image.

[0016] S5: Use the instance segmentation model to detect the dial image and obtain the dial scale lines, dial pointer letters, and dial numbers.

[0017] S6: Obtain the point set consisting of the centroids of each scale mask and the point set consisting of the center points of the digital frame, and after adjusting these two point sets, fit the center of the dial.

[0018] S7: Calculate the reading of the meter using the adjusted point set and the angle between the pointer mask and the farthest point from the center of the circle, and return the result.

[0019] In the present invention, a deep fusion of image and text information is achieved by multimodally matching the dial image information with the text information in the camera preset point template. Through this multimodal combination, not only can the image position be corrected, the quality of the recognized image be improved, and the impact caused by image distortion, insufficient light, and inaccurate focus be reduced, but also the accuracy of feature matching can be compared and enhanced, thereby optimizing the dial recognition process. This fusion process significantly improves the accuracy and reliability of single-pointer meter readings, providing a more stable foundation for subsequent data analysis. It effectively avoids the impact of changes in ambient light and camera shooting position offset on the quality of the captured image; it also avoids the fluctuation of lighting conditions that may cause the image to be overexposed or too dark, ensuring the visibility of the pointer and scale, thereby improving the recognition accuracy and meeting the needs of actual applications.

[0020] Furthermore, in step S3, when aligning the dial, if the dial image is offset, calibration is performed using the point image in the template information; the specific process is as follows.

[0021] S31: The feature points in the image will pay attention to all the feature points in the same image, and perform self-attention calculation, and filter the feature points by self-attention scores. The specific algorithm process is shown in Formula 3.1;

[0022]

[0023] where p i 、p j are two feature descriptors, q i , k i For p i The linear projection vector, R(p j -p i ) is the position encoding of the two feature descriptors.

[0024] S32: Linearly project the feature points of the point image in the template information and the image of the captured dial area position, calculate the inner product of the feature projection vectors of the two images to obtain the attention scores of the two images, match the feature points of the two images by calculating the attention scores of the two images, and calibrate the images; the specific algorithm process is shown in Formula 3.2;

[0025]

[0026] in are the matrices composed of the feature projection vectors of the i graph and the k graph, respectively. is the attention score.

[0027] Further, in step S5, the dial image detected by using the instance segmentation model is a calibrated dial image.

[0028] Furthermore, in step S3, it further includes: performing image enhancement on the subsequent dial image. The method for performing image enhancement is any one of the following methods;

[0029] Scale the grayscale value of the image: transform the input image through the operator scale_image, the formula is g': = g*Mult+Add, where Mult and Add are parameters determined by the grayscale range [GMin, GMax], which are used to increase the contrast of the image, making the black areas in the image darker and the bright areas brighter.

[0030] Enhance image contrast: First use low-pass (average image) filtering, then calculate the gray value (res) based on the obtained gray value (average) and the original gray value (original value), control the size and contrast intensity of the mean filter template through parameters, enhance the high-frequency area (edges and corners) of the image, and make the image look clearer.

[0031] Logarithmic transformation: Use the operator log_image to perform a logarithmic transformation on the image, the formula is O(x,y)=c*(e^I(x,y)-1), where c is a constant that controls the intensity of image brightness enhancement. Logarithmic transformation can enhance the darker or brighter parts of the image.

[0032] Gamma transformation: Gamma transformation is mainly used for image correction, to correct images with too high or too low grayscale and enhance contrast. The transformation formula is to multiply each pixel value on the original image: image_gamma = np.uint8(np.power((np.array(image) / 255.0),fgamma)*255.0), where fgamma is the gamma value, which is used to adjust the contrast of the image.

[0033] Histogram equalization: The principle of histogram equalization processing is to evenly distribute the grayscale image of the original image from a relatively concentrated grayscale interval in the entire grayscale space, realize nonlinear stretching of the image, and redistribute the image pixel values.

[0034] Formula for adjusting contrast: The formula for adjusting contrast in Photoshop is nRGB = RGB + (RGB-Threshold) * Contrast / 255, where nRGB represents the recalculated value, Threshold is usually the average brightness of the image (usually 127), and Contrast ranges from [-255, 255]. When Contrast is 0, it indicates the current contrast; when it is -255, the image becomes gray; when it is 255, the bright points become brighter and the dark points become darker.

[0035] Furthermore, in step S6, the specific steps are as follows:

[0036] S61: Perform cluster analysis on the two point sets detected by the model, and remove abnormal points by cluster analysis. The specific algorithm process is shown in Formula 6.1.

[0037]

[0038] Where J represents the sum of the squares of the distances between a data point and the center of its cluster, which is used to indicate the quality of the clustering effect. The smaller J is, the better the clustering effect is. K is the number of clusters, C is the k is the point set of the kth cluster, μk is the cluster C k The centroid of (i.e., the mean of all points in the cluster); ||x i -μ k || 2 Represents data point x i With cluster center μ kThe square of the Euclidean distance between them; by finding the distance between the data point and the centroid, the abnormal points in the point set are removed;

[0039] S62: Perform order-preserving regression on the point set in the non-abnormal cluster (i.e., perform regression analysis on the basis of preserving the order), and then perform weighted adjustment on the position of the point set elements based on the values ​​obtained by regression. The specific algorithm process is shown in Formula 6.2 and Formula 6.3;

[0040]

[0041]

[0042] In formula 6.2, y i is the actual value of each element in the point set, f(x i ) is the fitted value predicted by the ordinal regression model; by minimizing the square error between the fitted value and the actual value, an objective function f(x) that meets the monotonicity requirement is obtained, while being as close to each y as possible. i ; In formula 6.3, w i is the weight of point i, α is the parameter for adjusting the sensitivity, and the regression value is used to redistribute the position weight of the point so that the points close to the regression curve have a larger weight, while the points far from the regression curve have a smaller weight.

[0043] S63: Fit the corrected point set to the center position of the circle by the least square method. The specific process is as shown in 6.4:

[0044]

[0045] where x i ,y i is the coordinate of each data point in the corrected point set, a and b are the coordinates of the center of the circle found through the minimization process, and r is the radius. By minimizing this total error function, the optimal parameter value is found to fit the position of the center of the circle.

[0046] By adopting the above scheme, the present invention provides a multimodal-based intelligent reading method for a single-pointer meter in a substation. By combining the template prior information of the camera's prefabricated points with the image information in a multimodal manner, it can effectively reduce false detections caused by image offset, distortion, and blur, thereby significantly improving the accuracy of meter readings. The method first uses the text data provided by the template prior information to correct the image to reduce noise and distortion. Then, by combining feature matching and image enhancement technology, the recognizability of the pointer and scale is further improved. This multimodal fusion strategy not only optimizes the way information is integrated, but also enhances the adaptability and robustness of the system in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0048] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0049] The invention provides a multi-modal-based intelligent reading method for a single-pointer meter in a transformer substation, comprising the following steps.

[0050] S1: preset camera positions are set in the substation. Each preset position is configured with template prior information. The template prior information records text information of the preset position, including: image of the recognition area, point image, dial type, and image path.

[0051] S2: After obtaining the image captured by the camera at the preset point, the target detection model is applied to identify the position of the dial in the image captured by the camera.

[0052] S3: capture an image of the dial area in the image, match the image with the point image of the template prior information of the preset point, and align the dial image.

[0053] S4: Use the target detection model, instance segmentation model, and OCR detection model to detect the scale digital information on the dial image.

[0054] S5: Use the instance segmentation model to detect the dial image and obtain the dial scale lines, dial pointer letters, and dial numbers.

[0055] S6: Obtain the point set consisting of the centroids of each scale mask and the point set consisting of the center points of the digital frame, and after adjusting these two point sets, fit the center of the dial.

[0056] S7: Calculate the reading of the meter using the adjusted point set and the angle between the pointer mask and the farthest point from the center of the circle, and return the result.

[0057] In this embodiment, in step S3, when aligning the dial, if the dial image is offset, calibration is performed using the point image in the template information; the specific process is as follows.

[0058] S31: The feature points in the image will pay attention to all the feature points in the same image, and perform self-attention calculation, and filter the feature points by self-attention scores. The specific algorithm process is shown in Formula 3.1;

[0059]

[0060] where p i 、p j are two feature descriptors, q i , k iFor p i The linear projection vector, R(p j -p i ) is the position encoding of the two feature descriptors.

[0061] S32: Linearly project the feature points of the point image in the template information and the image of the captured dial area position, calculate the inner product of the feature projection vectors of the two images to obtain the attention scores of the two images, match the feature points of the two images by calculating the attention scores of the two images, and calibrate the images; the specific algorithm process is shown in Formula 3.2;

[0062]

[0063] in are the matrices composed of the feature projection vectors of the i graph and the k graph, respectively. is the attention score.

[0064] In this embodiment, in step S5, the dial image detected using the instance segmentation model is a calibrated dial image.

[0065] In this embodiment, in step S3, it further includes: performing image enhancement on the subsequent dial image. The method for performing image enhancement is any one of the following methods;

[0066] Scale the grayscale value of the image: transform the input image through the operator scale_image, the formula is g': = g*Mult+Add, where Mult and Add are parameters determined by the grayscale range [GMin, GMax], which are used to increase the contrast of the image, making the black areas in the image darker and the bright areas brighter.

[0067] Enhance image contrast: First use low-pass (average image) filtering, then calculate the gray value (res) based on the obtained gray value (average) and the original gray value (original value), control the size and contrast intensity of the mean filter template through parameters, enhance the high-frequency area (edges and corners) of the image, and make the image look clearer.

[0068] Logarithmic transformation: Use the operator log_image to perform a logarithmic transformation on the image, the formula is O(x,y)=c*(e^I(x,y)-1), where c is a constant that controls the intensity of image brightness enhancement. Logarithmic transformation can enhance the darker or brighter parts of the image.

[0069] Gamma transformation: Gamma transformation is mainly used for image correction, to correct images with too high or too low grayscale and enhance contrast. The transformation formula is to multiply each pixel value on the original image: image_gamma = np.uint8(np.power((np.array(image) / 255.0),fgamma)*255.0), where fgamma is the gamma value, which is used to adjust the contrast of the image.

[0070] Histogram equalization: The principle of histogram equalization processing is to evenly distribute the grayscale image of the original image from a relatively concentrated grayscale interval in the entire grayscale space, realize nonlinear stretching of the image, and redistribute the image pixel values.

[0071] Formula for adjusting contrast: The formula for adjusting contrast in Photoshop is nRGB = RGB + (RGB-Threshold) * Contrast / 255, where nRGB represents the recalculated value, Threshold is usually the average brightness of the image (usually 127), and Contrast ranges from [-255, 255]. When Contrast is 0, it indicates the current contrast; when it is -255, the image becomes gray; when it is 255, the bright points become brighter and the dark points become darker.

[0072] In this embodiment, in step S6, the specific steps are as follows:

[0073] S61: Perform cluster analysis on the two point sets detected by the model, and remove abnormal points by cluster analysis. The specific algorithm process is shown in Formula 6.1;

[0074]

[0075] Where J represents the sum of the squares of the distances between a data point and the center of its cluster, which is used to indicate the quality of the clustering effect. The smaller J is, the better the clustering effect is. K is the number of clusters, C is the k is the point set of the kth cluster, μk is the cluster C k The centroid of (i.e., the mean of all points in the cluster); ||x i -μ k || 2 Represents data point x i With cluster center μ k The square of the Euclidean distance between them; by finding the distance between the data point and the centroid, the abnormal points in the point set are removed;

[0076] S62: Perform order-preserving regression on the point set in the non-abnormal cluster (i.e., perform regression analysis on the basis of preserving the order), and then perform weighted adjustment on the position of the point set elements based on the values ​​obtained by regression. The specific algorithm process is shown in Formula 6.2 and Formula 6.3;

[0077]

[0078]

[0079] In formula 6.2, y i is the actual value of each element in the point set, f(x i ) is the fitted value predicted by the ordinal regression model; by minimizing the square error between the fitted value and the actual value, an objective function f(x) that meets the monotonicity requirement is obtained, while being as close to each y as possible. i ; In formula 6.3, w i is the weight of point i, α is the parameter for adjusting the sensitivity, and the regression value is used to redistribute the position weight of the point so that the points close to the regression curve have a larger weight, while the points far from the regression curve have a smaller weight.

[0080] S63: Fit the corrected point set to the center position of the circle by the least square method. The specific process is as shown in 6.4:

[0081]

[0082] where x i ,y i is the coordinate of each data point in the corrected point set, a and b are the coordinates of the center of the circle found through the minimization process, and r is the radius. By minimizing this total error function, the optimal parameter value is found to fit the position of the center of the circle.

[0083] The present invention achieves deep fusion of image and text information by multimodally matching the dial image information with the text information in the camera preset point template. This multimodal combination can not only correct the image position, improve the quality of the recognized image, reduce the impact caused by image distortion, insufficient light, and inaccurate focus, but also compare and enhance the accuracy of feature matching, thereby optimizing the dial recognition process. This fusion process significantly improves the accuracy and reliability of single-pointer meter readings, providing a more stable foundation for subsequent data analysis.

[0084] In summary, the present invention provides a multimodal-based intelligent reading method for a single-pointer meter in a substation. By combining the template prior information of the camera's pre-set points with the image information in a multimodal manner, it can effectively reduce false detections caused by image offset, distortion, and blur, thereby significantly improving the accuracy of meter readings. The method first uses the text data provided by the template prior information to correct the image to reduce noise and distortion. Then, by combining feature matching and image enhancement technology, the recognizability of the pointer and scale is further improved. This multimodal fusion strategy not only optimizes the way information is integrated, but also enhances the adaptability and robustness of the system in complex environments.

[0085] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-modal intelligent reading method for a single pointer meter in a substation, characterized in that: The following steps are involved: S1: Set preset camera points in the substation, and configure template prior information for each preset point. The template prior information records text information of the preset point, including: image of the recognition area, point image, dial type, and image path; S2: After obtaining the image captured by the camera at the preset point, the object detection model is used to identify the position of the dial in the image captured by the camera; S3: intercepting an image of the dial area in the image, matching the image with the point image of the template prior information of the preset point, and aligning the dial image; S4: Use the target detection model, instance segmentation model, and OCR detection model to detect the scale digital information on the dial image; S5: Use the instance segmentation model to detect the dial image and obtain the dial scale lines, dial pointer letters, and dial numbers; S6: Obtain a point set consisting of the centroids of each scale mask and a point set consisting of the center points of the digital frame, and after adjusting these two point sets, fit the center of the dial; S7: Calculate the reading of the meter using the adjusted point set and the angle between the pointer mask and the farthest point from the center of the circle, and return the result.

2. The multi-modal substation single pointer meter intelligent reading method according to claim 1 is characterized in that: In step S3, when aligning the dial, if the dial image is offset, calibration is performed using the point image in the template information; the specific process is as follows: S31: The feature points in the image will pay attention to all the feature points in the same image, and perform self-attention calculation, and filter the feature points by self-attention scores. The specific algorithm process is shown in Formula 3.1; where p t 、p j are two feature descriptors, q i , k i For p i The linear projection vector, R(p j -p i ) is the position encoding of the two feature descriptors; S32: Linearly projecting the feature points obtained from the point image in the template information and the image of the intercepted dial area position, obtaining the attention scores of the two images by calculating the inner product of the feature projection vectors of the two images, matching the feature points of the two images by calculating the attention scores of the two images, and calibrating the images; The specific algorithm process is as shown in formula 3.2; in are the matrices composed of the feature projection vectors of the i graph and the k graph, respectively. is the attention score.

3. The multi-modal-based intelligent reading method for a substation single pointer meter according to claim 2 is characterized in that: In step S5, the dial image detected by using the instance segmentation model is a calibrated dial image.

4. The multi-modal-based intelligent reading method for a substation single-pointer meter according to claim 1 is characterized in that: In step S3, it also includes: performing image enhancement on the subsequent dial image.

5. The multi-modal-based intelligent reading method for a substation single-pointer meter according to claim 4 is characterized in that: The method for image enhancement is any one of the following methods; Scaling the grayscale value of the image: The input image is transformed through the operator scale_image, the formula is g': = g*Mult+Add, where Mult and Add are parameters determined by the grayscale range [GMin, GMax], which are used to increase the contrast of the image, making the black areas in the image darker and the bright areas brighter; Enhance image contrast: First use low-pass filtering, then calculate the grayscale value based on the obtained grayscale value and the original grayscale value, control the size and contrast intensity of the mean filter template through parameters, enhance the high-frequency area of ​​the image, and make the image look clearer; Logarithmic transformation: Use the operator log_image to perform a logarithmic transformation on the image, the formula is O(x,y)=c*(e^I(x,y)-1), where c is a constant that controls the intensity of image brightness enhancement. Logarithmic transformation can enhance the darker or brighter parts of the image; Gamma transformation: Gamma transformation is mainly used for image correction, to correct images with too high or too low grayscale and enhance contrast. The transformation formula is to perform a product operation on each pixel value in the original image: image_gamma = np.uint8(np.power((np.array(image) / 255.0),fgamma)*255.0), where fgamma is the gamma value, which is used to adjust the contrast of the image; Histogram equalization: The principle of histogram equalization is to evenly distribute the grayscale image of the original image from a relatively concentrated grayscale interval in the entire grayscale space, realize nonlinear stretching of the image, and redistribute the image pixel values; Formula for adjusting contrast: The formula for adjusting contrast in Photoshop is nRGB = RGB + (RGB-Threshold) * Contrast / 255, where nRGB represents the recalculated value, Threshold is usually the average brightness of the image, and Contrast ranges from [-255, 255]. When Contrast is 0, it indicates the current contrast; when it is -255, the image becomes gray; when it is 255, the bright points become brighter and the dark points become darker.

6. The multi-modal-based intelligent reading method for a substation single-pointer meter according to claim 1 is characterized in that: In step S6, the specific steps are as follows: S61: Perform cluster analysis on the two point sets detected by the model, and remove abnormal points by cluster analysis. The specific algorithm process is shown in Formula 6.

1. Where J represents the sum of the squares of the distances between a data point and the center of its cluster, which is used to indicate the quality of the clustering effect. The smaller J is, the better the clustering effect is. K is the number of clusters, C is the k is the point set of the kth cluster, μk is the cluster C k The center of mass of ||x i -μ k || 2 Represents data point x i With cluster center μ k The square of the Euclidean distance between them; by finding the distance between the data point and the centroid, the abnormal points in the point set are removed; S62: Perform rank-preserving regression on the point set in the non-abnormal cluster, and then perform weighted adjustment on the position of the point set elements based on the values ​​obtained by regression. The specific algorithm process is shown in Formula 6.2 and Formula 6.3; In formula 6.2, y i is the actual value of each element in the point set, f(x i ) is the fitted value predicted by the ordinal regression model; by minimizing the square error between the fitted value and the actual value, an objective function f(x) that meets the monotonicity requirement is obtained, while being as close to each y as possible. i ; In formula 6.3, w i is the weight of point i, α is the parameter for adjusting sensitivity, and the regression value is used to redistribute the position weight of the point, so that the weight of the point close to the regression curve is larger, and the weight of the point far from the regression curve is smaller; S63: Fit the corrected point set to the center position of the circle by the least square method. The specific process is as shown in 6.4: where x i ,y i is the coordinate of each data point in the corrected point set, a and b are the coordinates of the center of the circle found through the minimization process, and r is the radius. By minimizing this total error function, the optimal parameter value is found to fit the position of the center of the circle.

Images