Weld defect detection method based on multi-feature extraction and hierarchical SVM fusion

Abstract

The invention discloses a weld defect detection method based on multi-feature extraction and hierarchical SVM (Support Vector Machine) fusion, which comprises the following steps of: extracting image features of a weld surface through passive vision and laser vision sensing technologies, and inputting obtained weld parameters as features of a hierarchical SVM; and converting a multi-classification problem into a plurality of dichotomy problems through the structure of the classifier, and identifying and classifying the six welding seam targets to obtain a final result. According to the method, multi-feature extraction of weld defects is introduced, geometric shapes, texture features and spectral information in weld images can be comprehensively captured through the multi-feature extraction technology, so that the defect recognition precision and reliability are remarkably improved, multi-feature extraction of passive vision and active vision is adopted, feature information of the weld defects is obtained from multiple dimensions, and the defect recognition accuracy is improved. And a multi-classification problem is converted into a plurality of dichotomy problems, so that the welding defects on the surface of the workpiece in a welding scene can be quickly classified and identified.

Description

Technical Field

[0001] The present invention relates to a method for detecting surface defects of welds, specifically a method for detecting weld defects based on multi-feature extraction and hierarchical SVM fusion, belonging to the technical field of visual inspection of surface weld defects of workpieces. Background Art

[0002] With the wide application of welding technology in industries such as construction, shipbuilding, automotive, and aviation, the quality of welds is directly related to the strength, safety, and service life of structures. According to the statistics of the IIW (International Institute of Welding), welding defects are one of the main causes of industrial structure failures, accounting for more than 60% of all welding-related accidents. These defects include pores, cracks, lack of fusion, slag inclusions, etc. If not detected and processed in time, they may lead to a decrease in structural strength or even overall failure. Traditional defect identification methods mainly rely on manual visual inspection and non-destructive testing techniques. Manual visual inspection depends on the experience and skills of operators, is highly subjective, and is prone to missed or false detections due to operator fatigue or judgment errors. Non-destructive testing techniques have limited applicability and certain limitations, making it difficult to comprehensively cover the detection requirements of different defects.

[0003] Therefore, the use of machine learning and image processing techniques can effectively improve the accuracy and efficiency of weld defect identification, providing an effective means for the efficient detection of weld defects. In the prior art, for example, a method disclosed in CN115082444B uses visible light means to obtain the surface image of the weld of the copper pipe to be detected, and then analyzes whether there are welding defects in the material. This method uses a deep neural network (DNN) to extract the weld area in the surface image of the weld of the copper pipe to be detected, obtaining the copper pipe weld area image, and converting it into a grayscale image to reduce the data dimension and highlight the grayscale information. Construct an updated pixel matrix corresponding to the grayscale image of the copper pipe weld area, and accordingly construct a first-order difference sequence, calculate the range and perform normalization processing. Obtain the probability of the left part of the pixel matrix having a welding defect, and similarly calculate the probability of the right side of the matrix having a defect. If the determination result is that there is a welding defect, use a Gaussian mixture model (GMM) to divide the weld surface into bright and dark areas, and calculate and judge the defect gradient direction and area. Such methods rely on high-quality surface images. If the image has problems such as noise, blur, or uneven illumination, it may affect the extraction of the weld area and the accuracy of defect detection; steps such as constructing a pixel matrix, calculating the sum of each column element, constructing a first-order difference sequence, calculating the range, and normalization processing have a large amount of calculation. Especially when processing high-resolution images, it may lead to insufficient real-time performance of the detection process; for some very fine defects, such as tiny pores or cracks, it may still be difficult to accurately detect and locate. Summary of the Invention

[0004] The object of the present invention is to provide a weld defect detection method based on multi-feature extraction and hierarchical SVM fusion to solve at least one of the above technical problems, which can effectively identify the surface defects and types of welds and improve the real-time performance and efficiency of detection.

[0005] The present invention achieves the above object through the following technical solutions: A weld defect detection method based on multi-feature extraction and hierarchical SVM fusion, and this weld surface defect detection method includes the following steps:

[0006] S1. Real-time image acquisition, using passive vision sensing technology to obtain the surface information of the weld, providing information input for subsequent defect detection;

[0007] S2. Laser stripe image acquisition, using active vision sensing technology to obtain weld defect information according to the deformation of the laser stripe on the weld surface;

[0008] S3. Preprocessing and feature extraction of the weld image;

[0009] S4. Analysis of laser image stripe features;

[0010] S5. Analyze the image features of passive vision and active vision, and use the feature information corresponding to each defect to make labels;

[0011] S6. Construct a network model with multi-feature information of weld surface defects as the input of the hierarchical support vector machine, and use the defined feature parameters to train the hierarchical classifier model;

[0012] S7. Identify and classify the surface defects of the weld.

[0013] As a further solution of the present invention: The preprocessing and feature extraction of the weld surface defect image obtained by passive vision specifically include:

[0014] S31. To reduce the noise of the image, the image ROI feature region is processed by Gaussian filtering to improve the defect recognition rate;

[0015] S32. Define five types of two-dimensional feature parameters for welding defect features;

[0016] S33. Adopt the ROI waveform analysis method, and use the horizontal summation of the ROI region area and the average value as the feature input;

[0017] S34. For poor forming and burn-through defects, the corresponding waveform sequence is obtained by horizontally summing the defect area in the weld region, and the average value is taken as the feature input to distinguish the defect types.

[0018] As a further solution of the present invention: The five types of defined two-dimensional feature parameters specifically include:

[0019] The perimeter C of the defect area refers to the sum of the number of pixels in the defect area. Among them, R0 is the set of pixel points at the boundary of the defect area, which is used to distinguish the complexity of the shape of the defect area;

[0020] The aspect ratio K refers to the ratio of the length to the width of the minimum circumscribed rectangle of the defect area, which is used to measure the length of the defect. The formula is K = L / W;

[0021] The defect area s refers to the number of pixels in the area connected by the same defect. R1 refers to the set of all pixels in the defect area;

[0022] Roundness R: The area and perimeter of the defect area can be used to determine its proximity to a circle, and can roughly identify holes and weld nodules.

[0023] Benignity B refers to the ratio of the defect area to the weld area, which can effectively distinguish good welds from defective welds.

[0024] As a further solution of the present invention: the laser image fringe feature analysis specifically includes:

[0025] S41. For defects with unclear two-dimensional features, laser stripe images are used to distinguish defects;

[0026] S42, treating the obtained laser stripe image as a function curve, calculating its second-order derivative, judging the change in slope, and thus distinguishing;

[0027] S43, defining a maximum offset of the laser stripe image compared to the weld centerline, and using the maximum offset to reflect the approximate location of the function inflection point;

[0028] S44. Define the kurtosis coefficient to reflect the steepness of the laser stripe curve.

[0029] As a further solution of the present invention, defect differentiation using laser stripe images refers to extracting weld surface features using auxiliary lasers, specifically including:

[0030] Defect information is obtained based on the changes in the laser stripes on the weld surface. Compared with passive vision, it has the advantages of high accuracy and strong anti-interference ability. Three stripe feature parameters are defined as the feature input of the hierarchical support vector machine, which are the function slope change rate k as follows:

[0031]

[0032] Kurtosis coefficient K u Reflects the steepness of the weld laser line, and its expression is:

[0033]

[0034] Where H(k) is the height of each contour point of the laser stripe, is the average height of each contour point of the laser stripe, p 4 is the fourth-order central moment of each profile data point of the laser stripe, p 2 is the second-order central moment of each contour data point of the laser stripe, and n is the number of laser stripe contour points.

[0035] As a further solution of the present invention: the construction of the network model specifically includes the following steps:

[0036] S61. Construct a data set, collect visible light images and laser images under welding working conditions, perform preprocessing, and use a portion of them to construct a sample training set and the other portion to construct a test set;

[0037] S62. Constructing a network model of hierarchical support vector machine;

[0038] S63, using the dataset feature input defined and created in S5 to train the hierarchical support vector machine model until convergence is reached or the set maximum number of iterations is reached, and using the test set to evaluate the performance of the trained neural network model. If the performance requirements are not met, continue training;

[0039] S64. The hierarchical support vector machine model trained to meet the expected requirements is used for weld defect recognition and classification in actual welding scenarios.

[0040] As a further solution of the present invention: the network model of the hierarchical support vector machine specifically includes:

[0041] The input layer receives the weld surface image data to be detected, with a size of 512×512×1;

[0042] Feature extraction is performed through multiple levels of support vector machine classifiers, each of which focuses on identifying a specific type of surface defect. Each support vector machine classifier is followed by a radial basis function kernel to enhance the nonlinear expression of complex features.

[0043] The fusion layer uses a weighting mechanism and feature selection module to integrate the features extracted from each layer to improve the expression effect and classification performance of key features;

[0044] The output layer integrates the classification results of each layer through a hierarchical decision-making mechanism;

[0045] Among them, the entire model is optimized using a hierarchical loss function through layer-by-layer iterative training and parameter tuning.

[0046] As a further solution of the present invention: the radial basis function kernel formula is as follows:

[0047] K(x i ,x j )=exp(-γ||x i -x j || 2 )

[0048] where x i and x j are the feature vectors of two samples in the input space respectively, γ controls the decay rate of the kernel function, and thus affects the distribution of sample points in the feature space and the selection of support vectors;

[0049] As a further solution of the present invention: the optimization of the hierarchical loss function includes:

[0050] The constructed hierarchical support vector machine model consists of five classifiers, and the loss function form of each classifier is the same as that of the traditional SVM:

[0051]

[0052] where w is the weight vector, b is the bias term, C is the regularization parameter used to control the penalty strength of misclassification, D k refers to the training subset participating in the training at node k, is the label at node k, which depends on the specific classification task at this node, is the feature mapping that maps the input features to a high-dimensional space;

[0053] The overall loss function is the weighted sum of the losses of all classifiers:

[0054]

[0055] where α k is the weight coefficient used to balance the losses of different classifiers.

[0056] The beneficial effects of the present invention are:

[0057] 1) Based on the classification method of the traditional support vector machine, the present invention introduces the multi-feature extraction of weld defects. For some weld defects with unclear two-dimensional features, the use of laser stripes to extract three-dimensional features has a high recognition success rate in the recognition of weld defects such as undercut;

[0058] 2) In the field of weld defect recognition, compared with the traditional technology, it also shows higher accuracy, robustness and processing speed. At the same time, through the multi-feature extraction technology, it can comprehensively capture the geometric shape, texture features and spectral information in the weld image, thus significantly improving the accuracy and reliability of defect recognition;

[0059] 3) The present invention adopts multi-feature extraction of passive vision and active vision to obtain the feature information of weld defects from multiple dimensions. For passive vision, it can accurately obtain the appearance information of weld defects, but is greatly affected by light and has a low resolution accuracy;

[0060] 4) Taking advantage of the advantages of active vision, such as high precision, strong anti-interference ability, and little influence by light changes, eight feature parameters are defined as the input of the hierarchical support vector machine, converting the multi-classification problem into multiple binary classification problems, and being able to quickly and accurately classify and identify the welding defects on the surface of the workpiece in the welding scene. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flowchart of the welding defect classification system of the present invention;

[0062] Figure 2 It is a structural diagram of the hierarchical support vector machine of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0064] Embodiment 1, as Figures 1 to 2 shown, a weld defect detection method based on the fusion of multi-feature extraction and hierarchical SVM, the weld surface defect detection method includes the following steps:

[0065] S1. Real-time image acquisition, using passive vision sensing technology to obtain the surface information of the weld, providing information input for subsequent defect detection;

[0066] S2. Laser stripe image acquisition, using active vision sensing technology to obtain weld defect information according to the deformation of the laser stripe on the weld surface;

[0067] S3. Preprocessing and feature extraction of the weld image;

[0068] S4. Laser image stripe feature analysis;

[0069] S5. Analyze the image features of passive vision and active vision, and make labels using the feature information corresponding to each defect;

[0070] S6. Construct a network model with multi-feature information of weld surface defects as the input of the hierarchical support vector machine, and train the hierarchical classifier model using the defined feature parameters;

[0071] S7. Identify and classify weld surface defects.

[0072] In addition to all the technical features of the first embodiment, the second embodiment also includes:

[0073] The preprocessing and feature extraction of weld surface defect images acquired by passive vision specifically include:

[0074] S31, further processing the image using Gaussian filtering on the ROI feature area of the image to reduce image noise and improve the recognition rate of defects;

[0075] S32. Define five types of two-dimensional feature parameters for welding defect characteristics;

[0076] S33, using ROI waveform analysis method, by summing the lateral area of the ROI region and calculating the average value as feature input;

[0077] S34. For defects such as poor forming and weld penetration, the corresponding waveform sequence is obtained by summing the transverse areas of the defect area in the weld area, and the average value is taken as the feature input to distinguish the defect type.

[0078] Furthermore, the five types of two-dimensional feature parameters defined specifically include:

[0079] The perimeter C of the defect area refers to the sum of the number of pixels in the defect area. Among them, R0 is the set of pixel points at the boundary of the defect area, which is used to distinguish the complexity of the shape of the defect area;

[0080] The aspect ratio K refers to the ratio of the length to the width of the minimum circumscribed rectangle of the defect area, which is used to measure the length of the defect. The formula is K = L / W;

[0081] The defect area s refers to the number of pixels in the area connected by the same defect. R1 refers to the set of all pixels in the defect area;

[0082] Roundness R: The area and perimeter of the defect area can be used to determine its proximity to a circle, and can roughly identify holes and weld nodules.

[0083] Benignity B refers to the ratio of the defect area to the weld area, which can effectively distinguish good welds from defective welds.

[0084] In addition to all the technical features of the first embodiment, this embodiment also includes:

[0085] Laser image fringe feature analysis specifically includes:

[0086] S41. For defects with unclear two-dimensional features, such as undercut, use the laser stripe image to distinguish the defects.

[0087] S42. Regard the obtained laser stripe image as a function curve, calculate its second derivative, and judge the change of the slope to make the distinction.

[0088] S43. Define the maximum offset of the laser stripe image relative to the weld center line, and use the maximum offset to reflect the approximate position of the function inflection point.

[0089] S44. Define the kurtosis coefficient to reflect the steepness of the laser stripe curve.

[0090] Using the laser stripe image to distinguish defects means using auxiliary laser to extract the weld surface features, specifically including:

[0091] Obtain defect information according to the change of the laser stripe on the weld surface, which has the advantages of high precision and strong anti-interference ability compared with passive vision; define three stripe feature parameters as the feature input of the hierarchical support vector machine, namely the function slope change rate k, the formula is as follows:

[0092]

[0093] Kurtosis coefficient K u Reflect the steepness of the weld laser line, and its expression is:

[0094]

[0095] Among them, H(k) is the height of each contour point of the laser stripe, is the average value of the heights of each contour point of the laser stripe, p 4 is the fourth-order central moment of each contour data point of the laser stripe, p 2 is the second-order central moment of each contour data point of the laser stripe, and n is the number of laser stripe contour points.

[0096] Example 4. In this example, in addition to including all the technical features in Example 1, it also includes:

[0097] The construction of the network model specifically includes the following steps:

[0098] S61. Construct a data set, collect visible light images and laser images under welding working conditions, perform preprocessing, take a part of them to construct a sample training set, and the other part to construct a test set;

[0099] S62. Construct a network model of the hierarchical support vector machine.

[0100] S63. Use the dataset feature input defined and created in S5 to train the hierarchical support vector machine model until convergence or the set maximum number of iterations is reached. Use the test set to evaluate the performance of the trained neural network model. If the performance requirements are not met, continue training;

[0101] S64. Apply the hierarchical support vector machine model that has been trained to meet the expected requirements to identify and classify the defects of weld seams in actual welding scenarios.

[0102] In S62, the network model of the hierarchical support vector machine specifically includes:

[0103] The input layer receives the weld seam surface image data to be detected, with a size of 512×512×1;

[0104] Feature extraction is performed through multiple levels of support vector machine classifiers. Each classifier focuses on identifying specific types of surface defects, such as cracks, pores, and weld beads, etc.; A radial basis function kernel is adopted behind each support vector machine classifier to enhance the non-linear expression ability of complex features;

[0105] The fusion layer uses a weighting mechanism and a feature selection module to integrate the features extracted from each layer, improving the expression effect and classification performance of key features;

[0106] The output layer synthesizes the classification results of each layer through a hierarchical decision-making mechanism;

[0107] Among them, the entire model is optimized using a hierarchical loss function. Through layer-by-layer iterative training and parameter tuning, the overall detection accuracy and robustness are improved. This hierarchical SVM network model can effectively improve the classification accuracy and processing speed in weld seam surface defect detection, meeting the requirements of real-time monitoring and quality control in complex industrial environments.

[0108] The formula of the radial basis function kernel is as follows:

[0109] K(x i ,x j )=exp(-γ||x i -x j || 2 )

[0110] For the non-linear problem of weld defect detection and classification, the radial basis function kernel has good generalization ability; Among them, x i and x j are the feature vectors of two samples in the input space respectively. γ controls the decay rate of the kernel function, which in turn affects the distribution of sample points in the feature space and the selection of support vectors. Since the defect features on the weld seam surface are complex and diverse, a relatively large γ value is selected to capture the subtle differences between different defects. Here, take

[0111] The optimization of the hierarchical loss function includes:

[0112] The constructed hierarchical support vector machine model consists of five classifiers, and the form of the loss function of each classifier is the same as that of the traditional SVM:

[0113]

[0114] where w is the weight vector, b is the bias term, C is the regularization parameter used to control the penalty for misclassification, and D k refers to the training subset participating in the training at node k, is the label at node k, which depends on the specific classification task at this node, is the feature mapping that maps the input features to a high-dimensional space;

[0115] The overall loss function is the weighted sum of the losses of all classifiers:

[0116]

[0117] where α k is the weight coefficient used to balance the losses of different classifiers.

[0118] Extract the image features of the weld surface through passive vision and laser vision sensing technologies, and use the obtained parameters such as the geometric shape features of the weld surface, the waveform diagram features of the weld area, and the laser stripe features as the feature inputs of the hierarchical support vector machine. By cleverly designing the structure of the classifier, the multi-classification problem is transformed into multiple binary-classification problems to identify and classify six types of weld targets to obtain the final result.

[0119] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic features of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

[0120] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A weld defect detection method based on multi-feature extraction and hierarchical SVM fusion, characterized in that The weld surface defect detection method includes the following steps: S1. Real-time image acquisition: Use passive vision sensing technology to obtain the weld surface information, providing information input for subsequent defect detection; S2. Laser stripe image acquisition: Use active vision sensing technology and obtain weld defect information according to the deformation of the laser stripe on the weld surface; S3. Preprocessing and feature extraction of the weld image; S4. Analysis of laser image stripe features; S5. Analyze the image features of passive vision and active vision, and make labels using the feature information corresponding to each defect; S6. Construct a network model with multi-feature information of weld surface defects as the input of the hierarchical support vector machine, and train the hierarchical classifier model using the defined feature parameters; S7. Identify and classify weld surface defects.

2. The weld surface defect detection method according to claim 1, characterized in that: In S3, the preprocessing and feature extraction of the weld surface defect image obtained by passive vision specifically include: S31. To reduce the noise of the image on the ROI feature area of the image, use Gaussian filtering to process the image to improve the defect recognition rate; S32. Define five types of two-dimensional feature parameters for welding defect features; S33. Adopt the ROI waveform analysis method, and use the horizontal summation of the ROI area and calculate its average value as the feature input; S34. For poor forming and burn-through defects, obtain the corresponding waveform sequence by horizontally summing the defect area of the weld area, and take its average value as the feature input to distinguish defect types.

3. The weld surface defect detection method according to claim 2, characterized in that: In S32, the five types of two-dimensional feature parameters specifically include: The perimeter C of the defect area refers to the sum of the number of pixels in the defect area. Among them, R0 is the set of pixel points at the boundary of the defect area, which is used to distinguish the complexity of the shape of the defect area; Aspect ratio K: It refers to the ratio of the length to the width of the minimum circumscribed rectangle of the defect area, and is used to measure the length and shortness of the defect. The formula is K = L / W; The area s of the defective region refers to the number of pixel points in the region connected by the same defect formed. R1 refers to the set of all pixel points in the defective region; Roundness R: Using the area and perimeter of the defect area can judge its closeness to a circle, and can identify holes and weld beads; Goodness B: It refers to the ratio of the defect area to the weld area, which can effectively distinguish good welds and defective welds.

4. The weld surface defect detection method according to claim 1, characterized in that: In S4, the laser image stripe feature analysis specifically includes: S41. For defects with unclear two-dimensional features, use the laser stripe image to distinguish defects; S42. Regard the obtained laser stripe image as a function curve, calculate its second derivative, judge the change of the slope, and thus distinguish; S43. Define the maximum offset of the laser stripe image relative to the weld center line, and use the maximum offset to reflect the approximate position of the function inflection point; S44. Define the kurtosis coefficient to reflect the steepness of the laser stripe curve.

5. The weld surface defect detection method according to claim 4, characterized in that: In S41, using the laser stripe image to distinguish defects means using auxiliary lasers to extract the weld surface features, specifically including: Obtain defect information according to the change of the laser stripe on the weld surface. Define three stripe feature parameters as the feature input of the hierarchical support vector machine. The function slope change rate k is as follows: Kurtosis coefficient K u It reflects the steepness of the laser line of the weld, and its expression is: Among them, H(k) is the height of each contour point of the laser stripe, is the average value of the heights of each contour point of the laser stripe, p 4 is the fourth-order central moment of each contour data point of the laser stripe, p 2 is the second-order central moment of each contour data point of the laser stripe, and n is the number of contour points of the laser stripe.

6. The weld surface defect detection method according to claim 1, wherein: In S6, the construction of the network model specifically includes the following steps: S61. Construct a data set, collect visible light images and laser images under welding working conditions, perform preprocessing, take a part of them to construct a sample training set, and the other part to construct a test set; S6 S63. Use the dataset feature inputs defined and created in S5 to train the hierarchical support vector machine model until convergence or the set maximum number of iterations is reached. Use the test set to evaluate the performance of the trained neural network model. If the performance requirements are not met, continue training; S64. Apply the hierarchical support vector machine model that has been trained to meet the expected requirements to defect identification and classification of weld seams in actual welding scenarios.

7. The weld surface defect detection method according to claim 6, wherein: In S62, the network model of the hierarchical support vector machine specifically includes: The input layer receives the weld surface image data to be detected, with a size of 512×512×1; Feature extraction is performed through multiple levels of support vector machine classifiers. Each classifier focuses on identifying specific types of surface defects. A radial basis function kernel is used behind each support vector machine classifier to enhance the non-linear expression ability of complex features; The fusion layer uses a weighting mechanism and a feature selection module to integrate the features extracted from each layer, improving the expression effect of key features and the classification performance; The output layer synthesizes the classification results of each layer through a hierarchical decision-making mechanism; Among them, the entire model is optimized using a hierarchical loss function through layer-by-layer iterative training and parameter tuning.

8. The weld defect detection method based on multi-feature extraction and hierarchical SVM fusion according to claim 7, characterized in that: The formula of the radial basis function kernel is as follows: K(x i ,x j ) = exp(-γ||x i -x j || 2 ) where x i and x j are the feature vectors of two samples in the input space respectively, and γ controls the decay rate of the kernel function, thereby affecting the distribution of sample points in the feature space and the selection of support vectors.

9. The weld surface defect detection method according to claim 7, characterized in that: The optimization of the hierarchical loss function includes: The constructed hierarchical support vector machine model consists of five classifiers. The form of the loss function of each classifier is the same as that of the traditional SVM: where \(w\) is the weight vector, \(b\) is the bias term, \(C\) is the regularization parameter used to control the penalty for misclassification, and \(D\) k refers to the training subset participating in the training at node \(k\), is the label at node \(k\), which depends on the specific classification task at that node, is the feature mapping that maps the input features to a high-dimensional space; The overall loss function is the weighted sum of the losses of all classifiers: where α k is the weight coefficient used to balance the losses of different classifiers.

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