A strip steel tensile property rapid matching method based on a naive Bayes principle identification model

Abstract

The application discloses a strip steel tensile property fast matching method based on a naive Bayes principle recognition model, and performs electromagnetic nondestructive detection on a strip steel material with ferromagnetism to obtain electromagnetic characteristic parameters representing the strip steel material, a group of electromagnetic characteristic parameters are jointly measured by four electromagnetic detection modes, each electromagnetic detection mode outputs a curve signal, and each curve signal is converted into a quantitative parameter by definition for representation; meanwhile, based on the importance degree of the electromagnetic characteristic parameters and the tensile property, electromagnetic characteristic parameters with great influence on the tensile property of the strip steel material are determined; the electromagnetic characteristic parameters of the strip steel material are taken as input, the category of the strip steel material is taken as output, and the tensile property value of the strip steel material is determined, a naive Bayes principle recognition model based on the electromagnetic characteristic parameters is established, and thus the mode recognition of the material category and the tensile property representation are nondestructively realized. The application is used for online detection of the tensile property of the strip steel in online operation.

Description

Technical Field

[0001] This invention relates to electromagnetic nondestructive testing technology for ferromagnetic metallic materials, and more specifically, to a rapid matching method for the tensile properties of strip steel based on a Naive Bayes principle identification model. Background Technology

[0002] Strip steel has wide applications in automobiles, construction, and home appliances, and its tensile properties (such as yield strength, tensile strength, and elongation) are key indicators for quality assessment. Traditional strip steel tensile property testing mainly relies on laboratory testing, which is time-consuming and costly. In large-scale production, there is an urgent need to achieve real-time testing of strip steel properties. However, due to the complexity of parameters, high-dimensional data, and significant nonlinear relationships in the production process, traditional methods struggle to meet the requirements in terms of both real-time performance and accuracy.

[0003] The advantage of offline strip testing is its simplicity and intuitive, accurate results. However, it has the following drawbacks: First, the data has a significant time lag, making it unsuitable for effectively guiding production and unable to achieve real-time online control. Second, the data sampling is limited, only reflecting the performance data of the strip's beginning and end. Third, relying on experience to judge that "if the beginning and end are qualified, the middle is qualified," when encountering shutdowns or low-speed operation during production, it is usually necessary to cut off a portion of the "potentially unqualified" strip. The lack of a clear standard for the cutting length often results in the removal of too much strip, leading to material waste. Fourth, it requires operators to be on duty around the clock, resulting in high labor intensity and high labor costs.

[0004] These types of testing methods cannot achieve online real-time detection, have long testing cycles, lack intelligence, and waste significant resources. Therefore, rapid and non-destructive material tensile property testing technology is particularly important.

[0005] Non-destructive testing (NDT) technology involves detecting or measuring changes in physical quantities caused by defects or localized inhomogeneities in an object without damaging it. This allows for the assessment of the presence of defects in the internal structure or surface, and the determination of physical properties such as structural integrity, continuity, and safety. Due to its non-destructive nature, high reliability, and strong safety, NDT has gained widespread attention and rapid development in industries such as energy, machinery, and steel, playing a crucial role in quality control, raw material conservation, and process optimization.

[0006] As an efficient probabilistic classification algorithm, the Naive Bayes algorithm can significantly improve the matching efficiency and accuracy of material tensile properties by utilizing the mapping relationship between electromagnetic detection data (multi-source electromagnetic parameters) and tensile properties. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a rapid matching method for the tensile properties of strip steel based on a Naive Bayes principle recognition model. This method enables non-destructive testing of the tensile properties of ferromagnetic metal materials using electromagnetic characteristic parameters as the judgment criteria. It can be used to perform online testing of the tensile properties of strip steel in operation, obtaining high-density tensile property data along the entire length of the strip steel. Within a relative error accuracy range of 10%, the sample pass rate is over 90%.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model;

[0010] Electromagnetic nondestructive testing is performed on ferromagnetic strip steel to obtain electromagnetic characteristic parameters characterizing the strip steel. A set of electromagnetic characteristic parameters is measured jointly using four electromagnetic detection methods. Each electromagnetic detection method outputs a curve signal, and each curve signal is converted into a quantized parameter for characterization by definition.

[0011] Meanwhile, based on the importance of electromagnetic characteristic parameters and tensile properties, the electromagnetic characteristic parameters that have a significant impact on the tensile properties of the strip steel are determined.

[0012] Using the electromagnetic characteristic parameters of the strip steel material as input and the category of the strip steel material as output, and determining the tensile property value of the strip steel material, a Naive Bayes principle recognition model based on the electromagnetic characteristic parameters is established, thereby achieving non-destructive pattern recognition of material categories and characterization of tensile properties.

[0013] Preferably, the method for rapidly matching the tensile properties of the strip steel specifically includes the following steps:

[0014] S1, processing and preparing the test sample;

[0015] S2, Electromagnetic non-destructive testing of the strip steel material is performed using a multi-magnetic detection device, and electromagnetic characteristic parameters of the strip steel material are extracted by combining data processing methods.

[0016] S3, perform a correlation analysis between the tensile properties of the strip steel and the electromagnetic characteristic parameters of the strip steel;

[0017] S4, The tensile properties of the strip steel are characterized using the electromagnetic characteristic parameters of the strip steel.

[0018] S5, Establish a Naive Bayes principle recognition model;

[0019] S6. Repeat the training of the Naive Bayes principle recognition model and take the mean of the training results as the final detection value.

[0020] Preferably, step S1 specifically includes:

[0021] The strip steel material is processed into tensile specimens and strip specimens using laser cutting technology or water jet cutting technology;

[0022] The tensile specimen is used to obtain tensile property values, and the strip specimen is used for detection by the multi-magnetic detection device.

[0023] Preferably, in step S2, the multi-magnetic detection device uses the magnetic Barkhausen noise method, incremental permeability method, tangential magnetic field harmonic analysis method, and multi-frequency eddy current detection method to jointly measure the strip steel material.

[0024] Preferably, during the detection process, the multi-magnetic detection device applies an alternating magnetic field excitation to the strip material. The magnetization process includes gradually increasing the magnetic field excitation from zero to positive saturation, then decreasing it back to zero magnetic field, then increasing it to negative saturation and finally returning to zero magnetic field, thereby obtaining the electromagnetic characteristic parameters of the MBN signal and MIP signal.

[0025] Preferably, step S4 further includes:

[0026] The tensile properties of the strip steel are then modularized, that is, a unique identification code is assigned to different samples based on the tensile property value of the strip steel, and the assigned identification code is used as the result of the patterning.

[0027] Preferably, step S5 specifically includes the following steps:

[0028] S51, PCA is used to reduce the dimensionality of the electromagnetic characteristic parameters;

[0029] S52, In the reduced-dimensional space, KDE is used to replace the normal distribution assumption to fit the data distribution;

[0030] S53, combining the features after PCA dimensionality reduction and the probability density value estimated by KDE, the Naive Bayes principle recognition model is established based on the Naive Bayes principle.

[0031] Preferably, in step S6, the Naive Bayes principle recognition model is trained and validated using a cross-validation modeling method, specifically including:

[0032] The k-fold cross-validation method is used to divide the data into k non-overlapping subsets. Each time, one subset is selected as the validation set, and the remaining subsets are used as the training set for model training and validation. This process is repeated k times, and the output of the model is recorded each time.

[0033] The present invention provides a method for rapid matching of tensile properties of strip steel based on a Naive Bayes principle identification model, which has the following beneficial effects:

[0034] (1) This invention can achieve rapid matching of ferromagnetic metal material categories;

[0035] (2) This invention can realize non-destructive testing of the tensile properties (yield strength, tensile strength and elongation) of ferromagnetic steel materials, and the characterization confidence rate is greater than 90% under the condition that the error is less than 10%.

[0036] (3) This invention provides a digital and rapid matching method for characterizing the tensile properties of ferromagnetic steel materials, thereby improving the detection speed and reducing the detection cost. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the rapid matching method for the tensile properties of strip steel according to the present invention;

[0038] Figure 2 This is a schematic diagram of the multi-magnetic detection device in the rapid matching method for tensile properties of strip steel of the present invention;

[0039] Figure 3 This is the MBN (MIP) butterfly curve obtained by the multi-magnetic detection device in the rapid matching method for tensile properties of strip steel of the present invention;

[0040] Figure 4 This is a schematic diagram of the correlation analysis between electromagnetic characteristic parameters and tensile properties in the rapid matching method for tensile properties of strip steel of the present invention. (a) represents yield strength, (b) represents tensile strength, and (c) represents elongation.

[0041] Figure 5 This is a schematic diagram of the yield strength evaluation results in the rapid matching method for tensile properties of strip steel of the present invention;

[0042] Figure 6 This is a schematic diagram of the tensile strength evaluation results in the rapid matching method for tensile properties of strip steel of the present invention.

[0043] Figure 2 In the middle, 1-shell, 2-electronic board (preamplifier), 3-magnetic yoke, 4-electromagnetic coil, 5-connecting cable, 6-Hall sensor, 7-transmitter coil, 8-receiver coil, 9-electromagnetic non-destructive testing sample. Detailed Implementation

[0044] To better understand the above-mentioned technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0045] This invention provides a rapid matching method for the tensile properties of strip steel based on a Naive Bayes principle recognition model. It realizes a pattern recognition (classification) method for non-destructive testing of the tensile properties of ferromagnetic metal materials using electromagnetic characteristic parameters of ferromagnetic steel materials as the judgment standard. It can be used to perform online testing of the tensile properties of strip steel in operation, obtain high-density tensile property data of the entire length of the strip steel, and achieve a sample qualification rate of over 90% within a relative error accuracy range of 10%.

[0046] Combination Figure 1 As shown, this invention uses a multi-magnetic detection device to perform electromagnetic non-destructive testing on ferromagnetic strip steel materials to obtain electromagnetic characteristic parameters characterizing the strip steel materials. Among them, a set of electromagnetic characteristic parameters are obtained by joint measurement of four electromagnetic detection methods: Barkhausen noise, incremental permeability, tangential magnetic field harmonic analysis, and multi-frequency eddy current. Each electromagnetic detection method outputs a curve signal, and each curve signal is transformed into a quantitative parameter through definition for characterization.

[0047] Meanwhile, based on the importance of electromagnetic characteristic parameters and tensile properties, electromagnetic characteristic parameters that have a significant impact on the tensile properties of strip steel are determined.

[0048] Using the electromagnetic characteristic parameters of the strip steel as input and the category of the strip steel as output, and determining the tensile properties of the strip steel, a Naive Bayesian recognition model based on the electromagnetic characteristic parameters is established, thereby achieving non-destructive pattern recognition of material categories and characterization of tensile properties.

[0049] The rapid matching method for the tensile properties of strip steel of the present invention specifically includes the following steps:

[0050] S1. Using laser cutting or waterjet cutting technology, the strip steel material is processed into tensile test specimens (the size is determined by the thickness and is used to obtain tensile property values) and strip specimens with a size of 200mm*150mm (obtained by testing with multi-magnetic detection equipment).

[0051] S2 utilizes multi-magnetic detection equipment to perform electromagnetic non-destructive testing on strip steel materials, while combining data processing methods (such as wavelet transform or principal component analysis) to define and extract the electromagnetic characteristic parameters of the strip steel materials.

[0052] Multi-magnetic detection equipment integrates various electromagnetic detection technologies, applying different excitation magnetic fields to stimulate different electromagnetic principles, including magnetic Barkhausen noise method, incremental permeability method, tangential magnetic field harmonic analysis method, and multi-frequency eddy current detection method.

[0053] During the testing process, an alternating magnetic field is applied to the strip steel material for excitation. The magnetization process involves gradually increasing the magnetic field excitation from zero to positive saturation, then decreasing it back to zero, subsequently increasing it to negative saturation, and finally returning to zero. Throughout the repeated magnetization cycles, due to the differences in the microstructure of the strip steel material, its magnetization process exhibits significantly different characteristics. The cumulative effect of magnetic domain movement causes changes in the material's permeability, and the degree of magnetization continuously deepens, ultimately leading to a significant change in the magnetization curve. The signals acquired through this process can accurately reflect the different magnetic properties of the strip steel material and are closely related to its tensile properties (such as yield strength and tensile strength).

[0054] The probe of the multi-magnetic testing equipment inherits four micro-electromagnetic non-destructive testing technologies and selects 41 micro-electromagnetic properties to characterize the magnetic parameters of automotive sheet steel.

[0055] Combination Figure 2 As shown, in MBN technology, a high-amplitude, low-frequency sinusoidal current is fed into an electromagnetic coil 4 wound around a U-shaped magnetic yoke 3. To ensure that the signal of irreversible magnetic domain motion is detected by the receiver coil 8, the applied magnetization amplitude is sufficient to excite the detected strip material to reach saturation level.

[0056] The detected MBN signal undergoes a combination of bandpass and low-pass / high-pass filters, followed by amplification, post-amplification, and signal smoothing rectification. The MBN butterfly curve is shown below. Figure 3 As shown, it uses the digitally transformed and smoothed MBN amplitude timing signal as the vertical axis and the excitation magnetic field strength corresponding to the MBN amplitude signal as the horizontal axis, resulting in a butterfly diagram of the MBN signal (the curve shape resembles a butterfly with outstretched wings). From this, the maximum amplitude (the maximum value of the MBN signal, MMAX) can be derived as a test statistic. Correspondingly, the magnetic field strength at MMAX is assigned to the test statistic (the horizontal axis value corresponding to the maximum value, HCM). The expansion of the profile curve is evaluated at 25%, 50%, and 75% of MMAX (referred to as the width, defined as "the distance (width) between the two intersections of the vertical axis value at the 25%, 50%, and 75% positions of the maximum value with the two points of the butterfly diagram," DH25M, DH50M, and DH75M). An additional test statistic is MMEAN, which is the average value of the profile curve over a certain period (the average value of the MBN signal amplitude over one butterfly period).

[0057] During the reorganization of magnetic domains, displacement of the Bloch walls occurs, happening in a discrete, hopping manner. Bloch domain walls are influenced by different microstructures, thus exhibiting different motion characteristics. These microstructural variations can be reflected by the properties of the MBN. MMAX test statistics can be used to quantitatively obtain finishing conditions such as depth hardness and surface hardness. When grain boundaries represent the main barrier to Bloch wall displacement, HCM can be quantitatively correlated with grain size. Relationships between the expansion of profile curves (DH25M, DH50M, and DH75M) and internal stress or plastic deformation have been observed.

[0058] Unlike the MBN detection method, in the MIP technique, high- and low-frequency sinusoidal currents are necessary for obtaining reversible motion information. Similar to the MBN method, the high-amplitude, low-frequency (10–1000 Hz) excitation of the U-shaped yoke 3 generates hysteresis loops in the material. Simultaneously, a low-amplitude (milliampere level), high-frequency (10 kHz–1 MHz) sinusoidal current is fed into the transmitter coil 7, similar to the MFEC method, to generate small asymmetric hysteresis loops that superimpose on the main hysteresis curve.

[0059] Similar to MBN, the maximum amplitude of the MIP (the maximum value of the signal, UMAX) is extracted as an important feature. The magnetic field strength at UMAX (the abscissa value at its maximum, HCU) is also derived as a statistical parameter. Furthermore, the curve extensions at 25%, 50%, and 75% (defined as above, DH25U, DH50U, and DH75U) and the average UMEAN over the time period are also used as MIP features. MIP can be used to characterize near-surface (surface hardened) material properties. Shell depth information is derived from the amplitude of the UMAX signal received from the core structure, and hardness information can be obtained from the associated forced field strength HCU. Stress state information is quantitatively described using curve extensions (DH25U, DH50U, and DH75U).

[0060] By using the aforementioned multi-magnetic detection equipment to conduct electromagnetic non-destructive testing on steel strip samples, a total of 14 electromagnetic characteristic parameters, including MBN and MIP, can be obtained. The testing time for each sample is 120 seconds, during which more than 100 sets of electromagnetic characteristic data can be acquired. After outlier cleaning, 100 sets of valid data are retained for subsequent analysis.

[0061] S3 involves a correlation analysis between the tensile properties of the strip steel and its electromagnetic characteristic parameters. For example... Figure 4As shown, the correlation analysis results between electromagnetic characteristic parameters and tensile properties (yield strength, tensile strength, and elongation) are presented. Comprehensive analysis reveals that the correlation between different electromagnetic characteristic parameters and tensile property indices (yield strength, tensile strength, and elongation) is generally high. This indicates that electromagnetic characteristic parameters can effectively characterize tensile properties, providing a reliable input variable basis for the subsequent construction of pattern recognition models.

[0062] S4. Based on the analysis results of step S3, it is known that there is a high correlation between electromagnetic characteristic parameters and tensile properties. Therefore, the electromagnetic characteristic parameters of the strip material are used to characterize its tensile properties. On this basis, the tensile properties of the strip material are patterned, that is, a unique identification code (i.e., pattern) is assigned to different samples based on their tensile property values ​​(yield strength, tensile strength, and elongation). This process is called patterning, and the assigned identification code is the result of patterning. The specific patterning results are shown in Table 1.

[0063] Table 1 Sample patterning results

[0064]

[0065] S5, Establish a Naive Bayes principle recognition model

[0066] The Naive Bayes algorithm is a simple and efficient classification algorithm based on Bayes' Theorem. Its defining characteristic is its "naivety," assuming that features are independent of each other. Although this assumption often doesn't hold true in real-world scenarios, the Naive Bayes algorithm still performs well in many applications, especially in high-dimensional data and classification tasks, where it shows significant advantages.

[0067] Because the linear relationship between some electromagnetic characteristic parameters and tensile properties is not obvious, and some parameters have a standard deviation of zero, a normal distribution cannot be fitted, rendering the Naive Bayes algorithm unsuitable in this case. Therefore, during the model training phase, Principal Component Analysis (PCA) and Kernel Density Estimation (KDE) methods are introduced to address the issues of high-dimensional feature redundancy and distribution assumptions, respectively, thereby improving the applicability and robustness of the classification model.

[0068] First, PCA (Principal Component Analysis) is used to reduce the dimensionality of the electromagnetic feature parameters. PCA projects high-dimensional data into a low-dimensional space through linear transformation, preserving the main variance information while removing redundant features and noise, thereby reducing data dimensionality and improving computational efficiency and the model's generalization ability. The number of principal components is selected based on the cumulative variance contribution rate to ensure that the reduced features retain the information of the original data to the greatest extent possible.

[0069] Secondly, in the reduced-dimensional space, KDE (kernel density estimation) is used to replace the normal distribution assumption to fit the data distribution. KDE estimates the probability density of the data through a kernel function (such as a Gaussian kernel), which can flexibly adapt to the characteristics of nonlinear data distributions and effectively solve the problem of dependence on the normal distribution in traditional Naive Bayes algorithms.

[0070] Finally, by combining the features after PCA dimensionality reduction and the probability density values ​​estimated by KDE, a Naive Bayes recognition model was established based on the Naive Bayes principle, which effectively classified high-dimensional nonlinear distributed data and significantly improved the training efficiency and performance stability of the model.

[0071] S6. Repeat the training of the Naive Bayes recognition model ten times, and take the average of the ten training results as the final detection value. Figure 5 and Figure 6 As shown, for the characterization of tensile properties (taking yield strength and tensile strength as examples), the confidence rate is greater than 90% under the condition that the error is less than 10%.

[0072] Cross-validation is used to train and validate the Naive Bayes recognition model, ensuring its robustness and generalization ability. Specifically, this includes:

[0073] The k-fold cross-validation method is used to divide the data into k non-overlapping subsets. Each time, one subset is selected as the validation set, and the remaining subsets are used as the training set for model training and validation. This process is repeated k times, and the output of the model is recorded each time.

[0074] This invention employs 8-fold cross-validation, which allows for full utilization of the data during model training and avoids random errors caused by data segmentation methods, thereby improving model stability. Furthermore, the model is trained five times, and the average of the ten training results is used as the final detection value.

[0075] Combined Figure 5 and Figure 6 As shown, for the characterization results of tensile properties (taking yield strength and tensile strength as examples), the confidence rate is greater than 90% when the error is less than 10%. The introduction of cross-validation further enhances the consistency of the model's performance on different subsets of data, and improves the model's prediction accuracy and reliability for tensile properties.

[0076] Those skilled in the art should recognize that the above embodiments are merely illustrative of the present invention and are not intended to limit the present invention. Any variations or modifications to the above embodiments that are within the spirit and essence of the present invention will fall within the scope of the claims of the present invention.

Claims

1. A method for rapid matching of tensile properties of strip steel based on a Naive Bayes principle identification model, characterized in that: Electromagnetic nondestructive testing is performed on ferromagnetic strip steel to obtain electromagnetic characteristic parameters characterizing the strip steel. A set of electromagnetic characteristic parameters is measured jointly using four electromagnetic detection methods. Each electromagnetic detection method outputs a curve signal, and each curve signal is converted into a quantized parameter for characterization by definition. Meanwhile, based on the importance of electromagnetic characteristic parameters and tensile properties, the electromagnetic characteristic parameters that have a significant impact on the tensile properties of the strip steel are determined. Using the electromagnetic characteristic parameters of the strip steel material as input and the category of the strip steel material as output, and determining the tensile property value of the strip steel material, a Naive Bayes principle recognition model based on the electromagnetic characteristic parameters is established, thereby achieving non-destructive pattern recognition of material categories and characterization of tensile properties.

2. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 1, characterized in that, The method for rapidly matching the tensile properties of strip steel specifically includes the following steps: S1, processing and preparing the test sample; S2, Electromagnetic non-destructive testing of the strip steel material is performed using a multi-magnetic detection device, and electromagnetic characteristic parameters of the strip steel material are extracted by combining data processing methods. S3, perform a correlation analysis between the tensile properties of the strip steel and the electromagnetic characteristic parameters of the strip steel; S4, The tensile properties of the strip steel are characterized using the electromagnetic characteristic parameters of the strip steel. S5, Establish a Naive Bayes principle recognition model; S6. Repeat the training of the Naive Bayes principle recognition model and take the mean of the training results as the final detection value.

3. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 2, characterized in that, Step S1 specifically includes: The strip steel material is processed into tensile specimens and strip specimens using laser cutting technology or water jet cutting technology; The tensile specimen is used to obtain tensile property values, and the strip specimen is used for detection by the multi-magnetic detection device.

4. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 2, characterized in that: In step S2, the multi-magnetic detection device uses the magnetic Barkhausen noise method, incremental permeability method, tangential magnetic field harmonic analysis method and multi-frequency eddy current detection method to jointly measure the strip steel material.

5. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 4, characterized in that: During the detection process, the multi-magnetic detection device applies an alternating magnetic field excitation to the strip material. The magnetization process includes gradually increasing the magnetic field excitation from zero to positive saturation, then decreasing it back to zero magnetic field, then increasing it to negative saturation and finally returning to zero magnetic field, ultimately obtaining the electromagnetic characteristic parameters of the MBN signal and MIP signal.

6. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 2, characterized in that, Step S4 further includes: The tensile properties of the strip steel are then modularized, that is, a unique identification code is assigned to different samples based on the tensile property value of the strip steel, and the assigned identification code is used as the result of the patterning.

7. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 2, characterized in that, Step S5 specifically includes the following steps: S51, PCA is used to reduce the dimensionality of the electromagnetic characteristic parameters; S52, In the reduced-dimensional space, KDE is used to replace the normal distribution assumption to fit the data distribution; S53, combining the features after PCA dimensionality reduction and the probability density value estimated by KDE, the Naive Bayes principle recognition model is established based on the Naive Bayes principle.

8. The method for rapid matching of tensile properties of strip steel based on the Naive Bayes principle identification model according to claim 2, characterized in that, In step S6, the Naive Bayes principle recognition model is trained and validated using a cross-validation modeling method, specifically including: The k-fold cross-validation method is used to divide the data into k non-overlapping subsets. Each time, one subset is selected as the validation set, and the remaining subsets are used as the training set for model training and validation. This process is repeated k times, and the output of the model is recorded each time.

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