Method, device and storage medium for predicting fatigue strength of material

By using an adaptive kernel density estimation framework and multiple kernel functions and global smoothing parameters, the problem of inaccurate fatigue strength distribution in the traditional rise and fall method is solved, and accurate prediction of material fatigue strength is achieved, improving the accuracy and reliability of the prediction.

CN120977458BActive Publication Date: 2026-02-10SHENZHEN POWEROAK NEWENER CO LTD
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Patent Information

Application Number
CN202511500415.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-10-21
Publication Date
2026-02-10
Estimated Expiration
2045-10-21

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Abstract

The application relates to the technical field of machine learning and intelligent manufacturing, in particular to a material fatigue strength prediction method, equipment and a storage medium. The method comprises the following steps: acquiring the load level of each sample of a measured material; determining a global smoothing parameter with a Gaussian kernel function as a reference based on the load level of each sample, and determining the smoothing parameter of each kernel function based on the global smoothing parameter; estimating the probability density function of the fatigue strength of the measured material based on each kernel function and the smoothing parameter of each kernel function; and calculating an expected value and a standard deviation based on the estimated probability density function, and taking the expected value and the standard deviation as the estimated value and the estimated standard deviation of the fatigue strength of the measured material respectively. The method of the application effectively improves the accuracy and reliability of the estimated average value and the estimated standard deviation of the fatigue strength.
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Description

Technical Field

[0001] This application relates to the interdisciplinary field of machine learning and intelligent manufacturing, and in particular to a method, device and storage medium for predicting the fatigue strength of a material. Background Technology

[0002] The cyclic stress method is a widely used experimental method for predicting the fatigue strength of metallic materials. It involves applying cyclic stresses under different loads, recording whether the specimens experience fatigue failure, and then using statistical analysis to predict the fatigue strength distribution of the tested material.

[0003] In traditional fatigue strength testing, a probability distribution is assumed to govern the fatigue strength of the material before the experiment. This assumed probability distribution is usually derived from materials published in the literature. For materials that have never been tested, it is difficult to find a matching fatigue strength probability distribution, and the fatigue probability distribution of similar or related materials must be used as a premise. This significantly limits the accuracy of fatigue tests. Especially in the determination of fatigue strength of composite materials, their probability distribution is usually unknown, and it is difficult to deduce the fatigue strength probability distribution of composite materials from the fatigue distribution of existing materials, thus greatly increasing the difficulty of fatigue strength testing of composite materials.

[0004] With the development of intelligent manufacturing and digital twin technologies, the requirements for the accuracy and real-time performance of material fatigue strength data are constantly increasing. This is especially true for novel composite materials and 3D printed materials, whose fatigue strength distribution often exhibits multi-peak characteristics and nonlinear features. Existing methods based on parametric distribution assumptions can no longer meet these demands. Fatigue strength measurement methods in intelligent manufacturing environments urgently need to break through the limitations of traditional probability and statistics to achieve data-driven adaptive analysis. Summary of the Invention

[0005] The embodiments of this application aim to provide a method, device and storage medium for predicting the fatigue strength of materials, so as to solve the inaccuracy problem caused by the traditional rise and fall method based on the assumed probability distribution to predict the fatigue strength distribution of the test material.

[0006] To address the aforementioned technical problems, the embodiments of this application provide the following technical solutions:

[0007] According to a first aspect of this application, a method for predicting the fatigue strength of a material is provided, comprising pre-setting multiple kernel functions, including a Gaussian kernel function, the method comprising:

[0008] Obtain the load level for each specimen of the tested material;

[0009] Based on the load level of each specimen, a global smoothing parameter with reference to the Gaussian kernel function is determined, and based on the global smoothing parameter, the smoothing parameter of each kernel function is determined.

[0010] The probability density function of the fatigue strength of the tested material is estimated based on each kernel function and the smoothing parameter of each kernel function.

[0011] The expected value and standard deviation are calculated based on the estimated probability density function, and the expected value and standard deviation are used as the estimated value and estimated standard deviation of the fatigue strength of the tested material, respectively.

[0012] Optionally, the expression for the probability density function is:

[0013]

[0014] in, For the first The load level of each specimen, The number of kernel functions, The number of samples. The weight coefficients of the j-th kernel function are... Let j be the smoothing parameter of the j-th kernel function. Let j be the j-th kernel function.

[0015] Optionally, the plurality of kernel functions may also include one or more combinations of the Epanechnikov kernel function, the double-weighted kernel function, the triangular kernel function, and the cosine kernel function.

[0016] Optionally, the weight coefficients of each kernel function are determined based on the weight optimization method of cross-validation, and the objective function for optimization is:

[0017]

[0018] in, The number of samples. Based on removing the first All other samples and weight vectors after the first sample The obtained probability density function is The value at that location, Based on all samples and weight vectors The obtained probability density function is The value at that location.

[0019] Optionally, the formula for calculating the smoothing parameter of each kernel function is as follows:

[0020]

[0021] in, The global smoothing parameter is... The smoothing parameter is the one corresponding to the j-th kernel function. It is the j-th kernel function. It is a Gaussian kernel function. It is the square integral of the kernel function. It is the second moment of the kernel function.

[0022] Optionally, determining the global smoothing parameters based on the load level of each specimen, with reference to the Gaussian kernel function, includes:

[0023] Based on the load level distribution, multi-peak characteristics, and sample size of each sample, a global smoothing parameter with a Gaussian kernel function as a reference was determined.

[0024] Optionally, the formula for calculating the global smoothing parameter is:

[0025]

[0026] in, The global smoothing parameter is... The number of samples. The standard deviation of the sample. This is the interquartile range of the sample. For data feature adaptive coefficients, This is the distribution morphology adjustment factor for each sample. This is the adjustment factor for the multi-peak characteristics of each sample. This is the sample size adjustment factor for each sample.

[0027] Optionally, the distribution morphology adjustment factor The calculation formula is:

[0028]

[0029] in, , For weight parameters, For sensitivity parameters, For sample skewness, For sample kurtosis, The number of samples. The standard deviation of all samples, For the first The load level of each specimen, The average load water value for all samples;

[0030] The multi-peak characteristic adjustment factor The calculation formula is:

[0031]

[0032] in, To adjust the intensity parameters for multiple peaks, It is a multi-peak characteristic index. The dip statistic is for all samples. To achieve the preset dip threshold, For indicator functions;

[0033] The sample size adjustment factor The calculation formula is:

[0034]

[0035] in, This represents the actual number of samples. For reference sample quantity, To adjust the index.

[0036] According to a second aspect of this application, an electronic device is provided, including at least one processor and a memory communicatively connected to the at least one processor, the memory storing instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method described above.

[0037] According to a third aspect of this application, a computer storage medium is provided, the computer storage medium storing instructions or programs that, when executed by at least one processor, cause the at least one processor to perform the method described above.

[0038] The beneficial effects of this application's embodiments are as follows: Unlike existing technologies, this application provides a method for predicting the fatigue strength of materials. First, the load level of each specimen of the tested material is obtained. Then, based on the load level of each specimen, a global smoothing parameter with a Gaussian kernel function as a reference is determined, and the smoothing parameters of each kernel function are determined based on the global smoothing parameter. Next, the probability density function of the fatigue strength of the tested material is estimated based on each kernel function and its smoothing parameters. Finally, the expected value and standard deviation are calculated based on the estimated probability density function, and the expected value and standard deviation are used as the estimated value and estimated standard deviation of the fatigue strength of the tested material, respectively. This application's method designs an adaptive kernel density estimation framework, which not only overcomes the dependence of the traditional rise-fall method on probability distribution but also achieves accurate capture of material fatigue characteristics through dynamically optimized smoothing parameters. Compared to the traditional rise-fall method, this application effectively improves the accuracy and reliability of the estimated average value and estimated standard deviation of fatigue strength. Furthermore, the advantages of this application's method become more pronounced when the number of valid experimental specimens is larger; when the number of valid experimental specimens is smaller, the method of this application can still guarantee sufficient prediction accuracy and reliability. Attached Figure Description

[0039] One or more embodiments are illustrated by way of example with reference numerals in the accompanying drawings. These illustrations do not constitute a limitation on the embodiments. Elements with the same reference numerals in the drawings are denoted as similar elements. Unless otherwise stated, the figures in the drawings are not to be limited by scale.

[0040] Figure 1 This is a flowchart of a method for predicting the fatigue strength of a material provided in an embodiment of this application;

[0041] Figure 2 This is a fatigue limit rise and fall diagram of carbon steel material provided in an embodiment of this application;

[0042] Figure 3 This is a structural diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0044] Furthermore, the technical features involved in the various embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0045] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0046] The key terms used in this application are explained below:

[0047] 1. Fatigue Strength: refers to the cyclic stress value at which a material will fail due to fatigue after being subjected to cyclic stress for a specific period. Exceeding this stress will lead to fatigue failure of the material.

[0048] 2. Probability Density Function: This is a function that describes the probability of a random variable occurring around a specific value.

[0049] 3. Kernel Density Estimation: This is a nonparametric statistical method used to estimate the probability density function of a random variable.

[0050] 4. Indicator function: In set theory, an indicator function is a function defined on a set X that indicates which elements belong to a subset A. The indicator function for set A is denoted as 1. A Defined as:

[0051]

[0052] 5. First Quartile: A value in a dataset that represents 25% of the data that is less than or equal to this value.

[0053] 6. Third Quartile: A value in a dataset that indicates that 75% of the data are less than or equal to this value.

[0054] 7. Interquartile Range (IQR): The difference between the third quartile and the first quartile, used to measure the dispersion of data.

[0055] 8. Cross-validation: This is a statistical method used to evaluate the generalization ability of machine learning models. Its core idea is to divide the dataset multiple times, combining the data into different training and test sets, and repeat the training and validation process to reduce the dependence of the model evaluation results on a single data split.

[0056] 9. Gradual increase / decrease method: This is an experimental method used to determine the fatigue limit by gradually increasing or decreasing the load to determine the fatigue strength of a material.

[0057] 10. Cyclic Stress: refers to the stress applied to a material that changes periodically over time.

[0058] 11. Fatigue Failure: refers to the phenomenon where a material gradually accumulates damage under cyclic loading, eventually leading to fracture.

[0059] 12. Composite Material: It is composed of two or more materials with different properties and has excellent mechanical properties.

[0060] 13. Experimental Determination Method: This refers to the method of determining the properties or parameters of a material through experimental means.

[0061] 14. Load Level: refers to the intensity of stress or force applied to a material.

[0062] 15. Specimen: refers to the material or component used for testing in an experiment.

[0063] 16. Probability Distribution: A function that describes the possible values ​​of a random variable and their corresponding probabilities.

[0064] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a method for predicting the fatigue strength of a material according to an embodiment of this application. The method includes:

[0065] Step S101: Obtain the load level of each sample of the tested material.

[0066] In one embodiment, the load level of each specimen of the test material is obtained using a lifting method. For example, the test material is carbon steel, with an initial stress value of 260 MPa, a stress range of 10 MPa, and a set fatigue life of [missing information]. The process is repeated. Within the set fatigue life, if the specimen fails, the next specimen will have a lower stress level (one level lower than the previous one); if the specimen passes, the next specimen will have a higher stress level (one level higher than the previous one). The specific experimental conditions and methods are consistent with existing stress increase / decrease methods. The final fatigue limit curve for this material is shown below. Figure 2 As shown.

[0067] Step S102: Determine the global smoothing parameter with reference to the Gaussian kernel function based on the load level of each sample, and determine the smoothing parameter of each kernel function based on the global smoothing parameter.

[0068] In this embodiment, multiple kernel functions are preset. These kernel functions include at least the Gaussian kernel function, and may also include one or more combinations of the Epanechnikov kernel function, the double-weighted kernel function, the triangular kernel function, and the cosine kernel function. The specific expressions of each kernel function are as follows:

[0069] 1) Gaussian kernel function

[0070] (1-1)

[0071] 2) Epanechnikov kernel function

[0072] (1-2)

[0073] 3) Dual-weight kernel function

[0074] (1-3)

[0075] 4) Triangular kernel function

[0076] (1-4)

[0077] 5) Cosine kernel function

[0078] (1-5)

[0079] in, , It is the load level of all specimens. For the first The load level of each specimen, Let j be the smoothing parameter of the j-th kernel function. This is an indicator function that takes the value 1 when the condition is met, and 0 otherwise.

[0080] Among the five kernel functions mentioned above, the Gaussian kernel function is suitable for smooth distributions and performs well for continuously varying fatigue strength characteristics. The Epanechnikov kernel function has the best asymptotic mean square integral error and is suitable for situations requiring high-precision boundary processing. The dual-weight kernel function has stronger resistance to outliers and is suitable for fatigue data with high noise. The triangular kernel function is simple and efficient to calculate and is suitable for scenarios requiring fast processing. The cosine kernel function has good continuity and is suitable for distributions requiring smooth transitions. Those skilled in the art can select the required kernel function using the following two methods: 1) Select several kernel functions that are most likely to represent the material's fatigue distribution based on existing scientific literature, technical reports, etc., or based on publicly available experimental results and experience; 2) Randomly select multiple kernel functions from the above-mentioned kernel functions. Since the core innovation of this invention is to adaptively determine the potential fatigue distribution of materials through machine learning, the potential fatigue distribution of materials can be accurately estimated regardless of the method used to select the kernel function.

[0081] In one embodiment, a global smoothing parameter, referenced to a Gaussian kernel function, is determined based on the load level distribution, multimodal characteristics, and sample size of each specimen. Specifically, the formula for calculating the global smoothing parameter is:

[0082] (2-1)

[0083] in, For global smoothing parameters, The number of samples. The standard deviation of the sample. This is the interquartile range of the sample. For data feature adaptive coefficients, This is the distribution morphology adjustment factor for each sample. This is the adjustment factor for the multi-peak characteristics of each sample. This is the sample size adjustment factor for each sample.

[0084] Unlike conventional methods for calculating the smoothing parameters of Gaussian kernel functions, this application adds an adaptive coefficient for data features to the global smoothing parameters. The adaptive coefficient of this data feature It allows for adaptive adjustment based on the distribution characteristics of each specimen, such as the load level distribution pattern, multi-peak characteristics, and sample size, thereby obtaining the optimal smoothing parameters and achieving accurate estimation of the fatigue strength distribution of different materials.

[0085] In one embodiment, the distribution morphology adjustment factor The calculation formula is:

[0086] (2-2)

[0087] in, , For weight parameters, For sensitivity parameters, For sample skewness, For sample kurtosis, The number of samples. The standard deviation of all samples, For the first The load level of each specimen, This represents the average load water value for all samples. When the data distribution deviates from a normal distribution, Increasing the value causes a corresponding increase in the global smoothing parameter to cope with complex distribution characteristics.

[0088] Multi-peak characteristic adjustment factor The calculation formula is:

[0089] (2-3)

[0090] in, To adjust the intensity parameters for multiple peaks, It is a multi-peak characteristic index. The dip statistic is for all samples. To achieve the preset dip threshold, The dip statistic is an indicator function. It measures how much a set of univariate data deviates from a unimodal distribution; it is used to test whether the distribution of a dataset is unimodal. The dip critical value is a threshold used to determine whether the dip statistic is significant. When data exhibits obvious multimodal characteristics, Increasing the value makes the global smoothing parameter more suitable for capturing multi-peak structures.

[0091] Sample size adjustment factor The calculation formula is:

[0092] (2-4)

[0093] in, This represents the actual number of samples. For reference sample quantity, To adjust the index. When the sample size is small, Increasing the value increases the global smoothing parameter to reduce estimation fluctuations caused by small samples.

[0094] In one embodiment, the smoothing parameter of each kernel function is determined based on the global smoothing parameter and the ratio of the smoothing parameter of each kernel function to that of the Gaussian kernel function. Specifically, the formula for calculating the smoothing parameter of each kernel function is as follows:

[0095] (2-5)

[0096] in, The global smoothing parameter is... The smoothing parameter is the one corresponding to the j-th kernel function. It is the j-th kernel function. It is a Gaussian kernel function. It is the square integral of the kernel function. It is the second moment of the kernel function.

[0097] The square integral and second moment of the kernel function are common knowledge in the field of statistics and will not be elaborated here. To facilitate the use of the method of this invention, the second moment and square integral of the selected kernel function can be pre-calculated. Table 1 below shows the second moment and square integral of the aforementioned five kernel functions:

[0098] Table 1

[0099]

[0100] Step S103: Estimate the probability density function of the fatigue strength of the tested material based on each kernel function and the smoothing parameter of each kernel function.

[0101] In one embodiment, the expression for the probability density function based on kernel density estimation is:

[0102] (3)

[0103] in, It is the load level of all specimens. For the first The load level of each specimen, The number of kernel functions, The number of samples. The weight coefficients of the j-th kernel function are... Let j be the smoothing parameter of the j-th kernel function. Let j be the j-th kernel function.

[0104] The calculation method for the smoothing parameters of each kernel function has been given in step S102. To estimate the probability density function, it is necessary to estimate the weight coefficients of each kernel function. In this embodiment, the weight coefficients of each kernel function are determined based on the weight optimization method of cross-validation. The specific method is as follows:

[0105] First, define the objective function as the cross-validation error:

[0106] (4)

[0107] in, The number of samples. Based on removing the first All other samples and weight vectors after the first sample The obtained probability density function is The value at that location, Based on all samples and weight vectors The obtained probability density function is The value at that location.

[0108] Secondly, gradient-free optimization algorithms, such as evolutionary algorithms, genetic algorithms, and particle swarm optimization algorithms, are used to solve formula (4). Since the testing time required for each sample is relatively long when using the lifting method for fatigue testing, in order to shorten the testing time, formula (4) is solved once for each new sample, and this process is repeated until the number of samples meets the requirements.

[0109] Step S104: Calculate the expected value and standard deviation based on the estimated probability density function, and use the expected value and standard deviation as the estimated value and estimated standard deviation of the fatigue strength of the tested material, respectively.

[0110] Specifically, the expected value is the weighted average of all possible values ​​of the random variable (i.e., the fatigue strength of the tested material), with the weights being its probability density. It represents the long-term average or central position of the random variable; therefore, in this embodiment, the expected value is used as a predicted value of the fatigue strength of the tested material. The formula for calculating the expected value of the random variable X is:

[0111] (5)

[0112] in, The load level of the tested material. for The corresponding probability density.

[0113] Standard deviation is the square root of variance, used to measure the dispersion or volatility of a random variable's values ​​relative to its expected value. The formula for calculating standard deviation is:

[0114] (6)

[0115] Furthermore, the applicant uses the method of this invention in conjunction with commonly used industry methods such as DM (Degradation Modeling) and MLE (Maximum Likelihood Estimation) to simultaneously... Figure 2 The obtained experimental data were post-processed and compared with the fatigue strength reference values ​​of carbon steel in the publicly available materials database. The error of the average fatigue strength prediction and the error of the standard deviation of fatigue strength prediction for each method were calculated, as shown in Table 2 below.

[0116] Table 2

[0117]

[0118] As can be seen from Table 2, the error of the present invention is smaller than that of the other two methods, both in terms of the average value and the standard deviation of the fatigue strength prediction. In other words, the method of the present invention is more accurate in predicting the fatigue strength of materials compared to the two traditional methods mentioned above.

[0119] The fatigue strength prediction method for materials provided in this application first obtains the load level of each specimen of the tested material; then, based on the load level of each specimen, a global smoothing parameter with a Gaussian kernel function as a reference is determined, and the smoothing parameter of each kernel function is determined based on the global smoothing parameter; then, the probability density function of the fatigue strength of the tested material is estimated based on each kernel function and its smoothing parameter; finally, the expected value and standard deviation are calculated based on the estimated probability density function, and the expected value and standard deviation are used as the estimated value and estimated standard deviation of the fatigue strength of the tested material, respectively. This application's method designs an adaptive kernel density estimation framework, which not only overcomes the dependence of the traditional rise-fall method on probability distribution, but also achieves accurate capture of material fatigue characteristics through dynamically optimized smoothing parameters. Compared with the traditional rise-fall method, this application effectively improves the accuracy and reliability of the estimated average value and estimated standard deviation of fatigue strength. Furthermore, the advantages of this application's method are more obvious when the number of valid experimental specimens is larger; when the number of valid experimental specimens is small, the method of this application can still guarantee sufficient prediction accuracy and reliability.

[0120] According to an embodiment of this application, an electronic device is provided, such as... Figure 3This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device 100 may include a processor 10, a communication interface 30, a memory 20, and a communication bus. The processor 10, the communication interface 30, and the memory 20 communicate with each other through the communication bus. The processor 10 can call logical instructions in the memory 20 to execute the above-described method for predicting the fatigue strength of materials.

[0121] Furthermore, the logical instructions in the aforementioned memory 20 can be implemented as software functional units and sold or used as independent products, and can be stored on several computer-readable storage media. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the fatigue strength prediction method of the aforementioned materials of this application. The aforementioned storage media include: USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, optical disks, and other media capable of storing program code.

[0122] According to an embodiment of this application, a computer-readable storage medium of the type described above is provided. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor performs the steps of the fatigue strength prediction method for materials described above.

[0123] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a general-purpose hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to enable a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments.

[0124] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of variations or substitutions within the technical scope disclosed in this application. Therefore, any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the fatigue strength of a material, characterized in that, The method includes: (1) Presetting multiple kernel functions, including a Gaussian kernel function. Obtain the load level for each specimen of the tested material; Based on the load level of each specimen, a global smoothing parameter with reference to the Gaussian kernel function is determined, and based on the global smoothing parameter, the smoothing parameter of each kernel function is determined. The probability density function of the fatigue strength of the tested material is estimated based on each kernel function and the smoothing parameter of each kernel function. The expected value and standard deviation are calculated based on the estimated probability density function, and the expected value and standard deviation are used as the estimated value and estimated standard deviation of the fatigue strength of the tested material, respectively. The expression for the probability density function is: in, For the first The load level of each specimen, The number of kernel functions, The number of samples. The weight coefficients of the j-th kernel function are... Let j be the smoothing parameter of the j-th kernel function. Let j be the kernel function; The formulas for calculating the smoothing parameters of each kernel function are as follows: in, The global smoothing parameter is... The smoothing parameter is the one corresponding to the j-th kernel function. It is the j-th kernel function. It is a Gaussian kernel function. It is the square integral of the kernel function. It is the second moment of the kernel function.

2. The method according to claim 1, characterized in that, The multiple kernel functions also include one or more combinations of the Epanechnikov kernel function, the double-weighted kernel function, the triangular kernel function, and the cosine kernel function.

3. The method according to claim 1, characterized in that, The weight coefficients of each kernel function are determined based on the weight optimization method of cross-validation, and the objective function for optimization is: in, The number of samples. Based on removing the first All other samples and weight vectors after the first sample The obtained probability density function is The value at that location, Based on all samples and weight vectors The obtained probability density function is The value at that location.

4. The method according to any one of claims 1 to 3, characterized in that, The global smoothing parameters, determined based on the load levels of each specimen and referencing the Gaussian kernel function, include: Based on the load level distribution, multi-peak characteristics, and sample size of each sample, a global smoothing parameter with a Gaussian kernel function as a reference was determined.

5. The method according to claim 4, characterized in that, The formula for calculating the global smoothing parameter is as follows: in, The global smoothing parameter is... The number of samples. The standard deviation of the sample. This is the interquartile range of the sample. For data feature adaptive coefficients, This is the distribution morphology adjustment factor for each sample. This is the adjustment factor for the multi-peak characteristics of each sample. This is the sample size adjustment factor for each sample.

6. The method according to claim 5, characterized in that, The distribution pattern adjustment factor The calculation formula is: in, , For weight parameters, For sensitivity parameters, For sample skewness, For sample kurtosis, The number of samples. The standard deviation of all samples, For the first The load level of each specimen, The average load water value for all samples; The multi-peak characteristic adjustment factor The calculation formula is: in, To adjust the intensity parameters for multiple peaks, It is a multi-peak characteristic index. The dip statistic is for all samples. To achieve the preset dip threshold, For indicator functions; The sample size adjustment factor The calculation formula is: in, This represents the actual number of samples. For reference sample quantity, To adjust the index.

7. An electronic device, characterized in that, The method includes at least one processor and a memory communicatively connected to the at least one processor, the memory storing instructions executable by the at least one processor to enable the at least one processor to perform the method as described in any one of claims 1 to 6.

8. A computer storage medium, characterized in that, The computer storage medium stores instructions or programs that, when executed by at least one processor, cause the at least one processor to perform the method as described in any one of claims 1 to 6.

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