Intelligent structural ceramic strength prediction method and device based on statistical characteristics
By extracting statistical features from the three-dimensional information of pores in structural ceramics and training an intelligent model, the problem of insufficient prediction accuracy in existing technologies has been solved, and accurate prediction of strength attenuation caused by multiple defects has been achieved.
Patent Information
- Application Number
- CN202511679953.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-17
- Publication Date
- 2026-02-03
AI Technical Summary
Existing machine learning models rely on the extreme or mean values of pore parameters in predicting the strength of structural ceramics, ignoring complex pore combinations and their interactions. This results in insufficient accuracy and generalization ability of the prediction results, and makes it impossible to effectively evaluate the material fracture and strength reduction caused by multiple defects.
Three-dimensional information of internal pores in structural ceramics was obtained by nano-CT scanning. Statistical features were extracted, including pore size, shape, orientation, and spatial distribution. An intelligent strength prediction model was constructed, and an enhanced sample set was generated using the SMOTE method. The model was then trained using random forest, adaptive enhancement model, and extreme random tree regression model to select a high-precision prediction model.
It enables the comprehensive acquisition of pore structure characteristics without damaging the specimen, establishes a mapping relationship between pore statistical characteristics and bending strength, improves the accuracy and reliability of the prediction model, and can predict strength decay caused by multiple defects.
Smart Images
Figure CN121459989A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to an intelligent structural ceramic strength prediction method and device based on statistical characteristics, belonging to the field of material mechanical property evaluation technology. Background Technology
[0002] Structural ceramics are widely used in harsh service environments such as aerospace and energy equipment due to their excellent high-temperature stability, corrosion resistance, and high hardness. However, the inherent brittleness of ceramic materials and the unavoidable micropores within them severely affect their mechanical properties, resulting in significant dispersion in flexural strength and limiting their reliable engineering applications.
[0003] Existing research has shown that the size, shape, orientation, and spatial distribution of pores are crucial factors determining the strength and failure behavior of structural ceramics. For example, larger pores significantly reduce material strength, while sharp pores enhance local stress concentration, and different pore orientations lead to variations in crack propagation paths. To address complex pore problems, researchers have introduced statistical modeling methods, using log-normal distribution, Weibull distribution, and extreme value theory to describe pore size and defect characteristics, and attempting to establish strength models using these statistical parameters as predictive variables. This work has made some progress in quantifying the relationship between pore size and strength.
[0004] Meanwhile, with the development of artificial intelligence technology, machine learning, due to its advantages in high-dimensional data processing and nonlinear modeling, has been introduced into ceramic strength prediction. Scholars have already used methods such as μCT, deep neural networks, and convolutional neural networks to predict ceramic strength, and the coefficient of determination R0 for some results has been achieved. 2 The accuracy has reached above 0.9. However, the feature space of most existing machine learning models still mainly relies on the pore parameters after extreme value or mean processing, such as the maximum pore diameter, the average pore diameter, and the maximum sphericity of the pore. This data processing method obviously ignores the complex pore combinations and their interactions in real-world situations, and does not fully explore the intrinsic value of defect statistical distribution and spatial configuration. Therefore, when dealing with the more complex brittle fracture problem of ceramic materials, the accuracy and reliability of the prediction model still need to be further improved. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art: existing models generally rely on the extreme values or mean values of the pore parameters as input features, resulting in insufficient accuracy and generalization ability of the prediction results, and most of them reflect the strength reduction problem caused by a single defect, and cannot evaluate the material fracture and strength reduction problem caused by multiple defects.
[0006] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:
[0007] A method for predicting the strength of structural ceramics based on statistical features is provided, comprising the following steps:
[0008] Acquire three-dimensional information data of the internal pores of the ceramic structure under test;
[0009] Statistical features are extracted from the three-dimensional information data of the internal holes, and the results obtained after the statistical feature extraction are combined to obtain a statistical feature descriptor characterizing the distribution characteristics of the holes;
[0010] The intelligent strength prediction model is obtained, and the statistical feature descriptor is input into the intelligent strength prediction model. Based on the output of the intelligent strength prediction model, the strength prediction value of the ceramic structure to be tested is obtained.
[0011] Furthermore, the three-dimensional information data of the internal pores of the ceramic structure under test is obtained in the following way:
[0012] The ceramic structure under test is scanned using a nano-CT device, and the middle area of the sample span is selected as the scanning interval.
[0013] The intermediate region ranges from 30% to 60%, and the three-dimensional information data of the internal pores of the ceramic structure to be tested are the pores located in the region below the neutral layer.
[0014] Furthermore, the statistical feature extraction includes: fitting the pore size in the three-dimensional information data of the internal pores of the ceramic structure under test with a log-normal distribution, and describing the distribution characteristics with probability density function parameters, the corresponding probability density function being:
[0015] ;
[0016] Where D is the pore size, μ is the logarithmic mean of the pore size, and σ is the logarithmic standard deviation of the pore size.
[0017] Furthermore, the statistical feature extraction includes: representing the shape of the pores in the three-dimensional information data of the internal pores of the ceramic structure under test using sphericity, and fitting it with a Beta distribution. The probability density function corresponding to the sphericity of the pores is:
[0018] ;
[0019] Where S is the sphericity of the hole; B(S) α S β ) is the Beta function; S α and S β This indicates the shape parameters of the hole.
[0020] Furthermore, the statistical feature extraction includes: fitting the pore orientation in the three-dimensional information data of the internal pores of the ceramic structure under test using a Weibull distribution, and the probability density function corresponding to the pore orientation is:
[0021] ;
[0022] Where θ represents the angle between the major axis of the circumscribed ellipsoid of the hole and the direction of the bending load, A λ and A k This indicates the statistical characteristics of the hole orientation.
[0023] Furthermore, the statistical feature extraction includes: characterizing the spatial distribution of pores in the three-dimensional information data of the internal pores of the ceramic structure under test using the local Moran's I index to represent their aggregation; and taking the local Moran's I index for each pore in a sample and averaging the values. The expression for the local Moran's I index is as follows:
[0024] ;
[0025] in, Let be the diameter of the i-th hole. The average diameter of all holes. Let be the spatial weight between the i-th and j-th holes.
[0026] Furthermore, the results of statistical feature extraction from the three-dimensional information data of the internal pores also include:
[0027] The statistical characteristics include: the maximum radius of the hole, the average ratio of the projected length of the hole in the y and z directions, the average value of the hole center on the y-axis coordinate, and the location of the hole;
[0028] The formula for calculating the location of the hole is as follows:
[0029] Loc= ;
[0030] L is the span during the bending strength test, and t is the sample thickness. This represents the average value of the hole center on the x-axis. This represents the average value of the hole center on the z-axis coordinate.
[0031] The statistical feature descriptors are filtered using the Pearson correlation coefficient |r|=0.8 as a threshold, and the filtered statistical feature descriptors are input into the intelligent intensity prediction model.
[0032] Furthermore, the method for constructing the intelligent intensity prediction model includes:
[0033] An enhanced sample set was constructed using the SMOTE method and randomly divided into a training set and a test set in an 8:2 ratio.
[0034] Candidate models are constructed using a grid search combined with 10-fold cross-validation, including random forest, adaptive boosting, and extreme random tree regression models.
[0035] The candidate models are trained, evaluated, and screened using the training and test sets, and the screened candidate models are used as the intelligent strength prediction models.
[0036] The SMOTE method generates enhanced samples based on the original samples through interpolation, and then divides the original samples and enhanced samples into training and testing sets.
[0037] Furthermore, evaluating and screening candidate models includes: evaluating and screening models by obtaining model evaluation metrics;
[0038] The model evaluation metrics include: mean absolute error, coefficient of determination, and root mean square error.
[0039] The formula for calculating the mean absolute error (MAE) is as follows:
[0040] ;
[0041] The formula for calculating the coefficient of determination R² is as follows:
[0042] ;
[0043] The formula for calculating the root mean square error (RMSE) is as follows:
[0044] ;
[0045] Where n is the number of samples. Let y be the intensity prediction value for the i-th sample. i Let i be the true intensity value of the i-th sample. This represents the average sample intensity.
[0046] Secondly, an intelligent structural ceramic strength prediction device based on statistical characteristics is provided, employing the intelligent structural ceramic strength prediction method based on statistical characteristics as described in the first aspect.
[0047] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:
[0048] This invention comprehensively acquires geometric information such as the size, shape, orientation, and spatial distribution of internal pores in structural ceramic samples through non-destructive scanning. Statistical feature extraction and enhancement are then performed on this information to construct a set of statistical features reflecting the structural characteristics of the pores without damaging the sample. Simultaneously, by establishing and training an intelligent strength prediction model, the mapping relationship between the statistical characteristics of structural ceramic pores and bending strength is realized, demonstrating the strength attenuation fracture caused by multiple defects. This allows the model to output strength prediction results based on the statistical characteristics of the sample. Attached Figure Description
[0049] Figure 1 The diagram shown is a flowchart of the intelligent structural ceramic strength prediction method based on statistical features provided in a specific embodiment of the present invention.
[0050] Figure 2 The diagram shows the non-destructive testing process and typical fracture morphology of the intelligent prediction method for the bending strength of structural ceramics provided in a specific embodiment of the present invention.
[0051] Figure 3 The image shown is a scatter plot of predictions from the Random Forest (RF) model provided in a specific embodiment of the present invention.
[0052] Figure 4 The figure shows a performance comparison between the model provided in the specific embodiment of the present invention and existing prediction models, as well as the fracture morphology of different fracture mechanisms. Detailed Implementation
[0053] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.
[0054] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.
[0055] This embodiment provides an intelligent structural ceramic strength prediction method based on statistical features, such as... Figure 1As shown, the first step is to obtain three-dimensional information data of the internal pores of the ceramic structure under test. Specifically, the sintered Si3N4 ceramic is processed into a standard rod-shaped sample of 5mm × 6mm × 48mm. Then, the ceramic structure under test is scanned using a nano-CT device, with the middle region of the sample span selected as the scanning interval. Specifically, nano-CT is used to scan and extract the spatial distribution information of the pores. The detection area covers the portion below the neutral layer (tensile stress zone) under bending loading to ensure the representativeness of the pore data. It should be noted that the range of the middle region is 30%–60%. Figure 2 As shown in the figure, (a) is a SEM image of the ceramic surface, (b) is a SEM image of the ceramic fracture surface, (c) is a physical diagram of the non-destructive testing process, and (d) is a schematic diagram of the fracture area in the strength test.
[0056] Based on the hole information extracted by non-destructive testing, statistical features are extracted from the three-dimensional information data of the internal holes. Specifically, statistical feature parameters are extracted for hole size, shape, orientation and spatial distribution. The results obtained after statistical feature extraction are combined to obtain a statistical feature descriptor characterizing the hole distribution characteristics.
[0057] Specifically, the results of the extracted statistical feature parameters include, but are not limited to: the radius R of the circumscribed sphere of the hole, the equivalent diameter deq of the hole (the diameter of the circle with the same projected area as the hole), and the projected area S of the hole. xy (i.e., the projected area of the hole in the xy plane), the convexity area of the hole (the area of the smallest convex polygon region surrounding the hole), the perimeter C of the hole, and the sphericity S of the hole. w (i.e., the ratio between the surface area of a sphere with the same volume as the hole and the surface area of the hole), hole location X (i.e., the coordinate value of the hole center on the x-axis), hole location Y (i.e., the coordinate value of the hole center on the y-axis), hole location Z (i.e., the coordinate value of the hole center on the z-axis), hole projection size L. y (i.e., the projection of the hole boundary dimensions onto the y-axis in the coordinate system), and the hole projection dimensions L. z (i.e., the projection of the hole boundary dimensions onto the z-axis in the coordinate system), and the projected area S of the hole. xy (i.e., the projected area of the hole in the xy plane), the projected area S of the hole xz (i.e., the projected area of the hole in the xz plane) and the projected area S of the hole yz (That is, the projected area of the hole on the yz plane).
[0058] Based on the extracted information, the statistical fitting feature values obtained through statistical fitting were preprocessed using a standardization method, and the linear correlation between all candidate features was evaluated. Using the Pearson correlation coefficient |r|=0.8 as a threshold, feature pairs with correlations higher than this value were optimized and integrated. Finally, 10 features with rich information content, strong expressive power, and high linear independence (including the logarithm and standard deviation D of the diameter distribution) were selected. shape The logarithmic mean exponent D of the diameter distribution scale The degree of concentration of sphericity S α and S β The degree of dispersion and alignment trend of hole orientation A k Mean angle of the hole A λ Does all the pore spaces exhibit a clustering or dispersion trend? (M) I The maximum radius value R of the hole max The average value L of the ratio of the projected lengths of the hole in the y and z directions y / L z The average value of the hole center on the y-axis coordinate Y avg The location of the hole, etc., are used as structural representation variables as input to the machine learning model. The calculation expression for the location of the hole is as follows:
[0059]
[0060] Where Loc represents the location of the hole, L is the span of the three-point bending strength test, t is the thickness of the ceramic structure under test, x is the average value of the hole center on the x-axis coordinate, and z is the average value of the hole center on the z-axis coordinate.
[0061] Specifically, in this embodiment, a statistical feature extraction method for pore size is provided: the pore size in the three-dimensional information data of the internal pores of the ceramic structure to be tested is fitted with a log-normal distribution, and the distribution characteristics are described by probability density function parameters. The corresponding probability density function is:
[0062] ;
[0063] Where D is the pore size, μ is the logarithmic mean of the pore size, and σ is the logarithmic standard deviation of the pore size.
[0064] In this embodiment, a statistical feature extraction method for pore shape is provided: the pore shape in the three-dimensional information data of the internal pores of the ceramic structure under test is represented by sphericity, and fitted by a Beta distribution. The probability density function corresponding to the sphericity of the pores is:
[0065] ;
[0066] Where S is the sphericity of the hole; B(S) α Sβ ) is the Beta function; S α and S β This indicates the shape parameters of the hole.
[0067] In this embodiment, a statistical feature extraction method for pore orientation is provided: the pore orientation in the three-dimensional information data of the internal pores of the ceramic structure under test is fitted with a Weibull distribution, and the probability density function corresponding to the pore orientation is:
[0068] ;
[0069] Where θ represents the angle between the major axis of the circumscribed ellipsoid of the hole and the direction of the bending load, A λ and A k This indicates the statistical characteristics of the hole orientation.
[0070] In this embodiment, a statistical feature extraction method for the spatial distribution of pores is provided: the spatial distribution of pores in the three-dimensional information data of the internal pores of the ceramic structure under test is characterized by the local Moran's I index, and in a sample, the local Moran's I index is taken for each pore and the average value is calculated. The expression corresponding to the local Moran's I index is:
[0071] ;
[0072] in, Let be the diameter of the i-th hole. The average diameter of all holes. Let be the spatial weight between the i-th and j-th holes.
[0073] A SMOTE-like interpolation enhancement method is constructed and trained. The method includes: constructing an enhancement sample set using the SMOTE method and randomly dividing it into a training set and a test set in an 8:2 ratio.
[0074] Candidate models are constructed using a grid search combined with 10-fold cross-validation, including random forest, adaptive boosting, and extreme random tree regression models.
[0075] The candidate models are trained, evaluated, and screened using the training and test sets, and the screened candidate models are used as the intelligent strength prediction models.
[0076] The SMOTE method generates enhanced samples based on the original samples through interpolation, and then divides the original samples and enhanced samples into training and testing sets.
[0077] The screening process requires obtaining model evaluation metrics, which include: mean absolute error, coefficient of determination, and root mean square error.
[0078] Specifically, this embodiment also provides a calculation expression for the mean absolute error (MAE):
[0079] ;
[0080] The formula for calculating the coefficient of determination R² is as follows:
[0081] ;
[0082] The formula for calculating the root mean square error (RMSE) is as follows:
[0083] ;
[0084] Where n is the number of samples. Let be the predicted intensity value of the i-th sample, and yi be the true intensity value of the i-th sample. This represents the average sample intensity.
[0085] Based on actual test data, the specific steps are as follows: Based on the original 12 samples, 100 enhanced samples are generated using the SMOTE method. The original samples and enhanced samples are merged and then randomly divided into training set and test set in an 8:2 ratio.
[0086] The parameter ranges for algorithm tuning are shown in Table 1:
[0087]
[0088] Table 1
[0089] As shown in Table 2, this embodiment also provides performance comparison results for other models:
[0090]
[0091] Table 2
[0092] It should be noted that the smaller the RMSE and MAE values, the better the R... 2 The closer the value is to 1, the better the accuracy and generalization of the model. Based on this, a better algorithm is selected as the intelligent prediction model.
[0093] Specifically, for the three high-performing algorithms—Random Forest (RF), Adaptive Boosting (AdaBoost), and Extra TreesRegressor (ETR)—we employ random forest, adaptive boosting, and extreme random tree regression, respectively, to optimize parameters using grid search and construct models. The selection is based on the model's generalization ability. Figure 3As shown, the average absolute error and average relative error are 31.4 MPa and 4.3%, 34.6 MPa and 4.7%, and 33.7 MPa and 4.8%, respectively. Taking all factors into consideration, the Random Forest (RF) algorithm is adopted as the final intelligent prediction model for the strength of structural ceramics.
[0094] like Figure 4 As shown, through actual sample strength testing and application of D shape M I The description revealed that both methods can effectively understand the bending fracture behavior of ceramics and predict strength values. Strength prediction for the sample was 676 MPa, while strength testing yielded a value of 671 MPa, with an error of only 0.7%. Furthermore, considering the presence of several samples with cracks caused by multiple crack initiations, the new model effectively avoids errors, resulting in results closer to reality.
[0095] This embodiment also provides an intelligent structural ceramic strength prediction device based on statistical features, which is implemented using the intelligent structural ceramic strength prediction method based on statistical features provided in this embodiment.
[0096] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for predicting the strength of structural ceramics based on statistical characteristics, characterized in that: Includes the following steps: Acquire three-dimensional information data of the internal pores of the ceramic structure under test; Statistical features are extracted from the three-dimensional information data of the internal holes, and the results obtained after the statistical feature extraction are combined to obtain a statistical feature descriptor characterizing the distribution characteristics of the holes; The intelligent strength prediction model is obtained, and the statistical feature descriptor is input into the intelligent strength prediction model. Based on the output of the intelligent strength prediction model, the strength prediction value of the ceramic structure to be tested is obtained.
2. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 1, characterized in that, The three-dimensional information data of the internal pores of the ceramic structure under test is obtained through the following method: The ceramic structure under test is scanned using a nano-CT device, and the middle area of the sample span is selected as the scanning interval. The intermediate region ranges from 30% to 60%, and the three-dimensional information data of the internal pores of the ceramic structure to be tested are the pores located in the region below the neutral layer.
3. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 2, characterized in that, The statistical feature extraction includes: fitting the pore size in the three-dimensional information data of the internal pores of the ceramic structure under test with a log-normal distribution, and describing the distribution characteristics with probability density function parameters. The corresponding probability density function is: ； Where D is the pore size, μ is the logarithmic mean of the pore size, and σ is the logarithmic standard deviation of the pore size.
4. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 2, characterized in that, The statistical feature extraction includes: representing the shape of the pores in the three-dimensional information data of the internal pores of the ceramic structure under test using sphericity, and fitting it with a Beta distribution. The probability density function corresponding to the sphericity of the pores is: ； Where S is the sphericity of the hole; B(S) α S β ) is the Beta function; S α and S β This indicates the shape parameters of the hole.
5. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 2, characterized in that, The statistical feature extraction includes: fitting the pore orientation in the three-dimensional information data of the internal pores of the ceramic structure under test using a Weibull distribution, and the probability density function corresponding to the pore orientation is: ； Where θ represents the angle between the major axis of the circumscribed ellipsoid of the hole and the direction of the bending load, A λ and A k This indicates the statistical characteristics of the hole orientation.
6. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 2, characterized in that, The statistical feature extraction includes: characterizing the spatial distribution of pores in the three-dimensional information data of the internal pores of the ceramic structure under test using the local Moran's I index to represent their aggregation; and taking the local Moran's I index for each pore in a sample and averaging the values. The expression for the local Moran's I index is as follows: ； in, Let be the diameter of the i-th hole. The average diameter of all holes. Let be the spatial weight between the i-th and j-th holes.
7. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claims 3-6, characterized in that, The results of statistical feature extraction from the three-dimensional information data of internal pores also include: The maximum radius of the hole, the average ratio of the projected length of the hole in the y and z directions, the average value of the hole center on the y-axis coordinate, and the location of the hole; The formula for calculating the location of the hole is as follows: Place= ; L is the span during the bending strength test, and t is the sample thickness. This represents the average value of the hole center on the x-axis. This represents the average value of the hole center on the z-axis coordinate. The statistical feature descriptors are filtered using the Pearson correlation coefficient |r|=0.8 as a threshold, and the filtered statistical feature descriptors are input into the intelligent intensity prediction model.
8. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 1, characterized in that, The method for constructing the intelligent intensity prediction model includes: An enhanced sample set was constructed using the SMOTE method and randomly divided into a training set and a test set in an 8:2 ratio. Candidate models are constructed using a grid search combined with 10-fold cross-validation, including random forest, adaptive boosting, and extreme random tree regression models. The candidate models are trained, evaluated, and screened using the training and test sets, and the screened candidate models are used as the intelligent strength prediction models. The SMOTE method generates enhanced samples based on the original samples through interpolation, and then divides the original samples and enhanced samples into training and testing sets.
9. The intelligent structural ceramic strength prediction method based on statistical characteristics according to claim 8, characterized in that, Evaluating and screening candidate models includes: evaluating and screening models by obtaining model evaluation metrics; The model evaluation metrics include: mean absolute error, coefficient of determination, and root mean square error. The formula for calculating the mean absolute error (MAE) is as follows: ； The formula for calculating the coefficient of determination R² is as follows: ； The formula for calculating the root mean square error (RMSE) is as follows: ； Where n is the number of samples. Let be the predicted intensity value of the i-th sample, and yi be the true intensity value of the i-th sample. This represents the average sample intensity.
10. An intelligent structural ceramic strength prediction device based on statistical characteristics, characterized in that, The method for predicting the strength of structural ceramics based on statistical features, as described in any one of claims 1-9, is adopted.