Crack propagation model data-driven modeling method suitable for additive metal

Abstract

The invention provides a crack propagation model data-driven modeling method suitable for additive metal, which belongs to the field of aircraft structure fatigue safety design research and comprises the steps of classification and combination of multi-source crack propagation experimental data, generation and evolution of alternative crack propagation models, model evaluation and staged strategy-guided population evolution. By introducing physical constraints, the alternative crack propagation model can obtain reasonable parameters even in the face of sparse data and perform prediction conforming to a crack propagation rule in an extrapolation area; a step-by-step characterization method of an alternative crack propagation model of first overall and then individual is constructed, the alternative crack propagation model firstly extracts an overall trend from all merged data containing multiple influence factors, and then overall trend constraint is introduced to carry out individualized characterization on data under different influence factors; therefore, more stable and reliable representation can be realized for sparse data under different influence factors. According to the method, a simple, high-generalization and stable crack propagation model can be directly learned from wide sparse data of multiple influence factors.

Description

Technical Field

[0001] This invention belongs to the field of aircraft structural fatigue safety design research, specifically involving a data-driven modeling method for crack propagation models applicable to additive metals. Background Technology

[0002] Metal additive manufacturing, through layer-by-layer fabrication, can efficiently produce structures with complex shapes, providing greater freedom in structural design and potentially revolutionizing structural design paradigms in critical fields such as aerospace. To fully unleash the potential of metal additive structures for load-bearing and other critical applications, rigorous and reliable structural durability and damage tolerance analysis and verification are essential prerequisites.

[0003] However, numerous studies have shown that the crack propagation performance of additive structures is influenced by multiple factors, exhibiting a high degree of dispersion. Establishing a comprehensive characterization of the crack propagation performance of additive structures, taking into account all influencing factors, presents significant challenges. On the one hand, the agile and flexible manufacturing methods, accompanied by complex processes, introduce more influencing factors into the structure's performance. Conducting sufficient crack propagation experiments to create an experimental database for all influencing factors is costly and unacceptable. On the other hand, stable quality control remains difficult to achieve at present, making it difficult to establish a stable and reliable correlation between process and quality in additive manufacturing. Even if a complete and sufficient characterization of crack propagation performance under individual additive processes is established, the credibility of its widespread application remains questionable.

[0004] Therefore, existing studies mostly control for variables under loading conditions, focusing on comparing the influence of different factors on crack propagation behavior. The data either only include a few stress ratios or are concentrated in specific crack propagation stages, which can be summarized as "the studied influencing factors are broad, but the data for a specific factor is sparse and incomplete." This poses a significant challenge to constructing characterization models for crack propagation performance in additive structures. First, existing classic crack propagation models do not specifically consider the characteristics of additive manufacturing processes in their structural forms, and their parameter determination relies on existing experience, making it impossible to obtain reliable references for additive crack propagation data. Second, data-driven modeling methods also face challenges in addressing this issue. Data under a single influencing factor is sparse, making it difficult to support the model's generalization ability; while data under multiple influencing factors are highly dispersed, making it difficult to directly utilize to improve the model's characterization ability.

[0005] Existing data-driven crack propagation model building methods include: acquiring multi-source crack propagation experimental data and classifying the data; acquiring an initial crack propagation model containing unknown correction terms; randomly constructing multiple functional expressions of the basis functions in the correction terms according to preset operators and terminators; substituting the constructed basis functions into the initial crack propagation model to obtain candidate crack propagation models; constructing an initial crack propagation model population from the candidate crack propagation models; using gene crossover and mutation behavior to evolve individuals in the initial crack propagation model population; fitting the model parameters of each individual based on the crack propagation experimental data of each classification; calculating the evaluation index of each individual to select the optimal crack propagation model. This invention has been verified to reliably learn a unified crack propagation model that meets the requirements based on multi-source crack propagation experimental data.

[0006] However, there are problems with learning a unified model from additive crack propagation data based on this method. This is because although the method has the ability to use multiple additive crack propagation datasets under different influencing factors as input to learn the model, the additive crack propagation experimental datasets often exhibit sparse and incomplete characteristics compared to experimental datasets under traditional processes. For example, some datasets only have data from a few stages, and some datasets only have data under a few stress ratio conditions. When the candidate crack propagation model is fitted to these sparse datasets, it is difficult to obtain reliable and reasonable parameters, which in turn affects the evaluation process of the candidate crack propagation model. Summary of the Invention

[0007] To address the bottleneck of constructing characterization models for crack propagation performance in additive manufacturing, this invention provides a data-driven modeling method for crack propagation models applicable to additive metals.

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

[0009] A data-driven modeling method for crack propagation models applicable to additive metals includes the following steps:

[0010] Step 1: Classify the additive crack propagation experimental data from multiple sources according to influencing factors, and merge all data into a full dataset;

[0011] Step 2: Under physical constraints, extract the overall trend of crack propagation from the full dataset. Using this overall trend of crack propagation as a reference, perform individualized parameter fitting on the classified experimental data to obtain individualized fitting results.

[0012] Step 3: Using the individualized fitting results as the evaluation basis, conduct multi-index evaluation on the candidate crack propagation model population, screen to obtain a unified model, and obtain the evaluation results;

[0013] Step 4: Based on the evaluation results, guide the evolution of the candidate crack propagation model population through a phased strategy until a simple, generalizable, and stable crack propagation model is obtained.

[0014] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described data-driven modeling method for crack propagation models applicable to additive metals.

[0015] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described data-driven modeling method for crack propagation models applicable to additive metals.

[0016] Beneficial effects:

[0017] Compared to previous methods, the focus of this invention is to help candidate crack propagation models achieve reasonable and reliable parameter fitting even when faced with sparse and incomplete data influenced by multiple factors, thereby enabling a reasonable evaluation of each candidate crack propagation model. In other words, the main innovations of this invention are: First, for incomplete experimental data concentrated in specific stages, physical constraints conforming to the laws of crack propagation behavior are established for candidate crack propagation models, enabling them to make reasonable predictions of extrapolated regions even when using only local data for parameter fitting. Second, for insufficient experimental data, such as only specific stress ratios or very few experimental data points, a step-by-step characterization method of "overall first, then individual" is constructed for candidate crack propagation models. The candidate crack propagation model first extracts the overall trend from all merged data containing multiple influencing factors, and then, based on this, performs individualized characterization of data under different influencing factors. Because the overall trend is introduced as a reference, the candidate crack propagation model can achieve a more stable and reliable characterization when faced with sparse data under different influencing factors. Attached Figure Description

[0018] Figure 1 This is a flowchart of a data-driven modeling method for crack propagation models applicable to additive metals according to the present invention;

[0019] Figure 2 An example schematic diagram for loading basis functions in an alternative crack propagation model;

[0020] Figure 3This is an example illustration of generating a new model through gene crossover; where (a) represents simulating "gene crossover" behavior by exchanging sub-model trees to generate two new model individuals; (b) represents simulating "gene mutation" behavior by changing sub-model trees to generate a new model individual; and (c) represents simulating "gene mutation" behavior by changing tree nodes to generate a new model individual.

[0021] Figure 4 A schematic diagram of the experimental dataset of crack propagation in AlSi10Mg under 23 different influencing factors;

[0022] Figure 5 Data from different influencing factors are merged into a full dataset, and the candidate crack propagation model first learns the overall trend surface diagram from it;

[0023] Figure 6 This is a schematic diagram of the three stages of crack propagation rate.

[0024] Figure 7 The diagrams illustrate the datasets under different influencing factors for the alternative crack propagation models; where, ( ) represents the experimental dataset j = 1-12;

[0025] Figure 8 The diagrams illustrate the datasets under different influencing factors for the alternative crack propagation models; where, ( ) represents the experimental dataset , j=13-23. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] like Figure 1 As shown, this invention provides a data-driven modeling method for crack propagation models in additive metals, comprising the following steps:

[0028] Step 1: Classification and merging of multi-source input data:

[0029] To enable the learned crack propagation model to predict crack propagation under varying load conditions, additive crack propagation data with different stress ratios under the same conditions are first merged. The crack propagation model is then required to characterize these data using the same parameters, allowing this set of parameters to be used for prediction under any stress ratio. Furthermore, since additive crack propagation data often exhibits sparse and incomplete characteristics under specific influencing factors, sparse data makes reliable parameter fitting difficult for the model, thus posing a challenge to model evaluation. Therefore, this invention adds a full dataset, which is a dataset formed by merging data under all different influencing factors. The candidate crack propagation model first learns the overall trend from this dataset. Based on this overall trend as a reference, the candidate crack propagation model can more reliably fit parameters when characterizing different datasets.

[0030] Step 2: Generation and updating of the candidate crack propagation model population:

[0031] In generating candidate crack propagation models, an initial crack propagation model is first obtained. This initial model includes a preset classic crack propagation model and preset correction terms. Then, various correction terms are generated based on a randomly generated model tree. These correction terms are substituted into the initial crack propagation model to obtain multiple differentiated candidate crack propagation models, forming a candidate crack propagation model population. In updating the candidate crack propagation models, a gene programming algorithm is used. A tournament algorithm is used to randomly select high-performing individuals from the candidate crack propagation model population as "parents." New model individuals are generated as "offspring" based on gene mutation and gene crossover, thus simulating the survival of the fittest in biological populations. Specifically, this includes:

[0032] Step 2.1: Construct an improved form of the initial crack propagation model based on the Paris model:

[0033] (1)

[0034] in, These are the variable parameters in the Paris model. Indicates the crack length. Indicates the number of fatigue load cycles. The differential symbol, This represents the amount of crack front extension after a single fatigue load cycle. The correction function for the Paris model is unknown and needs to be obtained through symbolic regression training, while the variables... It includes constant terms, variable parameters, and independent variables that represent the driving force for crack propagation. and . The range of stress intensity factor in a single fatigue load cycle. This represents the maximum stress intensity factor value in a single fatigue load cycle.

[0035] Furthermore, since most experimental data are represented in a double logarithmic coordinate system, formula (1) is transformed to a double logarithmic coordinate system as the structural form of the crack propagation model. At the same time, to facilitate a more consistent description of the variable parameters in the model below, a double logarithmic coordinate system is adopted. Corresponding substitution Formula (2) is obtained:

[0036] (2)

[0037] Furthermore, basis functions are used. ( Denotes any basis function, Linear combinations of ) are used to represent the unknown correction term. :

[0038] (3)

[0039] in, These are the newly introduced, undetermined variable parameters corresponding to these basis functions, where N1 represents the number of basis functions in each model individual. The random function in formula (3) The expression form is unknown and needs to be randomly constructed in step 2.2 based on the preset operators and preset terminators. In addition, the expression form of the correction term shown in formula (3) is predetermined by the engineer based on the knowledge of the crack propagation field. Depending on the actual needs, the expression form of the correction term can also be other forms. The form shown in formula (3) does not have a limiting effect.

[0040] Furthermore, due to directly using and When used as input, after complex calculations, formula (3) may contain confusing dimensions, which is detrimental to the interpretability of the model. Therefore, in this embodiment, [the following is omitted as the text is incomplete and cannot be translated]. and Dimensionless processing was performed, and with As a dimensionless input variable in the model:

[0041] (4)

[0042] in, For the two newly introduced undetermined parameters, this embodiment specifies... Having the same dimensions as the stress intensity factor, after processing with formula (4), formula (3) becomes a dimensionless correction function. Specifically, because... Having the same dimensions as the stress intensity factor, it is required that the model obtained after construction... It should meet certain physical constraints, therefore... The following constraints shall be imposed:

[0043] (5)

[0044] Therefore, the parameters currently included in formula (3) are: and These are all parameters that can change with experimental data, reflecting the dispersion of multi-source experimental data due to differences in experimental factors.

[0045] Furthermore, in order to reflect the constants that may appear in the crack propagation model, this invention uses randomly generated basis functions. Introducing symbols As representatives of constants in the model, their values, once determined, will not change with the data. This represents the maximum number of constants in an alternative crack propagation model.

[0046] Step 2.2: Construct diverse model correction terms based on the form of a model tree, and then substitute them into the initial crack propagation model to form diverse candidate crack propagation models, thereby forming a candidate crack propagation model population.

[0047] The function expression of various basis functions is randomly constructed based on preset operators and preset terminators. For example... Figure 2 As shown, the model It can be represented in the form of a model tree, where the edge nodes of the model tree are terminators represented by constants or variables, and the internal nodes of the model tree are operators represented by computation functions. In order to avoid blindly expanding the search space of the initial crack expansion model, the operators are determined to be addition, subtraction, multiplication, logarithm, and reciprocal functions (represented by the symbol "inv") based on domain knowledge.

[0048] Substituting the constructed basis functions into the initial crack propagation model yields several alternative crack propagation models; each alternative crack propagation model includes multiple unknown variable parameters; the variable parameters refer to the parameters in the alternative crack propagation models that change with experimental data.

[0049] Several candidate crack propagation models constitute an initial crack propagation model population; each candidate crack propagation model is regarded as an individual; each element of the basis function in the candidate crack propagation model is regarded as a gene; each element includes the operator and terminator in the constructed basis function.

[0050] Step 2.3: Update the model based on gene programming algorithms to achieve model population evolution:

[0051] Based on the crack propagation experimental datasets obtained from step 1, the representational ability of each candidate crack propagation model individual in the face of different experimental data can be examined, thereby measuring the performance differences among the candidate crack propagation models. Furthermore, following the biological principle of "survival of the fittest," poorly performing model individuals can be continuously eliminated, and new potentially superior model individuals can be generated based on the high-performing model individuals. Specifically, this invention uses a tournament method to randomly select high-performing model individuals as "parents," setting the tournament size (e.g., setting the tournament size to 100). Each time, 100 individuals are randomly selected from the current generation population to compete in the tournament. The individual with the best performance wins and is selected. The selected individual with the best performance in the tournament is then used to generate new individuals for the current generation through gene mutation / gene crossover / direct inheritance. Figure 3 (a) If the "gene crossover" method is used to generate new model individuals, two model individuals are selected from the tournament as parents. Their child model trees are exchanged to simulate the "gene crossover" behavior, thus forming two new model individuals. If the "gene mutation" method is used to generate new individuals, one model individual is selected from the tournament as a parent. The child model tree of this model is mutated to obtain a new model individual (e.g., ...). Figure 3 (b)), or the edge terminator node mutation of the model to obtain a new model individual (e.g. Figure 3 (c)). Figure 3 In this context, x and y represent individuals.

[0052] Step 3: For each candidate crack propagation model in the candidate crack propagation model population generated in Step 2, use it to represent each dataset, and obtain the mean squared error and model parameter fitting values ​​obtained from the representation. Further, establish an evaluation index for the candidate crack propagation model based on its representation performance on different datasets.

[0053] Step 3.1: Preliminary verification of candidate crack propagation models, removing redundant parameters to improve the robustness and reliability of parameter fitting.

[0054] Since the basis functions in formula (3) are randomly generated, they may be linearly correlated with each other and affect the parameter fitting. Therefore, we first test any two basis functions in formula (3). and Can it be simplified to the same expression (where...) , (used to indicate different basis functions), thereby removing identical basis functions and retrieving mutually independent variable parameters. Subsequently, the inspection and Can it be simplified to the same form to determine? Is the ratio related? If so, then let .

[0055] Step 3.2: In the evaluation process of the candidate crack propagation models, the candidate crack propagation models are first made to learn the overall trend of the data based on the full amount of data.

[0056] like Figure 4 As shown, based on the crack propagation performance data of all additive aluminum-silicon-magnesium alloys (AlSi10Mg) extracted from open-source data (Zhang, Z., Xu, Z. Fatigue database of additively manufactured alloys. Sci Data 10, 249 (2023). https: / / doi.org / 10.1038 / s41597-023-02150-x), following the data merging operation in step 1, 23 sets of crack propagation datasets under different influencing factors were finally obtained (e.g., Figure 4 ), used for learning crack propagation models, Figure 4 In the table, different colors represent different influencing factors. These data cover the impact of various factors on crack propagation rate, including additive manufacturing direction and heat treatment conditions. The differences in influencing factors across different datasets are shown in Table 1. It is important to note that the last column of Table 1 records six different additive manufacturing processes. These processes cannot be considered as having the same process parameters; therefore, data from different processes are not combined to represent different influencing factors. The differences in influencing factors reflected in the 23 datasets are shown in Table 1. Figure 5 As shown, they are first merged into a full dataset, from which each candidate crack propagation model first learns the overall trend of the data.

[0057] Table 1 shows the differences in influencing factors reflected in the 23 datasets.

[0058]

[0059] Step 3.2.1 Generate a test point space and introduce physical constraints on the candidate crack propagation model in the test point space so that the candidate crack propagation model's representation of the experimental data conforms to physical laws.

[0060] The characteristics exhibited by crack propagation performance data, as described in the international standard ASTM E647-24 for crack propagation testing, can generally be divided into three stages: the stage near the crack propagation threshold (Stage I), the stable crack propagation stage (Stage II), and the rapid crack propagation stage (Stage III).

[0061] like Figure 6As shown, in the three stages, the slope of the curves in stages I and III is generally higher than the slope of the curve in stage II. Meanwhile, in the context of... When characterizing crack propagation performance as a driving force, with Increase crack propagation rate It should also increase monotonically. Therefore, the physical constraints of the model in this invention are as follows:

[0062] (6)

[0063] in, This is used to represent the parameterized alternative crack propagation model defined in this invention. For the independent variables of the model defined above, This represents the test point. Formula (6) indicates the test point. The curve must exhibit a monotonically increasing trend, meaning that as the crack propagation driving force increases, the crack propagation rate will only increase. Test points Unlike actual experimental data points, the test points set in this invention are broader spatial sampling points within the model's domain, thereby imposing more comprehensive physical constraints across the entire domain during the model's parameter fitting process. By utilizing... and and stress ratio Relationship The test point space in formula (6) can be transformed to better define the test point space:

[0064] (7)

[0065] in, Used to represent the model At the test points The partial derivative of, For test points The equivalent representation of this allows for a more convenient definition of the range of test points. , Due to the diversity and complexity of the candidate crack propagation models, the domain of each candidate crack propagation model is not exactly the same. Therefore, only the test points that actually fall within the domain are used for actual physical constraint analysis.

[0066] To penalize points where physical constraints are not met at test points, this invention uses the Softplus function to penalize points with negative derivatives:

[0067] (8)

[0068] in, This represents the output value of the Softplus function, and the parameters are... Used to adjust the intensity of the punishment. Simultaneously, to ensure that the slopes of the curves in stages I and III are higher than the slope of the curve in stage I, this invention ultimately defines the physical constraint as follows:

[0069] (9)

[0070] in, Let it be denoted as the physical constraint term, the second term on the right side of the equals sign This indicates the test point that falls within Phase II. This is the index value of the Phase II test point. This refers to the number of these Phase II test points. The first term on the right-hand side of the equation... This indicates the test point that falls within phase I. Used to indicate these Phase I test points, The number of test points in these phases I, Used to represent the results obtained based on test points in Phase II. The average value. The third term on the right side of the equals sign. This indicates the test point that falls within Phase III. Used to indicate these Phase III test points, This represents the number of test points in Phase III. The first term on the right-hand side of the equation requires the model to be positioned at the Phase II test points, predicting the slope of the model. If the value is greater than 0, If less than 0, then Greater than 0, thus increasing physical constraints. The value. The second and third terms on the right-hand side of the equation additionally require the slope of the prediction model. The slope at the test points in Phase I and Phase III is higher than the average slope. Therefore, the model's predicted values ​​are required to meet the following conditions. Figure 6 The three-stage characteristics are shown. Specifically, Calculated based on test points in Phase II Average value:

[0071] (10)

[0072] in, Indicates the use of calculation The number of test points in stage II of the value, specifically, the number of test points in stage II with different stress ratios. The test points below are respectively according to Sort the data by size and select the middle 20% of test points for calculation. .

[0073] Furthermore, this invention employs a very simple yet efficient method to divide the test points into stages, applicable to any stress ratio. The following test points, according to The test points are sorted by size, and the first 5% are designated as Phase I test points, the last 5% as Phase III test points, and the rest as Phase II test points.

[0074] Step 3.2.2: The candidate crack propagation model is characterized in the context of the full dataset to obtain the fitting parameters as the overall data trend learned by the candidate crack propagation model.

[0075] Define the objective function when fitting the alternative crack propagation model to the full dataset. for:

[0076] (11)

[0077] The first term on the right side of the equation reflects the model's overall ability to represent all experimental data. These are experimental data values ​​for crack propagation rate in logarithmic coordinates. This indicates the total number of experimental data points. Indicates the experimental data points. The second term on the right-hand side of the equation represents the physical constraint penalty imposed on the model in the test point space, with a coefficient. This is used to adjust the strength of the penalty term. Meanwhile, to avoid parameter fitting getting trapped in local optima, this invention employs multiple initial parameters for parameter fitting.

[0078] Step 3.3: The alternative crack propagation models are based on the overall trend learned from the full dataset as a reference, and each dataset is characterized separately.

[0079] Step 3.3.1: Select candidate initial surface references. In Step 3.1.2, parameter fitting with multiple initial parameters may lead to the candidate crack propagation model learning multiple overall trend surfaces with similar objective function values. This invention selects several representative overall trend surfaces, and the candidate crack propagation model will use their corresponding parameters as multiple parameter initial values ​​to further personalize the representation of each dataset. Specifically, firstly, through clustering, based on the similarity of parameters, overall trend surfaces that are close in distance are grouped into the same class, and overall trend surfaces that are far apart are grouped into different classes. Secondly, from each class, the overall trend surface with the lowest objective function value in that class is selected as the candidate overall trend surface.

[0080] Step 3.3.2: Generate a test point space and apply physical constraints that conform to the crack propagation law to the parameter fitting process of the candidate crack propagation model representing a single dataset. The specific constraint method is the same as in step 3.1.1.

[0081] Step 3.3.3: Based on the overall trend learned from the full dataset by the alternative crack propagation model, introduce the overall trend constraint of the alternative crack propagation model in the process of representing individual data.

[0082] This invention establishes constraints by measuring the distance between the parameters represented by the candidate crack propagation model on a single dataset and the parameters of the overall trend surface. The overall trend learned from the merged data can be represented by a set of parameters. The above-described parameters are represented as follows: Adding a superscript "0" indicates the overall trend parameter:

[0083] (12)

[0084] Based on this set of parameters, the alternative crack propagation models were tested on datasets under various influencing factors. When performing the representation, the objective function can be as follows: Constraints between establishment and overall trend:

[0085] (13)

[0086] In this case, the first and second terms on the right side of the equal sign have the same meaning as the corresponding terms in formula (11), the difference being that the experimental data has been replaced with an experimental dataset under a specific influencing factor. , This represents the number of data points in the dataset. Specifically, the third term is used as a constraint on the alternative crack propagation model pair. When performing characterization, the specific model obtained by fitting should be based on the overall trend and should not deviate too far from it; the coefficients Used to control the strength of constraints. This invention defines an overall trend constraint. for:

[0087] (14)

[0088] in, The number of all parameters in the alternative crack propagation models. For the experimental dataset, alternative crack propagation models were developed. The One fitting parameter, The corresponding overall trend parameters are used. The candidate crack propagation models are then applied to the experimental dataset. All fitting parameters are denoted as a parameter vector. :

[0089] (15)

[0090] Because the actual x-coordinate in the double logarithmic coordinate system is... It means, and Since it has the dimension of stress intensity factor, the parameters in formulas (12) and (15) are... The constraints are also in logarithmic coordinates to maintain consistency.

[0091] Step 3.3.4 Starting from the parameters corresponding to different candidate overall trend surfaces, characterize different datasets respectively to obtain the characteristics of different datasets. The mean square error value (MSE) is denoted as .Pick The maximum value in the curve is denoted as the representation of the overall trend surface. Ultimately, different overall trend curves correspond to different representational expressions. Select the lowest representational value The situation serves as a characterization result for the candidate crack propagation model, and based on this, an evaluation index for the candidate crack propagation model is established.

[0092] Step 3.3.5 Establishment of evaluation indicators for alternative crack propagation models.

[0093] The evaluation metrics include model complexity, the number of variable parameters in the model, model fit, and the dispersion of the variation in the values ​​of the variable parameters.

[0094] Step 4: Guide the evolution of the model population based on a phased model selection strategy:

[0095] In step 3, multidimensional evaluation indicators were established for each candidate crack propagation model to fully reflect the performance of the candidate crack propagation model as a unified model. In order to enable the model population to eventually evolve into individual models that perform well in all evaluation indicators, a phased model selection strategy was adopted to guide the evolution of the model population.

[0096] The first stage of evolution is set to 30 generations, using a complexity of... with goodness of fit As a performance indicator for each candidate crack propagation model, the goal is to ensure that by the end of the first stage, the population contains as many models as possible that can fit the different labeled data well without being overly complex. As an example, a second stage of 10 generations of evolution is set. In this second stage, these models with strong fitting abilities are further screened, using complexity... The degree of dispersion of changes in the variable parameter values ​​of the model This serves as the evaluation metric for each candidate crack propagation model. In addition, it requires that all model individuals in the second-stage population... The value must not exceed 0.12 to further select candidate crack propagation models that fit well to different labeled data and have small fluctuations in the fitted parameters. As an example, a third-stage evolution of 10 generations is set, using a complexity of... With the number of variable parameters in the model This serves as the evaluation metric for each candidate crack propagation model. In addition, the third stage requires all model individuals in the population to... It must not exceed 0.12, and the value of all individual models must be [not specified]. The value must not exceed 2.0. Finally, a population of 2000 model individuals was used for symbolic regression. The model evolved for a total of 50 generations, yielding the optimal model individual:

[0097] (16)

[0098] This model describes the inherent similarity of data from different influencing factors using a unified model structure, and reflects the differences between different influencing factors through parameter variations. Its representation of different datasets is as follows: Figure 7 and Figure 8 As shown, this demonstrates that even with very limited experimental data, the parameter fitting process constructed in this paper can help to reasonably and reliably characterize candidate crack propagation models, thereby helping parametric signed regression methods to ultimately find a simple and generalizable unified crack propagation model. Among these, Figure 7 of( ) represents the experimental dataset j = 1-12; Figure 8 of( ) represents the experimental dataset , j=13-23.

[0099] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the data-driven modeling method for additive metal crack propagation model applicable to multi-factor sparse data.

[0100] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described data-driven modeling method for additive metal crack propagation models applicable to multi-factor sparse data.

[0101] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A data-driven modeling method for crack propagation model of additive metal, characterized in that, Includes the following steps: Step 1: Classify the additive crack propagation experimental data from multiple sources according to influencing factors, and merge all data into a full dataset; Step 2: Under physical constraints, extract the overall trend of crack propagation from the full dataset. Using this overall trend of crack propagation as a reference, perform individualized parameter fitting on the classified experimental data to obtain individualized fitting results. Step 3: Using the individualized fitting results as the evaluation basis, conduct multi-index evaluation on the candidate crack propagation model population, screen to obtain a unified model, and obtain the evaluation results; Step 4: Based on the evaluation results, guide the evolution of the candidate crack propagation model population through a phased strategy until a simple, generalizable, and stable crack propagation model is obtained.

2. The data-driven modeling method for crack propagation model suitable for additive metal according to claim 1, wherein, Step one involves classifying additive crack propagation experimental data from multiple sources according to influencing factors, including: first, merging experimental data with different stress ratios under the same process conditions into a group, and then keeping the data from different process conditions independent.

3. The data-driven modeling method for crack propagation model suitable for additive metal according to claim 2, wherein, The full dataset in step one is obtained by directly concatenating all the experimental data of the classification, and is used in step two to provide a unique and unified overall trend learning benchmark for the candidate crack propagation models.

4. The data-driven modeling method for crack propagation model suitable for additive metal of claim 1, wherein, The physical constraints in step two are established by forcing the crack propagation rate to increase monotonically with the driving force and conform to the three-stage slope characteristics within the test point space. The test point space covers the model domain and is independent of the experimental data points.

5. The data-driven modeling method for crack propagation model for additive metal according to claim 1, wherein, In step two, the individualized parameter fitting uses the overall trend parameter as the initial value and adds an overall trend distance constraint to the objective function to control the degree to which the fitting results of a single dataset deviate from the overall trend.

6. The data-driven modeling method for crack propagation models applicable to additive metals according to claim 1, characterized in that, The multi-index evaluation in step three considers model complexity, number of variable parameters, fitting error, and parameter variation dispersion, and uses the maximum error of all datasets as the unified evaluation benchmark for the model.

7. The data-driven modeling method for crack propagation models applicable to additive metals according to claim 1, characterized in that, The phased strategy in step four is as follows: the first phase uses complexity and fitting error for screening, the second phase uses complexity and parameter dispersion for further screening, and the third phase uses complexity and number of parameters for final screening. Each phase sets a decreasing upper limit for the maximum error.

8. The data-driven modeling method for crack propagation models applicable to additive metals according to claim 1, characterized in that, After the evolution in step four is completed, the candidate crack propagation model with the simplest structure and that satisfies all stage constraints is output as the final crack propagation model, which is used to uniformly predict the crack propagation behavior of additive metals under different influencing factors.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the data-driven modeling method for crack propagation models applicable to additive metals as described in any one of claims 1-8.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the data-driven modeling method for crack propagation models applicable to additive metals as described in any one of claims 1-8.

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