Ardealite concrete strength prediction method based on dynamic weighted transfer learning

Abstract

The invention relates to a dynamic weighted transfer learning-based ardealite concrete strength prediction method, which comprises the following steps of: collecting conventional concrete data of a source domain and ardealite concrete data of a target domain, and realizing cross-domain feature alignment through feature expansion and deletion; utilizing a self-service resampling technology to generate an enhanced sample conforming to a real mix proportion constraint so as to expand the sample size of the target domain; an error-driven dynamic weight calculation mechanism is constructed, and a weighted mean square error loss function based on dynamic weight adjustment is adopted, so that the model learns a general material strength rule in source domain big data, and meanwhile, the fitting capability of a target domain small sample high-error region is enhanced; and knowledge migration is realized through cross-domain joint training, and finally, visual charts such as an intensity prediction result and a feature action mechanism are output. The technical problems that in existing ardealite concrete strength prediction, cross-material domain migration is difficult, and small samples are under-fitted are solved, and the precision of the prediction model is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of civil engineering material strength prediction, and in particular to a phosphogypsum concrete strength prediction method based on dynamic weighted transfer learning. Background Art

[0002] The global stockpile of industrial phosphogypsum has exceeded 7 billion tons, and its resource utilization has become a key path to achieving the "dual carbon" strategic goals. Replacing phosphogypsum with traditional cementitious materials or aggregates in concrete production has attracted widespread attention from academia and engineering communities in recent years, as it not only disposes of large amounts of industrial solid waste but also reduces natural resource consumption and carbon emissions. In the mix design of phosphogypsum concrete, compressive strength is a core mechanical parameter, and its prediction accuracy directly determines the feasibility of the material's engineering application.

[0003] Traditional strength prediction theories are primarily based on the assumption of linear component superposition, lacking the ability to explain the nonlinear coupling between phosphogypsum, cement, and aggregate. Machine learning techniques offer a new approach to unlocking these multi-component nonlinear relationships. However, existing research has largely relied on conventional concrete data. Limited by small sample sizes in the phosphogypsum system, this often leads to underfitting models due to data scarcity, making it difficult to meet engineering-level prediction accuracy requirements.

[0004] Transfer learning, with its ability to transfer knowledge across domains, offers the potential to overcome data barriers in phosphogypsum concrete. However, existing methods face two limitations: First, small-sample data augmentation techniques face an adaptability bottleneck. Pseudosamples generated by traditional oversampling methods easily violate the conservation laws of material components, resulting in samples that fail to meet the basic laws of materials science. Second, fixed weight allocation strategies struggle to adapt to the dynamic evolution of samples in blind spots in the target domain. This inability to effectively capture the nonlinear coupling effects between phosphogypsum's unique characteristics and the lack of a dynamic adjustment mechanism driven by error feedback results in inefficient cross-domain knowledge transfer. These technical bottlenecks severely restrict the generalization ability of prediction models in small-sample scenarios.

[0005] Therefore, current research urgently needs to construct a new strength prediction method suitable for phosphogypsum concrete to solve the problem of insufficient prediction accuracy under small sample conditions and provide a theoretical basis for the development of new prediction models.

[0006] The defects of the prior art are:

[0007] 1. Traditional strength prediction theory is mainly based on the assumption of linear superposition of components, and lacks the ability to explain the nonlinear coupling between phosphogypsum, cement and aggregate.

[0008] 2. Machine learning technology provides a new approach to deciphering the nonlinear relationships among multiple components. However, existing studies are mostly based on conventional concrete data. Limited by small sample sizes in the phosphogypsum system, data scarcity often leads to underfitting of the model, making it difficult to meet engineering-level prediction accuracy requirements. Summary of the Invention

[0009] In response to the above problems, the present invention provides a method for predicting the strength of phosphogypsum concrete based on dynamic weighted transfer learning, which aims to solve technical problems such as difficulty in cross-material domain migration and underfitting of small samples in existing phosphogypsum concrete strength prediction; cross-domain knowledge transfer is achieved through feature space alignment, self-service resampling data enhancement, dynamic weight calculation and weighted loss optimization, and a high-precision model for predicting the strength of phosphogypsum concrete is constructed.

[0010] In order to solve the above problems, the technical solution provided by the present invention is:

[0011] A method for predicting the strength of phosphogypsum concrete based on dynamic weighted transfer learning is characterized by comprising the following steps:

[0012] S100. Collect source domain data and target domain data; wherein the source domain data is large-sample conventional concrete data, the features of the large-sample conventional concrete data include conventional concrete parameters, and the sample size of the large-sample conventional concrete data is no less than a manually preset large sample size threshold; the target domain data is small-sample phosphogypsum concrete data, the features of the small-sample phosphogypsum concrete data include phosphogypsum concrete parameters, and the sample size of the small-sample phosphogypsum concrete data is no less than a manually preset small sample size threshold;

[0013] S200. Align the cross-domain features between the source domain and the target domain; add the target domain-specific features of the dataset of the small sample phosphogypsum concrete data in the target domain to the dataset of the large sample conventional concrete data in the source domain, and fill the missing values ​​of the added features with 0; at the same time, delete the source domain-specific features in the source domain to ensure that the features of the source domain are exactly the same as those of the target domain;

[0014] S300. Execute the self-service resampling data enhancement process; use the self-service resampling technology to expand the target domain training set and generate enhanced samples that meet the mix ratio constraints;

[0015] S400. Constructing a dynamic weighted transfer learning algorithm framework; the dynamic weighted transfer learning algorithm framework includes a dynamic weight calculation process and a weighted loss function optimization process;

[0016] S500. Execute a cross-domain joint training process; during training, uniformly assign a basic weight to the samples of the source domain, wherein the basic weight value is 1; obtain a dynamic weight for the enhanced samples of the target domain according to the error ratio; and adjust the loss function according to the dynamic weight;

[0017] S600. Output strength prediction results and visualization charts of feature action mechanisms; based on the trained transfer learning model, predict the strength of phosphogypsum concrete according to the input mix ratio; combined with SHAP interpretability analysis, output visualization charts such as feature importance analysis charts and SHAP coupling charts.

[0018] Preferably, the conventional concrete parameters include but are not limited to cement, water, aggregate, water reducer, and age, and the label is compressive strength; the phosphogypsum concrete parameters include but are not limited to phosphogypsum, cement, water, aggregate, water reducer, and age, and the label is the compressive strength.

[0019] Preferably, all the source domain data are divided into a training set for model training; the target domain data are divided into a 60% training set, a 20% validation set, and a 20% test set using a random sampling principle; the training set is used to learn model parameters by fitting the data to minimize prediction errors; the validation set is used to adjust hyperparameters and monitor the training process during model development; the test set is completely independent of the training and tuning process, and is used to ultimately evaluate the generalization performance of the model on unseen data, providing objective performance indicators.

[0020] Preferably, the bootstrap resampling technique is a statistical inference method based on empirical distribution, the goal of which is to generate a large number of simulated sample sets from the original data set through repeated sampling with replacement, thereby expanding the data.

[0021] Preferably, the self-service resampling technique comprises the following steps:

[0022] Sa100. Establish an independent and identically distributed data set, wherein the independent and identically distributed data set obeys an unknown distribution; the independent and identically distributed data set is expressed as follows:

[0023] D={x1,x2,…,x n}

[0024] Wherein: D is used to characterize the independent and identically distributed data set;

[0025] Sa200. Bootstrap resampling constructs an empirical distribution function as an approximation of the unknown distribution, which is expressed as follows:

[0026]

[0027] in: Used to characterize the empirical distribution function; I is used to characterize the indicator function;

[0028] Sa300. Based on the empirical distribution function, a preset number of samples are extracted from the independent and identically distributed data set with replacement each time to generate a bootstrap sample set; the bootstrap sample set is expressed as follows:

[0029]

[0030] Wherein: D* is used to characterize the self-help sample set;

[0031] The probability mass function of the bootstrap sample set satisfies the following formula:

[0032]

[0033] Sa400. Repeat steps Sa100 to Sa300 to the target number of times, and then generate the target number of independent self-service sample sets; expand the data distribution from the empirical distribution function to the empirical distribution function after amplifying the target number of times, thereby expanding the data by the target number of times.

[0034] Preferably, the dynamic weight calculation formula in the dynamic weight calculation process is expressed as follows:

[0035] w i =β+γ·e i / max(e),i=1,2,...,N

[0036] Among them, e i Used to represent the absolute value of the prediction error of the i-th sample; β and γ are used to represent hyperparameters, with β = 2 and γ = 3; max(e) is used to represent the error normalization factor; N is used to represent the number of samples.

[0037] Preferably, the weighted loss function optimization process refers to using the weighted mean square error as the optimization target of the model, and the calculation formula of the weighted mean square error is expressed as follows:

[0038]

[0039] in, Used to characterize the loss function; w i The weight used to represent the i-th sample; y i and They are used to represent the true value and predicted value of the sample label respectively.

[0040] Preferably, the large sample size threshold in step S100 is 500; the small sample size threshold is 15.

[0041] Preferably, the sample expansion multiple of the target domain training set expanded in step S300 is no less than 4 times.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] (1) The self-service resampling data augmentation technology breaks through the limitations of traditional oversampling methods and significantly expands the training samples in the target domain while maintaining the constraints of the true sample ratio, successfully solving the problem of model underfitting under extremely small sample conditions;

[0044] (2) The dynamic weighted transfer learning algorithm framework adjusts the sample weight distribution in real time through error feedback, so that the model can not only learn the general rules of the source domain but also adapt to the unique rules of the target domain, achieving a significant reduction in the root mean square error of the target domain test set and a significant improvement in prediction accuracy.

[0045] (3) The integration of SHAP interpretability analysis method can reveal the nonlinear coupling effect of the unique characteristics of phosphogypsum concrete on strength, providing a theoretical basis for the design of high-dosage phosphogypsum concrete mix ratio in industrial scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of a dynamic weighted transfer learning model provided by an embodiment of the present invention.

[0047] Figure 2 Schematic diagram of the feature importance ranking output by the dynamic weighted transfer learning model provided in an embodiment of the present invention.

[0048] Figure 3 Schematic diagram of the SHAP overview graph output by the dynamic weighted transfer learning model provided in an embodiment of the present invention.

[0049] Figure 4 Schematic diagram comparing the prediction results of the dynamic weighted transfer learning model provided by an embodiment of the present invention and the baseline model. DETAILED DESCRIPTION

[0050] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0051] A method for predicting the strength of phosphogypsum concrete based on dynamic weighted transfer learning is characterized by comprising the following steps:

[0052] S100. Collect source domain data and target domain data; wherein the source domain data is large-sample conventional concrete data, the features of the large-sample conventional concrete data include conventional concrete parameters, and the sample size of the large-sample conventional concrete data is not less than a manually preset large sample size threshold; the target domain data is small-sample phosphogypsum concrete data, the features of the small-sample phosphogypsum concrete data include phosphogypsum concrete parameters, and the sample size of the small-sample phosphogypsum concrete data is not less than a manually preset small sample size threshold.

[0053] S200. Align the cross-domain features between the source domain and the target domain; add the target domain-specific features of the data set of the small sample phosphogypsum concrete data in the target domain to the data set of the large sample conventional concrete data in the source domain, and fill the missing values ​​of the added features with 0; at the same time, delete the source domain-specific features in the source domain to ensure that the features of the source domain are exactly the same as those of the target domain.

[0054] S300. Execute the self-service resampling data enhancement process; use the self-service resampling technology to expand the target domain training set and generate enhanced samples that meet the mix ratio constraints.

[0055] S400. Construct a dynamic weighted transfer learning algorithm framework; the dynamic weighted transfer learning algorithm framework includes a dynamic weight calculation process and a weighted loss function optimization process; the model realizes cross-domain knowledge transfer through a closed-loop "error perception-weight allocation-loss optimization" iterative mechanism.

[0056] S500. Execute the cross-domain joint training process; during training, the samples in the source domain are uniformly assigned basic weights, and the basic weight value is 1; the enhanced samples in the target domain are dynamic weighted according to the error ratio; the loss function is adjusted according to the dynamic weight, so that the model can learn the general material strength law in the source domain big data, while strengthening the fitting ability of the high error area in the small sample of the target domain.

[0057] S600. Output strength prediction results and visualization charts of characteristic action mechanisms; based on the trained transfer learning model, predict the strength of phosphogypsum concrete according to the input mix ratio; combined with SHAP interpretability analysis, output visualization charts such as feature importance analysis charts and SHAP coupling charts to reveal the nonlinear coupling effect of phosphogypsum characteristic parameters on strength.

[0058] In this specific embodiment, the large sample size threshold in step S100 is 500, and the small sample size threshold is 15. In step S300, the sample expansion multiple of the target domain training set is not less than 4 times.

[0059] It should be noted that the parameters of conventional concrete include cement, water, aggregate, water reducer, and age, and the label is compressive strength; the parameters of phosphogypsum concrete include phosphogypsum, cement, water, aggregate, water reducer, and age, and the label is compressive strength.

[0060] It should be noted that all source domain data are divided into training sets for model training; target domain data are divided into 60% training sets, 20% validation sets, and 20% test sets using the random sampling principle; the training set is used to learn model parameters and minimize prediction errors by fitting data; the validation set is used to adjust hyperparameters and monitor the training process during model development; the test set is completely independent of the training and tuning process, and is used to ultimately evaluate the generalization performance of the model on unseen data, providing objective performance indicators.

[0061] It should be noted that the bootstrap resampling technique is a statistical inference method based on empirical distribution. Its goal is to generate a large number of simulated sample sets from the original data set through repeated sampling with replacement, thereby expanding the data.

[0062] It should be noted that the self-service resampling technique includes the following steps:

[0063] Sa100. Set up an independent and identically distributed data set, which follows an unknown distribution. The independent and identically distributed data set is expressed as follows:

[0064] D={x1,x2,...,x n}(1)

[0065] Where: D is used to characterize independent and identically distributed data sets.

[0066] Sa200.Bootstrapped resampling constructs an empirical distribution function as an approximation of the unknown distribution, expressed as Equation 2:

[0067]

[0068] in: Used to characterize the empirical distribution function; I is used to characterize the indicator function.

[0069] Sa300. Based on the empirical distribution function, a preset number of samples are drawn from the independent and identically distributed dataset with replacement each time to generate a bootstrap sample set; the bootstrap sample set is expressed as Equation 3:

[0070]

[0071] Where: D* is used to characterize the bootstrap sample set.

[0072] The probability mass function of the bootstrap sample set satisfies Equation 4:

[0073]

[0074] Repeat steps Sa100-Sa300 to the target number of times, thereby generating the target number of independent bootstrap sample sets; expand the data distribution from the empirical distribution function to the empirical distribution function after amplifying the target number of times, thereby expanding the data by the target number of times. The bootstrap resampling data is derived from real samples to avoid generating invalid samples that violate the law of conservation of material composition.

[0075] It should be noted that the dynamic weight calculation formula in the dynamic weight calculation process is expressed as Formula 5:

[0076] w i =β+γ·e i / max(e),i=1,2,...,N (5)

[0077] Among them, e i Used to represent the absolute value of the prediction error of the i-th sample; β and γ are used to represent hyperparameters, with β = 2 and γ = 3; max(e) is used to represent the error normalization factor; N is used to represent the number of samples.

[0078] It should be noted that the weighted loss function optimization process refers to the use of weighted mean square error as the optimization target of the model. The calculation formula of the weighted mean square error is expressed as follows:

[0079]

[0080] in, Used to characterize the loss function; w i The weight used to represent the i-th sample; y i and They are used to represent the true value and predicted value of the sample label respectively.

[0081] It should be noted that in this specific embodiment, the method for predicting the strength of phosphogypsum concrete based on dynamic weighted transfer learning is described in detail as follows:

[0082] (1) Source and target domain data preparation

[0083] The source data comes from the publicly available concrete compressive strength dataset from the UCI Machine Learning Database, consisting of 1,030 experimental samples (denoted as S1). This dataset comprehensively covers the main component parameters of conventional concrete. Input features include eight key variables: cement, blast furnace slag, fly ash, water, superplasticizer, coarse aggregate, fine aggregate, and curing age. The target output is the compressive strength of the concrete specimens under standard curing conditions.

[0084] The target domain data was derived from independently conducted compressive strength tests on phosphogypsum concrete. A total of 19 valid samples (denoted as S2) were obtained from the tests. Input features included nine key parameters: cement, water, superplasticizer, coarse aggregate, fine aggregate, phosphogypsum ceramsite, retarder, phosphogypsum, and curing age. The target output was the compressive strength of concrete under standard curing conditions.

[0085] (2) Cross-domain feature alignment

[0086] Add feature columns for phosphogypsum, phosphogypsum aggregate, and retarder to the source domain S1, and fill missing values ​​with 0; delete the unique features of the source domain S1, including blast furnace slag and fly ash, to ensure that the features of the source domain S1 are exactly the same as those of the target domain S2.

[0087] (3) Self-service resampling data enhancement

[0088] The entire source domain S1 data is used as the training set. The target domain is divided into a 60% training set, a 20% validation set, and a 20% test set using stratified random sampling. A self-service resampling technique is used to expand the target domain training set to four times its original size. The enhanced target domain data is then combined with the source domain data to form a joint training set.

[0089] (4) Comparative experimental design

[0090] In order to systematically evaluate the performance of the proposed dynamic weighted transfer learning model in cross-domain transfer and small sample scenarios, two sets of comparison models were designed, namely the target domain benchmark modeling (denoted as BLM) and the transfer learning model (denoted as TLM). The experiments uniformly used the root mean square error (RMSE) and the coefficient of determination (R 2 ) and mean absolute percentage error (MAPE) as evaluation indicators to comprehensively evaluate the prediction effect of the model.

[0091] The target domain benchmark model (BLM) was tested on the target domain S2 using the Random Forest (RF) and XGBoost algorithms. During the experiment, the model was trained using a randomly divided 80% training set and the model performance was evaluated on the 20% test set.

[0092] The transfer learning model TLM is based on the dynamic weighted transfer learning algorithm framework, such as Figure 1As shown in Figure 2, the source domain S1 and the target domain S2 are jointly trained using augmented training sets. An error feedback mechanism dynamically adjusts the weights of target domain samples, prioritizing learning of samples in target domain prediction blind spots. The experiment simultaneously outputs model evaluation metrics and feature importance distributions, comparing and analyzing the contributions of unique components such as phosphogypsum and retarders. This set of experiments verifies the effectiveness of the dynamic weighted transfer learning model.

[0093] (5) Prediction results and visualization analysis

[0094] The evaluation indicators of the XGBoost and RF baseline models trained on the target domain S2 dataset on the test set are shown in Table 1. The RMSE of the prediction results of the XGBoost model is 3.39MPa, the determination coefficient R2 is 0.81, and the mean absolute percentage error (MAPE) is 7.70%. The RF model performs slightly better with an RMSE of 3.17MPa and an R2 of 0.83, but the MAPE rises slightly to 9.18%. The average results of the two models are: RMSE = 3.28MPa, R2 = 0.81, and MAPE = 7.70%. 2 =0.82, MAPE=8.44%.

[0095] Table 1 Comparison of target domain benchmark model BLM results

[0096] Baseline Model RMSE (MPa) <![CDATA[R 2 ]]> MAPE XGBoost 3.39 0.81 7.70％ RF 3.17 0.83 9.18％ average value 3.28 0.82 8.44％

[0097] In testing on the target domain dataset S2, the predictive capabilities of traditional machine learning models were limited by the sample size. The average R² score calculated by the XGBoost and RF models on the test set was 0.82. While this provided basic predictive capabilities, it was insufficient to support engineering-level robust prediction requirements.

[0098] Table 2 shows the test results of the TLM model built based on the dynamic weighted transfer learning algorithm on the target domain S2 test set. Compared with the baseline model, TLM reduced the RMSE from 3.28 MPa to 2.86 MPa, a decrease of 12.8%. The coefficient of determination (R2) increased from 0.82 to 0.95, a 15.9% increase. The mean absolute percentage error (MAPE) decreased from 8.44% to 7.78%. These results validate the benefits of the dynamic weighted transfer learning model in small sample scenarios and demonstrate that the model successfully overcomes the performance bottleneck of traditional methods under extremely small sample conditions.

[0099] Table 2 Performance comparison between TLM and BLM

[0100] Model Type RMSE (MPa) R2 MAPE Baseline Model (BLM) 3.28 0.82 8.44％ Transfer Model (TLM) 2.86 0.95 7.78％

[0101] Figure 2The feature importance distribution plot output by the TLM is shown. As can be seen from the figure, the feature "Age" has the highest importance score, close to 0.35, indicating its key role in the model's predictions. Next are "Cement" and "Water," with importance scores of 0.27 and 0.14, respectively. The importance of other secondary features is ranked as follows: "Fine Aggregate," "Coarse Aggregate," "Superplasticizer," "Blast Furnace Slag," "Fly Ash," "Phosphogypsum," "Retarder," and "PGA," demonstrating that the transfer learning model has successfully learned the general patterns of conventional concrete. The figure shows that the feature parameters unique to the target domain S2, such as "Phosphogypsum," "Retarder," and "PGA," have low feature importance, but none are zero, indicating that the TLM model successfully captures the influence patterns of components unique to the target domain.

[0102] Figure 3 A SHAP overview of feature contributions is shown. It shows that the "Age" and "Cement" features have a significant impact on the model output. Specifically, small values ​​for the "Age" feature have a significant negative impact on strength. However, high values ​​for the "Cement" feature have a significant positive impact on strength. The SHAP values ​​for other feature parameters are more concentrated, indicating that their impact on strength results is relatively small.

[0103] Figure 4 The comparison of the prediction results of the transfer learning model (TLM) and the benchmark model (BLM) is shown. As can be seen from the figure, the predicted value of the TLM model (blue dots) is closer to the true value, and most of the points are distributed near the ideal prediction line, indicating that its prediction performance is better. In contrast, the predicted value of the BLM model (red cross) deviates greatly from the true value, especially in the low value area, the predicted value of the benchmark model deviates significantly from the ideal prediction line, showing that its prediction performance is poor. The above analysis shows that the dynamic weighted transfer learning model proposed in the present invention is superior to the benchmark model in terms of prediction accuracy and generalization ability, indicating that transfer learning has achieved good results.

[0104] In summary, the dynamic weighted transfer learning model developed in this paper enables cross-material knowledge transfer, resolving the small sample size challenge in predicting the strength of phosphogypsum concrete. In industrial scenarios, this model can provide a reliable prediction tool for mix design of high-phosphogypsum concrete, furthering the engineering process of solid waste resource utilization.

[0105] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0106] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0107] The foregoing description includes examples of one or more embodiments. Of course, it is not possible to describe all possible combinations of components or methods for the purposes of describing the above embodiments, but one of ordinary skill in the art will recognize that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to encompass all such changes, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including," as explained in terms of "including," used as a transitional word in the claims. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or."

[0108] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the strength of phosphogypsum concrete based on dynamic weighted transfer learning, characterized by: The following steps are involved: S100. Collect source domain data and target domain data; wherein the source domain data is large-sample conventional concrete data, the features of the large-sample conventional concrete data include conventional concrete parameters, and the sample size of the large-sample conventional concrete data is no less than a manually preset large sample size threshold; the target domain data is small-sample phosphogypsum concrete data, the features of the small-sample phosphogypsum concrete data include phosphogypsum concrete parameters, and the sample size of the small-sample phosphogypsum concrete data is no less than a manually preset small sample size threshold; S200. Aligning cross-domain features between the source domain and the target domain; Adding target domain-specific features of the dataset of the small sample phosphogypsum concrete data in the target domain to the dataset of the large sample conventional concrete data in the source domain, and filling the missing values ​​with 0; at the same time, deleting the source domain-specific features in the source domain to ensure that the features of the source domain are exactly the same as those of the target domain; S300. Execute the self-service resampling data enhancement process; use the self-service resampling technology to expand the target domain training set and generate enhanced samples that meet the mix ratio constraints; S400. Constructing a dynamic weighted transfer learning algorithm framework; the dynamic weighted transfer learning algorithm framework includes a dynamic weight calculation process and a weighted loss function optimization process; S500. Execute cross-domain joint training process; During training, the samples in the source domain are uniformly assigned a basic weight, the value of which is 1; the enhanced samples in the target domain are given a dynamic weight according to the error ratio; The loss function is adjusted according to the dynamic weight; S600. Output strength prediction results and visualization charts of feature action mechanisms; based on the trained transfer learning model, predict the strength of phosphogypsum concrete according to the input mix ratio; combined with SHAP interpretability analysis, output visualization charts such as feature importance analysis charts and SHAP coupling charts.

2. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The conventional concrete parameters include but are not limited to cement, water, aggregate, water reducer, and age, and the label is compressive strength; the phosphogypsum concrete parameters include but are not limited to phosphogypsum, cement, water, aggregate, water reducer, and age, and the label is the compressive strength.

3. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The source domain data is all divided into a training set for model training; the target domain data is divided into a 60% training set, a 20% validation set, and a 20% test set using the random sampling principle; the training set is used to learn model parameters by fitting the data to minimize prediction errors; the validation set is used to adjust hyperparameters and monitor the training process during model development; the test set is completely independent of the training and tuning process and is used to ultimately evaluate the generalization performance of the model on unseen data, providing objective performance indicators.

4. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The bootstrap resampling technique is a statistical inference method based on empirical distribution, which aims to generate a large number of simulated sample sets from the original data set through repeated sampling with replacement, thereby expanding the data.

5. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 4 is characterized in that: The self-service resampling technique comprises the following steps: Sa100. Establish an independent and identically distributed data set, wherein the independent and identically distributed data set obeys an unknown distribution; the independent and identically distributed data set is expressed as follows: D={x1,x2,...,x n } Wherein: D is used to characterize the independent and identically distributed data set; Sa200. Bootstrap resampling constructs an empirical distribution function as an approximation of the unknown distribution, which is expressed as follows: in: Used to characterize the empirical distribution function; I is used to characterize the indicator function; Sa300. Based on the empirical distribution function, a preset number of samples are extracted from the independent and identically distributed data set with replacement each time to generate a bootstrap sample set; the bootstrap sample set is expressed as follows: Wherein: D* is used to characterize the self-help sample set; The probability mass function of the bootstrap sample set satisfies the following formula: S400. Repeat steps Sa100 to Sa300 to the target number of times, thereby generating the target number of independent self-service sample sets; expand the data distribution from the empirical distribution function to the empirical distribution function after amplifying the target number of times, thereby expanding the data by the target number of times.

6. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The dynamic weight calculation formula in the dynamic weight calculation process is expressed as follows: w i =β+γ·e i / max(e),i=1,2,...,N Among them, e i Used to represent the absolute value of the prediction error of the i-th sample; β and γ are used to represent hyperparameters, with β = 2 and γ = 3; max(e) is used to represent the error normalization factor; N is used to represent the number of samples.

7. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The weighted loss function optimization process refers to using the weighted mean square error as the optimization target of the model. The calculation formula of the weighted mean square error is expressed as follows: in, Used to characterize the loss function; w i The weight used to represent the i-th sample; y i and They are used to represent the true value and predicted value of the sample label respectively.

8. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: The large sample size threshold in step S100 is 500; the small sample size threshold is 15.

9. The method for predicting phosphogypsum concrete strength based on dynamic weighted transfer learning according to claim 1, characterized in that: In step S300 , the sample expansion multiple of the target domain training set is no less than 4 times.

Images