Machine learning-based shear capacity analysis method for reinforced concrete beam with stirrups

Abstract

The invention discloses a shear capacity analysis method for a reinforced concrete beam with stirrups based on machine learning, and the method comprises the steps: constructing a training set and a test set based on a shear capacity database of the beam with stirrups; establishing an interpretable prediction model by utilizing machine learning, setting hyper-parameters for the interpretable prediction model, and performing training; obtaining a shear bearing capacity prediction value of the samples in the test set by using the trained prediction model; and quantifying the contribution of each key anti-shearing characteristic to the anti-shearing bearing capacity predicted value, and analyzing and judging the reasonability of the anti-shearing bearing capacity predicted value output by the prediction model according to the anti-shearing theory. According to the method, the problems of high prediction difficulty, high discreteness, lack of reliable physical models, large calculation amount of high-precision numerical simulation and the like in machine learning are solved for the first time; the prediction model can accurately reflect the complex nonlinear relation between the shear bearing capacity and the influence factors, and meanwhile, the model reasonability is verified and improved in combination with a prediction result and priori knowledge, so that the man-machine interaction trust in practical application is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of shear bearing capacity analysis of concrete beams, and in particular to a shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning. Background Art

[0002] The basic properties of concrete structures, such as shear bearing capacity and ductility, are important parameters in the process of structural design and evaluation. Due to the nonlinear mechanical properties of concrete and the complex interaction between steel bars and concrete, there is currently no unified formula to calculate the shear bearing capacity of the structure. Accurately predicting the basic properties of concrete structures directly determines the accuracy and reliability of structural design and analysis.

[0003] Traditional basic performance modeling methods are mostly based on mechanical derivation or semi-theoretical and semi-empirical methods. They are difficult to fully reflect the influence of many factors and introduce a large number of assumptions and simplifications, resulting in low prediction accuracy and large variance. In recent years, the rise of artificial intelligence and the introduction of technologies such as machine learning have provided new ideas for solving the above problems. Machine learning technology can efficiently utilize a large amount of test data accumulated from different regions and different periods over the past few decades, directly mine the mapping relationship within the data, and then establish an accurate and stable prediction model. Although the application of the above machine learning methods has demonstrated the unique advantages of this method in predicting the basic performance of concrete structures, most of the current research is a "black box" model, which can give accurate predictions based on the input, but cannot give an explanation for the model prediction, which reduces the credibility and application scope of the machine learning model.

[0004] The concrete structure performance prediction model established based on interpretable machine learning methods and interpretable enhanced models not only achieves high-precision predictions, but also can explain the prediction results from both global and local perspectives, clearly display the model decision-making process, and reveal how the model gives a certain prediction value. It integrates prior knowledge into the model, improves users' trust in the model, and provides new ideas for concrete structure performance prediction. It is of great significance to further promote the practical application of machine learning and the development of concrete structure performance theory. Summary of the invention

[0005] The purpose of the present invention is to provide a shear bearing capacity analysis method for reinforced concrete beams with stirrups based on machine learning in view of the deficiencies in the prior art.

[0006] The object of the present invention is achieved through the following technical solution: A method for analyzing the shear bearing capacity of reinforced concrete beams with stirrups based on machine learning, comprising the following steps: (1) Based on the shear bearing capacity database of beams with stirrups, the simply supported beam samples were screened and evaluated according to the structural design specifications to construct a dataset. The dataset was then divided into a training set and a test set in proportion. (2) Use machine learning to establish an interpretable prediction model. The input of the prediction model is the key shear characteristics of the simply supported beam, and the output is the predicted value of the shear bearing capacity of the simply supported beam. Set hyperparameters for the prediction model, and then use the training set to iteratively train the prediction model. During the training process, compare and analyze the predicted values ​​of the shear bearing capacity, and adjust the hyperparameters of the prediction model based on the results of the comparative analysis to obtain a trained prediction model. (3) Input the samples in the test set into the trained prediction model to obtain the corresponding shear bearing capacity prediction value; (4) Based on the predicted shear bearing capacity value obtained in step (3), the contribution of each key shear characteristic to the predicted shear bearing capacity value is quantified, and the rationality of the predicted shear bearing capacity value output by the prediction model is judged based on shear theory analysis.

[0007] Furthermore, the step (1) includes the following sub-steps: (1.1) The shear bearing capacity of rectangular simply supported beams under concentrated load in the shear bearing capacity database of stirrup reinforced beams is measured by using a hydraulic press to pressurize the simply supported beam. When the simply supported beam fails in shear or reaches the maximum shear force and no longer increases, the load at this time is recorded as the shear bearing capacity limit value. (1.2) Screen the simply supported beam samples in the shear bearing capacity database of beams with stirrups, specifically: remove the simply supported beam samples that have bending failure, and retain the simply supported beam samples that have shear failure; remove the simply supported beam samples with an effective section height of less than 100mm, and remove the simply supported beam samples with an effective section height of more than 1000mm; remove the simply supported beam samples with a shear bearing capacity limit value greater than 1000kN; (1.3) For the simply supported beam samples remaining after screening, the calculated shear bearing capacity values ​​are determined according to the structural design code, and the accuracy of the structural design code used is calculated according to the calculated shear bearing capacity values ​​and the shear bearing capacity limit values, so as to construct a data set; wherein the data set includes the shear characteristics of the simply supported beam samples, the calculated shear bearing capacity values, the shear bearing capacity limit values, and the accuracy of the structural design code used; (1.4) Divide the dataset into training and test sets in proportion.

[0008] Furthermore, the shear resistance characteristics include effective section height, section width, concrete cube compressive strength, stirrup yield strength, stirrup ratio, longitudinal reinforcement ratio and shear span ratio.

[0009] Furthermore, the step (2) includes the following sub-steps: (2.1) Feature engineering is used to select multiple anti-shear features in the dataset to determine the key anti-shear features; (2.2) Based on the determined key shear features, combined with digital image correlation measurement technology, an interpretable prediction model is established using machine learning; the prediction model is represented as the sum of contribution value functions corresponding to multiple key shear features and shear feature interaction terms; the input of the prediction model is a feature vector composed of multiple key shear features of a simply supported beam, and the output is a predicted value of the shear bearing capacity of the simply supported beam; (2.3) Set hyperparameters for the prediction model and use the ten-fold cross-validation method to determine the optimal hyperparameters; the hyperparameters include the total number of anti-shear feature interaction terms and the learning rate; (2.4) Use the training set to train the prediction model. Each training is performed only on a single contribution value function. During the training process, the prediction model is gradient improved based on the prediction error of the prediction model and the optimal learning rate obtained in step (2.3), and finally a trained prediction model is obtained.

[0010] Furthermore, the prediction model is expressed as:

[0011] Where y represents the predicted value of shear bearing capacity output by the prediction model, Represents key shear features The contribution value function of n is the total number of key shear features, Represents key shear features and key shear features The contribution value function of the interaction term, p represents the p-th anti-shear feature interaction term, and P represents the total number of anti-shear feature interaction terms.

[0012] Furthermore, the step (2.4) specifically includes: Each time, only the contribution value function corresponding to one key anti-shear feature is trained; for each key anti-shear feature The corresponding contribution function or , when multiple rounds of training are performed, the remaining contribution functions remain fixed; in the contribution function or In each round of training, the key anti-shear features in the feature vector composed of multiple key anti-shear features are updated based on the training set. and / or , get the updated feature vector, input the updated feature vector into the prediction model, get the predicted value of shear bearing capacity, calculate the error between the predicted value of shear bearing capacity and its corresponding true value as the current residual, fit the residual by using the gradient boosting regression tree technique, and update the current contribution value function according to the learning rate in the hyperparameter or Parameters, where the true value is the shear bearing capacity limit value in the training set; the contribution value function or Perform M rounds of training, learn M regression trees, and gradually reduce the prediction error after M rounds of cyclic training so that the contribution value function or The parameters of the gradually converge to obtain the trained contribution value function or , and finally obtain the trained prediction model.

[0013] Furthermore, the step (4) includes the following sub-steps: (4.1) Based on the predicted shear capacity value obtained in step (3), the contribution of each key shear feature to the predicted shear capacity value is quantified using the global interpretation of the prediction model to obtain the overall importance ranking of each key shear feature and each shear feature interaction term; wherein the overall importance is equal to the absolute average of the contribution values ​​of each key shear feature or shear feature interaction term to the predicted shear capacity value on the test set samples; (4.2) Using the prediction model to obtain a local interpretation of each sample, so as to quantify the contribution of each key shear feature in the individual sample to the predicted shear bearing capacity, and obtain the shear contribution value of each key shear feature in the individual sample; (4.3) Based on the prior knowledge of shear theory, the overall importance ranking of each key shear feature and each shear feature interaction term obtained in step (4.1) and the shear contribution value of each key shear feature in the individual sample obtained in step (4.2) are analyzed to determine the rationality of the shear bearing capacity prediction value output by the prediction model and to infer the cause of the prediction error.

[0014] Compared with the existing method, the beneficial effects of the present invention are: (1) The present invention uses an interpretable machine learning method to understand the model's reasoning process and the rationality of the prediction, thereby ensuring the accuracy and credibility of the shear bearing capacity prediction results; (2) The present invention incorporates the prior knowledge of concrete shear force transmission into the model, which enhances the user's trust in the model and promotes the combination of interpretability and model performance; (3) The interpretable machine learning method of the present invention helps to deepen the understanding of the shear force transmission mechanism of concrete, promote the application of machine learning in engineering practice and the development of shear theory. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning provided by the present invention; Figure 2 It is a training schematic diagram of the prediction model provided by the present invention; Figure 3 It is a scatter plot of the predicted value of shear bearing capacity output by the prediction model provided by the present invention and the actual value; Figure 4 It is a ranking diagram of the average absolute value (i.e., overall importance) of the shear contribution of each input key shear resistance feature and the shear resistance feature interaction item provided by the present invention; Figure 5 It is a function curve diagram of the contribution value of the single key shear resistance feature provided by the present invention, namely, the effective height of the cross section to the predicted value of the shear bearing capacity; Figure 6 It is a heat map of the contribution value function of the shear resistance characteristic interaction term of the prediction model provided by the present invention; Figure 7 It is a local explanation diagram of a typical sample in the test set provided by the present invention; Figure 8 It is a ranking diagram of the contribution values ​​of each key anti-shear feature and each anti-shear feature interaction item in the sample provided by the present invention. DETAILED DESCRIPTION

[0016] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. Instead, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the attached claims. It should be understood that the above general description and the detailed description that follows are merely exemplary and explanatory and cannot limit the present application.

[0017] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0018] It should be understood that, although the term first, second, third, etc. may be used in the present application to describe various information, these information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of..." or "when..." or "in response to determination". Moreover, the term "include", "comprise" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process and method including a series of elements include not only those elements, but also include other elements not clearly listed, or also include elements inherent to such process and method. In the absence of more restrictions, the elements limited by the statement "including one..." do not exclude the existence of other identical elements in the process, method, article or equipment including the elements.

[0019] The present invention is described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the features of the following embodiments and implementations can be combined with each other.

[0020] See also Figure 1 The shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning of the present invention specifically comprises the following steps: (1) Based on the shear bearing capacity database of beams with stirrups, the simply supported beam samples were screened and evaluated according to the structural design specifications to construct a dataset. The dataset was then divided into a training set and a test set in proportion.

[0021] It should be noted that the shear bearing capacity database of beams with stirrups is an existing public database, such as the shear bearing capacity database of beams with stirrups collected by Yuan Jian (Yuan Jian. Research on shear bearing capacity and reliability of reinforced concrete beams [D]. Hunan University, 2017.).

[0022] (1.1) A shear bearing capacity test was conducted on a rectangular simply supported beam under concentrated load in the shear bearing capacity database of stirrup reinforced beams. Specifically, a hydraulic press was used to pressurize the simply supported beam. When the simply supported beam underwent obvious shear failure or reached the maximum shear force and no longer increased, the load at this time was recorded as the shear bearing capacity limit value.

[0023] (1.2) Screening the simply supported beam samples in the shear bearing capacity database of beams with stirrups, specifically: eliminating the simply supported beam samples with bending failure and retaining the simply supported beam samples with shear failure; eliminating the simply supported beam samples with effective section height less than 100mm and the simply supported beam samples with effective section height greater than 1000mm, which helps to improve the practicality of the prediction model; eliminating the simply supported beam samples with shear bearing capacity limit greater than 1000kN, which helps to reduce the impact of data discreteness on the prediction model evaluation. In this embodiment, the original database of shear bearing capacity of beams with stirrups contains 472 rectangular simply supported beams under concentrated loads, and 419 simply supported beam samples remain after the above screening.

[0024] (1.3) For the simply supported beam samples remaining after screening, the calculated shear bearing capacity values ​​are determined according to the structural design code, and the accuracy of the structural design code used is calculated based on the calculated shear bearing capacity values ​​and the shear bearing capacity limit values ​​to construct a data set. The data set includes the shear characteristics of the simply supported beam samples, the calculated shear bearing capacity values, the shear bearing capacity limit values, and the accuracy of the structural design code used.

[0025] It should be noted that the structural design specifications are intended to determine structural parameters, including cross-sectional dimensions and distribution of reinforcement, etc., to ensure structural performance. The structural design specifications in this embodiment are respectively the Chinese specification GB50010-2010 (GB 50010—2010, Specification for Design of Concrete Structures [S]. Beijing: China Building Industry Press, 2010.), the European specification EN1992-1-1:2004 (CEN, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings [S]. Brussels: EUROPEAN COMMITIEE FORSTANDARDIZATION, 2004.) and the American specification ACI318-19 (ACI 318-19, Building Code Requirements for Structural Concrete [S]. Washington: American Concrete Institute, 2019.).

[0026] Furthermore, for the simply supported beam samples remaining after screening, the shear characteristics of the simply supported beam samples are substituted into the shear bearing capacity calculation formula in the structural design code for calculation to obtain the calculated shear bearing capacity value; the calculated shear bearing capacity value is compared with its corresponding shear bearing capacity limit value to evaluate the accuracy of the currently used structural design code; after the evaluation, the error accuracy between the calculated shear bearing capacity value calculated by the currently used structural design code and the shear bearing capacity limit value (i.e., the actual value obtained from the shear bearing capacity measurement experiment) can be obtained, which is conducive to evaluating the accuracy of the structural design code currently used.

[0027] Furthermore, the shear characteristics include effective section height, section width, concrete cube compressive strength, stirrup yield strength, stirrup ratio, longitudinal reinforcement ratio and shear span ratio, as shown in Table 1.

[0028] Table 1: Shear characteristics of simply supported beam specimens

[0029] (1.4) Divide the data set into a training set and a test set in proportion, such as 8:2, that is, the training set accounts for 80% (335 simply supported beams) and the test set accounts for 20% (84 simply supported beams). The training set is used to train the prediction model and establish a mapping from input to output; the test set is used to evaluate the performance of the prediction model to avoid overfitting, that is, although the prediction model performs well on the training set, it is likely to be inaccurate on an untrained or new data set, so the test set needs to be used to fine-tune the prediction model.

[0030] (2) An interpretable prediction model is established using machine learning. The input of the prediction model is the key shear characteristics of a simply supported beam, and the output is the predicted shear bearing capacity of the simply supported beam. Hyperparameters are set for the prediction model, and the prediction model is iteratively trained using the training set. During the training process, a comparative analysis is performed on the predicted shear bearing capacity values, and the hyperparameters of the prediction model are adjusted based on the results of the comparative analysis to obtain a trained prediction model.

[0031] It should be understood that machine learning is to enable machines (computers) to discover the laws of things and acquire the ability to analyze and solve problems by observing large amounts of data and training, just like humans. In other words, it allows machines to learn and execute.

[0032] (2.1) Feature engineering is used to select multiple anti-shear features in the dataset to determine the key anti-shear features.

[0033] It should be noted that the data set contains multiple shear features. For complex shear bearing capacity prediction problems, the number of shear features that affect the shear bearing capacity is very large. However, due to data limitations, the number of shear features used in the interpretable prediction model established by machine learning should be reasonably controlled. Therefore, it is necessary to use feature engineering to select typical features that affect the shear bearing capacity based on the data set to further improve the quality and analyzability of the data set. In this embodiment, there are seven key shear features determined, namely: effective height d of the section, width b of the section, compressive strength of the concrete cube, and the relative position of the cross section. , stirrup yield strength , Stirrup ratio , longitudinal reinforcement ratio and shear span ratio λ.

[0034] (2.2) Based on the determined key shear features and combined with the Digital Image Correlation (DIC) measurement technology, an interpretable prediction model is established using machine learning; the prediction model is represented as the sum of contribution value functions corresponding to multiple key shear features and shear feature interaction terms; the input of the prediction model is a feature vector composed of multiple key shear features of a simply supported beam, and the output is the predicted value of the shear bearing capacity of the simply supported beam.

[0035] Specifically, since machine learning determines the prediction model by observing the rules between a large amount of data, the initial expression of the prediction model can be expressed as: , where y represents the predicted value of shear bearing capacity output by the prediction model, Represents key shear features The corresponding shape function, Represents the total number of critical shear features. In the generalized additive model, each critical shear feature A complex nonlinear shape function can be learned , so the accuracy of the generalized additive model can be significantly higher than that of the simple linear model; and because the shape function It is a one-dimensional function, and the key shear resistance features can be intuitively displayed through images. The contribution to the predicted value of shear bearing capacity is obtained With the key shear features The specific law of changes with different inputs, therefore, the General Algebraic Modeling System (GAMs) is highly interpretable like a simple linear model. Therefore, the prediction model is modeled as the sum of the contribution values ​​of each key shear feature to the predicted value of shear bearing capacity, plus a global bias, expressed as:

[0036] Where y represents the predicted value of shear bearing capacity output by the prediction model, represents the global bias, Represents key shear features Contribution function of the key shear characteristics The specific impact on the predicted shear capacity, n is the total number of key shear features.

[0037] Furthermore, despite adding a global bias to GAMs , but it is not completely accurate, because GAMs does not consider the interaction between anti-shear features at all, and its accuracy is still not as good as that of advanced machine learning models. Further improvements are made on the basis of GAMs, and interactive feature pairs, namely anti-shear feature interaction terms, are introduced, called GA2Ms model, that is, the global bias The deformation is the sum of the contributions of multiple shear characteristic interaction terms to the predicted shear bearing capacity, expressed as . Shape function Although it is a two-dimensional function, it can still show the specific influence of the shear feature interaction term on the predicted value of shear bearing capacity in the form of a plane heat map, while improving the accuracy, it still ensures the interpretability of the prediction model. However, when the number of shear features is large, it is impossible for the GA2Ms model to model all the shear feature interaction terms. In order to solve this problem, the interaction term strength is defined for the shear feature of the prediction model, and the shear feature interaction terms are sorted from high to low according to their interaction term strength. When modeling the prediction model, the first P shear feature interaction terms can be selected for modeling according to the ranking of the shear feature interaction term strength, which can greatly improve the efficiency of modeling and obtain the final expression of the prediction model:

[0038] in, Represents key shear features and key shear features The contribution value function of the interaction term, p represents the p-th anti-shear feature interaction term, and P represents the total number of anti-shear feature interaction terms.

[0039] (2.3) Set hyperparameters for the prediction model and use the ten-fold cross-validation method to determine the optimal hyperparameters; the hyperparameters include the total number P of anti-shear feature interaction terms and the learning rate lr.

[0040] Specifically, first set multiple groups of different hyperparameter value combinations, as shown in Table 2; then, for each group of hyperparameter value combinations, randomly divide the training set into 10 subsets, use one subset each time to verify the prediction model, and the remaining 9 subsets are used to train the prediction model. According to the predicted value of shear bearing capacity and its corresponding true value, calculate the performance evaluation index of each subset, and take the average value of the performance evaluation index of the 10 subsets as the model accuracy under the current hyperparameter value combination; traverse all hyperparameter value combinations, select the hyperparameter value combination with the highest model accuracy as the optimal hyperparameter of the prediction model, and then start the formal training of the prediction model. Among them, the performance evaluation indicators include mean absolute error (MAE), root mean square error (RMSE), determination coefficient ( ) and the mean safety factor , the smaller the MAE and RMSE, and The closer it is to 1, the better the performance of the prediction model is, and the better the model accuracy of the prediction model is. In this embodiment, the determination coefficient is selected as the performance evaluation index to obtain the optimal hyperparameter.

[0041] It should be understood that in order to train the best prediction model as much as possible, it is necessary to select appropriate hyperparameters for the prediction model. A prediction model based on machine learning usually contains multiple hyperparameters, such as the total number P of anti-shear feature interaction terms and the learning rate lr in this embodiment, but it is certainly not limited to this. In order to improve the selection efficiency, this embodiment uses a ten-fold cross-validation method to determine the optimal hyperparameters, which is easy to implement and has a small estimated deviation.

[0042] Table 2: Average values ​​of coefficient of determination for different hyperparameter value combinations Results Table

[0043] For example, multiple sets of different hyperparameter value combinations are set based on experience, as shown in Table 2, from which it can be seen that the average values ​​of the determination coefficients corresponding to different hyperparameter value combinations are , 0.8738 is the best, so the optimal hyperparameters are determined to be P=8, lr=0.0001.

[0044] (2.4) Use the training set to train the prediction model. Each training is performed only on a single contribution value function. During the training process, the prediction model is gradient improved based on the prediction error of the prediction model and the optimal learning rate obtained in step (2.3), and finally a trained prediction model is obtained.

[0045] Specifically, for the training of the prediction model, the shallow regression decision tree technology, gradient boosting technology and bagging technology are combined to further improve the accuracy of the prediction model. In this embodiment, only the contribution value function corresponding to one key anti-shear feature is trained each time; Figure 2 As shown, for each key shear feature The corresponding contribution function or , when training it for multiple rounds, the remaining contribution value functions are fixed; in the contribution value function or In each round of training, the key anti-shear features in the feature vector composed of multiple key anti-shear features are updated based on the training set. and / or , get the updated feature vector, input the updated feature vector into the prediction model, get the shear bearing capacity prediction value, calculate the error between the shear bearing capacity prediction value and its corresponding true value as the current residual (res), fit the residual by using the gradient boosting regression tree technique, and update the current contribution value function according to the learning rate in the hyperparameter or Parameters, where the true value is the shear bearing capacity limit value in the training set; the contribution value function or Perform M rounds of training, learn M regression trees, and gradually reduce the prediction error after M rounds of cyclic training. The contribution value function or The parameters of the gradually converge to obtain the trained contribution value function or , and then obtain the trained prediction model.

[0046] It should be noted that the prediction model needs to learn the contribution value function of a single key anti-shear feature, so it is trained on only one key anti-shear feature each time to obtain a shallow regression tree, and then gradient boosting is performed at a very small learning rate and all key anti-shear features and anti-shear feature interactions are traversed in turn. For each of the n key anti-shear features, after M rounds of cyclic training, M trees will be learned, so there are a total of n*M trees in the prediction model. For each key anti-shear feature, the sum of all its vertical trees is the shape function f of the key anti-shear feature.

[0047] (3) Input the samples in the test set into the trained prediction model to obtain the corresponding shear bearing capacity prediction value.

[0048] Specifically, the samples in the test set are input into the trained prediction model. Each contribution value function can quickly give the contribution value of the corresponding key shear feature and the contribution value of each shear feature interaction term. The shear bearing capacity prediction value output by the prediction model can be obtained by simply adding the contribution values ​​of all key shear features and the contribution values ​​of all shear feature interaction terms. Therefore, the prediction efficiency of the prediction model is very high. The prediction model takes into account the interaction between key shear features. Its accuracy is no less than that of advanced machine learning models, while maintaining the interpretability of the model. Among them, the shear bearing capacity prediction value output by the prediction model is The corresponding true value (i.e. the shear bearing capacity limit obtained in step (1)) is compared to obtain a scatter plot as shown below: Figure 3 shown.

[0049] (4) Based on the predicted shear bearing capacity value obtained in step (3), the contribution of each key shear characteristic to the predicted shear bearing capacity value is quantified, and the rationality of the predicted shear bearing capacity value output by the prediction model is judged based on shear theory analysis.

[0050] (4.1) Based on the predicted shear capacity value obtained in step (3), the contribution of each key shear feature to the predicted shear capacity value is quantified using the global interpretation of the prediction model to obtain the overall importance ranking of each key shear feature and each shear feature interaction term, as follows: Figure 4 As shown in Figure 2, where the overall importance is equal to the absolute average of the contribution of each key shear feature or shear feature interaction term to the predicted shear bearing capacity on the test set samples.

[0051] It should be understood that the global explanation can give an overall importance ranking of the input features. To obtain a global explanation of the prediction model, you can use the InterpretML library, train an ExplainableBoostingClassifier or ExplainableBoostingRegressor model, extract the importance of key anti-shear features, generate feature effect plots and interaction effect plots, and visualize them to fully understand the decision-making process of the prediction model. After that, sort the features according to the extracted feature importance scores to obtain the overall feature importance ranking.

[0052] Furthermore, the global interpretation of the prediction model is used to obtain a curve graph of the contribution value of each key shear feature and shear feature interaction term to the predicted shear bearing capacity and the feature input value. Specifically, in the prediction model, each key shear feature and shear feature interaction term has a corresponding contribution value function, which is used to represent how the input value of the key shear feature affects the output of the prediction model. The contribution value function can be directly extracted from the prediction model, and the contribution value function curve of the key shear feature can be drawn through visualization tools such as the interpret Python library, such as Figure 5 As shown in the figure, the upper part is a curve chart of the contribution value of the effective height of the section to the predicted value of the shear bearing capacity and its input value, the vertical axis is the contribution value of the effective height of the section to the shear bearing capacity, in kN, and the lower part is a histogram of the data distribution. Similarly, the contribution value function heat map of the shear characteristic interaction term can be obtained, as shown in Figure 6 As shown, the horizontal axis represents the shear span ratio (λ), which is the ratio of the span to the height of the beam. In structural design, the shear span ratio affects the shear bearing capacity of the structure; the vertical axis represents the stirrup ratio ( ), which describes the ratio of stirrups in concrete structures and is usually closely related to shear resistance; the heat map shows the interaction between these two parameters ( ×λ) on the shear capacity, and the colors represent different predicted values ​​of shear capacity.

[0053] (4.2) The prediction model is used to obtain a local interpretation of each sample to quantify the contribution of each key shear feature in the individual sample to the predicted value of shear bearing capacity. The shear contribution value of each key shear feature in the individual sample is obtained. The key shear features with larger shear contribution values ​​have a greater impact on the predicted value of shear bearing capacity than the key shear features with smaller shear contribution values.

[0054] It should be noted that since the prediction model is the sum of the contribution value functions corresponding to multiple key shear features and shear feature interaction terms, the prediction model can be used to obtain a local explanation of each sample, and then obtain the specific contribution value of each key shear feature to the shear bearing capacity. Based on the trained prediction model, the explain_local method is used to obtain the local explanation of each sample, which will return the contribution value of each key shear feature in each sample to the predicted value of shear bearing capacity, that is, the shear contribution value of each key shear feature in the individual sample, and then use a visual chart to process it, which can directly display the shear contribution value of each key shear feature, such as Figure 7 shown.

[0055] (4.3) Based on the prior knowledge of shear theory, the overall importance ranking of each key shear feature and each shear feature interaction term obtained in step (4.1) and the shear contribution value of each key shear feature in the individual sample obtained in step (4.2) are analyzed to determine the rationality of the shear bearing capacity prediction value output by the prediction model and to infer the cause of the prediction error.

[0056] Specifically, the analysis results are visualized, such as Figure 8 As shown in the figure, it can be seen that the most important key shear feature in the positive contribution is the stirrup yield strength and section width b, which contribute +57kN and +57kN respectively. However, the third most important key shear characteristic is the stirrup ratio , with a negative contribution of -40 kN and a stirrup ratio of only 0.07%. This is much smaller than the minimum stirrup ratio specified in the shear theory specification. Moreover, concrete beams with larger cross-sectional sizes are designed with higher stirrup ratios, which is reflected in the local interpretation because the contribution of the key shear feature of most samples is positive. It can be concluded that for this sample, a smaller stirrup ratio This is the reason for the lower shear bearing capacity and the prediction error of the prediction model.

[0057] Exemplarily, the above operations can calculate the predicted shear bearing capacity of a group of beams and the contribution value of each key shear feature to the predicted shear bearing capacity. For example, in a group of prediction models for predicting the shear bearing capacity of beams, by comparing other advanced machine learning technologies with the prediction results obtained by the present invention, it can be found that the prediction accuracy of the present invention is comparable to that of XGBoost, and is better than that of random forests and decision trees. In addition, the contribution value function curve of the key shear features provided by the global interpretation of the interpretable prediction model and the shear contribution value of each key shear feature of a single sample provided by the local interpretation can clearly understand and explain the shear bearing capacity prediction process of the interpretable prediction model.

[0058] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing the shear bearing capacity of reinforced concrete beams with stirrups based on machine learning, characterized in that: The following steps are involved: (1) Based on the shear bearing capacity database of beams with stirrups, the simply supported beam samples were screened and evaluated according to the structural design specifications to construct a dataset. The dataset was then divided into a training set and a test set in proportion. (2) Use machine learning to establish an interpretable prediction model. The input of the prediction model is the key shear characteristics of the simply supported beam, and the output is the predicted value of the shear bearing capacity of the simply supported beam. Set hyperparameters for the prediction model, and then use the training set to iteratively train the prediction model. During the training process, compare and analyze the predicted values ​​of the shear bearing capacity, and adjust the hyperparameters of the prediction model based on the results of the comparative analysis to obtain a trained prediction model. (3) Input the samples in the test set into the trained prediction model to obtain the corresponding shear bearing capacity prediction value; (4) Based on the predicted shear bearing capacity value obtained in step (3), the contribution of each key shear characteristic to the predicted shear bearing capacity value is quantified, and the rationality of the predicted shear bearing capacity value output by the prediction model is judged based on shear theory analysis.

2. The shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning according to claim 1 is characterized in that: The step (1) comprises the following sub-steps: (1.1) The shear bearing capacity of rectangular simply supported beams under concentrated load in the shear bearing capacity database of stirrup reinforced beams is measured by using a hydraulic press to pressurize the simply supported beam. When the simply supported beam fails in shear or reaches the maximum shear force and no longer increases, the load at this time is recorded as the shear bearing capacity limit value. (1.2) Screen the simply supported beam samples in the shear bearing capacity database of beams with stirrups, specifically: remove the simply supported beam samples that have bending failure, and retain the simply supported beam samples that have shear failure; remove the simply supported beam samples with an effective section height of less than 100mm, and remove the simply supported beam samples with an effective section height of more than 1000mm; remove the simply supported beam samples with a shear bearing capacity limit value greater than 1000kN; (1.3) For the simply supported beam samples remaining after screening, the calculated shear bearing capacity values ​​are determined according to the structural design code, and the accuracy of the structural design code used is calculated according to the calculated shear bearing capacity values ​​and the shear bearing capacity limit values, so as to construct a data set; wherein the data set includes the shear characteristics of the simply supported beam samples, the calculated shear bearing capacity values, the shear bearing capacity limit values, and the accuracy of the structural design code used; (1.4) Divide the dataset into training and test sets in proportion.

3. The shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning according to claim 2 is characterized in that: The shear resistance characteristics include effective section height, section width, concrete cube compressive strength, stirrup yield strength, stirrup ratio, longitudinal reinforcement ratio and shear span ratio.

4. The shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning according to claim 1 is characterized in that: The step (2) includes the following sub-steps: (2.1) Feature engineering is used to select multiple anti-shear features in the dataset to determine the key anti-shear features; (2.2) Based on the determined key shear features, combined with digital image correlation measurement technology, an interpretable prediction model is established using machine learning; the prediction model is represented as the sum of contribution value functions corresponding to multiple key shear features and shear feature interaction terms; the input of the prediction model is a feature vector composed of multiple key shear features of a simply supported beam, and the output is a predicted value of the shear bearing capacity of the simply supported beam; (2.3) Set hyperparameters for the prediction model and use the ten-fold cross-validation method to determine the optimal hyperparameters; the hyperparameters include the total number of anti-shear feature interaction terms and the learning rate; (2.4) Use the training set to train the prediction model. Each training is performed only on a single contribution value function. During the training process, the prediction model is gradient improved based on the prediction error of the prediction model and the optimal learning rate obtained in step (2.3), and finally a trained prediction model is obtained.

5. The method for analyzing the shear bearing capacity of reinforced concrete beams with stirrups based on machine learning according to claim 4 is characterized in that: The expression of the prediction model is: ； Where y represents the predicted value of shear bearing capacity output by the prediction model, Represents key shear features The contribution value function of n is the total number of key shear features, Represents key shear features and key shear features The contribution value function of the interaction term, p represents the p-th anti-shear feature interaction term, and P represents the total number of anti-shear feature interaction terms.

6. The method for analyzing the shear bearing capacity of reinforced concrete beams with stirrups based on machine learning according to claim 4 is characterized in that: The step (2.4) specifically includes: Each time, only the contribution value function corresponding to one key anti-shear feature is trained; for each key anti-shear feature The corresponding contribution function or , when multiple rounds of training are performed, the remaining contribution functions remain fixed; in the contribution function or In each round of training, the key anti-shear features in the feature vector composed of multiple key anti-shear features are updated based on the training set. and / or , get the updated feature vector, input the updated feature vector into the prediction model, get the predicted value of shear bearing capacity, calculate the error between the predicted value of shear bearing capacity and its corresponding true value as the current residual, fit the residual by using the gradient boosting regression tree technique, and update the current contribution value function according to the learning rate in the hyperparameter or Parameters, where the true value is the shear bearing capacity limit value in the training set; the contribution value function or Perform M rounds of training, learn M regression trees, and gradually reduce the prediction error after M rounds of cyclic training so that the contribution value function or The parameters of the gradually converge to obtain the trained contribution value function or , and finally obtain the trained prediction model.

7. The shear bearing capacity analysis method of reinforced concrete beams with stirrups based on machine learning according to claim 1 is characterized in that: The step (4) includes the following sub-steps: (4.1) Based on the predicted shear capacity value obtained in step (3), the contribution of each key shear feature to the predicted shear capacity value is quantified using the global interpretation of the prediction model to obtain the overall importance ranking of each key shear feature and each shear feature interaction term; wherein the overall importance is equal to the absolute average of the contribution values ​​of each key shear feature or shear feature interaction term to the predicted shear capacity value on the test set samples; (4.2) Using the prediction model to obtain a local interpretation of each sample, so as to quantify the contribution of each key shear feature in the individual sample to the predicted shear bearing capacity, and obtain the shear contribution value of each key shear feature in the individual sample; (4.3) Based on the prior knowledge of shear theory, the overall importance ranking of each key shear feature and each shear feature interaction term obtained in step (4.1) and the shear contribution value of each key shear feature in the individual sample obtained in step (4.2) are analyzed to determine the rationality of the shear bearing capacity prediction value output by the prediction model and to infer the cause of the prediction error.

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