Reinforced concrete column failure mode probability prediction method based on machine learning

Abstract

The invention discloses a reinforced concrete column failure mode probability prediction method based on machine learning. The method comprises the following steps: S1, establishing a Vp / Vn data set; s2, obtaining characteristic parameters influencing the reinforced concrete column damage model, and constructing a test data set based on the characteristic parameters and the Vp / Vn data set; s3, establishing a reinforced concrete column damage model probability prediction model; s4, training the Vp / Vn prediction model based on the test data set to obtain a trained Vp / Vn prediction model, and performing prediction based on the trained Vp / Vn prediction model to obtain a new Vp / Vn data set; s5, training the Bayesian probability model based on the destruction mode data and the new Vp / Vn data set to obtain a trained Bayesian probability model; and S6, based on the trained Vp / Vn prediction model and the trained Bayesian probability model, obtaining the occurrence probability of the reinforced concrete column corresponding to each failure mode. According to the method, the RC column failure mode is predicted through the established reinforced concrete column failure model probability prediction model, the prediction process is divided into two stages, compared with a traditional method, the efficiency is remarkably improved, meanwhile, the accuracy of the prediction result is improved, and the method is suitable for failure mode prediction of reinforced concrete columns of different types.

Description

Technical Field

[0001] The present invention relates to the technical field of reinforced concrete column detection, and in particular to a reinforced concrete column failure mode probability prediction method based on machine learning. Background Art

[0002] Reinforced concrete columns, or RC columns, are key components in building structures and bridges, and their overall safety is closely related to the stability of the structure / bridge. Under strong earthquake excitation, RC columns may fail in a variety of failure modes, mainly including flexural failure (FF), bending-shear failure (FSF), and shear failure (SF). Among them, flexural failure is a ductile failure, while bending-shear failure and shear failure are brittle failures. In the design process, FF is the most expected failure type in RC columns because it has obvious signs before losing bearing capacity. However, due to insufficient reinforcement ratio and parameter uncertainty, FSF and SF are also common in existing RC column components. Different failure modes lead to significant differences in the seismic performance of components, and the seismic performance of RC columns is directly related to the overall safety of the building or bridge structure; especially in shear failure, the longitudinal reinforcement cannot yield, showing a completely brittle characteristic, and cannot support the safety of the entire structure through energy dissipation. Therefore, this failure mode must be avoided in seismic design. In addition, bending-shear failure, where the deformation capacity of the longitudinal reinforcement after yielding is not as good as that of bending failure, also needs to be controlled in the design.

[0003] The existing single failure mode prediction methods predict a possible failure mode by directly inputting parameters, which cannot fully reflect the various possible failure situations of the structure under different conditions. This lack of information may lead to one-sidedness in design and reinforcement decisions. In addition, many models do not explicitly consider the uncertain aspects of failure mode prediction, such as the possibility of RC columns developing into other failures due to changes in material properties or environment. Therefore, they cannot effectively describe and capture the complex mechanical relationship between input parameters and failure modes, which may reduce the reliability of prediction results. Summary of the invention

[0004] The present invention provides a method for predicting the failure mode probability of reinforced concrete columns based on machine learning, so as to overcome the technical problem that the existing failure mode prediction methods are usually used to predict one failure mode, and do not explicitly consider the uncertain aspects of failure mode prediction, such as the possibility of the RC column developing into other failures due to changes in material properties or environment. Therefore, the complex mechanical relationship between input parameters and failure modes cannot be effectively described and captured, which may lead to reduced reliability of prediction results.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for predicting the probability of failure mode of reinforced concrete columns based on machine learning, the specific steps include:

[0007] S1: Obtain structural parameters of reinforced concrete columns, calculate section shear force demand and section total shear force based on the structural parameters, and establish a data set including a ratio of section shear force demand to section total shear force, i.e., a Vp / Vn data set;

[0008] S2: Acquire characteristic parameters that affect the failure model of reinforced concrete columns, and construct a test data set based on the characteristic parameters and the Vp / Vn data set; the characteristic parameters include shear span ratio, stirrup spacing, concrete strength, steel strength, reinforcement ratio, and stirrup ratio of reinforced concrete columns;

[0009] S3: Establishing a probability prediction model for a reinforced concrete column failure model, wherein the probability prediction model for a reinforced concrete column failure model includes a Vp / Vn prediction model and a Bayesian probability model;

[0010] S4: training the Vp / Vn prediction model based on the test data set to obtain a trained Vp / Vn prediction model, and predicting a new Vp / Vn data set based on the trained Vp / Vn prediction model;

[0011] S5: acquiring failure mode data corresponding to a number of reinforced concrete columns, and training the Bayesian probability model based on the failure mode data and the new Vp / Vn data set to obtain a trained Bayesian probability model;

[0012] S6: Based on the trained Vp / Vn prediction model and the trained Bayesian probability model, the occurrence probability of each failure mode of the reinforced concrete column is obtained.

[0013] Furthermore, the calculation process of the section shear force requirement is:

[0014] The moment curvature analysis of the reinforced concrete column section is performed to calculate the value of Vp. The calculation formula is:

[0015]

[0016] Where M max is the maximum bending moment of the reinforced concrete column section, and a is the shear span of the column member.

[0017] Furthermore, the calculation process of the total shear force of the section is:

[0018] The empirical model proposed by Sezen is used to calculate the total shear force of the section, i.e., the shear strength. The calculation formula is:

[0019]

[0020] Where, h0 is the effective height of the section; P is the axial load; Ag is the cross-sectional area of ​​the column; Asv is the cross-sectional area of ​​the stirrup; u Δ is the displacement ductility coefficient, that is, the ratio of the maximum displacement to the yield displacement.

[0021] Furthermore, in S3, the Vp / Vn prediction model is a prediction model using a BP neural network architecture.

[0022] Furthermore, in S5, the process of training the Bayesian probability model based on the predicted value of Vp / Vn is:

[0023] S51: Calculate the prior probability P(X) of each failure mode, the calculation formula is:

[0024]

[0025] Where X represents a certain failure mode; the failure mode includes bending failure FF, bending-shear failure FSF or shear failure SF, N is the total number of samples of all failure modes of RC columns, N X is the number of samples corresponding to one failure mode of the RC column;

[0026] S52: Calculate the probability of each Vp / Vn corresponding to the three different damage modes based on the likelihood function. The calculation formula is:

[0027]

[0028] In the formula, μ X is the average value of Vp / Vn corresponding to the failure mode, is the variance of the Vp / Vn value corresponding to the failure mode;

[0029] S53: Calculate the marginal probability, the calculation formula is:

[0030] P(V p / V n )=∑P(V p / V n |X)·P(X)(12)

[0031] S54: Based on the prior probability P(X), likelihood function P(V p / V n |X) and marginal probability P(V p / V n ) to construct a Bayesian probability model, and calculate the posterior probability P(X|V p / V n ), that is, the probability of occurrence of each failure mode, is calculated as follows:

[0032]

[0033] Beneficial effects: The present invention predicts the failure mode of RC columns by establishing a probability prediction model for the failure model of reinforced concrete columns. The prediction process is divided into two stages. In the first stage, the Vp / Vn value is obtained by the trained Vp / Vn prediction model, and then the predicted Vp / Vn value is input into the trained Bayesian probability model to obtain the probability of occurrence of each failure mode of the RC column. Compared with the traditional method, this method significantly improves the efficiency, and at the same time, it uses the ability of machine learning algorithms to process large-scale data and complex nonlinear relationships, improves the accuracy of the prediction results, and fully reflects the influence of characteristic parameters on Vp / Vn values. In addition, the model can be continuously optimized and expanded according to characteristic parameters and data to adapt to the prediction of failure modes of different types of reinforced concrete columns. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0035] Figure 1 It is a flow chart of a method for predicting probability of failure mode of reinforced concrete columns based on machine learning in the present invention;

[0036] Figure 2 : is a probability distribution diagram of three failure modes measured in an embodiment of the present invention;

[0037] Figure 3 It is a schematic diagram of the GUI interface for measuring VP / VN and failure mode in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] This embodiment provides a method for predicting the probability of failure mode of reinforced concrete columns based on machine learning. Figure 1 As shown, the specific steps include:

[0040] S1: Obtain structural parameters of reinforced concrete columns, calculate section shear force demand and section total shear force based on the structural parameters, and establish a data set including a ratio of section shear force demand to section total shear force, i.e., a Vp / Vn data set;

[0041] Specifically, the cross-sectional shear force demand may also be referred to as the actual cross-sectional shear strength. Since the cross-sectional shear force demand is a more conventional technical term in this field, the term cross-sectional shear force demand is used in this embodiment.

[0042] In a specific embodiment, the calculation process of the cross-section shear force requirement is:

[0043] The moment curvature analysis of the reinforced concrete column section is performed to calculate the value of Vp. The calculation formula is:

[0044]

[0045] Where M max is the maximum bending moment of the reinforced concrete column section, and a is the shear span of the column member.

[0046] In a specific embodiment, the calculation process of the total cross-section shear force is:

[0047] The empirical model proposed by Sezen is used to calculate the total shear force of the section, i.e., the shear strength. The calculation formula is:

[0048]

[0049] Where, h0 is the effective height of the section; P is the axial load; Ag is the cross-sectional area of ​​the column; Asv is the cross-sectional area of ​​the stirrup; u Δ is the displacement ductility coefficient, that is, the ratio of the maximum displacement to the yield displacement.

[0050] S2: Acquire characteristic parameters that affect the failure model of reinforced concrete columns, and construct a test data set based on the characteristic parameters and the Vp / Vn data set; the characteristic parameters include shear span ratio, stirrup spacing, concrete strength, steel strength, reinforcement ratio, and stirrup ratio of reinforced concrete columns;

[0051] S3: Establishing a probability prediction model for a reinforced concrete column failure model, wherein the probability prediction model for a reinforced concrete column failure model includes a Vp / Vn prediction model and a Bayesian probability model;

[0052] S4: training the Vp / Vn prediction model based on the test data set to obtain a trained Vp / Vn prediction model, and predicting a new Vp / Vn data set based on the trained Vp / Vn prediction model;

[0053] In a specific embodiment, in S3, the Vp / Vn prediction model is a prediction model using a BP neural network architecture; the structure of the neural network includes an input layer, multiple hidden layers and an output layer. The following are the specific calculation steps and data transmission process of each layer in the BP neural network:

[0054] The input layer receives the characteristic parameters related to reinforced concrete columns, namely, the shear span ratio, stirrup spacing, concrete strength, steel strength, reinforcement ratio, and stirrup ratio of reinforced concrete columns, and passes the input data to the first hidden layer for processing. The processing formula of the first hidden layer is:

[0055] z (1) =W (1) a (0) +b (1) (3)

[0056] In the formula, z (1) is the linear combination result of the first hidden layer; W (1) is the weight matrix of the first hidden layer; a (0) is the activation output of the previous layer (or the input data of the first layer); b (1) is the bias vector.

[0057] Use the first activation function to perform a nonlinear transformation on the linear combination result to obtain the output result a of the first hidden layer (1) , expressed as:

[0058] a (1) =f(z (1) ) (4)

[0059] A (1) As input, it is passed to the second hidden layer. The calculation process of the second hidden layer is similar to that of the first hidden layer. The calculation formula is:

[0060] z (2) =W (2) a (1) +b (2) (5)

[0061] Among them, a (1) is the output from the first hidden layer, W (2) is the weight matrix of the second hidden layer, b (2) is the bias vector for the second hidden layer.

[0062] Use the second activation function to (2) Perform nonlinear transformation to obtain the output a of the second layer (2) , expressed as:

[0063] a (2) =f(z (2) ) (6)

[0064] A (2) As input, it is passed to the third hidden layer. The calculation process of the third hidden layer is similar to the first two hidden layers. The calculation formula is:

[0065] z (3) =W (3) a (2) +b (3) (7)

[0066] Among them, a (2) is the output from the second hidden layer, W (3) is the weight matrix of the third hidden layer, b (3) is the bias vector of the third hidden layer.

[0067] Use the third activation function to (3) Perform nonlinear transformation to obtain the output a of the third layer (3) , expressed as:

[0068] a (3) =f(z (3) ) (8)

[0069] A (3) As input, it is passed to the output layer, which receives the output from the third hidden layer and performs the final calculation. The calculation formula is:

[0070] z (l) =W (l) a (3) +b (l) (9)

[0071] Among them, a (3) is the output from the third hidden layer, W (l) is the weight matrix of the output layer, b (l) is the bias vector of the output layer.

[0072] Use the fourth activation function to (l) Perform nonlinear transformation to obtain the final output a (l) , that is, the predicted Vp / Vn value, expressed as:

[0073] a (l) =f(z (l) ) (10)

[0074] After the forward propagation calculation of the output layer is completed, the difference between the predicted value Vp / Vn of the Vp / Vn prediction model and the actual value is measured by calculating the loss function. The calculation formula is:

[0075]

[0076] In the formula, m is the number of samples, y is i is the true value of the i-th sample, is the predicted value of the i-th sample.

[0077] After calculating the loss function, back propagation is used to calculate the gradient of the loss function for each parameter (weight and bias). The error of each layer is calculated through the back propagation algorithm, and the parameters of the Vp / Vn prediction model are updated. The purpose of back propagation is to adjust the weight and bias of each layer in the Vp / Vn prediction model according to the gradient of the loss function. The expression is as follows:

[0078]

[0079] In the formula, δ (l) is the error term at level l.

[0080] At the same time, in each iteration, from the beginning to the end of training, the parameter update of the Vp / Vn prediction model is a continuous process, as shown in formulas (13) and (14). This continuous updating of parameters makes the Vp / Vn prediction model gradually approach the optimal solution, thereby minimizing the loss function and improving the prediction performance.

[0081]

[0082] In the formula, η is the learning rate, which determines the step size of parameter update and is usually 10 -3 .

[0083] Specifically, during the training process of the Vp / Vn prediction model, the model parameters are adjusted layer by layer through back propagation to minimize the loss function, so that the Vp / Vn prediction model can eventually accurately predict the Vp / Vn ratio of reinforced concrete columns.

[0084] S5: acquiring failure mode data corresponding to a number of reinforced concrete columns, and training the Bayesian probability model based on the failure mode data and the new Vp / Vn data set to obtain a trained Bayesian probability model;

[0085] S6: Based on the trained Vp / Vn prediction model and the trained Bayesian probability model, the occurrence probability of each failure mode of the reinforced concrete column is obtained.

[0086] Specifically, in this embodiment, the predicted value of Vp / Vn obtained in the first stage is used as an input value for the failure mode probability prediction in the second stage.

[0087] In a specific embodiment, in S5, the process of training the Bayesian probability model based on the predicted value of Vp / Vn is:

[0088] S51: Calculate the prior probability P(X) of each failure mode, the calculation formula is:

[0089]

[0090] Where X represents a certain failure mode, and the failure mode includes bending failure FF, bending-shear failure FSF or shear failure SF; N is the total number of samples of all failure modes of RC columns, N x is the number of samples corresponding to one failure mode of the RC column;

[0091] Specifically, in this embodiment, the prior probability of each failure mode is first calculated, that is, the initial likelihood of each class in the absence of observed data. Using 80% of the data of the Vp / Vn values ​​predicted in the first stage as the training set, the prior distribution of RC column failure modes is established based on the Bayesian method, which reflects the initial assumptions about the failure modes of reinforced concrete columns.

[0092] S52: Calculate the probability of each Vp / Vn corresponding to the three different damage modes based on the likelihood function. The calculation formula is:

[0093]

[0094] In the formula, μ X is the average value of Vp / Vn corresponding to the failure mode, is the variance of the Vp / Vn value corresponding to the failure mode;

[0095] Specifically, a normal distribution is adopted for the Vp / Vn value of each failure mode, the Vp / Vn data predicted in the first stage are used as the data set of this stage, 80% of the data are used as the training set, and the mean and variance are used to define the likelihood function.

[0096] S53: Calculate the marginal probability, which represents the total probability of observing the Vp / Vn value in all failure modes, and the calculation formula is:

[0097] P(V p / V n )=∑P(V p / V n |X)·P(X) (12)

[0098] Specifically, the sum of the posterior probabilities of all failure modes is guaranteed to be equal to 1 by the marginal probability, which is obtained by the weighted sum of the likelihood function and the prior probability of 80% of the training set.

[0099] S54: Based on the prior probability P(X), likelihood function P(V p / V n|X) and marginal probability P(V p / V n ) to construct a Bayesian probability model, and calculate the posterior probability P(X|V p / V n ), that is, the probability of occurrence of each failure mode, such as Figure 2 As shown, the calculation formula is:

[0100]

[0101] Specifically, the occurrence probability of each failure mode corresponding to the reinforced concrete column can be known through the posterior probability. In this embodiment, 20% of the predicted Vp / Vn data is used as a test set to test the possibility of each failure mode under a given Vp / Vn value. Specifically, a higher posterior probability indicates that the failure mode is more likely to occur in the observed data.

[0102] Specifically, in the two-stage method proposed in this embodiment, the first stage uses a machine learning method to associate the characteristic parameters of the RC column with the failure mode of the RC column through the intermediate parameter Vp / Vn, that is, the value of Vp / Vn is predicted by the BP neural network model, and the probability of the failure mode is predicted according to the predicted value of Vp / Vn in the second stage. The two-stage method enables the reinforced concrete column failure mode probability prediction model to better capture the relationship between the input characteristic parameters and the failure mode, thereby improving the prediction performance; by introducing Vp / Vn, not only the maximum bending moment of the RC column under load is considered, but also the influence of the characteristic parameters related to the failure mechanism of the RC column (such as steel bar strength, concrete strength, etc.) on the failure mode can be fully reflected. The input method is as follows: Figure 3 As shown, by inputting the characteristic parameters, the value of Vp / Vn and the probability of the corresponding failure mode can be obtained. In summary, the two-stage method adopted by the present invention can more comprehensively integrate the influence of characteristic parameters and force behavior on the failure mode, thereby improving the prediction performance of the failure mode of RC columns.

[0103] Specifically, when training the Bayesian probability model, the training set is used in formulas (10), (11) and (12), and the test set is used in formula (13). Since the likelihood function measures the probability of observing the training set data under a given hypothesis (such as a certain damage mode), the likelihood function is usually estimated using the data in the training set. The marginal probability is the sum of the probabilities of observing the data under all possible hypotheses. Therefore, when calculating the marginal probability, the data in the training set is also used to evaluate the comprehensive probability of all possible events. The posterior probability is the probability of the event occurring after observing the new test set data using the prior probability and the likelihood function. Therefore, the posterior probability is obtained by combining the prior probability, the likelihood function, the marginal probability and the new test set data.

[0104] In this embodiment, in order to verify the effectiveness of the method proposed in this embodiment, the following experiments were conducted. In the first stage, the characteristic parameters of the reinforced concrete column of a typical engineering component, the shear span ratio, stirrup spacing, concrete strength, steel strength, reinforcement ratio and stirrup ratio were obtained through data investigation and statistics, and the data of Vp / Vn were calculated. The characteristic parameters were used as input parameters and Vp / Vn output parameters to construct a test data set, and the test data set was randomly divided into a training set and a test set; in this embodiment, 268 cyclic test data of reinforced concrete columns were collected, and the Vp / Vn prediction model was trained using the training set to obtain the trained Vp / Vn prediction model; specifically, the number of input layer neural networks n1 of the Vp / Vn prediction model was set to 8, the number of hidden layer neural networks n2 was set to 2×n1+1=17, and the number of output layer neural networks was set to 1. In the second stage, the occurrence probabilities of the three failure modes were obtained through the Bayesian probability model.

[0105] The present invention adopts artificial neural network algorithm and Bayesian learning algorithm to obtain reinforced concrete column mode probability prediction model, so as to predict three failure modes, and compare the prediction results with other machine learning models such as support vector machine SVM, random forest RF, gradient boosting tree GB, etc., including comparing the first stage test indicators MSE, RMSE, MAE, R 2 The results of the Log Loss and Brier Score indicators in the second stage are tested. The smaller the MSE, RMSE, and MAE in the first stage, the better the R 2 The larger the value, the better the model. In the second stage, the smaller the Log Loss and Brier Score are, the better the model is. The comparison results are shown in Tables 1 and 2. The BP neural network proposed in the present invention has the best effect.

[0106] Table 1:

[0107]

[0108]

[0109] Table 2:

[0110]

[0111] Compared with the traditional theoretical formula method, the method proposed in the present invention avoids complex formula calculations and theoretical derivations, can process high-dimensional data, has faster and more comprehensive processing capabilities and efficiency, and also proves the ability of machine learning models in predicting the failure modes of concrete columns. The reinforced concrete column mode probability prediction model has the flexibility to adapt to new experimental data results, and can be applied to various combinations of characteristic parameters, thereby predicting the failure modes of different reinforced concrete columns.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the probability of failure mode of reinforced concrete columns based on machine learning, characterized in that: The specific steps include: S1: Obtain structural parameters of reinforced concrete columns, calculate section shear force demand and section total shear force based on the structural parameters, and establish a data set including a ratio of section shear force demand to section total shear force, i.e., a Vp / Vn data set; S2: Acquire characteristic parameters that affect the failure model of reinforced concrete columns, and construct a test data set based on the characteristic parameters and the Vp / Vn data set; the characteristic parameters include shear span ratio, stirrup spacing, concrete strength, steel strength, reinforcement ratio, and stirrup ratio of reinforced concrete columns; S3: Establishing a probability prediction model for a reinforced concrete column failure model, wherein the probability prediction model for a reinforced concrete column failure model includes a Vp / Vn prediction model and a Bayesian probability model; S4: training the Vp / Vn prediction model based on the test data set to obtain a trained Vp / Vn prediction model, and predicting a new Vp / Vn data set based on the trained Vp / Vn prediction model; S5: acquiring failure mode data corresponding to a number of reinforced concrete columns, and training the Bayesian probability model based on the failure mode data and the new Vp / Vn data set to obtain a trained Bayesian probability model; S6: Based on the trained Vp / Vn prediction model and the trained Bayesian probability model, the occurrence probability of each failure mode of the reinforced concrete column is obtained.

2. The method for predicting the probability of failure mode of reinforced concrete columns based on machine learning according to claim 1 is characterized in that: The calculation process of the cross-sectional shear demand is: The moment curvature analysis of the reinforced concrete column section is performed to calculate the value of Vp. The calculation formula is: Where M max is the maximum bending moment of the reinforced concrete column section, and a is the shear span of the column member.

3. The method for predicting the probability of failure mode of reinforced concrete columns based on machine learning according to claim 2 is characterized in that: The calculation process of the total shear force of the section is: The empirical model proposed by Sezen is used to calculate the total shear force of the section, i.e., the shear strength. The calculation formula is: Where, h0 is the effective height of the section; P is the axial load; Ag is the cross-sectional area of ​​the column; Asv is the cross-sectional area of ​​the stirrup; u Δ is the displacement ductility coefficient, that is, the ratio of the maximum displacement to the yield displacement.

4. The method for predicting the probability of failure mode of reinforced concrete columns based on machine learning according to claim 3 is characterized in that: In S3, the Vp / Vn prediction model is a prediction model using a BP neural network architecture.

5. According to the method for predicting the probability of failure mode of reinforced concrete columns based on machine learning in claim 4, in S5, the process of training the Bayesian probability model based on the predicted value of Vp / Vn is: S51: Calculate the prior probability P(X) of each failure mode, the calculation formula is: Where X represents a certain failure mode; the failure mode includes bending failure FF, bending-shear failure FSF or shear failure SF, N is the total number of samples of all failure modes of RC columns, N X is the number of samples corresponding to one failure mode of the RC column; S52: Calculate the probability of each Vp / Vn corresponding to the three different damage modes based on the likelihood function. The calculation formula is: In the formula, μ X is the average value of Vp / Vn corresponding to the failure mode, is the variance of the Vp / Vn value corresponding to the failure mode; S53: Calculate the marginal probability, the calculation formula is: P(V p / V n )=∑P(V p / V n |X)·P(X) (12) S54: Based on the prior probability P(X), likelihood function P(V p / V n |X) and marginal probability P(V p / V n ) to construct a Bayesian probability model, and calculate the posterior probability P(X|V p / V n ), that is, the probability of occurrence of each failure mode, is calculated as follows:

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