Structural security assessment method based on Bayesian integrated neural network

Abstract

According to the structure safety evaluation method based on the Bayesian integrated neural network, the uncertainty of network parameters is estimated through Bayesian inference to enhance the interpretability of a network model, and the network model is made to be suitable for small sample sets or application needing high network robustness; meanwhile, a BENN is constructed by utilizing a Bagging ensemble learning mechanism and taking BNNs as a base learner, and the accuracy of a network prediction result is improved by combining membership calculation and an information entropy value; the BNNs adopted by the method can represent the uncertainty of neural network parameters through probability distribution, the trained network has interpretability, the problem of a black box operation mechanism generally existing in the neural network is solved to a certain degree, meanwhile, the BENNs are formed by combining a Bagging ensemble learning mechanism, and the problem that a BNNs prediction result has certain randomness can be solved. The provided BENNs method can be suitable for a frame structure or a beam structure or other target structures.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering structure analysis, in particular to a structure safety assessment method based on a Bayesian integrated neural network. Background Art

[0002] Civil engineering structures are susceptible to environmental erosion and overload during their service life, and the material and mechanical properties of the components deteriorate, affecting the safety of the structural system. Therefore, it is necessary to evaluate the actual operating status of the structure through detection and monitoring, especially the online health monitoring system can provide real-time data for structural safety evaluation. However, civil engineering structures have complex structural forms, large geometric dimensions of components, a wide variety of types, unclear boundaries and connection conditions, and considering the characteristics of "massive but poor information" of response monitoring data, it is difficult to extract information related to the structural status from it.

[0003] Neural networks can achieve nonlinear mapping between structural response and parameters, or automatically extract features from massive monitoring data through unsupervised learning. They have been widely used in different engineering science fields over the past two decades, including health monitoring of civil engineering. For example, neural networks are combined to establish nonlinear mapping relationships between multi-source monitoring data in actual engineering. However, neural network methods often require a large number of high-quality samples for network parameter training, and factors such as test noise and incomplete data during the monitoring data acquisition process have an impact on the training samples of the neural network, making small sample sets possible. At the same time, the uncertainty factors that always exist in actual engineering also have an adverse effect on the neural network training process and subsequent safety assessments, resulting in one-sided evaluation results when relying on a single neural network. To this end, it is necessary to develop neural networks that can operate under small sample sets and uncertainty conditions for structural safety assessment.

[0004] In addition to traditional shallow neural networks, deep neural networks such as convolutional neural networks, generative adversarial networks, and recurrent neural networks have also been applied to the field of structural health monitoring in recent years, and have achieved high training accuracy and recognition effects on specific tasks and data sets. However, whether it is a shallow or deep neural network, its network parameters (such as weights and biases) are usually determined values ​​based on point estimates, and cannot effectively measure the uncertainty contained in the sample. At this time, probabilistic neural networks (PNNs) show their advantages in dealing with uncertainty. PNNs are a classification model that uses Bayesian decision theory. The uncertainty of network parameters is represented by probability distribution, and network parameters are estimated based on maximum likelihood estimation or expectation maximization algorithm. However, the network interpretability of PNNs is general. It usually only outputs probability distribution and cannot provide specific values ​​of parameters. Bayesian inference is not used in the network training process, which is not suitable for small sample sets. Bayesian Neural Networks (BNNs) use Bayesian inference to estimate the uncertainty of network parameters and estimate their posterior distribution through parameter prior distribution. They are more interpretable than PNNs and are suitable for small sample sets and situations requiring higher network robustness, but have higher computational complexity.

[0005] Specifically, BNNs converts network parameters from point estimates to probability distribution estimates. The training process regards network parameters as distributions rather than fixed values, which can be regarded as integrated learning of multiple neural networks. That is, in each round of network training, the posterior distribution of network parameters of multiple neural networks can be updated simultaneously, and the final prediction results are jointly determined by the output prediction values ​​of multiple networks. However, the probability distribution expression of network parameters often requires high-dimensional calculations, which makes BNNs computationally complex and requires more time for the convergence of loss functions in the training phase. The existing solutions can be roughly divided into Monte Carlo sampling and variational inference. The former requires a large amount of sampling and calculation to approximate the true solution in a large sample set manner; while the latter uses parameter variational distribution to approximate the true parameter probability posterior distribution, thereby converting the approximate solution problem into a function optimization problem, avoiding huge computational costs. In the network testing phase, BNNs need to sample the optimized parameter distribution to determine the prediction results of the network's final output, but the parameter sampling process has a certain degree of randomness, making it difficult to confirm the weights of the prediction results under different sampling conditions, which has a great impact on the structural safety assessment results. Summary of the invention

[0006] The present invention proposes a structural safety assessment method based on Bayesian integrated neural network. Compared with the traditional neural network method, BNNs can represent the uncertainty of neural network parameters by probability distribution. The trained network is interpretable, which solves the black box operation mechanism problem that is common in neural networks to a certain extent. At the same time, the present invention combines the Bagging integrated learning mechanism to form BENNs, which can solve the problem that the prediction results of BNNs have certain randomness. The proposed BENNs method can be applied to target structures such as frame structures or beam structures.

[0007] The present invention adopts the following technical solutions.

[0008] A structural safety assessment method based on Bayesian ensemble neural network is proposed. The method uses Bayesian inference to estimate the uncertainty of network parameters to enhance the interpretability of the network model, making the network model suitable for small sample sets or applications requiring high network robustness. At the same time, the Bagging ensemble learning mechanism is used to construct BENN with BNNs as the base learner, and the membership calculation and information entropy value are combined to improve the accuracy of the network prediction results.

[0009] The method comprises the following steps:

[0010] Step S1, data acquisition and preprocessing, firstly, the target structure is divided into multiple substructures, the probability distribution and degradation range of the physical parameters of each substructure are set, the parameter probability density function is sampled and the sampled values ​​of different parameters are combined, and then the structural dynamic characteristics under different parameter combinations are calculated by finite element simulation, and a training sample set is formed after standardization;

[0011] Step S2, Bayesian ensemble neural network construction: firstly, the training sample set is randomly sampled in combination with the Bagging ensemble learning mechanism, and the training sets required by different base learners are respectively constructed;

[0012] Step S3: Structural safety assessment.

[0013] In step S1, when dividing the target structure into a plurality of substructures, if the target structure is a frame structure, the substructures are divided according to different layer structures; if the target structure is a beam structure, the substructures are divided according to equal distances.

[0014] In step S1, the physical parameters of the substructure include stiffness; and the structural dynamic characteristics include modal frequency.

[0015] In step S2, each group of base learners are BNNs with the same network topology, the input is the structural dynamic characteristics, the output is the physical parameters of each substructure, and the number of output neurons is equal to the number of substructures; the network parameters of the base learners are initialized according to the normal distribution and the prior distribution of the network parameters is defined.

[0016] In step S2, the network parameters of the base learner are initialized, including weights and biases;

[0017] In step S2, the training process adopts the Adam algorithm, and uses the lower limit of evidence between the prior and posterior distributions as the loss function of the network training. When the loss function is less than a pre-set threshold, the network training is considered completed.

[0018] Step S3 includes the following steps:

[0019] Step A1: Input the measured data of the current structure into each trained base learner BENN constructed, first sample the network parameter distribution of each base learner, and obtain the prediction results of the base learner under different network parameter combinations, that is, the predicted values ​​of the physical parameters of each substructure;

[0020] Step A2: Calculate the membership of different prediction results, measure the similarity between the predicted value and the true value, and use this to determine the weight of each prediction result, and then determine the final prediction result of the base learner by weighted summation;

[0021] Step A3: Determine the final prediction result of the base learner by weighted summation.

[0022] In step A1, the uncertainty of the prediction results of different substructures is measured by information entropy. The entropy value θ of the jth substructure is j The calculation formula is as follows:

[0023]

[0024] In the formula, p is the number of base learners, q i,j represents the parameter value of substructure j predicted by the i-th base learner.

[0025] In step A2, the substructure weight δ is determined based on the calculated substructure information entropy value and the entropy weight. j ; The larger the information entropy weight is, the greater the uncertainty of the prediction result of the substructure is, and the smaller the corresponding weight is; conversely, a larger weight is given to the substructure.

[0026] In step A3, the membership of the final prediction results of all base learners in BENN is calculated, and after secondary weighting, the prediction results of different substructures are obtained. Combined with the corresponding weight δ j , and finally the state index γ of the structural system under unknown working conditions is obtained to measure the state of the structure;

[0027]

[0028] Where n is the number of substructures divided.

[0029] The present invention proposes a structural safety assessment method based on Bayesian ensemble neural network, which has the following advantages: (1) Bayesian inference is used to estimate the uncertainty of network parameters, which enhances the interpretability of the network model and is more suitable for small sample sets and situations requiring higher network robustness. (2) Bagging ensemble learning mechanism is used to construct BENN with BNNs as the base learner, and the accuracy of network prediction results is improved by combining membership calculation and information entropy value.

[0030] Compared with traditional neural network methods, the BNNs used in the present invention can use probability distribution to represent the uncertainty of neural network parameters. The trained network is interpretable, which to a certain extent solves the black box operation mechanism problem that is common in neural networks.

[0031] The present invention combines the Bagging ensemble learning mechanism to form BENNs, which can solve the problem that the prediction results of BNNs have certain randomness; the proposed BENNs method can be applied to target structures such as frame structures or beam structures.

[0032] The invention can be used for safety assessment of long-span structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0034] Attached Figure 1 It is a schematic diagram of the process of the structural safety assessment method based on the Bayesian integrated neural network of the present invention. DETAILED DESCRIPTION

[0035] As shown in the figure, a structural safety assessment method based on a Bayesian ensemble neural network uses Bayesian inference to estimate the uncertainty of network parameters to enhance the interpretability of the network model, making the network model suitable for small sample sets or applications that require high network robustness; at the same time, the Bagging ensemble learning mechanism is used to construct a BENN with BNNs as the base learner, combining membership calculation and information entropy value to improve the accuracy of network prediction results.

[0036] The method comprises the following steps:

[0037] Step S1, data acquisition and preprocessing, firstly, the target structure is divided into multiple substructures, the probability distribution and degradation range of the physical parameters of each substructure are set, the parameter probability density function is sampled and the sampled values ​​of different parameters are combined, and then the structural dynamic characteristics under different parameter combinations are calculated by finite element simulation, and a training sample set is formed after standardization;

[0038] Step S2, Bayesian ensemble neural network construction: firstly, the training sample set is randomly sampled in combination with the Bagging ensemble learning mechanism, and the training sets required by different base learners are respectively constructed;

[0039] Step S3: Structural safety assessment.

[0040] In step S1, when dividing the target structure into a plurality of substructures, if the target structure is a frame structure, the substructures are divided according to different layer structures; if the target structure is a beam structure, the substructures are divided according to equal distances.

[0041] In step S1, the physical parameters of the substructure include stiffness; and the structural dynamic characteristics include modal frequency.

[0042] In step S2, each group of base learners are BNNs with the same network topology, the input is the structural dynamic characteristics, the output is the physical parameters of each substructure, and the number of output neurons is equal to the number of substructures; the network parameters of the base learners are initialized according to the normal distribution and the prior distribution of the network parameters is defined.

[0043] In step S2, the network parameters of the base learner are initialized, including weights and biases;

[0044] In step S2, the training process adopts the Adam algorithm, and uses the lower limit of evidence between the prior and posterior distributions as the loss function of the network training. When the loss function is less than a pre-set threshold, the network training is considered completed.

[0045] Step S3 includes the following steps:

[0046] Step A1: Input the measured data of the current structure into each trained base learner BENN constructed, first sample the network parameter distribution of each base learner, and obtain the prediction results of the base learner under different network parameter combinations, that is, the predicted values ​​of the physical parameters of each substructure;

[0047] Step A2: Calculate the membership of different prediction results, measure the similarity between the predicted value and the true value, and use this to determine the weight of each prediction result, and then determine the final prediction result of the base learner by weighted summation;

[0048] Step A3: Determine the final prediction result of the base learner by weighted summation.

[0049] In step A1, the uncertainty of the prediction results of different substructures is measured by information entropy. The entropy value θ of the jth substructure is j The calculation formula is as follows:

[0050]

[0051] In the formula, p is the number of base learners, q i,j represents the parameter value of substructure j predicted by the i-th base learner.

[0052] In step A2, the substructure weight δ is determined based on the calculated substructure information entropy value and the entropy weight. j ; The larger the information entropy weight is, the greater the uncertainty of the prediction result of the substructure is, and the smaller the corresponding weight is; conversely, a larger weight is given to the substructure.

[0053] In step A3, the membership of the final prediction results of all base learners in BENN is calculated, and after secondary weighting, the prediction results of different substructures are obtained. Combined with the corresponding weight δ j , and finally the state index γ of the structural system under unknown working conditions is obtained to measure the state of the structure;

[0054]

[0055] Where n is the number of substructures divided.

[0056] Example:

[0057] The usage process of this example is as follows: First, the target structure is divided into multiple substructures, and the probability density functions of the physical parameters of the substructures are sampled and combined respectively, and the corresponding structural dynamic characteristics are calculated by finite element simulation. Secondly, the training sample set is sampled using the Bagging ensemble learning mechanism, and different base learners are trained respectively, and the posterior distribution of the network parameters is output. Then, the currently collected structural measured responses are input into each trained base learner of the constructed BENN, and the prediction results of the base learners under different network parameter combinations are obtained by random sampling. Next, the membership degree is calculated to confirm the weights of different prediction results, and the final prediction result of the base learner is determined by weighted summation. Finally, the membership degree of the final prediction results of all base learners in BENN and the information entropy values ​​of the prediction results of different substructures are calculated to confirm the weights of the base learners and substructures. By weighted summation of the prediction results and weights of the base learners, the physical parameter values ​​of each substructure predicted by BENN are obtained, and then the current state index of the structural system is obtained in combination with the weight value of the substructure to evaluate the structural state.

[0058] The technical solution adopted in this case mainly includes three modules: data collection and preprocessing, BENNs construction and structural safety assessment. The specific flow chart is as follows Figure 1 shown.

[0059] The method comprises the following steps:

[0060] Step 1: Data collection and preprocessing.

[0061] First, the target structure is divided into multiple substructures. The frame structure can be divided into substructures according to different floors, and the beam structure can be divided into substructures at equal distances. Assuming the probability distribution and degradation range of the physical parameters (such as stiffness) of each substructure, the parameter probability density function is sampled and the sampled values ​​of different parameters are combined. Then, the structural dynamic characteristics (such as modal frequency) under different parameter combinations are calculated through finite element simulation, and the training sample set is formed after standardization.

[0062] Step 2: Bayesian ensemble neural network construction

[0063] Combined with the Bagging ensemble learning mechanism, the training sample set is randomly sampled to construct the training sets required for different base learners (BaseLearner). Each group of base learners are BNNs with the same network topology. The input is the structural dynamic characteristics, and the output is the physical parameters of each substructure. The number of output neurons is equal to the number of substructures. The network parameters (such as weights and biases) of the base learners are initialized according to the normal distribution and the prior distribution of the network parameters is defined. The Adam algorithm is used in the training process, and the evidence lower bound (Evidence Lower Bound) between the prior and posterior distributions is used as the loss function of network training. When the loss function is less than the threshold set in advance, the network training is considered to be completed. Different base learners output the posterior distribution of the trained network parameters according to the corresponding training samples, and all base learners constitute a BENN. Subsequently, the validation set is used to test the prediction performance of the BENN, that is, the samples in the validation set are respectively input into the trained base learners to obtain the corresponding prediction results and compare them with the actual results. The BENN that has passed the validation can be used for subsequent structural safety assessment.

[0064] Step 3: Structural Safety Assessment

[0065] The measured data of the current structure is input into the constructed BENN (i.e., each trained base learner). The network parameter distribution of each base learner is first sampled to obtain the prediction results of the base learner under different network parameter combinations (i.e., the predicted values ​​of the physical parameters of each substructure). The membership of different prediction results is then calculated to measure the similarity between the predicted value and the true value. The weight of each prediction result is determined in this way, and the final prediction result of the base learner is determined by weighted summation.

[0066] Furthermore, the degree of uncertainty of the prediction results of different substructures is measured by information entropy. For example, the entropy value θ of the jth substructure j The calculation of is as follows:

[0067]

[0068] In the formula, p is the number of base learners, q i,j represents the parameter value of substructure j predicted by the i-th base learner.

[0069] According to the calculated substructure information entropy value, the substructure weight δ is further determined by combining the entropy weight (EntropyWeight) j The larger the information entropy weight is, the greater the uncertainty of the prediction result of the substructure is, and the smaller the corresponding weight is; conversely, a larger weight is given to the substructure.

[0070] Calculate the membership of the final prediction results of all base learners in BENN, and after secondary weighting, obtain the prediction results of different substructures Combined with the corresponding weight δ j , and finally the state index γ of the structural system under unknown working conditions is obtained to measure the state of the structure.

[0071]

[0072] Where n is the number of substructures divided.

Claims

1. A structural safety assessment method based on Bayesian integrated neural network, characterized by: The method uses Bayesian inference to estimate the uncertainty of network parameters to enhance the interpretability of the network model, making the network model suitable for small sample sets or applications requiring high network robustness; at the same time, the Bagging ensemble learning mechanism is used to construct BENN with BNNs as the base learner, and the membership calculation and information entropy value are combined to improve the accuracy of the network prediction results.

2. The structural safety assessment method based on Bayesian integrated neural network according to claim 1 is characterized in that: The method comprises the following steps: Step S1, data collection and preprocessing, firstly, the target structure is divided into multiple substructures, the probability distribution and degradation range of the physical parameters of each substructure are set, the parameter probability density function is sampled and the sampled values ​​of different parameters are combined, and then the structural dynamic characteristics under different parameter combinations are calculated by finite element simulation, and a training sample set is formed after standardization; Step S2, Bayesian ensemble neural network construction: firstly, the training sample set is randomly sampled in combination with the Bagging ensemble learning mechanism, and the training sets required by different base learners are respectively constructed; Step S3: Structural safety assessment.

3. The structural safety assessment method based on Bayesian integrated neural network according to claim 2 is characterized in that: In step S1, when dividing the target structure into a plurality of substructures, if the target structure is a frame structure, the substructures are divided according to different layer structures; if the target structure is a beam structure, the substructures are divided according to equal distances.

4. The structural safety assessment method based on Bayesian integrated neural network according to claim 2 is characterized in that: In step S1, the physical parameters of the substructure include stiffness; and the structural dynamic characteristics include modal frequency.

5. The structural safety assessment method based on Bayesian integrated neural network according to claim 2 is characterized in that: In step S2, each group of base learners are BNNs with the same network topology, the input is the structural dynamic characteristics, the output is the physical parameters of each substructure, and the number of output neurons is equal to the number of substructures; the network parameters of the base learners are initialized according to the normal distribution and the prior distribution of the network parameters is defined.

6. The structural safety assessment method based on Bayesian integrated neural network according to claim 2 is characterized in that: In step S2, the network parameters of the base learner are initialized, including weights and biases; in step S2, the training process adopts the Adam algorithm, and the lower limit of evidence between the prior and posterior distributions is used as the loss function of the network training. When the loss function is less than a threshold set in advance, the network training is considered to be completed.

7. The structural safety assessment method based on Bayesian integrated neural network according to claim 2 is characterized in that: In step S3, The steps include: Step A1: Input the measured data of the current structure into each trained base learner BENN constructed, first sample the network parameter distribution of each base learner, and obtain the prediction results of the base learner under different network parameter combinations, that is, the predicted values ​​of the physical parameters of each substructure; Step A2: Calculate the membership of different prediction results, measure the similarity between the predicted value and the true value, and use this to determine the weight of each prediction result, and then determine the final prediction result of the base learner by weighted summation; Step A3: Determine the final prediction result of the base learner by weighted summation.

8. The structural safety assessment method based on Bayesian integrated neural network according to claim 7 is characterized in that: In step A1, the uncertainty of the prediction results of different substructures is measured by information entropy. The entropy value of the jth substructure is The calculation formula is as follows: In the formula, p is the number of base learners, q i,j represents the parameter value of substructure j predicted by the i-th base learner.

9. The structural safety assessment method based on Bayesian integrated neural network according to claim 7 is characterized in that: In step A2, the substructure weight δ is determined based on the calculated substructure information entropy value and the entropy weight EntropyWeight. j ; The larger the information entropy weight is, the greater the uncertainty of the prediction result of the substructure is, and the smaller the corresponding weight is; conversely, a larger weight is given to the substructure.

10. The structural safety assessment method based on Bayesian integrated neural network according to claim 7 is characterized in that: In step A3, the membership of the final prediction results of all base learners in BENN is calculated, and after secondary weighting, the prediction results of different substructures are obtained. Combined with the corresponding weight δ j , and finally the state index γ of the structural system under unknown working conditions is obtained to measure the state of the structure; Where n is the number of substructures divided.

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