Structural damage assessment method based on nonparametric Bayesian model and measured data

Abstract

The invention discloses a structural damage assessment method based on a nonparametric Bayesian model and measured data. Belongs to the technical field of measurement. Acceleration data detected by a sensor are processed through an NE < x > T method to obtain inherent frequency of a structure, and clustering analysis is carried out on the obtained inherent frequency of vibration of different orders of a building through a non-parametric Bayesian mixture method. And carrying out recognition and quantitative analysis on a clustering analysis result in combination with a maximum likelihood heterovariance Gaussian process and a structural damage degree of a Bayesian factor, and carrying out regression analysis by adopting a maximum likelihood heterovariance Gaussian process model MLHGP based on a nonparametric Bayesian model to realize accurate recognition of the structural damage of the building. According to the method, the damage degree is judged through the size of the Bayesian factor, the early and middle stage development condition of the structural damage can be accurately defined, and the method is small in calculation amount, high in evaluation precision and high in universality.

Description

Technical Field

[0001] The invention proposes a structural damage assessment method based on a non-parametric Bayesian model and measured data, belonging to the technical field of measurement. Background Art

[0002] At present, many major engineering structures in long-term service have been installed with structural health monitoring systems. Obtaining structural response data through structural health monitoring systems, conducting structural damage assessment based on monitoring data, and further carrying out structural safety operation and maintenance management are currently one of the research hotspots in the field of structural health monitoring.

[0003] Structural health monitoring data has the characteristics of large quantity and large data noise, and the working state of civil engineering structures is generally complex, so it is difficult to make reasonable inferences about the distribution form of data in advance. Clustering is a commonly used unsupervised machine learning method that can classify data according to the characteristics of the data structure. It is more suitable for processing data pattern recognition problems that cannot be labeled in advance, such as K-means clustering, Gaussian mixture model, support vector clustering, self-organizing map, etc. Therefore, the application of clustering methods in structural damage identification has also received great attention. For example, Alamdari et al. improved the K-means clustering method to eliminate the adverse effects of outliers in the clustering process, and identified crack damage and sensor failure in a steel arch bridge; at the same time, Zhou et al. used a hierarchical clustering method to identify the cross-sectional damage of a free beam model, which can avoid the setting of the structural reference state compared to the distance metric-based method.

[0004] However, clustering methods also have certain limitations, especially in terms of parameter settings. Different parameter settings will have a significant impact on the clustering effect, so different algorithms need to be used for different data structures. Solving the parameter setting problem is crucial to improving the accuracy of clustering methods in structural damage identification.

[0005] In the field of structural damage assessment, Jiang et al. used non-parametric Bayesian hypothesis testing in the early stage to obtain the Bayesian factor evaluation index for evaluating the accuracy of system identification through the difference between experimental data and model prediction values, and thus carried out damage probability assessment. Lindley proposed a clustering method for automatically identifying acoustic emission events from a probability perspective, introduced the non-parametric Bayesian algorithm of the Dirichlet process, and provided a more sensitive damage identification method. Summary of the invention

[0006] Purpose of the invention: In view of the shortcomings of the prior art, a structural damage assessment method based on a non-parametric Bayesian model and measured data is proposed. The method has simple steps and is easy to use. It can automatically perform clustering analysis on building structure health monitoring data without specifying clustering parameters, thereby achieving accurate identification of building structure damage.

[0007] To achieve the above technical objectives, the present invention discloses a structural damage assessment method based on a non-parametric Bayesian model and measured data, and the specific steps are as follows:

[0008] Installing a structural health monitoring system on the building, the structural health monitoring system comprising a plurality of vibration monitoring sensors arranged at different locations on the building, and a computer for recording data from the vibration monitoring sensors;

[0009] When the building is not affected by the outside world and the structure is healthy, the vibration monitoring sensor of the structural health monitoring system is used to collect the acceleration data of the building within a set time. Then the natural excitation NExT method is used to process the acceleration data measured by the vibration monitoring sensor to obtain the natural frequencies of vibrations of different orders of the building when the building is not affected by the outside world and the structure is healthy. The natural frequency data is defined as the health status data.

[0010] The nonparametric Bayesian hybrid method is used to perform cluster analysis on the natural frequencies of different orders of vibration of the building.

[0011] The cluster analysis results are combined with the maximum likelihood heteroskedastic Gaussian process and Bayesian factor to identify and quantify the degree of structural damage;

[0012] The maximum likelihood heteroskedastic Gaussian process model MLHGP based on the non-parametric Bayesian model is used for regression analysis: the obtained regression model is set as the null hypothesis condition, and then the natural frequency data generated by the building that needs to be evaluated for health is subjected to regression analysis using the MLHGP model. The closer the regression model formed by the regression analysis is to the natural frequency data regression model in a healthy state, the healthier the structural state of the building in this time period is considered to be; the more the regression model deviates from the natural frequency data regression model in a healthy state, the more the structural state of the building in this time period is considered to be damaged; by combining the regression model form, original data, model mean, and variance for comprehensive evaluation, the Bayesian factor results of the natural frequency data regression models of different orders in different time periods are obtained, and the Bayesian factor results are obtained by comparing the natural frequency data regression models of different orders in a healthy state with the Bayesian factor results. The larger the value of the Bayesian factor, the higher the deviation between its regression model and the regression model in a healthy state.

[0013] Achieve accurate identification of building structural damage.

[0014] Furthermore, the nonparametric Bayesian hybrid method adopts a nonparametric Bayesian model based on an infinite-dimensional Gaussian mixture model for cluster analysis. The infinite-dimensional Gaussian mixture model is in the form of:

[0015]

[0016] in w i is the proportion of different Gaussian distributions in the infinite-dimensional Gaussian mixture model, and satisfies the condition w i ≥0, There exists a random probability distribution G on the measurable space Ω, with a positive real number α as a parameter. The probability distribution G satisfies the following conditions: for any finite partition of the measurable space, A1,…,A k All of them meet [G(A1),…,G(A k )]~Dir[αG0(A1),…,αG0(A k )], then the probability distribution G obeys the Dirichlet process with base distribution G0 and hyperparameter α, denoted as G~DP(α,G0); the infinite dimensional Gaussian mixture model y with Dirichlet process as prior distribution i for:

[0017] y i ~N(y i ; μ, Σ) (2),

[0018] Among them μ, Σ~G, G~DP(α, G0), G0(μ; Σ) = N(μ; m, B)·W(Σ -1 ; r, R), μ represents the mean vector, ∑ represents the covariance matrix, G represents the random probability distribution, DP represents the Dirichlet process, α represents the hyperparameter, G0 represents the basis distribution, m represents the mean vector, B represents the covariance matrix, r represents the degree of freedom, the scale matrix R, where N is the multivariate normal distribution and W is the Wishart distribution.

[0019] Furthermore, it is assumed that the acceleration data obtained by the structural health monitoring system is a mixture of multiple independent Gaussian distributions, and the probability model of the behavior is constructed using the mixed Gaussian distribution;

[0020] The data points collected by a vibration monitoring sensor placed on the building are organized into a polynomial distribution set Π according to time. Each Π in the set k , represents the probability that the data point belongs to category k, where k = 1, 2, 3…, K, K represents the number of categories, and satisfies Each state of the data point structure is defined by a corresponding Gaussian distribution, and each Gaussian distribution is defined by a mean μ k and variance∑ k ; For each data point collected by the sensor, set x i ,get:

[0021]

[0022] where c i Subordinate to the multinomial distribution Π, c i~Mult(Π); When defining the classification, it is necessary to determine the parameters of the non-parametric Bayesian model, including the number of classifications K, the mixing ratio π, the clustering parameters {μ1,…,μx,∑1,…,∑ K}; or use the total parameter vector to represent: Θ = {K, π, μ1, ..., μ K ,∑1,…,∑ K},θ k ={π k , μ k ,∑ k}; Use the expectation maximization method to determine the parameter θ k , the Bayesian information criterion or Akaike information criterion is used to determine the number of classifications K.

[0023] Furthermore, the observed prior data is used to shape the nonparametric Bayesian model on the Bayesian basis:

[0024] First, in the nonparametric Bayesian model, the clustering parameter μ k and∑ k Set the prior value on the prior data μ k and∑ k Set to be conjugate with the Gaussian distribution, which is the likelihood distribution. Therefore, the prior on the mean is a multivariate Gaussian distribution, and the prior on the covariance is an inverse Wishart distribution. These prior distributions have their own hyperparameters, namely the prior mean μ0 of the mean vector of the Gaussian distribution, the weight of the mean vector of the Gaussian distribution k 0, the weight Σ0 of the mean vector of the Gaussian distribution, the degree of freedom parameter v0 of the inverse Wishart distribution, and combining these on a prior distribution clustering parameter H, we get:

[0025]

[0026] IW represents inverse Wishart distribution, ∑ represents variance;

[0027] In order to perform Bayesian inference on the mixture ratio π and clustering parameters, another prior is set first, and the prior conjugate of the multinomial distribution set is selected. The multinomial distribution set is a Dirichlet distribution controlled by the intensity parameter α. The limit of classification K→∞ is set to form an infinite Gaussian mixture model, which is expressed as:

[0028]

[0029]

[0030] The clustering parameters, mean, and covariance in the infinite Gaussian mixture model are inferred by analytical marginalization, which eliminates the need for sampling and is obtained by using the posterior predictive distribution p(x i |D -i) gives the posterior distribution of each parameter, point x i Given the likelihood of the remaining observations, the new data are evaluated using collapsed Gibbs sampling;

[0031] For the Gaussian distribution in folded Gibbs sampling, the frequency data extracted from the acceleration data of the data point are first assigned to random clusters, and then a data point is selected for evaluation in each iteration, and if it is already assigned a cluster, it is re-evaluated; this data point is assigned c from its current cluster i , and update the parameters of the cluster; if the data point is the only point assigned to the cluster, destroy the data point and update the total number of clusters K; for each classification, k = 1, ..., K, the prior likelihood of the point being extracted from cluster K is evaluated; the prior is a Dirichlet process prior, and for existing clusters it is equal to:

[0032]

[0033] The prior likelihood is determined by the hyperparameter α and the current assignment to the cluster N -i，k The hyperparameter α encourages cluster growth. Increasing α will make it more likely that more clusters will appear. Since the clustering process also needs to include information from other data points, the likelihood term must be calculated to obtain the posterior likelihood of the points belonging to each cluster until a constant is obtained. When n data points are observed, the conjugate update calculation is as follows:

[0034]

[0035] After conjugate update calculation k n =k0+n,v n =v0+n, In the formula, S represents the sample mean The surrounding square and matrix, When updating the clusters with a single data point, it is performed as a rank update to the Cholesky decomposition of the posterior covariance matrix. For n data points, v n represents the posterior degrees of freedom, T represents the transpose, represents the inverse of the covariance matrix;

[0036] For each existing cluster k=1,...,K, we explain the new cluster k by computing the prior and likelihood * The generation of these prior possibilities needs to be scaled by the marginal possibilities, so that the cluster label c of data point i can be obtained i A cluster label c is randomly sampled from the multinomial distribution i , the data point i is assigned to this cluster c i, if data point i is added to an existing cluster, then the parameters of the cluster will be updated according to formula (7) and the update formula; if data point i is assigned to a new cluster, the cluster will be initialized by NIW prior and the point will be added to it according to formula (7) and the update formula; the total number of clusters is also updated to reflect the increase, K = K + 1, once these updates are completed, another point is sampled, and the above steps are repeated until all vibration monitoring sensor sampling points arranged on all buildings are traversed.

[0037] Furthermore, the quantitative analysis process of structural damage based on maximum likelihood heteroskedastic Gaussian process and Bayesian factor is as follows:

[0038] For solving the Bayesian factor, a nonlinear regression model is generated by the monitoring data of the vibration monitoring sensor. If the regression curve form and its mean of the regression model are closer to the regression curve form and mean of the natural frequency data regression model under the healthy state data, the data is considered to be healthier. It is necessary to perform nonlinear regression on the data and obtain the parameters in its regression curve. The purpose of solving the nonlinear regression problem by Gaussian process is to obtain the regression equation formula (8). The data in the polynomial distribution set composed of each sensor monitoring data corresponds to the data in the time series t to form a time series. The Gaussian process calculates each sensor sampling point once, and uses the identity of the multivariate Gaussian distribution to recalculate the variance of the sum of all sensor monitoring data. The regression modeling of all sensor monitoring data without changing the variance is performed, as shown in the following formula:

[0039] s i =f(t i )+ε i (8)

[0040] The natural frequency data of the period to be tested is subjected to regression analysis using the MLHGP model to obtain the regression data:

[0041]

[0042] In the formula, q is the sample size, Output s for training i The posterior predictive distribution of is sampled, which is a Gaussian distribution with mean The variance is gi2 represents the noise level;

[0043] Construct Bayesian factor: First, calculate the residual between the actual measurement point sensor data and the regressed data, and identify the residual calculation result as a random variable that obeys Gaussian distribution. Then, perform Bayesian hypothesis test on the residual calculation result. Set zero H0 as: the mean of the residual calculation result is near 0, that is, the acceleration data of the sensor is no different from the building health status data, then the building structure is judged to be in a healthy state. Set H1 as: the mean of the residual calculation result is not 0 and there is a difference with the building health status data, then the structure is judged to be in a damaged state; the Bayesian factor is defined as the posterior probability likelihood ratio of two hypotheses:

[0044]

[0045] In the formula, B represents the Bayes factor, P represents the probability, and D represents the evidence.

[0046] Furthermore, by calculating the value of the Bayesian factor, a quantitative analysis of the damage degree of the building structure can be achieved. Due to different structures, the damage inspection criteria can be defined after judgment by expert data: the damage standard is defined as: the range of 1 to 3 corresponds to "minor damage"; the range of 3 to 10 corresponds to "substantial damage"; the range of 10 to 100 corresponds to "relatively serious damage"; >100 corresponds to "complete damage". The degree of damage is determined by the size of the Bayesian factor, and the early and middle stage development of the damage is defined.

[0047] A computer device comprising: a processor, a memory and a network interface;

[0048] The processor is connected to the memory and the network interface, wherein the network interface is used to provide a network communication function, the memory is used to store program code, and the processor is used to call the program code to execute the above-mentioned structural damage assessment method based on the non-parametric Bayesian model and measured data.

[0049] A computer-readable storage medium stores a computer program, which is suitable for being loaded by a processor and executing the above-mentioned structural damage assessment method based on a non-parametric Bayesian model and measured data.

[0050] Beneficial effects: (1) After clustering analysis using a non-parametric Bayesian model, this method can determine whether the data format has changed. Even if the data values ​​are not very different, the non-parametric Bayesian model can still be used to make an accurate cluster analysis due to the different change patterns. (2) When clustering the data of different orders of natural frequencies detected by sensors, the clustering results of the non-parametric Bayesian model are basically consistent, which is in line with the law of structural damage development. Through quantitative analysis of the clustering results, it is found that the overall differences in the clustering results of different natural frequency data are small. When the difference is the largest, the overall clustering similarity rate can reach 91.78%, indicating that the clustering results are stable and accurate. It can also be found from the autocorrelation diagram of the natural frequency data that in the process of changes in the degree of structural damage, the three different natural frequency data can reflect the structural damage situation; (3) The bridge structure was quantitatively analyzed for damage by combining the MLHGP based on the non-parametric Bayesian method with the Bayesian factor. The results are consistent with the results of the cluster analysis of the natural frequency data using the non-parametric Bayesian model, proving that the non-parametric Bayesian model combined with the structural modal parameters can accurately identify structural damage; (4) This method has low computational complexity, high evaluation accuracy, and strong versatility. The degree of damage is determined by the size of the Bayesian factor, and the early and middle stages of the structural damage can be accurately defined. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the structural damage assessment method based on the non-parametric Bayesian model and measured data of the present invention;

[0052] Figure 2 A schematic diagram of the sensor arrangement of the Yonghe Bridge in Tianjin in an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the structural natural frequency obtained by analyzing the NExT method in an embodiment of the present invention;

[0054] Figure 4 Schematic diagram of cluster analysis results of the non-parametric Bayesian method in an embodiment of the present invention; (a) is the clustering result of extracting the accelerated 1st-order natural frequency data, (b) is the clustering result of the 3rd-order natural frequency, (c) shows the result of clustering the 7th-order natural frequency data using the non-parametric Bayesian method, and (d) is the three-dimensional display result of the 3 groups of natural frequency data;

[0055] Figure 5 Schematic diagram of the relationship between the 1st, 3rd, and 7th order natural frequencies extracted from the acceleration data of the Yonghe Bridge in an embodiment of the present invention; (a)-(i) represent the relationship between the 1st, 3rd, and 7th order natural frequencies at different time nodes during the gradual destruction of the structure;

[0056] Figure 6Schematic diagram of the specific difference between the first-order and third-order clustering results of acceleration data extraction in an embodiment of the present invention;

[0057] Figure 7 Schematic diagram of specific differences between the 3rd order and 7th order clustering results of acceleration data extraction in an embodiment of the present invention;

[0058] Figure 8 A schematic diagram of the specific number of clusters of 7th-order natural frequency data extracted from acceleration data in an embodiment of the present invention;

[0059] Fig. 9 Schematic diagram of Bayesian factor results of various orders at three time nodes selected in an embodiment of the present invention;

[0060] Fig.10 Schematic diagram of Bayesian factor results of different nodes in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The embodiments of the present invention are further described below in conjunction with the accompanying drawings:

[0062] like Figure 1 As shown, the present invention discloses a structural damage assessment method based on a non-parametric Bayesian model and measured data. The bridge acceleration data measured by the structural health monitoring system cannot directly identify the damage of the structure, but the natural frequency of the structure must be obtained by the NExT method, and then the natural frequency is clustered. Since the non-parametric Bayesian method does not require accurate setting of parameters in advance, it is suitable for data sets where the specific number of structural states is not exact, so the non-parametric Bayesian method is used for cluster analysis. After clustering, in order to test the clustering accuracy, the maximum likelihood heteroscedastic Gaussian process based on non-parametric Bayes is used, and the Bayesian factor is set to test the degree of damage. Through the test, it is determined that the non-parametric Bayesian can be used in damage identification, and the natural frequencies of different damage states can be accurately clustered. Starting from the monitoring data, this method does not require structural physical models and finite element model information. It is a data-driven damage identification method, so the algorithm is applicable to different structural types (such as high-rise buildings, wind power towers, etc.).

[0063] Nonparametric Bayesian mixture model: A nonparametric Bayesian model based on an infinite-dimensional Gaussian mixture model is used for cluster analysis. The basic form of the infinite-dimensional Gaussian mixture model is:

[0064]

[0065] Here w i is the proportion of different Gaussian distributions in the mixed model and satisfies the condition w i ≥0, The definition of the Dirichlet process is that there exists a random probability distribution G on the measurable space Ω, with a positive real number α as a parameter, and the probability distribution G satisfies the following conditions: for any finite partition of the measurable space, A1,…,A k All of them meet the requirements of [G(A1),…,G(A k )]~Dir[αG0(A1),…,αG0(A k )], then the probability distribution G obeys the Dirichlet process of the base distribution G0 and the hyperparameter α, denoted as G~DP(α,G0). The infinite dimensional Gaussian mixture model with the Dirichlet process as the prior distribution is:

[0066] y i ~N(y i ; μ,∑),

[0067] Among them μ, Σ ~ G, G ~ DP (α, G0), G0 (μ, ∑) = N (μ; m, B)·W (Σ -1 ; r, R), where N is the multivariate normal distribution and E is the Wishart distribution.

[0068] Damage identification steps based on non-parametric Bayesian mixture model: The data obtained by the structural health monitoring system does not always conform to the Gaussian distribution. For non-Gaussian distributed data, it is known that the problem can be simplified by assuming that it is a mixture of multiple independent Gaussian distributions. More Gaussian distributions can be used to describe the current state of the bridge and construct a probabilistic model to describe this behavior. First, a polynomial distribution set π is constructed. Each π in the set k Represents the probability that the data point belongs to category k, where k = 1, 2, 3…, K. K represents the number of categories and satisfies Each state of the structure is defined by a corresponding Gaussian distribution, each with mean μ k and variance Σ k For every point x i ,get:

[0069]

[0070] where c i ~Mult(π). When using this method to define the classification, it is necessary to determine the parameters of the model. These parameters include the number of categories K, the mixing ratio π, and the clustering parameters {μ1,…,μ K ,Σ1,…,∑ K}. It can be represented by a total parameter vector, namely Θ={K,π,μ1,…,μ K ,∑1,…,∑ K}, and θ k ={π k ,μk ,∑ k}. The expectation maximization method can be used to determine the parameter θ k , the Bayesian information criterion or Akaike information criterion is used to determine K, and this paper uses a Bayesian method to better confirm these parameters.

[0071] The ideal modification of this hierarchical finite Gaussian mixture model is to perform inference on a Bayesian basis. This will 1:K (i.e., the parameters θ for all categories k=1,…,k k ) gives more stable estimates and allows the use of a Dirichlet process prior to make a probabilistic choice of K. Bayesian methods are able to incorporate prior knowledge (e.g. the expected impact of damage) and shape the model using observed data.

[0072] First, in the clustering parameter μ k and∑ k To facilitate inference of the model, these priors are set to be conjugate to the Gaussian distribution. The Gaussian distribution is a likelihood distribution, so the prior on the mean is a multivariate Gaussian distribution, and the prior on the covariance is an inverse Wishart distribution. These prior distributions have their own hyperparameters, namely μ0, k0, ∑0, v0, and these are usually combined in a prior distribution clustering parameter H, namely

[0073] In order to perform Bayesian inference on the mixture ratio π and the clustering parameters, another prior must be set. We can choose the prior conjugate of a multinomial distribution, which is a Dirichlet distribution controlled by the intensity parameter α. We can take the limit of K→∞ to form an infinite Gaussian mixture model, which has the form The advantage of this modeling approach is that you only need to specify hyperparameters to use the model without adjusting thresholds or calibration, which means that you do not need to specify some expected normal or damaged conditions to run the model. At the same time, there is no need to specify what changes the damage to the structure will bring to the data. If there is such data with known damage categories, clusters can also be added to the model. When known data is added to the clusters, the priors of these clusters are the posterior of the parameters. Based on this model, for the Dirichlet infinite-dimensional Gaussian mixture model, the clustering parameters, mean, and covariance can all be inferred through analytical marginalization, without the need to sample them. Through the posterior predictive distribution p(x i |D -i ) gives the posterior distribution of each parameter, point x iGiven the likelihood of the remaining observations, new data can be evaluated. The folded Gibbs sampling solution is used here, the essence of which is that each data point is evaluated slightly in the sampler, and new points can be added online without the need for batch updates.

[0074] For the case of a Gaussian distribution, the Gibbs sampling procedure is as follows. The data are initially assigned to random clusters, and then at each iteration a data point is selected for evaluation, or re-evaluated if it has already been assigned a cluster. This point is assigned the value c from its current cluster. i , and update the parameters of the cluster. If the data point is the only point assigned to the cluster, the data point is destroyed and the total number of clusters X is updated. For each classification, k = 1, ..., K, the prior likelihood of the point being extracted from cluster K is evaluated. The prior is a Dirichlet process prior, which for existing clusters is equal to

[0075]

[0076] The prior likelihood is determined by the hyperparameter α and the current assignment to the cluster N -i,k The former encourages cluster growth, and increasing α will make it more likely that more clusters will appear. Since the clustering process also needs to include information from other data points, the likelihood term must be calculated to obtain the posterior likelihood of the points belonging to each cluster until a constant is obtained. When n data points are observed, the conjugate update calculation is as follows.

[0077]

[0078] Update calculation after k n =k0+n,v n =v0+n, Here, S is defined as the sample mean The surrounding square and matrix, When updating the clustering with a single data point, it can be performed as a rank update to the Cholesky decomposition of the posterior covariance matrix, which greatly improves the calculation speed.

[0079] For each existing cluster, k = 1, ..., K, we explain the new cluster k by computing the prior and likelihood * These possibilities need to be scaled by the marginal possibilities to obtain the cluster label c of point i. i A cluster label c is sampled from a multinomial distribution i, the point is assigned to this cluster, which is either an existing cluster or a new cluster. If the point is added to an existing cluster, the parameters of the cluster are updated according to equation (5) and the update formula. If the point is assigned to a new cluster, the cluster is initialized with the NIW prior and the point is added to it according to equation (5) and the update formula. The total number of clusters is also updated to reflect the increase, K = K + 1. Once these updates are completed, another point is sampled and the process is repeated.

[0080] Quantitative analysis of structural damage based on maximum likelihood heteroskedastic Gaussian process and Bayesian factor

[0081] For solving the Bayesian factor, we can perform nonlinear regression on the data and obtain alternative hypothesis 1: if the regression curve form and its mean are the same as those of the healthy data, the data can be considered to be in a healthy state. Here, we need to perform nonlinear regression on the data and obtain the parameters in its regression curve. The Gaussian process can effectively solve the nonlinear regression problem and can better deal with the overfitting problem in the regression process. The purpose of using the Gaussian process for monitoring data is to obtain a function F, which corresponds the data in each monitoring data set S to the data in the time series t. The Gaussian process calculates each observation data point once, and uses the identity of the multivariate Gaussian distribution to recalculate the variance of the overall data. The data can be modeled with a regression model whose variance does not change, as shown in the following formula.

[0082] s i =f(t i )+ε i ,

[0083] However, in actual engineering, due to environmental changes or the influence of the sensor itself, the discreteness of the data will also change. Using a general Gaussian process to regress data with large noise changes will result in large deviations. Therefore, some scholars use the maximum likelihood heteroscedastic Gaussian process MLHGP to process data with large variance changes. The heteroscedastic Gaussian process estimates the variance of each point and introduces a new Gaussian process. This process cannot be accurately solved by learning or analysis, but can only be approximated by MCMC sampling or analysis. The MLHGP algorithm replaces the complete posterior distribution of the changing noise with a point on the most likely value, so that the noise variance can be accurately analyzed, as shown in the following formula.

[0084]

[0085] In order to quantify the degree of structural damage, the Bayes factor is introduced as a standard for determining the degree of structural damage. The Bayes factor is a Bayesian test hypothesis indicator that measures the degree to which the data supports or opposes a hypothesis. The specific construction method of the Bayes factor is to first calculate the residuals between the actual data and the regressed data, and identify the results as random variables that obey the Gaussian distribution, and then perform a Bayesian hypothesis test on them, where the null hypothesis H0 is: the mean of the residuals is near 0, that is, the data is no different from the healthy data, then the structure can be considered to be in a healthy state, and the alternative hypothesis H1 is: the mean of the residuals is not 0 and there is a large difference from the healthy data, then the structure can be considered to be in a damaged state. The Bayes factor is defined as the posterior probability likelihood ratio of two hypotheses:

[0086]

[0087] By calculating the value of the Bayesian factor, the degree of damage to the structure can be quantitatively analyzed. Due to different structures, the criteria can be defined by human judgment and the damage inspection criteria are defined as follows: 1 to 3 corresponds to "slight damage"; 3 to 10 corresponds to "substantial damage"; 10 to 100 corresponds to "relatively serious damage"; >100 corresponds to "complete damage". Therefore, the degree of damage is determined by the size of the Bayesian factor, and the early and mid-term development of the damage is defined.

[0088] The following is an example of the Yonghe Bridge in Tianjin to illustrate a structural damage assessment method based on a non-parametric Bayesian model and measured data:

[0089] Yonghe Bridge consists of a 260-meter main span and two side spans of 25.15 meters and 99.85 meters respectively. The bridge is 510 meters long and 11 meters wide (including a 9-meter carriageway and two 1-meter sidewalks). The concrete bridge tower is 60.5 meters high and consists of two beams. The design cable tension range under dead load is 559.4 to 17706.8 kN, and the design stress under live load is 160 MPa. The bridge was built in 1983 and opened to traffic in December 1987. As the vehicle load was much greater than the design expectation, cracks with a maximum width of 2 cm appeared at the bottom of the middle beam section of Yonghe Bridge in 2006, and the inclined cables were severely corroded. The bridge was repaired from December 2008 to May 2009. Before the repair, a structural health monitoring system (SHM) was designed for the bridge. The SHM system includes acceleration sensors installed at different locations on the bridge to detect structural damage that causes major bridge disasters in a timely manner and improve the safety and reliability of the bridge. The structural dynamic response system in the SHM system fully records the vibration data of the Tianjin Yonghe Bridge from the healthy state to the damaged state (January to July 2008) as a health state parameter model for structural health monitoring damage identification.

[0090] The SHM system of Yonghe Bridge includes sensors installed on the cables, towers and beams of the bridge and data acquisition equipment located in the control room. For the acceleration sensor, 14 single-axis accelerometers are installed on the bridge deck, and the acceleration direction is vertically downward; a dual-axis accelerometer is installed on the top of the bridge tower on the Tianjin side to record the acceleration response in the horizontal plane in the longitudinal and transverse directions of the bridge. The specific layout of the acceleration sensor is shown in Figure 2 It also includes anemometers and temperature sensors, dynamic weighing systems installed in all lanes, and fiber grating sensors installed at key locations on the bridge to measure strain and temperature.

[0091] In August 2008, during an inspection of the bridge, it was found that the bridge was damaged. The degree of damage can be confirmed to have gradually developed over time. The SHM system recorded the acceleration data of the bridge from January to August 2008. The modal characteristics of the bridge obtained by processing the acceleration data can reflect the health status of the bridge. There are two main damages in the structure of Tianjin Yonghe Bridge. The first damage is located in the closed section of the main beam. The closed section is severely cracked and the steel bars are exposed. The second damage is located at the pier. The bridge limit device is offset and the steel bars are broken. Both damage locations are in Figure 2 Near the No. 1 and No. 2 acceleration sensors in the figure. Due to the high sampling frequency and large data volume of acceleration data, the data storage method of Tianjin Yonghe Bridge is to randomly select 1-3 days per month and retain the 24-hour acceleration data of these selected days. Therefore, this paper uses 12 days of acceleration data from January 1 to July 31, with 360,000 acceleration data per hour.

[0092] Natural frequency extraction of Tianjin Yonghe Bridge

[0093] The original information of the structural health monitoring system of Tianjin Yonghe Bridge lacks accurate information on bridge damage between January 17 and July 30, and it is difficult to judge the change of structural state through intuitive analysis of the original monitoring data. Modal parameters are an important basis for damage identification, and natural frequency is a more accurate modal parameter reflecting bridge damage. It often fluctuates very little within a day, but will change significantly when the bridge structure is damaged. Therefore, it is often used in structural damage identification. At present, the main methods for solving natural frequency are fast Fourier transform method and natural excitation technique (NExT) method. The analysis data selected in this paper are all vibration response monitoring time under environmental excitation. The noise is small and the fluctuation is uniform. It can be regarded as Gaussian white noise. The environment of this study can be regarded as the vibration response under the natural environment of white noise. For different environmental parameters, such as temperature, which will have an impact on modal parameters, this paper mainly uses data from the same time period of each day to try to eliminate the influence of temperature and improve the reliability of damage identification. The natural frequency analysis and processing of vibration data using the NExT method is highly accurate, and the natural frequency band is clear in image analysis. Obtaining relatively accurate natural frequency data is an important prerequisite for identifying the damage state of bridges. Based on this, this paper selects the NExT method to solve the natural frequency data of bridges. Obtaining natural frequency data through the NExT method requires relatively stable acceleration data, and the acceleration data during the operation of the bridge often has large disturbances during the period when there are more vehicles running. Therefore, the analysis data is selected from the early morning or midnight of the day.

[0094] like Figure 3 This is the natural frequency result obtained after processing the acceleration data of Yonghe Bridge at 0:00 on January 1 by the NExT method. The figure marks the 1st to 7th order natural frequencies extracted from the acceleration data. The 1st order frequency is 0.3601 Hz, the 2nd order frequency is 0.5524 Hz, the 3rd order frequency is 0.9491 Hz, the 4th order frequency is 1.0315 Hz, the 5th order frequency is 1.0895 Hz, the 6th order frequency is 1.2573 Hz, and the 7th order frequency is 1.4923 Hz.

[0095] Damage identification based on nonparametric Bayesian mixture model and SHM measured structural health monitoring data

[0096] The accurate prior information of Tianjin Yonghe Bridge is that the bridge was in a healthy state on January 17, and substantial damage was found in the bridge during the routine inspection on July 31. There is no accurate information about the structural state of the bridge between January 17 and July 31, that is, the possible states of health, slight damage, moderate damage, and severe damage, and it is not clear how many states exist. The non-parametric Bayesian model can analyze the form of data change. The natural frequency data affected by the environment has different characteristics in the form of change from the natural frequency data caused by damage. Therefore, the non-parametric Bayesian model can cluster the natural frequency data more accurately. At the same time, the non-parametric Bayesian model does not need to specify key parameters such as the specific number of clusters before performing cluster analysis. Combining the above two points, this study applies the non-parametric Bayesian model to the natural frequency data for cluster analysis, and judges the different states of the bridge in the process of gradual development of the degree of damage through the cluster analysis results, so as to verify the effectiveness of the algorithm.

[0097] Figure 4 The results of cluster analysis of the 1st, 3rd, and 7th order natural frequency data obtained by processing the acceleration data of the Yonghe Bridge in Tianjin using the non-parametric Bayesian clustering method are shown, and the relationship between the three types of natural frequency data of different orders is shown. The clustering results are named Cluster 1, Cluster 2, Cluster 3, and Cluster 4 in order of appearance, and are marked as green O-shaped, red rectangle, purple X-shaped, and blue cross-shaped, respectively.

[0098] exist Figure 4 (a)~ Figure 4 (c) shows that the non-parametric Bayesian clustering method divides the data into four clusters in the results of clustering the natural frequency data of different orders.

[0099] Figure 4 (a) is the clustering result of the 1st-order natural frequency data. On January 1 and January 17, the data were all classified as cluster 1. Cluster 2 appeared on February 3, but some cluster 1 results still existed. On April 9, the clustering results were still mainly cluster 2, but a small amount of cluster 3 began to appear. After May 31, the clustering results were all cluster 3, and finally cluster 4 appeared on June 16. In addition, the non-parametric Bayesian clustering analysis was compared with the neural network clustering analysis results. For the neural network, 70% of the first two types of clustering data of the 1st-order natural frequency were used for training, 10% for verification, and 20% for testing to obtain the cluster analysis confusion matrix. For the first two types of clustering data, the total accuracy of the neural network clustering analysis was 91.3%; Figure 5 The accuracy of the first two types of cluster analysis of nonparametric Bayesian is 97.6%, which is higher than the accuracy of the neural network analysis results. Therefore, the accuracy of the nonparametric Bayesian analysis results is verified.

[0100] Figure 4 (b) is the clustering result of the third-order natural frequency. Similarly, the data before January 17 is classified as cluster 1, and cluster 2 appears on February 3. Figure 5 (a) The difference is that Figure 5 (b) Cluster 1 did not appear on February 3. The main reason is that different natural frequencies of the same structure under the same damage condition sometimes show different change patterns. For the data on April 9, Figure 5 The number of cluster 3 in (b) is compared with Figure 5 (a) More. Subsequent changes and Figure 5 (a) Similarly, Figure 5 (a) and Figure 5 (b) It was found that the change pattern of the natural frequency data on June 16 was significantly different from that before, and the non-parametric Bayesian clustering method can accurately identify this data change, and the same conclusion can be obtained in the cluster analysis results of the first-order natural frequency data and the third-order natural frequency data.

[0101] Figure 4 (c) shows the results of clustering the 7th-order natural frequency data using the non-parametric Bayesian method. Different-order natural frequency data are affected differently by environmental changes and damage state changes, and the change patterns also show different trends, which are mainly reflected in the clustering results of April 9 and May 5. Figure 5 (c) The content of cluster 3 during this period is compared with Figure 5 (b) is less, but less than Figure 5 (a) is more. In other time periods, the clustering results of the 7th-order natural frequency data are exactly the same as those of the 3rd-order natural frequency data.

[0102] According to the above natural frequency clustering results, it can be found that the non-parametric Bayesian model divides the natural frequency data of different orders into 4 categories. The non-parametric Bayesian model can accurately cluster the natural frequency data on January 1 and January 17 when the bridge was in a healthy state, and on July 31 when the bridge structure had substantial damage, and it can be found that the structure had already suffered substantial damage on June 16. For the period from February 3 to June 7 when the health status of the structure was less clear, the natural frequency data did not show a significant change in the data mean, but the non-parametric Bayesian model did not determine the natural frequency data in this period as the same type of clustering, but based on the different ways of data change. From February 3 to June 7, the natural frequency data of this period were determined by the non-parametric Bayesian model as two different clusters. The specific degree of damage in this period requires further quantitative analysis. April 9 and May 5 are periods where the clustering results of the three natural frequency data are quite different. The clustering results are all a mixture of cluster 2 and cluster 3. The difference is mainly reflected in the mixing ratio of cluster 2 and cluster 3. The above results show that when non-parametric Bayesian cluster analysis is performed on natural frequency data of different orders, the results obtained are accurate and stable, and the clustering results can be used to accurately identify the damage condition of the structure.

[0103] Figure 4 (d) is the three-dimensional display result of the three groups of natural frequency data. Different colors represent different clustering results of the 7th-order natural frequency data. It can be seen from the figure that there is a positive correlation between the three groups of natural frequency data. Among them, the distribution of cluster 1 and cluster 4 is relatively independent, while the distribution of cluster 2 and cluster 3 is relatively concentrated. The non-parametric Bayesian model can accurately cluster these two forms of data.

[0104] The specific correlation analysis between different order natural frequency data is carried out by Figure 5 To display, Figure 5 It expresses the relationship between the 1st, 3rd, and 7th order natural frequencies. In order to reflect the relationship, all data are normalized. From left to right in the horizontal direction, they represent the 1st, 3rd, and 7th order natural frequencies, and from top to bottom in the vertical direction, they represent the 1st, 3rd, and 7th order natural frequencies.

[0105] use Figure 5 (a)-(i) in the figure represent the relationship between the 1st, 3rd, and 7th order natural frequencies at different time points during the gradual destruction of the structure; Figure 5 It was found that in the process of gradual structural destruction, the different natural frequencies showed a gradual downward trend as a whole. Figure 5 In (a), the change of the first-order natural frequency is relatively continuous, and the boundaries of the four clustering results are not obvious. Figure 5In the third-order natural frequency autocorrelation of (e), the boundary between the data in the healthy state on January 1 and January 17 and the later time period is very obvious. Similar phenomena also appear in Figure 5 The main reason for this result is that under the same structural state, different-order natural frequency data will show different change trends. For the natural frequency data from February 3 to June 7, Figure 5 (a) It can be found that in the first-order natural frequency, the overall natural frequency value of cluster 2 is significantly larger than that of cluster 3, while Figure 5 In the 7th order natural frequency of (i), there is no difference in the overall natural frequency values ​​between cluster 2 and cluster 3. The minimum natural frequency value during this period even appears in cluster 2. This phenomenon shows that the non-parametric Bayesian model does not simply cluster the data by the size of the value, but combines the change form of the data to avoid misjudgment of data with similar values ​​but different change forms. Figure 5 It can be seen that under the same structural state, the data expressions of different-order natural frequencies are not exactly the same, but the results obtained by clustering the data using the non-parametric Bayesian method are very similar, indicating that the use of non-parametric Bayesian clustering analysis on data can accurately identify the form of data changes and thus perform precise clustering.

[0106] The quantitative analysis of the clustering results of different natural frequency data is based on Figure 6-Figure 8 for display. Figure 6 and Figure 7 They are the overall difference rate and the same rate of specific dates of the clustering results of the 1st and 3rd order, and the 3rd and 7th order natural frequency data. Figure 8 The specific number of clusters of the 7th-order natural frequency data is shown to analyze its clustering effect.

[0107] exist Figure 6-Figure 8 Among the specific differences in clustering results, the overall difference rates of clustering results between the 1st and 3rd order, and between the 3rd and 7th order natural frequencies are 8.12% and 5.69% respectively. Figure 6 The clustering results of the first-order natural frequency data are different from those of the other two-order natural frequency data on February 3, April 9, May 5, and May 18, while Figure 7 The clustering results of the 3rd and 7th order natural frequency data are quite different on April 9 and May 5, but slightly different on May 18. Figure 6 and Figure 7, it was found that the first-order clustering results were partially misjudged on February 3. At the same time, the structure was in a period of structural state change from April 9 to May 18, so clusters 2 and 3 coexisted. The overall difference in the clustering results of different-order natural frequency data is small, and the overall similarity rate can reach as low as 91.78%, indicating that the results obtained by clustering analysis of different-order natural frequency data using the non-parametric Bayesian method are stable and can be used to accurately identify the structural damage state.

[0108] Since the clustering results of the 7th-order natural frequency data and the 3rd-order natural frequency data were relatively accurate in the early stage, and the difference between the clustering results of the 7th-order natural frequency and the other two-order natural frequency data was small, Figure 7 The 7th-order natural frequency data clustering results are used to perform quantitative damage analysis. Figure 7 , in chronological order, combined with the development of structural damage, cluster 1, cluster 2, cluster 3, and cluster 4 can be defined as four state levels. According to the information of Tianjin Yonghe Bridge, cluster 1 is in a "healthy" state, cluster 4 is in substantial damage, and clusters 2 and 3 are in an intermediate damage transition state. This proves that the results obtained by clustering the modal parameters obtained through measured structural health monitoring data using a non-parametric Bayesian model can be used in structural damage identification analysis.

[0109] Quantitative damage analysis based on Bayesian factor

[0110] In order to verify the accuracy of the clustering results obtained by processing the natural frequency data through non-parametric Bayesian cluster analysis, the structural damage status can be quantitatively analyzed by Bayesian factors and compared with the results of non-parametric Bayesian cluster analysis to reflect its accuracy. The Bayesian factor is constructed by comparing the posterior probability ratio of the null hypothesis and the alternative hypothesis about the data. In this study, the null hypothesis is that the form and value of the natural frequency data are the same as those in the healthy state, and the alternative hypothesis is that the form and value of the natural frequency data are very different from those in the healthy state. That is, the construction of the Bayesian factor is to compare the two models built for the natural frequency data. The closer the ratio is to 0, the closer the data is to the healthy state. The advantage of using Bayesian factors for quantitative damage analysis is that Bayesian factors do not simply confirm or deny the hypothesis, but quantify the degree to which the data is close to the null hypothesis or the alternative hypothesis, so that the degree of damage can be determined by the size of the Bayesian factor. By calculating the Bayesian factor value, the degree of structural damage is quantitatively analyzed and the early and middle development of damage is defined.

[0111] The Bayesian factor construction method for the 1st, 3rd, and 7th order natural frequency data of the Yonghe Bridge in Tianjin is to first perform regression analysis on the natural frequency data of January 1 and January 17, which are known to be in a healthy state, using the MLHGP model based on the non-parametric Bayesian model, and set the resulting regression model as the null hypothesis condition H0. Then, the natural frequency data of the period that needs to be tested is regressed using the MLHGP model. The closer the regression model is to the regression model of the natural frequency data in a healthy state, the healthier the bridge structure state is during this period; the more the regression model deviates from the regression model of the natural frequency data in a healthy state, the more damaged the bridge structure state is during this period. The judgment of the proximity or deviation of the regression model is not simply defined by the numerical value, but is comprehensively evaluated in combination with the regression model form, original data, model mean, variance, etc. Considering that the numerical value of the natural frequency is one of the important factors in judging the structural state, its proportion in the assessment is appropriately increased. The Bayesian factor results are as follows: Fig. 9 shown. Fig. 9 The regression models of the 1st, 3rd, and 7th order natural frequency data on February 3, June 7, and July 31 are shown, and the Bayes factor results obtained by comparing them with the regression models of different order natural frequency data under healthy conditions. The larger the value of the Bayes factor, the greater the deviation between its regression model and the regression model under healthy conditions.

[0112] exist Fig. 9In the data, the Bayesian factor obtained from the 1st order natural frequency data shows an upward trend as the structural damage develops, but its value is lower than 3, which is judged as a state of minor damage. The Bayesian factors obtained from the 3rd and 7th order natural frequency data also show an upward trend as the structural damage develops. Before June 7, their values ​​were all less than 3, which was judged as a state of minor damage. On July 31, the Bayesian factor value was between 3 and 10, which determined that the bridge structure had substantial damage at this time. For the Bayesian factor results of different order natural frequency data, on February 3 and June 7, the judgment on the structural damage state was unified, and both believed that the structure was in a state of minor damage. On July 31, the Bayesian factor obtained from the 1st order natural frequency data did not reflect the problem of substantial structural damage. This is because high-order natural frequencies are more sensitive to damage. When damage occurs, the results of analyzing high-order natural frequency data are more accurate. Similar rules also appear in the non-parametric Bayesian frequency cluster analysis of different order natural data. At the same time, in the Bayes factors obtained from different natural frequencies in the same period of time, it can also be observed that the Bayes factors obtained by analyzing the data of higher natural frequencies have larger values. Therefore, the Bayes factors can be used to quantitatively evaluate the structural damage. The results show that the structure of Tianjin Yonghe Bridge was in the stage of minor damage on February 3 and June 7. Compared with February 3, the degree of structural damage on June 7 increased; and on July 31, the structure of Tianjin Yonghe Bridge was substantially damaged.

[0113] The specific method for determining the damage location is as follows. After combining the MLHGP regression model based on non-parametric Bayesian and the natural frequency data at different times to obtain the Bayesian factor, the quantitative analysis of structural damage was realized. This method quantified the damage by analyzing the numerical differences and change trends in the healthy and unhealthy state data, and finally found that the structure of Tianjin Yonghe Bridge was substantially damaged on July 31. Due to the different layout positions of the structural acceleration sensors, the Bayesian factor was obtained by combining the MLHGP regression model and the natural frequency data of different parts of the bridge to further realize the structural damage location analysis. Before the damage location analysis, the overall structure of the bridge needs to be divided into substructures. The bridge nodes can be divided according to the installation position, structural characteristics and damage location needs of the monitoring sensors. This study divides the overall structure of the bridge into 6 substructures according to the sensor layout. Substructure 1 and substructure 6 are located at both ends of the bridge, respectively. Substructure 1 contains acceleration sensors No. 1 and No. 2, and substructure 6 contains acceleration sensors No. 13 and No. 14. The remaining substructures are located in the middle of the bridge. Substructure 2 contains acceleration sensors No. 3 and No. 4, substructure 3 contains acceleration sensors No. 5 and No. 6, substructure 4 contains acceleration sensors No. 7, No. 8, No. 9, and No. 10, and substructure 5 contains acceleration sensors No. 11 and No. 12.

[0114] It is known that substantial damage occurred to the bridge structure on July 31, so the acceleration monitoring data on July 31 was used to analyze the damage location of the structure. The Bayesian factor construction method for the six substructures of Tianjin Yonghe Bridge is as follows: first, the acceleration data of each node is analyzed using the NExT method to obtain the natural frequency data at the node, and the natural frequency data in the healthy state on January 1 is obtained; then the obtained natural frequency data in the healthy state is regressed using the MLHGP method, and the obtained regression model is set as the null hypothesis condition H0; finally, the natural frequency data of the nodes to be tested are regressed using MLHGP. The closer the regression model is to the natural frequency data regression model in the healthy state, the more the bridge structure state is considered to be healthy during this time period; the more the regression model deviates from the natural frequency data regression model in the healthy state, the more the bridge structure state is considered to be damaged during this time period, and finally the Bayesian factor results of each substructure are obtained as follows: Fig.10 shown.

[0115] Depend on Fig.10 It can be seen that the Bayes factor of substructure 1 is 19.1, which is much higher than the Bayes factors of other substructures. This shows that among the six substructures, the most likely location for damage to the bridge system is at substructure 1. In fact, the damage location of the bridge does appear at substructure 1, near sensors 1 and 2. Its closed section is severely cracked, the bridge pier is damaged, and the steel bars are broken, which verifies the accuracy of the damage location analysis based on the Bayes factor.

Claims

1. A structural damage assessment method based on a nonparametric Bayesian model and measured data, characterized in that: The specific steps are as follows: Installing a structural health monitoring system on the building, the structural health monitoring system comprising a plurality of vibration monitoring sensors arranged at different locations on the building, and a computer for recording data from the vibration monitoring sensors; When the building is not affected by the outside world and the structure is healthy, the vibration monitoring sensor of the structural health monitoring system is used to collect the acceleration data of the building within a set time. Then the natural excitation NExT method is used to process the acceleration data measured by the vibration monitoring sensor to obtain the natural frequencies of vibrations of different orders of the building when the building is not affected by the outside world and the structure is healthy. The natural frequency data is defined as the health status data. The nonparametric Bayesian hybrid method is used to perform cluster analysis on the natural frequencies of different orders of vibration of the building. The cluster analysis results are combined with the maximum likelihood heteroskedastic Gaussian process and Bayesian factor to identify and quantify the degree of structural damage; The maximum likelihood heteroskedastic Gaussian process model MLHGP based on the non-parametric Bayesian model is used for regression analysis: the obtained regression model is set as the null hypothesis condition, and then the natural frequency data generated by the building that needs to be evaluated for health status is subjected to regression analysis using the MLHGP model. The closer the regression model formed by the regression analysis is to the regression model of the natural frequency data in the healthy state, the more the structural state of the building is considered to be healthy; The more the regression model deviates from the natural frequency data regression model under the healthy state, the more the building structure state tends to be damaged; by combining the regression model form, original data, model mean, and variance for comprehensive evaluation, the Bayesian factor results of the natural frequency data regression models of different orders in different time periods are obtained, and the Bayesian factor results obtained by comparing the natural frequency data regression models of different orders under the healthy state are obtained. The larger the value of the Bayesian factor, the higher the deviation of its regression model from the regression model under the healthy state; Achieve accurate identification of building structural damage.

2. The structural damage assessment method based on non-parametric Bayesian model and measured data according to claim 1 is characterized in that: The nonparametric Bayesian mixture method uses a nonparametric Bayesian model based on an infinite-dimensional Gaussian mixture model for cluster analysis. The basic form of the infinite-dimensional Gaussian mixture model is: where f i (x)~N(μ i , σ i 2 ), i = 1, 2, ..., w i is the proportion of different Gaussian distributions in the infinite-dimensional Gaussian mixture model, and satisfies the condition w i ≥0, There exists a random probability distribution G on the measurable space Ω, with a positive real number α as a parameter. The probability distribution G satisfies the following conditions: for any finite partition of the measurable space, A1,…,A k All of them meet [G(A1),…,G(A k )]~Dir[αG0(A1),…,aG0(A k )], then the probability distribution G obeys the Dirichlet process of the base distribution G0 and the hyperparameter α as the prior distribution process, denoted as G~DP(α,G0); the infinite dimensional Gaussian mixture model y with the Dirichlet process as the prior distribution i for: y i ~N(y i ;m,S) (2), Among them μ, ∑ ~ G, G ~ DP (α, G0), G0 (μ, ∑) = N (μ; m, R)·W (∑ -1 ; r, R), μ represents the mean vector, ∑ represents the covariance matrix, G represents the random probability distribution, DP represents the Dirichlet process, α represents the hyperparameter, G0 represents the basis distribution, m represents the mean vector, B represents the covariance matrix, r represents the degree of freedom, the scale matrix R, where N is the multivariate normal distribution and W is the Wishart distribution.

3. The structural damage assessment method based on nonparametric Bayesian model and measured data according to claim 2 is characterized in that The acceleration data obtained by the structural health monitoring system is a mixture of multiple independent Gaussian distributions, and the mixed Gaussian distribution is used to build a probabilistic model of behavior; The data points collected by a vibration monitoring sensor arranged on the building are organized into a polynomial distribution set ∏ according to time. Each ∏k in the set represents the probability that the data point belongs to category k, where k = 1, 2, 3…, K, K represents the number of categories, and satisfies Each state of the data point structure is defined by a corresponding Gaussian distribution, and each Gaussian distribution is defined by a mean μ k and variance∑ k ; For each data point collected by the sensor, set x i ,get: where c i Subordinate to the multinomial distribution ∏, c i ~Mult(∏); When defining the classification, it is necessary to determine the parameters of the non-parametric Bayesian model, including the number of classifications K, the mixing ratio π, the clustering parameters {μ1,…,μ K ,∑1,…,Σ K }; or use the total parameter vector to represent: Θ = {K, π, μ1, ..., μ K ,∑1,…,∑ K }, θ k ={π k , μ k ,∑ k }; Use the expectation maximization method to determine the parameter θ k , the Bayesian information criterion or Akaike information criterion is used to determine the number of classifications K.

4. The structural damage assessment method based on non-parametric Bayesian model and measured data according to claim 3 is characterized in that: Using observed prior data, model nonparametric Bayesian models on a Bayesian basis: First, in the nonparametric Bayesian model, the clustering parameter μ k and∑ k Set the prior value on the prior data μ k and∑ k Set to be conjugate with the Gaussian distribution, which is the likelihood distribution. Therefore, the prior on the mean is a multivariate Gaussian distribution, and the prior on the covariance is an inverse Wishart distribution. These prior distributions have their own hyperparameters, namely the prior mean μ0 of the mean vector of the Gaussian distribution, the weight ∑0 of the mean vector of the Gaussian distribution, and the degree of freedom parameter v0 of the inverse Wishart distribution. These are combined in a prior distribution clustering parameter H, that is, we get: 1W represents inverse Wishart distribution, ∑ represents variance; In order to perform Bayesian inference on the mixture ratio π and clustering parameters, another prior is set first, and the prior conjugate of the multinomial distribution set is selected. The multinomial distribution set is a Dirichlet distribution controlled by the intensity parameter α. The limit of the number of classifications K→∞ is set to form an infinite Gaussian mixture model, which is expressed as: The clustering parameters, mean, and covariance in the infinite Gaussian mixture model are inferred by analytical marginalization, which eliminates the need for sampling and is obtained by using the posterior predictive distribution p(x i |D -i ) gives the posterior distribution of each parameter, point x i Given the likelihood of the remaining observations, the new data are evaluated using collapsed Gibbs sampling; For the Gaussian distribution in folded Gibbs sampling, the frequency data extracted from the acceleration data of the data point are first assigned to random clusters, and then one data point is selected for evaluation in each iteration, and if it is already assigned to a cluster, it is re-evaluated; This data point will be assigned c from its current cluster i Delete it and update the parameters of the cluster; If the data point is the only point assigned to the cluster, the data point is destroyed and the number of clusters K is updated; for each classification, k = 1, ..., K, the prior likelihood that the point is extracted from cluster K is evaluated; The prior is the Dirichlet process prior, which for an existing cluster is equal to: The prior likelihood is determined by the hyperparameter α and the current assignment to the cluster N -ik The hyperparameter α encourages cluster growth. Increasing α will make it more likely that more clusters will appear. Since the clustering process also needs to include information from other data points, the likelihood term must be calculated to obtain the posterior likelihood of the points belonging to each cluster until a constant is obtained. When n data points are observed, the conjugate update calculation is as follows: After conjugate update calculation k n =k0+n,v n =v0+n, In the formula, S represents the sample mean The surrounding square and matrix, When updating the clusters with a single data point, it is performed as a rank update to the Cholesky decomposition of the posterior covariance matrix. For n data points, v n represents the posterior degrees of freedom, T represents the transpose, represents the inverse of the covariance matrix; For each existing cluster k=1,...,K, we explain the new cluster k by computing the prior and likelihood * The generation of these prior possibilities needs to be scaled by the marginal possibilities, so that the cluster label c of data point i can be obtained i A cluster label c is randomly sampled from the multinomial distribution i , the data point i is assigned to this cluster c i , if data point i is added to an existing cluster, then the parameters of the cluster will be updated according to formula (7) and the update formula; if data point i is assigned to a new cluster, the cluster will be initialized by NIW prior and the point will be added to it according to formula (7) and the update formula; the total number of clusters is also updated to reflect the increase, K = K + 1, once these updates are completed, another point is sampled, and the above steps are repeated until all vibration monitoring sensor sampling points arranged on all buildings are traversed.

5. The structural damage assessment method based on non-parametric Bayesian model and measured data according to claim 4 is characterized in that: The quantitative analysis process of structural damage based on maximum likelihood heteroskedastic Gaussian process and Bayesian factor is as follows: For solving the Bayesian factor, a nonlinear regression model is generated by using the monitoring data of the vibration monitoring sensor. If the regression curve form and its mean of the regression model are closer to the regression curve form and mean of the natural frequency data regression model under the healthy state data, the data is considered to be healthier, and it is necessary to perform nonlinear regression on the data and obtain the parameters in its regression curve. The purpose of solving the nonlinear regression problem by using Gaussian process is to obtain the regression equation formula (8), and the data in the polynomial distribution set composed of each sensor monitoring data corresponds to the data in the time series t to form a time series. The Gaussian process is calculated once for each sensor sampling point, and the variance of the sum of all sensor monitoring data is recalculated using the identity of multivariate Gaussian distribution. The regression modeling of all sensor monitoring data without changing the variance is shown in the following formula: s i =f(t i )+ε i (8), The natural frequency data of the period to be tested is subjected to regression analysis using the MLHGP model to obtain the regression data: In the formula, q is the sample size, Output s for training i The posterior predictive distribution of is sampled, which is a Gaussian distribution with mean The variance is gi2 represents the noise level; Construct Bayesian factor: First, calculate the residual between the actual measurement point sensor data and the regressed data, and identify the residual calculation result as a random variable that obeys Gaussian distribution. Then, perform Bayesian hypothesis test on the residual calculation result. Set zero H0 as: the mean of the residual calculation result is near 0, that is, the acceleration data of the sensor is no different from the building health status data, then the building structure is judged to be in a healthy state. Set H1 as: the mean of the residual calculation result is not 0 and there is a difference with the building health status data, then the structure is judged to be in a damaged state; the Bayesian factor is defined as the posterior probability likelihood ratio of two hypotheses: In the formula, B represents the Bayes factor, P represents the probability, and D represents the evidence.

6. The structural damage assessment method based on non-parametric Bayesian model and measured data according to claim 5 is characterized in that: By calculating the value of the Bayesian factor, a quantitative analysis of the damage degree of the building structure can be achieved. Due to different structures, the damage inspection criteria can be defined after judgment by expert data: the damage standard is defined as: 1 to 3 corresponds to minor damage; 3 to 10 corresponds to substantial damage; 10 to 100 corresponds to relatively serious damage; >100 corresponds to complete damage. The damage degree is determined by the size of the Bayesian factor, and the early and mid-term development of the damage is defined.

7. A computer device, characterized in that: include: Processor, memory, and network interface; The processor is connected to the memory and the network interface, wherein the network interface is used to provide a network communication function, the memory is used to store program code, and the processor is used to call the program code to execute the structural damage assessment method based on the non-parametric Bayesian model and measured data as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which is suitable for being loaded by a processor and executing the structural damage assessment method based on a non-parametric Bayesian model and measured data as described in any one of claims 1 to 6.

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