Bridge monitoring data anomaly identification method based on weighted principal component analysis

Abstract

The invention provides a bridge monitoring data anomaly identification method based on weighted principal component analysis, which comprises the following steps of: firstly, establishing a probability density function of multi-dimensional damage feature data by using nondestructive monitoring data; sequentially and respectively performing eigenvalue decomposition on covariance matrixes of Gaussian components; further obtaining a principal component analysis model and a residual subspace corresponding to the principal component analysis model and used for calculating a damage index; and finally, defining a damage judgment threshold value, and taking the threshold values of the two damage indexes as 1, namely, when the damage indexes are greater than 1, judging that the structure is in a damaged state, and otherwise, judging that the structure is in a lossless state. According to the invention, the nonlinear data of the bridge structure under the change of the operation environment is monitored online, the sensitivity of the damage data identification of the bridge structure can be effectively improved, and the missed judgment rate of the damage identification is significantly reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge structure health monitoring, and particularly relates to a method for identifying abnormal bridge monitoring data based on weighted principal component analysis. Background Art

[0002] Under the combined action of factors such as long-term load, environmental erosion, and fatigue effect, the service performance of bridge structures often degrades to varying degrees. Currently, vibration-based damage identification methods are mostly used for online monitoring. Vibration-based damage identification methods usually use structural dynamic characteristics (such as modal parameters like frequency and mode shape) as damage characteristics of the structure, and judge the damage state of the structure through changes in dynamic characteristics. However, changes in the operating environment (such as factors like temperature, humidity, and wind speed) during the service period will also cause significant changes in structural dynamic characteristics, which may completely mask the dynamic characteristic changes caused by damage, resulting in unsatisfactory damage identification effects. Therefore, in structural damage identification, it is crucial to eliminate the influence of operating environment changes on damage characteristics. For this reason, a method for identifying abnormal bridge monitoring data based on weighted principal component analysis is invented. Summary of the Invention

[0003] In view of this, the present invention aims to overcome the defects in the prior art, and proposes a method for identifying abnormal bridge monitoring data based on weighted principal component analysis, which realizes Gaussian fitting of multi-dimensional bridge monitoring data and local principal component analysis modeling, and redefines damage indicators and discrimination thresholds.

[0004] To achieve the above object, the technical solution of the present invention is realized as follows:

[0005] A method for identifying abnormal bridge monitoring data based on weighted principal component analysis, comprising the following steps:

[0006] S1. Establish a probability density function of multi-dimensional damage feature data using non-destructive monitoring data:

[0007]

[0008] In the formula: K is the number of Gaussian components; ω k is the combination coefficient of the k-th Gaussian component μ k and Σ k are respectively the mean vector and covariance matrix of the k-th Gaussian component; p(x|k) is the probability density function of the k-th Gaussian component, and the expression is as follows:

[0009]

[0010] S2. Let Denote the parameter set consisting of all parameters in the GMM, and calculate the log-likelihood function corresponding to the data set to obtain the optimal estimate of the parameter set Θ.

[0011]

[0012] S3. Successively perform eigenvalue decomposition on the covariance matrix Σ of the k-th Gaussian component, and then obtain K principal component analysis models and their corresponding residual subspaces for calculating damage indicators. k

[0013] S4. Respectively perform weighted normalization on the Mahalanobis squared distance and the Euclidean squared distance as the damage indicators in the framework of hybrid principal component analysis: First, calculate the damage indicator corresponding to the k-th Gaussian component; then perform normalization processing on the damage indicator through the corresponding thresholds T Mah,k and T Euc,k respectively; finally, perform weighted summation on all normalized damage indicators.

[0014] S5. Define the damage discrimination threshold, and take the thresholds of both damage indicators as 1, that is, when the damage indicator is greater than 1, it is judged that the structure is in a damaged state, otherwise, it is judged that the structure is in a non-damaged state.

[0015] Furthermore, in step S4, when performing weighted summation on all normalized damage indicators, the weight coefficient is the posterior probability p(k|x) of the sample from each Gaussian component of the GMM. Specifically, transform the optimal parameter estimation problem of the GMM into the following optimization problem:

[0016]

[0017] Solve it using the expectation-maximization algorithm.

[0018] Furthermore, when using the expectation-maximization algorithm to solve, first set the initial parameters of the GMM as Θ (0) , and then perform iterative calculation in two steps: the E step and the M step. In the E step, based on the current parameters Θ (i) , calculate the posterior probability that the j-th sample vector x j belongs to the k-th Gaussian component:

[0019]

[0020] Furthermore, in the M step, iteratively update the parameters Θ (i+1) :

[0021]

[0022] Repeat the E step and the M step until convergence to obtain the optimal parameters of the GMM. ​

[0023] Further, in step S4, the method for standardizing the damage index is: dividing the damage index by its threshold value.

[0024] Further, in step S4, calculating the damage index corresponding to the k-th Gaussian component includes the Mahalanobis squared distance DI Mah,k and the Euclidean squared distance DI Euc,k .

[0025] Further, when performing weighted summation on all standardized damage indices; the specific expression is:

[0026]

[0027]

[0028] In the formula: represents the weighted standard Mahalanobis squared distance; represents the weighted standard Euclidean squared distance.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] Traditional monitoring methods are only effective when the data approximately satisfies linear correlation, but when the data is non-linearly correlated, the recognition effect is poor. This invention patent uses the Gaussian Mixture Model (GMM) to fit the joint probability density function of multi-dimensional non-Gaussian distributed and non-linearly correlated monitoring data into a linear combination of multiple local Gaussian components. Then, corresponding principal component analysis models are established for all Gaussian components respectively, and the Mahalanobis squared distance and the Euclidean squared distance are calculated respectively for the residual parts of each principal component analysis model. After weighted standardization, they are used as the damage indices of the structure, and the non-linear data of the bridge structure under the change of the operating environment is monitored online, which can effectively improve the sensitivity of identifying the damage data of the bridge structure, significantly reduce the missed judgment rate of damage recognition, provide a more reliable guarantee for the safety performance of in-service bridges, and the patent method has low implementation difficulty, great promotion value and good social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0032] Figure 1 is the technical route diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0034] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0035] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", and "connection" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific circumstances.

[0036] The present invention will be described in detail below with reference to the drawings and in conjunction with embodiments.

[0037] During the on-line monitoring of bridge structures, it is usually affected by the operating environment, resulting in non-linear correlation phenomena in the monitoring data, and further leading to unsatisfactory damage identification effects of traditional methods. How to reduce or eliminate the influence of many environmental factors to obtain the true condition of the bridge structure is a crucial issue in bridge structure monitoring. Therefore, the present invention provides a method for abnormal identification of bridge monitoring data based on weighted principal component analysis, as Figure 1 shown, including the following steps:

[0038] S1. Establish the probability density function of multi-dimensional damage feature data using non-destructive monitoring data:

[0039]

[0040] In the formula: K is the number of Gaussian components; ω k is the combination coefficient of the k-th Gaussian component μk and Σ k are the mean vector and covariance matrix of the k-th Gaussian component respectively; p(x|k) is the probability density function of the k-th Gaussian component, and the specific expression is as follows:

[0041]

[0042] S2. Let denote the parameter set composed of all parameters in the GMM. To obtain the optimal estimate of the parameter set Θ first calculate the log-likelihood function corresponding to the data set:

[0043]

[0044] Furthermore, the optimal parameter estimation problem of the GMM can be transformed into the following optimization problem:

[0045]

[0046] The Expectation-Maximization (EM) algorithm is used to solve this problem. First, set the initial parameters of the GMM as Θ (0) , and then perform iterative calculations in two steps, namely the E step and the M step. In the E step, based on the current parameter Θ (i) , calculate the posterior probability that the j-th sample vector x j belongs to the k-th Gaussian component:

[0047]

[0048] In the M step, iteratively update the parameter Θ (i+1) :

[0049]

[0050]

[0051] Repeat the E step and the M step until convergence to obtain the optimal parameters of the GMM.

[0052] S3. Perform eigenvalue decomposition on the covariance matrix Σ k of the k-th Gaussian component in turn, and then obtain K principal component analysis models and their corresponding residual subspaces for calculating damage indicators.

[0053] S4. Perform weighted standardization on the Mahalanobis squared distance and the Euclidean squared distance respectively as the damage indicators in the framework of hybrid principal component analysis: First, calculate the damage indicators corresponding to the k-th Gaussian component, that is, the Mahalanobis squared distance DI Mah,k and the Euclidean squared distance DI Euc,k ; secondly, through the corresponding threshold TMah,k and T Euc,k Standardize the damage indicators respectively, that is, divide the damage indicators by their thresholds; finally, perform a weighted sum of all the standardized damage indicators, and the weight coefficients are the posterior probabilities p(k|x) of the sample from each Gaussian component of the GMM. The specific expression is:

[0054]

[0055] In the formula: represents the weighted standard Mahalanobis squared distance; represents the weighted standard Euclidean squared distance.

[0056] S5. Define the damage discrimination threshold. Due to the weighted standardization process, the thresholds of both damage indicators are taken as 1, that is, when the damage indicator is greater than 1, it is judged that the structure is in a damaged state, otherwise, it is judged that the structure is in a non-damaged state.

[0057] The present invention provides a method for abnormal identification of bridge monitoring data based on weighted principal component analysis to effectively identify abnormal conditions in bridge structure monitoring data. The main technical solution is as follows: First, use the Gaussian mixture model (GMM) to fit the joint probability density function of multi-dimensional monitoring data into a linear combination of multiple local Gaussian components; second, establish a local principal component analysis model for each Gaussian component; finally, calculate the Mahalanobis squared distance and the Euclidean squared distance respectively for the residual parts of all principal component analysis models, and use them as the damage indicators of the structure after weighted standardization. It can realize the Gaussian fitting and local principal component analysis modeling of multi-dimensional bridge monitoring data, and redefine the damage indicators and discrimination thresholds.

[0058] Adopting the method of the present invention to perform online monitoring on the non-linear data of bridge structures under changing operating environments can effectively improve the sensitivity of identifying bridge structure damage data, significantly reduce the missed judgment rate of damage identification, provide a more reliable guarantee for the safety performance of in-service bridges, and the patent method has low implementation difficulty, great promotion value and good social benefits.

[0059] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A bridge monitoring data anomaly identification method based on weighted principal component analysis, characterized in that: The steps include: S1. Use nondestructive monitoring data to establish the probability density function of multi-dimensional damage characteristic data: Where: K is the number of Gaussian components; ω k is the combination coefficient of the kth Gaussian component μ k and Σ k are the mean vector and covariance matrix of the kth Gaussian component respectively; p(x|k) is the probability density function of the kth Gaussian component, expressed as follows: S2. Order Represents the parameter set composed of all parameters in GMM, and calculates the log-likelihood function corresponding to the data set to obtain the optimal estimate of the parameter set Θ S3, the covariance matrix Σ of the k-th Gaussian component k Perform eigenvalue decomposition respectively, and then obtain K principal component analysis models and their corresponding residual subspaces for calculating damage indicators; S4. Weighted normalization is performed on the Mahalanobis square distance and the Euclidean square distance respectively as damage indicators under the framework of mixed principal component analysis: First, the damage indicator corresponding to the k-th Gaussian component is calculated; then, the corresponding threshold T is used to calculate the damage indicator. Mah,k and T Euc,k The damage indicators are standardized respectively; finally, all the standardized damage indicators are weighted summed; S5. Define the damage discrimination threshold, and take the thresholds of the two damage indicators as 1. That is, when the damage indicator is greater than 1, the structure is judged to be in a damaged state, otherwise, the structure is judged to be in a non-damaged state.

2. The bridge monitoring data anomaly identification method based on weighted principal component analysis according to claim 1 is characterized by: In step S4, when all the standardized damage indicators are weighted and summed, the weight coefficient is the posterior probability p(k|x) that the sample comes from each Gaussian component of the GMM. Specifically, the optimal parameter estimation problem of the GMM is transformed into the following optimization problem: The expectation maximization algorithm is used to solve the problem.

3. The bridge monitoring data anomaly identification method based on weighted principal component analysis according to claim 2 is characterized by: When using the expectation maximization algorithm to solve, first set the initial parameters of GMM to Θ (0) Then it is iterated in two steps: E step and M step. The E step is calculated based on the current parameter Θ (i) , calculate the jth sample vector x j The posterior probability of belonging to the kth Gaussian component is:

4. The bridge monitoring data anomaly identification method based on weighted principal component analysis according to claim 2 is characterized by: Iterate the update parameters Θ in M ​​steps (i+1) : Repeat steps E and M until convergence and obtain the optimal parameters of GMM.

5. The bridge monitoring data anomaly identification method based on weighted principal component analysis according to claim 1 is characterized in that: In step S4, the damage index is normalized by dividing the damage index by its threshold value.

6. The bridge monitoring data anomaly identification method based on weighted principal component analysis according to claim 1 is characterized by: In step S4, the damage index corresponding to the k-th Gaussian component is calculated, including the Mahalanobis square distance DI Mah,k and Euclidean square distance DI Euc,k .

7. A bridge monitoring data anomaly identification method based on weighted principal component analysis according to any one of claims 1 to 5, characterized in that: When all standardized damage indicators are weighted and summed, the specific expression is: Where: represents the weighted standard Mahalanobis square distance; represents the weighted standard squared Euclidean distance.

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