CN106802879A - A kind of structure monitoring data exception recognition methods based on multivariate statistical analysis - Google Patents

Abstract

The invention belongs to the field of health monitoring of civil engineering structures and provides a method for identifying abnormality of structural monitoring data based on multivariate statistical analysis. First, a multivariate statistical analysis model is established for the normal monitoring data of the structure; second, the anomaly identification process of the monitoring data is transformed into a statistical hypothesis testing problem in the noise subspace of the model; then, the statistical hypothesis testing problem is solved to derive a new The statistic is used to identify abnormal monitoring data; finally, a reasonable threshold of the statistic is determined, and when the statistic exceeds the threshold, it can be judged that there is an anomaly in the monitoring data.

Description

A Method for Identifying Abnormalities of Structural Monitoring Data Based on Multivariate Statistical Analysis

technical field

The invention belongs to the field of health monitoring of civil engineering structures, and proposes an abnormal identification method of structural monitoring data based on multivariate statistical analysis.

Background technique

Under the combined action of long-term load, environmental erosion and fatigue effects, the degradation of service performance of civil engineering structures is inevitable. In-depth analysis of structural monitoring data can detect the abnormal state of the structure in time and provide accurate safety warnings, which is of great practical significance to ensure the safe operation of civil engineering structures. At present, the abnormal identification of structural monitoring data is mainly realized by statistical methods, which are generally divided into two categories: 1) Univariate control charts, such as Shewhart control charts, cumulative sum control charts, etc. Establish control charts for monitoring data to identify abnormalities in monitoring data; 2) Multivariate statistical analysis, such as principal component analysis, independent component analysis, etc. This type of method uses the correlation between monitoring data at multiple measuring points to establish a statistical model, And define corresponding statistics to identify anomalies in monitoring data.

Due to the continuity of structural deformation, the response data between adjacent measuring points of the structure also has a certain correlation. Therefore, in practical engineering applications, the multivariate statistical analysis method that can consider this correlation is more superior. In addition, this type of method only needs to define 1 or 2 statistics to determine whether the monitoring data is abnormal, which is very convenient for a structural health monitoring system that includes many sensors. However, commonly used multivariate statistical analysis methods are sometimes not sensitive enough to small anomalies in structural monitoring data. If this problem can be effectively solved, multivariate statistical analysis will be more practical in identifying abnormalities in structural monitoring data.

Contents of the invention

The invention aims to propose a method for identifying anomalies in structural monitoring data to effectively solve the problem that multivariate statistical analysis is not sensitive to tiny anomalies in structural monitoring data. The technical solution is: firstly, establish a multivariate statistical analysis model for the normal monitoring data of the structure; secondly, convert the anomaly identification process of the monitoring data into a statistical hypothesis testing problem in the noise subspace of the model; then, solve the statistical hypothesis testing problem The problem is to derive a new statistic to identify abnormal monitoring data; finally, determine the reasonable threshold of the statistic, and when the statistic exceeds the threshold, it can be judged that there is an anomaly in the monitoring data.

A method for identifying anomalies in structural monitoring data based on multivariate statistical analysis, the steps of which are as follows:

Step 1: Monitoring data modeling

(1) Establish a multivariate statistical analysis model for the normal monitoring data of the structure:

S=E{xx ^T }=VΞV ^T

In the formula: x=[x ₁ ,x ₂ ,...,x _m ] ^T represents a certain normal monitoring data of the structure, including m variables; S represents the covariance matrix; Ξ=diag(ξ ₁ ,ξ ₂ ,...,ξ _m ) contains all eigenvalues ξ _i ; V=[v ₁ ,v ₂ ,...,v _m ] contains all eigenvectors v _i , and v _i is the ith main direction;

(2) Assuming that the noise subspace contains r main directions, its expression is N=[v _m-r+1 ,v _m-r+2 ,...,v _m ] ^T , and r is determined according to the following conditions :

and

Step 2: Transform the anomaly identification process into a statistical hypothesis testing problem

(3) The projection of normal monitoring data x on the noise subspace N is n=Nx;

(4) Let the abnormal monitoring data of the structure be expressed as δ represents the abnormal quantity, then its projection on the noise subspace N is n=Nx+Nδ;

(5) Let η=Nx and ε=Nδ, then the anomaly identification process can be transformed into the following statistical hypothesis testing problem:

In the formula: Η ₀ represents the null hypothesis, and there is no abnormality under this condition; Η ₁ represents the alternative hypothesis, and there is an abnormality under this condition; it is generally believed that the monitoring data under the normal or abnormal state obeys the Gaussian distribution, and then there is n under the condition of Η ₀ ～G(0, _Ση ), and under the condition of Η ₁ , there are n～G(ε, _Ση ), and Ση represents the covariance matrix of variable _η ;

Step 3: Solve statistical hypothesis testing problems and derive statistics

(6) Using a moving window containing l monitoring data, calculate the projection n _i of the i-th sample on N within the moving window, i=1,2,...,l; when the following conditions are met, _The generalized likelihood ratio test method judges that Η is established, that is, there is anomaly in the monitoring data in the moving window:

In the formula: Indicates the maximum likelihood estimation of ε; p( ) indicates the probability of a variable; T indicates a statistic; τ indicates a threshold;

(7) Further derivation, the log likelihood ratio in the above formula is expressed as:

(8) The above formula contains The term is a fixed value, moving it to the threshold part, the discriminant is further simplified as:

(9) Since the maximum likelihood estimate of ε is Then the discriminant finally simplifies to:

In the formula: n _j represents the projection of the jth sample in the moving window on N, j=1,2,...,l; when the statistic T exceeds the threshold τ, it indicates that the monitoring data in the moving window is abnormal;

Step 4: Determine a reasonable threshold for the statistic

(10) For the normal monitoring data of the structure, after setting the moving window length l, calculate the statistics corresponding to each moving window Until all the monitoring data are calculated; then, estimate the probability density distribution of all statistics, and then determine a reasonable threshold τ according to the 99% confidence criterion (that is, the significance level is 1%).

The beneficial effect of the present invention is that the abnormal identification process of structural monitoring data is converted into a statistical hypothesis testing problem, and then a new statistical quantity can be derived, which can effectively identify abnormal monitoring data.

Description of drawings

Figure 1 is a schematic diagram of a moving window.

Fig. 2 is the recognition result of structural anomaly monitoring data.

detailed description

The specific implementation manners of the present invention will be further described below in conjunction with the accompanying drawings and technical solutions.

Select a two-span highway bridge model with a length of 5.4864m and a width of 1.8288m. A finite element model was established to simulate the structural response, and the responses of 12 measuring points were collected as monitoring data. A total of two data sets are generated: training data set and test data set; among them, the training data set is a normal monitoring data set, and a part of the test data set is used to simulate abnormal monitoring data; both data sets last for 120s, and the sampling frequency is 256Hz . The specific implementation is as follows:

(1) Model the training data set. After calculation, the number of main directions contained in the noise subspace is r=2; therefore, the noise subspace is composed of the last two main directions, that is, N=[v ₁₁ ,v ₁₂ ] ^T.

(2) Set the moving window length l, and calculate the statistics corresponding to each moving window (see Figure 1) in the training data set After calculating the statistics corresponding to all moving windows, estimate the probability density distribution of the statistics, and then determine a reasonable threshold τ according to the 99% confidence criterion.

(3) Simulate the abnormal monitoring data in the test data set, that is, the monitoring data collected by the No. 2 sensor is abnormal during 48-120s; comparing the monitoring data of the No. Abnormalities in monitoring data are not easy to detect. For the test data set after simulating the abnormality, calculate the statistics corresponding to each moving window All anomalous data were successfully identified.

Claims (1)

1. A structural monitoring data abnormal identification method based on multivariate statistical analysis, characterized in that the steps are as follows: Step 1: Monitoring data modeling (1) Establish a multivariate statistical analysis model for the normal monitoring data of the structure: S=E{xx ^T }=VΞV ^T In the formula: x=[x ₁ ,x ₂ ,...,x _m ] ^T represents a certain normal monitoring data of the structure, including m variables; S represents the covariance matrix; Ξ=diag(ξ ₁ ,ξ ₂ ,...,ξ _m ) contains all eigenvalues ξ _i ; V=[v ₁ ,v ₂ ,...,v _m ] contains all eigenvectors v _i , and v _i is the ith main direction; (2) Assuming that the noise subspace contains r main directions, its expression is N=[v _m-r+1 ,v _m-r+2 ,...,v _m ] ^T , and r is determined according to the following conditions : and Step 2: Transform the anomaly identification process into a statistical hypothesis testing problem (3) The projection of normal monitoring data x on the noise subspace N is n=Nx; (4) Let the abnormal monitoring data of the structure be expressed as δ represents the abnormal quantity, then its projection on the noise subspace N is n=Nx+Nδ; (5) Let η=Nx and ε=Nδ, then the anomaly identification process can be transformed into the following statistical hypothesis testing problem: $\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; :</span>& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; :</span>& \mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}\end{array}\right.$ In the formula: Η ₀ represents the null hypothesis, and there is no abnormality under this condition; Η ₁ represents the alternative hypothesis, and there is an abnormality under this condition; it is generally believed that the monitoring data under the normal or abnormal state obeys the Gaussian distribution, and then there is n under the condition of Η ₀ ～G(0, _Ση ), and under the condition of _Η1 , there are n～G(ε, _Ση ), and Ση represents the covariance matrix of variable _η ; Step 3: Solve statistical hypothesis testing problems and derive statistics (6) Using a moving window containing l monitoring data, calculate the projection n _i of the i-th sample on N within the moving window, i=1,2,...,l; when the following conditions are met, _The generalized likelihood ratio test method judges that Η is established, that is, there is anomaly in the monitoring data in the moving window: $\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}$ In the formula: Indicates the maximum likelihood estimation of ε; p( ) indicates the probability of a variable; T indicates a statistic; τ indicates a threshold; (7) Further derivation, the log likelihood ratio in the above formula is expressed as: $\begin{array}{c}\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&rsqb;</span>\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&rsqb;</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}\end{array}$ (8) The above formula contains The term of is a fixed value, moving it to the threshold part, the discriminant is further simplified as: $\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}$ (9) Since the maximum likelihood estimate of ε is Then the discriminant finally simplifies to: $\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; l</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; \&tau;</span>}$ In the formula: n _j represents the projection of the jth sample in the moving window on N, j=1,2,...,l; when the statistic T exceeds the threshold τ, it indicates that the monitoring data in the moving window is abnormal; Step 4: Determine a reasonable threshold for the statistic (10) For the normal monitoring data of the structure, after setting the moving window length l, calculate the statistics corresponding to each moving window Until all the monitoring data are calculated; then, estimate the probability density distribution of all statistics, and then determine a reasonable threshold τ according to the 99% confidence criterion (that is, the significance level is 1%).