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

Abstract

The invention belongs to civil engineering works structure health monitoring field, there is provided a kind of structure monitoring data exception recognition methods based on multivariate statistical analysis.First, the normal Monitoring Data to structure sets up multivariate statistical analysis model；Secondly, the anomalous identification process of Monitoring Data is converted into assumed statistical inspection problem in the noise subspace of model；Then, the assumed statistical inspection problem is solved to derive a new statistic, for recognizing thundering observed data；Finally, the reasonable threshold value of the statistic is determined, when statistic is the presence of exception in can determine whether Monitoring Data more than threshold value.

Description

A kind of structure monitoring data exception recognition methods based on multivariate statistical analysis

Technical field

The invention belongs to civil engineering works structure health monitoring field, it is proposed that a kind of structure based on multivariate statistical analysis Monitoring Data abnormality recognition method.

Background technology

Civil engineering structure under the collective effect of the factors such as long duration load, environmental attack and fatigue effect, its military service The degeneration of energy is inevitable.Structure monitoring data are analysed in depth, the abnormality of structure can be in time found and be provided accurate Safe early warning, the safe operation to ensuring civil engineering structure has important practical significance.At present, structure monitoring data is different General knowledge mainly by statistical method realization, is not generally divided into two major classes：1) single argument control figure, such as Shewhart control chart, accumulation With control figure etc., such method sets up control figure respectively to the Monitoring Data of each measuring point, to recognize the exception in Monitoring Data； 2) multivariate statistical analysis, such as principal component analysis, independent component analysis, such method is using between multi-measuring point Monitoring Data Correlation sets up statistical model, and defines corresponding statistic to recognize the exception in Monitoring Data.

Due to the continuity of malformation, the response data between structure adjacent measuring point also has certain correlation.Cause This, in practical engineering application, it can be considered that the multivariate statistical analysis method of this correlation has more superiority.Additionally, should Class method only needs 1~2 statistic of definition, you can differentiate whether Monitoring Data is abnormal, and this is for the knot comprising numerous sensors It is very convenient for structure health monitoring system.However, conventional multivariate statistical analysis method to structure monitoring data in it is micro- Small exception is sometimes not sensitive enough, if the problem can be solved effectively, multivariate statistical analysis is recognized in structure monitoring data exception In will more have practical value.

The content of the invention

The present invention is directed to propose a kind of structure monitoring data exception recognition methods, effectively to solve multivariate statistical analysis pair The insensitive problem of minor anomaly in structure monitoring data.Its technical scheme is：First, the normal Monitoring Data to structure is set up Multivariate statistical analysis model；Secondly, the anomalous identification process of Monitoring Data is converted into system in the noise subspace of model Meter Hypothesis Testing Problem；Then, the assumed statistical inspection problem is solved to derive a new statistic, for recognizing abnormal prison Survey data；Finally, determine the reasonable threshold value of the statistic, when statistic be more than threshold value exist in can determine whether Monitoring Data it is different Often.

A kind of structure monitoring data exception recognition methods based on multivariate statistical analysis, step is as follows：

Step one：Monitoring Data is modeled

(1) the normal Monitoring Data to structure sets up multivariate statistical analysis model：

S=E { xx^T}=V Ξ V^T

In formula：X=[x₁,x₂,...,x_m]^TThe a certain normal Monitoring Data of structure is represented, altogether comprising m variable；S is represented Covariance matrix；Ξ=diag (ξ₁,ξ₂,...,ξ_m) include all characteristic value ξ_i；V=[v₁,v₂,...,v_m] include all features Vector v_i, v_iAs i-th principal direction；

(2) set comprising r principal direction in noise subspace, then its expression formula is N=[v_m-r+1,v_m-r+2,...,v_m]^T, r presses Following condition determines：

And

Step 2：Anomalous identification process is converted into assumed statistical inspection problem

(3) normal Monitoring Data x is projected as n=Nx on noise subspace N；

(4) a certain thundering observed data for setting structure is expressed asδ represents abnormal amount, then it is empty in noise Between be projected as n=Nx+N δ on N；

(5) η=Nx and ε=N δ are made, then anomalous identification process can be exchanged into following assumed statistical inspection problem：

In formula：Η₀Null hypothesis is represented, in the absence of abnormal under the conditions of being somebody's turn to do；Η₁Alternative hvpothesis are represented, is existed under the conditions of being somebody's turn to do different Often；It is generally acknowledged that the Monitoring Data Gaussian distributed under normal or abnormality, then Η₀Under the conditions of have n~G (0, Σ_η), and Η₁Under the conditions of have n~G (ε, Σ_η), Σ_ηRepresent the covariance matrix of variable η；

Step 3：Assumed statistical inspection problem is solved, statistic is derived

(6) using the l Moving Window of Monitoring Data is included, the throwing of i-th sample on N is calculated respectively in the Moving Window Shadow n_i, i=1,2 ..., l；When following condition is met, generalized likelihood-ratio test method judges Η₁Set up, i.e., in the Moving Window Monitoring Data exist it is abnormal：

In formula：Represent the maximal possibility estimation of ε；P () represents the probability of certain variable；T represents statistic；τ represents threshold Value；

(7) further derive, the log-likelihood ratio in above formula is expressed as：

(8) included in above formulaItem be fixed value, move it to threshold portion, then discriminate further simplifies For：

(9) because the maximal possibility estimation of ε isThen discriminate is finally reduced to：

In formula：n_jRepresent the projection of j-th sample on N, j=1,2 ..., l in Moving Window；When statistic T exceedes threshold During value τ, show that the Monitoring Data in Moving Window is present abnormal；

Step 4：Determine the reasonable threshold value of statistic

(10) for the normal Monitoring Data of structure, after setting Moving Window length l, the corresponding system of each Moving Window is calculated MeteringUntil all of Monitoring Data has all been calculated；Then, the general of all statistics is estimated Rate Density Distribution, then determine rational threshold tau according to 99% confidence criterion (i.e. significance is 1%).

Beneficial effects of the present invention：The anomalous identification process of structure monitoring data is converted into assumed statistical inspection problem, And then a new statistic is derived, the statistic can effectively recognize thundering observed data.

Brief description of the drawings

Fig. 1 is Moving Window schematic diagram.

Fig. 2 is the recognition result of textural anomaly Monitoring Data.

Specific embodiment

Below in conjunction with accompanying drawing and technical scheme, specific embodiment of the invention is further illustrated.

Two across a highway bridge models are chosen, its length is 5.4864m, width is 1.8288m.Finite element mould is set up to it Type is responded with model configuration, and 12 responses of measuring point of collection are used as Monitoring Data.Symbiosis is into two datasets：Training dataset and Test data set；Wherein, training dataset is normal Monitoring Data collection, and the part that test data is concentrated is used to simulate abnormal prison Survey data；Two datasets continue 120s, and sample frequency is 256Hz.Specific embodiment is as follows：

(1) training dataset is modeled, is computed, the principal direction number included in noise subspace is r=2；Cause This, noise subspace is made up of most latter two principal direction, i.e. N=[v₁₁,v₁₂]^T。

(2) Moving Window length l is set, each corresponding statistic of Moving Window (see Fig. 1) that training data is concentrated is calculatedAfter the corresponding statistic of all Moving Windows has been calculated, the probability density point of statistic is estimated Cloth, then determine rational threshold tau according to 99% confidence criterion.

(3) Monitoring Data of simulation thundering observed data, i.e., No. 2 sensor collection is concentrated in 48~120s in test data Period occurs abnormal；No. 2 Monitoring Datas of sensor after the Monitoring Data and simulation exception of extremely preceding No. 2 sensors of comparative simulation Understand：The exception of Monitoring Data is difficult to discover.For the test data set after simulating exception, each of which Moving Window pair is calculated The statistic answeredAll abnormal datas are successfully identified out.

Claims (1)

1. a kind of structure monitoring data exception recognition methods based on multivariate statistical analysis, it is characterised in that step is as follows：

Step one：Monitoring Data is modeled

(1) the normal Monitoring Data to structure sets up multivariate statistical analysis model：

S=E { xx^T}=V Ξ V^T

In formula：X=[x₁,x₂,...,x_m]^TThe a certain normal Monitoring Data of structure is represented, altogether comprising m variable；S represents covariance Matrix；Ξ=diag (ξ₁,ξ₂,...,ξ_m) include all characteristic value ξ_i；V=[v₁,v₂,...,v_m] include all characteristic vector v_i, v_iAs i-th principal direction；

(2) set comprising r principal direction in noise subspace, then its expression formula is N=[v_m-r+1,v_m-r+2,...,v_m]^T, r is by as follows Condition determines：

And

Step 2：Anomalous identification process is converted into assumed statistical inspection problem

(3) normal Monitoring Data x is projected as n=Nx on noise subspace N；

(4) a certain thundering observed data for setting structure is expressed asδ represents abnormal amount, then it is in noise subspace N On be projected as n=Nx+N δ；

(5) η=Nx and ε=N δ are made, then anomalous identification process can be exchanged into following assumed statistical inspection problem：

$\left\{\begin{array}{cc}{H}_0:& n=\mathrm{\η}\\ H_1:& n=\mathrm{\ϵ}+\mathrm{\η}\end{array}\right.$

In formula：Η₀Null hypothesis is represented, in the absence of abnormal under the conditions of being somebody's turn to do；Η₁Alternative hvpothesis are represented, is existed under the conditions of being somebody's turn to do abnormal；One As think under normal or abnormality Monitoring Data Gaussian distributed, then Η₀Under the conditions of have n~G (0, Σ_η), and Η₁Bar There are n~G (ε, Σ under part_η), Σ_ηRepresent the covariance matrix of variable η；

Step 3：Assumed statistical inspection problem is solved, statistic is derived

(6) using the l Moving Window of Monitoring Data is included, the projection n of i-th sample on N is calculated respectively in the Moving Window_i, I=1,2 ..., l；When following condition is met, generalized likelihood-ratio test method judges Η₁Set up, i.e. prison in the Moving Window Survey data and there is exception：

$T=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\ln \frac{p(n_i;\widehat{\mathrm{\ϵ}},H_1)}{p(n_i;H_0)}>\mathrm{\τ}$

In formula：Represent the maximal possibility estimation of ε；P () represents the probability of certain variable；T represents statistic；τ represents threshold value；

(7) further derive, the log-likelihood ratio in above formula is expressed as：

$\begin{array}{c}\ln \frac{p(n_i;\widehat{\mathrm{\ϵ}},H_1)}{p(n_i;H_0)}=-\frac{1}{2}\[{(n_i-\widehat{\mathrm{\ϵ}})}^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}{(n_i-\widehat{\mathrm{\ϵ}})}^T-n_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}{n}_i\]\\ =-\frac{1}{2}\[n_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}{n}_i-2n_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}\widehat{\mathrm{\ϵ}}+{\widehat{\mathrm{\ϵ}}}^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}\widehat{\mathrm{\ϵ}}-n_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}{n}_i\]\\ =n_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}\widehat{\mathrm{\ϵ}}-\frac{1}{2}{\widehat{\mathrm{\ϵ}}}^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}\widehat{\mathrm{\ϵ}}\end{array}$

(8) included in above formulaItem be fixed value, move it to threshold portion, then discriminate is further simplified as：

$T=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{n}_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}\widehat{\mathrm{\ϵ}}>\mathrm{\τ}$

(9) because the maximal possibility estimation of ε isThen discriminate is finally reduced to：

$T=\frac{1}{l}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{n}_i^T{\mathrm{\Σ}}_{\mathrm{\η}}^{-1}{n}_j>\mathrm{\τ}$

In formula：n_jRepresent the projection of j-th sample on N, j=1,2 ..., l in Moving Window；When statistic T exceedes threshold tau, Show that the Monitoring Data in Moving Window is present abnormal；

Step 4：Determine the reasonable threshold value of statistic

(10) for the normal Monitoring Data of structure, after setting Moving Window length l, the corresponding statistic of each Moving Window is calculatedUntil all of Monitoring Data has all been calculated；Then, estimate that the probability of all statistics is close Degree distribution, then determine rational threshold tau according to 99% confidence criterion (i.e. significance is 1%).