KR101988956B1 - Structural Health Monitoring Method Using Adaptive Multivariate Statistical Process Monitoring Under Environmental Variability - Google Patents

Abstract

The present invention relates to a method of evaluating structural integrity using adaptive multivariate statistical process monitoring in consideration of external environmental variation, and more particularly, to a method for evaluating structural integrity of a structure, A statistical model is constructed using a moving window, and if a nonlinear relationship between features susceptible to damage of the structure is found, it is possible to locally divide and linearize a region where damage-sensitive characteristics of the structure appear nonlinearly, By applying the Variable Moving Window Principal Component Analysis (VMWPCA) to vary the size of the moving window, it is possible to reflect the change rate of the sound state of the structure of the structure, It has a non-linear dependency of the effect of to handle.

Description

TECHNICAL FIELD [0001] The present invention relates to a method for evaluating structure health based on adaptive multivariate statistical process monitoring,

The present invention relates to a structural integrity evaluation method, and more particularly, to a real-time structural integrity evaluation method using adaptive multivariate statistical process monitoring in consideration of external environment variations.

As is well known, structural health monitoring (SHM) is to monitor and quantify damage to structural systems.

The above-mentioned structural integrity evaluation is mainly used to evaluate whether there is a problem in the parts through the data measured through the measurement system in the mechanical field. The evaluation concept used for evaluating the soundness of the structures in the civil engineering and construction fields, To be performed.

The structural integrity evaluation (SHM) process measures the main response periodically through the sensor system and extracts features sensitive to the damage of the structure from these responses. The structure of the structural system is analyzed in real time And performing an evaluation.

The metrology system periodically (or continuously) measures responses such as vibration response, impedance or electrical resistance change. However, since features that are sensitive to structure damage are not directly measured, these features are extracted from the measured responses using Feature Extraction Techniques.

In addition, since most of the structures are exposed to the outside and the surrounding environment changes over time, it is difficult and unclear to grasp the damage and deterioration mechanism itself over time.

Therefore, a data normalization method for reflecting the above-described external environment variation has been continuously studied. These typical normalization methods can be roughly divided into regression analysis for identifying input / output relations and multivariate statistical analysis using only output. More attention is paid to multivariate statistical analysis, which is generally easy to apply.

Multivariate Statistical Analysis (PCA) and Factor Analysis (FA) are mainly used, and the main advantage of these methods is that they only analyze patterns of features that are sensitive to structural damage No data is needed for the input.

Multivariate Statistical Analysis assumes that the variability of features sensitive to damage to a structure is due to the linear combination of environmental factors and other factors not related thereto due to various properties, Can not be explained by a linear combination pattern, this provides a value that greatly deviates from the sound state of the structure.

Therefore, constructing a statistical model that can grasp the abnormal state with the characteristics of the healthy state of the structure, and recognizing that the characteristic that deviates from the pattern of the constructed statistical model is the occurrence of the abnormal state.

Therefore, multivariate statistical process monitoring (MSPM) based on principal component analysis (PCA) is widely used to more effectively reflect external environmental volatility [3, 4, 7].

Yan, Kerschen, and De Boe and Golinval [4] used Squared Prediction Error based on Linear PCA to identify structural damage using simulated natural frequencies.

Mujica, Rodellar, Fernandez and Guemes [7] use the waveform signals obtained by Piezoelectric Transducers (PZT) and use this signal as a distance index based on Linear Principal Component Analysis (PCA) Statistic and T2-statistic were applied.

Wursten and De Roeck used the long-term natural frequencies of actual bridge structures to capture artificial damage [3]. Linear PCA can not handle the nonlinearity of these correlations because it has nonlinearity of the natural frequencies of the corresponding long-term data.

Therefore, Kernel PCA and Local Linear PCA were used to solve the limitation of Linear PCA and to confirm the damage successfully [8]. Here, Local Linear PCA is a method of dividing nonlinear correlation into several partial groups having a linear relationship.

Yan, Kerschen, De Boe, and Golinval [8] first applied Local Linear PCA to long-term monitoring to compute nonlinear correlations.

In order to develop a statistical model for the diagnosis of damage, it is important to build and utilize teacher data well from instrumentation data. Therefore, the development of statistical models such as the Baseline Model is the most important task for MSPM based on Structural Health Assessment (SHM).

Theoretically, the statistical model built through the teacher data should be able to describe the major variability of the healthy condition. In other words, the teacher data should include a variation relationship between features and environmental conditions (linear or non-linear relationships of temperature-dependent variations) [3, 9] and a correlation-changing relationship between features [10].

If the implemented statistical model lacks the ability to express a sound state of the structure, there may be a lot of misinformation that can be used to evaluate external fluctuations in the sound state of the structure. The reliability of the implemented statistical model can therefore be very poor. [11, 12]. The relationship with these external environmental factors can not be completely understood. These influences can be identified through long-term measurements. However, since the change of the external environment has a characteristic that changes with time, information on the sound state of the structure is partially grasped. In addition, it is difficult to obtain enough teacher data at the beginning of monitoring.

Since Linear PCA is a technique based on the assumption that the linear relationship of features is a function, it gives false analysis results under nonlinear conditions.

As described above, the structural soundness evaluation methods using the linear linear principal component analysis (PCA) have a problem that the structure can not deal with nonlinear correlation between the time variation of the sound state and the characteristics.

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SUMMARY OF THE INVENTION It is an object of the present invention to solve the problems described above and to provide a structure capable of effectively reflecting a nonlinear relationship between features sensitive to damage of a measured structure used, And to provide a structural integrity evaluation method based on adaptive multivariate statistical process monitoring in consideration of external environment variations.

According to an aspect of the present invention, there is provided a method for evaluating structural integrity using adaptive multivariate statistical process monitoring, the method comprising: installing a measurement system on a structure; Extracting features sensitive to damage to the structure from the measured data from the metrology system; Constructing a statistical model of the healthy state of the structure using features of the extracted structure that are sensitive to damage; And a structural abnormality state diagnosis step of evaluating newly measured features based on the statistical model to determine whether or not damage to a structure has occurred, and the step of constructing the statistical model includes: A statistical model is constructed using a moving window moving along the measurement data newly obtained from the existing measurement data so as to update the nonlinear characteristic of the structure when the nonlinear relationship between the feature vectors is found, (Variable Moving Window Principal Component Analysis) that varies the size of the moving window so that the moving window can be linearly divided by locally dividing the moving window.

Here, it is preferable that the size of the moving window is made smaller as the change in the sound state of the structure is larger, and larger as the change in the sound state of the structure is slower.

The optimal size of the moving window is preferably determined through k-means clustering using the Linde-Buzo-Gray algorithm (KMC-LBG) having a Bayesian information criterion (BIC)

Also, the number of optimal clusters for k-means clustering can be calculated by the following equation.

는 전체 군집 수이고,

는

번째 군집 내의 샘플 수고,

은 전체 샘플 수며,

는

번째 군집의 분산(variance)이다. here,

Is the total number of clusters,

The

The number of samples in the second cluster,

Can be a whole sample,

The

Is the variance of the second cluster.

Also, the dispersion of the cluster can be calculated by the following equation.

는

번째 군집의 중심 평균이고, Linde-Buzo-Gray 알고리즘(KMC-LBG) 사전에 사용자 정의된 범위 내에 적용된다.here,

The

And the Linde-Buzo-Gray algorithm (KMC-LBG) is applied within the user-defined range in advance.

Also, Bayesian Information Criterion (BIC) is performed in a predefined number of clusters, Bayesian information is calculated for each cluster number, and the first cluster maximum And the number of clusters having a value.

According to the method for evaluating the structural integrity of the structure based on the adaptive multivariate statistical process monitoring in consideration of the external environment variation of the present invention, the structure is moved along the newly obtained data in the existing data so as to update the change in the sound state A variable moving window principal component analysis (VMWPCA) that varies the size of the moving window so as to linearize the nonlinearity of features according to the external environment while constructing a statistical model through a moving window , It is possible to reflect such a change and to have an effect of processing nonlinear correlation between the features.

FIG. 1 is a flowchart schematically illustrating a structural integrity evaluation process according to an embodiment of the present invention. Referring to FIG.
Figure 2 is a schematic diagram illustrating a conceptual description of Variable Moving Window Principal Component Analysis (VMWPCA).
FIG. 3 is a diagram showing a variable moving window principal component analysis (VMWPCA) process based on block linearization for health diagnosis.
4 is a graph illustrating the basic principle of Principal Component Analysis.
FIG. 5 is a schematic diagram showing a health check process using principal component analysis (PCA). FIG.
Figure 6 is a schematic diagram illustrating a conceptual description of the moving window linear principal component analysis (MWPCA).
FIG. 7 is a schematic diagram showing a comparison between a fixed moving window linear principal component analysis and a variable moving window linear principal component analysis.
8 is a graph showing a block linearization process for adaptive process monitoring.
9 is a graph illustrating a k-means clustering process using the Linde-Buzo-Gray algorithm (KMC-LBG) with BIC.
10 is a chart showing a variable moving window principal component analysis (VMWPCA) process using BIC and KMC-LBG.
11 is a side view and a front cross-sectional view of the Z24 bridge.
12 is a graph showing the natural frequency of long-term monitoring (about one year) of the Z24 bridge.
Fig. 13 is a chart showing the progress of the progressive damage test of the Z24 bridge. Fig.
14 is a chart showing the initial teacher data used to analyze the effect of the initial teacher data.
15 is a graph showing the double linear dependency between the natural frequency and the temperature.
16 is a graph showing a correlation between natural frequencies.
FIG. 17 is a graph showing other teacher data used to analyze the effect of the initial teacher data composition.
18 is a graph showing the results of the soundness evaluation of the output-only structure of the Z24 bridge using the variable moving window principal component analysis (VMWPCA) of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and the same or similar components are denoted by the same reference numerals throughout the specification.

FIG. 1 is a flowchart schematically illustrating a structural integrity evaluation process according to an embodiment of the present invention. Referring to FIG.

1, a structure integrity evaluation method (hereinafter, referred to as "structural integrity evaluation method") using adaptive multivariate statistical process monitoring in consideration of external environment variation according to an embodiment of the present invention includes a measurement system , A feature extraction step (ST20), a statistical model construction step (ST30), and a structural abnormality diagnosis step (ST40).

First, in the measurement step ST10 through the measurement system, main responses such as vibration response, electromechanical impedance, or electrical resistance change, which can extract characteristics susceptible to damage to a structure in a structure to be evaluated for soundness, Each sensor should be installed in a structure that can be measured periodically (or continuously).

In the step of extracting features sensitive to damage to a structure (ST20), features sensitive to the damage of the structure are extracted from the response data measured from the measurement system.

In the statistical model building step (ST30), a statistical model of the structure for determining the abnormal state is constructed by using features extracted from the damage of the structure.

In the structural integrity diagnosis step (ST40), newly measured features are evaluated based on the statistical model to determine whether or not the structure is damaged.

Particularly, in the present invention, Variable Moving Window Principal Component Analysis (VMWPCA) is applied in the statistical model building step ST30.

FIG. 2 is a schematic diagram illustrating a conceptual description of a variable motion window principal component analysis (VMWPCA), and FIG. 3 is a diagram showing a variable motion window principal component analysis (VMWPCA) process based on block linearization for soundness diagnosis.

2 and 3, the Variable Moving Window Principal Component Analysis (VMWPCA) is a moving window that moves along the measurement data newly obtained from the existing measurement data so as to update the change in the sound state of the structure due to the external environment change A nonlinear relationship between features susceptible to damage of the structure is found, a size of the moving window is determined so as to linearly divide a region in which damage-sensitive characteristics of the structure are nonlinearly localized, .

Variable Moving Window Principal Component Analysis (VMWPCA) is based on Principal Component Analysis and Moving Window Principal Component Analysis (VMWPCA) for output-only statistical process monitoring.

Therefore, the principle principle analysis and the moving window principle component analysis (VMWPCA) for explaining Variable Moving Window Principal Component Analysis (VMWPCA) First, it is as follows.

Principal component analysis (PCA) is a representative multivariate statistical analysis, with multivariate variables generally correlated with each other.

The correlation between the data (features) can be handled like hidden processes that contain information about the process.

4 is a graph illustrating the basic principle of Principal Component Analysis.

As shown in FIG. 4, the goal of principal component analysis (PCA) is to identify the coordinate axes (P1, P2, etc.) of the new coordinate system (Coordinate System) with respect to the high variability of the original data. Here, the identified coordinate axes are referenced to the principal component (PC) and are the subspace of the uncorrelated variables.

Mathematically, the principal components (PC) can be obtained by minimizing the sum of the original data and the squared distance between these projections projected into the subspace by Least-square Sense. Equation (1) below is an equivalent expression for finding a subspace that minimizes the variables of the projections.

)으로 투영된 선형 조합이다. Here, X is original data and T is a partial space (

). ≪ / RTI >

The subspace can be obtained by diagonalizing a covariance matrix for X. [ The covariance matrix for X can be obtained by the following equation (2).

-변수들을 갖는

행렬이며, 위 첨자 T는 전치 행렬(Transpose)이다. Here, N is the number of the original data, and the original data X is

- having variables

Matrix, and the superscript T is a transpose.

The subspace can be obtained by solving the eigenvalue problem by the following equation (3).

는 고유값이고,

는

고유 벡터와 일치한다. 대수학적으로 수학식 3은 공분산 행렬(C)의 고유치 분해(Eigen-Decomposition)나 특이치 분해(SVD; Singular Value Decomposition)를 통해 수행될 수 있다. 상기한 공분산 행렬(C)은 아래 수학식 4를 통해 구할 수 있다. here,

Is a unique value,

The

Coincides with the eigenvector. Mathematically, equation (3) can be performed through Eigen-Decomposition or Singular Value Decomposition (SVD) of the covariance matrix C. The covariance matrix C can be obtained by the following equation (4).

는 고유값 (

의 대각선 행렬이고,

는 고유벡터 행렬 (

)과 일치한다.here,

Is the eigenvalue (

, ≪ / RTI >

Is an eigenvector matrix (

).

Eigenvalues and eigenvectors coincide with the principal component (PC), which are the latent variables and the main vectors, respectively.

)는 변수(

)의 개수와 같거나 더 작다, 여기서

이고 PC들은 다음과 같은 특징들을 갖는다.

일 때

이고

이다. Number of principal components (

) Is the variable

), ≪ / RTI > where < RTI ID =

And PCs have the following characteristics.

when

ego

to be.

Figure 1 shows the results of principal component analysis (PCA) in a two-dimensional space. Each point represents the original data X and the two arrows represent the first and second coordinate axes (1st PC (P1), 2stPC (P2)) for the principal components (PC), respectively.

는 변동성의 총합이다. 여기서,

.

는 부분 공간의

번째 축들이고, 이들은 서로 직교한다. 첫 번째 주성분(

)는 원본 데이터(

)의 가장 큰 변동성을 표현한 것이고, 첫 번째 주성분(1stPC(P1)) 원본 데이터에서 관찰된 주된 효과와 일치하는 것으로 해석할 수 있고, 두 번째 주성분(2stPC(P2);

)는 첫 번째 주성분(1st PC(P1))과 비상관된 2차적 효과를 나타낸다.

Is the sum of the volatility. here,

.

Of the subspace

Axis, and they are orthogonal to each other. The first active ingredient (

) Is the original data (

) And the first principal component (1stPC (P1)) can be interpreted as being consistent with the main effect observed in the original data, and the second principal component (2stPC (P2);

) Represents the secondary effect uncorrelated with the first principal component (1st PC (P1)).

Prior to performing Principal Component Analysis (PCA), scaling must be done on the original data in order for the variables to have an equal effect.

In the Structural Integrity Assessment (SHM), the above standardization process can refer to Data-Cleansing. In previous studies, the standardization process has been widely used in two standardization methods: Mean-Centering [4] and Auto-Scaling [7].

Mean-Centering is to normalize the original data so that the mean is zero for each variable, whereas Auto-Scaling, known as z-Scaling, takes zero mean for each variable And the unit variance (Unit Variance).

In general, mean-centering is recommended when the variance (variability) of the original data is uniform, and auto-scaling is suitable for situations where the original data has heterogeneous variability (variability) 14].

Often, statistical features of the data are not known in advance. To handle common situations, Auto-Scaling is used for Data Cleansing. Normal-distribution normalization can be performed through the following equations (5) to (7).

와

는 각각 원본 데이터의 평균과 변동성이다.

는

번째에 연속하는

번째 변수의 정규분포 표준화(auto-scaling)된 데이터이다. here,

Wow

Are the mean and variability of the original data, respectively.

The

Consecutive

The second parameter is the auto-scaled data.

우선 주성분들(PCs)의 (

)를 구하기 위해 두 개의 모니터링 통계가 사용된다. In order to carry out structural integrity evaluation (SHM)

First of all,

), Two monitoring statistics are used.

고, 이는 가장 중요한 주성분들의 (

)를 이용해 표준화된 데이터(

)와 재구성된 데이터(

) 사이의 유클리디안 거리(Euclidean Distance)이다. at first

This means that the most important components (

) To standardize the data (

) And reconstructed data (

(Euclidean Distance).

The Euclidean distance can be obtained from Equation (8) below.

는 표준화된 데이터 행렬 (

)이고,

는

PCs가 유지된 행렬 (

)이며,

는 항등 행렬(

) 이고,

는 유클리디안 거리를 나타낸다. here,

Is a standardized data matrix (

)ego,

The

PCs are retained in the matrix (

),

Is an identity matrix (

) ego,

Represents the Euclidean distance.

-statistic는 첫 번째 PC의 정사각 모양의 직교 거리이고,

-statistic는 유지된 주성분들(

)에 의해 구할 수 없는 변수들의 합계를 구할 수 있다. As shown in Fig. 1,

-statistic is the orthogonal distance of the square shape of the first PC,

-statistic is the retained principal components (

) Can be obtained.

-statisticd이고, 이는 중심으로부터 재구성된 데이터(

)의 거리를 측정한다. 상기 재구성된 데이터(

)의 거리는 아래 수학식 9를 통해 구할 수 있다. The second measure is Hotelling's

-statisticd, which is the data reconstructed from the center (

) Is measured. The reconstructed data (

) Can be obtained by the following equation (9).

는

우선 PCs 유지하는 대각선 행렬(

)이다. 도 1에 도시한 바와 같이.

-statistic는 중심과 재구성된 데이터 (

) 사이의 마할라노비스 거리(Mahalanobis Distance)이다. here,

The

First, keep the PCs diagonal matrix (

)to be. As shown in Fig.

-statistic is the center and the reconstructed data (

) Is the Mahalanobis Distance.

-statistic는 유지된 PC들의 변수들을 측정하고, 부분 공간(주성분들 등의)의 중심으로부터 가장 떨어진 정도를 진단할 수 있다.

-statistic measures the variables of the PCs maintained and can diagnose the most distant from the center of the subspace (such as principal components).

(

)을 가지는

-statistic 과

-statistic의 상한값은 시간 독립성(Temporal Independence)과 투영된 데이터 (

)의 정규성(Normality)을 가정함으로써 구할 수 있다[15].

-statistic(

)의 상한값은 아래 수학식 10의 카이제곱분포(Chi-Squared Distribution)를 통해 구할 수 있다[16].Significance level

(

)

-statistic and

The upper limit of the statistic is the temporal independence and the projected data

), And the normality of [(15)].

-statistic (

) Can be obtained through the Chi-Squared distribution of Equation (10) [16].

이고,

과

는 표본 평균(Sample Mean)과

-statistic의 변동성을 각각 나타낸다, 그리고,

는 자유도

와 유의수준

를 가지는 카이제곱분포이다. here,

ego,

and

Is the sample mean and

-statistic variability, respectively,

The degree of freedom

And significance level

≪ / RTI >

-statistic (

) 의 상한 값은 아래 수학식 11과 같다On the other hand,

-statistic (

) Is expressed by Equation (11) below

과

자유도를 가지는

-분포이다here,

and

Having a degree of freedom

- Distribution.

)의 최적 수는 선택될 수 있다. 변동성 누적률(CPV; Cumulative Percentage of Variance)이 많은 연구에서 폭 넓게 사용되었다. 변동성 누적률(CPV)은 최초 r 잠재변수들(

)에 의해 변동량을 측정한다. To perform Principal Component Analysis (PCA), the principal components (PCs)

) Can be selected. Cumulative Percentage of Variance (CPV) was widely used in many studies. The volatility cumulative rate (CPV)

).

However, the above volatility cumulative rate (CPV) is a subjective approach. Thus, the value of the volatility cumulative rate (CPV) is generally estimated from 80% to 99% in previous studies [3, 12, 17-19].

Rather than using a heuristic choice of volatility cumulative rate (CPV), this study used the Eigengap Technique for the optimal number of PCs [20-23].

When the eigenvalues are sorted in descending order, the eigenvalue difference is calculated by Equation (12).

. 가장 큰

고유치 차이(Eigengap)은 투영과 재구성(

)에 대해 주성분들을 유지하도록 선택된다. here,

. biggest

The eigenvalue difference (Eigengap) is the projection and reconstruction

) ≪ / RTI >

A new diagnostic using principal component analysis (PCA) can be widely used in the structural health assessment (SHM) process, and the root cause of the new diagnosis is that the value of the monitoring statistics is small during the sound state of the structure. When a new feature is acquired, this new feature is projected and reconstructed in the subspace of the base model (principal component analysis (PCA) from teacher data).

and/or

), 이 것은 구조적 손상이 존재하는 것을 나타낸다. 그렇지 않으면, 구조 시스템은 현재 구조물이 건전한 상태와 같이 비손상 상태이다. If the monitoring statistics for new features are greater than their upper limit value (

and / or

), Indicating that structural damage exists. Otherwise, the rescue system is in an undamaged state, such as the current state of the structure.

FIG. 5 is a schematic diagram showing a health check process using principal component analysis (PCA). FIG.

Referring to FIG 5, the principal component analysis (PCA) integrity evaluation of the structure with the (a) the main component extract (PC), and, (b) the first main component to the coordinate axes of the (1 ^th PC) projected in a one-dimensional (C) two-dimensionally reconstructing the original space, (d) computing the remainder of the information loss, and (e) diagnosing the new defect through the monitoring chart.

FIG. 6 is a schematic view showing a conceptual description of a moving window linear principal component analysis (MWPCA), and FIG. 7 is a schematic diagram showing a comparison between a fixed moving window linear principal component analysis and a variable moving window linear principal component analysis.

)와 함께 시작한다.

을 토대로, 초기 기저 모델 (

)이 구성된다. Referring to Figures 6 and 7, the moving window linear principal component analysis (MWPCA)

).

, The initial baseline model (

).

)가 획득된 후 구조물이 건전한 상태로 평가되면, 이동 창은 최신 데이터를 따라 이동한다. New data (

) Is obtained and the structure is evaluated as sound, the moving window moves along with the latest data.

이고, 기저 모델(

)이 새로운 계측데이터에 의해 획득되는 것을 말한다. This new window

, And the base model (

) Is obtained by the new measurement data.

)은 구조물이 건전한 상태의 변화를 채택할 수 있게 된다. The mechanism of the move window is repeated until new data is available. By doing so,

) Allows the structure to adopt a sound state of change.

If the structure is healthy and the moving window size increases rapidly, the moving base window will contain too old data, so the current base model can not reflect the sound state of the structure. In this regard, the moving window linear principal component analysis (MWPCA) using a fixed moving window is insufficient to capture the change in the state of the structure.

The movement window size is related to the rate of change of the state of the structure. The size of the smaller moving window is appropriate when the structure is changing abruptly, while the size of the larger moving window is preferred when the structure is changing slowly. Often, the rate of change of a sound state of a structure is not known in advance. That is, the change in the sound state of the structure is time varying.

Therefore, the present invention proposes a variable moving window linear principal component analysis (VMWPCA).

Here, the most general method of the moving window is to update the average and covariance of the healthy state of the changed structure and extract the principal components based on the updated average.

And, Principal Component Analysis (PCA) described above is essentially a linear tool. Therefore, if the teacher data has a nonlinear dependence in the moving window, it is not possible to effectively deal with nonlinear dependence with the moving window linear principal component analysis (MWPCA) based on the sample mean change and covariance [15, 23, 27, 29].

On the other hand, (a) Kernel PCA method and (b) Local Linear PCA method are used to solve the nonlinear dependence in the skeleton of PCA.

을 사용하는 것이 한 가지 방법이고, (b) 국부 선형 주성분분석(Local Linear PCA)은 비선형 시스템에 선형 PCA를 확장하는 것이 다른 한 가지 방법이다[8, 32, 33].(a) Kernel PCA is a kernel technique for plotting original data in future space [3, 31]

(B) Local Linear PCA is another way to extend the linear PCA to a nonlinear system [8, 32, 33].

Also, the variable movement window strategy proposed in the present invention was developed using the concept of Local Linear PCA. That is, the basic goal of the variable moving window size is block linearization of the moving window.

FIG. 8 is a graph illustrating a block linearization process for adaptive process monitoring, FIG. 9 is a graph illustrating a k-means clustering process using a Linde-Buzo-Gray algorithm having a BIC (KMC-LBG) (VMWPCA) process using BIC and KMC-LBG.

 Referring to Figures 8-10, nonlinear data is locally partitioned, and these locally partitioned portions may be close to linear data.

In order to perform block linearization, k-means clustering using the Linde-Buzo-Gray algorithm (KMC-LBG) is used [34, 35].

The KMC-LBG algorithm is an extended version of the k-means clustering (KMC) algorithm. The KMC-LBG algorithm is a centroid-based clustering for finding k clusters.

In general, the centroid is the average of each cluster. They require the most appropriate conditions to find the central trajectories of the k clusters, and locate the samples in the closest cluster center trajectory.

In order to position the samples, distance measurements such as geometric and mathematical distances are calculated from the central locus of the cluster.

Based on the calculated distance, the samples are placed at the minimum distance of the cluster. The main difference between KMC-LBG and KMC is that the KMC-LBG algorithm uses a binary splitting algorithm to obtain the center trajectory, whereas the KMC algorithm uses arbitrary points for the initial center trajectory.

Because it utilizes a binary segmentation algorithm, the KMC-LBG algorithm provides better distributed clusters than the KMC algorithm.

)을 구할 수 있다는 것이다. 베이시안 정보 기준(BIC)은 다양한 모델 군에서 최적의 모델을 선택하는데 기준으로 활용된다. BIC는 모델들의 특징들에 대한 정보를 담고 있기 때문에 BIC는 모델 기반 군집(Model-Based Clustering)에 폭넓게 적용되어 왔다[36]. 최적 군집 수는 다음 수학식 13과 같이 계산된다.The main purpose of the clustering algorithm is to determine the optimal cluster

) Can be obtained. The Bayesian Information Standard (BIC) is used as a basis for selecting the best model in various model groups. Since BIC contains information about the characteristics of models, BIC has been extensively applied to model-based clustering [36]. The optimal number of clusters is calculated by the following equation (13).

는 전체 군집 수이고,

는

번째 군집 내의 샘플 수이며,

은 전체 샘플 수이고,

는

번째 군집의 분산(variance)이다. here,

Is the total number of clusters,

The

The number of samples in the second cluster,

Is the total number of samples,

The

Is the variance of the second cluster.

는

번째 군집의 중심 궤적(평균)이고, KMC-LBG알고리즘이 미리 정의된 범위 내에 적용되며, BIC의 값들이 산출된다. here,

The

(Average) of the first cluster, the KMC-LBG algorithm is applied within a predefined range, and the values of BIC are calculated.

When using equation (13), the BIC value is a negative value.

The first local maximum of the BIC is the optimal number of clusters [36,37]. Therefore, the optimal cluster numbers can be selected according to the number of clusters at the first maximum value.

To evaluate the performance of the KMC-LBG algorithm with BIC for the optimal cluster number, we apply it to three clustering problems as shown in FIG.

The predicted range of clusters was set to form one of the three. In the first problem, the data is generated by a single Uni-modal Gaussian distribution in two-dimensional space.

A KMC-LBG with BIC is performed, and a single cluster is correctly selected by the BIC value. A KMC-LBG with BIC can provide the correct population for different clustering problems. Thus, we provide three clusters for the second problem (nonlinear trend) and two clusters for the third problem (a bi-modal Gaussian distribution).

The second problem is a good example of block linearization. By an optimal number of clusters (for example, three), data having a nonlinear tendency is divided into local groups having a linear tendency (FIG. 8).

With respect to the variable moving window method, the moving window size can be obtained by clustering so as to include the latest data. The main reason for using these clusters is that data in these clusters have recently been measured, because they contain recent changes in the sound state of the structure.

The Variable Moving Window Principal Component Analysis (VMWPCA) proposed in the present invention includes two main mechanisms. The first mechanism is a moving window for updating a sound state of the structure, and the remaining mechanism is a variable moving window using a KMC-LBG having a BIC for providing an optimum number of moving windows.

)를 산정한다. Here, depending on the variable moving window size and the computational efficiency, the maximum moving window size (

).

(VMWPCA) of the present invention is applied to artificially damaged actual bridges at the end of long-term monitoring to compare whether the structure can take into account both the rate of change of the sound state and the nonlinear dependence of features susceptible to damage to the structure Respectively.

Experimental Example

Long-term monitoring was performed on Z24 bridges within the framework of the Brite Euram project in the system identification project (No. BE96-3157) for monitoring civil engineering structures [38].

Artificial damage scenarios have been applied at the end of monitoring [3, 39]. The proposed method is applied to Z24 bridges. The Z24 bridges are prestressed concrete bridges with three spans in Switzerland

Fig. 11 is a side view and a front sectional view of a Z24 bridge, and Fig. 12 is a graph showing natural frequencies of long-term monitoring (about one year) of a Z24 bridge.

Referring to Figs. 11 and 12, the Z24 bridge is a post-tensioned concrete box girder bridge [13, 38].

Long - term monitoring was carried out to quantify the environmental changes of bridge dynamic characteristics for 305 days from November 11, 1997 to September 11, 1998, before the bridge collapse (late 1999). Vibration responses and environmental variables were measured every hour [3].

The actual damage process is shown in Fig. Reynders, Wursten and De Roeck [3] found that the initial structural combination could be caused by the inevitable loss of flexural stiffness of the piers during the installation of the Pier Settlement System on August 9.

)인 고유진동수 추계론적 부공간 식별기법(SSI; Stochastic Subspace Identification)과 아스팔트 층의 온도(T)에 의해 확인될 수 있다. Features that are sensitive to damage to four structures (

) Stochastic Subspace Identification (SSI) and the temperature (T) of the asphalt layer.

이하일 때, 4개의 고유진동수(Natural Frequencies)가 급하게 변화되는 것을 나타낸다. Here, the asphalt layer

, It indicates that four natural frequencies are rapidly changed.

)와 온도 (

) 사이의 상관 관계를 실험하기 위해, 도 12에서와 같이

와

사이에 산점도(Scatter Plots)들을 설명하였다.Natural frequency

) And temperature (

), As shown in FIG. 12,

Wow

(Scatter Plots).

를 기준으로 모든 고유진동수에 대해

와

사이의 이중 선형 관계가 관측되었다. 추가적으로, 몇몇 고유진동수는 비선형적인 상관관계를 갖고 있다. 이들이 관찰되는 이유는 아스팔트 층의 탄성계수(Young's Modulus)가 온도 종속성을 갖기 때문이다[3].here,

For all natural frequencies

Wow

Were observed. Additionally, some natural frequencies have non-linear correlations. These are observed because the Young's Modulus of the asphalt layer has temperature dependency [3].

FIG. 13 is a chart showing the progress of the damage test of the Z24 bridge, FIG. 14 is a chart showing the initial teacher data used to analyze the influence of the initial teacher data, and FIG. FIG. 16 is a graph showing the correlation between the natural frequencies, and FIG. 17 is a graph showing other initial teacher data used to analyze the influence of the initial teacher data structure.

Referring to FIGS. 13 to 17, the Young's modulus of the asphalt layer has a relatively low value at 0 ° C. or higher, but increases sharply at 0 ° C. or lower.

Depending on the damage detection feature, four lower order natural frequencies are used. To effectively assess the initial teacher data, the proposed technique was run with a different number of initial teacher data.

In this regard, studies on three cases (Case 1-Case 3) can be considered as shown in FIG.

In the first case, the initial teacher data does not have information that changes nonlinearly below 0 ° C because it constitutes measurement data above 0 ° C.

The second initial teacher data has a small nonlinear change characteristic because it contains measurement data over 0 ℃ and some measurement data below 0 ℃.

Finally, the third initial teacher data has strong nonlinear change characteristics because it has both data above 0 ℃ and sufficient measurement data below 0 ℃.

To apply the proposed method, normal-distribution normalization (Auto-Scaling) using Equation (7) is applied to the measurement data. The number of principal components (PC) to be used is selected by the above eigenvalue difference technique.

T2-statistic statistics in monitoring statistics were not considered in this study. Typically, T2-statistic measures the sensitivity of unusual changes or large deviations within the PC model.

The extracted features have discontinuous intervals of measurement due to failure of the metrology system. T ² -statistic is not suitable for this case because the discontinuity of these measurements occurs due to large variability even under sound conditions of the structure.

For this reason, the Q-statistic of Equation (8) is used for monitoring statistics having a 95% confidence level. The Q-statistic assumes that five consecutive data have out-of-tolerance values, that the current condition is defective, and the proposed technique stops updating the base model (PC model).

Variable Mobile Window The maximum size of the moving window (L _max ) is expected to be 1,500 to show the trend of change for two months in the principal component analysis (VWMPCA). The maximum size can be customized by the user. Therefore, the maximum size (L _max ) of the moving window can be obtained by the following equation (15).

Here, the maximum size (L _max ) of the moving window can be adjusted.

18 is a graph showing the results of the soundness evaluation of the output-only structure of the Z24 bridge using the variable moving window principal component analysis (VMWPCA) of the present invention.

Referring to FIG. 18, all cases (Case 1-Case 3) of the variable moving window principal component analysis (VMWPCA) were successful in diagnosing the damage.

In other words, the proposed variable moving window principal components analysis (VMWPCA) can explain the changes in the sound state of the structure and update the base model properly. From these observations, we can see that the proposed variable moving window principal component analysis (VMWPCA) is not affected by the initial teacher data.

In other words, when the structure is sound, the size of the moving window must be small so as to place a weight on the recent data. On the other hand, when the structure is smoothly changed, essential information about the sound state of the structure Move window size should be increased to accommodate long term. Also, when nonlinear dependencies appear in the features, the size of the smaller movement window is selected.

As described above, in the method for evaluating the sound quality of the output structure using the adaptive multivariate statistical process monitoring in consideration of the external environment variation of the present invention, by applying Variable Moving Window Principal Component Analysis (VMWPCA) A statistical model is constructed through a moving window moving along continuous data so as to update the nonlinear characteristic of the structure, and the size of the moving window is changed so that the nonlinear characteristic of the structure is soundly localized, It has the effect of reflecting the rate of change and also of handling the nonlinear dependence of the data reflecting the rate of change of the sound state of the structure.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but many variations and modifications may be made without departing from the spirit and scope of the invention. And it goes without saying that they belong to the scope of the present invention.

Claims (6)

Measuring a major response by installing a metrology system on the structure;
Extracting features sensitive to damage to the structure from the measured data from the metrology system;
Constructing a statistical model of the structure in a sound state for determining an abnormal state using features extracted from the damage of the structure; And
And a structural abnormality diagnosis step of evaluating newly measured features based on the statistical model to determine whether a damage of a structure has occurred,

In the statistical model building step,
The statistical model is constructed using the moving window moving along with the newly obtained measurement data from the existing measurement data so that the structure is updated with the change of the sound state due to the external environment change,
If a nonlinear relationship between features susceptible to damage of the structure is found, variable movement window principal component analysis (hereinafter referred to as " variable movement window principal component analysis ") that varies the size of the moving window so as to locally divide and linearize the non- A Method for Evaluating Structural Integrity Using Adaptive Multivariate Statistical Process Monitoring Considering Variation of External Environment Performed by Applying Variable Moving Window Principal Component Analysis (VMWPCA).
The method of claim 1,
The size of the moving window may be,
A method for evaluating structural integrity using adaptive multivariate statistical process monitoring that takes into account the external environment variation in which the structure becomes smaller as the change in the sound state becomes larger and the structure becomes larger as the change in the sound state becomes smaller.
3. The method of claim 2,
The optimal size of the moving window is determined by the following equation
Adaptive multivariate statistical process monitoring based on k-means clustering using the Linde-Buzo-Gray algorithm (KMC-LBG) with Bayesian information criterion (BIC) Method for Evaluating Structural Integrity Using.
4. The method of claim 3,
Wherein the number of optimal clusters for k-means clustering is calculated by the following equation: < EMI ID = 1.0 >

here,

Is the total number of clusters,

The

The number of samples in the second cluster,

Can be a whole sample,

The

Is the variance of the second cluster.
5. The method of claim 4,
Wherein the dispersion of the cluster is evaluated by adaptive multivariate statistical process monitoring that takes into account the external environment variation calculated by the following equation.

here,

The

, And the Linde-Buzo-Gray algorithm (KMC-LBG) is applied within a pre-defined range.
The method of claim 5,
The number of optimal clusters may be determined,
Bayesian information criterion (BIC) is performed in a predefined population size, Bayesian information is calculated for each cluster number, and the number of clusters having the first local maximum value A Method for Evaluating Structural Integrity Using Adaptive Multivariate Statistical Process Monitoring Considering External Environment Variation.

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