Model Free Interpretation of Monitoring Data Daniele Posenato1, Francesca Lanata2, Daniele Inaudi1and Ian F.C. Smith3 1
Smartec SA, via Pobiette 11,CH-6928 Manno, Switzerland
[email protected],
[email protected] 2 Department of Structural and Geotechnical Engineering University of Genoa Via Montallegro, 116145 Genoa, Italy 3 Ecole Polytechnique Fédérale de Lausanne (EPFL) GC G1 507, Station 18, CH-1015 Lausanne, Switzerland
[email protected]
Abstract. No current methodology for detection of anomalous behavior from continuous measurement data can be reliably applied to complex structures in practical situations. This paper summarizes two methodologies for model-free data interpretation to identify and localize anomalous behavior in civil engineering structures. Two statistical methods i) moving principal component analysis and ii) moving correlation analysis have been demonstrated to be useful for damage detection during continuous static monitoring of civil structures. The algorithms memorize characteristics of time series generated by sensor data during a period called the initialisation phase where the structure is assumed to behave normally. This phase subsequently helps identify anomalous behavior. No explicit (and costly) knowledge of structural characteristics such as geometry and models of behaviour is necessary. The methodologies have been tested on numerically simulated elements with sensors at a range of damage severities. A comparative study with wavelets and other statistical analyses demonstrates superior performance for identifying the presence of damage.
1 Introduction Structural health monitoring engineers may employ sensors to perform nondestructive in-situ structural evaluation. These sensors produce data (either continuously or periodically) that are analyzed to assess the safety and performance of structures [1]. For static monitoring, damage can be identified through comparing static structural response with predictions of behavior models [2]. However, models can be expensive to create and may not accurately reflect undamaged behavior. Difficulties and uncertainties increase in the presence of complex civil structures so that well defined and unique behavior models often cannot be clearly identified [3]. Furthermore, multiple-model system identification may not succeed in identifying the right damage [4]. Despite important research efforts into interpretation of continuous static monitoring data [5], no reliable strategy for identifying damage has been proposed and verified for broad classes of civil structures [3][6]. Another approach is to evalu-
ate changes statistically [7]. This methodology is completely data driven; the evolution of the data is estimated without information of physical processes [8-10]. The objective of this paper is to propose methodologies that discover anomalous behavior in data generated by sensors without using behavior models. The paper is organized as follows: Section 2 provides a description of the numerical simulation used to compare the damage detection performances of several algorithms and a description of the moving PCA and correlation analysis. Section 3 explains how PCA and correlation analysis are used in structural health monitoring. Section 4 presents a comparison between these algorithms and continuous wavelet analysis [11-12]. More details of this work are contained in [13].
2 Numerical Simulation and Model-Free Data Interpretation 2.1 Numerical Simulation Due to difficulties in retrieving databases from real structures with a range of damage severities, a finite element model [3] of a two-span continuous beam in healthy and in damaged states has been used to evaluate the efficiency of algorithms to detect damage [5]. A thermal load simulates structural behavior under varying environmental conditions. The response is measured by means of a ‘virtual’ monitoring system composed of twelve elongation sensors, see Figure 1. SENSOR 7
SENSOR 1
SENSOR 8
SENSOR 2
SENSOR 9
SENSOR 3
SENSOR 10
SENSOR 11
SENSOR 12
SENSOR 4
SENSOR 5
SENSOR 6
Fig.1. The FE model used to test the methodology showing where sensors are placed (bold lines) and positions of simulated damage (black squares). The beam is 10x0.5x0.3 m, and each cell of the mesh is 10x8 cm.
2.2 Moving Principal Components Analysis (MPCA) PCA is based on an orthogonal decomposition of the process variables along the direction that explains the maximum variation of the data (the components that contain most of the information) [15]. PCA is applied to the data in this study in an effort to reduce the dimensionality of the data and to enhance the discrimination between features of undamaged and damaged structures. To reduce the dimensionality of the space, values of sensor measurements are projected onto the eigenvectors that correspond to the largest eigenvalues of the covariance matrix. Most of the variance is contained in the first few principal components while the remaining components are defined by measurement noise. Each eigenvalue expresses the variance in time associated with the corresponding eigenvector. Orthogonal eigenvectors are time-invariant: the eigenvector associated with the maximum eigenvalue represents the spatial behavior corresponding to the time function with the maximum variance. Normally the PCA is computed on the covariance matrix computed for all the measurements in the time series. To reduce
the computation time and thus the time required to detect new situations in the time series, a Moving Principal Components Analysis is used [13], in which a window (a subset of time series) containing only a fixed number of last measurements is used. The original aspect of this method is that the covariance matrix of all the sensors is computed only for a moving window of constant size. This means that after each measurement session, the covariance matrix and principal components are computed only for the points inside the active window. 2.3 Moving Correlation Analysis This method is used to calculate the correlations between all sensor pairs for a reference period with the aim to quantify the tendency of sensors to change in similar ways. During the reference period, variations of correlations are calculated for each sensor pair. After the initialisation phase, all correlations are calculated at each step to determine the presence of anomalies in the evolution of values. Anomalous behaviour is observed through correlations lying outside the thresholds defined during the initialisation phase. In normal conditions the correlation should be constant or stationary. However, when damage occurs, correlations between the sensors change. To follow the evolution of the time series more effectively, a moving window of fixed size is employed [13]. After each session of measurement the correlation is calculated only for the points inside the moving window. The size of the window has to guarantee stability of average values, to ensure rapid damage identification and to reduce the effects of noise.
3 Application to Structural Health Monitoring Application of MPCA and Moving Correlation to structural health monitoring involves an initial phase (called initialization) where the structure is assumed to behave in an undamaged condition. The aim of this initialization period is to estimate the variability of the time series and to define thresholds for detecting anomalous behavior [14]. This period is normally one or two years because in this manner all the expected variations in the behavior of health structure, due to periodic environmental and load changes, is supposed to be recorded. In order to make all the further recorded behavior comparable with those recorded during the initialization the schedule of measurements has to be unchanged during the monitoring. Once thresholds have been fixed, the parameters of the process are monitored (main eigenvectors for MPCA and Correlations on all sensor pairs for the Moving Correlation) to ensure that they are inside predefined ranges. For identifying damage location, the rule has been used that candidate damage zones are close to sensors that have the status parameters exceeding a threshold.
4 Results
sn2 sn3 sn5
Normalized eigenvector [-]
Normalized eigenvector [-]
A comparative study between the proposed algorithms and wavelet transform (CWT) [11-12], short-term Fourier transform (STFT) [12], the instance-based method (IBM) [15-16] has been carried out for several damage scenarios [13]. In this paper, only comparisons with using the algorithms and CWT for damage between sensors 2 and 3 (4 cells with reduction to 20% of original stiffness) are presented, see Figure 1. Results show that the algorithms proposed in this paper identify anomalous behaviour more effectively than CWT. Figure 2 shows plots of the eigenvectors related to the two main MPCA eigenvalues. The moment when damage occurs and its location are visible in both plots. Specifically, one of the eigenvectors (eigenvector 11) indicates a new state when it becomes stable, while the other (eigenvector 12) indicates when the damage occurred. The location of the damage is detected by the fact that within the main eigenvectors, there are one or more rapidly changing components that are associated with sensors close to the damage. In Figure 2 the location of the damage can be detected by the fact that the sensor 3 (Sn3), which is the closest to the damage location has variation bigger than the other sensors. Figure 3 shows Moving Correlation results for sensor pairs that are closest to the damage. The moment when damage occurred and when the behavior of the structure can be considered to be stable are visible. Figure 4 shows CWT results. The moment when damage occurred is not visible and there is no information regarding whether the anomaly is due to a new temporary situation or due to permanent damage.
Fig. 2. MPCA plots of eigenvectors related to the two main eigenvalues. They show the moment when damage occurs and its location. One eigenvector (eigenvector 11, only values of sensors 2, 3 and 5 are presented) gives an indication of the new state of the structure when it becomes stable while the second eigenvector (eigenvector 12) gives an indication of the damage. In figure the sn1, sn2, ... are the components of the eigenvector referred respectively to sensor 1, sensor 2, etc.
Correlation
Coefficients
Sensor 3 vs Sensor 9
Scale Days
Fig. 3. Diagnostic plots of Moving Correlation calculated from measurements of two sensors close to the damage. Calculations were performed using a moving window of one year.
Days
Fig. 4. CWT calculated from the difference between results of the two sensors normalized, closest to the damage. The Gauss wavelet with a scale of 1024 has been used.
5 Conclusions Moving Principal Component Analysis and Moving Correlation are useful tools for identifying and locating anomalous behavior in civil engineering structures. These approaches can be applied over long periods to a range of structural systems to discover anomalous states even when there are large quantities of data. A comparative study has shown that for quasi-static monitoring of civil structures, these new methodologies perform better than wavelet methods. While these methodologies have good capacities to detect and locate damage, they also require less computational resources. Another important characteristic is adaptability. Once new behavior is identified, adaptation allows detection of further anomalies. The next step of the research is to apply the proposed methodology to a database of measurements taken from full-scale structures.
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