다변량 통계분석을 이용한 지반구조물의 이상거동 평가

Abstract

In the geotechnical structures, collapse or failure time can not predict exactly. Because there involve many difficult things such as nonlinear behavior of soil, difficulty of field representation in the laboratory and technical limits of various investigations and experiments. Therefore monitoring system using instruments is installed after construction. This monitoring system provides information about damage and abnormal event of structure before collapse or failure. To detect abnormal event is difficult in the measured data because of nonlinear time dependency and seasonal effects, which affect the data. Therefore a unique approach cannot be defined to model movement of geotechnical structures. As technology becomes more and more advanced, measuring instruments are highly diversified and intelligent. However, there are alert thresholds of only some kinds of gauges. In addition, data measured from each gauge have analyzed by univariate statistical method despite installing gauges in the same structure. The monitoring using univariate analysis does not take into account that variables are not independent of each other and their correlation information can be important for understanding process behavior. Univariate statistical analysis does not function well for multivariable processes. In contrast, multivariate analysis takes advantage of the correlation information between data for multivariable processes.

This paper presents an evaluation and application of Multivariate Statistical Analysis(MSA). The MSA is used in order to understand the relationships between variables. This method can analyze together data measured from installed gauges in the same structure. The proposed method is a data-driven method that can separate unknown, statistically uncorrelated source processes from observed mixed processes. In the data-driven approaches, no physical assumptions of target systems are required. Instead, the "best" mathematical relationship is estimated for the given data sets measured from target structures. As a consequence, data-driven approaches are advantageous in modeling systems whose geomechanical properties are unknown or difficult to be measured. The proposed method can analyze data obtained from all kinds of gauges and between different kinds of gauges. In addition, analysis model is updated by moving the time-window in the real time monitoring system.

In this study, MSA is applied to slopes having collapse histories. The -statistic and the Hotelling -statistic(-statistics) in Principal Component Analysis(PCA) are used. They can be monitored in order to detect abnormal events. The index reflects a variation in the model subspace, whereas the index indicates a variation from the model subspace. Multivariate control charts based on can be plotted based on the first N principal components. This control chart only detects variation in the plane of the first N principal components which are greater than what can be explained by the common-cause variations. When a new type of special event occurs which is not present in the in-control data used to build the PCA model, the new observations move off the plane. This type of event can be detected by computing the -statistic of the residual for new observations.

The MSA is successfully tested for detection of an abnormal event. -statistic and -statistic detect every collapsed events of slopes and abnormal symptoms before collapese. Results show that proposed method is robust technique for monitoring of structures.

This method is expected to be a useful tool for management and alarm systems of geotechnical structures. The proposed method is expected to be applied to various other infrastructures such as tunnel, bridge, retaining wall and dam during construction precess and management.