파워스펙트럼밀도의 확률특성을 고려한 모드-하중 동시식별법
A Concurrent Modal-Load Identification framework Based on the Probability Analogy of Power Spectral Density Function
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초록
외부하중을 받는 구조물로부터 계측된 신호의 파워 스펙트럴 밀도함수는 모달 파라미터(고유진동수, 감쇠비)에 대한 상당량의 정보를 함축하고 있다. 시스템 식별기술은 이러한 신호나 해당 스펙트럼으로부터 모달 파라미터를 추출하는 기법이라고 볼 수 있다. 파라미터를 추출하는 또 다른 기법으로는 샘플링(신호)을 이용하여한 확률분포의 모수(평균, 분산)를 추정하는 기법이다. 본 연구에서는 파워 스펙트럼 밀도함수를 확률분포로 치환함으로써 기존 확률통계분야에서 모수를 추출하는 기법(최대우도법)에 의해 모달 파라미터를 추정하는 기법을 제안한다. 모드형상을 추정하는 기법을 개발하고 모드형상에 의해 분해된 모드응답으로부터 고유진동수, 고유감쇠비를 순차적으로 산정하는 기법을 제시한다. 더 나아가, 외부하중이 스펙트럼 해석모델로 치환 가능한 경우에는 이 하중모델은 통합하여 모델 파라미터까지 산정하는 기법으로 확대한다. 본 연구에서 제시된 기법을 검증하기 위한 수치해석과 실구조물의 응답에 대한적용이 이루어졌으며, 검증결과 제안된모드식별체계가 안정적이며, 신뢰도가 높은 모달파라미터 추정이 가능함을 알 수 있었다.
Abstract
The power spectral density function of signals measured from structures subjected to external loads contains a significant amount of information about the modal parameters (natural frequencies, damping ratios). System identification techniques can be illustrated as techniques for extracting modal parameters from these signals or their spectra. Another technique to extract parameters is to estimate the parameters(mean, variance) of a probability distribution using sampling(signals). In this study, it is proposed a technique to estimate the modal parameters by replacing the power spectral density function with a probability density function and using the existing parameter extraction technique (maximum likelihood method) in the field of probability statistics. A technique is developed to estimate the mode shape and to sequentially calculate the natural frequency and damping ratio from the mode response decomposed by the mode shape. Furthermore, if the external load can be replaced by a spectral model, the load model is integrated in the modal identification framework. Numerical analysis and application to the response of a real structure are performed to verify the proposed method in this study, and the verification results show that the proposed mode identification framework is stable and is able to estimate modal parameters with high reliability.
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