Controllability and Observability of Modal Characteristics for Self-identification of Adaptive Structures

Paper number

IAC-06-C2.5.10

Author

Dr. Atsuhiko Senba, Tokyo Institute of Technology, Japan

Coauthor

Prof. Hiroshi Furuya, Tokyo Institute of Technology, Japan

Year

2006

Abstract

The purpose of this study is to derive the controllability and observability of the eigen-value and eigen-vector for the self-identification of adaptive structures. The concept of the self-identification has been proposed for the structural identification of the adaptive structures that change internal variable structural parameters to overcome the problem of rank-deficient or ill conditioned problems, for which numerous algorithms have been proposed in many research works on structural identification and finite element model updating. 

Some numerical examples of the self-identification have been already shown in our previous studies, and they indicate that the self-identification using the Variable Matrices Method is capable of adapting to the rank-deficiency in structural identification. From the studies, it is shown that the necessary and rigorous requirements for the self-identification are needed to determine the locations of variable structural parameters as well as the location of sensors for general adaptive structures. Thus, this study describes the necessary requirements for the self-identification of adaptive structures by introducing the controllability and observability of modal characteristics. 

We explain the fundamental basis of the self-identification with the Variable Matrices Method, showing that the eigen-values and eigen-vectors can be changed independently by using quasi-static variations of the variable structural parameters of adaptive structures. Consequently, we can formulate the additional equations about unknown structural parameters increasing the rank of the equation, if the sensitivity of these eigen-parameters with respect to the control input of variable structural parameters is not zero, and accordingly the general requirements for the controllability and observability are derived as the requirements of the sensitivities. Finally, present controllability and observability are examined using simple numerical examples and basic experiments. Using a spring-mass system with additional mass or spring, we demonstrate that the derived controllability can be used to determine the location of additional mass or spring to implement its self-identification.  Experimental results of the self-identification are shown through the identification of unknown structural parameters of a cantilevered beam with an additional spring at the controllable location of the mode shape of the lower vibration modes. 

Abstract document

IAC-06-C2.5.10.pdf

Manuscript document

IAC-06-C2.5.10.pdf (🔒 authorized access only).

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