INVERSE ANALYSIS BASED ON PROJECTION FILTER GROUP OF FRAME MODEL USING FIRST VIBRATION MODE AS THE ACTUAL MEASUREMENT OBSERVATIONS

Abstract

 Inverse analyses are performed for 5-story frame model to identify lateral stiffness using projection and parametric projection filtering algorithms. The actual measurement 1st vibration mode measured by Experimental Modal Analysis (EMA) is adopted as observation data. Because the mode vector are obtained as ratio of displacement, the natural frequency of 1st vibration mode as well as mode displacements was used to determine the necessary inverse solutions. And also, to compose the observation vector by dimensionless displacements and frequency of 1st mode, not projection filter, but parametric projection filter with regularization parameter to control the iterative calculations of the filter equation were used as inverse analysis procedure effectively. In series of our inverse calculations, applicability and effectiveness of regularization parameter are presented through the comparison with inverse calculations used various kind of positive- definite parameter.

 

 New results obtained in this study are summarized as follows.

 

 (1) It is also possible to obtain highly precise solutions using projection filtering algorithm, when initial values are given as the neighborhood of the designed lateral stiffness.

 (2) Inverse analysis used parametric projection filtering algorithm are able to obtain a lot of collect inverse solutions by using appropriate value of regularization parameter for many initial values.

 (3) Physical quantity which are each element of sensitivity matrix, filter gain and determinant of sensitivity matrix change gently to regularization parameter of large value, oppositely, these quantities change drastically to parameter of small number. Namely, iterative process of filtering algorithm is similar to that of Kalman filter to large values of regularization parameter, on the other hand, iterative process of that is similar to projection filter to small values of regularization parameter.

 (4) Even if, filtering process is similar to projection filter, the tendency which goes suddenly up and down has not formed in the calculation process of parametric projection filtering step.

 (5) In practical use of this procedure, when regularization parameter which does not fit in with structure is used, a lot of same inverse solutions can be not obtained on each initial value. However, when regularization parameter which can fit in with structure is used, because straight line is formed on each initial value, the appropriate parameter which corresponds to the structure can be inspected.

 (6) The parametric projection filtering algorithm which used regularization parameter appropriately can develop the effective and practical computer programming easily.