Confidence ellipsoids for static response of trusses with load and structural uncertainties

This paper presents a semidefinite relaxation technique for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain truss. We assume that the parameters both of member stiffnesses and external forces are uncertain but bounded. By using a combination of the quadratic embedding technique of the uncertainty and the SS-procedure, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Our approach has polynomial computational complexity of the problem size, if the SDP problem presented is solved by using the primal-dual interior-point method. The minimum bounding ellipsoids are computed for various trusses under several uncertain circumstances.