A multiplicative regularized Gauss-Newton method with trust region Sequential Quadratic Programming for structural model updating. (15th September 2019) - Mazzotti, Matteo; Mao, Qiang; Bartoli, Ivan; Livadiotis, Stylianos
Highlights: A new method for sensitivity-based model updating is proposed. Ill-conditioning is mitigated by a multiplicative regularization approach. A trust region Sequential Quadratic Programming with bound constraints is used. The size of the trust region is a parameter of the regularization functional. The damaged bearing of an in-service bridge is identified by leveraging modal data. Abstract: The paper focuses on the development of an iterative minimization algorithm for structural identification. The algorithm consists of a Gauss-Newton method in which the ill-conditioning caused by noise pollution is mitigated by means of a multiplicative regularization technique used in conjunction with a bound constrained trust region method. Unlike the classic additive regularization technique, the amount of regularization is not determined a priori, but computed in an automatic fashion at each step of the iterative procedure. Specifically, the strength of the regularization is controlled by the norm of the model parameters weighted by a factor proportional to the current values of the least-square cost functional and the size of the trust region. The iterative procedure consists in solving a sequence of regularized local quadratic subproblems in a Sequential Quadratic Programming framework, for which a local convexity condition is given. The proposed method is finally tested in the retrieval of the equivalent stiffness of the soil and bearings of a real, in-service bridge pier that was tested using experimental modal analysis.