A multiplicative regularized Gauss-Newton method with trust region Sequential Quadratic Programming for structural model updating

•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...

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Bibliographic Details
Published in:Mechanical systems and signal processing Vol. 131; pp. 417 - 433
Main Authors: Mazzotti, Matteo, Mao, Qiang, Bartoli, Ivan, Livadiotis, Stylianos
Format: Journal Article
Language:English
Published: Berlin Elsevier Ltd 15.09.2019
Elsevier BV
Subjects:
Algorithms
Bridge piers
Convexity
Gauss-Newton method
Ill-conditioned problems (mathematics)
Inverse problem
Iterative methods
Modal analysis
Model updating
Multiplicative regularization
Newton methods
Noise pollution
Quadratic programming
Regularization
Sequential Quadratic Programming
Stiffness
Multiplicative regularization
Modal analysis
Model updating
Inverse problem
Sequential Quadratic Programming
ISSN:0888-3270, 1096-1216
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Summary:•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. 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.
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ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2019.05.062