Numerical damage identification of structures by observability techniques based on static loading tests

Abstract

This paper proposes the application of the observability techniques to deal with damage detection in bridges from their structural response under static loading tests. Unlike previous works based on a symbolic approach to this technique, this paper presents its first numerical application. With this aim, a novel algorithm is presented, which reduces the unavoidable numerical errors produced by the lack of precision of computers. To achieve an adequate accuracy in estimations, this numerical algorithm is complemented with another method to define the proper geometry of the corresponding finite element model. The comparison of the observability technique with other existing methods presented in the literature shows that the number of required measurements is significantly lower. Furthermore, contrary to other analyzed methods, no information from the undamaged structure is required. The accuracy in estimations provided by the proposed method is very high as the differences with actual values are lower than 1%.

Static structural system identification for beam-like structures using compatibility conditions

“…[26] When the observability of unknown variables is determined, the values of those observable variables are determined by the particular solution z p of Equation 4. It is to highlight that in SSI by OM, if any deflection, force, or structural parameter is observed, this information might help to observe new parameters in the adjacent beam elements through a recursive process.…”

“…For Equation 4 to have a solution, it is sufficient to check that the product of the transpose of the right-hand side vector, D T , and the null space matrix N * of the transpose of the matrix B, is a null (zero) vector, that is, D T ·N * = 0. If this holds, the solution of Equation 4 has the structure:…”

“…In both probabilistic and deterministic methods, optimization technique is closely involved. The objective of the optimization might be minimizing the discrepancy between the measured response and the predicted response, for example, displacements, [4,5] strains, [2,5] loads vector, [5,6] acceleration, [18] mode shapes and frequencies, [9] or maximizing the sensitivity of the frequency response functions. [19] Observability Method (OM) is a mathematical tool dealing with the observability, that is, the existence and the uniqueness of the solution of a system of equations (or a subset of it).…”

“…A comprehensive description and the associated categories of SSI are provided in the technical report of the American Society of Civil Engineers. [1] These categories include static [2][3][4][5][6][7] and dynamic excitations, [8][9][10][11][12][13][14] parametric [3,5] and non-parametric models, [8,[15][16][17] deterministic [2,[4][5][6]9,18,19] and probabilistic approaches. [10,[20][21][22][23][24] For both static and dynamic SSI methods, structural responses have to be measured to provide the necessary information.…”

“…Later, a numerical development of this method was provided to determine the values of those observable parameters. [4] The observability problem in power system [28] considers a system with n parameters and m potential measurements. For the sake of economy and identifiability of the system, it is always desirable to know the least number of sensors required to identify these n parameters.…”