Sparsity constraints are now very popular to regularize inverse problems in the field of applied mathematics. Structural damage identification is a typical inverse problem of structural dynamics and Structural damage is a spatial sparse phenomenon, i.e., structural damage occurs, only part of elements or substructures are damaged. In this paper, a structural damage identification method based on the substructure-based sensitivity analysis and the sparse constraints regularization is proposed. Substructure sensitivity analysis, the establishment of structural damage stiffness parameter variation and change of modal parameters of linear equations between the measured degrees of freedom is limited, the equations for a morbid equation. The introduction of structural damage sparsity conditions, to minimize the <i>l</i>1 norm optimization solution. The numerical example of the 20 bay-truss structure with considering measurement noise, incomplete of measurements and multi-damage cases are carried out. The effects of number sensor and layout to the identification results are also investigated. The results indicated that the damage locations and extents can be effectively identified by the proposed method. Additionally, the sensor location can be random arrangement, which has great significance to the sensor placement of the actual structural health monitoring because robust structural damage identification also can be obtained even a few of sensor are failure.
Optimal sensor placement is key issues of structures health monitoring (SHM). In study of sensor placement, the main
achievement focus on optimal criterions of sensor locations based on modal test, while optimal criterions of sensor
locations based on damage identification, optimal method of sensor locations and optimal sensor number should be
In this study, a novel optimal sensor placement strategy based on sensitivity is proposed. Optimal sensor placement
based on sensitivity analysis is an alternation method to consider damage identification. The basic idea of the proposed
methodology is that influence range of different damage parameters is different.
First, damage sensitivities in every element based on modal parameters are calculated. Then the elements that are
sensitive to damage are selected. According to the detection of damage sensitivity in these elements, minimums number
can be found by sensitivity. At last, the elements that are not selected are considered as not sensitive to modal parameters
and would be placed the strain sensors.
Numerical simulation of a three-dimensional truss structure is implemented to evaluate the minimum sensor number of
different damage parameters according to the above methods. Moreover, damage location can be detected under singledamage
situation and the element with most severe damage can be identified in multi-damage case using the proposed