Structural Elements Damage Identification Based On Energy Measurements And Optimization Methods

Structural damage identification is a type of non-destructive detection technique. The main purpose of this technique is to determine the status of the structural health through analysis of the test results obtained using various experimental methods without destRictions to the existing structures. Three levels of problems can be dealt with structural damage identification, namely, (1) to judge if a structural damage exists; (2) to locate the positions of the damage; (3) to determine the extent of the damage.In the literatures, many damage identification methods have been applied in the practical engineering. A great variety of test techniques, such as magnetic power, ultrasonic wave, X-ray and industrial CT, have found wide applications in the structural damage identification problems. Particularly, the damage identification approach based on structural response changes have drawn much attention of both engineering and academic communities for the last two decades, due to its ease of implementation and low cost. This treatise is devoted to the study on avoiding the weakness and limitations of existing approaches based on response changes. The major difficulties of damage identification techniques relying on response changes are: (1) structural response are not sensitive enough with respect to the damage parameters; (2) the identification model are usually ill-posed; (3) the approaches using optimization techniques may fail in case of multiple damages as a result of too many variables in the mathematical model.Structural response includes static response, natural vibration properties and forced vibration response. In conventional damage identification methods, the problem is formulated in different ways according to the structural response adopted. In this research, the concept of structural energy "measurements" is proposed, thus different kinds of structural response are unified in the problem formulation. In this context, only the structural strain energy is needed in the derivation, regardless of the source of test data and the mathematical formula.To alleviate the difficulty caused by the insufficient sensitivities of the structural response to the damage parameters, the idea of "additional sub-system" is proposed, in which additional external system, such as external force, additional mass, additional supports, damping and similar, are attached to the structure to be tested. By this means, the distribution of the structural strain density is adjusted and the strain density in the vicinity of the damage position is maximized. As a result, the sensitivities of the response changes with respect to the damage are substantially increased. Theoretical derivations and numerical examples demonstrated theapplicability and the validity of the proposed method.For identification of multi-damages, the optimization approach may fail due to the extremely large number of design variables (parameters to be identified) if the damages are modeled as elemental stiffness changes and therefore all the elemental stiffness parameters in the finite element model become the design variables of the optimization model for the damage identification problem. On the other hand, if the damage position and the damage size are used for description of the structural damage, the mathematical model is actually stated as a discrete structural optimization problem with unknown number of design variables, since the number of damages can not be given in advance. Such a problem can not be easily solved. An approach is proposed in this treatise by introducing a new type of damage index function. The number of damages is firstly determined, and then, the stiffnesses decreases of structural elements are used as a description of the damage size. The least square of the damage index functions of the test data and the finite element prediction is used as the objective function of the optimization model for the damage identification. The difficulties mentioned above are therefore successfully avoided.The damage identification problem is formulated as a Min-ma...