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A novel static identification approach to beam damage is presented. It is based on the minimum constitutive relation error (CRE) principle where the exact stiffness, the exact displacement and the exact bending moment are shown to make the CRE functional minimal. For practical implementation, two cases regarding full-field displacement measurements and finite-point displacement data, respectively, are considered. For full-field displacement measurements, the CRE functional is directly treated as the objective functional while in case of finite-point measurement data, the CRE functional along with additional penalty terms for treatment of the finite-point displacement measurements is defined as the objective functional. Multiple loads and associated sets of measurements are also considered to improve the identifiability and robustness of the procedure. Convergence is finally verified through numerical examples. [ABSTRACT FROM AUTHOR]

Summary: Structures are usually subjected to some specific local damages or weaknesses, which cannot be explained by uniformly distributed stiffness or mass changes, especially when the local damages or weaknesses have slight influences on global natural periods or vibration modes. Furthermore, large amounts of measurement positions are in need to capture the damage location and severity in traditional damage identification, and results easily depend on the initial estimates of the unknown parameters for the iterative update. To circumvent the above problems, a novel framework is proposed, involving strategies for physical‐based parametrization and local damage identification for frame‐type structures. The novelty of this research lies in the careful integration of the physical‐based parameterization and the identification techniques to robustly quantify commonly encountered local damages, namely, the weakness in exposed column base and partially fractured beam end. In this framework, the guidance for the application of physical‐based parametrization is provided, and thus, the above‐mentioned local damages of structures could be parametrized in an appropriate and convenient way. The response sensitivity approach is employed to derive the parameters by directly using time domain data. Derivatives of the stiffness matrix with respective to the newly introduced physical parameters are directly proposed so that no finite difference method is involved. Furthermore, trust‐region restriction is adopted to enhance the efficiency and stability of the identification approach when facing strong convergence difficulty or way‐out initial estimates. Two case studies are presented to validate the effectiveness and accuracy of the proposed framework. The shell element‐based models with intentional damage and weakness are built in ABAQUS to provide the data source. Two corresponding beam element‐based models are developed in MATLAB as physical‐based parametrized models. Results show that damages are accurately and efficiently estimated by the proposed framework, and the original dynamic responses are well reproduced by the identified models. Comparisons to the results by Bayesian estimation are also discussed. [ABSTRACT FROM AUTHOR]

Practical damage identification often suffers from the ill-posedness and the unavoidable model errors. On the one hand, the regularization techniques including the Tikhonov regularization and the sparse regularization have been well recognized as effective tools to circumvent the ill-posedness. On the other hand, the model errors render the established baseline/analytical model inconsistent with the real structural and thereof, would introduce unexpected errors into damage identification. To deal with the model errors, the two-step strategy is often adopted for damage identification in practice: firstly update the baseline model so as to minimize the inconsistence and secondly, identify the damage upon the updated baseline model; Another empirical and not-yet-widely-recognized way is to use the measurement changes and motivated by this, a new MC (Measurement Changes) strategy that simply revises the measured data with measurement changes is developed in this paper for sensitivity-based damage identification. This work aims to present experimental investigations and comparative studies on the possible remedies for the difficulties in damage identification: the Tikhonov or sparse regularization for the ill-posedness and the two-step or MC strategy for the model errors. Final results show that the MC strategy is rather effective and efficient for damage identification and synthesis of the sparse regularization and the MC strategy is found as the appreciated way to practical damage identification. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to provide a new damage identification method using frequency response data. In this approach, the inverse identification problem is treated as a nonlinear optimization problem whose objective function is just the constitutive relation error (CRE). To circumvent the ill-posedness of the inverse problem which is caused by use of the possibly insufficient data and enhance the robustness of the identification process, the sparse regularization is introduced where the ℓ 1 -norm regularization term is added to the original CRE function. In regard to the minimum solution of the sparse-regularized CRE objective function, the alternating minimization (AM) method is established. The attractive features of the present damage identification approach are: (a) while coping with the sparse regularization, a closed-form solution is obtained due to the decoupling of the CRE function with respect to the damage parameters and hence the sparse regularization term would introduce little computational complexity; (b) the sparse regularization parameters are directly determined by a simple threshold setting method; (c) no sensitivity analysis is involved herein. Numerical examples are conducted to verify the proposed approach and the results show that the sparse regularization obviously improves the accuracy and robustness for the identified damages. [ABSTRACT FROM AUTHOR]

• Guidance for the application of power spectrum density data based on minimum constitutive relation error principle has been provided. • Only measurement power spectrum density data from few limited sensors are needed for damage identification. • Sparse regularization has demonstrated a pronounced effect on the accuracy and robustness for the identification results. This paper proposes a novel model-based damage identification strategy based on minimum constitutive relation error and sparse regularization using the power spectrum density data. Firstly, the stationary random vibration problem is transformed into a series of harmonic vibrations by the pseudo excitation method and the error in constitutive relation is established by the admissible stress field and admissible displacement field. A much more general and simpler strategy so as to build the admissible stress field is addressed by requiring only an extra decomposition of the stiffness matrix. Then, the sparse regularization is added to the original constitutive relation error objective function to circumvent the ill-posedness of the inverse problem. Finally, the solution of this nonlinear optimization problem is solved by the alternating minimization method. The proposed method has the advantage that only measurement power spectrum density data from few limited sensors are needed in the inverse analysis. Numerical and experimental results show the effectiveness and robustness of this approach. [ABSTRACT FROM AUTHOR]

• A vision-based measurement framework using the camera system for damage identification is proposed, which is composed of four procedures: camera calibration, image processing, system identification and sensitivity analysis. • Less number of modes is required for modal-based damage identification problems and more physical parameters could be extracted, taking advantage of the plentiful experimental data. • Suitable strategies to circumvent the major drawback that the camera system suffers high levels of noise in small vibration responses at higher frequencies are developed. Extracting physical parameters for damage identification problems from full-field measurements is a promising research because of the recent spread of vision-based measurement techniques in the experimental mechanics. This paper presents a vision-based measurement framework using the camera system for damage identification. The framework is composed of four procedures: camera calibration, image processing, system identification and sensitivity analysis. In contrast to traditional finite-point measurements, the camera system allows considerably greater non-contact measurement flexibility. Such flexibility has two important benefits: first, less number of modes is required for modal-based damage identification problems; and second, more physical parameters could be extracted, taking advantage of the plentiful experimental data. A laboratory test comparing the camera system to traditional accelerometer measurement is conducted to confirm the above advantages. Further statistic analysis shows that the major drawback of this technique is that the camera system presents high levels of noise in small vibration responses at higher frequencies. Suitable strategies to circumvent this disadvantage are developed. Moreover, a technique for practical camera calibration without the requirement that the objective plane should be strictly perpendicular to the camera axis is also demonstrated and verified by the proposed laboratory test. [ABSTRACT FROM AUTHOR]