Modal Strain Energy Sensitivity Research Articles

Structural damage identification based on dual sensitivity analysis from optimal sensor placement

The structural damage identification (SDI) methods based on incomplete modal information can avoid the extension for unmeasured degrees of freedom, but the absence of essential damage information often leads to the failure of SDI. To address this problem, a novel SDI method based on dual sensitivity analysis and optimal sensors placement technique is proposed in this study. Firstly, in the optimal sensor placement technique, an improved eigenvector sensitivity method combined with weighted modal kinetic energy is proposed, which enables the acquisition of eigenvector information related to damage sensitivity, and incorporates it into the modal strain energy sensitivity matrix to obtain the dual sensitivity analysis matrix. Then, the sparsity of structural damage is considered, and the L1 sparse regularization is selected and introduced into the dual sensitivity analysis damage equation for better SDI results. Finally, to assess the effectiveness of the proposed method, a series of numerical simulations and experimental verifications were carried out under different structural damage scenarios. The results indicate that the proposed method can efficiently localize and quantify the structural damage with minimal modal information in one single step.

Analysis and structural optimisation of bed structure for CNC lathe based on modal strain energy sensitivity

Based on the modal analysis of the finite element model of the bed, the position of the modal strain energy (MSE) concentration in the first mode is selected, and the sensitivity analysis method is used to optimise the design size of the bed. The optimisation results show that the first-order MSE can be distributed evenly after optimisation, and the quality of the bed can be reduced. At the same time, the blindness of structural optimisation can be reduced and the optimisation efficiency can be improved. This optimisation design process and method can be extended to other machine tool parts, and provide the important approach and theory reference for machine tool dynamic characteristics improvement and structure optimisation.

Direct method for second-order sensitivity analysis of modal strain energy

This paper proposed a Lagrange-based method for calculation of the second-order sensitivity of modal strain energy (MSE) values. According to scheme of the direct method, a Lagrange functional of the element MSE, which added the eigenproblem and the normalization augmented by Lagrange multipliers as constraints, is constructed firstly. After that, the Lagrange multipliers can be decided by setting variations of the Lagrange functional with respect to state variables to zeros. And then, the sensitivity of MSE can be yielded by derivative of the Lagrange functional easily. The accuracy of the new method and the affection of normalization criterion are verified by the numerical instances of a simply supported beam and a truss structure. A portal frame is employed to testify the prediction ability of both the first-order and the second-order sensitivities of MSE values. As the numerical example of the portal frame shows, the computation complexity of the new method can be reduced significantly in comparison of indirect methods at similar accuracy.

On the study of element modal strain energy sensitivity for damage detection of functionally graded beams

In this paper, a modeling framework based on element modal strain energy sensitivity is developed for identifying damage of functionally graded beams. The element damage equation set of functionally graded Euler-Bernoulli beam is established built on element modal strain sensitivity and the rate of change of element modal strain energy from healthy to damage. The Tikhonov regularization algorithm incorporated with the generalized cross validation is used to solve the reliability problem of damage equation set. Numerical illustrative examples contain a simply supported and continuous functionally graded Euler-Bernoulli beams are considered to demonstrate the performance of the method. The influences of gradient index, damage extent, mode shape and noise level are investigated respectively. Damage results imply that the proposed method can give a valid way to accurately detect the damage of beam-like structures, also has excellent resistance to measurement noise.

Structural Damage Detection Based on Ridge Estimation Method

In order to identify structural damage locations and extent, a method based on ridge estimation and modal strain energy is presented in this paper. First, structural modal strain energy is given and a modal strain energy sensitivity damage equation is obtained. Then, considering the TikhonovTT regularization theoryTT, a ridge estimation method is proposed to solve the damage equation and ridge parameter of the method is optimized. Simulation results demonstrate that the proposed damage detection method based on ridge estimation and modal strain energy can identify structural damage locations and extent with good accuracy.

Damage detection in structural systems by improved sensitivity of modal strain energy and Tikhonov regularization method

In this article, new methods for detecting damage in structural systems are presented. These methods are categorized as damage localization and damage quantification, respectively. Hence, direct changes of modal strain energy are applied to identify locations of damage. Moreover, some restraints such as incomplete measured modes and simple assumptions in structural modeling may cause failure in the results of damage localization. Therefore, a correlation-based method is utilized to obviate these limitations and precisely detect damage sites. Subsequently, an improved sensitivity of modal strain energy is generated to determine damage severities. To achieve appropriate results in damage quantification, Tikhonov regularization approach is utilized instead of classical methods such as applying penalty function and current inverse problem techniques. Applicability and effectiveness of proposed methods are numerically verified using two practical examples consisting of a planner truss and a portal frame, respectively. Eventually, numerical results indicate that the proposed damage localization approach provides an influential algorithm for precisely identifying damage sites. Furthermore, obtained damage severities show that utilizing the sensitivity of modal strain energy and also solving the damage equation by Tikhonov regularization makes it possible to accurately determine damage extents in the case of incomplete modal data.

Statistic structural damage detection based on the closed-form of element modal strain energy sensitivity

Modal strain energy has been widely utilized as a damage-sensitive feature to detect structural damage. Based on the closed-form of element modal strain energy sensitivity, a statistic structural damage detection algorithm is proposed in this paper. The method is oriented to the ambient vibration measurements where only the operational mode shapes are available. The established element damage equations are incorporated with the modal scaling factors so that the damage and modal scaling factor can be solved simultaneously. The statistic analysis is implemented to take into account the uncertainties existing in the structural model and measured structural modal parameters. The sensitivity formulas of system matrix and residual vector with respect to noise are derived. The proposed statistics based element damage equations have a compact algebraic form, which does not require a large computation time and a high storage capacity. The method is verified by a numerical simply supported beam with different assumed damage. The effects of noise and damage levels on damage detection are investigated. It is demonstrated that the proposed method can identify most likely damaged elements.

Damage Detection Method Based on Element Modal Strain Energy Sensitivity

In this paper, a damage detection method based on an efficient algebraic algorithm of element modal strain energy sensitivity is proposed for detecting damage location and severity. The method adopts a closed form of element modal strain energy sensitivity. The element damage equations have been systematically established and a solution technique incorporated with the singular value decomposition-based regularization algorithm is used to ensure the correct solutions. A number of assumed damage scenarios for numerically simulated beams and two-dimensional frame structure have been used to demonstrate the applicability of proposed method. The noise effect is also presented. It is demonstrated that the proposed method is efficient in a one-step (non-iterative) procedure.