A Novel Two-Stage Structural Damage Identification Method Based on Superposition of Modal Flexibility Curvature and Whale Optimization Algorithm

A novel two-stage method is proposed to properly identify the location and severity of damage in plate structures. In the first stage, a superposition of modal flexibility curvature (SMFC) is adopted to locate the damage accurately, and the identification index of modal flexibility matrix is improved. The low-order modal parameters are used and a new column matrix is formed based on the modal flexibility matrix before and after the structure is damaged. The difference of modal flexibility matrix is obtained, which is used as a damage identification index. Meanwhile, based on SMFC, a method of weakening the “vicinity effect” is proposed to eliminate the impact of the surrounding elements to the damaged elements when damage identification is carried out for the plate-type structure. In the second stage, the objective function based on the flexibility matrix is constructed, and according to the damage location identified in the first stage, the actual damage severity is determined by the enhanced whale optimization algorithm (EWOA). In addition, the effects of 3% and 10% noise on damage location and severity estimation are also studied. By taking a simply supported beam and a four-side simply supported plate as examples, the results show that the method can accurately estimate the damage location and quantify the damage severity without noise. When considering noise, the increase of noise level will not affect the assessment of damage location, but the error of quantifying damage severity will increase. In addition, damage identification of a steel-concrete composite bridge (I-40 Bridge) under four damage cases is carried out, and the results show that the modified method can evaluate the damage location and quantify 5%–92% of the damage severity.

Research on the dynamic hammering method for identifying weak parts in cantilever structures

Identification of the vulnerabilities in the structural stiffness is one of the most crucial issues in improving this property of machine tools. In this paper, the Flexibility Matrix Diagonal element method, based on hammer testing, is proposed as an effective approach to identifying the stiffness weakness of cantilever structures. To verify the proposed method, the element stiffness weakening is used to simulate the weak parts regarding stiffness. Several scenarios, with single and multiple weakness points, including various noise levels, are studied, using finite element simulations. Next, a novel method, to measure the accuracy of the algorithm and quantify the weakness level, under noise conditions, is proposed. The advantage of this method, compared to the ones based on Flexibility Difference Method, is the higher identification accuracy under noise interference. Finally, the cantilever beam with elastic support is experimentally studied. The natural frequencies and modal shapes are obtained, according to the singular value decomposition method, to establish the flexibility matrix. In addition, using only the lowest three modes, a series of numerical examples and experiments are provided, to illustrate the validity and the considerable practical engineering value of the method.

FEM Free Damage Detection of Beam Structures Using the Deflections Estimated by Modal Flexibility Matrix

The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

Spring Cell Equivalence of Simplex Finite Elements – Exploration of an Iterative Approach

Natural spring cell substitutes of triangular and tetrahedral finite elements at constant strain take advantage of a formalism oriented along the element sides/edges. Two different models in use account just for the diagonal entities of either the flexibility matrix of the element or of its stiffness matrix. Both are incomplete substitutes, and defective to a degree depending on the significance of the off-diagonal parts of the element matrices. The present work discusses an iterative completeness of the substitution accounting for the discarded parts by additives to the spring members of the cell. In this connection, the iteration schemes are set up for either model at the material and at the element level, and convergence criteria are defined in terms of the spectral radii of the iteration operators. The convergence regions are confined for triangular elements, and are demonstrated with reference to a case study.

Output-Only Damage Detection in Plate-Like Structures Based on Proportional Strain Flexibility Matrix

For engineering structures, strain flexibility-based approaches have been widely used for structural health monitoring purposes with prominent advantages. However, the applicability and robustness of the method need to be further improved. In this paper, a novel damage index based on differences in uniform load strain field (ULSF) is developed for plate-like structures. When estimating ULSF, the strain flexibility matrix (SFM) based on mass-normalized strain mode shapes (SMSs) is needed. However, the mass-normalized strain mode shapes (SMSs) are complicated and difficult to obtain when the input, i.e., the excitation, is unknown. To address this issue, the proportional strain flexibility matrix (PSFM) and its simplified construction procedure are proposed and integrated into the frames of ULSF, which can be easily obtained when the input is unknown. The identification accuracy of the method under the damage with different locations and degrees is validated by the numerical examples and experimental examples. Both the numerical and experimental results demonstrate that the proposed method provides a reliable tool for output-only damage detection of plate-like structures without estimating the mass-normalized strain mode shapes (SMSs).

Natural Spring Cell Substitutes of Simplex Finite Elements

Spring cell models are presented which derive from the natural description of simplex finite elements, that is in conformity with the geometry of the triangle in the plane and of the tetrahedron in space. Thereby, the spring cells are interpreted as part of the finite elements. The deduction of two spring cells as defective substitutes is demonstrated for the triangular element. One approximates the flexibility matrix of the element, the other approximates the stiffness matrix. The performance with respect to the finite element is analyzed, the issue of elastic anisotropy is discussed. In space, the spring cell substitute of the tetrahedral element is derived from the flexibility matrix, an inherent difference to the plane case is pointed out. Remarks on the implication of plasticity are added. The account gives a brief summary of recent work on the subject.