Wavelet Packet Singular Entropy-Based Method for Damage Identification in Curved Continuous Girder Bridges under Seismic Excitations

Seismic Damage Identification Method for Curved Beam Bridges Based on Wavelet Packet Norm Entropy

Curved beam bridges, whose line type is flexible and beautiful, are an indispensable bridge type in modern traffic engineering. Nevertheless, compared with linear bridges, curved beam bridges have more complex internal forces and deformation due to the curvature; therefore, this type of bridge is more likely to suffer damage in strong earthquakes. The occurrence of damage reduces the safety of bridges, and can even cause casualties and property loss. For this reason, it is of great significance to study the identification of seismic damage in curved beam bridges. However, there is currently little research on curved beam bridges. For this reason, this paper proposes a damage identification method based on wavelet packet norm entropy (WPNE) under seismic excitation. In this method, wavelet packet transform is adopted to highlight the damage singularity information, the Lp norm entropy of wavelet coefficient is taken as a damage characteristic factor, and then the occurrence of damage is characterized by changes in the damage index. To verify the feasibility and effectiveness of this method, a finite element model of Curved Continuous Rigid-Frame Bridges (CCRFB) is established for the purposes of numerical simulation. The results show that the damage index based on WPNE can accurately identify the damage location and characterize the severity of damage; moreover, WPNE is more capable of performing damage location and providing early warning than the method based on wavelet packet energy. In addition, noise resistance analysis shows that WPNE is immune to noise interference to a certain extent. As long as a series of frequency bands with larger correlation coefficients are selected for WPNE calculation, independent noise reduction can be achieved.

Performance of Damage Identification Based on Directional Wavelet Transforms and Entopic Weights Using Experimental Shearographic Testing Results

The paper aims to analyze the performance of the damage identification algorithms using the directional wavelet transforms, which reveal higher sensitivity for various orientations of spatial damage together with lower susceptibility to noise. In this study, the algorithms based on the dual-tree, the double-density, and the dual-tree double-density wavelet transforms were considered and compared to the algorithm based on the discrete wavelet transform. The performed analyses are based on shearographic experimental tests of a composite plate with artificially introduced damage at various orientations. It was shown that the directional wavelet transforms are characterized by better performance in damage identification problems than the basic discrete wavelet transform. Moreover, the proposed approach based on entropic weights applicable to the resulting sets of the detail coefficients after decomposition of mode shapes can be effectively used for automatic selection and emphasizing those sets of the detail coefficients, which contain relevant diagnostic information about damage. The proposed processing method allows raw experimental results from shearography to be significantly enhanced. The developed algorithms can be successfully implemented in a shearographic testing for enhancement of a sensitivity to damage during routine inspections in various industrial sectors.

Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems

A system’s response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann’s equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.