Entification objective function translates into over-determined form when structural modal info
Entification objective function translates into over-determined type when structural modal information and facts is expanded by the added virtual mass approach, which will lead to non-sparse result due to the fact of noise. Hence, the sparse damage identification method can highlight the sparsity of optimization benefits, to enhance accuracy. The deterministic sparse harm identification method introduces a sparse constraint term, commonly the l p norm of damage-factor, in to the objective function for determining the sparse answer. Wang et al. [26]. proposed a brand new Tikhonov iterative process for solving illconditioned equations of damage identification and created a singular-value dichotomy program to identify regularization parameters. Wu et al. [27]. modified a structural model and identified its damage applying the l1 regularization approach of sparse recovery theory based on the structural frequency and mode shape. Weber et al. [28]. updated a structural model applying the regularization GLPG-3221 manufacturer technique and performed damage identification of three-dimensional truss towers primarily based on the sensitivity. Hou et al. [29]. established two strategies to determine the parameters of the l1 regularization system. One particular technique ensures that the remaining norm and (-)-Irofulven Biological Activity resolution norm from the optimization dilemma are both smaller, and the other technique makes the variance between the theoretical and measured responses close to one another.Appl. Sci. 2021, 11,3 ofIn this study, the additional virtual mass along with the sparse damage identification approaches had been combined for greater identification precision and consistency with actual harm distribution. At first, these traditional sparse approaches, for example the greedy iteration-orthogonal matching pursuit (OMP) algorithm with all the damage-factor l0 norm as the sparse constraint, the Lasso regression model together with the l1 norm as the constraint item, along with the ridge regression model using the l2 norm as the constraint term, have been compared and analyzed primarily based around the extra virtual mass technique. Furthermore, aiming at the shortage of above conventional sparse methods that the Lasso regression plus the ridge regression need to get regularization coefficient with complex course of action, and lack of integrity in the recognition procedure from the OMP technique, the enhanced OMP (IOMP) technique was created. Lastly, via numerical simulations and experimental verification, the advantages and disadvantages of each and every approach were proved. 2. Harm Identification Approach Based on Additional Virtual Mass and Harm Sparsity 2.1. Added Virtual Mass Method Actual engineering structures are usually significant, and there is a tendency for their sizes to increase. Therefore, the corresponding modal data is also many, so generally, we are able to only apply several lower-order modal information and facts. Nonetheless, incomplete modal facts results in deviations when identifying the structural harm location and extent. The additional virtual mass approach can conveniently and correctly expand the modal information used for structural damage identification in actual complex circumstances. The structure is divided into n substructures, and is set as the damage issue of the lth substructure, which is the ratio of broken substructural stiffness kl to undamaged substructural stiffness kl , which is, kl = kl . The entire structure damage-factor is expressed as = [ , . . . , , . . . , ] T , along with the harm structural stiffness matrix is expressed as follows: k =l =l kln(1)A single-point excitation Fi is applied for the ith subst.
