A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization

Structural damage detection is the kernel technique in deploying structural health monitoring. The structural damage–detection technique using heuristic algorithms has been developed at an astounding pace over the past years. However, some existing structural damage–detection methods are prone to easily fall into the local optimum and to be unstable when they are applied to complex structures. In order to make full use of advantages of heuristic algorithms and overcome abovementioned shortcomings, a hybrid algorithm, which combines the ant lion optimizer with an improved Nelder–Mead algorithm, is proposed to solve the constrained optimization problem of complex structural damage detection. First, an objective function is established for damage identification using structural modal parameters, that is, frequencies and mode shapes. The solution to the objective function is accurately attained by a newly improved weighted trace lasso which can improve the computing performance and stability of procedure and reduce randomness of weighted coefficients. After assessing the computing performance of the proposed hybrid algorithm using three classical mathematical benchmark functions, two structural damage–detection numerical simulations and a laboratory verification are then conducted to fully assess the structural damage–detection capability of the proposed method. Meanwhile, the equivalent element stiffness-reduction model is introduced to estimate the real damage severities of cracks which are created in laboratory structures and to compare with the structural damage–detection results by the proposed method. The illustrated results show that the proposed hybrid algorithm can locate damage and quantify damage severity more accurately and stably with a good robustness to noise.