## 1 Introduction
The solution space, for example, is directly reduced by setting the upper limits in close proximity to the baseline characteristics. It is done by incorporating a weighted norm of the parameter changes to keep the parameter changes small. The most usual form is known as the Tikhonov regularization [33], as it was introduced to resolve the ill-conditioning of systems with the aim to control the condition number of the problem. Addressing the ill-conditioning using a regularization technique is a topic of interest in FE model updating problems. Sensitivity-based regularization techniques have been explored in this context by various researchers. [PERSON] et al. [34] addressed the problem by incorporating side constraints and used singular value decomposition, generalized cross-validation (GCV) and L curves for the determination of the regularization parameter. The L curve approach and the generalized singular value approach are used reliably to get updated parameters with physical understanding. [PERSON] et al. [35] investigated structural damage detection with Tikhonov regularization, and [PERSON] et al. [36] introduced consistent regularization for a non-linear model updating problem. Further studies of regularization techniques in model updating include [PERSON] and [PERSON] [37] and [PERSON] et al. [38]. In these studies, the sensitivity-based updating with a special focus on optimization of the response prediction and a priori information about the uncertain parameters has been investigated with the help of an additional regularization criterion. [PERSON] and [PERSON] [39] investigated dynamic perturbation theory for incomplete noisy modal data and used the L-curve approach for regularization parameter determination. [PERSON] et al. [40] proposed a new sensitivity-based damage detection method in which an improved sensitivity function related to modal strain energy and modified GCV is presented. [PERSON] et al. [41] proposed a new regularization method that is based on the minimization of total variation on sensitivity-based model updating. GA, an EA, has been used in this research to exploit the search space fully instead of sensitivity-based local search optimization. For efficient damage detection, an effective objective function is needed to match the experimental data with the analytical predictions. Therefore, to harness the benefits associated with EA and to handle ill-conditioning using the concept of regularization,this paper aims to propose a new objective function using EA. Initially, the performance of different objective functions has been compared for damage detection in noisy conditions to select the best objective function. The updated parameters may not turnout to be necessarily realistic in noisy conditions, thus making damage detection difficult. Therefore, an additional regularization criterion has been proposed especially in noisy conditions to assess the damage correctly. In Section 2, theories related to objective functions, noise additions, mass normalization and regularization using EA are detailed. In Section 3, the different objective functions are compared in terms of their efficiency in damage assessment of two simulated beams and one experimental beam, and the proposed regularization has been applied. The results are analyzed and conclusions are drawn from the current study finally.