###### Abstract
As a result of its convenience and feasibility, the interval analysis approach is extensively used in damage identification and other domains [27; 28]. The interval optimization technique, which combines interval analysis with an intelligent algorithm, is a new way to handle interval problems [29]. Based on an auto-regressive model and interval optimization, [PERSON] and [PERSON] [30] presented a non-probabilistic damage detection approach. To determine interval bounds of uncertain variables, [PERSON] et al. [31] suggested a non-probabilistic Least Square Support Vector Machine (LS-SVM) approach. The results show that the proposed method can successfully identify the structural damage elements. However, the interval optimization method is still immature and suffers from the problem of high computational cost, especially when handling a large-scale structure. In comparison with probabilistic methods, research on non-probabilistic uncertain damage identification has been relatively limited. Scholars have used various algorithms to raise the calculation precision of interval methods, but interval expansion is still a severe problem [32]. Therefore, in this study, a non-probabilistic structural damage identification (NSDI) approach based on a model updating scheme and interval mathematics is proposed in order to address the aforementioned shortcomings. Damage estimation strategies using modal data are mainly based on model updating methods. These methods rely on a structure's parametric model and the optimization of the designated objective functions based on the differences between measured data and model predictions [33; 34]. The accuracy of the FE model, the quality of the modal tests, the formulation of the optimization problem, and the capabilities of the optimization algorithm all play a role in the success of the finite element (FE) model updating process. In this paper, a new optimization algorithm is proposed. [PERSON] et al. [35] recently developed SMA, a simple and effective continuous optimization technique for optimization problems. The performance of SMA is improved in this study by deleting unchanging variables after a certain number of iterations. This aspect increases the approach's adaptability for a larger range of practical applications while retaining the fundamental SMA's attractive features. Based on the aforementioned discussion and in order to tackle the shortcomings of non-probabilistic based schemes, the objective of this paper is to investigate the influence of uncertainty on damage identification of civil and mechanical structures. To consider the uncertainties in the measurement data, a novel non-probabilistic approach is introduced. Using this method, [PERSON]'s modulus, which acts as an elemental stiffness parameter (ESP), is defined as a variable of the SMA algorithm. Moreover, damage indexes are defined by utilizing the natural frequencies and mode shapes of the structure. Furthermore, measurement noise of the structural responses is assumed to be coupled rather than statistically distributed using the interval analysis approach [21]. It is worth noting that, in previous work of the authors [31], LS-SVM acts as a non-probabilistic surrogate model for damage detection of structures, whereas the exact FE model is implemented in this work. Furthermore, ESMA acts as a metaheuristic search algorithm and is used as the main algorithm of the model updating process. A 31-bar planar truss, a 120-bar dome truss, and a four-story building of Phase II of the IASC-ASCE SHM benchmark are used to demonstrate the robustness of the developed procedure. The impact of various noise levels and damage severity levels on the damage detection results are also investigated using parametric computations. The study's main contribution is to provide an effective strategy for implementing a damage detection procedure that takes uncertainty into account, based on the interval optimization method and ESMA. The article is structured as follows. Section 2 presents the process of damage detection using a correlation index.