## 1 Introduction  
In general, civil structures are prone to damage during their service life, leading to the loss of their serviceability and safety. Thus, the integrity and the state of the health of these structural systems is essential for structural safety assessment and decision-making management [1]. Although significant progress has been made in this area, the high level of variability due to noise and other interferences, the uncertainties associated with data collection, structural performance, and in-service operational environments pose significant challenges in finding the necessary information to support decision-making [2; 3]. In addition to the effect of measuring noise, some uncertainties are due to undamaged stiffness in real structures, which is also caused by reasons such as connections, infills, and others [4]. Normally, the natural frequencies of the structure are used as damage-sensitive feature because of ability to estimate the condition of the structure even if a small number of sensors are installed [3; 5]. However, estimation based on natural frequencies is sensitive to environmental and operational variables (EOVs), and in practice the structural acceleration response is usually used [4]. Moreover, despite advancements in computer capacity, the enormous computational cost of running complex engineering simulations makes it impractical to rely solely on simulation for structural health monitoring applications [6]. To cut down the cost, surrogate models, also known as meta-models, are constructed and then used in place of the actual simulation models [7]. The effectiveness of surrogate models when applied in vibration-based damage detection has been demonstrated in numerous studies [7; 8]. However, in the face of uncertainty, the use of surrogate models has been questioned in terms of their reliability [9]. Surrogate models in damage detection suffer from two inevitable uncertainties: modeling error and measurement noise [10]. The existence of error in finite element (FE) modeling, due to the inaccuracy of physical parameters and non-ideal boundary conditions, and also finite element discretization, together with nonlinear structural properties, may result in generating the vibration parameters from such an FE model not exactly representing the relationship between the modal parameters and the damage parameters of the real structure [11]. On the other hand, the presence of a measurement error in the collected data, which is usually used in a surrogate model as the test data, is often inevitable. Since the efficacy of the prediction of a surrogate model relies on both components' accuracy, the existence of these uncertainties may result in false and inaccurate predictions. Thus, it is necessary to analyze the effect of uncertainties on surrogate model's reliability for structural damage detection. [PERSON] et al. [12] and [PERSON] et al. [13] demonstrated the effect of uncertainties on the output of support vector machine (SVM) and artificial neural networks (ANNs) in training and testing results, and proposed the use of a probabilistic surrogate model that considered the presence of uncertainties in the FE model and the measurement data. Their research work showed that the probabilistic approach can facilitate accurate detection of damage even in noisy data [12; 13]. However, the probabilistic methods presented in the literature suffer from several shortcomings, such as assuming uncertain parameters as random variable with a Gaussian distribution with a given variance that subsequently produce statistical structural damage results [13]. In practice, the probability density function cannot be accurately obtained because of the complexity of uncertainty sources [14]. Moreover, the assumption of Gaussian distribution for uncertain parameters is not valid. In addition, the lack of experimental data reduces the possibility to obtain a suitable probability density function.