## 1 Introduction
Creating an acceptable and reliable probabilistic model also requires different data sets in order to train and upgrade the model. This data set is created through finite element analysis or simulation by utilizing surrogate models such as ANN algorithms or response surface method [13]. This approach requires an iterative simulation procedure that takes a very long time and, again, mostly relies on the Gaussian assumption. Due to these challenges and shortcomings, [PERSON] and [PERSON] [15] emphasized the need to introduce non-probabilistic interval analysis methods. Unlike the standard probabilistic approach, no assumptions about uncertainty distributions for estimating the probability of damage existence (PoDE) are needed for the non-probabilistic interval approach. Only the upper and lower bounds of uncertain variables are needed, thereby simplifying the detection of damage with noisy data and reducing complex computation compared to the probabilistic approach [9; 16]. In this paper, the applicability of non-probabilistic methods is extended by using a non-probabilistic surrogate model based on wavelet weighted least squares support vector machine (WWLS-SVM) [17; 18]. This surrogate model is a combination of weighted least squares support vector machine (WLS-SVM) [19] and thin plate spline Littlewood-Paley wavelet kernel function, which is called WWLS-SVM [17]. The input data for this model consists of extracted features of acceleration response of structures, and the output is the Young's modulus (E values), which acts as an elemental stiffness parameter (ESP). Through the interval analysis method [9; 10], noise in the measured response of the structure is considered to be coupled rather than statistically distributed. The interval bound (lower and upper bounds) of the ESP changes is computed based on an interval analysis method. By considering the uncertainties in the input parameters, the surrogate models are used to predict this interval-bound output. A possibility of damage existence (PoDE) parameter is used for the undamaged and damaged states to determine the relationship between the input and output parameters [20]. To provide an indicator of damage severity, the damage measure index (DMI) suggested by [PERSON] et al. [21] is adopted. The proposed method's feature extraction phase will be carried out using wavelet packet decomposition (WPD) method [22]. In this study, the measured structural dynamic response is decomposed into wavelet component functions [23]. Then wavelet pocket relative energies of these components are used as input of the proposed meta-model. The proposed method's applicability is demonstrated by performing damage detection on the 4-story building of Phase I of IASC-ASCE SHM benchmark [24]. The results show that the proposed method is able to accurately determine the location and the severity of damage in structural elements by considering the uncertainties caused by modeling and noise in the sensors. The main contributions of this paper may be summarized as follows:  
1. In this study, a non-probabilistic wavelet packet transform method is proposed that resolves the problem of uncertainties in vibration-based damage detection. The damaged and undamaged structure's acceleration responses are decomposed to obtain the wavelet pocket relative energies of the signal. 2. Different levels of detection of structural damage, including the occurrence of damage, location and severity of it, are evaluated using a computational approach. Furthermore, the effect of different levels of uncertainties on damage identification are presented. 3. Furthermore, the applicability of WWLS-SVM to act as a non-probabilistic surrogate model for damage detection of structures, with consideration of uncertainties, will be examined through simulating a damage in the benchmark model. This paper is organized as follows. In Section 2, three main steps of the proposed method are defined. Feature extraction method utilizing wavelet pocket transform (WPT) is described in Section 3.