## An Extreme Learning Machine for the Simulation of Different Hysteretic Behaviors
One of the MFFNNs' drawbacks is that they are static systems with no internal memory. Nonlinear autoregressive exogenous (NARX) neural networks [16] rectify this lack by putting a past state memory in the input layer of the MFFNNs. [PERSON] and [PERSON] [17] have utilized an MFFNN as part of the Preisach model to evaluate the mapping. In other research studies, [PERSON] and [PERSON] [18] utilized an MFFNN to simulate the hysteresis converted into a single-valued static mapping by [PERSON]'s rules. Recently inspired by the Preisach and [PERSON] models, new Artificial Neural Networks (ANNs) have been proposed [19; 20; 21; 22]. They use stop and play operators in their activation functions. These activation functions make them successful in hysteresis simulation. However, they have some major drawbacks in practical implementation. In the neural network method, this is important to determine the neural network's architecture before training. Unfortunately, there is no common way to assign the ANN architecture in terms of the number of hidden layers and the number of hidden neurons in every layer. Additionally, ANN creates overfitting problems by reaching a local minimum during training [23]. Overfitting is not a serious issue in Support Vector Machines (SVMs) compared to neural networks. Furthermore, as a version of the SVM, the least-squares support vector machine (LS\(-\)SVM) uses equality equations rather than inequality constraints. LS\(-\)SVM is less complicated than SVM and more efficient computationally [24]. Another benefit of LS\(-\)SVM is that there are less parameters that need to be adjusted in order to detect hysteretic behaviors [25]. How to transfer a multiple-valued hysteretic behavior to a single-valued mapping is the most difficult problem in hysteretic simulation using the LS\(-\)SVM model. The literature contains several solutions that have been suggested. For example, piezoelectric actuator hysteresis has been transformed into a single-valued mapping by the LS\(-\)SVM model by [PERSON] [26] using a NARX\(-\)based memory. Although his simulation was effective, hysteresis without measurable states cannot be completely recalled by NARX systems. As a result of the required feedback, they are vulnerable to error accumulation. In another research study, [PERSON] [23] proposed an intelligent hysteretic model that utilizes the LS\(-\)SVM. This model was influenced by the Preisach hysteresis model, which transformed a hysteretic system into a single-valued mapping using hysteresis operators. An LS\(-\)SVM then picks this up and learns it. Compared to neural networks, the model has fewer over\(-\)fitting issues. Additionally, unlike neural\(-\)based models, this model is not concerned with identifying a suitable architecture. Due to the use of the LS\(-\)SVM component as an intelligent tool, it can actually be operated much more easily than the Preisach model. Additionally, because it is theoretically equivalent to the Preisach model, which is only appropriate for congruent hysteresis behavior, this model can produce congruent hysteresis loops. This paper proposes an intelligent hysteresis model based on a combination of ELM and LS\(-\)SVM. The proposed model uses several deteriorating stop operators by which a hysteretic system is converted into a single\(-\)valued mapping. Then, the one\(-\)to\(-\)one mapping is learned by an LS\(-\)SVM. The paper structure is as follows. Firstly, short reviews of the deteriorating stop operator, LS\(-\)SVM, and ELM are undertaken. Then, the ELM\(-\)SVM architecture and its training algorithm are proposed. Finally, the capabilities of the proposed ELM\(-\)SVM model are assessed on several hysteretic systems with different behaviors. In this regard, the ELM\(-\)SVM model achievement compared with other models is investigated.