## 1 Introduction
Many training models were developed with different paradigms such as hybrid, ensemble, and deep learning attempting to access more meaningful data representations through an accurate prediction. However, the effect of dynamic changes at the level of the training mini batches of data on the training models is not discussed in this case, which may allow the weights and biases to diverge in some mini batches to under-fit gradually the NN. In other cases, the use of old mini batch training algorithms for NN such as the Backpropagation (BP) algorithm can increase computational costs and time consumption. Through this analysis, the main challenges for RUL predictions task are:  
* Update the training model based on data variation during time (adaptive learning). * Decide whether the newly arrived data is important (new) for the training model or not. * Make the training model in line with the actual health state of the equipment by giving more attention to newly acquired data and discarding gradually the old ones. * Reduce time consumption during training. In the recent decade, ELM has been widely used for prediction purposes due to the fast training and fewer parameters tuning based on the best fit of a linear function approximation [12]. [PERSON] et al. [13] proposed a Stacked ELM (S-ELM) where a stack of small ELMs is specially designed for solving large and complex data problems. [PERSON] et al. [14] presents a new unsupervised learning classification tool of extracted data based on the Adaptive Resonance Theory 2 (ART2) for high-speed shaft bearing prognosis. [PERSON] et al. [15] proposed an improved OS-ELM which is one of the ELM variantswith an adaptive forgetting factor and an update selection strategy to predict gas utilization ratio using time-varying data. [PERSON] et al. (2016) developed a new approach of regularization of the recursive learning of the OS-ELM to reduce over-fitting and both empirical and structural risks of the prediction model. [PERSON] et al. (2017) enhanced the recursive learning of the OS-ELM by introducing ensemble Kalman filter propagation for output weights tuning of NN under RUL prediction of aircraft engines. [PERSON] et al. (2018) proposed a (TD-RLS(\(\lambda\))) with a forgetting factor to enhance the RLS adaptation to linear function approximation by updating its parameters based on environmental feedback. OS-ELM can address online learning in real time such as our RUL prediction problem without iterative tuning, which strongly contribute to computational costs reduction. Training rules of OS-ELM allows recursive learning with any driven chunks of data easily even with different or fixed sizes. In general, one of the limitations of OS-ELM or ELM algorithms is the interpolation caused by the pseudo inverse of the matrix ([PERSON] et al., 2018), which makes ELM variants suffering from structural risks. In this paper, an improved data-driven approach based on OS-ELM is proposed for RUL estimation to enhance the novelty of the prediction algorithm and its adaptability to time-varying data. In fact, the main contributions of this work attempting to solve adaptive learning and ill-posed problems are:  
* SAEs based OS-ELM is modified for best features extraction and selection via unsupervised learning. * An OS-ELM is introduced. Tikhonov regularization is involved to reduce structural risk and over-fitting by minimizing the norm of the training weights. Dynamic forgetting of old data, USS and TD error objective functions are all integrated into both SAEs and OS-ELM to achieve better accuracy and adaptability to newly arrived data. The proposed approach is applied to the public dataset of the turbofan engine ([PERSON] et al., 2018), where obtained results compared to other recent used approaches in the literature show higher performance. The remainder of this work is organized as follows: In Section 2, a general description of the turbofan engine dataset is presented. Section 3 elaborates on the proposed approach used in this paper.