###### Abstract  
High precision and multi information prediction results of bearing remaining useful life (RUL) can effectively describe the uncertainty of bearing health state and operation state. Aiming at the problem of feature efficient extraction and RUL prediction during rolling bearings operation degradation process, through data reduction and key features mining analysis, a new feature vector based on time-frequency domain joint feature is found to describe the bearings degradation process more comprehensively. In order to keep the effective information without increasing the scale of neural network, a joint feature compression calculation method based on redefined degradation indicator (DI) was proposed to determine the input data set. By combining the temporal convolution network with the quantile regression (TCNQR) algorithm, the probability density forecasting at any time is achieved based on kernel density estimation (KDE) for the conditional distribution of predicted values. The experimental results show that the proposed method can obtain the point prediction results with smaller errors. Compared with the existing quantile regression of long short-term memory network(LSTMQR), the proposed method can construct more accurate prediction interval and probability density curve, which can effectively quantify the uncertainty of bearing running state. s 2021 11, 4773. [[https://doi.org/10.3390/app11114773](https://doi.org/10.3390/app11114773)]([https://doi.org/10.3390/app11114773](https://doi.org/10.3390/app11114773))  
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Footnote †: journal: Applied  
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Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
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Footnote †: journal: Applied  
termine rules in a probabilistic manner [1,2] and artificial intelligence algorithms that rely on machine learning tools [3]. Some experts and scholars have put forward the rolling bearing RUL prediction method based on nonlinear degradation and model [4,5]. At the same time, under the background of rapid development of technology, mechanical equipment status monitoring data shows a trend of massive growth, which provides information basis for real-time acquisition and advance prediction of equipment operation status information. However, when a significant measurement error is introduced due to the complex and changeable operating environment of the equipment, environmental interference, abnormal sensor or system disturbance, some isolated singularities deviating from expected values may occur in the original monitoring data. During the operation of the equipment, due to the occurrence of faults or defects, the monitoring data will also appear abnormal. Obviously, such data contains important information, which cannot be processed in the same way as noise data, anomalous sensor data, and anomalous data caused by environmental interference. Therefore, in obtaining the running state of the equipment, noise processing, and key features mining analysis become the essential work of predicting the operating state of the material and carrying out PHM tasks. Because of the problem that the high dimension original monitoring data often contain different types of noise signals, it is necessary to extract sufficient information from the contaminated original monitoring data and restore the pure data to achieve the effectiveness of degradation indicators. In recent years, key features mining analysis technology has made rapid development in the field of deep learning. Many degradation indicators construction methods and neural networks have achieved satisfactory performance in different scenarios, vibration signal feature extraction technology based on wavelet transform [6,7], wavelet packet decomposition technology [8] has been frequently used in health indicator construction task, and has been proved to be effective.