Prediction models based on deep learning methods is difficult to measure the uncertainty of the remaining life of mechanical equipment. In particular， statistical data-driven predictive models are difficult to describe the coupling relationship between multi-dimensional sensor data. And the data-driven fusion model has the problem of loss of key information. To solve these problems， an end-to-end remaining useful lifetime interval prediction method is proposed based on feature attention-lognorm-bidirectional gated recurrent unit （FA-LN-BiGRU）. First， the feature attention mechanism is used to extract key feature vectors from multi-dimensional， nonlinear and large-scale sensor signals. Then， the BiGRU network is used to model the time-varying characteristics of the attention-weighted features from both forward and backward directions. And the network parameters are trained through the maximum likelihood estimation loss function to obtain the probability distribution of the network hidden state output vector. Thus， the probability density function based on log-normal distribution is calculated to realize the measurement of equipment remaining useful life （RUL） uncertainty. The analysis results show that the proposed method can deeply mine performance degradation information for multi-dimensional monitoring data with complex operating conditions and variable failure modes. The accuracy and reliability of the remaining life point prediction and interval prediction of mechanical equipment are effectively improved.