In this paper, we present a novel approach for multivariate time series data analysis with special emphasis on industrial sensor data sets. The approach applies deep convolutional neural networks as a base architecture, incorporating a generalization of the dilated convolution operation on the receptive fields. The dilation operation allows for the aggregation of distributed information in the input space compared to standard convolution operation. The proposed dilation methodology allows for a trainable selection and ignorance of individual sensor features, based on their relevance to the prediction task. Furthermore, arbitrary patterns in the input feature space, including in the temporal dimension of the multivariate time series data can be extracted. In contrast to the standard dilation methodology, the proposed generalized dilation technique is end-to-end differentiable and hence can be trained with off the shelf gradient descent optimizers. Two methodologies have been proposed for the resulting constrained optimization problem namely, the Barrier Function and Top-K sampling approach. We apply the dilated convolutional neural networks to remaining useful lifetime (RUL) estimation problems where degradation recognition over a longer time horizon is crucial for precise estimation. We test the approach on two challenging benchmark datasets, namely the PRONOSTIA Bearing Dataset and the C-MAPSS Aircraft Engine Dataset for RUL prediction. The experimental results obtained for RUL estimation show the superior prediction capability of the proposed generalized dilation methodologies and constitute a new state of the art compared to previous results in literature.