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Remaining Useful Life (RUL) of an equipment or one of its components is defined as the time left until the equipment or component reaches its end of useful life. Accurate RUL estimation is exceptionally beneficial to Predictive Maintenance, and Prognostics and Health Management (PHM). Data driven approaches which leverage the power of algorithms for RUL estimation using sensor and operational time series data are gaining popularity. Existing algorithms, such as linear regression, Convolutional Neural Network (CNN), Hidden Markov Models (HMMs), and Long Short-Term Memory (LSTM), have their own limitations for the RUL estimation task. In this work, we propose a novel Functional Data Analysis (FDA) method called functional Multilayer Perceptron (functional MLP) for RUL estimation. Functional MLP treats time series data from multiple equipment as a sample of random continuous processes over time. FDA explicitly incorporates both the correlations within the same equipment and the random variations across different equipment's sensor time series into the model. FDA also has the benefit of allowing the relationship between RUL and sensor variables to vary over time. We implement functional MLP on the benchmark NASA C-MAPSS data and evaluate the performance using two popularly-used metrics. Results show the superiority of our algorithm over all the other state-of-the-art methods.

One of the key challenges in predictive maintenance is to predict the impending downtime of an equipment with a reasonable prediction horizon so that countermeasures can be put in place. Classically, this problem has been posed in two different ways which are typically solved independently: (1) Remaining useful life (RUL) estimation as a long-term prediction task to estimate how much time is left in the useful life of the equipment and (2) Failure prediction (FP) as a short-term prediction task to assess the probability of a failure within a prespecified time window. As these two tasks are related, performing them separately is sub-optimal and might results in inconsistent predictions for the same equipment. In order to alleviate these issues, we propose two methods: Deep Weibull model (DW-RNN) and multi-task learning (MTL-RNN). DW-RNN is able to learn the underlying failure dynamics by fitting Weibull distribution parameters using a deep neural network, learned with a survival likelihood, without training directly on each task. While DW-RNN makes an explicit assumption on the data distribution, MTL-RNN exploits the implicit relationship between the longterm RUL and short-term FP tasks to learn the underlying distribution. Additionally, both our methods can leverage the non-failed equipment data for RUL estimation. We demonstrate that our methods consistently outperform baseline RUL methods that can be used for FP while producing consistent results for RUL and FP. We also show that our methods perform at par with baselines trained on the objectives optimized for either of the two tasks.

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Given a very large data set distributed over a cluster of several nodes, this paper addresses the problem of selecting a few data instances that best represent the entire data set. The solution to this problem is of a crucial importance in the big data era as it enables data analysts to understand the insights of the data and explore its hidden structure. The selected instances can also be used for data preprocessing tasks such as learning a low-dimensional embedding of the data points or computing a low-rank approximation of the corresponding matrix. The paper first formulates the problem as the selection of a few representative columns from a matrix whose columns are massively distributed, and it then proposes a MapReduce algorithm for selecting those representatives. The algorithm first learns a concise representation of all columns using random projection, and it then solves a generalized column subset selection problem at each machine in which a subset of columns are selected from the sub-matrix on that machine such that the reconstruction error of the concise representation is minimized. The paper then demonstrates the effectiveness and efficiency of the proposed algorithm through an empirical evaluation on benchmark data sets.

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