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The increasing availability of condition-monitoring data for components/systems has incentivized the development of data-driven Remaining Useful Life (RUL) prognostics in the past years. However, most studies focus on point RUL prognostics, with limited insights into the uncertainty associated with these estimates. This limits the applicability of such RUL prognostics to maintenance planning, which is per definition a stochastic problem. In this paper, we therefore develop probabilistic RUL prognostics using Convolutional Neural Networks. These prognostics are further integrated into maintenance planning, both for single and multiple components. We illustrate our approach for aircraft turbofan engines. The results show that the optimal replacement time for the engines is close to the lower bound of the 99% confidence interval of the RUL estimates. We also show that our proposed maintenance approach leads to a cost reduction of 53% compared to a traditional Time-based maintenance strategy. Moreover, compared with the ideal case when the true RUL is known in advance (perfect RUL prognostics), our approach leads to a limited number of failures. Overall, this paper proposes an end-to-end framework for data-driven predictive maintenance for multiple components, and showcases the potential benefits of data-driven predictive maintenance on cost and reliability.

A good weight initialization is crucial to accelerate the convergence of the weights in a neural network. However, training a neural network is still time-consuming, despite recent advances in weight initialization approaches. In this paper, we propose a mathematical framework for the weight initialization in the last layer of a neural network. We first derive analytically a tight constraint on the weights that accelerates the convergence of the weights during the back-propagation algorithm. We then use linear regression and Lagrange multipliers to analytically derive the optimal initial weights and initial bias of the last layer, that minimize the initial training loss given the derived tight constraint. We also show that the restrictive assumption of traditional weight initialization algorithms that the expected value of the weights is zero is redundant for our approach. We first apply our proposed weight initialization approach to a Convolutional Neural Network that predicts the Remaining Useful Life of aircraft engines. The initial training and validation loss are relatively small, the weights do not get stuck in a local optimum, and the convergence of the weights is accelerated. We compare our approach with several benchmark strategies. Compared to the best performing state-of-the-art initialization strategy (Kaiming initialization), our approach needs 34% less epochs to reach the same validation loss. We also apply our approach to ResNets for the CIFAR-100 dataset, combined with transfer learning. Here, the initial accuracy is already at least 53%. This gives a faster weight convergence and a higher test accuracy than the benchmark strategies.

Most Remaining Useful Life (RUL) prognostics are obtained using supervised learning models trained with many labelled data samples (i.e., the true RUL is known). In aviation, however, aircraft systems are often preventively replaced before failure. There are thus very few labelled data samples available. We therefore propose a Long Short-Term Memory (LSTM) autoencoder with attention to develop health indicators for an aircraft system instead. This autoencoder is trained with unlabelled data samples (i.e., the true RUL is unknown). Since aircraft fly under various operating conditions (varying altitude, speed, etc.), these conditions are also integrated in the autoencoder. We show that the consideration of the operating conditions leads to robust health indicators and improves significantly the monotonicity, trendability and prognosability of these indicators. These health indicators are further used to predict the RUL of the aircraft system using a similarity-based matching approach. We illustrate our approach for turbofan engines. We show that the consideration of the operating conditions improves the monotonicity of the health indicators by 97%. Also, our approach leads to accurate RUL estimates with a Root Mean Square Error (RMSE) of 2.67 flights only. Moreover, a 19% reduction in the RMSE is obtained using our approach in comparison to existing supervised learning models.