Predictive maintenance for modern machines requires a dynamic process of decision making, where updated information about the health of machines steers the maintenance decisions. For this, it is important to consider the uncertainty associated with the health of the machines. In this paper, we propose a multi-stage stochastic program to schedule maintenance for machines that are continuously monitored by sensors. First, we model the uncertainty associated with the health of the machines by means of probabilistic Remaining Useful Life (RUL) prognostics. With this, the proposed stochastic program schedules maintenance for multiple machines sharing a limited capacity and spare parts. These machines can only be maintained if these resources are available. For failed machines, this may require rescheduling the maintenance of other machines. To reduce the computational time, we formulate the multi-stage stochastic program such that the constraint matrix is totally unimodular, and we can therefore solve it using nested Benders decomposition. We apply our approach to a case study on aircraft engines, planning maintenance 12 weeks ahead. We simulate the maintenance schedule over a period of 10 years. Based on this case study, the results show that our approach reduces the expected costs by 1.4% compared to a non-stochastic approach.

Complex systems such as aircraft engines are continuously monitored by sensors. In predictive aircraft maintenance, the collected sensor measurements are used to estimate the health condition and the Remaining Useful Life (RUL) of such systems. However, a major challenge when developing prognostics is the limited number of run-to-failure data samples. This challenge could be overcome if multiple airlines would share their run-to-failure data samples such that sufficient learning can be achieved. Due to privacy concerns, however, airlines are reluctant to share their data in a centralized setting. In this paper, a collaborative federated learning framework is therefore developed instead. Here, several airlines cooperate to train a collective RUL prognostic machine learning model, without the need to centrally share their data. For this, a decentralized validation procedure is proposed to validate the prognostics model without sharing any data. Moreover, sensor data is often noisy and of low quality. This paper therefore proposes four novel methods to aggregate the parameters of the global prognostic model. These methods enhance the robustness of the FL framework against noisy data. The proposed framework is illustrated for training a collaborative RUL prognostic model for aircraft engines, using the N-CMAPSS dataset. Here, six airlines are considered, that collaborate in the FL framework to train a collective RUL prognostic model for their aircraft's engines. When comparing the proposed FL framework with the case where each airline independently develops their own prognostic model, the results show that FL leads to more accurate RUL prognostics for five out of the six airlines. Moreover, the novel robust aggregation methods render the FL framework robust to noisy data samples.

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.

The increasing availability of condition monitoring data for aircraft components has incentivized the development of Remaining Useful Life (RUL) prognostics in the past years. However, only few studies consider the integration of such prognostics into maintenance planning. In this paper we propose a dynamic, predictive maintenance scheduling framework for a fleet of aircraft taking into account imperfect RUL prognostics. These prognostics are periodically updated. Based on the evolution of the prognostics over time, alarms are triggered. The scheduling of maintenance tasks is initiated only after these alarms are triggered. Alarms ensure that maintenance tasks are not rescheduled multiple times. A maintenance task is scheduled using a safety factor, to account for potential errors in the RUL prognostics and thus avoid component failures. We illustrate our approach for a fleet of 20 aircraft, each equipped with 2 turbofan engines. A Convolution Neural Network is proposed to obtain RUL prognostics. An integer linear program is used to schedule aircraft for maintenance. With our alarm-based maintenance framework, the costs with engine failures account for only 7.4% of the total maintenance costs. In general, we provide a roadmap to integrate imperfect RUL prognostics into the maintenance planning of a fleet of vehicles.

Remaining-useful-life prognostics for aircraft components are central for efficient and robust aircraft maintenance. In this paper, we propose an end-to-end approach to obtain online, model-based remaining-useful-life prognostics by learning from clusters of components with similar degradation trends. Time-series degradation measurements are first clustered using dynamic time-warping. For each cluster, a degradation model and a corresponding failure threshold are proposed. These cluster-specific degradation models, together with a particle filtering algorithm, are further used to obtain online remaining-useful-life prognostics. As a case study, we consider the operational data of several cooling units originating from a fleet of aircraft. The cooling units are clustered based on their degradation trends and remaining-useful-life prognostics are obtained in an online manner. In general, this approach provides support for intelligent aircraft maintenance where the analysis of cluster-specific component degradation models is integrated into the predictive maintenance process.