Predictive aircraft maintenance is a maintenance strategy that aims to reduce the number of failures, the number of inspections, the number of maintenance tasks and the aircraft maintenance costs. Aircraft are equipped with health monitoring systems, where sensors continuously measure the condition of the aircraft components. In predictive maintenance, these sensor measurements are used to estimate the time left until the failure of these components, called the Remaining Useful Life (RUL). These RUL prognostics are subsequently used to optimize the aircraft maintenance schedule. There are several challenges that complicate the implementation of predictive aircraft maintenance in practice. In this thesis, the threemain challenges are addressed.@en

We pose the maintenance planning for systems using probabilistic Remaining Useful Life (RUL) prognostics as a renewal reward process. Data-driven probabilistic RUL prognostics are obtained using a Convolutional Neural Network with Monte Carlo dropout. The maintenance planning model is illustrated for aircraft turbofan engines. The results show that in the initial monitoring phase, the accuracy and sharpness of the RUL prognostics is relatively small. The maintenance of the engines is therefore scheduled far in the future. As the usage of the engine increases, the accuracy of the prognostics improves, while the sharpness remains relatively small. As soon as the estimated probability of the RUL is skewed towards 0, the maintenance planning model consistently indicates it is optimal to replace the engines immediately, i.e., "now". This shows that probabilistic RUL prognostics support an effective maintenance planning of the engines, despite being imperfect with respect to accuracy and sharpness. @en

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.

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Health indicators are crucial to assess the health of complex systems. In recent years, several studies have developed data-driven health indicators using supervised learning methods. However, due to preventive maintenance, there are often not enough failure instances to train a supervised learning model, i.e., the data is unlabelled with an unknown actual Remaining Useful Life (RUL). In this paper, we therefore propose an unsupervised learning model to construct a health indicator for an aircraft system. The considered system is operated under highly-varying operating conditions. We train a Convolutional Neural Network (CNN) to predict the sensor measurements from the operating conditions. We train this neural network solely with the sensor measurements of just-installed, non-degraded systems. The CNN therefore learns the normal range of the sensor measurements, given the operating conditions, for non-degraded systems only. For a degraded system, the predicted sensor measurements deviate from the actual sensor measurements. Based on the prediction errors, we construct a health indicator for the aircraft system. We apply this approach to develop a health indicator for the aircraft turbofan engines of dataset DS02 and DS06 of N-CMAPSS. The resulting health indicators have a high prognosability of 0.91 for DS02 and of 0.83 for DS06, a mean trendability of 0.86 for DS02 and of 0.87 for DS06, and a mean monotonicity of 0.31 for DS02 and of 0.33 for DS06, and can thus be used to make a reliable assessment of the system's health. @en

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.

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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.

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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.

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Well-established metrics such as the Root Mean Square Error or the Mean Absolute Error are not suitable to evaluate estimated distributions of the Remaining Useful Life (i.e., probabilistic prognostics). We therefore propose novel metrics to evaluate the quality of probabilistic Remaining Useful Life prognostics. We estimate the distribution of the Remaining Useful Life of turbofan engines using a Convolutional Neural Network with Monte Carlo dropout. The accuracy and sharpness of the obtained probabilistic prognostics are evaluated using the Continuous Ranked Probability Score (CRPS) and weighted CRPS. The reliability of the obtained probabilistic prognostics is evaluated using the α-Coverage and the Reliability Score. The results show that the estimated distributions of the Remaining Useful Life of turbofan engines are accurate, reliable and sharp when using a Convolutional Neural Network with Monte Carlo dropout. In general, the proposed metrics are suitable to evaluate the accuracy, sharpness and reliability of probabilistic Remaining Useful Life prognostics.@en

Several studies have proposed Remaining-Useful-Life (RUL) prognostics for aircraft components in the last years. However, few studies focus on integrating these RUL prognostics into maintenance planning frameworks. This paper proposes an optimization model for opportunistic maintenance scheduling of aircraft components that integrates RUL prognostics and that groups the maintenance of these components to reduce costs. We illustrate our approach for the maintenance of a fleet of aircraft, each equipped with multiple landing gear brakes. RUL prognostics for the landing gear brakes are obtained using a Bayesian regression model. Based on these RUL prognostics, we group the replacement of brakes using an integer linear program. As a result, we obtain a cost-optimal RUL-driven opportunistic-maintenance schedule for the brakes of a fleet of aircraft. Compared with traditional maintenance strategies, our approach leads to a reduction of up to 20% of the total maintenance costs.@en

We propose a criticality-based scheduling model for aircraft component replacements.We schedule maintenance for a fleet of aircraft, each equipped with a multi-component system. The maintenance schedule takes into account a limited stock of spare components and the Remaining-Useful-Life prognostics for the components. We propose a component replacement scheduling model with three stages of maintenance criticality: i) critical aircraft that are not airworthy due to a lack of sufficient operational components, ii) predictive alerts for expected component failures, and iii) non-critical aircraft with some failed components. An Adaptive Large Neighborhood Search (ALNS) algorithm is developed to solve this criticality-based aircraft maintenance planning problem. The framework is illustrated for a fleet of aircraft, each equipped with a k-out-of-N system of components. A predictive maintenance planning is obtained within an outstanding computational time (less than 6 seconds for a fleet of 50 aircraft). Moreover, it is shown that the proposed planning with 3-levels of criticality ensures aircraft airworthiness while making cost-efficient use of maintenance slots. @en

Aircraft maintenance is undergoing a paradigm shift towards predictive maintenance, where the use of sensor data and Remaining-Useful-Life prognostics are central. This paper proposes an integrated approach for predictive aircraft maintenance planning for multiple multi-component systems, where the components are repairables. First, model-based Remaining-Useful-Life prognostics are developed. These prognostics are updated over time, as more sensor data become available. Then, a rolling horizon integer linear program is developed for the maintenance planning of multiple multi-component systems. This model integrates the Remaining-Useful-Life prognostics with the management of a limited stock of spare repairable components. The maintenance of the multiple systems is linked through the availability of spare components and shared maintenance time slots. Our approach is illustrated for a fleet of aircraft, each equipped with a Cooling System consisting of four Cooling Units. For an aircraft to be operational, a minimum of two Cooling Units out of the four need to be operational. The maintenance planning results show that our integrated approach reduces the costs with maintenance by 48% relative to a corrective maintenance strategy and by 30% relative to a preventive maintenance strategy. Moreover, using predictive maintenance, components are replaced in anticipation of failure without wasting their useful life. In general, our approach provides a roadmap from Remaining-Useful-Life prognostics to maintenance planning for multiple multi-component systems of repairables with a limited stock of spares.@en

Prognostics for the Remaining-Useful-Life (RUL) of aircraft components are crucial to support efficient aircraft maintenance planning and, in particular, to limit unscheduled maintenance due to unexpected component failures. As such, predictive methods for the RUL of aircraft components are increasingly a priority for aircraft Maintenance, Repair and Operations (MROs). In this paper we develop model-based RUL prognostics for aircraft Cooling Units using operational data recorded during the flights of several wide-body aircraft. A Cooling Unit is a vapor cycle refrigeration unit consisting of a condenser, a flash tank, an evaporator and a compressor. After some time of usage, the filter of these Cooling Units is clogged with burned oil, moist and sludge from the compressor. This accelerates the wear of the components. Long time utilization of these components in these conditions leads to a failure. To model the degradation of the Cooling Units, we use an exponential functional form for the degradation. Together with sequential Monte Carlo methods, we estimate the probability distribution of the RUL of these components. The exponential functional form of the degradation is based on the fact that the cumulative damage in the components has an effect on the degradation rate. It has been shown that an exponential model is a good approximation for non-linear degradation processes like corrosion, bearing degradation, or deterioration of LED lighting. In fact, the Cooling Units can also be seen as subject to corrosion and accelerated wear. We evaluate our RUL prognostics for various prediction horizons, i.e., at 30, 20 and 10 flight cycles before failure. The results show that our proposed methodology is able to estimate the RUL of the Cooling Units well, and that the uncertainty associated with the prognostics decreases as the prediction horizon decreases, i.e., as the components approach failure. The choice of the prediction horizon is relevant from the point of view of MROs, which re-evaluate periodically their aircraft maintenance schedules. In practice, regular maintenance checks are scheduled every two weeks. Having accurate RUL prognostics over such time horizons enables the maintenance planners to better plan tasks, limiting unscheduled failures. In addition, the fact that we estimate the uncertainty associated with the RUL prognostics enables the maintenance planners to prioritize the maintenance of the components. Overall, our results provide support for maintenance planners to make informed and efficient maintenance schedules.@en

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.

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