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Accurately estimating a Health Index (HI) from condition monitoring data (CM) is essential for reliable and interpretable prognostics and health management (PHM) in complex systems. In most scenarios, complex systems operate under varying operating conditions and can exhibit different fault modes, making unsupervised inference of an HI from CM data a significant challenge. Hybrid models combining prior knowledge about degradation with deep learning models have been proposed to overcome this challenge. However, previously suggested hybrid models for HI estimation usually rely heavily on system-specific information, limiting their transferability to other systems. In this work, we propose an unsupervised hybrid method for HI estimation that integrates general knowledge about degradation into the convolutional autoencoder's model architecture and learning algorithm, enhancing its applicability across various systems. The effectiveness of the proposed method is demonstrated in two case studies from different domains: turbofan engines and lithium batteries. The results show that the proposed method outperforms other competitive alternatives, including residual-based methods, in terms of HI quality and their utility for Remaining Useful Life (RUL) predictions. The case studies also highlight the comparable performance of our proposed method with a supervised model trained with HI labels.

To maximize its value, the design, development and implementation of Structural Health Monitoring (SHM) should focus on its role in facilitating decision support. In this position paper, we offer perspectives on the synergy between SHM and decision-making. We propose a classification of SHM use cases aligning with various dimensions that are closely linked to the respective decision contexts. The types of decisions that have to be supported by the SHM system within these settings are discussed along with the corresponding challenges. We provide an overview of different classes of models that are required for integrating SHM in the decision-making process to support management and operation and maintenance of structures and infrastructure systems. Fundamental decision-theoretic principles and state-of-the-art methods for optimizing maintenance and operational decision-making under uncertainty are briefly discussed. Finally, we offer a viewpoint on the appropriate course of action for quantifying, validating and maximizing the added value generated by SHM. This work aspires to synthesize the different perspectives of the SHM, Prognostic Health Management (PHM), and reliability communities, and deliver a roadmap towards monitoring-based decision support.

Prognostic Health Management aims to predict the Remaining Useful Life (RUL) of degrading components/systems utilizing monitoring data. These RUL predictions form the basis for optimizing maintenance planning in a Predictive Maintenance (PdM) paradigm. We here propose a metric for assessing data-driven prognostic algorithms based on their impact on downstream PdM decisions. The metric is defined in association with a decision setting and a corresponding PdM policy. We consider two typical PdM decision settings, namely component ordering and/or replacement planning, for which we investigate and improve PdM policies that are commonly utilized in the literature. All policies are evaluated via the data-based estimation of the long-run expected maintenance cost per unit time, using monitored run-to-failure experiments. The policy evaluation enables the estimation of the proposed metric. We employ the metric as an objective function for optimizing heuristic PdM policies and algorithms' hyperparameters. The effect of different PdM policies on the metric is initially investigated through a theoretical numerical example. Subsequently, we employ four data-driven prognostic algorithms on a simulated turbofan engine degradation problem, and investigate the joint effect of prognostic algorithm and PdM policy on the metric, resulting in a decision-oriented performance assessment of these algorithms.

The dynamic, real-time, and accurate inference of model parameters from empirical data is of great importance in many scientific and engineering disciplines that use computational models (such as a digital twin) for the analysis and prediction of complex physical processes. However, fast and accurate inference for processes with large and high dimensional datasets cannot easily be achieved with state-of-the-art methods under noisy real-world conditions. The primary reason is that the inference of model parameters with traditional techniques based on optimisation or sampling often suffers from computational and statistical challenges, resulting in a trade-off between accuracy and deployment time. In this paper, we propose a novel framework for inference of model parameters based on reinforcement learning. The contribution of the paper is twofold: 1) We reformulate the inference problem as a tracking problem with the objective of learning a policy that forces the response of the physics-based model to follow the observations; 2) We propose the constrained Lyapunov-based actor-critic (CLAC) algorithm to enable the robust and accurate inference of physics-based model parameters in real time under noisy real-world conditions. The proposed methodology is demonstrated and evaluated on two model-based diagnostics test cases utilizing two different physics-based models of turbofan engines. The performance of the methodology is compared to that of two alternative approaches: a state update method (unscented Kalman filter) and a supervised end-to-end mapping with deep neural networks. The experimental results demonstrate that the proposed methodology outperforms all other tested methods in terms of speed and robustness, with high inference accuracy., Comment: 18 pages, 10 figures

Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2) limited representativeness of the training dataset for data-driven models. Combining the advantages of these two directions while overcoming some of their limitations, we propose a novel hybrid framework for fusing the information from physics-based performance models with deep learning algorithms for prognostics of complex safety-critical systems under real-world scenarios. In the proposed framework, we use physics-based performance models to infer unobservable model parameters related to a system's components health solving a calibration problem. These parameters are subsequently combined with sensor readings and used as input to a deep neural network to generate a data-driven prognostics model with physics-augmented features. The performance of the hybrid framework is evaluated on an extensive case study comprising run-to-failure degradation trajectories from a fleet of nine turbofan engines under real flight conditions. The experimental results show that the hybrid framework outperforms purely data-driven approaches by extending the prediction horizon by nearly 127\%. Furthermore, it requires less training data and is less sensitive to the limited representativeness of the dataset compared to purely data-driven approaches., Comment: 18 pages, 8 figures, Under Review

The Single-Particle Model (SPM) of Li ion cell \cite{Santhanagopalan06, Guo2011} is a computationally efficient and fairly accurate model for simulating Li ion cell cycling behavior at weak to moderate currents. The model depends on a large number of parameters describing the geometry and material properties of a cell components. In order to use the SPM for simulation of a 18650 LP battery cycling behavior, we fitted the values of the model parameters to a cycling data. We found that the distribution of parametric values for which the SPM fits the data accurately is strongly delocalized in the (nondimensionalized) parametric space, with variances in certain directions larger by many orders of magnitude than in other directions. This property of the SPM is known to be shared by a multitude of the so-called "sloppy models" \cite{Brown2003, Waterfall2006}, characterized by a few stiff directions in the parametric space, in which the predicted behavior varies significantly, and a number of sloppy directions in which the behavior doesn't change appreciably. As a consequence, only stiff parameters of the SPM can be inferred with a fair degree of certainty and these are the parameters which determine the cycling behavior of the battery. Based on geometrical insights from the Sloppy Models theory, we derive an hierarchy of reduced models for the SPM. The fully reduced model depends on only three stiff effective parameters which can be used for the battery state of health characterization., Comment: 16 pages, 11 figures

With the increased availability of condition monitoring data and the increased complexity of explicit system physics-based models, the application of data-driven approaches for fault detection and isolation has recently grown. While detection accuracy of such approaches is generally good, their performance on fault isolation often suffers from the fact that fault conditions affect a large portion of the measured signals thereby masking the fault source. To overcome this limitation and enable a more accurate fault detection, we propose a hybrid approach combining physical performance models with deep learning algorithms. Unobserved process variables are inferred with a physics-based performance model to enhance the input space of a data-driven diagnostics model. To validate the effectiveness of the proposed method, we generate a condition monitoring dataset of an advanced gas turbine during flight conditions under healthy and four faulty operative conditions based on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dynamical model. We evaluate the performance of the proposed method in combination with two different deep learning algorithms: feed forward neural networks and Variational Autoencoders, both of which demonstrate a significant improvement when applied within the hybrid fault detection and diagnostics framework. The proposed method is able to outperform pure data-driven solutions, particularly for systems with a high variability of operating conditions. It provides superior results both for fault detection as well as for fault isolation. For fault isolation, it overcomes the smearing effect that is observed in pure data-driven approaches and enables a precise isolation of the affected signal. We also demonstrate that deep learning algorithms provide a better performance on fault detection compared to the traditional machine learning algorithms., Comment: 25 pages, 19 figures, submitted to the International Journal of Prognostics and Health Management (IJPHM), July 2019

Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuna and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time . Results for ToF estimation using Acuna's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition. Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.