The growing number of electric-powered vehicles and the associated large demand for energy storage have created the need for reliable management of a fleet of Li-ion batteries over long periods of time. The aging of such batteries is mostly attributed to capacity degradation that operators desire to monitor (and potentially, slow down) to extend battery cycle life. An important tool for this purpose are prognosis models for battery state-of-charge (SOC) and state-of-health (SOH). These models are used to forecast capacity degradation and help operators to optimize their usage profiles. In addition, they are useful tools for discharge predictions and to ensure safe and reliable operation by correctly forecasting end-of-discharge (EOD). A hybrid electro-chemistry-based model fused with neural network and Gaussian processes is presented to capture the contributions of large variations in operating conditions and temperature to SOC and SOH. The goal of this approach is to create a SOC model capable of predicting battery discharge depending on a large variety of loading conditions where, apart from the current amplitude, we also leverage data from cell temperature build-up during discharge. Additionally, our model captures the aging mechanisms in the form of degradation, which relate those to the SOH in form of battery capacity; and failure prediction through a probabilistic classifier based on Gaussian processes. For model training and validation purposes, we use an accelerated battery life testing dataset, where we applied various loading conditions to battery packs. Our model predictions for SOC, SOH and battery failure show close alignment with experimental data for all loading conditions. Note to Practitioners-This work proposes a Li-ion battery modeling approach for battery health and aging estimation using a hybrid approach using physics-based model fused with neural networks and probabilistic models to capture contributions of large variations in operating conditions. The goal is to develop a model capable of predicting battery discharge depending on a wide spectrum of loading conditions where, apart from the current amplitude, cell temperature data is leveraged. Additionally, our model captures the aging mechanisms in the form of degradation of electro-chemistry-based model variables related in form of capacity loss and resistance, it can perform battery failure prediction through a probabilistic classification model. Researchers are encouraged to use the dataset used in this work which is publicly available at the NASA Diagnostics and Prognostics group link provided in the main article.

The current surge in the need for Li-ion batteries to power electric vehicles has also translated in a need for more advanced models that can predict their behavior, but also quantify the uncertainty in their predictions, given the amount of variables involved and the varying operating conditions. This manuscript proposes a new Bayesian physics-informed recurrent neural network, where the battery discharge curve is described using the Nernst and Butler–Volmer equations, the activity correction term within such equations is modeled with two multilayer perceptrons, and approximate Bayesian computation by subset-simulation is used to train the weights, bias and the physical parameters representing the maximum charge available and the internal resistance. The challenges found during the adaptation and implementation of the Bayesian training algorithm to the recurrent physics-informed cell are described, along with the approaches proposed to overcome them. The performance of the Bayesian hybrid model presented in this paper has also been evaluated using data from NASA Ames Prognostics Data Repository, and the results show comparable accuracy to the standard approach with backpropagation, and a flexible and realistic quantification of the uncertainty. Furthermore, the uncertainty related to the physical parameters of the hybrid model can be evaluated in semi-isolation of the weights and bias of the MLPs, providing a sensitivity tool to assess the relative importance between different parameters.

This manuscript proposes a physics-guided Bayesian neural network, which combines Approximate-Bayesian-Computation training with physics-based models. This hybrid algorithm uses the laws of physics to mitigate the lack of data, and the flexibility of neural networks to model the complexities inherent in nature. The state-of-the-art approaches often introduce the physics in the loss function, or through some known boundary conditions, and then use backpropagation to adjust the weights. However, this training method involves some rigidity and drawbacks, mostly related to the adoption of a predefined loss/likelihood function and the evaluation of its gradient during training. The use of approximate Bayesian computation as the learning engine results in a greater prediction accuracy and flexibility to quantify the uncertainty, due to the gradient-free nature of the algorithm, the absence of loss/likelihood function and the non-parametric formulation of the weights. Furthermore, the physics-based model is introduced in the forward pass of the neural network, which significantly increases the extrapolation capabilities of the proposed hybrid model. The proposed algorithm has been applied to lateral-load tests in reinforced concrete columns, providing promising results when making predictions about future loading cycles, surpassing the purely data-driven and physics-based methods as well as the state-of-the-art physics-guided neural networks. In light of the performance shown during the experiments, the proposed algorithm has the potential to become a useful tool for fast evaluation of critical buildings after seismic events.

Lithium-ion batteries are a popular choice to electric and hybrid power vehicles. When dealing with safety-critical and costly applications, such as in urban air mobility, the ability to model and forecast the state of charge and state of health is very important. When managing fleets of electric/hybrid vehicles, the lack of complete datasets, in which battery usage is recorded since first commissioning, adds a layer of complexity to building models for diagnosis, prognosis, and risk management. Building accurate models based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. These simplifications lead to residual discrepancy between model predictions and observed data. Alternatively, machine learning is attractive, but obtaining large and well curated datasets is often unfeasible due to safety constraints or costs. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We then overcome the limitation of requiring the full historical usage of individual batteries through Bayesian update. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with limited and partially observed data.

Insights from life cycle simulations of Unmanned Air Vehicles (UAVs) can help in the introduction of the anticipated Advanced Air Mobility in a safe and economical manner. This includes (but is not limited to) effects between demand, utilization, fleet availability, and maintenance downtime. In a collaborative effort between NASA and DLR, we aim to evaluate different maintenance strategies for UAVs using uncertainty-driven and discrete event-based life cycle simulation. Computational efficiency is a prevalent issue with this type of research, particularly when expensive-to-evaluate submodels are added into already complex life cycle simulation frameworks. Surrogate modeling solutions reduce execution time but sacrifice output accuracy to do so. In this paper, we present the initial outcomes of the collaboration, which comprise the derivation and development of operational scenarios and a performance model. With the latter being the computational bottleneck, we have performed a comparative analysis of four commonly used surrogate modeling techniques, namely (a) Multilinear Interpolation (MLI), (b) Multilinear Regression, (c) Random Forest (RFo) supervised machine learning, and (d) Polynomial Chaos Expansions (PCE). Inputs for the models include the UAV's flown distance and direction, carried payload, wind magnitude and direction, turbulence level, and battery health. The model's output is the change in the battery's state of charge. The comparison focuses on accuracy, and decrease in computational expense. Calculated sensitivity measures revealed the flown distance, carried payload, and battery health to be the most influential parameters. All models show good overall accuracy values of 99% and above but differ significantly in execution time. In addition, only the MLI model was able to capture the influences of head winds and tail winds correctly.

Li-ion batteries are the main power source used in electric propulsion applications (e.g., electric cars, unmanned aerial vehicles, and advanced air mobility aircraft). Analytics-based monitoring and forecasting for metrics such as state of charge and state of health based on battery-specific usage data are critical to ensure high reliability levels. However, the complex electrochemistry that governs battery operation leads to computationally expensive physics-based models; which become unsuitable for prognosis and health management applications. We propose a hybrid physics-informed machine learning approach that simulates dynamical responses by directly implementing numerical integration of principle-based governing equations through recurrent neural networks. While reduced-order models describe part of the voltage discharge under constant or variable loading conditions, model-form uncertainty is captured through multi-layer perceptrons and battery-to-battery aleatory uncertainty is modeled through variational multi-layer perceptrons. In addition, we use a Bayesian approach to merge fleet-wide data in the form of priors with battery-specific discharge cycles, where the battery capacity is fully available or only partially available. We illustrate the effectiveness of our proposed framework using the NASA Prognostics Data Repository Battery dataset, which contains experimental discharge data on Li-ion batteries obtained in a controlled environment.

Current growth of unmanned aerial vehicles (UAVs) suggests heavier low altitude traffic in urban airspace in the nearby future. UAV application areas include small package delivery drones, larger on demand mobility vehicles, and emergency fire suppression drones among numerous others. Safe and reliable operations of such vehicles become a more critical issue in low altitude and high number of takeoff/landing situations. In such applications, fast and accurate fault detection and isolation are very crucial safety and mission concerns. Efficient health monitoring also facilitates real-time decision support and repair/return-to-fleet decisions. Powertrains are vital subsystems of any electric UAV. Failures in any component or module of a powertrain may cause a mission failure, safety issues, and overall reliability concern. Moreover, timely information about failure in the powertrain helps to make decisions on whether to abort the mission or complete the mission with some functions limited (limp mode). This work presents a framework for fault detection and diagnosis techniques that are suitable for powertrain failures in UAV systems. For certain faults, signal based detection techniques are fast and reliable whereas for certain other faults, parameter estimation algorithms may be more suitable for better accuracy. In this work, we present an integrated model-based and data driven approach of fault detection and fault isolation at two different levels.

The development of new modes of transportation such as electric vertical takeoff and landing aircraft and the use of drones for package and medical delivery have increased the demand for reliable and powerful electric batteries. Therefore, accurately predicting the degradation of a battery’s state-ofhealth (SOH) and state-of-charge (SOC) is a crucial albeit still challenging task. There is a need for models that can accurately predict the SOH and SOC while taking into account the specific characteristics of a battery cell and its usage profile. While traditional physics-based and data-driven approaches are used to monitor the SOH and SOC, they both have limitations related to computational costs or that require engineers to continually update their prediction models as new battery cells are developed and put into use in battery-powered vehiclefleets.Battery capacity degradation can vary from battery to battery and can also be influenced by changes in load due to internal thermal stress. While sophisticated electrochemistry-based models can provide precise predictions of the SOC during adischarge cycle when parameters are well-tuned, using highfidelity models for prognostics purposes can be computationally expensive. Those models also require tuning to specific battery types and at times to specific specimens, thus hindering generalization. In contrast, purely data-driven approaches can learn the relationship between input and output for SOC prediction based on load input, but they require a large and diverse training dataset and lack any physical or electrochemical understanding, making far-ahead predictions challenging if test loading conditions fall outside the training distribution. To address some of the drawbacks of the aforementioned modeling approaches, in this paper, we enhance a hybrid physics-informed machine learning version of a battery SOC model we presented in previous work to predict voltage dropduring discharge. The enhanced model captures the effect of wide variation of load levels, in the form of input current,which causes large thermal stress cycles. The cell temperature build-up during a discharge cycle is used to identify temperature-sensitive model parameters. Additionally, we enhance an existing aging model built upon cumulative energy drawn by introducing the effect of the load level. We then map cumulative energy and load level to battery capacity with a Gaussian process model. To validate our approach we use a battery aging dataset collected on a self-developed testbed, where we used a wide current level range to age battery packs in accelerated fashion. Prediction results show that our model can be successfully calibrated and generalizes across all applied load levels.

This paper shows the application of hybrid physics-informed machine learning to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived principles and empirical equations, as well as fully connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fitting driven by heuristics or empirical observations is replaced by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This approach allows training of networks deep inside the model and unknown parameters in a single learning stage. It has already been applied to Li-ion batteries in the past, and in this work the application is extended to include other electric powertrain components, specifically an electronic speed controller with pulse-width modulation, and brush-less DC motor with connected propeller. Training and testing of the model is carried out using experimental data from Li-ion battery discharge in a laboratory environment and synthetic data from simulated speed controller, three-phase motor and fixed-pitch propeller.

Prognostics of engineering systems or systems of systems is the prediction of future performance and/or the time at which one or more events of interest occur.Prognostics can be applied in a variety of applications, from spacecraft and aircraft to wind turbines, oil and gas infrastructure, and assembly lines.Prognostic results are used to inform action to extend life or prevent failures through changes in use or predictive maintenance.The NASA Prognostics Python Packages (ProgPy) (Teubert et al., 2022) are a set of opensourced Python packages supporting research and development of prognostics and health management for engineering systems, as described in (Goebel et al., 2017).ProgPy builds upon the architecture of the Matlab Prognostics Libraries (Daigle, 2016c(Daigle, , 2016a(Daigle, , 2016b)), Generic Software Architecture for Prognostics (Teubert et al., 2017), and Prognostics As-A-Service (Watkins et al., 2019).ProgPy implements architectures and common functionalities of prognostics, supporting both researchers and practitioners.

The development of new modes of transportation, such as electric vertical takeoff and landing (eVTOL) aircraft and the use of drones for package and medical delivery, has increased the demand for reliable and powerful electric batteries. The most common batteries in electric-powered vehicles use Lithium-ion (Li-ion). Because of their long cycle life, they are the preferred choice for battery packs deployed over a lifespan of many years. Thus, battery aging needs to be well understood to achieve safe and reliable operation, and life cycle experiments are a crucial tool to characterize the effect of degradation and failure. With the importance of battery durability in mind, we present an accelerated Li-ion battery life cycle data set, focused on a large range of load levels, for batteries composed of two 18650 cells. We tested 26 battery packs grouped by: (i) constant or random loading conditions, (ii) loading levels, and (iii) number of load level changes. Furthermore, we conducted load cycling on second-life batteries, where surviving cells from previously-aged packs were assembled to second-life packs. The goal is to provide the PHM community with an additional data set characterized by unique features. The aggressive load profiles create large temperature increases within the cells. Temperature effects becomes therefore important for prognosis. Some samples are subject to changes in amplitude and number of load levels, thus approaching the level of variability encountered in real operations. Reassembling of survival cells into new packs created additional data that can be used to evaluate the performance of recommissioned batteries. The data set can be leveraged to develop and test models for state-of-charge and state-of-health prognosis. This paper serves as a companion to the data set. It outlines the design of experiment, shows some exemplifying time-series voltage curves and aging data, describes the testbed design and capabilities, and also provides information about the outliers detected thus far. Upon acceptance, the data set will be made available on the NASA Ames Prognostics Center of Excellence Data Repository.

Incorporating unmanned aerial vehicles (UAVs) into the United States National Airspace System would demand enhanced airspace safety technologies for the safety of the UAVs, people, and property on the ground. One of the safety-critical factors to consider is the risk of a UAV deviating from its planned trajectory, which may result in loss of separation between other vehicles or obstacles or may cause early depletion of battery power. In this paper, we studied the effect of wind on UAV trajectory deviation by incorporating wind velocity as a drag component in a six-degrees-of-freedom trajectory simulation comprising a rotorcraft lumped-mass model. Both steady-state wind and wind turbulence effects were investigated. We validated our approach using real flight data from UAV experiments conducted at NASA Langley Research Center. The proposed approach would enable risk-informed decision making by timely mitigation of current and future collision events in an uncertain and dynamic environment.

Current forecasts on the future of aeronautics suggest an increasing number of unmanned aerial vehicles entering the low-altitude airspace in the next decades. Small vehicles for package delivery as well as larger vehicles for urban air mobility will change the dynamics of the airspace, increasing density of operations both in time, i.e. high number of take-off and landings per unit time, and in space, operating in dense urban environment. This scenario poses challenges to the current approach to air traffic control, and large efforts from academia, industry and regulatory bodies are dedicated to the development of new traffic management strategies that leverage higher computing and simulating capabilities avail-able today. In this paper, we propose a simple look-ahead approach to predict potential minimum separation violations at the strategic level, that is before vehicles start flying, depending on the predefined 4D trajectories and uncertainty affecting the wind acting along those routes. Wind forecast data are provided by True Weather Solutions, Inc. on a sparse grid of latitude/longitude coordinates. We then interpolate the sparse data using Gaussian process regression to obtain an estimate of wind speed and direction, while uncertainty affecting the expected ground speed is propagated through error intervals. The approach allows the prediction of aircraft separation as a function of time, highlighting potential safety violations that would go undetected if uncertainty affecting the expected 4D trajectories was not considered. The paper will also discuss issues related to accuracy and scalability of the approach to multiple vehicle operations.

For incorporation of unmanned aerial vehicles into the National Airspace, ensuring safety of the airspace including the vehicles, people, and property on the ground is of utmost importance. One of the safety-critical factors for unmanned aviation flights is the risk of deviating from a planned trajectory resulting in a variety of hazards, including potential loss of separation between vehicle and obstacles or unexpected battery energy consumption. Off-nominal conditions introduced by component failures, degraded controllability and environmental disturbances such as wind gusts can lead to unacceptable unexpected deviations from the flight trajectory. It is essential to accurately model such effects on the flight trajectory while computing safety thresholds such as minimum separation from surrounding obstacles, available battery resource to complete the mission or determining delay in the expected time of arrival of flights. In this paper, a tool is presented based on Gaussian Process Regression for wind representation over a pre-defined trajectory for fast, yet approximated, in-time evaluation of possible trajectory deviations caused by wind gusts. The deviation in the planned trajectory caused by wind is further simulated utilizing a 6 degrees-of-freedom (DOF) UAV trajectory simulator comprising of a rotorcraft lumped-mass model with LQRI controller. Both steady-state wind and wind gust effects are investigated. The probability of collision with obstacle is computed and demonstrated on real flight data from experimental flights of an octocopter at NASA Langley Research Center in the presence of simulated obstacles and wind conditions. Effect of varying wind conditions and varying UAV airspeed is further demonstrated on experimental flights in the presence of wind measured by ground based weather service stations. The proposed approach would eventually benefit timely mitigation of current and future safety-critical events in autonomous systems by enabling risk-informed decision making.

Unmanned aerial vehicles (UAVs) are used in various industries such as agriculture and logistics, to name but a few, where their applications are beyond basic mapping, surveillance, and photography. In near future, UAVs are expected to be used in package delivery service and larger electric vertical takeoff and landing vehicles will be employed for urban air mobility applications (air taxi). Thus, several electric propulsion systems will enter the low-altitude airspace with frequent take offs and landings. To achieve state-of-the-art safety standards under such high traffic density, UAVs will require in-time fault detection and performance monitoring of critical powertrain components. This work focuses on propeller blade performance and damage detection in electric UAVs. Propellers are the fastest moving component in an UAV; even a minor defect in the propeller blades could cause performance deterioration, with consequent challenges in flying through the planned trajectory or adhere to the safety requirements of the operation. Monitoring and updating aerodynamic efficiency of each rotor would therefore enable the detection of off-nominal propeller conditions thus magnifying the state-awareness of powertrain monitoring systems based on the acquired electrical signals. An extended Kalman filter-based parameter estimation algorithm is being implemented that incorporates time history responses from UAV powertrain in conjunction with a full powertrain system model to identify changes in the propeller aerodynamic efficiency. Propeller fault detection is achieved by incorporating the aerodynamic parameters of the propeller into the powertrain model. The proposed technique is successfully validated with numerical simulations.

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the Prognostics and Health Management domain, where farahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. A potential solution was found by implementing Koopman theory, which considers the dynamics of nonlinear systems. Koopman theory provides a mechanism to trade-off low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the ProgPy python packages.

Lithium-ion batteries are commonly used to power electric unmanned aircraft vehicles (UAVs).Therefore, the ability to model both the state of charge as well as battery health is very important for reliable and affordable operation of UAV fleets.Even though models based on first principles are accurate and trustworthy, the complex electro-chemistry that governs battery discharge and aging makes it hard to build and use such models for in-time monitoring of battery conditions.Moreover, the careful tuning or estimation of high-fidelity model parameters hampers the straightforward deployment in the field.Alternatively, reduced order models have the advantage of capturing the overall behavior of battery discharge. Reduced-order principle-based models are built by carefully simplifying the physics/chemistry such that computational cost is dramatically reduced while the overall behavior of the system is still captured.These simplifications also lead to a number of parameters to be estimated based on data as well as residual discrepancy (model-form uncertainty).This approach can lead to a number of parameters to be estimated based on data as well as residual model-form uncertainty; a property shared with machine learning models. The latter are solely built on the basis of data, and can still capture unexpected nonlinearities.The drawback is that traditional machine learning tends to require large number of data points hard to retrieve in many scientific and engineering fields like, for example, the field of battery discharge and degradation prediction. In this paper, we will present a hybrid modeling approach for tracking and forecasting battery aging based on ``as-used'' conditions.Our approach directly implements a reduced-order model based on Nerst and Butler-Volmer equations within a deep neural network framework.While most of the input-output relationship is captured by reduced-order models, the data-driven kernels reduce the gap between predictions and observations.The hybrid model estimates the overall battery discharge, and a multilayer perceptron models the battery internal voltage.Battery aging is characterized by time-dependent internal resistance and the amount of available Li-ions.We address the difficult issue of building and updating the aging model by reducing the need for reference discharge cycles.This is beneficial to operators, since it reduces the need of taking the batteries out of commission.We compensate for lack of reference discharge cycles by using a probabilistic model that leverages previously available fleet-wide information. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence website.Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations.Moreover, the model can help optimizing battery operation by offering long-term forecast of battery capacity.

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs). The ability to model and forecast remaining useful life of these batteries enables UAV reliability assurance. Building principled accurate models is challenging due to the complex electrochemistry that governs battery operation. Alternatively, reduced order models have the advantage of capturing the overall behavior of battery discharge, although they suffer from simplifications and residual discrepancy. This paper presents a hybrid modeling approach that directly implements physics within deep neural networks. While most of the input–output relationship is captured by reduced-order models, data-driven kernels reduce the gap between predictions and observations. A reduced-order model based on Nernst and Butler–Volmer equations represents the overall battery discharge, and a multilayer perceptron models the battery non-ideal voltage. Battery aging is characterized by time-dependent internal resistance and the amount of available Li-ions, which are modeled through an ensemble of variational Bayesian multilayer perceptrons. The approach is validated using data publicly available through the NASA Prognostics Center of Excellence website. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations. Moreover, the model can help optimizing battery operation by offering long-term forecast of battery capacity.

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs)

This work proposes a perspective towards establishing a framework for uncertainty quantification of autonomous system tracking and health monitoring. The approach leverages the use of a predictive process structure, which maps uncertainty sources and their interaction according to the quantity of interest and the goal of the predictive estimation. It is systematic and uses basic elements that are system agnostic, and therefore needs to be tailored according to the specificity of the application. This work is motivated by the interest in low-altitude unmanned aerial vehicle operations, where awareness of vehicle and airspace state becomes more relevant as the density of autonomous operations grows rapidly. Predicted scenarios in the area of small vehicle operations and urban air mobility have no precedent, and holistic frameworks to perform prognostics and health management (PHM) at the system- and airspace-level are missing formal approaches to account for uncertainty. At the end of the paper, two case studies demonstrate implementation framework of trajectory tracking and health diagnosis for a small unmanned aerial vehicle.