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NASA NTRS2006

Value, Cost, and Sharing: Open Issues in Constrained Clustering

Clustering is an important tool for data mining, since it can identify major patterns or trends without any supervision (labeled data). Over the past five years, semi-supervised (constrained) clustering methods have become very popular. These methods began with incorporating pairwise constraints and have developed into more general methods that can learn appropriate distance metrics. However, several important open questions have arisen about which constraints are most useful, how they can be actively acquired, and when and how they should be propagated to neighboring points. This position paper describes these open questions and suggests future directions for constrained clustering research.

constraints↗

NASA NTRS2010

Lidar Ratios for Dust Aerosols Derived From Retrievals of CALIPSO Visible Extinction Profiles Constrained by Optical Depths from MODIS-Aqua and CALIPSO/CloudSat Ocean Surface Reflectance Measurements

CALIPSO's (Cloud Aerosol Lidar Infrared Pathfinder Satellite Observations) analysis algorithms generally require the use of tabulated values of the lidar ratio in order to retrieve aerosol extinction and optical depth from measured profiles of attenuated backscatter. However, for any given time or location, the lidar ratio for a given aerosol type can differ from the tabulated value. To gain some insight as to the extent of the variability, we here calculate the lidar ratio for dust aerosols using aerosol optical depth constraints from two sources. Daytime measurements are constrained using Level 2, Collection 5, 550-nm aerosol optical depth measurements made over the ocean by the MODIS (Moderate Resolution Imaging Spectroradiometer) on board the Aqua satellite, which flies in formation with CALIPSO. We also retrieve lidar ratios from night-time profiles constrained by aerosol column optical depths obtained by analysis of CALIPSO and CloudSat backscatter signals from the ocean surface.

Young, Stuart A.↗

NASA NTRS2010

The Use of Deep Moonquakes for Constraining the Internal Structure of the Moon

The installation of seismometers on the Moon s surface during the Apollo era provided a wealth of information that transformed our understanding of lunar formation and evolution. Seismic events detected by the nearside network were used to constrain the structure of the Moon s crust and mantle down to a depth of about 1000 km. The presence of an attenuating region in the deepest interior has been inferred from the paucity of farside events, as well as other indirect geophysical measurements. Recent re-analyses of the Apollo data have tentatively identified this region as a lunar core, although its properties are not yet constrained. Here we present new modeling in support of seismic missions that plan to build upon the knowledge of the Moon s interior gathered by Apollo. We have devised a method in which individual events can be linked to a known cluster using the observed S-P arrival time differences and azimuth to only two stations. Events can be further identified using each cluster's unique occurrence time signature

Weber, Renee↗

NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

NASA NTRS2011

Constraining the Braneworld with Gravitational Wave Observations

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, L, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining L via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain L at the approximately 1 micron level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of L less than or equal to 5 microns.

McWilliams, Sean T.↗

NASA NTRS2014

Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.

Hannan, Mike R.↗

NASA NTRS2013

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

X-rays↗

NASA NTRS2012

A Risk-Constrained Multi-Stage Decision Making Approach to the Architectural Analysis of Mars Missions

This paper presents a novel risk-constrained multi-stage decision making approach to the architectural analysis of planetary rover missions. In particular, focusing on a 2018 Mars rover concept, which was considered as part of a potential Mars Sample Return campaign, we model the entry, descent, and landing (EDL) phase and the rover traverse phase as four sequential decision-making stages. The problem is to find a sequence of divert and driving maneuvers so that the rover drive is minimized and the probability of a mission failure (e.g., due to a failed landing) is below a user specified bound. By solving this problem for several different values of the model parameters (e.g., divert authority), this approach enables rigorous, accurate and systematic trade-offs for the EDL system vs. the mobility system, and, more in general, cross-domain trade-offs for the different phases of a space mission. The overall optimization problem can be seen as a chance-constrained dynamic programming problem, with the additional complexity that 1) in some stages the disturbances do not have any probabilistic characterization, and 2) the state space is extremely large (i.e, hundreds of millions of states for trade-offs with high-resolution Martian maps). To this purpose, we solve the problem by performing an unconventional combination of average and minimax cost analysis and by leveraging high efficient computation tools from the image processing community. Preliminary trade-off results are presented.

entry, descent, and landing (EDL)↗

NASA NTRS2015

Constraining Black Carbon Aerosol over Asia using OMI Aerosol Absorption Optical Depth and the Adjoint of GEOS-Chem

Accurate estimates of the emissions and distribution of black carbon (BC) in the region referred to here as Southeastern Asia (70degE-l50degE, 11degS-55degN) are critical to studies of the atmospheric environment and climate change. Analysis of modeled BC concentrations compared to in situ observations indicates levels are underestimated over most of Southeast Asia when using any of four different emission inventories. We thus attempt to reduce uncertainties in BC emissions and improve BC model simulations by developing top-down, spatially resolved, estimates of BC emissions through assimilation of OMI observations of aerosol absorption optical depth (AAOD) with the GEOS-Chem model and its adjoint for April and October of 2006. Overwhelming enhancements, up to 500%, in anthropogenic BC emissions are shown after optimization over broad areas of Southeast Asia in April. In October, the optimization of anthropogenic emissions yields a slight reduction (1-5%) over India and parts of southern China, while emissions increase by 10-50% over eastern China. Observational data from in situ measurements and AERONET observations are used to evaluate the BC inversions and assess the bias between OMI and AERONET AAOD. Low biases in BC concentrations are improved or corrected in most eastern and central sites over China after optimization, while the constrained model still underestimates concentrations in Indian sites in both April and October, possibly as a. consequence of low prior emissions. Model resolution errors may contribute up to a factor of 2.5 to the underestimate of surface BC concentrations over northern India. We also compare the optimized results using different anthropogenic emission inventories and discuss the sensitivity of top-down constraints on anthropogenic emissions with respect to biomass burning emissions. In addition, the impacts of brown carbon, the formulation of the observation operator, and different a priori constraints on the optimization are investigated. Overall, despite these limitations and uncertainties, using OMI AAOD to constrain BC sources improves model representation of BC distributions, particularly over China.

Aerosols↗

NASA NTRS2013

Constraining Cometary Crystal Shapes from IR Spectral Features

A major challenge in deriving the silicate mineralogy of comets is ascertaining how the anisotropic nature of forsterite crystals affects the spectral features' wavelength, relative intensity, and asymmetry. Forsterite features are identified in cometary comae near 10, 11.05-11.2, 16, 19, 23.5, 27.5 and 33 microns [1-10], so accurate models for forsterite's absorption efficiency (Qabs) are a primary requirement to compute IR spectral energy distributions (SEDs, lambdaF lambda vs. lambda) and constrain the silicate mineralogy of comets. Forsterite is an anisotropic crystal, with three crystallographic axes with distinct indices of refraction for the a-, b-, and c-axis. The shape of a forsterite crystal significantly affects its spectral features [13-16]. We need models that account for crystal shape. The IR absorption efficiencies of forsterite are computed using the discrete dipole approximation (DDA) code DDSCAT [11,12]. Starting from a fiducial crystal shape of a cube, we systematically elongate/reduce one of the crystallographic axes. Also, we elongate/reduce one axis while the lengths of the other two axes are slightly asymmetric (0.8:1.2). The most significant grain shape characteristic that affects the crystalline spectral features is the relative lengths of the crystallographic axes. The second significant grain shape characteristic is breaking the symmetry of all three axes [17]. Synthetic spectral energy distributions using seven crystal shape classes [17] are fit to the observed SED of comet C/1995 O1 (Hale-Bopp). The Hale-Bopp crystalline residual better matches equant, b-platelets, c-platelets, and b-columns spectral shape classes, while a-platelets, a-columns and c-columns worsen the spectral fits. Forsterite condensation and partial evaporation experiments demonstrate that environmental temperature and grain shape are connected [18-20]. Thus, grain shape is a potential probe for protoplanetary disk temperatures where the cometary crystalline forsterite formed. The forsterite crystal shapes (equant, b-platelets, c-platelets, b-columns - excluding a- and c-columns) derived from our modeling [17] of comet Hale- Bopp, compared to laboratory synthesis experiments [18], suggests that these crystals are high temperature condensates. By observing and modeling the crystalline features in comet ISON, we may constrain forsterite crystal shape(s) and link to their formation temperature(s) and environment(s).

anisotropic crystal↗

NASA NTRS2013

Does Aspartic Acid Racemization Constrain the Depth Limit of the Subsurface Biosphere?

Previous studies of the subsurface biosphere have deduced average cellular doubling times of hundreds to thousands of years based upon geochemical models. We have directly constrained the in situ average cellular protein turnover or doubling times for metabolically active micro-organisms based on cellular amino acid abundances, D/L values of cellular aspartic acid, and the in vivo aspartic acid racemization rate. Application of this method to planktonic microbial communities collected from deep fractures in South Africa yielded maximum cellular amino acid turnover times of approximately 89 years for 1 km depth and 27 C and 1-2 years for 3 km depth and 54 C. The latter turnover times are much shorter than previously estimated cellular turnover times based upon geochemical arguments. The aspartic acid racemization rate at higher temperatures yields cellular protein doubling times that are consistent with the survival times of hyperthermophilic strains and predicts that at temperatures of 85 C, cells must replace proteins every couple of days to maintain enzymatic activity. Such a high maintenance requirement may be the principal limit on the abundance of living micro-organisms in the deep, hot subsurface biosphere, as well as a potential limit on their activity. The measurement of the D/L of aspartic acid in biological samples is a potentially powerful tool for deep, fractured continental and oceanic crustal settings where geochemical models of carbon turnover times are poorly constrained. Experimental observations on the racemization rates of aspartic acid in living thermophiles and hyperthermophiles could test this hypothesis. The development of corrections for cell wall peptides and spores will be required, however, to improve the accuracy of these estimates for environmental samples.

cellular↗

NASA NTRS2011

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions Based on a Bank of Norm-Inequality-Constrained Epoch-State Filters

Sequential probability ratio tests explicitly allow decision makers to incorporate false alarm and missed detection risks, and are potentially less sensitive to modeling errors than a procedure that relies solely on a probability of collision threshold. Recent work on constrained Kalman filtering has suggested an approach to formulating such a test for collision avoidance maneuver decisions: a filter bank with two norm-inequality-constrained epoch-state extended Kalman filters. One filter models 1he null hypothesis 1ha1 the miss distance is inside the combined hard body radius at the predicted time of closest approach, and one filter models the alternative hypothesis. The epoch-state filter developed for this method explicitly accounts for any process noise present in the system. The method appears to work well using a realistic example based on an upcoming highly-elliptical orbit formation flying mission.

Carpenter, J. R.↗

NASA NTRS2018

Evaluation of Multiple Flow Constrained Area Capacity Setting Methods for Collaborative Trajectory Options Program

The purpose of this study was to compare flow constrained area (FCA) capacity setting methods for Collaborative Trajectory Options Program (CTOP) as they pertain to the Integrated Demand Management (IDM) concept. IDM uses flow balancing to manage air traffic across multiple FCAs with a common downstream constraint, as well as constraints at the respective FCA locations. FCA capacity rates can be set manually, but generating capacities for multiple, interdependent FCAs could potentially over-burden a user. A new enhancement to CTOP called the FCA Balance Algorithm (FBA) was developed at NASA Ames Research Center to improve the process of allocating capacity across multiple flow constrained segments in the airspace. The FBA evaluates the predicted demand and capacity across multiple FCAs and dynamically generates capacity settings for the FCAs that best meet capacity limits for all identified constraints. In a human-in-the-loop simulation study, both manual and automated capacity setting methods were evaluated in terms of their overall feasibility using measures of system performance, human performance, and qualitative feedback. Subject matter experts were asked to use three different methods to allocate capacity to three FCAs, either (1) by manually setting capacity for every 60-minute time window, (2) by manually setting capacity for every 15-minute time window, or (3) by using the FBA capability to automatically generate capacity settings. Results showed no significant differences in terms of overall system performance, indicated by similar ground delay and airport throughput numbers between methods. However, differences in individual strategies afforded by the manual methods allowed some participants to achieve system-wide delay that was much lower than the average. The FBA was the fastest method of capacity setting, and it received the lowest subjective rating scores on physical task load, mental task load, task difficulty and task complexity out of the three methods. Finally, participants explained through qualitative feedback that there were many benefits to using the FBA, such as ease of use, accuracy, and low risk of human input error. Participants did not experience the same limitations with the FBA that they did with the manual methods, such as reduced accuracy in the 60-minute manual condition, or high complexity in the 15-minute/manual condition. These results suggest that the FBA automation enhancement to CTOP maintains system performance while improving human performance. Therefore, the FBA could be introduced as a way to mitigate operator workload while planning a CTOP.

NextGen↗

NASA NTRS2018

Evaluation of Multiple Flow Constrained Area Capacity Setting Methods for Collaborative Trajectory Options Program

NextGen↗

NASA NTRS2020

Constraining the Temperature of Impact Melt from the Mistastin Lake Impact Structure Using Zircon Crystal Structures

Impact melt is a product of hyper-velocity impact events formed by the instantaneous melting of near-surface target rocks. Constraining the temperature of impact melt is vital to understanding its prograde heating and cooling history, which can have implications for inferring the environment of early Earth ~4.0 billion years ago when microbial life potentially arose. To date, only one datum on the initial impact melt temperature has been derived by Timms et al. These authors studied zirconia microstructures and crystallographic orientations that revealed the former presence of cubic zirconia, found in a black impact glass at the Mistastin Lake impact structure, Canada. The presence of cubic zirconia indicates a minimum temperature for the impact melt of >2370°C from the dissociation temperature of zircon to cubic zirconia and liquid SiO2. With only one temperature datum, it is still difficult to constrain the entire temperature range experienced during the impact melting process; from its instantaneous formation to thermal equilibrium with the “cold” clasts collected along the crater floor and walls. In addition, obtaining a temperature value from only one type of impactite limits the inferred temperature range, because each impactite experiences a different cooling history. In this study, we present a preliminary investigation of 61 zircon crystals, 14 of which are similar to those studied by Timms et al., from the Mistastin Lake impact structure. To acquire a more accurate temperature profile representative of impact melt, zircon crystals were collected from different types of impactites containing impact melt, including additional samples of the black impact glass studied by Timms et al.

Tolometti, G. D.↗

NASA NTRS2020

Constraining Fossil Fuel CO2 Emissions from Urban Area Using OCO-2 Observations of Total Column CO2

Satellite observations of the total column dry-air CO2(XCO2) are expected to support the quantification and monitoring of fossil fuel CO2 (ffCO2) emissions from urban areas. We evaluate the utility of the Orbiting Carbon Observatory 2 (OCO-2) XCO2 retrievals to optimize whole-city emissions, using a Bayesian inversion system and high-resolution transport modeling. The uncertainties of constrained emissions related to transport model, satellite measurements, and local biospheric fluxes are quantified. For the first two uncertainty sources, we examine cities of different landscapes: “plume city” located in relatively flat terrain, represented by Riyadh and Cairo; “basin city” located in basin terrain, represented by Los Angeles (LA). The retrieved scaling factors of emissions and their uncertainties show prominent variabilities from track to track, due to the varying meteorological conditions and relative locations of the tracks transecting plumes. To explore the performance of multiple tracks in retrieving emissions, pseudo data experiments are carried out. The estimated least number of tracks required to constrain the total emissions for Riyadh (<10% uncertainty), Cairo (<10%), and LA (<5%) are 5, 8, and 7, respectively. Additionally, to evaluate the impact of biospheric fluxes on derivation of the ffXCO2 enhancements, we conduct simulations for Pearl River Delta metropolitan area. Significant fractions of local XCO2 enhancements associated with local biospheric XCO2 variations are shown, which potentially lead to biased estimates of ffCO2 emissions. We demonstrate that satellite measurements can be used to improve urban ffCO2 emissions with a sufficient amount of measurements and appropriate representations of the uncertainty components.

Xinxin Ye↗

NASA NTRS2019

Constraining global aerosol emissions using POLDER/PARASOL satellite remote sensing observations

We invert global black carbon (BC), organic carbon (OC) and desert dust (DD) aerosol emissions from POLDER/PARASOL spectral aerosol optical depth (AOD) and aerosol absorption optical depth (AAOD) using the GEOS-Chem inverse modeling framework. Our inverse modeling framework uses standard a priori emissions to provide a posteriori emissions that are constrained by POLDER/PARASOL AODs and AAODs. The following global emission values were retrieved for the three aerosol components: 18.4 Tg/yr for BC, 109.9 Tg/yr for OC and 731.6 Tg/yr for DD for the year 2010. These values show a difference of +166.7 %, +184.0 % and −42.4 %, respectively, with respect to the a priori values of emission inventories used in “standard” GEOS-Chem runs. The model simulations using a posteriori emissions (i.e., retrieved emissions) provide values of 0.119 for global mean AOD and 0.0071 for AAOD at 550 nm, which are +13.3 % and +82.1 %, respectively, higher than the AOD and AAOD obtained using the a priori values of emissions. Additionally, the a posteriori model simulation of AOD, AAOD, single scattering albedo, Ångström exponent and absorption Ångström exponent show better agreement with independent AERONET, MODIS and OMI measurements than the a priori simulation. Thus, this study suggests that using satellite-constrained global aerosol emissions in aerosol transport models can improve the accuracy of simulated global aerosol properties.

chemical transport model (CTM) simulations↗

NASA NTRSDate not supplied

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

In engineering and aerospace applications, it is vital to operational success to have insight into the expected performance and health of physical systems. The field of prognostics and health management provides quantitative methods for monitoring, predicting, and managing system health. Prognostics algorithms can be employed to assess the current state of a system, propagate the system throughout time, and predict potential anomalies or failures that may occur. While they can provide accurate prediction results, effective prognostics algorithms can be challenging to use in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for future remaining useful life predictions. In this work, we implement new algorithmic approaches for prediction, quantitatively compare them via a battery degradation use-case, and provide recommendations of potential improvements to a prognostics framework. One approach to prediction is through sampling, whereby the current state of a physical system is sampled many times and each sample is propagated forward until failure is reached, resulting in a distribution of failure values. To improve the efficiency of this process, we implemented five new algorithmic approaches to prediction, including three distinct sampling methods (standard Monte Carlo, Quasi-Monte Carlo, and Latin Hypercube Sampling), a variable time step algorithm, and a variable sample size algorithm. To compare the algorithms, we employ a variety of metrics designed specifically to analyze both computational efficiency and model accuracy. Our metrics include accuracy to compare the average predicted value to ground truth, mean absolute deviation to illustrate dispersion, specific percentile error to describe accuracy within a user-defined risk tolerance, and code run-time. To quantitatively analyze our results, we employ a use-case of degradation of a Lithium-ion battery. We use an electrochemistry-based model to describe the current health state of the battery, and implement our prediction algorithms to propagate forward in time until end-of-discharge (EOD) is reached. Notably, through this work it was found that none of our sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. We find that while the sampling methods are unique, the distributions they generate are similar, ultimately producing final predictions that are nearly identical. In exploring the effect of the time step within the prediction algorithm, we found that prediction accuracy was highly dependent on the time step used, and that implementing a variable time step within a particular prediction may provide an increase in computational efficiency while also maintaining prediction accuracy. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment can result in improved computation speed and maintained prediction accuracy. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency.

prognostics↗