MONTE Python for Deep Space Navigation; or Astrodynamic Computing with MONTE
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Smith, Jonathan↗
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The X-43A Six Degree of Freedom Monte Carlo Analysis
This report provides an overview of the Hyper-X research vehicle Monte Carlo analysis conducted with the six-degree-of-freedom simulation. The methodology and model uncertainties used for the Monte Carlo analysis are presented as permitted. In addition, the process used to select hardware validation test cases from the Monte Carlo data is described. The preflight Monte Carlo analysis indicated that the X-43A control system was robust to the preflight uncertainties and provided the Hyper-X project an important indication that the vehicle would likely be successful in accomplishing the mission objectives. The X-43A in-flight performance is compared to the preflight Monte Carlo predictions and shown to exceed the Monte Carlo bounds in several instances. Possible modeling shortfalls are presented that may account for these discrepancies. The flight control laws and guidance algorithms were robust enough as a result of the preflight Monte Carlo analysis that the unexpected in-flight performance did not have undue consequences. Modeling and Monte Carlo analysis lessons learned are presented.
Baumann, Ethan↗
The X-43A Six Degree of Freedom Monte Carlo Analysis
This report provides an overview of the Hyper-X research vehicle Monte Carlo analysis conducted with the six-degree-of-freedom simulation. The methodology and model uncertainties used for the Monte Carlo analysis are presented as permitted. In addition, the process used to select hardware validation test cases from the Monte Carlo data is described. The preflight Monte Carlo analysis indicated that the X-43A control system was robust to the preflight uncertainties and provided the Hyper-X project an important indication that the vehicle would likely be successful in accomplishing the mission objectives. The X-43A inflight performance is compared to the preflight Monte Carlo predictions and shown to exceed the Monte Carlo bounds in several instances. Possible modeling shortfalls are presented that may account for these discrepancies. The flight control laws and guidance algorithms were robust enough as a result of the preflight Monte Carlo analysis that the unexpected in-flight performance did not have undue consequences. Modeling and Monte Carlo analysis lessons learned are presented.
Baumann, Ethan↗
Development of Monte Carlo Capability for Orion Parachute Simulations
Parachute test programs employ Monte Carlo simulation techniques to plan testing and make critical decisions related to parachute loads, rate-of-descent, or other parameters. This paper describes the development and use of a MATLAB-based Monte Carlo tool for three parachute drop test simulations currently used by NASA. The Decelerator System Simulation (DSS) is a legacy 6 Degree-of-Freedom (DOF) simulation used to predict parachute loads and descent trajectories. The Decelerator System Simulation Application (DSSA) is a 6-DOF simulation that is well suited for modeling aircraft extraction and descent of pallet-like test vehicles. The Drop Test Vehicle Simulation (DTVSim) is a 2-DOF trajectory simulation that is convenient for quick turn-around analysis tasks. These three tools have significantly different software architectures and do not share common input files or output data structures. Separate Monte Carlo tools were initially developed for each simulation. A recently-developed simulation output structure enables the use of the more sophisticated DSSA Monte Carlo tool with any of the core-simulations. The task of configuring the inputs for the nominal simulation is left to the existing tools. Once the nominal simulation is configured, the Monte Carlo tool perturbs the input set according to dispersion rules created by the analyst. These rules define the statistical distribution and parameters to be applied to each simulation input. Individual dispersed parameters are combined to create a dispersed set of simulation inputs. The Monte Carlo tool repeatedly executes the core-simulation with the dispersed inputs and stores the results for analysis. The analyst may define conditions on one or more output parameters at which to collect data slices. The tool provides a versatile interface for reviewing output of large Monte Carlo data sets while preserving the capability for detailed examination of individual dispersed trajectories. The Monte Carlo tool described in this paper has proven useful in planning several Crew Exploration Vehicle parachute tests.
Moore, James W.↗
Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates
A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.
Barth, Timothy↗
Monte Carlo simulation of particle acceleration at astrophysical shocks
A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.
Campbell, Roy K.↗
Radiative interactions in multi-dimensional chemically reacting flows using Monte Carlo simulations
The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.
Liu, Jiwen↗
Monte Carlo Methods in Materials Science Based on FLUKA and ROOT
A comprehensive understanding of mitigation measures for space radiation protection necessarily involves the relevant fields of nuclear physics and particle transport modeling. One method of modeling the interaction of radiation traversing matter is Monte Carlo analysis, a subject that has been evolving since the very advent of nuclear reactors and particle accelerators in experimental physics. Countermeasures for radiation protection from neutrons near nuclear reactors, for example, were an early application and Monte Carlo methods were quickly adapted to this general field of investigation. The project discussed here is concerned with taking the latest tools and technology in Monte Carlo analysis and adapting them to space applications such as radiation shielding design for spacecraft, as well as investigating how next-generation Monte Carlos can complement the existing analytical methods currently used by NASA. We have chosen to employ the Monte Carlo program known as FLUKA (A legacy acronym based on the German for FLUctuating KAscade) used to simulate all of the particle transport, and the CERN developed graphical-interface object-oriented analysis software called ROOT. One aspect of space radiation analysis for which the Monte Carlo s are particularly suited is the study of secondary radiation produced as albedoes in the vicinity of the structural geometry involved. This broad goal of simulating space radiation transport through the relevant materials employing the FLUKA code necessarily requires the addition of the capability to simulate all heavy-ion interactions from 10 MeV/A up to the highest conceivable energies. For all energies above 3 GeV/A the Dual Parton Model (DPM) is currently used, although the possible improvement of the DPMJET event generator for energies 3-30 GeV/A is being considered. One of the major tasks still facing us is the provision for heavy ion interactions below 3 GeV/A. The ROOT interface is being developed in conjunction with the CERN ALICE (A Large Ion Collisions Experiment) software team through an adaptation of their existing AliROOT (ALICE Using ROOT) architecture. In order to check our progress against actual data, we have chosen to simulate the ATIC14 (Advanced Thin Ionization Calorimeter) cosmic-ray astrophysics balloon payload as well as neutron fluences in the Mir spacecraft. This paper contains a summary of status of this project, and a roadmap to its successful completion.
Pinsky, Lawrence↗
Mission Analysis, Operations, and Navigation Toolkit Environment (Monte) Version 040
Monte is a software set designed for use in mission design and spacecraft navigation operations. The system can process measurement data, design optimal trajectories and maneuvers, and do orbit determination, all in one application. For the first time, a single software set can be used for mission design and navigation operations. This eliminates problems due to different models and fidelities used in legacy mission design and navigation software. The unique features of Monte 040 include a blowdown thruster model for GRAIL (Gravity Recovery and Interior Laboratory) with associated pressure models, as well as an updated, optimalsearch capability (COSMIC) that facilitated mission design for ARTEMIS. Existing legacy software lacked the capabilities necessary for these two missions. There is also a mean orbital element propagator and an osculating to mean element converter that allows long-term orbital stability analysis for the first time in compiled code. The optimized trajectory search tool COSMIC allows users to place constraints and controls on their searches without any restrictions. Constraints may be user-defined and depend on trajectory information either forward or backwards in time. In addition, a long-term orbit stability analysis tool (morbiter) existed previously as a set of scripts on top of Monte. Monte is becoming the primary tool for navigation operations, a core competency at JPL. The mission design capabilities in Monte are becoming mature enough for use in project proposals as well as post-phase A mission design. Monte has three distinct advantages over existing software. First, it is being developed in a modern paradigm: object- oriented C++ and Python. Second, the software has been developed as a toolkit, which allows users to customize their own applications and allows the development team to implement requirements quickly, efficiently, and with minimal bugs. Finally, the software is managed in accordance with the CMMI (Capability Maturity Model Integration), where it has been ap praised at maturity level 3.
Sunseri, Richard F.↗
CFD 2030 Grand Challenge: CFD-in-the-Loop Monte Carlo Flight Simulation for Space Vehicle Design
Flight qualification of space vehicles is markedly different from those typically employed for aircraft. The concept of an extensive flight test campaign for a space vehicle does not exist, and vehicle designers must look to alternative techniques for demonstrating robust and reliable performance of their vehicles prior to operational flight. A space vehicle may undergo only a handful of flight tests in its development cycle, with each flight representing a drastically different flight phase or flight configuration. For instance, NASA’s Space Launch System (SLS) launch vehicle and Orion spacecraft will only see a total of four flight demonstrations before flying a crew on its first operational mission, and each flight demonstrates a unique vehicle configuration and/or set of flight conditions. The SLS will be flown only one time before it becomes operational (Artemis 1). The Orion spacecraft Crew Module (CM) will have been tested twice, once on a Delta IV launch vehicle (Exploration Flight Test 1) and once as a fully integrated system with the SLS launch vehicle (Artemis 1). The Orion Launch abort system will have been tested twice, once in a pad abort scenario (Pad Abort 1) and once in an inflight abort scenario (Ascent Abort 2) on a modified Peacekeeper booster. Both of these latter tests involve only a boiler plate CM, not a functional Orion spacecraft. Thus, unlike aircraft, there is very little opportunity for engineers to assess and evaluate their preflight predictions. Instead, space vehicle designers rely on Monte Carlo flight simulations with detailed dispersions of predicted nominal flight behavior to determine how robust their design is to errors and uncertainties in the flight conditions their vehicle may encounter. These Monte Carlo analyses entail thousands of trajectory simulations to demonstrate that the vehicle can meet design requirements at a specified level of reliability. From an aerodynamics and aerothermodynamics perspective, these trajectory simulations are fueled by an extensive aerodynamic database that covers the complete range of expected flight conditions, vehicle configurations, and flight attitudes expected in a given mission. Today, these databases amount to a table of engineering parameters that can be quickly interrogated by the trajectory simulator. The aerodynamic and aerothermodynamic databases are assembled via a series of ground tests, empirical and analytical analysis, physics-based computational analysis, applicable past flight performance data, and in some cases, engineering judgment. These databases generally take years to assemble for a new space vehicle system and in the case of SLS/Orion, over a decade of test and analysis have been expended to develop the extensive databases required to cover the myriad of configurations and potential flight conditions required for the system. Recently, it has been proposed that Computational Fluid Dynamic (CFD) and computing capability may be reaching a point where it is foreseeable that CFD could be integrated directly into the production trajectory simulation tools used to design NASA’s space vehicles. To demonstrate this, NASA has embarked on two demonstrations of this type of capability, one where six degree of freedom flight trajectory simulation equations are embedded in an existing CFD solver and another where a production CFD solver is loosely coupled with a production trajectory simulation tool. These efforts represent an initial demonstration of a future approach to flight trajectory simulation, but they are a far cry from the capability required to perform a full-up CFD-in-the-loop Monte Carlo trajectory simulation. Therefore, this represents a viable grand challenge for computational methods addressing space vehicle design and development. The final paper/presentation will discuss the many hurdles, beyond simply raw computational power, to realizing this grand challenge and how they map directly to the CFD Vision 2030 ojectives. Among these are the wide range of flight conditions, including accelerating/decelerating flight, encountered by a space vehicle during launch and/or entry. The vehicle can also encounter numerous configuration changes, some of which can be quite drastic, during the course of its flight, so robust, automated geometry modeling, grid generation, and adaptation will play a huge role in reaching this goal. Multiply this by 1000’s of trajectory simulations occurring simultaneously in a given Monte Carlo analysis, and the problem readily scales to absorb virtually any size of supercomputer envisioned today. The concept of CFD-in-the-loop Monte Carlo trajectory simulation poses a formidable challenge for emerging and future computing systems, and it has the potential to shave years off the development cycle for aerodynamic and aerothermodynamic performance predictions as compared to today’s space vehicle design approach.
CFD 2030↗
A modified Monte Carlo model for the ionospheric heating rates.
A Monte Carlo method is adopted as a basis for the derivation of the photoelectron-heat input into the ionospheric plasma. Since a great number of Monte Carlo runs are required normally for the computation of the heating rates, this approach is modified in an attempt to minimize the computation time. The heat-input distributions are computed for arbitrarily small source elements that are spaced apart at distances corresponding to the photoelectron dissipation range. By means of a nonlinear interpolation procedure their individual heating-rate distributions are utilized to produce synthetic ones that fill the gaps between the Monte Carlo generated distributions. By varying these gaps and the corresponding number of Monte Carlo runs the accuracy of the results is tested to verify the validity of this procedure. It is concluded that this model can reduce the computation time by as much as an order of magnitude, thus improving the feasibility of including Monte Carlo calculations in self-consistent ionosphere models.
Mayr, H. G.↗
Vectorized Monte Carlo methods for reactor lattice analysis
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Brown, F. B.↗
Independent pixel and Monte Carlo estimates of stratocumulus albedo
Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.
Cahalan, Robert F.↗
Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures
The last decade has seen tremendous growth in cloud dynamical and microphysical models that are able to simulate storms and storm systems with very high spatial resolution, typically of the order of a few kilometers. The fairly realistic distributions of cloud and hydrometeor properties that these models generate has in turn led to a renewed interest in the three-dimensional microwave radiative transfer modeling needed to understand the effect of cloud and rainfall inhomogeneities upon microwave observations. Monte Carlo methods, and particularly backwards Monte Carlo methods have shown themselves to be very desirable due to the quick convergence of the solutions. Unfortunately, backwards Monte Carlo methods are not well suited to treat polarized radiation. This study reviews the existing Monte Carlo methods and presents a new polarized Monte Carlo radiative transfer code. The code is based on a forward scheme but uses aliasing techniques to keep the computational requirements equivalent to the backwards solution. Radiative transfer computations have been performed using a microphysical-dynamical cloud model and the results are presented together with the algorithm description.
Kummerow, Christian↗
Uncertainty Optimization Applied to the Monte Carlo Analysis of Planetary Entry Trajectories
Recently, strong evidence of liquid water under the surface of Mars and a meteorite that might contain ancient microbes have renewed interest in Mars exploration. With this renewed interest, NASA plans to send spacecraft to Mars approx. every 26 months. These future spacecraft will return higher-resolution images, make precision landings, engage in longer-ranging surface maneuvers, and even return Martian soil and rock samples to Earth. Future robotic missions and any human missions to Mars will require precise entries to ensure safe landings near science objective and pre-employed assets. Potential sources of water and other interesting geographic features are often located near hazards, such as within craters or along canyon walls. In order for more accurate landings to be made, spacecraft entering the Martian atmosphere need to use lift to actively control the entry. This active guidance results in much smaller landing footprints. Planning for these missions will depend heavily on Monte Carlo analysis. Monte Carlo trajectory simulations have been used with a high degree of success in recent planetary exploration missions. These analyses ascertain the impact of off-nominal conditions during a flight and account for uncertainty. Uncertainties generally stem from limitations in manufacturing tolerances, measurement capabilities, analysis accuracies, and environmental unknowns. Thousands of off-nominal trajectories are simulated by randomly dispersing uncertainty variables and collecting statistics on forecast variables. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecasts outputs. It lacks a mechanism to affect or alter the uncertainties based on the forecast results. If the results are unacceptable, the current practice is to use an iterative, trial-and-error approach to reconcile discrepancies. Therefore, an improvement to the Monte Carlo analysis is needed that will allow the problem to be worked in reverse. In this way, the largest allowable dispersions that achieve the required mission objectives can be determined quantitatively.
Olds, John↗
MONTE Python for Deep Space Navigation
The Mission Analysis, Operations, and Navigation Toolkit Environment (MONTE) is the Jet Propulsion Laboratory’s (JPL) signature astrodynamic computing platform. It was built to support JPL’s deep space exploration program, and has been used to fly robotic spacecraft to Mars, Jupiter, Saturn, Ceres, and many solar system small bodies. At its core, MONTE consists of low-level astrodynamic libraries that are written in C++ and presented to the end user as an importable Python language module. These libraries form the basis on which Python-language applications are built for specific astrodynamic applications, such as trajectory design and optimization, orbit determination, flight path control, and more. The first half of this paper gives context to the MONTE project by outlining its history, the field of deep space navigation and where MONTE fits into the current Python landscape. The second half gives an overview of the main MONTE libraries and provides a narrative example of how it can be used for astrodynamic analysis.
aerospace↗
MONTE for Orbit Determination
Monte is the Jet Propulsion Laboratory’s (JPL) signature astrodynamic computing platform. Its main interface is a collection of Python-language libraries that can be used either for one-o analyses or to build high-quality software applications. Perhaps nowhere is Monte’s versatility and excellence better demonstrated than in its use for operational orbit determination (OD). Over the period from 2007 to 2016, Monte was the prime OD solution for fourteen JPL flight projects, and secondary for seven non-JPL projects. These missions span the range of Solar System destinations and operational protocols, yet each were successfully serviced by Monte’s flexible OD library. This paper reviews the missions on which Monte has been used for OD, with an eye toward pointing out the di erent ways it has been deployed to solve unique problems. It also gives an outline of the main elements of the orbit determination library and how they work together to navigate flight missions.
Martin-Mur, Tomas↗
Uncertainty Reduction With Multi-Model Monte Carlo for Crystal Plasticity Simulations of Additively Manufactured Metals
In this work, multi-model Monte Carlo estimators are developed to reduce uncertainty in quantities of interest (QoIs) extracted from crystal plasticity simulations of additively manufactured (AM) metals. A significant concern in AM parts is uncertainty in mechanical properties caused in part by complex microstructures that arise from the AM process. Quantifying uncertainty in microstructure-sensitive behavior using experiments alone is costly, especially when mechanical allowables must be established. Quantitative relationships among microstructure, micromechanical metrics like slip accumulation, crack initiation, and failure are also difficult to capture with limited experiments. Crystal plasticity material models instead enable computational prediction of micromechanical stress and strain fields given a discretized microstructure. However, high-fidelity finely discretized crystal plasticity simulations are computationally expensive, while lower-fidelity models are less accurate and generally biased, making uncertainty quantification and reduction computationally difficult as well. Multi-model Monte Carlo methods leverage correlations between high- and low-fidelity models to produce unbiased estimators for QoIs with reduced uncertainty relative to standard Monte Carlo. Crystal plasticity QoIs considered in this work include yield strength and the mean and extreme values of micromechanical fields that are relevant to crack initiation. Multi-model Monte Carlo estimators are developed for each individual QoI and several groups of QoIs. The results of this work establish relationships among model correlations, sample allocation, and uncertainty reduction for different combinations of QoIs and demonstrate a trend of less uncertainty reduction as QoIs become more sensitive to local microstructure. Limitations from using pilot samples to estimate model covariances and train low-fidelity models are also addressed. The uncertainty reduction achieved by multi-model Monte Carlo is an important step toward using computational mechanics models to predict microstructure-sensitive crack initiation and failure in AM parts.
uncertainty quantification↗