Multiscale modeling of cruciform dwell tests with the uncertainty-quantified parametrically homogenized constitutive model
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Maloth, Thirupathi↗
SEARCH · Engineering Papers
Results for “parametric uncertainty”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Minimum-Variance Control Allocation Considering Parametric Model Uncertainty
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Jared A. Grauer↗
A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty
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Luke J Miller↗
Multi-Model and Multi-Scale Global Sensitivity Analysis for Identifying Controlling Processes of Complex Systems
An environmental model consists of multiple process level sub-models, and each sub-model represents a process that is key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this project develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance-based global sensitivity analysis to address uncertainty in process models and parameters. The new method yields three process sensitivity indices. The first one is called first-order process sensitivity index, and it is derived as a single summary measure of relative process importance. Evaluating the index is computationally expensive, because it relies in a Monte Carlo scheme that requires thousands and even millions of model executions. To reduce computational cost, this project develops a computationally efficient, quasi Monte Carlo method, and this method is presented in Chapter 2 of this report with and a numerical example for demonstration. The numerical example shows that the results of the quasi Monte Carlo method are substantially close to those of the full Monte Carlo method, but the computational cost of the quasi Monte Carlo method is only 0.7% of that of the full Monte Carlo method. The second index is called total-effect process sensitivity index, and it measures interactions between different processes. Therefore, this sensitivity index includes the first-order process sensitivity index, and can be used to identify influential processes. On the other hand, the total-effect process sensitivity index can also be used to screen non-influential processes. This is demonstrated by two numerical examples using the Sobol-G* functions and groundwater flow models that consider recharge process, geological process, and snowmelt process. The numerical examples shows that the total-effect process sensitivity index is more informative than the first-order process sensitivity. The derivation of the process sensitivity index and the numerical examples are discussed in Chapter 3. Chapter 4 presents two computationally efficient methods for screening non-influential processes to exclude them from further investigation. The two methods are the multi-model difference-based sensitivity (MMDS) analysis method, which can be implemented using the Latin Hypercube Sampling. The second one is the implementation of MMDS method using a binning method. The numerical example for the Sobol-G* function indicates the two methods are capable of identifying non-influential models, and the numerical examples for the groundwater flow and reactive transport show that the two methods are effective for groundwater problems. However, it should be noted that the two methods are numerical approximations, and they can only be used for screening non-influential processes, not for ranking importance of system processes. All the sensitivity analysis methods are implemented by developing python codes, and the codes are in a software called SAMMPY: a python package for process sensitivity analysis under multiple models. The SAMMPY design and structure are discussed in Chapter 5, and the package is released to the public for free download.
54 ENVIRONMENTAL SCIENCES↗
Robust Landing Using Time-to-Collision Measurement with Actuator Saturation
This paper considers a landing problem for an MAV that uses only a monocular camera for guidance. Although this sensor cannot measure the absolute distance to the target, by using optical flow algorithms, time-to-collision to the target is obtained. Existing work has applied a simple proportional feedback control to simple dynamics and demonstrated its potential. However, due to the singularity in the time-to-collision measurement around the target, this feedback could require an infinite control action. This paper extends the approach into nonlinear dynamics. In particular, we explicitly consider the saturation of the actuator and include the effect of the aerial drag. It is shown that the convergence to the target is guaranteed from a set of initial conditions, and the boundaries of such initial conditions in the state space are numerically obtained. The paper then introduces parametric uncertainties in the vehicle model and in the time-to-collision measurements. Using an argument similar to the nominal case, the robust convergence to the target is proven, but the region of attraction is shown to shrink due to the existence of uncertainties. The numerical simulation validates these theoretical results.
parametric uncertainty↗
Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis
There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.
Uncertainty quantification↗
Sequential Design of Experiments for Pilot Testing of Novel Solvent System
The CCSI2 program is supporting a six-month test campaign at the National Carbon Capture Center (NCCC) for evaluation of a novel water-lean solvent. This presentation describes CCSI2’s efforts in process modeling of the solvent system for both coal and natural gas-based flue gas sources and initial uncertainty quantification (UQ) work to estimate parametric uncertainty in key sub-models of interest (e.g., thermodynamics, mass transfer, reaction kinetics). Moreover, perspective is provided on how UQ and sequential design of experiments (SDoE) tools are used to assess the impact of model uncertainty on projected process performance, use this information to optimize data collection during the campaign, and refine process models through data collection. This framework is expected to reduce the overall model uncertainty, and thus risk associated with scale-up as the process moves towards commercialization.
Morgan, Joshua↗
SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method
Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.
Uncertainty Quantification↗
A Robust Control Design Framework for Substructure Models
A framework for designing control systems directly from substructure models and uncertainties is proposed. The technique is based on combining a set of substructure robust control problems by an interface stiffness matrix which appears as a constant gain feedback. Variations of uncertainties in the interface stiffness are treated as a parametric uncertainty. It is shown that multivariable robust control can be applied to generate centralized or decentralized controllers that guarantee performance with respect to uncertainties in the interface stiffness, reduced component modes and external disturbances. The technique is particularly suited for large, complex, and weakly coupled flexible structures.
Lim, Kyong B.↗
New bounds on parameter uncertainties for robust stability
The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.
Gao, Zhiqiang↗
Robust linear quadratic designs with respect to parameter uncertainty
The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.
Douglas, Joel↗
Quantum surrogate models for uncertainty quantification
Surrogate models are a critical ingredient to computation-based design and validation of many DOE mission-relevant physical systems. When first-principles computation of properties of a physical systems becomes pro hibitive, surrogate models are the only path towards achieving tasks such as uncertainty quantification (UQ), exploration of design space, and validation of design choices. In this project we have developed and demonstrated a new surro gate modeling paradigm for complex models that is data-driven, non-intrusive, and has the potential to be versatile and equipped with performance guaran tees. This combination of features is absent in existing surrogate modeling tools. The framework we have developed in this project exploits a quantum-classical correspondence to establish a quantum system that mimics the dynamics of the classical Hamiltonian system from which data in the form of temporal snapshots is provided. Since quantum dynamics propagates distributions over observables, the framework is naturally suited to propagation of epistemic uncertainties in the form of distributions over initial state and parametric uncertainties. In this project, we take the first step in establishing this novel framework by deriving a quantization and de-quantization procedure, demonstrating the accuracy of the quantum surrogate models these define using two model systems, and defining the next steps in maturing the framework towards a tool applicable to Sandia mission-relevant problems.
97 MATHEMATICS AND COMPUTING↗
Characterization and Valuation of the Uncertainty of Calibrated Parameters in Microsimulation Decision Models
We evaluated the implications of different approaches to characterize the uncertainty of calibrated parameters of microsimulation decision models (DMs) and quantified the value of such uncertainty in decision making. We calibrated the natural history model of CRC to simulated epidemiological data with different degrees of uncertainty and obtained the joint posterior distribution of the parameters using a Bayesian approach. We conducted a probabilistic sensitivity analysis (PSA) on all the model parameters with different characterizations of the uncertainty of the calibrated parameters. We estimated the value of uncertainty of the various characterizations with a value of information analysis. We conducted all analyses using high-performance computing resources running the Extreme-scale Model Exploration with Swift (EMEWS) framework. The posterior distribution had a high correlation among some parameters. The parameters of the Weibull hazard function for the age of onset of adenomas had the highest posterior correlation of -0.958. When comparing full posterior distributions and the maximum-a-posteriori estimate of the calibrated parameters, there is little difference in the spread of the distribution of the CEA outcomes with a similar expected value of perfect information (EVPI) of $\$$653 and $\$$685, respectively, at a willingness-to-pay (WTP) threshold of $\$$66,000 per quality-adjusted life year (QALY). Ignoring correlation on the calibrated parameters’ posterior distribution produced the broadest distribution of CEA outcomes and the highest EVPI of $\$$809 at the same WTP threshold. Different characterizations of the uncertainty of calibrated parameters affect the expected value of eliminating parametric uncertainty on the CEA. Ignoring inherent correlation among calibrated parameters on a PSA overestimates the value of uncertainty.
97 MATHEMATICS AND COMPUTING↗
Hard Constraints in Optimization Under Uncertainty
This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.
Crespo, Luis G.↗
Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges
In this paper, the problem of controlling systems with failures and faults is introduced, and an overview of recent work on direct adaptive control for compensation of uncertain actuator failures is presented. Actuator failures may be characterized by some unknown system inputs being stuck at some unknown (fixed or varying) values at unknown time instants, that cannot be influenced by the control signals. The key task of adaptive compensation is to design the control signals in such a manner that the remaining actuators can automatically and seamlessly take over for the failed ones, and achieve desired stability and asymptotic tracking. A certain degree of redundancy is necessary to accomplish failure compensation. The objective of adaptive control design is to effectively use the available actuation redundancy to handle failures without the knowledge of the failure patterns, parameters, and time of occurrence. This is a challenging problem because failures introduce large uncertainties in the dynamic structure of the system, in addition to parametric uncertainties and unknown disturbances. The paper addresses some theoretical issues in adaptive actuator failure compensation: actuator failure modeling, redundant actuation requirements, plant-model matching, error system dynamics, adaptation laws, and stability, tracking, and performance analysis. Adaptive control designs can be shown to effectively handle uncertain actuator failures without explicit failure detection. Some open technical challenges and research problems in this important research area are discussed.
Tao, Gang↗
Shock Layer Radiation Modeling and Uncertainty for Mars Entry
A model for simulating nonequilibrium radiation from Mars entry shock layers is presented. A new chemical kinetic rate model is developed that provides good agreement with recent EAST and X2 shock tube radiation measurements. This model includes a CO dissociation rate that is a factor of 13 larger than the rate used widely in previous models. Uncertainties in the proposed rates are assessed along with uncertainties in translational-vibrational relaxation modeling parameters. The stagnation point radiative flux uncertainty due to these flowfield modeling parameter uncertainties is computed to vary from 50 to 200% for a range of free-stream conditions, with densities ranging from 5e-5 to 5e-4 kg/m3 and velocities ranging from of 6.3 to 7.7 km/s. These conditions cover the range of anticipated peak radiative heating conditions for proposed hypersonic inflatable aerodynamic decelerators (HIADs). Modeling parameters for the radiative spectrum are compiled along with a non-Boltzmann rate model for the dominant radiating molecules, CO, CN, and C2. A method for treating non-local absorption in the non-Boltzmann model is developed, which is shown to result in up to a 50% increase in the radiative flux through absorption by the CO 4th Positive band. The sensitivity of the radiative flux to the radiation modeling parameters is presented and the uncertainty for each parameter is assessed. The stagnation point radiative flux uncertainty due to these radiation modeling parameter uncertainties is computed to vary from 18 to 167% for the considered range of free-stream conditions. The total radiative flux uncertainty is computed as the root sum square of the flowfield and radiation parametric uncertainties, which results in total uncertainties ranging from 50 to 260%. The main contributors to these significant uncertainties are the CO dissociation rate and the CO heavy-particle excitation rates. Applying the baseline flowfield and radiation models developed in this work, the radiative heating for the Mars Pathfinder probe is predicted to be nearly 20 W/cm2. In contrast to previous studies, this value is shown to be significant relative to the convective heating.
Johnston, Christopher O.↗
Uncertainty Quantification of the FUN3D-Predicted NASA CRM Flutter Boundary
A nonintrusive point collocation method is used to propagate parametric uncertainties of the flexible Common Research Model, a generic transport configuration, through the unsteady aeroelastic CFD solver FUN3D. A range of random input variables are considered, including atmospheric flow variables, structural variables, and inertial (lumped mass) variables. UQ results are explored for a range of output metrics (with a focus on dynamic flutter stability), for both subsonic and transonic Mach numbers, for two different CFD mesh refinements. A particular focus is placed on computing failure probabilities: the probability that the wing will flutter within the flight envelope.
Stanford, Bret K.↗
Standard Model prediction of the Bc lifetime
Applying an operator product expansion approach we update the Standard Model prediction of the B c lifetime from over 20 years ago. The non-perturbative velocity expansion is carried out up to third order in the relative velocity of the heavy quarks. The scheme dependence is studied using three different mass schemes for the b ¯ and c quarks, resulting in three different values consistent with each other and with experiment. Special focus has been laid on renormalon cancellation in the computation. Uncertainties resulting from scale dependence, neglecting the strange quark mass, non-perturbative matrix elements and parametric uncertainties are discussed in detail. The resulting uncertainties are still rather large compared to the experimental ones, and therefore do not allow for clear-cut conclusions concerning New Physics effects in the B c decay.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗