Structural model choices regularly overshadow parametric uncertainty in agent-based simulations of household flood risk outcomes
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Uncertainties of a large space system (LSS) can be deterministic or stochastic in nature. The former may result in, for example, an energy spillover problem by which the interaction between unmodeled modes and controls may cause system instability. The stochastic uncertainties are responsible for mode localization and estimation errors, etc. We will address the effects of uncertainties on structural model formulation, use of available test data to verify and modify analytical models before orbiting, and how the system model can be further improved in the on-orbit environment.
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The focus is on a flexible structure experiment developed at the California Institute of Technology. The main thrust of the experiment is to address the identification and robust control issues associated with large space structures by capturing their characteristics in the laboratory. The design, modeling, identification and control objectives will be discussed. Also, the subject of uncertainty in structural plant models and the frequency shaping of performance objectives will be expounded upon. Theoretical and experimental results of control laws designed using the identified model and uncertainty descriptions will be presented.
The design, analysis, and simulation of a control law that guarantees a fine pointing performance under external disturbances and model uncertainties are investigated. The authors examine the achievable performance and modeling errors for the control-structure interaction (CSI) evolutionary model structure and highlight the importance of accurate knowledge of structural frequencies and damping values for very lightly damped structures. Numerical results indicate that a limited but significant line-of-sight pointing performance robustness can be attained in spite of modeled structured and unstructured uncertainties in the system. The simulation results reported demonstrate typical performance levels, types of uncertainties and their magnitudes, and design tradeoffs for a realistic laboratory model of a large flexible space structure.
Turbulent boundary layer (TBL) noise is considered a primary factor in the interior noise experienced by passengers aboard commercial airliners. There have been numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a challenge since the physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions have been assumed; however, realistic panels likely display a range of varying boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of actuators and sensors required to achieve the desired control. The impact of model uncertainties, uncertain boundary conditions in particular, on the selection of actuator and sensor locations for structural acoustic control are considered herein. Results from this research effort indicate that it is possible to optimize the design of actuator and sensor location and aperture, which minimizes the impact of boundary conditions on the desired structural acoustic control.
A structural uncertainty validation study for a large-scale, fire-engulfed, elevated object subjected to crosswind is presented to establish the credibility of a high-fidelity, low-Mach, turbulent reacting flow wall-modeled large-eddy simulation (WMLES) approach that includes multiphysics coupling to participating media radiation and conjugate heat transfer. To establish that WMLES can accurately predict surface quantities including drag and pressure coefficient in the low-Mach crosswind regime, a foundational elevated isothermal cylinder validation case is presented at a similar gap-to-diameter ratio of 0.25, spanning the subcritical to supercritical drag regime (Re 𝐷 = 1.1 × 10 5 and 4.3 × 10 5 , respectively). Here, this study exercised both static and dynamic coefficient LES (Smagorinsky and 𝑘 sgs ) with both local and exchange-based velocity sampling. Results showcase that the drag crisis (or the sudden drop in drag coefficient at increased Re 𝐷 ) is well captured when using an exchange-based dynamic coefficient WMLES methodology, while noting lack of mesh convergence and overall drag and pressure coefficient predictively when using a static coefficient, local velocity sampling WMLES. For the 𝒪(10) m JP-8 liquid pool fire crosswind validation study presented, two experimental crosswind configurations (2 m/s and 9.5 m/s) are showcased for a fire-engulfed mock fuselage roughly 4 m in diameter. Using the best model-form practices identified in the isothermal study, dynamic coefficient 𝑘 sgs exchange-based WMLES fire validation findings demonstrate accurate peak irradiation and skin temperature predictions as a function of crosswind magnitude. Excessive yaw in the low-crosswind fuselage configuration, consistent with experimental findings, captured a significant predicted asymmetry in flame attachment and heat flux toward the downwind cylindrical cap—indicative of axial vortex structures transporting the flame along the upper and lower fuselage leeward surface. All fire mesh resolution simulations captured the experimental finding that as crosswind increased, predicted flame shape and peak irradiation magnitude onto the fuselage transitioned from a windward to a leeward cylinder location due to the migration of the upper- to lower-shear fuel/air mixing layer thereby demonstrating the novelty, significance, and credibility of this high-fidelity WMLES reacting flow framework.
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.
We propose a surrogate modeling framework based on dimension reduction to facilitate the quantification of seismic risk of structural systems in performance-based earthquake engineering. The framework adopts incremental dynamic analysis (IDA) for addressing hazard variability, and promotes significant computational efficiency improvement for propagating epistemic uncertainties associated with the structural models. It utilizes both linear and nonlinear dimension reduction approaches, equipped with inverse mappings, to learn a functional between the input parameter space (e.g., the epistemic uncertainties of the structure) to the high-dimensional output space created through the IDA implementation across different ground motions and seismic intensity levels. Polynomial chaos expansion is adopted as the surrogate model to learn this functional in the reduced space. A nine-story steel moment-resisting frame with uncertain structural properties is used as a testbed. Furthermore, we select the seismic fragility curves as a measure of the structure’s seismic performance, since it provides an estimate of the probability of entering specified damage states for given levels of ground shaking.
The Pliocene Model Intercomparison Project (PlioMIP) is a co-ordinated international climate modelling initiative to study and understand climate and environments of the Late Pliocene, as well as their potential relevance in the context of future climate change. PlioMIP examines the consistency of model predictions in simulating Pliocene climate and their ability to reproduce climate signals preserved by geological climate archives. Here we provide a description of the aim and objectives of the next phase of the model intercomparison project (PlioMIP Phase 2), and we present the experimental design and boundary conditions that will be utilized for climate model experiments in Phase 2. Following on from PlioMIP Phase 1, Phase 2 will continue to be a mechanism for sampling structural uncertainty within climate models. However, Phase 1 demonstrated the requirement to better understand boundary condition uncertainties as well as uncertainty in the methodologies used for data-model comparison. Therefore, our strategy for Phase 2 is to utilize state-of-the-art boundary conditions that have emerged over the last 5 years. These include a new palaeogeographic reconstruction, detailing ocean bathymetry and land-ice surface topography. The ice surface topography is built upon the lessons learned from offline ice sheet modelling studies. Land surface cover has been enhanced by recent additions of Pliocene soils and lakes. Atmospheric reconstructions of palaeo-CO2 are emerging on orbital timescales, and these are also incorporated into PlioMIP Phase 2. New records of surface and sea surface temperature change are being produced that will be more temporally consistent with the boundary conditions and forcings used within models. Finally we have designed a suite of prioritized experiments that tackle issues surrounding the basic understanding of the Pliocene and its relevance in the context of future climate change in a discrete way.
This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.
This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.
The control system design for a Single Stage To Orbit (SSTO) air breathing vehicle will be central to a successful mission because a precise ascent trajectory will preserve narrow payload margins. The air breathing propulsion system requires the vehicle to fly roughly halfway around the Earth through atmospheric turbulence. The turbulence, the high sensitivity of the propulsion system to inlet flow conditions, the relatively large uncertainty of the parameters characterizing the vehicle, and continuous acceleration make the problem especially challenging. Adequate stability margins must be provided without sacrificing payload mass since payload margins are critical. Therefore, a multivariable control theory capable of explicitly including both uncertainty and performance is needed. The H(infinity) controller in general provides good robustness but can result in conservative solutions for practical problems involving structured uncertainty. Structured singular value mu framework for analysis and synthesis is potentially much less conservative and hence more appropriate for problems with tight margins. An SSTO control system requires: highly accurate tracking of velocity and altitude commands while limiting angle-of-attack oscillations, minimized control power usage, and a stabilized vehicle when atmospheric turbulence and system uncertainty are present. The controller designs using H(infinity) and mu-synthesis procedures were compared. An integrated flight/propulsion dynamic mathematical model of a conical accelerator vehicle was linearized as the vehicle accelerated through Mach 8. Vehicle acceleration through the selected flight condition gives rise to parametric variation that was modeled as a structured uncertainty. The mu-analysis approach was used in the frequency domain to conduct controller analysis and was confirmed by time history plots. Results demonstrate the inherent advantages of the mu framework for this class of problems.
Crop models are often employed to project crop yields under changing conditions such as global warming and associated management change for adaptation. Multi-model ensembles are promoted to enhance the robustness of projections, but questions remain on what causes often large differences between projections of individual models. Global Gridded Crop Models (GGCMs) are especially exposed to this question when applied for assessing climate change impacts, adaptation, environmental impacts of agricultural production, because their results are used in downstream analyses, such as in integrated assessment or economic modeling for projecting future land-use change. Even though global gridded crop models are often based on detailed field-scale models or have implemented similar modeling principles in other ecosystem models, global-scale models are subject to substantial uncertainties from both model structure and parametrization as well as from calibration and input data quality. AgMIP’s Global Gridded Crop Model Intercomparison (GGCMI) has thus set out to intercompare GGCMs in order to evaluate model performance, describe model uncertainties, identify inconsistencies within the ensemble and underlying reasons, and to ultimately improve models and modeling capacities. In phase 2 of the GGCMI activities, 12 modeling groups followed a modeling protocol that asked for up to 1404 31-year global simulations at 0.5 arc-degree spatial resolution to assess models’ sensitivities to changes in carbon dioxide (C; 4 different levels) temperature (T; 7 different offset levels), water supply (W; 9 levels), and nitrogen (N; 3 levels), the so-called CTWN experiment (Franke et al. 2020; http://dx.doi.org/10.5194/gmd-13-2315-2020). We here present analyses of model response types using impact response surfaces along the C, T, W, and N dimensions, respectively and collectively. Doing so, we can understand differences in simulated responses per driver rather than aggregated changes in yields. We find that models’ sensitivities to the individual driver dimensions are substantially different and often more different across models than across regions. A cluster analysis finds regional and model-specific patterns. There is some agreement across models with respect to the spatial patterns of response types but strong differences in the distribution of response type clusters across models suggests that models need to undergo further scrutiny. We suggest establishing standards in model process evaluation not only against historical dynamics but also against dedicated experiments across the CTWN dimensions.
This document is motivated by likely needs of the Quesst mission community response tests, which will culminate in data collection and estimation of dose-response regression relationships for consideration by domestic and international aviation regulators. Furthermore, basic research questions evaluating interactions between rates of community annoyance, dose levels, and indicators of the presence of rattle, vibration, and startle hinge on hypothesis testing in the context of regression models. For a variety of reasons, noise doses may be known only imprecisely and may not reflect the actual level experienced by responding subjects. These differences between true dose and estimated dose, be they systematic or random, constitute covariate measurement error. Available statistics literature speaks to the impacts of measurement error on regression models, both in terms of bias in estimated coefficients and predicted values, and in terms of the loss of statistical power for hypothesis testing. Given the particulars of a categorical annoyance response variable and a continuous noise dose predictor variable subject to measurement error during testing, the emphasis of this report is on findings and methods pertinent to generalized linear (and mixed) models likely to be employed during the Quesst mission community tests. We reach the following conclusions: 1. Of four reviewed methods, structural Bayesian measurement error models and simulation extrapolation (SIMEX) may be the most readily applicable to Quesst mission community noise study objectives. 2. If warranted, a linear measurement model can help model systematic sources of measurement error that the classical measurement error does not. 3. For its ready implementation and small additional input requirements, simulation extrapolation may be ideally suited for addressing secondary research questions involving interactions between annoyance, noise dose, and other factors through hypothesis testing. 4. For their flexibility and ability to propagate uncertainty, structural Bayesian hierarchical models have great appeal for mission purposes; some care may be needed in developing appropriate probability models describing actual noise exposure during testing. An annotated bibliography logs additional papers and resources that may be of value to analysts in other projects and disciplines.
The Forest Light (FLIGHT) radiative transfer model was used to examine the uncertainty of vegetation structure measurements from NASA's planned ICESat-2 photon counting light detection and ranging (LiDAR) instrument across a synthetic Larix forest gradient in the taiga-tundra ecotone. The simulations demonstrate how measurements from the planned spaceborne mission, which differ from those of previous LiDAR systems, may perform across a boreal forest to non-forest structure gradient in globally important ecological region of northern Siberia. We used a modified version of FLIGHT to simulate the acquisition parameters of ICESat-2. Modeled returns were analyzed from collections of sequential footprints along LiDAR tracks (link-scales) of lengths ranging from 20 m-90 m. These link-scales traversed synthetic forest stands that were initialized with parameters drawn from field surveys in Siberian Larix forests. LiDAR returns from vegetation were compiled for 100 simulated LiDAR collections for each 10 Mg · ha(exp -1) interval in the 0-100 Mg · ha(exp -1) above-ground biomass density (AGB) forest gradient. Canopy height metrics were computed and AGB was inferred from empirical models. The root mean square error (RMSE) and RMSE uncertainty associated with the distribution of inferred AGB within each AGB interval across the gradient was examined. Simulation results of the bright daylight and low vegetation reflectivity conditions for collecting photon counting LiDAR with no topographic relief show that 1-2 photons are returned for 79%-88% of LiDAR shots. Signal photons account for approximately 67% of all LiDAR returns, while approximately 50% of shots result in 1 signal photon returned. The proportion of these signal photon returns do not differ significantly (p greater than 0.05) for AGB intervals greater than 20 Mg · ha(exp -1). The 50m link-scale approximates the finest horizontal resolution (length) at which photon counting LiDAR collection provides strong model fits and minimizes forest structure uncertainty in the synthetic Larix stands. At this link-scale AGB greater than 20 Mg · ha(exp -1) has AGB error from 20-50% at the 95% confidence level. These results suggest that the theoretical sensitivity of ICESat-2 photon counting LiDAR measurements alone lack the ability to consistently discern differences in inferred AGB at 10 Mg · ha(exp -1) intervals in sparse forests characteristic of the taiga-tundra ecotone.
Focal Area 3: Explainable AI Our confidence in the projections made by Earth System Models (ESMs) depends on understanding them to be, in some important respects, faithful representations of the Earth system. Here we present an “explainable Artificial Intelligence (AI)” method that allows us to uncover the dynamical structure of the observed and modeled Earth system, discover hidden links across wide spatiotemporal scales, target model development efforts at poorly-represented dynamics, and optimize observed or modeled data collection to maximize predictive information. Science Challenge: Dynamical system science for the Earth system poses unique challenges given the large degree of internal climate variability. Thus, tools that help us understand how ESMs succeed and fail at representing these dynamics are crucial, particularly in relation to the observed system. Furthermore, the computational and memory constraints on ESM data output motivate in situ analysis of ESM dynamics, including automatic detection of dynamical shifts. Also, of key importance are procedures that leverage ESMs to optimize observational campaigns for improving process representation, reducing structural uncertainty and improving model skill.
In a warming climate, wildfires are becoming increasingly common, especially in semi-arid environments. Wildfires can disrupt forest ecosystems and induce changes to the land surface. Collectively, these impacts can alter the hydrologic response of a catchment following a fire, resulting in increased potential for surface runoff, reduced evapotranspiration, and, ultimately, a higher risk for flash flooding and mass wasting. The timescale for post-fire recovery of hydrological processes to return to pre-fire conditions is not well established due to the lack of ground measurements. Accurate characterization of fire impacts on hydrologic response is also challenging to simulate, given the complex interplay of various processes. Here, we present a generalized framework to quantify wildfire impacts on runoff generation. We consider the vegetation and soil disturbances as the primary contributors to post-fire floods. Using an ensemble modeling structure to account for parameter uncertainty and consider model sensitivity, remotely sensed leaf area index (LAI) is assimilated into a land surface model (LSM) to simulate vegetation disturbance, and the maximum land surface saturation LSM parameter is decreased to parameterize the soil disturbance following observed fires. We evaluated the impacts of fire-induced changes to LAI and soil saturation on hydrologic states like runoff and evapotranspiration. Analysis of two events in central California shows that 1) the LAI assimilation has a greater impact on water balance; and 2) the soil scheme captures a range of outcomes, with substantial impacts on surface runoff for some ensemble members, which could affect flood potential.