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A method is presented for improving the tolerance of LQG controllers to parameter errors. The improvement is achieved by introducing terms reflecting the structure of the errors into the LQR cost function and the process and measurement noise models. Adjusting the sizes of these additional terms permits a tradeoff between robustness and nominal performance.
We present a method for improving the tolerance of a conventional LQG controller to parameter errors in the plant model. The improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the LQR cost function, and also the process and measurement noise models. Adjusting the sizes of these additional terms permits a trade-off between robustness and nominal performance. Manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers. Conditions are developed under which the high-gain approach asymptotically recovers the robustness of the corresponding full-state feedback design, and the low-gain approach makes the closed-loop poles asymptotically insensitive to parameter errors.
Systems analysis techniques were developed and demonstrated for modeling the electroencephalographic (EEG) steady state visual evoked response (ssVER), for use in EEG data compression and as an indicator of mental workload. The study focused on steady state frequency domain stimulation and response analysis, implemented with a sum-of-sines (SOS) stimulus generator and an off-line describing function response analyzer. Three major tasks were conducted: (1) VER related systems identification material was reviewed; (2) Software for experiment control and data analysis was developed and implemented; and (3) ssVER identification and modeling was demonstrated, via a mental loading experiment. It was found that a systems approach to ssVER functional modeling can serve as the basis for eventual development of a mental workload indicator. The review showed how transient visual evoked response (tVER) and ssVER research are related at the functional level, the software development showed how systems techniques can be used for ssVER characterization, and the pilot experiment showed how a simple model can be used to capture the basic dynamic response of the ssVER, under varying loads.
The proposed manned Mars mission will need to be as weight efficient as possible. A way of lowering the weight of the vehicle by using aeroassist braking instead of retro-rockets to slow a craft once it reaches its destination is discussed. The two vehicles studied are a small vehicle similar in size to the Mars Rover Sample Return (MRSR) vehicle and a larger vehicle similar in size to a six-person Manned Mars Mission (MMM) vehicle. Simulated entries were made using various coefficients of lift (C sub L), coefficients of drag (C sub D), and lift-to-drag ratios (L/D). A range of acceptable flight path angles with their corresponding bank angle profiles was found for each case studied. These ranges were then compared, and the results are reported here. The sensitivity of velocity and acceleration to changes in flight path angle and bank angle is also included to indicate potential problem areas for guidance and navigation system design.
A parameter sensitivity study was conducted at the NASA Glenn Research Center's Icing Research Tunnel (IRT) using a 36 in. chord (0.91 m) NACA-0012 airfoil. The objective of this preliminary work was to investigate the feasibility of using ice shape feature changes to define requirements for the simulation and measurement of SLD icing conditions. It was desired to identify the minimum change (threshold) in a parameter value, which yielded an observable change in the ice shape. Liquid Water Content (LWC), drop size distribution (MVD), and tunnel static temperature were varied about a nominal value, and the effects of these parameter changes on the resulting ice shapes were documented. The resulting differences in ice shapes were compared on the basis of qualitative and quantitative criteria (e.g., mass, ice horn thickness, ice horn angle, icing limits, and iced area). This paper will provide a description of the experimental method, present selected experimental results, and conclude with an evaluation of these results, followed by a discussion of recommendations for future research.
A second parameter sensitivity study was conducted at the NASA Glenn Research Center's Icing Research Tunnel (IRT) using a 36 in. chord (0.91 m) NACA-0012 airfoil. The objective of this work was to further investigate the feasibility of using ice shape feature changes to define requirements for the simulation and measurement of SLD and appendix C icing conditions. A previous study concluded that it was feasible to use changes in ice shape features (e.g., ice horn angle, ice horn thickness, and ice shape mass) to detect relatively small variations in icing spray condition parameters (LWC, MVD, and temperature). The subject of this current investigation extends the scope of this previous work, by also examining the effect of icing tunnel spray-bar parameter variations (water pressure, air pressure) on ice shape feature changes. The approach was to vary spray-bar water pressure and air pressure, and then evaluate the effects of these parameter changes on the resulting ice shapes. This paper will provide a description of the experimental method, present selected experimental results, and conclude with an evaluation of these results.
Performance sensitivity calculated by back substitution. Original Lyapunov equation differentiated two times with respect to parameter p. Each differential turns out to yield Lyapunov equation for first and second derivatives with respective to parameter p of steady-state covariance of state variables. Derivatives desired closed-loop performance sensitivities.
Optimum design parameter sensitivity analysis has become an important topic in recent years. The principal reasons for obtaining optimum design sensitivity information with respect to various problem parameters are (l) to predict revised optimum designs, associated with specified perturbations of the problem parameters, without re-optimizing the problem and, (2) to provide sensitivity information in multilevel optimization strategies. Methods for calculating these derivatives were proposed by several authors. The most important drawback in estimating parameter sensitivities by the current methods is that they do not allow for changes in the active constraint set. Changes in the active constraint set produce discontinuities in the optimum design sensitivities, and therefore, a correct formulation has to be cast in terms of directional derivatives. Optimum design parameter sensitivity analysis is addressed in terms of directional derivatives so as to include possible discontinuities and it also presents a method for estimating optimum design sensitivities using finite differences.
The generation of design parameter sensitivity derivatives is required for gradient-based optimization. Such sensitivity derivatives are elusive at best when working with geometry defined within the solid modeling context of Computer-Aided Design (CAD) systems. Solid modeling CAD systems are often proprietary and always complex, thereby necessitating ad hoc procedures to infer parameter sensitivity. A new perspective is presented that makes direct use of the hierarchical associativity of CAD features to trace their evolution and thereby track design parameter sensitivity. In contrast to ad hoc methods, this method provides a more concise procedure following the model design intent and determining the sensitivity of CAD geometry directly to its respective defining parameters.
Accurate prediction of runoff is essential to water resources management, flood risk assessment, and ecosystem protection. However, many hydrological models still have relatively substantial limitations when representing the influence of land use and land cover (LULC) on runoff generation and routing. Changes in LULC, such as deforestation, urban expansion, agricultural intensification, and wetland loss, have been shown to alter the water balance at the land surface through fundamental hydrologic processes (e.g., interception, infiltration, evapotranspiration, and soil storage). However, it remains an open question what the exact magnitude and timing of these impacts are for the spatial and temporal scales commonly used in engineering applications. In this analysis we focus on one aspect of recent LULC change for assessing human impacts, which is urbanization. Specifically we seek to determine the impacts of urbanization on the magnitude and timing of surface runoff and baseflow in HUC-12 basins in Clark County, Nevada which has experienced rapid urbanization. We use the Variable Infiltration Capacity (VIC) hydrology model with a widely used off-the-shelf dataset of land surface parameters, VIC-Global, both of which have been commonly used in the past for water and energy balance modeling for large scale hydrologic studies. We examine two scenarios where the first scenario removes all urbanized land cover and parameterizes those areas of the basins as barren or open shrubland. The second scenario tests the opposite case where all areas of the basins are classified as urban regardless of their present classification. The results from the VIC model show there is a low sensitivity for daily surface runoff between scenarios. The daily baseflow values indicate similar low sensitivity to the classification change during specific periods, but then have substantial differences during other period when large precipitation events are occurring. This is likely due to the assumed parameter values for the urban land cover classification made by the VIC-Global dataset. Using a static land cover parameterization is reasonable for large domain hydrology models that are being used for near-term planning horizons (<30 years). However, longer planning horizons where feedbacks between the atmosphere and land surface are important, especially in transient climate situations, considerations for how to update land surface parameters should be incorporated.
A very efficient technique for computing the closed loop performance sensitivities to parameter variations of a dynamic system with a reduced order controller has been developed. The eigensystem of the closed loop system is computed once. With this information, the closed loop filter and state rms responses, and the first and second derivatives of these rms values with respect to given parameters are computed. Detailed numerical examples using the JPL flexible beam and a 55 meter offset fed, wrap-rib antenna are included.
For both models and tests, NPG and NSK parameters have only small effects on calculated sensitivity coefficients. Outside of NPG=100, only differences in CFP affected sensitivity coefficient values. Fission reactions ( 235 U) require more NPG values than scattering ( 238 U) reactions – more particles are needed to locate fission sources in the model more accurately. This work confirms the previous results with the IFP method where the CFP parameter has the greatest impact on calculated sensitivity coefficients. While immediate work focuses on fast systems, other model specifications may require a different set of MC parameters.
This presentation covers recent process improvements regarding environmental parameters, w.r.t convection, and future plans for thermal models.
This presentation describes the thought process for determining balloon thermal model design parameters, including environmental parameters taken form NASA's top-of-atmosphere (TOA) database, and shows the sensitivity of an example model's key temperature results to those input parameters.
The number of optical techniques that may potentially be used during a given wind tunnel test is continually growing. These include parameter sensitive paints that are sensitive to temperature or pressure, several different types of off-body and on-body flow visualization techniques, optical angle-of-attack (AoA), optical measurement of model deformation, optical techniques for determining density or velocity, and spectroscopic techniques for determining various flow field parameters. Often in the past the various optical techniques were developed independently of each other, with little or no consideration for other techniques that might also be used during a given test. Recently two optical techniques have been increasingly requested for production measurements in NASA wind tunnels. These are the video photogrammetric (or videogrammetric) technique for measuring model deformation known as the video model deformation (VMD) technique, and the parameter sensitive paints for making global pressure and temperature measurements. Considerations for, and initial attempts at, simultaneous measurements with the pressure sensitive paint (PSP) and the videogrammetric techniques have been implemented. Temperature sensitive paint (TSP) has been found to be useful for boundary-layer transition detection since turbulent boundary layers convect heat at higher rates than laminar boundary layers of comparable thickness. Transition is marked by a characteristic surface temperature change wherever there is a difference between model and flow temperatures. Recently, additional capabilities have been implemented in the target-tracking videogrammetric measurement system. These capabilities have permitted practical simultaneous measurements using parameter sensitive paint and video model deformation measurements that led to the first successful unified test with TSP for transition detection in a large production wind tunnel.
The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.
This study concentrates on results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities and assess surrogate model suitability for a novel inflatable airlock concept, specifically the Non-Axisymmetric Inflatable Pressure Structure (NAIPS) under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. The current studies extended the demonstration of probabilistic analysis tools to identify parameter sensitivities by: incorporating nonlinear material load-strain property curves and orthotropic representation of the fabric; and exploring the use of surrogate models to facilitate rapid evaluations as new information becomes available, as well as enable optimizations. The airlock model has been simplified to focus on the end dome section. Brief overviews of the finite element model and associated surrogate models are provided along with the probabilistic sensitivity analysis approaches. Responses of interest include the sensitivities of various loads in the structural elements of the NAIPS to material properties, cord lengths, inflation pressure and friction between softgoods components. The use of surrogate models was explored to facilitate rapid sensitivity evaluations as parameter ranges change. The completion of the sensitivity studies improved understanding of the dependence of load responses to several uncertain parameters and confidence in the ability to use surrogate models to represent the finite element simulations.
Improved techniques for estimating airplane stability and control derivatives and their standard errors are presented. A maximum likelihood estimation algorithm is developed which relies on an optimization scheme referred to as a modified Newton-Raphson scheme with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared to integrating the analytically-determined sensitivity equations or using a finite difference scheme. An aircraft estimation problem is solved using real flight data to compare MNRES with the commonly used modified Newton-Raphson technique; MNRES is found to be faster and more generally applicable. Parameter standard errors are determined using a random search technique. The confidence intervals obtained are compared with Cramer-Rao lower bounds at the same confidence level. It is observed that the nonlinearity of the cost function is an important factor in the relationship between Cramer-Rao bounds and the error bounds determined by the search technique.