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At least 1,117 records · Page 62

Parameter identification for nonlinear aerodynamic systems

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Pearson, Allan E.↗

Vertical wind estimation from horizontal wind measurements

The objective of this study was to assess the ability of simple vertical wind models to improve the hazard prediction capability of an airborne Doppler sensor in a realistic microburst environment. The results indicate that in the altitude region of interest (at or below 300 meters), both the linear and empirical vertical wind models improved the hazard estimate. The radar simulation study showed that the magnitude of the performance improvement was altitude dependent. The altitude of maximum performance improvement occurred at about 300 meters. At the lower altitudes the percent improvement was minimized by the diminished contribution of the vertical wind. The vertical hazard estimate errors from flight tests were less than those of the radar simulation study.

Vicroy, Dan D.↗

Mass center estimation of a drag-free satellite

The mass center location of a spinning drag-free satellite can be estimated because there is control required to accelerate the mass center along the axis of spin as long as there is some nutation in the spinning motion. Linear and nonlinear models are compared and observability discussed. Online estimation fails when nutation is damped so an offline mechanization is proposed. A new sensor has been designed to permit greater relative motion than was possible on the drag-free satellite flown in 1972 (JH-1). Experimental laboratory results using a spinning vehicle with the new sensor mounted 30 cm from a spherical air bearing support are presented which confirm earlier simulation results.

Sanz Fernandez De Cordova, S.↗

Identification evaluation methods

Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.

Klein, V.↗

Sensitivity Analysis of the Human Research Program’s Impact 1.0 Model

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Leave One Out (LOO) are methods of conducting sensitivity analysis on non-linear simulation models like the IMPACT Model. The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The “partial” part is due to the adjustments made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. LOO removes a medical condition from test suite and calculates the change in the outcome. This is used to identify the influence of the condition input in the model The inputs to the sensitivity procedures include the number of occurrences of each of the one hundred plus IMPACT medical conditions generated over the simulations, and the IMPACT outputs from the MEDPRAT mathematical model. The outputs total task time lost (TTL), number of return to definitive care (RTDC), and number of loss of crew lives (LOCL). The IMPACT team will report the results of using PRCC and LOO on IMPACT 1.0. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty, and input values could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMPACT 1.0.

Sensitivity Anaylsis↗

A Framework for Scaling in Filtering and Linear Covariance Analysis

Scaling is used extensively for numerical optimization and trajectory optimization. Its use in the estimation community is almost nonexistent. This paper creates the framework for practical scaling in space navigation, in general, and linear covariance analysis, in particular.

D'souza, Christopher N.↗

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

Park, Michael A.↗

TU-H-BRC-07: Therapeutic Benefit in Spatially Fractionated Radiotherapy (GRID) Using Helical Tomotherapy

Purpose: The aim of this project is to study the therapeutic ratio (TR) for helical Tomotherapy (HT) based spatially fractionated radiotherapy (GRID). Estimation of TR was based on the linear-quadratic cell survival model by comparing the normal cell survival in a HT GRID to that of a uniform dose delivery in an open-field for the same tumor survival. Methods: HT GRID plan was generated using a patient specific virtual GRID block pattern of non-divergent, cylinder shaped holes using MLCs. TR was defined as the ratio of normal tissue surviving fraction (SF) under HT GRID irradiation to an open field irradiation with an equivalent dose that result in the same tumor cell SF. The ratio was estimated from DVH data on ten patient plans with deep seated, bulky tumor approved by the treating radiation oncologist. Dependence of the TR values on radio-sensitivity of the tumor cells and prescription dose were also analyzed. Results: The mean ± standard deviation (SD) of TR was 4.0±0.7 (range: 3.1 to 5.5) for the 10 patients with single fraction dose of 20 Gy and tumor cell SF of 0.5 at 2 Gy. In addition, mean±SD of TR = 1±0.1 and 18.0±5.1 were found for tumor with SF of 0.3 and 0.7, respectively. Reducing the prescription dose to 15 and 10 Gy lowered the TR to 2.0±0.2 and 1.2±0.04 for a tumor cell SF of 0.5 at 2 Gy. In this study, the SF of normal cells was assumed to be 0.5 at 2 Gy. Conclusion: HT GRID displayed a significant therapeutic advantage over uniform dose from an open field irradiation. TR increases with the radioresistance of the tumor cells and with prescription dose.

60 APPLIED LIFE SCIENCES↗

A Reduced Dimension Static, Linearized Kalman Filter and Smoother

An approximate Kalman filter and smoother, based on approximations of the state estimation error covariance matrix, is described. Approximations include a reduction of the effective state dimension, use of a static asymptotic error limit, and a time-invariant linearization of the dynamic model for error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. Examples of use come from TOPEX/POSEIDON.

Kalman filter smoother modeling ocean simulation↗

Analysis of the Feasibility of UAS-Based EMI Sensing for Underground Utilities Detection and Mapping

This paper investigates the feasibility of using a linear current sensing (LCS) technique integrated on an unmanned aerial system (UAS) for detecting and mapping underground infrastructure rapidly and cost-effectively. The LCS technique is based on data from a wide band of electromagnetic induction frequencies (50 kHz to 2 MHz) using a vector magnetic field gradiometer. This technique takes advantage of a slowly decaying secondary magnetic field in order to achieve greater standoff detection distance ($\frac{1}{R^2}$ vs. $\frac{1}{R^6}$ for compact metallic targets during EMI sensing, where R is the distance from a target to the sensor). These secondary magnetic fields are produced by the excite current on long conductors, allowing detection at a distance of 10 meters or more. The system operates between tens of kHz to a few MHz and uses either an active EMI source or existing EM fields to excite this linear current on a long metallic subsurface target. Once excited, these linear currents produce a secondary magnetic field that is detected with an above ground triaxial magnetic field gradiometer. By moving and tracking its geolocation, the system outputs rich datasets sufficient to support high-fidelity forward and inverse EMI models for estimating the depth and orientation of deep underground long linear metallic infrastructure. The system’s hardware and its integration to a UAS system are outlined, along with the formulation of LCS theory, and numerical and experimental data are presented. The results illustrate that the LCS technique offers large standoff detection, is adaptable to UAS, and could be used effectively for detecting deep underground infrastructure such as wires and pipes.

54 ENVIRONMENTAL SCIENCES↗

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Cai, Z.↗

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

Measuring Epoxy-Curing Kinetics

Key reaction parameters estimated from single run. Single DSC Curve used to construct linearized plot from which kinetic reaction parameters are obtained: vertical axis intercept proportional to activation energy, while slope equals reaction order. DSC methods show promise for rapid screening and estimation of cure kinetic parameters of epoxy resins.

Cizmecioglu, M.↗

On the Relationship Between Global Land-Ocean Temperature and Various Descriptors of Solar-Geomagnetic Activity and Climate

Examined are sunspot cycle- (SC-) length averages of the annual January-December values of the Global Land-Ocean Temperature Index ( ) in relation to SC-length averages of annual values of various descriptors of solar-geomagnetic activity and climate, incorporating lags of 0-5 yr. For the overall interval SC12-SC23, the is inferred to correlate best against the parameter incorporating lag = 5 yr, where the parameter refers to the resultant aa value having removed that portion of the annual aa average value due to the yearly variation of sunspot number (SSN). The inferred correlation between the and is statistically important at confidence level cl > 99.9%, having a coefficient of linear correlation r = 0.865 and standard error of estimate se = 0.149 degC. Excluding the most recent cycles SC22 and SC23, the inferred correlation is stronger, having r = 0.969 and se = 0.048 degC. With respect to the overall trend in the , which has been upwards towards warmer temperatures since SC12 (1878-1888), solar-geomagnetic activity parameters are now trending downwards (since SC19). For SC20-SC23, in contrast, comparison of the against SC-length averages of the annual value of the Mauna Loa carbon dioxide ( ) index is found to be highly statistically important (cl >> 99.9%), having r = 0.9994 and se = 0.012 degC for lag = 2 yr. On the basis of the inferred preferential linear correlation between the and , the current ongoing SC24 is inferred to have warmer than was seen in SC23 (i.e., >0.526 degC), probably in excess of 0.68 degC (relative to the 1951-1980 base period).

Wilson, Robert M.↗

A modal parameter extraction procedure applicable to linear time-invariant dynamic systems

Modal analysis has emerged as a valuable tool in many phases of the engineering design process. Complex vibration and acoustic problems in new designs can often be remedied through use of the method. Moreover, the technique has been used to enhance the conceptual understanding of structures by serving to verify analytical models. A new modal parameter estimation procedure is presented. The technique is applicable to linear, time-invariant systems and accommodates multiple input excitations. In order to provide a background for the derivation of the method, some modal parameter extraction procedures currently in use are described. Key features implemented in the new technique are elaborated upon.

Kurdila, A. J.↗

Identification of motion parameters of a rigid body from its orthogonal and perspective projections

An estimate is made of the motion parameters, namely, linear and angular velocities, of a rigid body rotating and translating in three-space. The authors assume that the velocities are constant and that the motion is not completely observable. They consider two separate cases of partial observations corresponding to the orthogonal and the perspective projections, respectively. If (x, y, z) is the Cartesian coordinate of the three-space, the authors assume in the first case that the projection of the motion on the x-y plane is observed. If (r, theta, phi) is the polar coordinates of the three-space, they assume in the second case that the parameter vector (theta, phi) is observed. The use of both of these cases to estimate the motion parameters is discussed.

Ganguly, S.↗

Systems and methods for direct estimation of battery parameters using only charge/discharge curves

Electrochemical models for the lithium-ion battery are useful in predicting and controlling its performance. The values of the parameters in these models are vital to their accuracy. However, not all parameters can be measured precisely, especially when destructive methods are prohibited. In some embodiments of the present disclosure, a parameter estimation approach is used to estimate the open circuit potential of the positive electrode (Up) using piecewise linear approximation together with all the other parameters of a single particle model. Up and 10 more parameters may be estimated from a single discharge curve without knowledge of the electrode chemistry using a technique such as a genetic algorithm. Different case studies were presented for estimating Up with different types of parameters of the battery model. The estimated parameters were then validated by comparing simulations at different discharge rates with experimental data.

Qi, Yanbo↗

The Cauchy Problem for Boltzmann Bi-linear Systems: The Mixing of Monatomic and Polyatomic Gases

Abstract From a unified vision of vector valued solutions in weighted Banach spaces, this paper establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unified approach for vector valued solutions in weighted Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities, angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p -binomial forms producing sharper estimates for the k -moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only a $$2^+$$ 2 + moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann equation.

Physics↗