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At least 613 records · Page 34

Parameter identification for an abstract Cauchy problem by quasilinearization

A parameter identification problem is considered in the context of a linear abstract Cauchy problem with a parameter-dependent evolution operator. Conditions are investigated under which the gradient of the state with respect to a parameter possesses smoothness properties which lead to local convergence of an estimation algorithm based on quasi-linearization. Numerical results are presented concerning estimation of unknown parameters in delay-differential equations.

Brewer, Dennis W.↗

Control system estimation and design for aerospace vehicles with time delay

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Allgaier, G. R.↗

Effects of exposure estimation errors on estimated exposure-response relations for PM2.5

Highlights: • Recent literature has identified associations between concentrations of fine particulate matter (PM2.5) in ambient air and adverse health effects at estimated exposure concentrations below current air ambient quality standards. • The models and analyses used do not usually quantify uncertainty about exposure estimates. • Realistic errors in exposure estimates can be estimated from available air quality monitoring stations by predicting concentrations at each station from concentrations at neighboring stations. • Exposure estimation errors are large enough to obscure low-dose nonlinearities or thresholds in the true concentration-response (C-R) function, artificially making them appear to be linear at low doses. • Better estimates of C-R functions will require modeling exposure distributions and estimation errors, rather than just estimating average exposure concentrations. Associations between fine particulate matter (PM2.5) exposure concentrations and a wide variety of undesirable outcomes, from autism and auto theft to elderly mortality, suicide, and violent crime, have been widely reported. Influential articles have argued that reducing National Ambient Air Quality Standards for PM2.5 is desirable to reduce these outcomes. Yet, other studies have found that reducing black smoke and other particulate matter by as much as 70% and dozens of micrograms per cubic meter has not detectably affected all-cause mortality rates even after decades, despite strong, statistically significant positive exposure concentration-response (C-R) associations between them. This paper examines whether this disconnect between association and causation might be explained in part by ignored estimation errors in estimated exposure concentrations. We use EPA air quality monitor data from the Los Angeles area of California to examine the shapes of estimated C-R functions for PM2.5 when the true C-R functions are assumed to be step functions with well-defined response thresholds. The estimated C-R functions mistakenly show risk as smoothly increasing with concentrations even well below the response thresholds, thus incorrectly predicting substantial risk reductions from reductions in concentrations that do not affect health risks. We conclude that ignored estimation errors obscure the shapes of true C-R functions, including possible thresholds, possibly leading to unrealistic predictions of the changes in risk caused by changing exposures. Instead of estimating improvements in public health per unit reduction (e.g., per 10 µg/m{sup 3} decrease) in average PM2.5 concentrations, it may be essential to consider how interventions change the distributions of exposure concentrations.

54 ENVIRONMENTAL SCIENCES↗

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗

Distributed Data-Driven Power Iteration for Strongly Connected Networks

Here, this paper presents data-driven power iteration to distributively estimate the dominant eigenvalues of an unknown linear time-invariant system. The proposed strategy only requires a single trajectory data or measurements. Furthermore, in order to perform the distributed estimation, the communication network topology can be chosen to be any strongly connected directed graphs. The proposed data-driven power iteration is demonstrated using several numerical examples and is then applied to estimate the generalized algebraic connectivity of cooperative systems and to control the epidemic spreading.

Gusrialdi, Azwirman↗

Using Indirect Turbulence Measurements for Real-Time Parameter Estimation in Turbulent Air

The use of indirect turbulence measurements for real-time estimation of parameters in a linear longitudinal dynamics model in atmospheric turbulence was studied. It is shown that measuring the atmospheric turbulence makes it possible to treat the turbulence as a measured explanatory variable in the parameter estimation problem. Commercial off-the-shelf sensors were researched and evaluated, then compared to air data booms. Sources of colored noise in the explanatory variables resulting from typical turbulence measurement techniques were identified and studied. A major source of colored noise in the explanatory variables was identified as frequency dependent upwash and time delay. The resulting upwash and time delay corrections were analyzed and compared to previous time shift dynamic modeling research. Simulation data as well as flight test data in atmospheric turbulence were used to verify the time delay behavior. Recommendations are given for follow on flight research and instrumentation.

Martos, Borja↗

Random field estimation approach to multibody dynamics

The use of recursive techniques similar to random field models to factor and invert the inertia matrix of a multibody system is discussed. An equivalence is established between the composite multibody system inertia matrix and the covariance of the output of a described linear system model. Conditional mean estimation and sequential estimation problems are solved along with problems of filtering and smoothing. Formulas are developed to compute the covariance of several relevant quantities. The foregoing results are used to obtain the inverse of the composite multibody system inertia in closed form.

Rodriguez, G.↗

A digital twin solution for floating offshore wind turbines validated using a full-scale prototype

Abstract. In this work, we implement, verify, and validate a physics-based digital twin solution applied to a floating offshore wind turbine. The digital twin is validated using measurement data from the full-scale TetraSpar prototype. We focus on the estimation of the aerodynamic loads, wind speed, and section loads along the tower, with the aim of estimating the fatigue lifetime of the tower. Our digital twin solution integrates (1) a Kalman filter to estimate the structural states based on a linear model of the structure and measurements from the turbine, (2) an aerodynamic estimator, and (3) a physics-based virtual sensing procedure to obtain the loads along the tower. The digital twin relies on a set of measurements that are expected to be available on any existing wind turbine (power, pitch, rotor speed, and tower acceleration) and motion sensors that are likely to be standard measurements for a floating platform (inclinometers and GPS sensors). We explore two different pathways to obtain physics-based models: a suite of dedicated Python tools implemented as part of this work and the OpenFAST linearization feature. In our final version of the digital twin, we use components from both approaches. We perform different numerical experiments to verify the individual models of the digital twin. In this simulation realm, we obtain estimated damage equivalent loads of the tower fore–aft bending moment with an accuracy of approximately 5 % to 10 %. When comparing the digital twin estimations with the measurements from the TetraSpar prototype, the errors increased to 10 %–15 % on average. Overall, the accuracy of the results is promising and demonstrates the possibility of using digital twin solutions to estimate fatigue loads on floating offshore wind turbines. A natural continuation of this work would be to implement the monitoring and diagnostics aspect of the digital twin to inform operation and maintenance decisions. The digital twin solution is provided with examples as part of an open-source repository.

17 WIND ENERGY↗

Relationships between digital signal processing and control and estimation theory

Research directions in the fields of digital signal processing and modern control and estimation theory are discussed. Stability theory, linear prediction and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing are considered in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the disciplines.

Willsky, A. S.↗

JPL IGS Analysis Center Report, 2001-2003

Three GPS orbit and clock products are currently provided by JPL for consideration by the IGS. Each differs in its latency and quality, with later results being more accurate. Results are typically available in both IGS and GIPSY formats via anonymous ftp. Current performance based on comparisons with the IGS final products is summarized. Orbit performance was determined by computing the 3D RMS difference between each JPL product and the IGS final orbits based on 15 minute estimates from the sp3 files. Clock performance was computed as the RMS difference after subtracting a linear trend based on 15 minute estimates from the sp3 files.

Heflin, M. B.↗

Adaptive Control of Linear Modal Systems Using Residual Mode Filters and a Simple Disturbance Estimator

Flexible structures containing a large number of modes can benefit from adaptive control techniques which are well suited to applications that have unknown modeling parameters and poorly known operating conditions. In this paper, we focus on a direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend our adaptive control theory to accommodate troublesome modal subsystems of a plant that might inhibit the adaptive controller. In some cases the plant does not satisfy the requirements of Almost Strict Positive Realness. Instead, there maybe be a modal subsystem that inhibits this property. This section will present new results for our adaptive control theory. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for the troublesome modal subsystem, or the Q modes. Here we present the theory for adaptive controllers modified by RMFs, with attention to the issue of disturbances propagating through the Q modes. We apply the theoretical results to a flexible structure example to illustrate the behavior with and without the residual mode filter.

Balas, Mark↗

Observing the states of systems with unmeasurable disturbances

In order to estimate the state of a linear time-invariant multivariable system by using a Luenberger observer, it is generally assumed that all system inputs are measurable. This correspondence presents a simple and useful procedure for the construction of minimal-order state estimators for systems with unmeasurable disturbances.

Wang, S.-H.↗

Microwave remote sensing of soil moisture, volume 1

Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone.

Mcfarland, M. J.↗

A multi-variance analysis in the time domain

Recently a new technique for characterizing the noise processes affecting oscillators was introduced. This technique minimizes the difference between the estimates of several different variances and their values as predicted by the standard power law model of noise. The method outlined makes two significant advancements: it uses exclusively time domain variances so that deterministic parameters such as linear frequency drift may be estimated, and it correctly fits the estimates using the chi-square distribution. These changes permit a more accurate fitting at long time intervals where there is the least information. This technique was applied to both simulated and real data with excellent results.

Walter, Todd↗

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

An in-situ view cell system for investigating swelling behavior of elastomers upon high-pressure hydrogen exposure

The transition to hydrogen as a clean and efficient energy carrier is impeded by challenges in the compatibility of hydrogen with materials used within hydrogen infrastructure. Elastomers, crucial in sealing components, often exhibit premature failures in high-pressure hydrogen environments due to excessive swelling. This study employs an innovative in-situ view cell system to assess the swelling behavior of hydrogenated nitrile butadiene rubber (HNBR) under various hydrogen conditions. The system, designed to withstand pressures up to 96.5 MPa, incorporates Digital Image Correlation (DIC) for strain measurements and volume estimation. Results reveal non-linear volume increases during depressurization, challenging conventional assumptions. Furthermore, investigations into peak hydrogen pressures and pressure-holding scenarios during decompression highlight complex swelling trends. The introduction of a novel computer vision (CV) method enhances precision in volume estimation, overcoming DIC limitations. The study provides insights into mitigating elastomer swelling, crucial for developing robust materials to support future hydrogen-driven energy systems.

Elastomer↗