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At least 19 records

Covariate Dependent Sparse Functional Data Analysis

This study proposes a method to incorporate covariate information into sparse functional data analysis. The method aims at cases where each subject has a limited number of longitudinal measurements and is associated with static covariates. This research is motivated by several use cases in practice. One representative example is void swelling, a nuclear-specific material degradation mechanism. Void swelling is affected by many covariates, including alloy composition and irradiation type. How to accurately model the complicated joint effects of such covariates on the swelling process is the key to mitigating the effect of swelling and ensuring safe operation. Unlike most of the existing methods, the proposed method can handle high-dimensional covariates with the informative covariate identification procedure and sparse and irregularly spaced measurements, that is, does not require complete or dense observations. The main innovation of the proposed method is that we model the variation coming from covariates and the variation left conditioned on covariates, such that the functional principal component analysis and Gaussian process can be conducted in a unified manner. Further, we also propose a systematic approach to identify important covariates in the hypothesis testing context. The methodology is demonstrated on applications in nuclear engineering and healthcare and simulation studies.

42 ENGINEERING↗

Q-Markov covariance equivalent realization and its application to flexible structure identification

The Q-Markov covariance equivalent realization algorithm is applied to NASA's Minimast structure to identify state-space models for the purpose of designing closed-loop controllers, and laboratory test results are shown for the identification and for the closed-loop performance. The paper also presents for the first time a deterministic formulation of covariance parameters from a pulse response, a stochastic formulation of Markov parameters from a white-noise response, and a simple Q-Markov covariance equivalent realization formulation. This requires only pulse laboratory tests or only white-noise laboratory tests to generate Q-Markov covariance equivalent realizations.

Liu, Ketao↗

Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel -statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion () with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

97 MATHEMATICS AND COMPUTING↗

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Liu, K.↗

Edgewise Structural Damping of a 2.8-MW Land-Based Wind Turbine Rotor Blade

Modern wind turbines push the predictive capabilities of state-of-the-art aero-servo-elastic tools. The existing limitations hide across the numerical tool chain and can result in serious issues, such as missing aeroelastic instabilities during the design phase. Structural damping is an input that is usually hard to estimate, but also has a major impact on the turbine behavior. In this paper, we discuss an experiment that aims to accurately quantify the structural damping characterizing the edgewise modes of modern wind turbine blades. The experiment is carried out on a 2.8-MW land-based wind turbine and features a fast yaw actuation that induces an edgewise motion on one of the three blades. The Covariant-subspace system identification (Cov-SSI) method is then used to post-process the blade root moment to estimate the short-term edgewise structural damping. Despite limitations of the Cov-SSI method, which consistently under-predicts the absolute values of damping, we observe that structural damping decreases across the first three blade edgewise modes, which is different from the stiffness-proportional damping model that assumes that structural damping increases with the modes. This paper argues that a stiffness-proportional damping model, which is implemented in most aeroelastic tools, is therefore not conservative and might hide aeroelastic instabilities that can instead appear in the field.

17 WIND ENERGY↗

Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

Two off-line schemes are proposed for the identification of unknown noise covariance matrices Q and R of a discrete-time dynamic system. The first scheme is based on a maximum a posteriori cost function utilizing smoothed state estimates, while the second is based on a maximum likelihood cost function utilizing filtered state estimates. Sensitivity of the cost functions to Q and R is analyzed for the following cases: (1) single-input single-output systems; (2) multiinput single-output systems; and (3) single-input multioutput systems with a diagonal R. Identifiability criteria are presented for the cases considered and demonstrated by examples.

Tsang, W. L.↗

Minimum variance system identification with application to digital adaptive flight control

A new on-line minimum variance filter for the identification of systems with additive and multiplicative noise is described which embodies both accuracy and computational efficiency. The resulting filter is shown to use both the covariance of the parameter vector itself and the covariance of the error in identification. A bias reduction scheme can be used to yield asymptotically unbiased estimates. Experimental results for simulated linearized lateral aircraft motion in a digital closed loop mode are presented, showing the utility of the identification schemes.

Kotob, S.↗

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kaufman, H.↗

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise. The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean square convergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗

Analysis and application of minimum variance discrete linear system identification

An on-line minimum variance (MV) parameter identifier is developed which embodies both accuracy and computational efficiency. The formulation results in a linear estimation problem with both additive and multiplicative noise (AMN). The resulting filter which utilizes both the covariance of the parameter vector itself and the covariance of the error in identification is proven to be mean-square convergent and mean-square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗

Analysis and application of minimum variance discrete time system identification

An on-line minimum variance parameter identifier was developed which embodies both accuracy and computational efficiency. The new formulation resulted in a linear estimation problem with both additive and multiplicative noise. The resulting filter is shown to utilize both the covariance of the parameter vector itself and the covariance of the error in identification. It is proven that the identification filter is mean square covergent and mean square consistent. The MV parameter identification scheme is then used to construct a stable state and parameter estimation algorithm.

Kotob, S.↗

Maximum likelihood identification for large space structures

This paper examines the use of on-orbit identification based on Maximum Likelihood Estimation (MLE) to provide these high-order, high-accuracy control design models for large space structures (LSS's). First, it outlines a general MLE identification algorithm, together with a covariance-analysis procedure to assess algorithm performance in terms of systematic and stochastic errors. Next, it examines various simplifications appropriate for the LSS identification application. Simplified analytical performance results are presented, as are numerical results to support these analyses. Finally, a graphical interpretation of these results is given.

Barrett, Michael F.↗

OSIRIS-REx Orbit Determination Covariance Studies at Bennu

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the small, Earth-crossing asteroid (101955) Bennu in late 2018, ultimately returning a sample of regolith to Earth. Approximately three months before the encounter with Bennu, the asteroid becomes detectable in the narrow field PolyCam imager. The spacecraft's rendezvous with Bennu begins with a series of four Asteroid Approach Maneuvers, slowing the spacecraft's speed relative to Bennu beginning two and a half months prior to closest approach, ultimately delivering the spacecraft to a point 18 km from Bennu in Nov, 2018. An extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site will follow. This paper will discuss the challenges of navigating near a small 500-m diameter asteroid. The navigation at close proximity is dependent on the accurate mathematical model or digital terrain map of the asteroid's shape. Predictions of the spacecraft state are very sensitive to spacecraft small forces, solar radiation pressure, and mis-modeling of Bennu's gravity field. Uncertainties in the physical parameters of the central body Bennu create additional challenges. The navigation errors are discussed and their impact on science planning will be presented.

COVARIANCE↗

OSIRIS-REx Orbit Determination Covariance Studies at Bennu

The Origins Spectral Interpretation Resource Identification Security Regolith Explorer (OSIRIS-REx) mission is a NASA New Frontiers mission launching in 2016 to rendezvous with the small, Earth-crossing asteroid (101955) Bennu in late 2018, and ultimately return a sample of regolith to Earth. Approximately 3 months before the encounter with Bennu, the asteroid finally becomes detectable in the narrow field PolyCam imager. The spacecraft's rendezvous with Bennu begins with a series of four Asteroid Approach Maneuvers, which slow the spacecraft's speed relative to Bennu beginning two and a half months prior to closest approach, ultimately delivering the spacecraft to a point 18 km from Bennu on Nov 18, 2018. An extensive campaign of proximity operations activities to characterize the properties of Bennu and select a suitable sample site will follow. This paper will discuss the challenges of navigating near a small 500-m diameter asteroid. The navigation at close proximity is dependent on the accurate mathematical model or digital terrain map of the asteroids shape. Predictions of the spacecraft state are very sensitive to spacecraft small forces, solar radiation pressure, and mis-modeling of Bennu's gravity field. Uncertainties in the physical parameters of the central body Bennu create additional challenges. The navigation errors are discussed and their impact on science planning will be presented.

Covariance↗

Recursive identification and tracking of parameters for linear and nonlinear multivariable systems

The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking, and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally, asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.

Sidar, M.↗

Recursive identification and tracking of parameters for linear and non-linear multivariable systems

The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.

Sidar, M.↗

Identifying Nuclear Data Correlated Through Predicting Bias in Integral Experiments via Applying Principal Component Analysis to Random Forest

ABSTRACT Nuclear data (ND) are the input data for neutron‐transport simulations to answer questions related to nuclear technologies. Subsets of ND, here > 20,000 data points, are validated with respect to thousands of criticality experiments that represent various applications on a small scale. The aim of validation with these experiments is to find errors in ND or methods. The key challenge here is that several hundreds of ND are used to simulate one integral value. Hence, one cannot clearly identify what ND are leading to bias in criticality measurements. In fact, a mistake in one nuclear‐data observable can be compensated with an error in another, and the predicted criticality value would still be predicted in agreement with experimental data. Random forest (RF) was previously employed to predict bias in criticality measurements using sensitivities of simulated criticality experiments to ND. The SHapley Additive exPlanations (SHAP) metric was then applied to attribute the importance of each ND experiment and observable to bias prediction. This, however, did not highlight what ND were jointly related to predicting bias. This is important as it could inform us about where compensating errors in ND could hide. We tackle this shortcoming here by first decomposing the ND sensitivities to integral‐experiment simulations into principal components. Then we use principal component projections to predict bias via the RF and SHAP. The SHAP values and principal components are employed to reconstruct detailed SHAP values for each ND observable. We demonstrate that these extended SHAP bias predictions are more robust, less noisy, and more efficient. In addition, we show that this approach accounts for covariance in ND sensitivities and automates the identification of where compensating errors could hide in ND.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

System identification for modeling for control of flexible structures

The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.

Mettler, Edward↗