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Techniques developed originally for electronic systems also useful for multibody mechanical systems. Report summarizes methods developed to solve nonlinear forward-dynamics problem for robot of multiple-link arms connected by joints. Primary objective to show equivalence between recursive methods of dynamical analysis and some filtering and smoothing techniques from state-estimation theory.
Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi‐geostrophic model, in which we compare a recently developed ensemble filter using score‐based diffusion models with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will eventually be replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observing systems in the context of newly emerging algorithms.
Scanning speed and coupling efficiency of excitation light to optic fibres are two major technical challenges that limit the potential of fluorescence excitation-emission matrix (EEM) spectrometer for on-line applications and in vivo studies. In this paper, a novel EEM system, utilizing a supercontinuum white light source and acousto-optic tunable filters (AOTFs), was introduced and evaluated. The supercontinuum white light, generated by pumping a nonlinear photonic crystal fiber with an 800 nm femtosecond laser, was efficiently coupled into a bifurcated optic fiber bundle. High speed EEM spectral scanning was achieved using AOTFs both for selecting excitation wavelength and scanning emission spectra. Using calibration lamps (neon and mercury argon), wavelength deviations were determined to vary from 0.18 nm to −0.70 nm within the spectral range of 500–850 nm. Spectral bandwidth for filtered excitation light broadened by twofold compared to that measured with monochromatic light between 650 nm and 750 nm. The EEM spectra for methanol solutions of laser dyes were successfully acquired with this rapid fluorometer using an integration time of 5 s.
An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.
This paper presents a design method for optimal redundancy management for nonlinear systems with application to highly maneuvering aircraft. The approach taken is based on selecting the failure states to be covered by the system design and constructing a cost function that represents the cost of making an incorrect decision. The decision logic which minimizes the cost requires a bank of extended Kalman filters running in parallel. This produces a severe computational requirement. To reduce this requirement, a suboptimal logic is developed based on using a nonlinear single-stage prediction algorithm in the filters with filter gains and decision logic selected using steady-state results obtained from a linearization of the vehicle and sensor dynamics. The design process is then applied to designing a redundancy management system for the F8-C aircraft. Results indicate that the system is superior in failure detection to a system using the same structure but using a linear single-stage prediction algorithm in the filters.
Recent new methods in photonic signal processing based on stimulated Brillouin scattering, that enable the realization of photonic mixers with high conversion efficiency, ultra-wide continuously tunable high-resolution microwave photonic filters and programmable switchable microwave photonic tunable filters, are presented. These processors provide new capabilities for the realisation of high-performance and high-resolution signal processing.
We address the design of optimal correlation filters for pattern detection and recognition in the presence of signal-dependent image noise sources. The particular examples considered are film-grain noise and speckle. Two basic approaches are investigated: (1) deriving the optimal matched filters for the signal-dependent noise models and comparing their performances with those derived for traditional signal-independent noise models and (2) first nonlinearly transforming the signal-dependent noise to signal-independent noise followed by the use of a classical filter matched to the transformed signal. We present both theoretical and computer simulation results that demonstrate the generally superior performance of the second approach in terms of the correlation peak signal-to-noise ratio.
Systems using inertia wheels are evaluated in this report to determine their suitability for precise attitude control of a satellite and to select superior system configurations. Various possible inertia wheel system configurations are first discussed in a general manner. Three of these systems which appear more promising than the others are analyzed in detail, using the Orbiting Astronomical Observatory as an example. The three systems differ from each other only by the method of damping, which is provided by either a rate gyro, an error-rate network, or a tachometer in series with a high-pass filter. An analytical investigation which consists of a generalized linear analysis, a nonlinear analysis using the switching-time method, and an analog computer study shows that all three systems are theoretically capable of producing adequate response and also of maintaining the required pointing accuracy for the Orbiting Astronomical Observatory of plus or minus 0.1 second of arc. Practical considerations and an experimental investigation show, however, that the system which uses an error-rate network to provide damping is superior to the other two systems. The system which uses a rate gyro is shown to be inferior because the threshold level causes a significant amount of limit-cycle operation, and the system which uses a tachometer with a filter is shown to be inferior because a device with the required dynamic range of operation does not appear to be available. The experimental laboratory apparatus used to investigate the dynamic performance of the systems is described, and experimental results are included to show that under laboratory conditions with relatively large extraneous disturbances, a dynamic tracking error of less than plus or minus 0.5 second of arc was obtained.
With the expansion of distribution networks and increased penetration of distributed energy resources (DERs), it is becoming increasingly important to obtain accurate distribution network topology in real-time. In this paper, a robust principal component analysis coupled deep belief network (PCA-DBN) surrogate model is proposed for distribution system topology identification. It integrates the benefits of robust feature extraction from PCA to deal with data quality issues and filter out noise, and the strength of DBN in capturing the nonlinear relationship between voltage amplitudes and the binary states of switchable connections. This also significantly reduces the DBN training complexity without loss of accuracy. It is shown that the widely used standard deviation of voltage drop and the voltage covariance matrix features yield less accuracy as compared to that of the voltage amplitudes in presence of high penetration of DERs and ZIP loads. Comparison results with other alternatives, such as the random forest (RF), multi-output regression (MOR) and the traditional DBN methods demonstrate that the proposed method can achieve a much higher topology identification accuracy while maintaining robustness to missing data and measurement noise under various penetration levels of DERs.
Thermoacoustic instabilities in annular or circular combustors are often coupled with azimuthal modes. These modes can be characterized by a spin ratio (SR), which quantifies the dominant mode between two counter-rotating waves, and a phase difference between them, which is directly related to the orientation of the antinodal line. This study investigates the instability amplitudes, SR, and phase difference of two closely spaced (3% of their mean frequency), yet distinct azimuthal modes; one is the first azimuthal (1A) mode, and the other is a combination of first azimuthal and first longitudinal (1A1L) mode. Each mode itself consists of two peaks that are spaced even more closely in frequency (0.8%). Furthermore, distinct harmonics at 2× and 3× of these frequencies, presumably associated with nonlinearities, are also evident in the spectra. Each mode is bandpass filtered in spectrum to analyze them separately. For the 1A mode, the SR and phase difference exhibit a variety of behaviors—including quasi-periodic standing waves, spinning waves, and intermittency—depending on operating conditions such as thermal power and azimuthal fuel staging. Similar trends are observed for the 1A1 L mode. Moreover, there is clear coupling between the 1A and 1A1 L modes, as their SRs are almost synchronized during the quasi-periodic standing wave. This synchronization is observed in phase differences as well, but not in the instability amplitude. For spinning dominant wave conditions, the SRs of each mode have similar average values, but they fluctuate in a seemingly random fashion. For the phase difference, both average and fluctuation are not correlated. In contrast, the instability amplitudes are strongly correlated, with modulation of the 1A mode leading to that of the 1A1 L mode. Furthermore, these results clearly indicate that complex coupling occurs across closely spaced frequencies under instability conditions, coupling that must be understood in order to capture limit cycle dynamics.
The derivation of smoothed or filtered momentum and continuity equations for large-scale, energy-containing eddies is considered. Questions regarding the energy loss of large-scale turbulence are discussed along with aspects of turbulent diffusion of a passive scalar. It is found that the large-scale fluctuations satisfy filtered or averaged momentum and continuity equations. An averaging of the nonlinear advection term yields two terms.
This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) micro-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closed-loop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.
The performance of a second order filter which is identical to the algorithm developed by Athans et al. (1968) for the scalar case is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second order terms is evaluated.
We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Q{sub i} > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition, it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.
Remote sensing data from satellites typically have three dimensions: scan position, spacecraft position, and wavelength. Inversion of the radiometric data to infer geophysical parameters is a filtering problem in which the dimension of wavelength (or channel number) is transformed into a dimension of geophysical parameters, and the most general solution is a three-dimensional filter. Linear filters have the advantages of computational speed and easily described transfer functions; but often the measurements are nonlinear functions of the parameters to be inferred. To the extent that the nonlinear inversion problem is overdetermined, it can be modeled by a critically determined linear problem. As an example, inversion of Scanning Multichannel Microwave Radiometer (SMMR) data by means of a three-dimensional Wiener Filter is described. Atmospheric water vapor content, rain liquid water content, surface wind speed and surface temperature are the parameters inferred from the measurements. Nonprecipitating liquid water and water vapor scale height are also modeled but not retrieved. The a priori statistics on which the filter is trained have the effect of governing the selection of a trade-off point of noise as a function of resolution (in all three retrieval dimensions).
First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn–Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.
A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.
In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP{sub N}) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.