Successive linearization and nonlinear filtering
Optimal nonlinear filtering for nonlinear dynamic system subjected to additive white Gaussian noise with corrupted observations, using successive linearization scheme
Kau, S.↗
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Results for “Linear dynamics”
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Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. I. Linear acceleration responses during off-vertical axis rotation
1. The dynamic properties of otolith-ocular reflexes elicited by sinusoidal linear acceleration along the three cardinal head axes were studied during off-vertical axis rotations in rhesus monkeys. As the head rotates in space at constant velocity about an off-vertical axis, otolith-ocular reflexes are elicited in response to the sinusoidally varying linear acceleration (gravity) components along the interaural, nasooccipital, or vertical head axis. Because the frequency of these sinusoidal stimuli is proportional to the velocity of rotation, rotation at low and moderately fast speeds allows the study of the mid-and low-frequency dynamics of these otolith-ocular reflexes. 2. Animals were rotated in complete darkness in the yaw, pitch, and roll planes at velocities ranging between 7.4 and 184 degrees/s. Accordingly, otolith-ocular reflexes (manifested as sinusoidal modulations in eye position and/or slow-phase eye velocity) were quantitatively studied for stimulus frequencies ranging between 0.02 and 0.51 Hz. During yaw and roll rotation, torsional, vertical, and horizontal slow-phase eye velocity was sinusoidally modulated as a function of head position. The amplitudes of these responses were symmetric for rotations in opposite directions. In contrast, mainly vertical slow-phase eye velocity was modulated during pitch rotation. This modulation was asymmetric for rotations in opposite direction. 3. Each of these response components in a given rotation plane could be associated with an otolith-ocular response vector whose sensitivity, temporal phase, and spatial orientation were estimated on the basis of the amplitude and phase of sinusoidal modulations during both directions of rotation. Based on this analysis, which was performed either for slow-phase eye velocity alone or for total eye excursion (including both slow and fast eye movements), two distinct response patterns were observed: 1) response vectors with pronounced dynamics and spatial/temporal properties that could be characterized as the low-frequency range of "translational" otolith-ocular reflexes; and 2) response vectors associated with an eye position modulation in phase with head position ("tilt" otolith-ocular reflexes). 4. The responses associated with two otolith-ocular vectors with pronounced dynamics consisted of horizontal eye movements evoked as a function of gravity along the interaural axis and vertical eye movements elicited as a function of gravity along the vertical head axis. Both responses were characterized by a slow-phase eye velocity sensitivity that increased three- to five-fold and large phase changes of approximately 100-180 degrees between 0.02 and 0.51 Hz. These dynamic properties could suggest nontraditional temporal processing in utriculoocular and sacculoocular pathways, possibly involving spatiotemporal otolith-ocular interactions. 5. The two otolith-ocular vectors associated with eye position responses in phase with head position (tilt otolith-ocular reflexes) consisted of torsional eye movements in response to gravity along the interaural axis, and vertical eye movements in response to gravity along the nasooccipital head axis. These otolith-ocular responses did not result from an otolithic effect on slow eye movements alone. Particularly at high frequencies (i.e., high speed rotations), saccades were responsible for most of the modulation of torsional and vertical eye position, which was relatively large (on average +/- 8-10 degrees/g) and remained independent of frequency. Such reflex dynamics can be simulated by a direct coupling of primary otolith afferent inputs to the oculomotor plant. (ABSTRACT TRUNCATED).
NASA Discipline Neuroscience↗
Method and apparatus for creating time-optimal commands for linear systems
A system for and method of determining an input command profile for substantially any dynamic system that can be modeled as a linear system, the input command profile for transitioning an output of the dynamic system from one state to another state. The present invention involves identifying characteristics of the dynamic system, selecting a command profile which defines an input to the dynamic system based on the identified characteristics, wherein the command profile comprises one or more pulses which rise and fall at switch times, imposing a plurality of constraints on the dynamic system, at least one of the constraints being defined in terms of the switch times, and determining the switch times for the input to the dynamic system based on the command profile and the plurality of constraints. The characteristics may be related to poles and zeros of the dynamic system, and the plurality of constraints may include a dynamics cancellation constraint which specifies that the input moves the dynamic system from a first state to a second state such that the dynamic system remains substantially at the second state.
Tuttle, Timothy D.↗
Archetypes for Organisational Safety
We propose a framework using system dynamics to model the dynamic behavior of organizations in accident analysis. Most current accident analysis techniques are event-based and do not adequately capture the dynamic complexity and non-linear interactions that characterize accidents in complex systems. In this paper we propose a set of system safety archetypes that model common safety culture flaws in organizations, i.e., the dynamic behaviour of organizations that often leads to accidents. As accident analysis and investigation tools, the archetypes can be used to develop dynamic models that describe the systemic and organizational factors contributing to the accident. The archetypes help clarify why safety-related decisions do not always result in the desired behavior, and how independent decisions in different parts of the organization can combine to impact safety.
Marais, Karen↗
Direct synthesis of optimal linear filter from conditional probability concepts
State of randomly excited dynamical system estimated from noise measurements having finite duration, and optimal linear filter synthesized from conditional probability theory
EXCITED STATE↗
The Vestibular System and Human Dynamic Space Orientation
The motion sensors of the vestibular system are studied to determine their role in human dynamic space orientation and manual vehicle control. The investigation yielded control models for the sensors, descriptions of the subsystems for eye stabilization, and demonstrations of the effects of motion cues on closed loop manual control. Experiments on the abilities of subjects to perceive a variety of linear motions provided data on the dynamic characteristics of the otoliths, the linear motion sensors. Angular acceleration threshold measurements supplemented knowledge of the semicircular canals, the angular motion sensors. Mathematical models are presented to describe the known control characteristics of the vestibular sensors, relating subjective perception of motion to objective motion of a vehicle. The vestibular system, the neck rotation proprioceptors and the visual system form part of the control system which maintains the eye stationary relative to a target or a reference. The contribution of each of these systems was identified through experiments involving head and body rotations about a vertical axis. Compensatory eye movements in response to neck rotation were demonstrated and their dynamic characteristics described by a lag-lead model. The eye motions attributable to neck rotations and vestibular stimulation obey superposition when both systems are active. Human operator compensatory tracking is investigated in simple vehicle orientation control system with stable and unstable controlled elements. Control of vehicle orientation to a reference is simulated in three modes: visual, motion and combined. Motion cues sensed by the vestibular system through tactile sensation enable the operator to generate more lead compensation than in fixed base simulation with only visual input. The tracking performance of the human in an unstable control system near the limits of controllability is shown to depend heavily upon the rate information provided by the vestibular sensors.
VESTIBULAR APPARATUS↗
Identification and stochastic control of helicopter dynamic modes
A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.
Molusis, J. A.↗
Unsteady hovering wake parameters identified from dynamic model tests, part 1
The development of a 4-bladed model rotor is reported that can be excited with a simple eccentric mechanism in progressing and regressing modes with either harmonic or transient inputs. Parameter identification methods were applied to the problem of extracting parameters for linear perturbation models, including rotor dynamic inflow effects, from the measured blade flapping responses to transient pitch stirring excitations. These perturbation models were then used to predict blade flapping response to other pitch stirring transient inputs, and rotor wake and blade flapping responses to harmonic inputs. The viability and utility of using parameter identification methods for extracting the perturbation models from transients are demonstrated through these combined analytical and experimental studies.
Hohenemser, K. H.↗
A method for high order linear system reduction and nonlinear system simplification
Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).
Desrochers, A. A.↗
Input/output properties of the lateral vestibular nucleus
This article is a review of work in three species, squirrel monkey, cat, and rat studying the inputs and outputs from the lateral vestibular nucleus (LVN). Different electrophysiological shock paradigms were used to determine the synaptic inputs derived from thick to thin diameter vestibular nerve afferents. Angular and linear mechanical stimulations were used to activate and study the combined and individual contribution of inner ear organs and neck afferents. The spatio-temporal properties of LVN neurons in the decerebrated rat were studied in response to dynamic acceleration inputs using sinusoidal linear translation in the horizontal head plane. Outputs were evaluated using antidromic identification techniques and identified LVN neurons were intracellularly injected with biocytin and their morphology studied.
Efferent Pathways/anatomy & histology/physiology↗
The evaluation of the OSGLR algorithm for restructurable controls
The detection and isolation of commercial aircraft control surface and actuator failures using the orthogonal series generalized likelihood ratio (OSGLR) test was evaluated. The OSGLR algorithm was chosen as the most promising algorithm based on a preliminary evaluation of three failure detection and isolation (FDI) algorithms (the detection filter, the generalized likelihood ratio test, and the OSGLR test) and a survey of the literature. One difficulty of analytic FDI techniques and the OSGLR algorithm in particular is their sensitivity to modeling errors. Therefore, methods of improving the robustness of the algorithm were examined with the incorporation of age-weighting into the algorithm being the most effective approach, significantly reducing the sensitivity of the algorithm to modeling errors. The steady-state implementation of the algorithm based on a single cruise linear model was evaluated using a nonlinear simulation of a C-130 aircraft. A number of off-nominal no-failure flight conditions including maneuvers, nonzero flap deflections, different turbulence levels and steady winds were tested. Based on the no-failure decision functions produced by off-nominal flight conditions, the failure detection performance at the nominal flight condition was determined. The extension of the algorithm to a wider flight envelope by scheduling the linear models used by the algorithm on dynamic pressure and flap deflection was also considered. Since simply scheduling the linear models over the entire flight envelope is unlikely to be adequate, scheduling of the steady-state implentation of the algorithm was briefly investigated.
Bonnice, W. F.↗
Time-accurate unsteady aerodynamic and aeroelastic calculations for wings using Euler equations
A time-accurate approach to simultaneously solve the Euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings. The Euler flow eauations are solved by a time-accurate finite difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear acceleration method. The aeroelastic configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing. The unsteady flow calculations are validated wih experiment, both for a semi-infinite wing and a wall-mounted cantilever rectangular wings. Aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite-element method. The robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using the potential equations are demonstrated.
Guruswamy, Guru P.↗
A controller design for multi-body large angle maneuvers
Active large angle slewing maneuvers of a multi-body flexible dynamic system are investigated. An appropriate state variable transformation and a feedback linearization technique are employed to transform the dynamics of the nonlinear system to a new state that is more amenable to control design procedures. Closed-loop feedback algorithms are implemented to perform slewing maneuvers, while simultaneously suppressing flexural vibrations of the system. Stability of this class of nonlinear systems is also investigated, whereby a sufficient condition for asymptotic stability of the system is established. Numerical examples are presented to demonstrate the proposed active control algorithms.
Ghaemmaghami, Peiman↗
Sparse Linear Algebra Toolkit for Computational Aerodynamics
Finding solutions to sparse linear systems of equations is an essential step in Computational Engineering applications of interest to NASA. Linear systems of equations are composed and solved in almost every computational engineering application. The characteristics of linear systems vary greatly from one application to another. Accordingly, there are a wide variety of methods for the solution of linear systems of equations. The operations and methods prepared by the authors are focused on linear systems of interest to NASA, primarily those associated with Computational Fluid Dynamics (CFD), Aeroelasticity, and Aeroacoustics. The Sparse Linear Algebra Toolkit (SLAT) is a coordinated collection of software featuring operations, methods, and data structures that are useful when solving sparse linear systems of equations on modern computer architectures. The implemented operations and methods are designed and tuned for parallelism in shared memory, in distributed memory, and across the hybrid combination of distributed-shared memory. The toolkit includes novel methods and implementations for modern architectures and facilitates development of new approaches for meeting NASA’s evolving computational engineering challenges using evolving computer architectures that are not available in vendor libraries. In this paper, significant features and interfaces within SLAT are presented and verified for simulations performed with NASA’s CFD solver, FUN3D. The runtime and scaling performance of the Generalized Minimum Residual (GMRES) method implemented in SLAT is analyzed for the linear subproblems within the solution of turbulent Navier-Stokes equations employed in the simulation of high-lift configurations. Prior to this work, the SPARSKIT GMRES implementation was the only Krylov subspace method available within FUN3D. A strong scaling study shows the SLAT GMRES implementation facilitates accurate Reynolds-averaged Navier-Stokes CFD solutions between 15% and 56% faster than the SPARSKIT GMRES implementation.
Stephen L Wood↗
Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance
A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.
testing↗
Dynamic mechanical characterization of cure of a polyimide-graphite fiber composite (PMR 15/Celion 6000)
Dynamic mechanical studies of thermosetting PMR 15 polyimide/Celion 6000 composites were used to characterize cure behavior. Variation in composite shear modulus with cure time for laminates partially cured under 3.45 MPa pressure was compared with that of laminates fully cured under pressure to select a partially cured system whose behavior corresponded with that of the pressure-cured composites. An empirical kinetic model was developed that relates relative composite shear moduli to cure time and temperature. This model, coupled with standard statistical techniques, was used in the determination of an overall activation energy, E = 145 kj/mole (35 kcal/mole) and order of reaction, n, for the cure reaction(s). The empirical relationship defining dynamic modulus as a function of time and temperature remained linear well into the glassy region. Changes in dynamic glass-transition temperature and in the breadth of the transition peaks with cure time are discussed. Shear modulus and damping were found to be more sensitive measures of relative extent of cure than Fourier transform infrared spectroscopy.
Hurwitz, F. I.↗
Modeling Disturbance Dynamics in Transitional and Turbulent Boundary Layers
The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced across the boundary layer by the solid boundary. In addition, the dominating dynamics in the disturbance kinetic energy equation is governed by the energy production, pressure-transport and viscous diffusion - also in contrast to the fully turbulent regime. For the disturbance dissipation rate, a dynamic balance exists between the destruction and diffusion of dissipation.
Grosch, C. E.↗
Analysis of Transition-Sensitized Turbulent Transport Equations
The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced cross the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transition-sensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressure-gradient flow over a flat plate. Computed results are in good agreement with experimental data.
Rumsey, Christopher L.↗