SEARCH · Search NASA

Results for “Stochastic dynamical systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

All sources NASA NTRS DOE OSTI

NASA NTRS1999

Probabilistic Structural Analysis Methods (PSAM) for Select Space Propulsion System Components

Probabilistic Structural Analysis Methods (PSAM) are described for the probabilistic structural analysis of engine components for current and future space propulsion systems. Components for these systems are subjected to stochastic thermomechanical launch loads. Uncertainties or randomness also occurs in material properties, structural geometry, and boundary conditions. Material property stochasticity, such as in modulus of elasticity or yield strength, exists in every structure and is a consequence of variations in material composition and manufacturing processes. Procedures are outlined for computing the probabilistic structural response or reliability of the structural components. The response variables include static or dynamic deflections, strains, and stresses at one or several locations, natural frequencies, fatigue or creep life, etc. Sample cases illustrates how the PSAM methods and codes simulate input uncertainties and compute probabilistic response or reliability using a finite element model with probabilistic methods.

Source record↗

NASA NTRS2007

POD Model Reconstruction for Gray-Box Fault Detection

Proper orthogonal decomposition (POD) is the mathematical basis of a method of constructing low-order mathematical models for the "gray-box" fault-detection algorithm that is a component of a diagnostic system known as beacon-based exception analysis for multi-missions (BEAM). POD has been successfully applied in reducing computational complexity by generating simple models that can be used for control and simulation for complex systems such as fluid flows. In the present application to BEAM, POD brings the same benefits to automated diagnosis. BEAM is a method of real-time or offline, automated diagnosis of a complex dynamic system.The gray-box approach makes it possible to utilize incomplete or approximate knowledge of the dynamics of the system that one seeks to diagnose. In the gray-box approach, a deterministic model of the system is used to filter a time series of system sensor data to remove the deterministic components of the time series from further examination. What is left after the filtering operation is a time series of residual quantities that represent the unknown (or at least unmodeled) aspects of the behavior of the system. Stochastic modeling techniques are then applied to the residual time series. The procedure for detecting abnormal behavior of the system then becomes one of looking for statistical differences between the residual time series and the predictions of the stochastic model.

Park, Han↗

NASA NTRS1975

The stochastic control of the F-8C aircraft using the multiple model adaptive control /MMAC/ method

The purpose of this paper is to summarize results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method. The discussion includes the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the 'identification' aspects of the design using hypothesis testing ideas, and the performance of the closed loop adaptive system.

Athans, M.↗

NASA NTRS1984

Spiral structure and star formation. I - Formation mechanisms and mean free paths

The wide variety of optical appearances observed in spiral galaxies has encouraged the growth of two theoretical approaches to explain the spiral patterns exhibited by such young objects as OB associations, giant H II regions, and dark dust lanes. These approaches are related to the density wave theory of spiral structure and 'stochastic, self-propagating star formation'. Levinson and Roberts (1981) tried to reconcile these two theoretical approaches, and considered a disk filled with discrete gas clouds. The present investigation is concerned with refinements and extensions of the model of Levinson and Roberts. Attention is given to gravitational forces and dynamical propagation, cloud-cloud collisions, supernova interactions, computational models, a theory concerning the interactions of the gas cloud and stellar association systems, the time evolution of the gas cloud-stellar association systems, and aspects of collisionally triggered star formation.

Roberts, W. W., Jr.↗

NASA NTRS2013

Developing an Accurate CFD Based Gust Model for the Truss Braced Wing Aircraft

The increased flexibility of long endurance aircraft having high aspect ratio wings necessitates attention to gust response and perhaps the incorporation of gust load alleviation. The design of civil transport aircraft with a strut or truss-braced high aspect ratio wing furthermore requires gust response analysis in the transonic cruise range. This requirement motivates the use of high fidelity nonlinear computational fluid dynamics (CFD) for gust response analysis. This paper presents the development of a CFD based gust model for the truss braced wing aircraft. A sharp-edged gust provides the gust system identification. The result of the system identification is several thousand time steps of instantaneous pressure coefficients over the entire vehicle. This data is filtered and downsampled to provide the snapshot data set from which a reduced order model is developed. A stochastic singular value decomposition algorithm is used to obtain a proper orthogonal decomposition (POD). The POD model is combined with a convolution integral to predict the time varying pressure coefficient distribution due to a novel gust profile. Finally the unsteady surface pressure response of the truss braced wing vehicle to a one-minus-cosine gust, simulated using the reduced order model, is compared with the full CFD.

Bartels, Robert E.↗

NASA NTRS1975

The stochastic control of the F-8C aircraft using the Multiple Model Adaptive Control (MMAC) method

The purpose of this paper is to summarize results obtained for the adaptive control of the F-8C aircraft using the so-called Multiple Model Adaptive Control method. The discussion includes the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the 'identification' aspects of the design using hypothesis testing ideas, and the performance of the closed loop adaptive system.

Athans, M.↗

NASA NTRS1977

The stochastic control of the F-8C aircraft using a multiple model adaptive control /MMAC/ method. I - Equilibrium flight

The purpose of this paper is to summarize some results obtained for the adaptive control of the F-8C aircraft using the so-called MMAC method. The discussion includes the selection of the performance criteria for both the lateral and the longitudinal dynamics, the design of the Kalman filters for different flight conditions, the 'identification' aspects of the design using hypothesis testing ideas, and the performance of the closed-loop adaptive system.

Athans, M.↗

NASA NTRS1994

Pulsed acceleration in solar flares

We study the nonlinear dynamics of particle acceleration in solar flares by analyzing the time series of various quasi-periodic radio signatures during flares. In particular we present the radio and hard X-ray data of three flares which suppport the following tentative conclusions: (1) Particle acceleration and injection into magnetic structures occurs intrinsically in a pulsed mode (with a typical period of 1-2 s), produced by a single, spatially coherent, nonlinear system, rather than by a stochastic system with many spatially independent components ('statistical flare' produced by a fragmented primary energy release). (2) The nonlinear (quasi-periodic) mode of pulsed particle acceleration and injection into a coronal loop can be stabilized by phase locking with an MHD wave (oscillation) mode, if both periods are close to each other. (3) Pulsed injection of electron beams into a coronal loop may trigger nonlinear relaxational oscillations of wave-particle interactions. This is particularly likely when the limit cycles of both systems are similar.

Aschwanden, Markus J.↗

NASA NTRS2008

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Cohn, Stephen E.↗

NASA NTRS1994

State-space self-tuner for on-line adaptive control

Dynamic systems, such as flight vehicles, satellites and space stations, operating in real environments, constantly face parameter and/or structural variations owing to nonlinear behavior of actuators, failure of sensors, changes in operating conditions, disturbances acting on the system, etc. In the past three decades, adaptive control has been shown to be effective in dealing with dynamic systems in the presence of parameter uncertainties, structural perturbations, random disturbances and environmental variations. Among the existing adaptive control methodologies, the state-space self-tuning control methods, initially proposed by us, are shown to be effective in designing advanced adaptive controllers for multivariable systems. In our approaches, we have embedded the standard Kalman state-estimation algorithm into an online parameter estimation algorithm. Thus, the advanced state-feedback controllers can be easily established for digital adaptive control of continuous-time stochastic multivariable systems. A state-space self-tuner for a general multivariable stochastic system has been developed and successfully applied to the space station for on-line adaptive control. Also, a technique for multistage design of an optimal momentum management controller for the space station has been developed and reported in. Moreover, we have successfully developed various digital redesign techniques which can convert a continuous-time controller to an equivalent digital controller. As a result, the expensive and unreliable continuous-time controller can be implemented using low-cost and high performance microprocessors. Recently, we have developed a new hybrid state-space self tuner using a new dual-rate sampling scheme for on-line adaptive control of continuous-time uncertain systems.

Shieh, L. S.↗

NASA NTRS2003

Low Dimensional Tools for Flow-Structure Interaction Problems: Application to Micro Air Vehicles

A low dimensional tool for flow-structure interaction problems based on Proper Orthogonal Decomposition (POD) and modified Linear Stochastic Estimation (mLSE) has been proposed and was applied to a Micro Air Vehicle (MAV) wing. The method utilizes the dynamic strain measurements from the wing to estimate the POD expansion coefficients from which an estimation of the velocity in the wake can be obtained. For this experiment the MAV wing was set at five different angles of attack, from 0 deg to 20 deg. The tunnel velocities varied from 44 to 58 ft/sec with corresponding Reynolds numbers of 46,000 to 70,000. A stereo Particle Image Velocimetry (PIV) system was used to measure the wake of the MAV wing simultaneously with the signals from the twelve dynamic strain gauges mounted on the wing. With 20 out of 2400 POD modes, a reasonable estimation of the flow flow was observed. By increasing the number of POD modes, a better estimation of the flow field will occur. Utilizing the simultaneously sampled strain gauges and flow field measurements in conjunction with mLSE, an estimation of the flow field with lower energy modes is reasonable. With these results, the methodology for estimating the wake flow field from just dynamic strain gauges is validated.

Schmit, Ryan F.↗

NASA NTRS1986

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.↗

NASA NTRS2012

Markov Modeling of Component Fault Growth over a Derived Domain of Feasible Output Control Effort Modifications

This paper introduces a novel Markov process formulation of stochastic fault growth modeling, in order to facilitate the development and analysis of prognostics-based control adaptation. A metric representing the relative deviation between the nominal output of a system and the net output that is actually enacted by an implemented prognostics-based control routine, will be used to define the action space of the formulated Markov process. The state space of the Markov process will be defined in terms of an abstracted metric representing the relative health remaining in each of the system s components. The proposed formulation of component fault dynamics will conveniently relate feasible system output performance modifications to predictions of future component health deterioration.

Bole, Brian↗

NASA NTRS2010

Modeling Common-Sense Decisions in Artificial Intelligence

A methodology has been conceived for efficient synthesis of dynamical models that simulate common-sense decision- making processes. This methodology is intended to contribute to the design of artificial-intelligence systems that could imitate human common-sense decision making or assist humans in making correct decisions in unanticipated circumstances. This methodology is a product of continuing research on mathematical models of the behaviors of single- and multi-agent systems known in biology, economics, and sociology, ranging from a single-cell organism at one extreme to the whole of human society at the other extreme. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the three most recent and relevant being Characteristics of Dynamics of Intelligent Systems (NPO -21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; Self-Supervised Dynamical Systems (NPO-30634), NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72; and Complexity for Survival of Living Systems (NPO- 43302), NASA Tech Briefs, Vol. 33, No. 7 (July 2009), page 62. The methodology involves the concepts reported previously, albeit viewed from a different perspective. One of the main underlying ideas is to extend the application of physical first principles to the behaviors of living systems. Models of motor dynamics are used to simulate the observable behaviors of systems or objects of interest, and models of mental dynamics are used to represent the evolution of the corresponding knowledge bases. For a given system, the knowledge base is modeled in the form of probability distributions and the mental dynamics is represented by models of the evolution of the probability densities or, equivalently, models of flows of information. Autonomy is imparted to the decisionmaking process by feedback from mental to motor dynamics. This feedback replaces unavailable external information by information stored in the internal knowledge base. Representation of the dynamical models in a parameterized form reduces the task of common-sense-based decision making to a solution of the following hetero-associated-memory problem: store a set of m predetermined stochastic processes given by their probability distributions in such a way that when presented with an unexpected change in the form of an input out of the set of M inputs, the coupled motormental dynamics converges to the corresponding one of the m pre-assigned stochastic process, and a sample of this process represents the decision.

Zak, Michail↗

NASA NTRS1979

On reliable control system designs with and without feedback reconfigurations

This paper contains an overview of a theoretical framework for the design of reliable multivariable control systems, with special emphasis on actuator failures and necessary actuator redundancy levels. Using a linear model of the system, with Markovian failure probabilities and quadratic performance index, an optimal stochastic control problem is posed and solved. The solution requires the iteration of a set of highly coupled Riccati-like matrix difference equations; if these converge one has a reliable design; if they diverge, the design is unreliable, and the system design cannot be stabilized. In addition, it is shown that the existence of a stabilizing constant feedback gain and the reliability of its implementation is equivalent to the convergence properties of a set of coupled Riccati-like matrix difference equations. In summary, these results can be used for offline studies relating the open loop dynamics, required performance, actuator mean time to failure, and functional or identical actuator redundancy, with and without feedback gain reconfiguration strategies.

Birdwell, J. D.↗

NASA NTRS1988

On-orbit parametric identification methodology

On-orbit system identification (ID) of large space systems is essential for various reasons. For example, the complex composite structure of such systems cannot be ground-tested; their structural dynamic characteristics must be known accurately in order to accomplish active control. Furthermore, such capability can be used to characterize/identify various disturbances. The identification process is consisted of four principal elements: (1) modeling, (2) the estimation algorithm, (3) input system, and (4) measurement system. These elements are highly correlated and all togerher determine the success of the identification problem. Accurate modeling of large space systems is the most important element of the identification process. Large flexible structures are non-linear and infinite dimensional systems with highly coupled parameters and low frequency packed modes. In addition, these systems are subject to stochastic and time-varying disturbances, they have structural parameters which can vary due to on-orbit assembly deployment, and operations. These systems are generally; however, represented by constant coefficient, finite order differential equations. The non-linearities, coupling and noise effects are also often neglected. Moreover, identification experiment designs which lead to highly complex optimization problems usually require the simultaneous choice of ID algorithm, sensor, and actuator type and placement. On-orbit bandwidth and power restrictions on excitation, limited data window, and restrictions on sensor/actuator type, placement and number, has led to practical questions of implementations.

Hadaegh, Fred Y.↗

NASA NTRSDate not supplied

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗

NASA NTRS1984

Quadratic optimal cooperative control synthesis with flight control application

An optimal control-law synthesis approach is presented that involves simultaneous solution for two cooperating controllers operating in parallel. One controller's structure includes stochastic state estimation and linear feedback of the state estimates, while the other controller involves direct linear feedback of selected system output measurements. This structure is shown to be optimal under the constraint of linear feedback of system outputs in one controller. Furthermore, it is appropriate for flight control synthesis where the full-state optimal stochastic controller can be adjusted to be representative of an optimal control model of the human pilot in a stochastic regulation task. The method is experimentally verified in the case of the selection of pitch-damper gain for optimum pitch tracking, where optimum implies the best subjective pilot rating in the task. Finally, results from application of the method to synthesize a controller for a multivariable fighter aircraft are presented, and implications of the results of this method regarding the optimal plant dynamics for tracking are discussed.

Schmidt, D. K.↗