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At least 649 records · Page 36

Nonlinear infrared generation in alkali metal vapors: Steady state susceptibilities and dynamic behavior. Effective relaxation rates and preliminary Raman gain predictions for the Cs system

Effective relaxation rates for atomic cesium pumped by doubled Alexandrite radiation are presented. Laser radiation levels are 8S 1/2 and 9S 1/2; resonance levels 3 = 8P 1/2 and 8P 1/2, respectively. In addition, Raman gain is represented in two graphs which plot chi per atom (10 to the -13 power) at Raman peak versus the infrared wave number per centimeter and the corresponding doubled Alexandrite wave number. One graph covers resonance level 8P, the other 9P; in both cases cesium is pumped with a peak pulse height of 0.5 MW in a 200 micron diameter spot size.

Lawandy, N. M.↗

An Application of Flexible Multibody Simulations to Space Launch Systems Liftoff Pad Separation and Umbilical Disconnect

A flexible multibody dynamics approach is applied to the Space Launch System (SLS) liftoff Coupled Loads Analysis (CLA), enabling the inclusion of a large array of component nonlinearities with extreme computational efficiency. The nonlinearities include the cryogenic induced preloads due to the large rotations of the aft struts connecting the Core Stage (CS) to the boosters, the contact/separation and potential re-contact at the booster aft skirt to Mobile Launcher(ML) interface, contact/separation and potential re-contact at the ML/extensible columns interfaces, secondary disconnect of the CS umbilicals including the LOX and LH2 Tail Service Mast Umbilicals (TSMUs), and the disconnect of the upper stage umbilical, the Interim Cryogenic Propulsion Stage Umbilical (ICPSU). The ICPSU disconnect involves algorithms simulating the winch motors reeling lanyard ropes, the nonlinear modeling of ropes and hoses, the disconnect and capture of multiple umbilical ground plates by catch-nets (geometrically nonlinear models), and the large rotations of the ML gantry in order to track clearances between the lifting SLS vehicle and umbilicals rotating out of the way. The flexible multibody dynamics framework utilized for these simulations provided a systematic and efficient framework for adding complex nonlinearities at the system level which would have otherwise not been possible in standard CLAs or would have to be treated by separate local analyses thereby not accounting for the coupled system behavior.

Application↗

A Flexible Multibody Framework for Space Launch System Liftoff with Umbilical Separations

ICPSU clearances to the lifting SLS vehicle were computed utilizing a coupled system nonlinear simulation approach in order to accurately capture the impact of system flexibilities, SLS forcing functions, pad separation (twang), ML dynamics and timings • i.e., integrate ICPSU model into a SLS nonlinear Coupled Loads Analysis (CLA) This required utilizing a flexible multibody framework for the CLA and the integration of large displacements/rotations capabilities into that CLA • Gantry rotation • Disconnect and retraction of flexible hoses

Arya Majed↗

Simulation of a Controlled Airfoil with Jets

Numerical simulations of a two-dimensional airfoil, controlled by an applied moment in pitch and an airfoil controlled by jets, were investigated. These simulations couple the Reynolds-averaged Navier-Stokes equations and Euler's equations of rigid body motion, with an active control system. Controllers for both systems were designed to track altitude commands and were evaluated by simulating a closed-loop altitude step response using the coupled system. The airfoil controlled by a pitching moment used an optimal state feedback controller. A closed-loop simulation, of the airfoil with an applied moment, showed that the trajectories compared very well with quasi-steady aerodynamic theory, providing a measure of validation. The airfoil with jets used a controller designed by robust control methods. A linear plant model for this system was identified using open-loop data generated by the nonlinear coupled system. A closed-loop simulation of the airfoil with jets, showed good tracking of an altitude command. This simulation also showed oscillations in the control input as a result of dynamics not accounted for in the control design. This research work demonstrates how computational fluid dynamics, coupled with rigid body dynamics, and a control law can be used to prototype control systems in problematic nonlinear flight regimes.

Allan, Brian G.↗

Transient Response Dynamic Module Modifications to Include Static and Kinetic Friction Effects

A methodology that supports forced transient response dynamic solutions when both static and kinetic friction effects are included in a structural system model is described. Modifications that support this type of nonlinear transient response solution are summarized for the transient response dynamics (TRD) NASTRAN module. An overview of specific modifications for the NASTRAN processing subroutines, INITL, TRD1C, and TRD1D, are described with further details regarding inspection of nonlinear input definitions to define the type of nonlinear solution required, along with additional initialization requirements and specific calculation subroutines to successfully solve the transient response problem. The extension of the basic NASTRAN nonlinear methodology is presented through several stages of development to the point where constraint equations and residual flexibility effects are introduced into the finite difference Newmark-Beta recurrsion formulas. Particular emphasis is placed on cost effective solutions for large finite element models such as the Space Shuttle with friction degrees of freedom between the orbiter and payloads mounted in the cargo bay. An alteration to the dynamic finite difference equations of motion is discussed, which allows one to include friction effects at reasonable cost for large structural systems such as the Space Shuttle. Data are presented to indicate the possible impact of transient friction loads to the payload designer for the Space Shuttle. Transient response solution data are also included, which compare solutions without friction forces and those with friction forces for payloads mounted in the Space Shuttle cargo bay. These data indicate that payload components can be sensitive to friction induced loads.

Misel, J. E.↗

Minimum fuel control of a vehicle with a continuously variable transmission

The design and evaluation of a control system for a sedan with a heat engine and a continuously variable transmission, is considered in a effort to minimize fuel consumption and achieve satisfactory dynamic response of vehicle variables as the vehicle is driven over a standard driving cycle. Even though the vehicle system was highly nonlinear, attention was restricted to linear control algorithms which could be easily understood and implemented demonstrated by simulation. Simulation results also revealed that the vehicle could exhibit unexpected dynamic behavior which must be taken into account in any control system design.

Burghart, J. H.↗

Modeling Nonperturbative Field-Driven Vibronic Dynamics: Selective State Preparation and Nonlinear Spectroscopy

The partially linearized density matrix formalism for nonadiabatic dynamics is adapted to incorporate a classical external electromagentic field into the system Hamiltonian. This advancement encompasses the possibility of describing field-driven dynamics and computing a variety of linear and nonlinear spectroscopic signals beyond the perturbative limit. Here, the capabilities of the developed approach are demonstrated on a simple two-state vibronic model coupled to a bath, for which we (a) perform an exhaustive search in the field parameter space for optimal state preparation and (b) compute time-resolved transient absorption spectroscopy to monitor the effect of different pulse shapes on measurable experimental signals. While no restrictions on the form of the field have to be assumed, we focus here on Gaussian shaped (linearly) chirped pulses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-Driven Modeling and Correction of Vehicle Dynamics

We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

data-driven modeling↗

Physics-aware adaptive checkpointing with shadow systems for nonlinear PDE simulations

Large-scale simulations of nonlinear partial differential equations (PDEs) that exhibit strongly transient behavior and pattern-forming dynamics produce enormous amounts of data, which, even with modern storage systems, cannot be stored for later curation. Current I/O strategies either write dense time series of snapshots, which is often prohibitive in I/O and storage, or store a few checkpoints that enable restart but incur expensive recomputation cost and provide no control over post-restart error growth, especially when lossy compression is used. Moreover, most, if not all, existing strategies take no account of the actual physical state of the system. Here, we present a simple physics-aware I/O framework in which a low-cost shadow system adaptively triggers lossy checkpoints when the shadow system deviates from the fine-scale simulation. The shadow system can be a coarsened replica of the fine-scale simulation that evolves concurrently. This means that checkpoints are taken based on the physical state of the system: fewer checkpoints are triggered when the system is quiescent while more are taken when the system undergoes a rapid change. This type of behavior is observed in many systems such as Brusselator and FitzHugh–Nagumo. We illustrate that our framework maintains stable restarts, keeps fine-scale restart errors bounded by shadow errors, and reconstructs the time history with significantly lower error and storage than interpolating fixed-interval snapshots, with low-cost shadow replay and modest online synchronization overhead.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗

Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Here, we formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.

03 NATURAL GAS↗

Aerodynamic simulation on massively parallel systems

This paper briefly addresses the computational requirements for the analysis of complete configurations of aircraft and spacecraft currently under design to be used for advanced transportation in commercial applications as well as in space flight. The discussion clearly shows that massively parallel systems are the only alternative which is both cost effective and on the other hand can provide the necessary TeraFlops, needed to satisfy the narrow design margins of modern vehicles. It is assumed that the solution of the governing physical equations, i.e., the Navier-Stokes equations which may be complemented by chemistry and turbulence models, is done on multiblock grids. This technique is situated between the fully structured approach of classical boundary fitted grids and the fully unstructured tetrahedra grids. A fully structured grid best represents the flow physics, while the unstructured grid gives best geometrical flexibility. The multiblock grid employed is structured within a block, but completely unstructured on the block level. While a completely unstructured grid is not straightforward to parallelize, the above mentioned multiblock grid is inherently parallel, in particular for multiple instruction multiple datastream (MIMD) machines. In this paper guidelines are provided for setting up or modifying an existing sequential code so that a direct parallelization on a massively parallel system is possible. Results are presented for three parallel systems, namely the Intel hypercube, the Ncube hypercube, and the FPS 500 system. Some preliminary results for an 8K CM2 machine will also be mentioned. The code run is the two dimensional grid generation module of Grid, which is a general two dimensional and three dimensional grid generation code for complex geometries. A system of nonlinear Poisson equations is solved. This code is also a good testcase for complex fluid dynamics codes, since the same datastructures are used. All systems provided good speedups, but message passing MIMD systems seem to be best suited for large miltiblock applications.

Haeuser, Jochem↗

Sliding-Mode Control Applied for Robust Control of a Highly Unstable Aircraft

An investigation into the application of an observer based sliding mode controller for robust control of a highly unstable aircraft and methods of compensating for actuator dynamics is performed. After a brief overview of some reconfigurable controllers, sliding mode control (SMC) is selected because of its invariance properties and lack of need for parameter identification. SMC is reviewed and issues with parasitic dynamics, which cause system instability, are addressed. Utilizing sliding manifold boundary layers, the nonlinear control is converted to a linear control and sliding manifold design is performed in the frequency domain. An additional feedback form of model reference hedging is employed which is similar to a prefilter and has large benefits to system performance. The effects of inclusion of actuator dynamics into the designed plant is heavily investigated. Multiple Simulink models of the full longitudinal dynamics and wing deflection modes of the forward swept aero elastic vehicle (FSAV) are constructed. Additionally a linear state space models to analyze effects from various system parameters. The FSAV has a pole at +7 rad/sec and is non-minimum phase. The use of 'model actuators' in the feedback path, and varying there design, is heavily investigated for the resulting effects on plant robustness and tolerance to actuator failure. The use of redundant actuators is also explored and improved robustness is shown. All models are simulated with severe failure and excellent tracking, and task dependent handling qualities, and low pilot induced oscillation tendency is shown.

Vetter, Travis Kenneth↗

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

97 MATHEMATICS AND COMPUTING↗

Nonlinear observers with linearizable error dynamics

A new method for designing asymptotic observers for a class of nonlinear systems is presented. The error between the state of the systems and the state of the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.

Krener, A. J.↗

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Lin, Tsung-Chieh↗

On the Modeling of Shells in Multibody Dynamics

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the, constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Bauchau, Olivier A.↗

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Abarzhi, S. I.↗