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Real-Time Nonlinear Model Predictive Control for a Hypersonic Glider.
Abstract not provided.
Insights on the nonlinear modeling and characterization of bolted lap joint interface of beams.
Abstract not provided.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.
Grain2Mesh: Mesh Generation for Grain-Scale Nonlinear Elasticity Modeling
The nonlinear hysteretic behavior of rocks under cyclic loading is a crucial area of study in geomechanics. The macroscopic response of a variety of materials has been found to be contingent upon the behavior of the micro-scale structure. This project aims to develop a functional and maintainable software package for generating a multi-phase numerical mesh and accompanying simulation files for finite element modeling used in computational mechanics solvers. Meshes generated from images often lack key preprocessing that reduces noise and prevents mesh element distortion that can increase computational cost. By incorporating user feedback throughout, grain2mesh ensures a high-fidelity mesh that can be used to model grain-scale interactions such as shearing, crack propagation, and interfacial material contrast. Scientific applications of this software include material fracturing, stress-strain analysis for natural and engineered materials, and nonlinear meso-scale analysis.
NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model
A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.
A nonlinear Bloch model for Coulomb interaction in quantum dots
In this paper, we first derive a Coulomb Hamiltonian for electron–electron interaction in quantum dots in the Heisenberg picture. Then we use this Hamiltonian to enhance a Bloch model, which happens to be nonlinear in the density matrix. The coupling with Maxwell equations in case of interaction with an electromagnetic field is also considered from the Cauchy problem point of view. The study is completed by numerical results and a discussion about the advisability of neglecting intra-band coherences, as is done in part of the literature.
Nonlinear Finite Element Model Updating Part I: Experimental Techniques and Nonlinear Modal Model Parameter Extraction.
Abstract not provided.
A tensor approach to modeling of nonhomogeneous nonlinear systems
Model following control methodology plays a key role in numerous application areas. Cases in point include flight control systems and gas turbine engine control systems. Typical uses of such a design strategy involve the determination of nonlinear models which generate requested control and response trajectories for various commands. Linear multivariable techniques provide trim about these motions; and protection logic is added to secure the hardware from excursions beyond the specification range. This paper reports upon experience in developing a general class of such nonlinear models based upon the idea of the algebraic tensor product.
NLML: A Deep Neural Network Emulator for the Exact Nonlinear Interactions in a Wind Wave Model
Nonlinear wave interactions describe the resonant energy transfer between wave components, playing a fundamental role in the evolution of ocean wave spectra. Nonlinear wave interactions significantly influence wave growth and development, making them essential for accurate wave modeling. However, resolving the full six-dimensional Boltzmann integral of the exact nonlinear wave interactions (Webb-Resio-Tracy method, WRT) is computationally expensive, limiting its application in real-time operational wave forecasting and for research purposes. Current approximations, such as the Discrete Interaction Approximation (DIA), prioritize computational speed over accuracy, resulting in significant errors in wave mean parameters. Here, we introduce NLML, a machine learning (ML) emulator designed to approximate the exact nonlinear wave interactions within WAVEWATCH III (WW3), with the goal of achieving the accuracy of WRT while maintaining the stability and computational speed of DIA. By leveraging GPU capabilities such as half precision inference, we achieved substantial speedups, up to 136x mathematical equation faster than the WRT and only a modest 1.04x mathematical equation slowdown relative to DIA, while achieving 2x mathematical equation the accuracy of DIA in global wave spectral energy and mean wave parameters, with up to 7x mathematical equation higher accuracy in some regions. Unlike previous ML approaches, NLML maintained inherent stability throughout model integration in a standalone, year-long WW3 simulation, without requiring additional constraints. Our new ML parameterization bridges the gap between accuracy and efficiency, offering a promising alternative for improving wave modeling in operational settings and research purposes.
Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters
Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.
Performance of Nonlinear Modal Model in Predicting Complex Bilinear Stiffness.
Abstract not provided.
Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models
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Formulation of the linear model from the nonlinear simulation for the F18 HARV
The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.
Microstructure-based model of nonlinear ultrasonic response in materials with distributed defects
Nonlinear ultrasonic technique is one of promising NDE methods for monitoring defect evolution in irradiated nuclear materials. In this work, we have studied the effect of distributed defects on nonlinear ultrasonic response, in particular, the nonlinear parameter ß from the 2nd harmonic wave. A three-dimensional microstructure-based model has been developed for investigating the dynamic interaction between distributed defects and a propagating longitudinal sound wave. Both linear and nonlinear materials are considered. It is known that the 2nd harmonic wave is generated when a monochromatic wave propagates in a nonlinear elastic material. The results show that second phase particles with elastic heterogeneity and lattice mismatch have strong impact on the nonlinear parameter ß. Lattice mismatches have more effect on the nonlinear parameter no matter they are expansion or contraction. The developed model enables one to explore the contributions of different types of defects to the nonlinear ultrasonic signals and shed light on the development of nonlinear ultrasound nondestructive detection of material defects in nuclear reactors.
Nonlinear aerodynamic modeling using multivariate orthogonal functions
A technique was developed for global modeling of nonlinear aerodynamic coefficients using multivariate orthogonal functions based on the data. Each orthogonal function retained in the model was decomposed into an expansion of ordinary polynomials in the independent variables, so that the final model could be interpreted as selectively retained terms from a multivariable power series expansion. A predicted squared-error metric was used to determine the orthogonal functions to be retained in the model; analytical derivatives were easily computed. The approach was demonstrated on the Z-body axis aerodynamic force coefficient (Cz) wind tunnel data for an F-18 research vehicle which came from a tabular wind tunnel and covered the entire subsonic flight envelope. For a realistic case, the analytical model predicted experimental values of Cz very well. The modeling technique is shown to be capable of generating a compact, global analytical representation of nonlinear aerodynamics. The polynomial model has good predictive capability, global validity, and analytical differentiability.