Interpretation of Liapunov stability regions.
Interpretation of results obtained by Liapunov method, using parallelepiped imbedded in region of asymptotic stability
STABILITY↗
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Estimation of Directional Stability Derivatives at Moderate Angles and Supersonic Speeds
A study of some of the important aerodynamic factors affecting the directional stability of supersonic airplanes is presented. The mutual interference fields between the body, the lifting surfaces, and the stabilizing surfaces are analyzed in detail. Evaluation of these interference fields on an approximate theoretical basis leads to a method for predicting directional stability of supersonic airplanes. Body shape, wing position and plan form, vertical tail position and plan form, and ventral fins are taken into account. Estimates of the effects of these factors are in fair agreement with experiment.
Kaattari, George E.↗
Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks
Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.
97 MATHEMATICS AND COMPUTING↗
Role of reinforcement learning for risk-based robust control of cyber-physical energy systems
Critical infrastructures such as cyber-physical energy systems (CPS-E) integrate information flow and physical operations that are vulnerable to natural and targeted failures. Safe, secure, and reliable operation and control of CPS-E is critical to ensure societal well-being and economic prosperity. Automated control is key for real-time operations and may be mathematically cast as a sequential decision-making problem under uncertainty. Emergence of data-driven techniques for decision making under uncertainty, such as reinforcement learning (RL), have led to promising advances for addressing sequential decision-making problems for risk-based robust CPS-E control. However, existing research challenges include understanding the applicability of RL methods across diverse CPS-E applications, addressing the effect of risk preferences across multiple RL methods, and development of open-source domain-aware simulation environments for RL experimentation within a CPS-E context. This article systematically analyzes the applicability of four types of RL methods (model-free, model-based, hybrid model-free and model-based, and hierarchical) for risk-based robust CPS-E control. Problem features and solution stability for the RL methods are also discussed. We demonstrate and compare the performance of multiple RL methods under different risk specifications (risk-averse, risk-neutral, and risk-seeking) through the development and application of an open-source simulation environment. Motivating numerical simulation examples include representative single-zone and multizone building control use cases. Finally, six key insights for future research and broader adoption of RL methods are identified, with specific emphasis on problem features, algorithmic explainability, and solution stability.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Lean Premixed Combustion Stabilized by Low Swirl a Promising Concept for Practical Applications
Since its inception, the low-swirl burner (LSB) has shown to be a useful laboratory apparatus for fundamental studies of premixed turbulent flames. The LSB operates under wide ranges of equivalence ratios, flow rates, and turbulence intensities. Its flame is lifted and detached from the burner and allows easy access for laser diagnostics. The flame brush is axisymmetric and propagates normal to the incident reactants. Therefore, the LSB is well suited for investigating detailed flame structures and empirical coefficients such as flame speed, turbulence transport, and flame generated turbulence. Due to its capability to stabilize ultra-lean premixed turbulent flames (phi approx. = 0.55), the LSB has generated interest from the gas appliance industry for use as an economical low-NO(x) burner. Lean premixed combustion emits low levels of NO(x), due primarily to the low flame temperature. Therefore, it is a very effective NO(x) prevention method without involving selective catalytic reduction (SCR), fuel-air staging, or flue gas recirculation (FGR). En the gas turbine industry, substantial research efforts have already been undertaken and engines with lean premixed combustors are already in use. For commercial and residential applications, premixed pulsed combustors and premixed ceramic matrix burners are commercially available. These lean premixed combustion technologies, however, tend to be elaborate but have relatively limited operational flexibility, and higher capital, operating and maintenance costs. Consequently, these industries are continuing the development of lean premixed combustion technologies as well as exploring new concepts. This paper summarizes the research effects we have undertaken in the past few years to demonstrate the feasibility of applying the low-swirl flame stabilization method for a wide range of heating and power generation systems. The principle of flame stabilization by low-swirl is counter to the conventional high-swirl methods that rely on a recirculation zone to anchor the flame. In LSBS, flow recirculation is not promoted to allow the premixed turbulent flames to propagate freely. A LSB with an air-jet swirler is essentially an open tube with the swirler at its mid section. The small air-jets generate swirling motion only in the annular region and leaving the central core of the flow undisturbed, When this flow exits the burner tube, the angular momentum generates radial mean pressure gradient to diverge the non-swirling reactants stream. Consequently, the mean flow velocity decreases linearly. Propagating against this decelerating flow, the flame self-sustains at the position where the local flow velocity equals the flame speed, S(sub f). The LSB operates with a swirl number, S, between 0.02 to 0.1. This is much lower than the minimum S of 0.6 required for the high-swirl burners. We found that the swirl number needed for flame stabilization varies only slightly with fuel type, flow velocity, turbulent conditions and burner dimensions (i.e. throat diameter and swirl injection angle).
Cheng, R. K.↗
Methods for systematic generation of Liapunov functions /part one/
Review of Liapunov stability theory as applied to stability analysis on nonlinear control systems - methods for generation of Liapunov functions
GENERATION↗
A real-time digital program for estimating aircraft stability and control parameters from flight test data by using the maximum likelihood method
A computer program (Langley program C1123) has been developed for estimating aircraft stability and control parameters from flight test data. These parameters are estimated by the maximum likelihood estimation procedure implemented on a real-time digital simulation system, which uses the Control Data 6600 computer. This system allows the investigator to interact with the program in order to obtain satisfactory results. Part of this system, the control and display capabilities, is described for this program. This report also describes the computer program by presenting the program variables, subroutines, flow charts, listings, and operational features. Program usage is demonstrated with a test case using pseudo or simulated flight data.
Grove, R. D.↗
Storage stability and improvement of intermediate moisture foods, phase 2
Methods for improvement of shelf-life stability of intermediate moisture foods are considered. It was found that vitamin C is the most limiting vitamin from a nutritional standpoint with its rate of destruction increasing with a sub w. Techniques for microbial challenge studies were developed. It was shown that organisms have a higher growth a sub w limit if the IMF is prepared by the adsorption process and long times are needed for challenge studies. Several alternative antimycotic systems were found. It was also found that the vegetative cells of pathogens have a maximum heat resistance in the IMF a sub w range. If glycols are in the formula, the IMF should have as high an a sub w as possible. The reverse is true if lipid oxidation occurs. In addition, to prevent rancidity, antioxidants and a low O2 atmosphere are necessary. The package also must be a good moisture barrier.
Labuza, T. P.↗
Methods Used in the NACA Tank for the Investigation of the Longitudinal-Stability Characteristics of Models of Flying Boats
Report presents the results of tests of longitudinal stability characteristics of models of several flying boats conducted in the NACA Tank No. 1. These investigations were made for the purpose of (1) determining suitable methods for evaluating the stability characteristics of models of flying boats, and (2) determining the design parameters which have an important effect on the porpoising. This report is mainly concerned with the construction of suitable models, the apparatus, and methods used in the tests. The effect of changes in some design parameters is discussed.
Olson, Roland E↗
On the Hermite-Fujiwara theorem in stability theory.
Proof of Hermite-Fujiwara theorem of dynamic system stability based on Liapunov-type methods
DYNAMIC STABILITY↗
Two-measured variable method for wall interference assessment/correction
An iterative method for wall interference assessment and/or correction is presented for transonic flow conditions in wind tunnels equipped with two component velocity measurements on a single interface. The iterative method does not require modeling of the test article and tunnel wall boundary conditions. Analytical proof for the convergence and stability of the iterative method is shown in the subsonic flow regime. The numerical solutions are given for both 2-D and axisymmetrical cases at transonic speeds with the application of global Mach number correction.
Lo, C. F.↗
An efficient procedure for cascade aeroelastic stability determination using nonlinear, time-marching aerodynamic solvers
A numerical eigenvalue problem formulation and a practical calculation procedure for exact eigenvalues and corresponding eigenvectors are developed and applied to a nonlinear, two-dimensional, time-marching full potential solver for cascade aeroelastic stability analysis. This procedure is based on the Lanczos recursive method and it directly calculates stability information about a nonlinear steady state. It is compared to conventional approaches in the frequency and time domains developed earlier and is found to be 100-10.000 times more computationally efficient. Eigenvalue constellations and the flutter results for flow through a cascade SR5 propfan airfoil are presented.
Mahajan, Aparajit J.↗
Noise Diode Stability Measurements Using a 4.3 GHz Laboratory Radiometer
The need for passive microwave radiometry using aperture synthesis and phased arrays for large apertures requiring more stability has generated several studies. The in-flight calibration and, therefore, the stability of such systems is an important design consideration. A 4.3 GHz laboratory radiometry operating in a balanced Dicke mode has been developed for making precise brightness (noise) temperature measurements. The stability of the noise diode source used in the noise-injection loop is of interest. A statistical Allan variance method to characterize the stability of the radiometer and the noise diode is presented in this paper. Noise measurements which demonstrate this approach are also included.
Scherner, M. J.↗
Assessing Fan Flutter Stability in the Presence of Inlet Distortion Using One-way and Two-way Coupled Methods
Concerns regarding noise, propulsive efficiency, and fuel burn are inspiring aircraft designs wherein the propulsive turbomachines are partially (or fully)embedded within the airframe; such designs present serious concerns with regard to aerodynamic and aeromechanic performance of the compression system in response to inlet distortion. Previously, a preliminary design of a forward-swept high-speed fan exhibited flutter concerns in clean-inlet flows, and the present author then studied this fan further in the presence of off-design distorted in-flows. A three-dimensional, unsteady, Navier-Stokes computational fluid dynamics code is applied to analyze and corroborate fan performance with clean inlet flow. This code, already validated in its application to assess aerodynamic damping of vibrating blades at various flow conditions using a loosely-coupled approach, is modified to include a tightly-coupled aeroelastic simulation capability, and then loosely-coupled and tightly-coupled methods arecompared in their evaluation of flutter stability in distorted in-flows.
fluid-structure interaction↗
High speed transition prediction
The main objective of this work period was to develop, maintain and exercise state-of-the-art methods for transition prediction in supersonic flow fields. Basic state and stability codes, acquired during the last work period, were exercised and applied to calculate the properties of various flowfields. The development of a code for the prediction of transition location using a currently novel method (the PSE or Parabolized Stability Equation method), initiated during the last work period and continued during the present work period, was cancelled at mid-year for budgetary reasons. Other activities during this period included the presentation of a paper at the APS meeting in Tallahassee, Florida entitled 'Stability of Two-Dimensional Compressible Boundary Layers', as well as the initiation of a paper co-authored with H. Reed of the Arizona State University entitled 'Stability of Boundary Layers'.
Gasperas, Gediminis↗
Determining Pipeline Eigenfrequencies on the Basis of the Shock Response of Prefabricated Structures
Methods of calculating the dynamic characteristics of prefabricated structures are analyzed. A new method of calculating the vibrational stability of such structures is proposed. In sample calculations, the existing and proposed methods are compared for a prefabricated pipeline structure in a hydraulic system.
42 ENGINEERING↗
Elastic stability of biaxially loaded longitudinally stiffened composite structures.
A linear analysis method is presented for the elastic stability of structures of uniform cross section, that may be idealized as an assemblage of laminated plate-strips, flat and curved, and beams. Each plate-strip and beam covers the entire length of the structure and is simply supported on the edges normal to the longitudinal axis. Arbitrary boundary conditions may be specified on any external longitudinal side of plate-strips. The structure or selected plate-strips may be loaded in any desired combination of inplane biaxial loads. The analysis simultaneously considers all modes of instability and is applicable for the buckling of laminated composite structures. Some numerical results are presented to indicate possible applications.
Viswanathan, A. V.↗
Determination of Stability and Control Derivatives using Computational Fluid Dynamics and Automatic Differentiation
With the recent interest in novel control effectors there is a need to determine the stability and control derivatives of new aircraft configurations early in the design process. These derivatives are central to most control law design methods and would allow the determination of closed-loop control performance of the vehicle. Early determination of the static and dynamic behavior of an aircraft may permit significant improvement in configuration weight, cost, stealth, and performance through multidisciplinary design. The classical method of determining static stability and control derivatives - constructing and testing wind tunnel models - is expensive and requires a long lead time for the resultant data. Wind tunnel tests are also limited to the preselected control effectors of the model. To overcome these shortcomings, computational fluid dynamics (CFD) solvers are augmented via automatic differentiation, to directly calculate the stability and control derivatives. The CFD forces and moments are differentiated with respect to angle of attack, angle of sideslip, and aircraft shape parameters to form these derivatives. A subset of static stability and control derivatives of a tailless aircraft concept have been computed by two differentiated inviscid CFD codes and verified for accuracy with central finite-difference approximations and favorable comparisons to a simulation database.
Park, Michael A.↗