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Random decrement signatures have been introduced for use in the determination of the frequencies of oscillation, damping ratios and modes of vibration of structural systems from naturally induced vibration data. This paper gives an analysis of the random decrement method and the conditions which must be satisfied in order for the method to yield consistent estimates.
The random ray method is a recently developed stochastic method for solving neutral particle transport problems based on the method of characteristics. Perhaps surprisingly for a characteristics-based method using flat sources, we note that the random ray method can produce negative fluxes which may be numerically troublesome in several situations. These occur most severely in fixed source problems where the source is in a region with a small cross section. Additionally, we briefly discuss another source of bias which can occur in similar situations, namely a ray missing a mesh with a strong source and small cross section, resulting in the entirety of the source being unphysically deposited locally. This paper describes the mechanism by which negative fluxes may occur and several different methods to mitigate their effects. These fixes are tested on an eigenvalue problem, a ‘fusion-like’ shielding problem, and a shielding problem featuring an adjoint calculation. Even when extremely coarse random ray quadratures are used such that 20%–30% of cells are missed during a given iteration, use of the preferred fix technique ensures local flux tally errors remain trivial (below 1%). The preferred fix is now the default option in SCONE and OpenMC.
The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.
The random vortex method (RVM) of Chorin was developed by the recirculating flows. The RVM method models turbulence from first principles, tracking the vorticity and obtaining the interaction of vorticity with the bulk flow field. A computer program was produced called MIMOC, Modeling the Interface Motion of Combustion, which can be used to calculate the reacting flow field behind a rearward facing step. Several comparisons between experimental data and calculations were made. The RVM methood computes qualitatively good results, but the quantitative agreement as yet is not completely satisfactory. Much of the difficulty may be caused by the treatment of boundary conditions and the techniques used for obtaining statistical averages of velocities and turbulence quantities. For the rearward facing step the computed reattachment length equals the experimental value. However, the reverse velocity in the recirculation zone is over predicted by 300 percent. In the calculations, a uniform entrance velocity was assumed with no boundary layer at the step lip. This high velocity may be overdriving the reverse flow region.
A local Random Walk Method (RWM) for potential problems governed by Lapalace's and Paragon's equations is developed for two- and three-dimensional problems. The RWM is implemented and demonstrated in a multiprocessor parallel environment on a Beowulf cluster of computers. A speed gain of 16 is achieved as the number of processors is increased from 1 to 23.
Hierachy methods for random vibrations of elastic strings and beams, discussing stochastic eigenvalue problems
We review ray-optical methods of analyzing short-wavelength propagation in random media. The advantages and limitations of ray methods are discussed, and results of the statistical theory of ray segment fluctuations pertinent to ray tracing are summarized. The standard method of Monte Carlo ray tracing is compared to a new method which takes into account recent results on the statistics of ray segment fluctuations.
Glimm's (1965) random choice method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian methods. Many computed examples are given.
A numerical, grid-free algorithm is presented for one-dimensional reaction-diffusion model of laminar flame propagation in premixed gases. It is based on the random element method we developed for the analysis of diffusional processes. The effect of combustion is taken into account by applying the principle of fractional steps to separate the process of diffusion, modeled by the random walk of computational elements, from the exothermic effects of chemical reaction, monitoring their strength. The validity of the algorithm is demonstrated by application to flame propagation problems for which exact solutions exist. The flame speed evaluated by its use oscillates around the exact value at a relatively small amplitude, while the temperature and species concentration profiles are self-correcting in their convergence to the exact solution. A satisfactory resolution is obtained by the use of quite a small number of computational elements which automatically adjust their distribution of fit sharp gradients.
The feasibility of using a two-microphone, random-excitation technique for the measurement of acoustic impedance was studied. Equations were developed, including the effect of mean flow, which show that acoustic impedance is related to the pressure ratio and phase difference between two points in a duct carrying plane waves only. The impedances of a honeycomb ceramic specimen and a Helmholtz resonator were measured and compared with impedances obtained using the conventional standing-wave method. Agreement between the two methods was generally good. A sensitivity analysis was performed to pinpoint possible error sources and recommendations were made for future study. The two-microphone approach evaluated in this study appears to have some advantages over other impedance measuring techniques.
The simulation of the diffusion of a continuum field by the random walk (RW) displacement of a set of particles is considered. Elements of the gradients of the diffusive concentration are transported by computational particles. It is demonstrated that, by the use of concentration gradients in the RW process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. The algorithm is grid-free, and the computational elements move to follow the gradients; hence, the algorithm is self-adaptive, and uniform resolution is achieved for all times.
This work introduces automated machine learning workflows that address critical bottlenecks in surrogate model development for Ion Cyclotron Range of Frequencies (ICRF) heating applications. The automated framework includes data analysis tools that transform raw datasets into actionable insights in seconds, replacing weeks of manual exploratory effort and ensuring consistent, reproducible dataset characterization. By integrating advanced hyperparameter optimization (HPO) methods including Bayesian optimization via BoTorch and Tree-structured Parzen Estimators (TPE), the framework significantly reduces model development time from weeks to hours, decreasing computational cost and required expertise, while enabling high-accuracy surrogate models. Compared to traditional hyperparameter scanning (HPS) techniques such as methodical, randomized, and grid searches, HPO methods achieve superior convergence and predictive performance, even when compared to already well-tuned reference models. On NSTX High Harmonic Fast Wave (HHFW) heating datasets, both Random Forest Regressor (RFR) and neural network surrogates demonstrate improved accuracy, achieving R 2 values beyond 0.97 and 0.98, respectively. The results show that while HPO gains are modest for robust architectures like RFR, they become essential for more sensitive models such as neural networks, highlighting the trade-offs across optimization strategies. Through automated workflows that eliminate manual hyperparameter tuning and require minimal ML expertise, this work enables widespread adoption of high-fidelity surrogate models across the fusion community for real-time plasma control, uncertainty quantification, rapid experimental scenario development, and integrated system optimization.
An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.
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Identification scheme for scalar input and scalar output linear systems for wide class of random inputs
Convergence of identification scheme for scalar- input-scalar-output linear systems with random inputs, applying invariant set theorem for random systems
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