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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Multistep inversion workflow for 3D long-offset damped elastic waves in the Fourier domain

We present a new workflow for imaging damped three-dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short-offset and low-frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine-scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite-difference frequency-domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full-waveform inversion workflow is applied to the 3D Marmousi-2 and SEG/EAGE Salt models with long-offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one-third of the maximum offset length at a resolution consistent with the inverted frequencies.

3D full waveform inversion↗
DOE OSTI2017

Surfatron accelerator in the local interstellar cloud

Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~10{sup 7} GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of E{sub CH}/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being E{sub Ð}¡{sub L}/Z ≤ 3 × 10{sup 6} GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of E{sub CL} ~ 10{sup 17} eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 10{sup 6} GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Kramers–Kronig relation in attosecond transient absorption spectroscopy

The Kramers–Kronig relation (KKR) has a wide range of applications in extreme ultraviolet (XUV) and x-ray spectroscopy. However, the validity of KKR for many of these applications has not been systematically studied, while it is known to require careful attention in nonlinear and pump–probe experiments in optical domain spectroscopy. Here, we study the validity of KKR in XUV attosecond transient absorption spectroscopy pump–probe measurements both experimentally and theoretically using argon Fano resonances as a case study. Experiments are enabled by a phase-resolved method dubbed Complex Attosecond Transient-absorption Spectroscopy (CATS). Although the estimations based on the rotating-wave approximation suggest that KKR violation could be expected in the studied case, our results validate KKR and provide a solid basis for its application in a broad range of attosecond spectroscopy experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

RELAP-7 Development Updates

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory, and is the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is being developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). During Fiscal Year (FY) 2015, the RELAP-7 code has been further improved with expanded capability to support boiling water reactor (BWR) and pressurized water reactor NPPs analysis. The accumulator model has been developed. The code has also been coupled with other MOOSE-based applications such as neutronics code RattleSnake and fuel performance code BISON to perform multiphysics analysis. A major design requirement for the implicit algorithm in RELAP-7 is that it is capable of second-order discretization accuracy in both space and time, which eliminates the traditional first-order approximation errors. The second-order temporal is achieved by a second-order backward temporal difference, and the one-dimensional second-order accurate spatial discretization is achieved with the Galerkin approximation of Lagrange finite elements. During FY-2015, we have done numerical verification work to verify that the RELAP-7 code indeed achieves 2nd-order accuracy in both time and space for single phase models at the system level.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Compactly‐Supported Nonstationary Kernels for Computing Exact Gaussian Processes on Big Data

The Gaussian process (GP) is a widely used method for analyzing large-scale data sets, including spatio-temporal measurements of nonlinear processes that are now commonplace in the environmental sciences. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about 10,000 points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space–time prediction based on more than 1 million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.

Gaussian processes↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗
DOE OSTI2018

High Initial Sputter Rate Found for Vaccinia Virions Using Isotopic Labeling, NanoSIMS, and AFM

High-lateral-resolution secondary ion mass spectrometry (SIMS) has the potential to provide functional and depth resolved information from small biological structures, such as viral particles (virions) and phage, but sputter rate and sensitivity are not characterized at shallow depths relevant to these structures. Here we combine stable isotope labeling of the DNA of vaccinia virions with correlated SIMS imaging depth profiling and atomic force microscopy (AFM) to develop a nonlinear, nonequilibrium sputter rate model for the virions and validate the model on the basis of reconstructing the location of the DNA within individual virions. Our experiments with a Cs+ beam show an unexpectedly high initial sputter rate (~100 um 2 ·nm·pA –1 ·s –1 ) with a rapid decline to an asymptotic rate of 0.7 um 2 ·nm·pA –1 ·s –1 at an approximate depth of 70 nm. Correlated experiments were also conducted with glutaraldehyde-fixed virions, as well as O – and Ga + beams, yielding similar results. Based on our Cs + sputter rate model, the labeled DNA in the virion was between 50 and 90 nm depth in the virion core, consistent with expectations, supporting our conclusions. Virion densification was found to be a secondary effect. In conclusion, accurate isotopic ratios were obtained from the initiation of sputtering, suggesting that isotopic tracers could be successfully used for smaller virions and phage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2017

The Climate Response to Stratospheric Aerosol Geoengineering Can Be Tailored Using Multiple Injection Locations

By injecting different amounts of SO 2 at multiple different latitudes, the spatial pattern of aerosol optical depth (AOD) can be partially controlled. This leads to the ability to influence the climate response to geoengineering with stratospheric aerosols, providing the potential for design. In this work, we use simulations from the fully coupled whole-atmosphere chemistry climate model CESM1(WACCM) to demonstrate that by appropriately combining injection at just four different locations, 30°S, 15°S, 15°N, and 30°N, then three spatial degrees of freedom of AOD can be achieved: an approximately spatially uniform AOD distribution, the relative difference in AOD between Northern and Southern Hemispheres, and the relative AOD in high versus low latitudes. For forcing levels that yield 1–2°C cooling, the AOD and surface temperature response are sufficiently linear in this model so that the response to different combinations of injection at different latitudes can be estimated from single-latitude injection simulations; nonlinearities associated with both aerosol growth and changes to stratospheric circulation will be increasingly important at higher forcing levels. Optimized injection at multiple locations is predicted to improve compensation of CO 2 -forced climate change relative to a case using only equatorial aerosol injection (which overcools the tropics relative to high latitudes). The additional degrees of freedom can be used, for example, to balance the interhemispheric temperature gradient and the equator to pole temperature gradient in addition to the global mean temperature. Further research is needed to better quantify the impacts of these strategies on changes to long-term temperature, precipitation, and other climate parameters.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

From graphical to model-based distillation column design: A McCabe-Thiele-inspired mathematical programming approach

We propose a mixed-integer nonlinear programming (MINLP) model for simple and complex distillation column design and optimization. The model is based upon the concepts and equations underpinning the McCabe-Thiele method. Generalizing this method, we introduce material balances at various locations of the column and employ binary variables to determine the optimal number of trays and optimal feed locations. We model the vapor–liquid equilibrium using continuous piecewise linear approximating functions. The model is extended to account for multicomponent mixtures and non-constant-molar overflow. We also discuss how to estimate the minimum number of trays and the minimum reflux ratio.

42 ENGINEERING↗
DOE OSTI2025

Challenges of standard halo models in constraining galaxy properties from cosmic infrared background anisotropies

The halo model, combined with halo occupation distribution (HOD) prescriptions, is widely used to interpret cosmic infrared background (CIB) anisotropies and extract physical information about star-forming galaxies and their connection to large-scale structures. Recent CIB-specific implementations of the halo model have adopted more physical parameterizations. However, the extent to which these models can reliably recover meaningful physical parameters remains uncertain. We assessed whether the current parameterization of CIB halo models is sufficient to recover astrophysical quantities, such as star formation efficiency, η(M h , z), and halo mass at which the peak of star formation efficiency occurs, M max , when fit to mock data. We also assessed whether discrepancies arise from assumptions about galaxy emission (the HOD ingredients) or from more fundamental components in the halo model, such as bias and matter clustering. We fit the M21 CIB HOD model, implemented within the halo model framework, to mock CIB power spectra and star formation rate density (SFRD) data generated from the SIDES-Uchuu simulation, and compared the best-fit parameters to the known simulation inputs. We then repeated the analysis using a simplified version of the simulation (SSU), explicitly designed to match the HOD assumptions. A detailed comparison of model and simulation outputs was carried out to trace the origin of observed discrepancies. While the M21 HOD model provides a good fit to the mock data, it failed to recover the intrinsic parameters accurately, particularly the halo mass at which star formation efficiency peaks. This mismatch persists even when fitting data generated with the same model assumptions. We find strong agreement (within 5%) in the emission-related components (SFRD, emissivity), but observe a scale- and redshift-dependent offset exceeding 20% in the two-halo term of the CIB power spectrum. This likely arises from limitations in the treatment of halo bias and matter clustering within the linear approximation. Additionally, incorporating scatter in the SFR–halo mass relation and the spectral energy distribution (SED) templates significantly affects the shot noise (∼50%), but has only a modest impact (less than 10%) on the clustered component. These results suggest that recovering physical parameters from CIB clustering requires improvements to the cosmological ingredients of the halo model framework, such as adopting scale-dependent halo bias and nonlinear matter power spectra in addition to careful modeling of emission physics.

cosmic background radiation↗
DOE OSTI2024

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Marchenko, V. S. (ORCID:0000000261480533)↗
DOE OSTI2020

Multidimensional Tests of a Finite-Volume Solver for MHD With a Real-Gas Equation of State

This work considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD discontinuities. This solver is modified to use the generalized sound speed from the real-gas EOS. Two methods are tested: EOS evaluation at cell centers and at flux interfaces where the former is more computationally efficient. A battery of 1D and 2D tests are employed: convergence of 1D and 2D linearized waves, shock tube Riemann problems, a 2D nonlinear circularly polarized Alfvén wave, and a 2D magneto-Rayleigh-Taylor instability test. The cell-centered EOS evaluation algorithm produces unresolvable thermodynamic inconsistencies in the intermediate states leading to spurious solutions while the flux-interface EOS evaluation algorithm robustly produces the correct solution. The linearized wave tests show this inconsistency is associated with the magnetosonic waves and the magneto-Rayleigh-Taylor instability test demonstrates simulation findings where the spurious solution leads to an unphysical simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

On Computation of Koopman Operator from Sparse Data

In this paper, we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has a considerable interest in operator theoretic methods for data-driven analysis of dynamical systems and existing techniques for the approximation of the Koopman operator require rich enough data-sets. However, in many applications, the data set may not be rich enough to approximate the operators to acceptable limits. In this paper, using ideas from robust optimization, we propose an algorithm to compute the Koopman operator from sparse data. In particular, we enrich the sparse data set with artificial data points and use robust optimization techniques to obtain the transfer operator. We illustrate the efficiency of our proposed approach in three different dynamical systems, namely, a linear system, a nonlinear system and a dynamical system governed by a partial differential equation.

Sinha, Subhrajit↗
DOE OSTI2021

Analytic Binary Alloy Volume–Concentration Relations and the Deviation from Zen’s Law

Alloys expand or contract as concentrations change, and the resulting relationship between atomic volume and alloy content is an important property of the solid. While a well-known approximation posits that the atomic volume varies linearly with concentration (Zen’s law), the actual variation is more complicated. Here we use the apparent size of the solute (solvent) atom and the elasticity to derive explicit analytical expressions for the atomic volume of binary solid alloys. Two approximations, continuum and terminal, are proposed. Deviations from Zen’s law are studied for 22 binary alloy systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Prediction of performance and turbulence in ITER burning plasmas via nonlinear gyrokinetic profile prediction

Burning plasma performance, transport, and the effect of hydrogen isotope (H, D, D-T fuel mix) on confinement has been predicted for ITER baseline scenario (IBS) conditions using nonlinear gyrokinetic profile predictions. Accelerated by surrogate modeling (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), high fidelity, nonlinear gyrokinetic simulations performed with the CGYRO code (Candy et al 2016 J. Comput. Phys. 324 73), were used to predict profiles of T i , T e , and n e while including the effects of alpha heating, auxiliary power (NBI + ECH), collisional energy exchange, and radiation losses inside of $r/a$ = 0.9. Predicted profiles and resulting energy confinement are found to produce fusion power and gain that are approximately consistent with mission goals ($P_\textrm{fusion} = 500$ MW at Q = 10) for the baseline scenario and exhibit energy confinement that is within 1σ of the H-mode energy confinement scaling. The power of the surrogate modeling technique is demonstrated through the prediction of alternative ITER scenarios with reduced computational cost. These scenarios include conditions with maximized fusion gain and an investigation of potential resonant magnetic perturbation (RMP) effects on performance with a minimal number of gyrokinetic profile iterations required (3–6). These predictions highlight the stiff ITG nature of the core turbulence predicted in the ITER baseline and demonstrate that $Q \gt$ 17 conditions may be accessible by reducing auxiliary input power while operating in IBS conditions. Prediction of full kinetic profiles allowed for the projection of hydrogen isotope effects around ITER baseline conditions. The gyrokinetic fuel ion species was varied from H, D, and 50/50 D-T and kinetic profiles were predicted. Results indicate that a weak or negligible isotope effect will be observed to arise from core turbulence in IBS conditions. The resulting energy confinement, turbulence, and density peaking, and the implications for ITER operations will be discussed.

gyrokinetics↗
DOE OSTI2020

Data-driven predictive probability density function control of fiber length stochastic distribution shaping in refining process

Pulp is the most important raw material in paper in paper industries, whose Fiber Length Stochastic Distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the output FLSD shaping, which display non-Gaussian distribution properties. Therefore, the traditional control, method based on the mean and variance of fiber length is difficult to control the FLSD shaping effectively. In this paper, a novel data-driven predictive probability density function (PDF) control method is proposed for output FLSD shaping in refining process. Primarily, in order to improve the approximation accuracy of the PDF employing RBF neural network, the parameters (center value and width) of each RBF basis functions are tuned via utilizing iterative learning control (ILC) law, and the corresponding estimations of weights law can be obtained. Secondly, considering that the conventional linear model of weights vector has drawbacks of low accuracy and weak generalization ability, random vector functional link networks (RVFLNs) based data driven nonlinear modelling method is employed to characterize the prediction model between the input variables and weights vector. Finally, in order to reduce the randomness of the output FLSD, a minimum entropy control method under mean constraint is employed to design the predictive PDF controller for the output FLSD shaping with the help of the established nonlinear stochastic distribution model. Both simulations and experiments are given to illustrate the effectiveness and practicability of the proposed method.

Probability debsity function, Fiber length distrib↗