Search NASA⌕ Search

SEARCH · Search NASA

Results for “EM Algorithms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

159 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Accelerating dissipative particle dynamics simulations on GPUs: Algorithms, numerics and applications

We present a scalable dissipative particle dynamics simulation code, fully implemented on the Graphics Processing Units (GPUs) using a hybrid CUDA/MPI programming model, which achieves 10-30 times speedup on a single GPU over 16 CPU cores and almost linear weak scaling across a thousand nodes. A unified framework is developed within which the efficient generation of the neighbor list and maintaining particle data locality are addressed. Our algorithm generates strictly ordered neighbor lists in parallel, while the construction is deterministic and makes no use of atomic operations or sorting. Such neighbor list leads to optimal data loading efficiency when combined with a two-level particle reordering scheme. A faster in situ generation scheme for Gaussian random numbers is proposed using precomputed binary signatures. We designed custom transcendental functions that are fast and accurate for evaluating the pairwise interaction. The correctness and accuracy of the code is verified through a set of test cases simulating Poiseuille flow and spontaneous vesicle formation. Computer benchmarks demonstrate the speedup of our implementation over the CPU implementation as well as strong and weak scalability. A large-scale simulation of spontaneous vesicle formation consisting of 128 million particles was conducted to further illustrate the practicality of our code in real-world applications.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Parallel physics-informed neural networks via domain decomposition

Here we develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈ {CPUs, GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Fracture Diagnostics Using Low Frequency Electromagnetic Induction and Electrically Conductive Proppants

The monitoring and diagnostics of induced fractures are important for the real-time performance evaluation of hydraulic fracturing operations. Previous electromagnetic (EM) based studies show that single backbone tri-axial induction logging tools are promising candidates for real-time monitoring and diagnosis of fractures in open-hole wells. To support the development of field deployable tools, the concept must be tested in experiments, in a controllable environment, before it is tested under field-like conditions. To this end, we have developed numerical tools which can simulate any wellbore environment while logging hydraulic fractures with the induction tool. We have designed and built a prototype induction tool and performed two sets of tests to compare with numerical simulation results. The computational and experimental setup consists of tri-axial transmitter- and receiver-coils in co-axial, co-planar and cross-polarized configurations. Both lab and shallow earth measurements are shown to be in good agreement with simulations for all examined cases. The average relative and maximum discrepancies of the measured signals from the simulated ones were lower than 3% and 10%, respectively. With the prototype tool, strong signals sensitive to the fracture’s surface area and dip-angle were measured in co-axial coil configuration, while weaker signals sensitive to the fracture’s aspect ratio were observed in the co-planar configuration. Cross-polarized signals are also shown to be strong and sensitive to the fracture’s dip. Lastly, we resolved the detectable components of the signal tensor to obtain parameters of simplified fracture geometries. The inversion algorithm, a derivative free directional search model, uses an objective function defined as a combination of co-axial and cross-polarized signals from different tool spacings to provide a well behaved global minimum. The robustness of inversion algorithm is tested on synthetic data for single cluster fractures in homogeneous and heterogeneous background electrical conductivity. All the effective model parameters for different cases, fracture conductivity (width), propped area (length) and dip-angle, are shown to be recovered with sufficient accuracy. We also evaluated the effect of multiple neighboring fractures and suggested a multi-cluster inversion algorithm that can accurately recover the proppant distribution in each fracture. Based on these results we provide a downhole tool design, with detailed specifications, that can effectively recover far-field proppant distribution in hydraulic fractures.

02 PETROLEUM↗
DOE OSTI2019

R and DE Robotic Sensor Intern Team: Remote 3D Mapping Overview

The Department of Energy (DOE) nuclear complex includes many hazardous and challenging environments that must be inspected remotely and routinely for structural integrity evaluation and long-term planning purposes. The H-Canyon Air Exhaust (HCAEX) Tunnel biannual inspection is an example of such an environment. Presently inspections are performed by teleoperated robotic crawlers provide low resolution video feedback to the structural engineers. Advanced sensors such as Lidar and panospheric hi-res cameras have the potential to provide additional valuable data in future inspections. UT-Austin Lidar work in support of an H-Canyon deployment began with the DOE EM sponsored H-Canyon Integrated Research Project. The R and DE Robotic Sensor intern team includes two of the UT-Austin Masters students working on Lidar development to facilitate the pulling of university developed solutions to the field. The goal of this project is to develop a suite of sensors that could be used to gather advanced data in future HCAEX tunnel inspections. Of particular interest is the ability to map the tunnel walls at an accuracy that will allow for the comparison of two scans performed at different time periods to estimate the concrete erosion rate. Additionally, the development of the 3D point cloud in the GPS denied environment is the first step in being able to collect and overlay other 3D data such as radiation mapping. Project specific goals include: - Design and develop 3D mapping sensor suite. Merge Lidar point cloud with high res camera images Incorporate Inertial Measurement Unit (IMU) to assist with positioning. - Develop sensor software and user GUI Sensor data collection and integration software User GUI for reach back system. - Test solution on crawler in tunnel test bed Use crawler base similar to H-Canyon planned crawler Design and build test bed simulating tunnel conditions. To facilitate rapid sensor integration, software coding and user GUI development, the Robot Operating System (ROS) was employed as the development platform. ROS is a set of open source software libraries and tools that assist with the building of robot applications. ROS includes drivers for many sensors, state-of-the-art algorithms, and powerful developer tools. Sensors selected for the summer intern solution included assessment as to whether they possessed ROS drivers and associated sample code. Additionally, the ROS 3D Robot Visualizer (rviz) tool has been employed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

MULTI-WAVELENGTH OBSERVATIONS OF THE SPATIO-TEMPORAL EVOLUTION OF SOLAR FLARES WITH AIA/SDO. II. HYDRODYNAMIC SCALING LAWS AND THERMAL ENERGIES

In this study we measure physical parameters of the same set of 155 M- and X-class solar flares observed with AIA/SDO as analyzed in Paper I, by performing a differential emission measure analysis to determine the flare peak emission measure EM{sub p} , peak temperature T{sub p} , electron density n{sub p} , and thermal energy E{sub th}, in addition to the spatial scales L, areas A, and volumes V measured in Paper I. The parameter ranges for M- and X-class flares are log (EM{sub p}) = 47.0-50.5, T{sub p} = 5.0-17.8 MK, n{sub p} = 4 × 10{sup 9}-9 × 10{sup 11} cm{sup –3}, and thermal energies of E{sub th} = 1.6 × 10{sup 28}-1.1 × 10{sup 32} erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T{sub p}{sup 2}∝n{sub p} L and H∝T {sup 7/2} L {sup –2} during the peak time t{sub p} of the flare density n{sub p} , when energy balance between the heating rate H and the conductive and radiative loss rates is achieved for a short instant and thus enables the applicability of the RTV scaling law. The application of the RTV scaling law predicts power-law distributions for all physical parameters, which we demonstrate with numerical Monte Carlo simulations as well as with analytical calculations. A consequence of the RTV law is also that we can retrieve the size distribution of heating rates, for which we find N(H)∝H {sup –1.8}, which is consistent with the magnetic flux distribution N(Φ)∝Φ{sup –1.85} observed by Parnell et al. and the heating flux scaling law F{sub H} ∝HL∝B/L of Schrijver et al.. The fractal-diffusive self-organized criticality model in conjunction with the RTV scaling law reproduces the observed power-law distributions and their slopes for all geometrical and physical parameters and can be used to predict the size distributions for other flare data sets, instruments, and detection algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Automated Sequence Design of 3D Polyhedral Wireframe DNA Origami with Honeycomb Edges

3D polyhedral wireframe DNA nanoparticles (DNA-NPs) fabricated using scaffolded DNA origami offer complete and independent control over NP size, structure, and asymmetric functionalization on the 10–100 nm scale. However, the complex DNA sequence design needed for the synthesis of these versatile DNA-NPs has limited their widespread use to date. While the automated sequence design algorithms DAEDALUS and vHelix-BSCOR apply to DNA-NPs synthesized using either uniformly dual or hybrid single-dual duplex edges, respectively, these DNA-NPs are relatively compliant mechanically and are therefore of limited utility for some applications. Further, these algorithms are incapable of handling DNA-NP edge designs composed of more than two duplexes, which are needed to enhance DNA-NP mechanical stiffness. As an alternative, here we introduce the scaffolded DNA origami sequence design algorithm TALOS, which is a generalized procedure for the fully automated design of wireframe 3D polyhedra composed of edges of any cross section with an even number of duplexes, and apply it to DNA-NPs composed uniformly of single honeycomb edges. We also introduce a multiway vertex design that enables the fabrication of DNA-NPs with arbitrary edge lengths and vertex angles and apply it to synthesize a highly asymmetric origami object. Sequence designs are demonstrated to fold robustly into target DNA-NP shapes with high folding efficiency and structural fidelity that is verified using single particle cryo-electron microscopy and 3D reconstruction. Furthermore, in order to test its generality, we apply TALOS to design an in silico library of over 200 DNA-NPs of distinct symmetries and sizes, and for broad impact, we also provide the software as open source for the generation of custom NP designs.

3D cryo-EM reconstruction↗
DOE OSTI2021

Physics-informed machine learning

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Design update on the transition beamline for the CEBAF Energy Upgrade

For Jefferson Lab’s 22GeV upgrade, two new permanent-magnet Fixed-Field Alternating Gradient (FFA) arcs will be integrated to serve the accelerator’s six highest-energy recirculation passes. Connecting these FFA arcs to the existing linear accelerator (linac) requires a carefully engineered transition section. The current design has two parts where the first part adiabatically matches the beam dispersion and orbit trajectories, while the second part aligns the Twiss parameters (alpha and beta functions) with those at the linac entrance. Given the tight spatial constraints and multiple matching requirements, a genetic algorithm is being explored to optimize the beam optics matching. This paper presents the current progress in developing and optimizing this transition.

Accelerator Physics↗
DOE OSTI2016

Pre-commercial Demonstration of Direct Non-iterative State Estimator for Operational Use of Synchrophasor Management Systems

The objective of this project was to demonstrate functionality and performance of a Direct Non-iterative State Estimator (DNSE) integrated with NYPA’s Energy Management System (EMS) and with enhanced Real Time Dynamics Monitoring System (RTDMS) synchrophasor platform from Electric Power Group (EPG). DNSE is designed to overcome a major obstacle to operational use of Synchro-Phasor Management Systems (SPMS) by providing to synchrophasor management systems (SPMS) applications a consistent and a complete synchrophasor data foundation in the same way that a traditional EMS State Estimator (SE) provides to EMS applications. Specifically, DNSE is designed to use synchrophasor measurements collected by a central PDC, Supervisory Control and Data Acquisition (SCADA) measurements, and Energy Management System (EMS) network model, to obtain the complete state of the utility’s operating model at rates that are close to the synchrophasor data rates. In this way, the system is comprehensive in that it does not only cover the part of the network that is “visible” via synchrophasors, but also the part that is only “visible” through the SCADA measurements. Visualization needs associated with the use of DNSE results are fulfilled through suitably enhanced Real Time Dynamics Monitoring System (RTDMS), with the enhancements implemented by EPG. This project had the following goals in mind: To advance the deployment of commercial grade DNSE software application that relies on synchrophasor and SCADA data ; Apply DNSE at other utilities, to address a generic and fundamental need for “clean” operational data for synchrophasor applications; Provide means for “live” estimated data access by control system operators; Enhance potential for situational awareness through full system operational model coverage; Sub-second execution rate of the Direct Non-iterative State Estimator, eventually at a near-phasor data rate execution speed, i.e. < 0.1 sec. Anticipated benefits from this projects are: Enhanced reliability and improvements in the economic efficiency of bulk power system planning and operations; Providing “clean” data to other synchrophasor applications; Enhancement of situational awareness by providing the full operational model updated at near synchrophasor rate; A production-grade software tool that incorporate synchrophasor and SCADA data; Provides a basis for development of next generation monitoring and control applications, based on both SCADA and PMU data. Quanta Technology (QT) team worked in collaboration with Electric Power Group (EPG) whose team has enhanced its commercial Real Time Dynamics Monitoring System (RTDMS) to accommodate the requirements posed by DNSE application. EPG also provided its ePDC and Model-less Data Conditioning (PDVC) software for integration with DNSE+. QT developed the system requirements for DNSE; developed system architecture and defined interfaces between internal DNSE components. The core DNSE algorithm with all surrounding interfaces was named DNSE+. Since the DNSE development was done in a simulated system environment, QT used its PMU simulator that was enhanced during this project for development and factory acceptance testing (FAT). SCADA data in this stage was simulated by commercial PSS/e software. The output of DNSE are estimates of System states in C37.118-2 format, sent to RTDMS for further processing and display. As the number of these states is large, it was necessary to expand the C37.111-2 standard to accommodate large data sets. This enhancement was implemented in RTDMS. The demonstration of pre-production DNSE technology was done at NYPA using streaming field data from NYPA PMUs and from its RTUs through their SCADA system. NYPA provided ICCP interface as well as Common Information Model (CIM). The relevance of the DNSE+ application is that it provides state estimation of the power system based on hybrid set of data, consisting of both available PMU data and SCADA measurements. As this is a direct, non-iterative method of calculation of the system states, if does not suffer from convergence issues which is potential problem for conventional state estimators. Also, it can take any available PMU measurements, so it does not need to have a high percentage of PMU coverage needed in the case of Linear State Estimator. As the DNSE calculates synchrophasors of the system states (both phase and absolute value) as sub-second rate, this application can provide a basis for development of next generation of applications based both on SCADA and PMU data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Development of NDE/NDT Tools for High-Volume & High-Speed Inspection of CFRP Structures in Automotive Manufacturing

Main advantages of the air-coupled ultrasound testing (ACUT) and electromagnetic testing (EMT) techniques for NDE of CFRP composites were non-contact sensing, scalability for high-speed inspection, cost-effectiveness, and non-hazardous operation. Despite these advantages, no systems that would satisfy the project requirements were commercially available. Hence, one of the major efforts of the Michigan State University (MSU) team at the initial stage of the project was to close this technological gap by developing, optimizing, and validating array sensors that would provide sufficient sensitivity, spatial coverage, and resolution for robust defect detection. Optimization of the ACUT and EMT sensor designs was performed using experimentally validated finite element models. Initial experiments using array probes were conducted on relatively flat CFRP samples. In parallel, the MSU team designed and assembled a portable platform with two robotic arms. The robots were equipped with newly designed sensors that enabled high-speed NDE of curved CFRP parts. Presently, the developed robotic platform can be used as a demo/template NDE system, which is easily adaptable to manufacturing environments and in-line NDE. The ACUT NDE system developed by the MSU team used a high-power 4-channel pulser receiver for parallel data acquisition. The array probes were designed by stacking commercially available ACUT transducers, which operated in the frequency range between 100 kHz and 500 kHz. MSU optimized the excitation procedure and developed wave focusing cones so as to reduce the crosstalk between the transducers and to provide higher pulse repletion frequency (PRF). The through-transmission (TT) and single-side access (SSA) inspection modes were successfully implemented. In the TT-ACUT, structural defects in CFRP were detected by passing ultrasonic waves through the test part. Hence, the ACUT transmitters and receivers needed to be placed on the opposite sides of the test part. In the SSA-ACUT, guided waves (GW) were excited in the test part using the transmitters and were sensed by the receivers from the same side. Multi-channel TT-ACUT and SSA-ACUT provided high-speed NDE, and were successfully validated on CFRP test samples with interlaminar delaminations and other embedded defects The EM techniques developed by the MSU team included: 1) eddy current testing (ECT), 2) capacitive imaging (CI) and hybrid dual-mode imaging. In ECT, structural damage was detected in CFRP using coils sensor arrays. In ECT, the excitation magnetic field is generated by passing an alternating current through a coil, which is placed above the test sample. The excitation field penetrates the conductive sample and induces the eddy currents in its transect. In turn, the eddy currents generate the reaction field, which affects the total field sensed by a coil. Hence, the presence of structural flaws will alter the eddy current flow and the picked-up signal. ECT is mostly sensitive to local changes of the electric conductivity of the test sample, and CFRPs are mostly conductive in the direction of carbon fibers. Hence, ECT was well suited for the detection of fiber damage/fiber irregularities. The MSU team developed printed circuit boards (PCB) with coil sensor arrays optimized for NDE of CFRP. Unlike most commercial probes designed for ECT of metallic structures, the MSU array probes were designed for operation in [1-10] MHz frequency range, which was optimal for low-conductive CFRP. Multiple sensing topologies (coil groups excitation/sensing arrangements) were implemented and successfully validated. Capacitive Imaging (CI) technique developed by MSU was complementary to ECT. In contrast to ECT, which was sensitive to local changes of the electrical conductivity, the CI was sensitive to local changes of the dielectric constant. Therefore, CI could provide information about matrix damage/matrix irregularities in CFRP. The MSU CI sensor arrays were made of multiple circular or rectangular open-plate capacitors printed on PCB. Sensors of this type are not commercially available. In addition to ECT and CI, the MSU team developed a hybrid (dual-mode) inductive/capacitive measurement technique that synergistically combined the benefits of inductive and capacitive sensing for rapid NDE of fiber reinforced polymer (FRP) composite structures. Fiber damage and fiber irregularities in FRPs were detected by configuring hybrid sensors as coil sensors. Similarly, matrix damage, matrix irregularities and interlaminar delaminations were detected by configuring hybrid sensors as capacitive sensors. ECT and CI were performed sequentially by means of electronic switching. Hence, eliminating the need for mounting two separate sensor arrays on the probe. Portable robotic platform was developed by MSU for multi-technique high-speed NDE of CFRP test parts. The platform had two 6-axis robots, which enabled inspection of curved parts in approximately a 6×6×6 ft 3 active scan area. On the software side, the MSU team integrated scripts for NDE hardware control with scripts for robot motion control. MSU also implemented automated path planning for the robots, reconstruction of part’s surfaces via stereovision, 3D rendering of inspection data, and image processing algorithms for enhanced defect detection. Automotive composite parts manufactured by Plasan Composites from Phase I were used to validate the ACUT and EMT techniques on representative testbeds. Among those parts were three X-braces for a Dodge Viper, one composite calibration plaque with known defects at known locations, and four other test sections, including sections from a front splitter, a corner section from a composite hood, and a high-pressure RTM panel made using non crimp fabric. Other test samples included CFRP and GFRP calibration plates with fiber/matrix defects fabricated at MSU/CVRC.

36 MATERIALS SCIENCE↗
DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗