Stochastic Reduced Order Models with Python (SROMPy)

Stochastic Reduced Order Models with Python (SROMPy) is a software package developed to enable user-friendly utilization of the stochastic reduced order model (SROM) approach for uncertainty quantification. A SROM is a low dimensional, discrete approximation to a random quantity that enables efficient and non-intrusive stochastic computations. With SROMPy, a user can easily generate a SROM to approximate a random variable or vector described by several different types of probability distributions using the Python programming language. Once a SROM is constructed, the software can be used to propagate uncertainty through a user-defined computational model to estimate statistics of a given quantity of interest. This report is meant to introduce the SROMPy module and brie y demonstrate its capabilities. A simple example of a spring-mass system with a random input is included to illustrate the practicality of the SROM approach to uncertainty quantification and relative ease of applying it with SROMPy. The example includes a comparison with a solution obtained using classical Monte Carlo simulation, demonstrating the similarities and advantages of using the SROM approach

Retinal Afferents Synapse with Relay Cells Targeting the Middle Temporal Area in the Pulvinar and Lateral Geniculate Nuclei

Considerable debate continues regarding thalamic inputs to the middle temporal area (MT) of the visual cortex that bypass the primary visual cortex (V1) and the role they might have in the residual visual capability following a lesion of V1. Two specific retinothalamic projections to area MT have been speculated to relay through the medial portion of the inferior pulvinar nucleus (PIm) and the koniocellular layers of the dorsal lateral geniculate nucleus (LGN). Although a number of studies have demonstrated retinal inputs to regions of the thalamus where relays to area MT have been observed, the relationship between the retinal terminals and area MT relay cells has not been established. Here we examined direct retino-recipient regions of the marmoset monkey (Callithrix jacchus) pulvinar nucleus and the LGN following binocular injections of anterograde tracer, as well as area MT relay cells in these nuclei by injection of retrograde tracer into area MT. Retinal afferents were shown to synapse with area MT relay cells as demonstrated by colocalization with the presynaptic vesicle membrane protein synaptophysin. We also established the presence of direct synapes of retinal afferents on area MT relay cells within the PIm, as well as the koniocellular K1 and K3 layers of the LGN, thereby corroborating the existence of two disynaptic pathways from the retina to area MT that bypass V1

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach

Near Real-Time Probabilistic Damage Diagnosis Using Surrogate Modeling and High Performance Computing

This work investigates novel approaches to probabilistic damage diagnosis that utilize surrogate modeling and high performance computing (HPC) to achieve substantial computational speedup. Motivated by Digital Twin, a structural health management (SHM) paradigm that integrates vehicle-specific characteristics with continual in-situ damage diagnosis and prognosis, the methods studied herein yield near real-time damage assessments that could enable monitoring of a vehicle's health while it is operating (i.e. online SHM). High-fidelity modeling and uncertainty quantification (UQ), both critical to Digital Twin, are incorporated using finite element method simulations and Bayesian inference, respectively. The crux of the proposed Bayesian diagnosis methods, however, is the reformulation of the numerical sampling algorithms (e.g. Markov chain Monte Carlo) used to generate the resulting probabilistic damage estimates. To this end, three distinct methods are demonstrated for rapid sampling that utilize surrogate modeling and exploit various degrees of parallelism for leveraging HPC. The accuracy and computational efficiency of the methods are compared on the problem of strain-based crack identification in thin plates. While each approach has inherent problem-specific strengths and weaknesses, all approaches are shown to provide accurate probabilistic damage diagnoses and several orders of magnitude computational speedup relative to a baseline Bayesian diagnosis implementation

HZETRN Radiation Transport Validation Using Balloon-Based Experimental Data

The deterministic radiation transport code HZETRN (High charge (Z) and Energy TRaNsport) was developed by NASA to study the effects of cosmic radiation on astronauts and instrumentation shielded by various materials. This work presents an analysis of computed differential flux from HZETRN compared with measurement data from three balloon-based experiments over a range of atmospheric depths, particle types, and energies. Model uncertainties were quantified using an interval-based validation metric that takes into account measurement uncertainty both in the flux and the energy at which it was measured. Average uncertainty metrics were computed for the entire dataset as well as subsets of the measurements (by experiment, particle type, energy, etc.) to reveal any specific trends of systematic over- or under-prediction by HZETRN. The distribution of individual model uncertainties was also investigated to study the range and dispersion of errors beyond just single scalar and interval metrics. The differential fluxes from HZETRN were generally well-correlated with balloon-based measurements; the median relative model difference across the entire dataset was determined to be 30%. The distribution of model uncertainties, however, revealed that the range of errors was relatively broad, with approximately 30% of the uncertainties exceeding 40%. The distribution also indicated that HZETRN systematically under-predicts the measurement dataset as a whole, with approximately 80% of the relative uncertainties having negative values. Instances of systematic bias for subsets of the data were also observed, including a significant underestimation of alpha particles and protons for energies below 2.5 GeV/u. Muons were found to be systematically over-predicted at atmospheric depths deeper than 50 g/cm(sup 2) but under-predicted for shallower depths. Furthermore, a systematic under-prediction of alpha particles and protons was observed below the geomagnetic cutoff, suggesting that improvements to the light ion production cross sections in HZETRN should be investigated

Effect of high rotor pressure-surface diffusion on performance of a transonic turbine

The subject turbine was investigated to determine the effect of high rotor pressure-surface diffusion on turbine performance. A comparison of the subject turbine with the most efficient transonic turbine in the present series of investigations showed that the efficiency of the subject turbine was almost as high, the suction-surface diffusion parameter was about the same, and the solidity was reduced by 36 percent. Because the loss per blade increased greatly with an increase in pressure-surface diffusion, the latter is also considered to be an important design consideration