A novel machine learning based lumping approach for the reduction of large kinetic mechanisms for plasma-assisted combustion applications
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Rekkas-Ventiris, Georgios (ORCID:0000000226586586)↗
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System identification for building thermal systems under the presence of unmeasured disturbances in closed loop operation: Lumped disturbance modeling approach
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Construction & Building Technology↗
Lumping and splitting: Toward a classification of mineral natural kinds
How does one best subdivide nature into kinds? All classification systems require rules for lumping similar objects into the same category, while splitting differing objects into separate categories. Mineralogical classification systems are no exception. Our work in placing mineral species within their evolutionary contexts necessitates this lumping and splitting because we classify “mineral natural kinds” based on unique combinations of formational environments and continuous temperature-pressure-composition phase space. Consequently, we lump two minerals into a single natural kind only if they: (1) are part of a continuous solid solution; (2) are isostructural or members of a homologous series; and (3) form by the same process. A systematic survey based on these criteria suggests that 2310 (~41%) of 5659 IMA-approved mineral species can be lumped with one or more other mineral species, corresponding to 667 “root mineral kinds,” of which 353 lump pairs of mineral species, while 129 lump three species. Eight mineral groups, including cancrinite, eudialyte, hornblende, jahnsite, labuntsovite, satorite, tetradymite, and tourmaline, are represented by 20 or more lumped IMA-approved mineral species. A list of 5659 IMA-approved mineral species corresponds to 4016 root mineral kinds according to these lumping criteria. The evolutionary system of mineral classification assigns an IMA-approved mineral species to two or more mineral natural kinds under either of two splitting criteria: (1) if it forms in two or more distinct paragenetic environments, or (2) if cluster analysis of the attributes of numerous specimens reveals more than one discrete combination of chemical and physical attributes. A total of 2310 IMA-approved species are known to form by two or more paragenetic processes and thus correspond to multiple mineral natural kinds; however, adequate data resources are not yet in hand to perform cluster analysis on more than a handful of mineral species. We find that 1623 IMA-approved species (~29%) correspond exactly to mineral natural kinds; i.e., they are known from only one paragenetic environment and are not lumped with another species in our evolutionary classification. Greater complexity is associated with 587 IMA-approved species that are both lumped with one or more other species and occur in two or more paragenetic environments. In these instances, identification of mineral natural kinds may involve both lumping and splitting of the corresponding IMA-approved species on the basis of multiple criteria. Based on the numbers of root mineral kinds, their known varied modes of formation, and predictions of minerals that occur on Earth but are as yet undiscovered and described, we estimate that Earth holds more than 10000 mineral natural kinds.
Philosophy of mineralogy↗
Lumping Techniques for Mixed Finite Element Diffusion Discretizations
We are interested in positivity preserving spatial discretizations applicable to arbitrary order mixed finite element spatial discretizations of the radiative diffusion equations. Though not guaranteed to yield strict positivity, matrix lumping is appealing as a method of increasing solution positivity because unlike ad hoc fixups or strictly non-negative, non-linear solution representations, matrix lumping keeps the mixed finite element diffusion equations as a linear system of equations. Self-lumping schemes have previously been shown to be a generalization of more traditional matrix lumping techniques. Self-lumping schemes restrict integration quadrature points to the interpolation points used to define interpolatory finite element basis functions. As shown previously, the positivity and order of accuracy of self-lumping schemes are directly related to the choice of finite element interpolation point. Here, we develop self-lumping schemes for arbitrary order, mixed finite element spatial discretizations of the diffusion equation in Cartesian geometry. After introducing several possible self-lumping schemes appropriate for mixed finite elements, we test the ability of each scheme to increase solution positivity relative to an unlumped discretization using a simple test problem designed to induce negative solutions, evaluating efficacy as a function of finite element order and finite element interpolation point type. The method of manufactured solutions is then used to evaluate order of convergence for promising self-lumping schemes.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Neural lumped parameter differential equations with application in friction-stir processing
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a “lumped” element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity physics simulations. Here, in this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.
97 MATHEMATICS AND COMPUTING↗
Model-based predictive control of multi-zone commercial building with a lumped building modelling approach
Here this study investigates the applicability of a lumped building modeling approach to model-based predictive control (MPC) to alleviate the complex modeling process of the grey-box multi-zone building model. Based on experimental data, two building models were estimated in this study. The detailed model as a reference case and a lumped model were estimated with decentralized and conventional approaches, respectively. Then, simulations were performed with two boundary conditions, including the comfort bound and electricity cost structure. The performances of the MPC with the detailed and lumped models were analyzed compared to the feedback control. More savings was achieved with a larger comfort bound and more aggressive electricity cost structure. The savings potential of the proposed lumped model approach was not as high as that of the detailed model. However, the proposed method yields good control performance, whose savings was approximately 8.6% over that of feedback control. These results suggest that the proposed method can be used to facilitate MPC implementation in multi-zone building applications.
42 ENGINEERING↗
Lumped Parameter Models of the Central Nervous System for VIIP Research
INTRODUCTION: Current long-duration missions to the International Space Station and future exploration-class missions beyond low-Earth orbit, such as to Mars and asteroids, expose astronauts to increased risk of Visual Impairment and Intracranial Pressure (VIIP) syndrome [1]. It has been hypothesized that the headward shift of cerebral spinal fluid (CSF) and blood in microgravity may cause significant elevation of intracranial pressure (ICP), which in turn induces VIIP syndrome through biomechanical pathways [1, 2]. However, there is insufficient evidence to confirm this hypothesis. In this light, we are developing lumped-parameter models of fluid transport in the central nervous system (CNS) as a means to simulate the influence of microgravity on ICP. The CNS models will also be used in concert with the lumped parameter and finite element models of the eye described in the realted IWS abstracts submitted by Nelson et al., Feola et al. and Ethier et al. METHODS: We have developed a nine compartment CNS model (Figure 1) capable of both time-dependent and steady state fluid transport simulations, based on the works of Stevens et al. [3]. The breakdown of compartments within the model includes: vascular (3), CSF (2), brain (1) and extracranial (3). The boundary pressure in the Central Arteries [A] node is prescribed using an oscillating pressure function PA(t) simulating the carotid pulsatile pressure wave as developed by Linninger et al. [4]. For each time step, pressures are integrated through time using an adaptive-timestep 4th and 5th order Runga-Kutta solver. Once pressures are found, constitutive equations are used to solve for flowrates (Q) between each compartment. In addition to fluid flow between the different compartments, compliance (C) interactions between neighboring compartments are represented. We are also developing a second CNS model based on the works of Linninger et al. [4] which takes a more granular approach to represent the interactions of the intracranial and spinal compartments with the inclusion of arteries, arterioles, capillaries, venules, veins, venous sinus, and ventricles. The flow through the arteries, veins and CSF compartments are governed by continuity, momentum and distensibility balance equations. Furthermore, unlike the Stevens et al. approach, the Monro-Kellie doctrine of constant cranial volume and the bi-phasic nature of the brain parenchyma are implemented. These features appear to be more consistent with the physiologic and anatomical behavior of the CNS, and follow a modeling philosophy similar to the lumped parameter eye model that is intended to be integrated with the CNS model. However, Linninger’s approach has never been implemented to include hydrostatic gradient and microgravity simulation capabilities. Therefore, we aim at implement this modeling approach for spaceflight simulations and assess its overall applicability to VIIP research. OBJECTIVES: We will present verification and validation test results for both models, as well as head-to-head comparison to explore their strengths and limitations with respect to mathematical implementation and physiological significance for VIIP research. In doing so, we hope to provide some guidance to the HRP research community on how to appropriately leverage lumped parameter models for space biomedical research.
Vera, J.↗
Analysis and synthesis of distributed-lumped-active networks by digital computer
The use of digital computational techniques in the analysis and synthesis of DLA (distributed lumped active) networks is considered. This class of networks consists of three distinct types of elements, namely, distributed elements (modeled by partial differential equations), lumped elements (modeled by algebraic relations and ordinary differential equations), and active elements (modeled by algebraic relations). Such a characterization is applicable to a broad class of circuits, especially including those usually referred to as linear integrated circuits, since the fabrication techniques for such circuits readily produce elements which may be modeled as distributed, as well as the more conventional lumped and active ones.
Source record↗
Lumped mass modelling for the dynamic analysis of aircraft structures
Aircraft structures may be modelled by lumping the masses at particular strategic points and the flexibility or stiffness of the structure is obtained with reference to these points. Equivalent moments of inertia for the section at these positions are determined. The lumped masses are calculated based on the assumption that each point will represent the mass spread on one half of the space on each side. Then these parameters are used in the differential equation of motion and the eigen characteristics are determined. A comparison is made with results obtained by other established methods. The lumped mass approach in the dynamic analysis of complicated structures provides an easier means of predicting the dynamic characteristics of these structures. It involves less computer time and avoids computational errors that are inherent in the numerical solution of complicated systems.
Abu-Saba, Elias G.↗
Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes
Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.
42 ENGINEERING↗
Deducing Electronic Unit Internal Response During a Vibration Test Using a Lumped Parameter Modeling Approach
During random vibration testing of electronic boxes there is often a desire to know the dynamic response of certain internal printed wiring boards (PWBs) for the purpose of monitoring the response of sensitive hardware or for post-test forensic analysis in support of anomaly investigation. Due to restrictions on internally mounted accelerometers for most flight hardware there is usually no means to empirically observe the internal dynamics of the unit, so one must resort to crude and highly uncertain approximations. One common practice is to apply Miles Equation, which does not account for the coupled response of the board in the chassis, resulting in significant over- or under-prediction. This paper explores the application of simple multiple-degree-of-freedom lumped parameter modeling to predict the coupled random vibration response of the PWBs in their fundamental modes of vibration. A simple tool using this approach could be used during or following a random vibration test to interpret vibration test data from a single external chassis measurement to deduce internal board dynamics by means of a rapid correlation analysis. Such a tool might also be useful in early design stages as a supplemental analysis to a more detailed finite element analysis to quickly prototype and analyze the dynamics of various design iterations. After developing the theoretical basis, a lumped parameter modeling approach is applied to an electronic unit for which both external and internal test vibration response measurements are available for direct comparison. Reasonable correlation of the results demonstrates the potential viability of such an approach. Further development of the preliminary approach presented in this paper will involve correlation with detailed finite element models and additional relevant test data.
random vibration response↗
Reducing the Susceptibility of Lumped-Element KIDs to Two-Level System Effects
Arrays of lumped-element kinetic inductance detectors (LEKIDs) optically coupled through an antenna-coupled transmission line are a promising candidate for future cosmic microwave background experiments. However, the dielectric materials used for the microstrip architecture are known to degrade the performance of superconducting resonators. In this paper, we investigate the feasibility of microstrip coupling to a LEKID, focusing on a systematic study of the effect of depositing amorphous silicon nitride on a LEKID. The discrete and spatially separated inductive and capacitive regions of the LEKID allow us to vary the degree of dielectric coverage and determine the limitations of the microstrip coupling architecture. We show that by careful removal of dielectric from regions of high electric field in the capacitor, there is minimal degradation in dielectric loss tangent of a partially covered lumped-element resonator. We present the effects on the resonant frequency and noise power spectral density and, using the dark responsivity, provide an estimate for the resulting detector sensitivity.
47 OTHER INSTRUMENTATION↗
Reliability of Lumped Thermodynamic Hydrogen Fueling Model under Slow-Fill Conditions
This study verifies the reliability of lumped thermodynamic fuel cell electric vehicle (FCEV) tank model under considerably slow-fill conditions. Many countries put efforts into research and development of FCEVs. As part of the efforts, thermodynamic hydrogen fueling models have been developed to understand the hydrogen temperature in the onboard tanks of FCEVs during the fueling process. Most of the models treat the hydrogen inside the tanks to be a lumped system and assume the hydrogen temperature to be uniform throughout the tanks. In other words, the hydrogen temperature is treated as average bulk temperature. This study certifies whether treating the hydrogen temperature in a tank as the bulk gas temperature is suitable by evaluating the temperature distributions inside the tank by a three-dimensional computational fluid dynamics (3D CFD) model.
DIRECT ENERGY CONVERSION,HYDROGEN↗
The distributed-lumped-active network - Its application to filtering problems.
Distributed RC networks combined with lumped passive and active elements to produce distributed-lumped-active /DLA/ networks for filter requirements
Huelsman, L. P.↗
Lumped parameter analysis of a stringer reinforced plate excited by band limited noise
The maximum root-mean-square response of a square clamped plate, subjected to a stationary random excitation, was determined both theoretically and empirically. For the tests, a 40 x 40 x 1/4 aluminum sheet was milled out to provide a thin waffle plate with 9 panels. The plate was acoustically excited, with the frequency range limited between 25 Hz and 500 Hz. The root-mean-square power of the random excitations, 149 decibels, was nearly constant for all natural frequencies of the plate system. Strain gage readings at 14 points were plotted as power spectral densities and root-mean-square displacements. A modal damping ratio matrix was determined from the response curves. Damping ratios were found to be a function of frequency, but not of location on the plate. For comparisons with the theoretical response, the plate was subdivided into 14 modes and anlayzed as a damped, lumped parameter system by use of an approximate normal-mode method. This method gave the best predictions of the power spectral densities for the lower frequencies. That prediction errors increased for the higher frequencies is attributed to improper assumptions for mass distribution and the insufficient number of lumped mass points.
Bilyeu, D. J.↗
Random vibrations of linear viscoelastic beams with lumped masses
A method is presented of determining the mean square transversal deflection of an isotropic and homogeneous linear viscoelastic beam having a certain number of lengthwise distributed lumped masses. It is assumed that the beam is acted upon by a stationary random process uniformly distributed along the beam. The method is useful in vibration level control by means of additional lumped masses.
Dinca, F.↗
Design of experiments for measuring heat-transfer coefficients with a lumped-parameter calorimeter
A theoretical investigation was conducted to determine optimum experimental conditions for using a lumped-parameter calorimeter to measure heat-transfer coefficients and heating rates. A mathematical model of the transient temperature response of the calorimeter was used with the measured temperature response to predict the heat-transfer coefficient and the rate of heating. A sensitivity analysis was used to determine the optimum transient experiment for simultaneously measuring the heat addition during heating and the convective heat-transfer coefficient during heating and cooling of a lumped-parameter calorimeter. Optimum experiments were also designed for measuring the convective heat-transfer coefficient during both heating and cooling and cooling only.
Vanfossen, G. J., Jr.↗