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DOE OSTI2021

Parametrizations of the spin density matrix

Highlights: • Proposed two methods for parametrizing the SDM of spinning, unstable particles. • All non-negativity conditions fulfilled; adaptability to various constraints. • First method: based on a theorem; applicable in a simple and flexible way. • Second method: particularly suitable for especial conditions. • Applications: two of them interesting in the search for new physics. We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Effect of likelihood misspecification in Gaussian process-driven autonomous experimentation

In recent years, several groups have designed Autonomous Experiment (AE) models with the aim of using them as an alternative method for neutron scattering scanning. In an AE, Gaussian processes (GPs) are most frequently used due to their interpretability, their non-parametric nature, their universal approximation, and their closed-form predictive distribution. GPs have two key components, namely, the model for the likelihood of a neutron count knowing the underlying dynamic structure factor and the acquisition function. In this paper, we investigate the impact, on the quality of an AE, of the likelihood and acquisition function choices, in energy scans and (Q, ω) ones, with respect to the signal-over-noise ratio. While we hypothesized that the quality of GP predictions would decrease when the normal to Poisson likelihood approximation breaks down at low count rates, we found that the use of the correct Poisson likelihood does not improve the quality of the data collected, as well as yields very poor results in (Q, ω) scans at low count rates. In fact, the best results are obtained with a combination of normal likelihood, including the observation noise, and the change in variance acquisition function. In addition, we find that the performance, or quality of the predictive distribution, is a misleading measure of efficiency, that is, of the quality of the data collected.

Perryman, David Elliott [Inst. Laue-Langevin (ILL)↗

DOE OSTI2021

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Electropolishing parameters study for surface smoothening of low-$\beta$650 MHz five-cell niobium superconducting radio frequency cavity

Electropolishing (EP) is applied to niobium (Nb) superconducting radio frequency (SRF) cavities, which are used in particle accelerators for their surface treatment. The EP process for 1.3 GHz cavities has been extensively studied earlier. In this work, a parametric study on EP of low-β (0.61) 650 MHz Nb SRF cavities (LB650), which will be used in pre-production cryomodule for proton improvement plan-II (PIP-II) linear accelerator, was conducted to determine adequate EP conditions for attaining a smooth surface of the cavities. EP performed with the standard parameters and an initial cathode (cathode-I) having a cathode surface area of ~5% of the cavity surface area yielded a rough equator surface of the cavity. The grain step height on the equator weld position was measured to be ~ 32 μm. The rough surface was attributed to preferential grain etching confirmed by a polarization curve showing a linear relationship between the EP current and voltage and the absence of the current plateau region. The cathode was modified to make its surface area twice that of cathode-I. The modified cathode (cathode-M) provided a current plateau region in the corresponding I-V curves measured at different cavity temperatures. The onset voltage for the plateau was found to be higher at higher cavity temperatures. Here this study revealed that even with cathode-M, the standard 18 V was low for EP of such large-sized cavities when the cavity temperature was 18 °C. EP performed at a higher voltage of 22–24.5 V with cathode-M yielded a smooth surface with a grain step height of only 0.6 μm. The applied EP conditions also improved removal uniformity along the cavity length. In contrast to the cavity treated with cathode-I, the cavities treated with cathode-M achieved a significantly higher accelerating gradient (E acc ) in vertical tests conducted in a cryostat at 2 K. The modified EP was found efficient to produce the cavities that achieved E acc of 22.4 MV/m, required by PIP II project in the baseline RF tests, to qualify for further surface processing used to enhance their quality factors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Dual-loop Solvent-based CCS for Net Negative CO 2 Emissions with Lower Cost

This final technical report details the successful design, construction, and operational validation of an innovative dual-loop CO 2 capture technology designed to achieve deep decarbonization (>99%) from Natural Gas Combined Cycle (NGCC) power plants that results in the electricity with carbon intensity of approximate 42 kg CO 2 -eq/MWh, less than the electricity produced by solar PV. The integrated process couples a primary aqueous solvent (in this project, a water lean solvent – WLS) absorption loop for bulk CO 2 removal with a secondary potassium hydroxide (KOH) polishing loop featuring electrochemical regeneration. This architecture leverages the higher exergy efficiency of the primary loop while utilizing the fastest kinetic of the secondary loop to capture dilute residual CO 2 , achieving an overall capture rate of 99.9% and co-producing pure hydrogen after moisture being condensed and dehydrated. Technical feasibility was established through a comprehensive 2,000-hour experimental campaign on a bench-scale fully-integrated unit (using 4” absorber and 4” stripper) with the feeding flue gas flowrate in the range of 8-20 cfm, confirming the attainment of Technology Readiness Level (TRL) 4. The project executed extensive parametric testing followed by 1,000 hours of continuous steady-state testing, demonstrating exceptional process stability with the electrochemical regenerator exhibiting less than a 10% reduction in electrical conductivity over the duration of the campaign. Operational characterization gathering on the bench unit revealed distinct energy profiles for the hybrid system: the primary loop required approximately 280 kJ mol -1 for bulk removal, while the polishing loop required approximately 1,600 kJ mol -1 specifically when reducing dilute CO 2 concentrations from ~740 ppm down to <50 ppm. (Please note those energy values/numbers can only be viewed as relative relationship and should not be extrapolated as absolute values required for CO 2 capture). Furthermore, dynamic testing validated the system’s flexibility for utility applications, demonstrating a rapid process response time of <30 minutes to changes in flue gas flowrate. Emission monitoring confirmed that the dual-loop architecture effectively mitigates solvent losses, utilizing a water wash to remove entrained aerosols to <1 ppm. The Techno-Economic Analysis (TEA) indicates a cost of capture of $\$$59.3/tonne and a Levelized Cost of Electricity (LCOE) of 71.7 $\$$/MWh at the overall capture efficiency of 99.8% of total carbon in the flue gas stream, with sensitivity analysis identifying an economic optimum when the primary loop captures 97% of the total CO 2 . A Life Cycle Assessment (LCA) confirms the technology’s potential for net-negative emissions, determining a Global Warming Potential (GWP) of 52 kg CO 2 -eq/MWh—significantly lower than the baseline—which further decreases to 42 kg CO 2 -eq/MWh when crediting the displacement of conventional hydrogen production.

03 NATURAL GAS↗

DOE OSTI2021

Discrete stochastic model of point defect-dislocation interaction for simulating dislocation climb

Dislocation climb is an important high temperature process in metals plasticity, responsible for the phenomena such as creep, swelling, or hardening. Climb is defined by the ability of dislocations to leave their original glide plane by interacting with point defects. As such, dislocation climb is controlled by point defect diffusion/absorption/emission, all of which involve thermal activation. The existing thermodynamically consistent models for climb are generally formulated in a continuum framework, through the definition of effective defect fluxes and climb propensities in response to thermodynamic driving forces. However, the point-wise discrete nature of vacancies (and/or self-interstitials) confers a highly discrete nature to the climb dynamics, which is also strongly affected by elastic forces. The combination of discreteness, thermal activation, and elasticity makes this process too challenging for direct atomistic methods such as molecular dynamics. Here we develop a kinetic Monte Carlo model that captures vacancy generation and transport kinetics acting in conjuction with the evolving elastic fields provided by discrete dislocation dynamics simulations. The two models are coupled via the applied stresses and stress gradients generated by dislocation structures at vacancy locations. Our simulations reveal two surprising results. First that climb is dominated by vacancy emission even when the background vacancy concentration is much higher than the equilibrium one. And, second, that climb velocities might be much faster than otherwise believed when one uses the classical theories of climb. These effects are due to the locality of vacancy-dislocation processes, which are not captured in classical treatments that assume smooth vacancy fluxes and homogeneous concentrations. We apply the method to study elementary climb processes in body-centered cubic iron and furnish climb mobility functions to be used in parametric dislocation dynamics and/or crystal plasticity simulations. Here, we apply the technique to study non-conservative plastic bypass of spherical precipitates by edge dislocations and point out the differences between our discrete approach and existing continuum formulations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Effect of Temperature on the Pilot-Scale Catalytic Pyrolysis of Loblolly Pine

A pilot-scale biomass catalytic pyrolysis unit with a nominal throughput of one tonne of biomass per day (1TPD) has been in operation since 2013 to investigate the process parameters that have the largest influence on biocrude yield, oxygen content, and chemical composition. A parametric study was conducted to investigate the effect of pyrolysis temperature, ranging from 433 to 581 °C, on biocrude yield and quality. A locally sourced loblolly pine feedstock and a commercially available, spray dried, nonzeolitic γ-Al 2 O 3 catalyst were used in individual experiments conducted at each pyrolysis temperature to achieve a minimum of 4 h of steady-state continuous operation. Typically, 600–800 kg of biomass was fed over a 12-h period, with one experiment extended to almost 29 h (1144-kg biomass fed) and one experiment interrupted by a process upset after just 7 h (411-kg biomass fed). Comprehensive analysis of collected gas, liquid, and solid products were used to calculate carbon balances (77% to 107%) for each experiment. The biocrude yield ranged from 12 to 18 wt % C and, in general, decreased with increasing pyrolysis temperature. The average steady-state biocrude yield as a function of temperature translated to a biocrude production rate between 40 and 50 gallons per dry ton. The biocrude oxygen content varied between 21 and 31 wt %, on a dry basis, and as expected, decreased with increasing pyrolysis temperature. The identified components in the semivolatile biocrude products are mostly methoxyphenols and other multiphenolic compounds. The multiphenolic compounds are demethoxylated at pyrolysis temperatures above 500 °C, producing biocrudes with higher concentrations of monophenols and polycyclic aromatic hydrocarbons. The concentration of anhydrosugars, like levoglucosan in the biocrudes, decreased with increasing pyrolysis temperature from ∼15 to ∼1 vol %.

biofuels↗

DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗

DOE OSTI2022

Singularities in the gravitational capture of dark matter through long-range interactions

Here, we re-examine the gravitational capture of dark matter (DM) through long-range interactions. We demonstrate that neglecting the thermal motion of target particles, which is often a good approximation for short-range capture, results in parametrically inaccurate results for long-range capture. When the particle mediating the scattering process has a mass that is small in comparison to the momentum transfer in scattering events, correctly incorporating the thermal motion of target particles results in a quadratic, rather than logarithmic, sensitivity to the mediator mass, which substantially enhances the capture rate. We quantitatively assess the impact of this finite temperature effect on the captured DM population in the Sun as a function of mediator mass. We find that capture of DM through light dark photons, as in e.g. mirror DM, can be powerfully enhanced, with self-capture attaining a geometric limit over much of parameter space. For visibly-decaying dark photons, thermal corrections are not large in the Sun, but may be important in understanding long-range DM capture in more massive bodies such as Population III stars. We additionally provide the first calculation of the long-range DM self-evaporation rate.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.

Electron-ion collisions↗

DOE OSTI2020

ENERGY STAR for Tenants: An Online Energy Estimation Tool for Commercial Office Building Tenants

The commercial building sector consumes over 18% of the total energy in the United States. According to the 2012 Commercial Building Energy Consumption Survey (CBECS), office buildings comprise nearly 16 billion square feet of floor space and consume 253 billion kWh of energy annually. Office buildings represent nearly one-fifth of the energy consumed by commercial buildings, more than any other building type. Therefore, monitoring and reducing energy consumption in office buildings has become an increasingly important focus across the United States. The goal of the ENERGY STAR for Tenants program is to recognize office building tenants who demonstrate commitment to energy efficiency and environmental stewardship. Tenants seeking recognition must complete five major steps: estimate energy use, meter energy use, use efficient lighting, use efficient equipment, and share data. NREL is responsible for the underlying analysis performed for step one, estimating energy use. An online survey was developed for tenants to input information about their office space and its internal loads. NREL performed a parametric analysis across a large parameter space of office buildings. The analysis results were processed to map the user inputs to output energy ranges. The mappings enable the web tool to provide users with instant energy usage estimates based on a limited number of inputs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Sorbent Based Post-Combustion CO 2 Slipstream Testing

TDA Research, Inc. has developed a low-cost sorbent (alkalized alumina) based technology for post-combustion CO 2 capture. The sorbent runs in an isothermal process for adsorption and regeneration. Neither temperature swing nor pressure swing is needed. TDA designed a system which operated 10 fixed beds to simulate a moving bed process. The flow pattern was optimized to minimize the steam usage for regeneration. An excellent sorbent (Batch 1) was also developed with collaboration with our partner. The sorbent degraded after long term operation. We developed a reprocessing procedure, which can be conducted in situ, to restore the sorbent capture capacity as the fresh sorbent after running for about 1250 hours. The reprocessing extended the sorbent longevity significantly. TDA designed a pilot unit (40’ x 32’ x 11.5’), processing flue gas equivalent to 0.5 MW of power generation. It had 10 beds and each bed could hold 1.75 m 3 of sorbent. We worked with Springs Fabrication, Inc. to complete the construction of the pilot unit. It was then shipped and installed at NCCC. The pilot unit was kept running in 24-hour mode when the flue gas and steam were available. It could run automatically without operator on site. Parametric and long-term (2 months) tests were carried out successfully. The results showed that TDA’s process can achieve 90% capture and 95% CO 2 purity for both coal and NG flue gases. For coal flue gas, the system reached performance target when processing up to 0.62 MW flue gas, 24% higher than the design capacity. Thus, capital cost could be saved on the reactors and sorbent. The strip air flow was designed to be 0.25 of that of the flue gas. The test data showed the strip/flue ratio can be reduced to as little as 0.18, which saves the power consumption for the strip air blower. The pressure drop was found to be lower than what the empirical equation calculated. The sorbent still had 91.7% of original capacity after 3-month test. With the data from the pilot test, we updated the TEA. For a 550-MW e supercritical coal fired power plant with CO 2 capture, the capture cost for TDA’s process is $34.9/tonne CO 2 captured, which meets DOE’s goal of $40/tonne and is 17.1% less than the DOE baseline Case 12. Therefore, TDA’s process has a good potential for commercialization.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2021

On-chip non-Hermitian optical parametric amplifiers with a large bandwidth

Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of ∼ <#comment/> 9 d B for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ( ∼ <#comment/> 600 n m ). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventional silicon-photonics-based four-wave mixing process.

Ahmed, Asif (ORCID:0000000152234392)↗

DOE OSTI2022

Stochastic Model for High Temperature Oxidation of Cr–Ni Austenitic Steels Assisted by Spallation

Abstract Cr–Ni austenitic steels offer significant high temperature corrosion protection by forming a surface oxide layer. However, above critical service conditions (temperature, atmosphere, thermal cycling), oxidized surface can experience intensive degradation because of scale spallation, which could be detrimental to the in-service life. To predict the effect of scale spallation on oxidation kinetics, a simulation was implemented using a stochastic model. The model considers topological parameters and intensity of spallation which can occur, while delivering a true oxidation constant. The experimental procedure identified the amount of formed spalled scale and topology of spallation based on the use of element mapping of the surface. This information was used to determine a true kinetic constant for a corresponding spallation intensity in oxidized Cr–Ni austenitic steel. To illustrate the capability of the stochastic model, a parametric analysis was performed. The model verified how the spallation parameters could change the oxidation processes from parabolic growth of an adhered oxide layer without spallation to a mixed linear-parabolic, or with a constant thickness of residual scale at high spallation intensity. The spallation model will be used in a separate article to characterize high temperature surface degradation of several Cr–Ni austenitic steels during harsh oxidation environments.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Experimentally validated high-fidelity simulations of a liquid jet in supersonic crossflow

Here, utilizing recent advancements in computational schemes for compressible, multiphase flows, this work features a parametric study of a pure liquid jet in supersonic crossflow that involves simulating the atomization process for four values of momentum-flux ratio. These simulations are validated against experimental results measured with high-speed X-ray imaging, which confirm the accuracy of the numerical approach. Also, the effect of numerical resolution on some flow behavior is investigated, revealing convergence of the jet shape and surface instability wavelength. Analysis of the resulting sprays includes statistical descriptions of the liquid distribution, liquid structures created through breakup, interfacial instabilities, and dominant flow features. As the flowrate increases, the spray penetrates further, it becomes more disperse, and less liquid impacts the wall, but the droplet size distribution changes little. The wavelength of instabilities on the windward side of the jet diverges from measured trends in subsonic crossflows. In a visualization of the time-averaged flow, counter-rotating vortices are observed along the jet core and in the wake, affecting the process of primary atomization and early droplet trajectories.

42 ENGINEERING↗

DOE OSTI2024

Novel Signatures Beyond the Standard Model: From Extreme Environments to Precision Measurements

Most of our universe is dark. It is dark literally—visible matter makes up only 5% of the energy density—and conceptually, as many outstanding questions remain unsolved. The discovery of particle dark matter would shed light on our dark universe and throw open a window on the highest energy scales. This research made progress toward dark matter and new particle searches in three ways. Extreme compact objects, such as black holes, neutron stars, and stellar cores, can parametrically increase the production rates of feebly interacting particles and yield observable signatures. Specifically, a process known as superradiance leads to exponential growth of the number of ultralight particles gravitationally bound to rotating black holes, and turns astrophysical black holes into particle detectors. This research broadened the scope of applicability of superradiance studies to particles with a wide range of interactions and masses, predicting multi messenger signals. When ultralight particles are produced as dark matter in the early universe, they can be detected directly in laboratory experiments. However, these feebly interacting particles lead to small signals that are inevitably difficult to tease out from backgrounds; their detection requires the theoretical development of unique signatures that can be searched for in low-noise experiments. Some dark matter particles could be detectable with thin film metamaterials combined with low noise single-photon detectors. This research develop the theoretical framework and supported experimental efforts for ambitious searches for a wider class of ultralight particles. Overall, the outcome of this theoretical particle physics program developed novel signatures of new dark matter particles, and thereby expanded the particle parameter space which can be explored with astrophysical observations and precision experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

A nonparametric approach to modeling dependence among production parameters for energy cost estimation

Dependence existing among production parameters can significantly affect energy costs. For material removal processes, processing times and material amounts to be cut have positive dependence, and the dependence can affect energy costs by varying a peak electricity load. Existing methods to model the dependence of production parameters are based on parametric approaches that cannot accurately represent the dependence due to the rigid nature of parametric models. To address this issue, this study proposes a method to quantify dependence among manufacturing parameters through the application of the empirical copula to the dependence between the milling processing time and the amount of volume to be cut. The proposed method is illustrated by a case study of a manufacturing facility consisting of milling machines; a total of 27 scenarios are simulated for energy cost estimations. The case study clearly shows that the proposed method can capture the dependence between the milling parameters more accurately than a conventional dependence measure from parametric correlation models. Furthermore, the findings from this study would be useful to estimate energy costs in that the proposed method provides a better fit to real production data than conventional parametric approaches can.

42 ENGINEERING↗