Energy Minimization Method Research Articles

Methods for solution of large optimal control problems that bypass open-loop model reduction

Three algorithms for efficient solution of optimal control problems for high-dimensional systems are presented. Each bypasses the intermediate (and, unnecessary) step of open-loop model reduction. Each also bypasses the solution of the full Riccati equation corresponding to the LQR problem, which is numerically intractable for large n. Motivation for this effort comes from the field of model-based flow control, where open-loop model reduction often fails to capture the dynamics of interest (governed by the Navier–Stokes equation). Our minimum control energy method is a simplified expression for the well-known minimum-energy stabilizing control feedback that depends only on the left eigenvectors corresponding to the unstable eigenvalues of the system matrix A. Our Adjoint of the Direct-Adjoint method is based on the repeated iterative computation of the adjoint of a forward problem, itself defined to be the direct-adjoint vector pair associated with the LQR problem. Our oppositely-shifted subspace iteration (OSSI, the main new result of the present paper) method is based on our new subspace iteration method for computing the Schur vectors corresponding, notably, to the \(m\ll n\) central eigenvalues (near the imaginary axis) of the Hamiltonian matrix related to the Riccati equation of interest. Prototype OSSI implementations are tested on a low-order control problem to illustrate its behavior.

Simulation and exergetic evaluation of hydrogen production from sorption enhanced and conventional steam reforming of acetic acid

The simulation and exergetic analysis on hydrogen production from conventional steam reforming (SR) and sorption enhanced steam reforming (SESR) of acetic acid, as a major component in the aqueous bio-oil fraction, are presented in this work. The simulation of acetic acid SR and SESR systems were performed in Aspen Plus software where the main chemical reactors used in this work were Gibbs reactors based on Gibbs free energy minimization method. The equilibrium compositions of acetic acid SR and SESR reactors were investigated at different conditions including temperature (200–1000 °C) and steam to carbon molar ratio (S/C, 1–4.5). The increase of temperature and S/C favored hydrogen production in both SR and SESR processes. Higher purity and yield of hydrogen was obtained via SESR reactor than SR reactor. In addition, less CO and no coke were formed in SESR reactor, which showed the advantages of SESR over SR. The exergy efficiencies of acetic acid SR and SESR systems were 61.80% and 66.80%, respectively. The burner and reforming reactor were responsible for major exergy destruction in both SR and SESR systems. At the same time, large exergy destruction was also found in CO2 separation process in SR system. These results and the simplification of hydrogen production system show the better performance of SESR, which can be a promising way for green hydrogen production via aqueous bio-oil fraction.

Simultaneous tumor segmentation, image restoration, and blur kernel estimation in PET using multiple regularizations

Accurate tumor segmentation from PET images is crucial in many radiation oncology applications. Among others, partial volume effect (PVE) is recognized as one of the most important factors degrading imaging quality and segmentation accuracy in PET. Taking into account that image restoration and tumor segmentation are tightly coupled and can promote each other, we proposed a variational method to solve both problems simultaneously in this study. The proposed method integrated total variation (TV) semi-blind de-convolution and Mumford–Shah segmentation with multiple regularizations. Unlike many existing energy minimization methods using either TV or L2 regularization, the proposed method employed TV regularization over tumor edges to preserve edge information, and L2 regularization inside tumor regions to preserve the smooth change of the metabolic uptake in a PET image. The blur kernel was modeled as anisotropic Gaussian to address the resolution difference in transverse and axial directions commonly seen in a clinic PET scanner. The energy functional was rephrased using the Γ-convergence approximation and was iteratively optimized using the alternating minimization (AM) algorithm. The performance of the proposed method was validated on a physical phantom and two clinic datasets with non-Hodgkin's lymphoma and esophageal cancer, respectively. Experimental results demonstrated that the proposed method had high performance for simultaneous image restoration, tumor segmentation and scanner blur kernel estimation. Particularly, the recovery coefficients (RC) of the restored images of the proposed method in the phantom study were close to 1, indicating an efficient recovery of the original blurred images; for segmentation the proposed method achieved average dice similarity indexes (DSIs) of 0.79 and 0.80 for two clinic datasets, respectively; and the relative errors of the estimated blur kernel widths were less than 19% in the transversal direction and 7% in the axial direction.

Production of Fermentable Sugars and Hydrogen-Rich Gas from Agave tequilana Biomass

The Mexican tequila industry annually processes approximately 1 × 106Agave tequilana plants, generating approximately 1.78 × 108 kg of bagasse per year. This biomass is considered an attractive alternative to fossil fuels as an energy source and to produce biofuels and/or chemical products because it is produced and used without adversely affecting the environment. The first aim of the present work was to determine the effect of temperature, the concentration of H2SO4, and reaction time on the hydrolysis of agave bagasse to maximize the fermentable sugars using a steam explosion. This step process generated 71.11 g/L of reducible sugars in the supernatant (59.29 % glucose, 29.05 % xylose, and 11.66 % fructose) and unconverted organic matter of enzymatic hydrolysis bagasse (35.4 % α-cellulose, 7.33 % hemicellulose, 49.91 % lignin, and 7.31 % ashes). A mathematical surface response analysis of the hydrolysis was used for process optimization. The second aim involves the study of the thermodynamics of the reforming of unconverted organic matter from enzymatic hydrolysis of Agave tequilana bagasse (ATB) evaluated by the Gibbs free energy minimization method for hydrogen production. The effect of the parameters on the system performance measures, such as reaction temperature (T), Water/Biomass ratio (WBR), and pressure (P), were also investigated. The maximum H2 production obtained was 23.2 mol of H2/271.5 g ATB with a WBR ≥ 11 and a temperature of 740 °C. These findings indicate that the temperature and WBR are essential factors in the production of H2, which was reflected in the efficiency of the process.

Simplified method for predicting the deflections of composite box girders

A simplified method for predicting the deflections of composite box girders with corrugated steel webs is presented in this paper. In the proposed method, the governing equations of the composite box girder bridge are derived based on the principles of the minimum total potential energy method. The vertical deflection of the composite box girder bridges with corrugated steel webs is obtained by solving the governing equations with the associated boundary and load conditions. The accuracy and efficiency of the proposed method are validated for three composite box girders with corrugated steel webs (single-cell and double-cell box girders) with the results obtained based on the finite element method.

A new non-electrolytic aluminum extraction method

A new method of primary aluminum extraction from alumina was proposed. The method is based on the new reaction AlI3+(3/2)Zn=Al+(3/2)ZnI2. In its turn, the exchange reaction AlCl3+CaI2→AlI3+CaCl2 is used to get aluminum iodide from aluminum chloride—the product of alumina carbochlorination. These reactions were studied in laboratory experiments as well as additional reactions, which were needed for the main chemicals recycling: Cl2, ZnI2→Zn, CaCl2→CaI2. XRD and SEM methods were used to investigate the phases and morphology of the reaction's solid products. The global free energy minimization method was used for the chemical equation's calculations. It was shown that aluminum can be effectively extracted from alumina without electrolysis, extreme high temperature and expended chemicals. The estimated specific carbon consumption and CO2 atmospheric pollution rate have to be halves of such values for the contemporary aluminum plant powered by the coal power station.

Thermodynamic analysis of carbon dioxide reforming of methane to syngas with statistical methods

The present theoretical work deals with thermodynamic analysis based on Gibbs energy minimization method combined with a statistical approach: response surface methodology. By combining these two methodologies, the conditions of optimal operation were obtained. This study brings a novel methodology for thermodynamic analyses, which are normally based only on the Gibbs energy minimization method. Thermodynamic analysis of carbon dioxide reforming of methane has been investigated by method of Gibbs free energy minimization for production of desirable products at a wide range of temperature (600–1300 K), pressure (1–20 bar) and carbon dioxide to methane ratio (0.5–3). Moreover, the surface response methodology was used to determine the cubic polynomial models for mole fraction of hydrogen, carbon monoxide and ratio of H2/CO based on temperature, pressure and carbon dioxide to methane ratio. Numerical optimization was employed for determining the maximum production of hydrogen while keeping the production of carbon dioxide, methane and carbon monoxide to a minimum; in addition, the optimum ratio of hydrogen to carbon monoxide (1–3) occurs at 1 bar, 1011.99 K and carbon dioxide to methane ratio of 0.5.

A study on the aromaticity and kinetic stability of fullerene C38 isomers and their molecular ions

ABSTRACTThe aromaticity of the fullerene C38 isomers and their molecular ions is examined by the topological resonance energy (TRE) method. The aromaticity order obtained by the TRE method is compared with relative energies found in DFT calculation results reported in literature. It is found that all C38 isomers exhibit antiaromaticity when in the neutral state. However, they are highly aromatic in the hexaanionic states. The minimum bond resonance energy (min BRE) method is utilized to estimate the kinetically stability of the C38 isomers and their molecular ions. According to the min BRE method, C38 isomers are only have kinetic stability in penta- and hexavalent molecular anionic states.

Modelling and thermodynamic assessment of biofuel production process from biomass with the SAFT-VR approach

Two reliable methods for fuel production from biomass including supercritical water gasification (SCWG) and hydrothermal upgrading (HTU) have been studied. The Gibbs free energy minimization method was used to calculate equilibrium mole fraction of the reaction products for glucose and cellulose supercritical water gasification and hydrothermal upgrading of wood as feed biomass. The phase behavior and phase equilibrium of the separators used for the target product separation (hydrogen in SCWG and biocrude in HTU processes) was carried out successfully using the SAFT-VR equation of state for the first time. The effect of pressure and temperature on SCWG process was investigated and turned out that temperature increase causes more hydrogen production while the pressure effect was insignificant. Finally, the exergy analysis and efficiency calculations were performed respectively for HTU and SCWG processes. According to the outcomes, the exergy efficiency and SCWG efficiency for glucose were obtained as 83.63% and 88.28%.

Thermodynamic evaluation of glycerol autothermal reforming in membrane reactors

The performance of glycerol autothermal reforming in membrane reactors with in situ hydrogen separation is investigated by means of thermodynamic analysis based on Gibbs free energy minimization method. The influence of operational parameters such as reaction temperatures and oxygen to glycerol ratios under different hydrogen separation fractions is evaluated. It is found that reaction temperatures have a more significant impact on hydrogen yield compared to other parameters. The hydrogen removal can promote the hydrogen production obviously and reduce the required temperature of the maximum hydrogen yield. The hydrogen separation effect on carbon formation is discussed. Meanwhile, the performance of ethanol–glycerol mixture autothermal reforming process is also analyzed.

Simplified analytical model for tapered sandwich beams using variable stiffness materials

A simplified layer-wise sandwich beam model to capture the effects of a combination of geometric taper and variable stiffness of the core on the static response of a sandwich beam is developed. In the present model, the face sheets are assumed to behave as Euler beams and the core is modelled with a first-order shear deformation theory. With geometrical compatibility enforced at both upper and lower skin/core interfaces, the beam’s field functions are reduced to only three, namely the extensional, transverse and rotational displacements at the mid-plane of the core. The minimum total potential energy method is used in combination with the Ritz technique to obtain an approximate solution. Geometrically nonlinear effects are considered in the present formulation by introducing von Kármán strains into the face sheets and core. Two types of sandwich beams, uniform and tapered, with different boundary conditions are studied. Results show that the proposed model provides accurate prediction of displacements and stresses, compared to three-dimensional finite element analysis. It is found that due to the axial stiffness variation in the core, displacements of beams and stresses of face sheets and core are significantly affected. The potential design space is shown to be expanded by utilizing variable stiffness materials in sandwich constructions.

Supercritical water gasification of glycerol and methanol mixtures as model waste residues from biodiesel refinery

The eco-friendly processing in biodiesel refineries is feasible with effective utilization of the byproducts and waste residues. The motive of this research is to convert the model byproducts of biodiesel refineries to H2. In this study, different glycerol⿿methanol mixtures were gasified in supercritical water at variable temperatures (450⿿600°C) and pressures (23⿿25MPa) for 45s in a continuous-flow tubular reactor. Glycerol and methanol concentrations were varied from 5 to 20wt% individually in the mixtures, and their impacts on gas yields were investigated both experimentally and thermodynamically. The thermodynamic simulations were performed using Aspen Plus based on Gibbs free energy minimization method. The thermodynamic yield (25.3mmol/g) of H2 was higher compared to experimental yields (19mmol/g) at 600°C, 25MPa and 1:1 glycerol-to-methanol feed solution. To enhance the gas yields, the effects of four alkali catalysts such as KOH, NaOH, K2CO3 and Na2CO3 at 0.5wt% concentration were examined. Among all the catalyst, 0.5wt% K2CO3 resulted in highest H2 yields (24.8mmol/g), total gas yields (1.24g/L) and carbon gasification efficiency (96.7%) at 600°C and 25MPa with 1:1 glycerol-to-methanol feed solution. The results suggest that effluents from biodiesel refineries can be used as potential feedstock for waste-to-energy conversion.

Vibration analysis of the embedded piezoelectric polymeric nano-composite panels in the elastic substrate

Abstract In the present study the vibrations of a smart thin micro panel of polymeric nano-composite reinforced by the Single-Walled Boron-Nitride Nano-Tubes (SWBNNTs) and the matrix Poly-VinyliDene Fluoride (PVDF) on an elastic substrate is studied. Using the micromechanics method, the nano-composite structural equations are obtained for a sample volume element and by considering a unidirectional electric field and stress in the field. The stress-strain relationships that include mechanical and electric terms are obtained for the micro-tubes. The micro-panel is considered as the thin wall shell and Donnell’s non-linear theory is used for the strain-displacement relations. To obtain the equations of motion, the minimum energy method or Hamilton’s principle is used. The external work is caused by the elastic environment as well as the magnetic field energies. Given that the work has been in small micro scale the strain gradient, modified coupled stress and classic theories are used to consider the small-scale effect in the equations. The results showed Stiffness of the panel is reduced by increasing length and reducing volume fraction of BNNT and lower frequencies are obtained. Angling nanotubes is reduced panel frequency and the severity of this reduction is increased at higher volume percentages. The maximum frequency is happened in the full cylinder sector.

Revisiting phase diagrams of two-mode phase-field crystal models

In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this study the modified two-mode PFC model (presented by Asadi and Asle Zaeem, 2015) was used, in which the free energy can be exactly minimized in each stable crystal structure allowing calculation of accurate phase diagrams for two-mode PFC models. Different crystal structures, such as square, triangle, body-centered cubic (bcc), face-centered cubic (fcc), and stripe lattice structures as well as their coexistence regions were considered in the calculations. The model parameters were discussed to calculate phase diagrams that can be used as a guideline by other researchers for studying solidification and solid state phase transformation using two-mode PFC model.

An energy minimization method for the correction of cupping artifacts in cone-beam CT.

The purpose of this study was to reduce cupping artifacts and improve quantitative accuracy of the images in cone‐beam CT (CBCT). An energy minimization method (EMM) is proposed to reduce cupping artifacts in reconstructed image of the CBCT. The cupping artifacts are iteratively optimized by using efficient matrix computations, which are verified to be numerically stable by matrix analysis. Moreover, the energy in our formulation is convex in each of its variables, which brings the robustness of the proposed energy minimization algorithm. The cupping artifacts are estimated as a result of minimizing this energy. The results indicate that proposed algorithm is effective for reducing the cupping artifacts and preserving the quality of the reconstructed image. The proposed method focuses on the reconstructed image without requiring any additional physical equipment; it is easily implemented and provides cupping correction using a single scan acquisition. The experimental results demonstrate that this method can successfully reduce the magnitude of cupping artifacts. The correction algorithm reported here may improve the uniformity of the reconstructed images, thus assisting the development of perfect volume visualization and threshold‐based visualization techniques for reconstructed images.PACS number(s): 87.57.cp

Adaptive Quasi-Static Modelling of Needle Deflection During Steering in Soft Tissue

In this letter, we present a model for needle deflection estimation in soft tissue. The needle is modelled as a vibrating compliant cantilever beam that experiences forces applied by the tissue as it is inserted. Each of the assumed vibration modes are associated with a weighting coefficient whose magnitude is calculated using the minimum potential energy method. The model only requires as input the tissue stiffness and needle-tissue cutting force. Contributions of this letter include the estimation of needle-tissue contact forces as a function of the tissue displacement along the needle shaft, while allowing for multiple bends of the needle. The model is combined with partial ultrasound image feedback in order to adaptively calculate the needle-tissue cutting force as the needle is inserted. The image feedback is obtained by an ultrasound probe that follows the needle tip and stops at an appropriate position to avoid further tissue displacement. Images obtained during early stages of the insertion are used to predict the deflection of the needle further along the insertion process. Experimental results in biological and phantom tissue show an average error in predicting needle deflection of 0.36 mm.

Bond breaking in epoxy systems: A combined QM/MM approach.

A novel method to combine quantum mechanics (QM) and molecular mechanics has been developed to accurately and efficiently account for covalent bond breaking in polymer systems under high strain without the use of predetermined break locations. Use of this method will provide a better fundamental understanding of the mechano-chemical origins of fracture in thermosets. Since classical force fields cannot accurately account for bond breaking, and QM is too demanding to simulate large systems, a hybrid approach is required. In the method presented here, strain is applied to the system using a classical force field, and all bond lengths are monitored. When a bond is stretched past a threshold value, a zone surrounding the bond is used in a QM energy minimization to determine which, if any, bonds break. The QM results are then used to reconstitute the system to continue the classical simulation at progressively larger strain until another QM calculation is triggered. In this way, a QM calculation is only computed when and where needed, allowing for efficient simulations. A robust QM method for energy minimization has been determined, as well as appropriate values for the QM zone size and the threshold bond length. Compute times do not differ dramatically from classical molecular mechanical simulations.

Thermodynamic and Transport Properties of Real Air Plasma in Wide Range of Temperature and Pressure**supported by the National Key Basic Research Program of China (973 Program)(No. 2015CB251002), National Natural Science Foundation of China (Nos. 51521065, 51577145), the Science and Technology Project Funds of the Grid State Corporation (SGTYHT/13-JS-177), the Fundamental Research Funds for the Central Universities, and State Grid Corporation

Air plasma has been widely applied in industrial manufacture. In this paper, both dry and humid air plasmas' thermodynamic and transport properties are calculated in temperature 300-100000 K and pressure 0.1-100 atm. To build a more precise model of real air plasma, over 70 species are considered for composition. Two different methods, the Gibbs free energy minimization method and the mass action law method, are used to determinate the composition of the air plasma in a different temperature range. For the transport coefficients, the simplified Chapman-Enskog method developed by Devoto has been applied using the most recent collision integrals. It is found that the presence of CO2 has almost no effect on the properties of air plasma. The influence of H2O can be ignored except in low pressure air plasma, in which the saturated vapor pressure is relatively high. The results will serve as credible inputs for computational simulation of air plasma.

Surveillance video synopsis generation method via keeping important relationship among objects

To reduce the efforts of human in browsing long surveillance videos, synopsis videos are proposed. Traditional synopsis video generation methods condense most of the activities in the video by simultaneously showing several actions, even when they originally occurred at different times. This inevitably causes ignorance of temporal relationship among objects. For example, two persons walk shoulder to shoulder and they are detected and tracked separately, but in the synopsis they never ‘met’. In this study, a trajectory mapping model is defined, whose energy function includes not only the cost caused by the synopsis video, but that of the original video. In this way, it tries to make the relationship between objects of the original video consistent with that of the synopsis. Finally, the video synopsis is generated by an energy minimisation method. Experiments show that the proposed video synopsis can reduce the spatiotemporal redundancies of the input video as much as possible. Moreover, it can keep the important relationship between objects and maintain the time consistency of important activities.

An energy minimization method for MS lesion segmentation from T1-w and FLAIR images

In this paper, we extend the multiplicative intrinsic component optimization (MICO) algorithm to multichannel MR image segmentation, with focus on segmentation of multiple sclerosis (MS) lesions. The MICO algorithm was originally proposed by Li et al. in Ref. [1] for normal brain tissue segmentation and intensity inhomogeneity correction of a single channel MR image, which exhibits desirable advantages over other methods for MR image segmentation and intensity inhomogeneity correction in terms of segmentation accuracy and robustness. In this paper, we extend the MICO algorithm to multi-channel MR image segmentation and enable the segmentation of MS lesions. We assign different weights for different channels to control the impact of each channel. The weighted channels allow the enhancement of the impact of the FLAIR image on the segmentation of MS lesions by assigning a larger weight to the FLAIR image channel than the other channels. With the inherent mechanism of estimation of the bias field, our method is able to deal with the intensity inhomogeneity in the input multi-channel MR images. In the application of our method, we only use T1-w and FLAIR images as the input two channel MR images. Experimental results show promising result of our method.