Lumped Method Research Articles

Combined semi-recursive formulation and lumped fluid method for monolithic simulation of multibody and hydraulic dynamics

The use of multibody simulation tools allows complex machinery to be described in detail while still providing a solution for the system in real time. As mechanical components are often accompanied by other dynamical systems, such as hydraulics, description of each subsystem is required to fully describe the dynamics of complex machinery. A potential candidate for solving the multiphysics problem at hand is known as the unified or monolithic approach. This strongly coupled approach yields a single set of equations to be integrated and, compared to co-simulation and co-integration approaches, a relatively simple integration procedure. In this paper, a monolithic formulation for a combined simulation of multibody and hydraulic dynamics using an efficient semi-recursive formulation and the lumped fluid method is introduced. The results indicate that the proposed method shows potential for efficient simulation of combined multibody and hydraulic problems. The robustness of the multibody method is maintained when combined with the hydraulic dynamics description and higher efficiency is observed than with an equivalent global approach.

The lumped mass finite element method for surface parabolic problems: Error estimates and maximum principle

The lumped mass method is extended to the surface finite element method for solving the surface parabolic equations. The main purpose of the proposed method is to overcome the difficulty that the surface finite element method does not guarantee the maximal principle of the surface heat equation. Optimal error estimates are given for the semi-discrete and fully-discrete schemes of the proposed method respectively. The maximum principle is shown for surface heat equations and its preservation by the lumped mass surface finite element under the Delaunay type triangulation. Moreover, some results of positivity and monotonicity are derived for nonlinear parabolic equations. Finally some numerical experiments are displayed to illustrate the validity and numerical performance of the proposed method.

PageRank Computation with MAAOR and Lumping Methods

PageRank is a numerical method that Google uses to compute a page’s importance, by assigning a score to every web page. PageRank is thus at the basis of Google’s search engine success and can be mathematically explored either as an eigenvalue problem or as the solution of a homogeneous linear system. In both cases the Google matrix involved is large and sparse, so tuned algorithms must be developed to tackle it with the lowest computational cost and minimum memory requirements. One of such tunings is the Lumping method approach. Furthermore, the accuracy of the ranking vector needs not to be very precise, so inexpensive iterative methods are preferred. In this work the recent Matrix Analogue of the Accelerated Overrelaxation (MAAOR) iterative method is explored for the PageRank computation. Additionally Lumping methods have been applied to the eigenproblem formulation and we propose a novel approach combining the Lumping and MAAOR methods for the solution of the linear system. Numerical experiments illustrating the MAAOR method and the MAAOR method combined with Lumping techniques applied to PageRank computations are presented.

A kinetic model for in situ coking denitrification of heavy oil with high nitrogen content based on starch using a structure-oriented lumping method.

In this study, in situ coking denitrification technology was utilized to simplify the entire process by adding an appropriate quantity of denitrification agents to the delayed-coking tower without any further follow-up denitrification process. The effect of starch as the denitrification agent in the in situ coking denitrification process was studied. The distribution of oil products was characterized by GC of simulated distillation. The results indicated that the nitrogen compounds present in heavy oil transformed to coke via in situ coking conversion by reacting with starch. A molecular-level process model for the coking process was developed. Product distribution on the complex reaction network could be described accurately by the model.

Trends and clinicopathological predictors of axillary evaluation in ductal carcinoma in situ patients treated with breast-conserving therapy.

The aim of this study was to investigate the trends of axillary lymph node evaluation in ductal carcinoma in situ (DCIS) patients treated with breast‐conserving therapy (BCT) and to identify the clinicopathological predictors of axillary evaluation. DCIS patients treated with BCT in 2006–2015 at our institute were retrospectively included in the analysis. Patients were categorized into three groups: sentinel lymph node biopsy (SLNB), axillary lymph node dissection (ALND), and non‐evaluation. Univariate and multivariate logistic regression analyses were performed to identify factors that predicted axillary evaluation. A total of 315 patients were identified, among whom 135 underwent SLNB, and 15 underwent ALND. The proportion of patients who underwent axillary evaluation increased from 33.0% in 2006–2010 to 53.8% in 2011–2015 (P < 0.001), however, no patients had lymph node metastasis based on final pathology. In multivariate analysis, high‐grade tumor favored axillary evaluation (OR = 4.376, 95% CI:1.410–13.586, P = 0.011); while excision biopsy favored no axillary evaluation compared with other biopsy methods (OR = 0.418, 95% CI: 0.192–0.909, P = 0.028). Subgroup analysis of patients treated in 2011–2015 revealed that high‐grade tumor (OR = 5.898, 95% CI: 1.626–21.390, P = 0.007) and palpable breast lump (OR = 2.497, 95% CI: 1.037–6.011, P = 0.041) were independent predictors of axillary lymph node evaluation. Despite the significant decrease in ALND and a concerning overuse of SLNB, we identified no axillary lymph node metastasis, which justified omitting axillary evaluation in these patients. High‐grade tumor, palpable lump, and biopsy method were independent predictors of axillary evaluations. Excision biopsy of suspicious DCIS lesions may potentially preclude the invasive component of the disease and help to avoid axillary surgery

Barlow's method of superconvergence for higher-order finite elements and for transverse stresses in structural elements

In this paper, Barlow's method for determining superconvergent stress/strain points is examined for higher-order finite elements, with particular interest in ones proven in lumped mass explicit dynamic methods, and for transverse stresses in structural elements computed via equilibrium equations. Others have found that for Lagrange polynomial finite elements with equidistant nodes, Barlow and Gauss-Legendre points are coincident for linear and quadratic elements, but are different for cubic and higher order interpolations. The reason for this non-coincidence is identified herein, whereby it is shown to be a result of poor-performing interpolation functions using equal nodal spacing Lagrange polynomials, which results in poor nodal displacement predictions—a violation of a basic premise of Barlow's method. The paradox is shown to be eliminated by using better interpolation functions with “optimal” nodal locations defined by Gauss-Lobatto points. These “optimal” higher-order elements are shown to compute exact superconvergent nodal displacements for one-dimensional bars, and consistent with lower-order elements, the stress/strain superconvergent points predicted by Barlow's method are found to be Gauss-Legendre points of the same precision rule as that of the Gauss-Lobatto rule used for the nodal locations. Barlow's method thus has a sound theoretical foundation for higher-order elements. The coincidence of Barlow with Gauss-Legendre points has been confirmed to be the case for up to 9th order “optimal” nodal location elements in one, two, and three dimensions, which retains the same number of degrees of freedom and also noticeably increases the critical time increment in explicit methods. In addition, calculation of transverse stresses in structural elements, via integration of three-dimensional equilibrium equations, is examined from Barlow's superconvergence viewpoint. Barlow's method provides a distinct means to determine superconvergent points for higher-order derivatives of displacement fields, as necessary for this procedure, and explains the observations of others in computing static transverse stresses from equilibrium equations. A brief catalogue of the newly defined Barlow points for transverse stresses in common element types is provided.

Five node pyramid elements for explicit time integration in nonlinear solid dynamics

Pyramid finite elements have become increasingly popular to facilitate meshing due to their distinctive shape and innate ability to transition naturally between elements with quadrilateral and triangular faces. This is especially important for explicit time integration, as the alternative of constraints can be problematic for wave propagation applications frequently modeled by such methods. Although formulations to alleviate singularity problems near the apex node have existed for decades, pyramid elements are not available in typical explicit solid dynamics software. Several 5-node pyramid approaches are evaluated herein for suitability as transition elements in lumped mass explicit methods for nonlinear solid dynamics. Several typical pyramid elements generated from both hexahedral shape functions and with Bedrosian rabbit functions are extended to explicit temporal methods by the development of mass lumping and critical time increment estimation schemes. Standard and uniform strain hexahedrons are also degenerated into a pyramid by simple nodal duplication in the connectivity. A focus of the study is on the viability of using only existing hexahedron capabilities typically available in many explicit codes. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving large strains/deformations, severe distortion, and contact-impact. Examples first evaluate the elements on their own and then for the principal case as transitions within a hexahedral-dominant model. Row-summation mass lumping is shown to be the best method for any pyramid element approach, which may require slight coding changes for degenerated hexahedrons. The results indicate that it may also be a good systematic method for mass lumping of general degenerate hexahedral types. The single quadrature point standard and Bedrosian pyramid elements are also found to be robust and the best performers, particularly requiring significantly fewer computations than the degenerated uniform strain hexahedron. If used properly, however, all element types are demonstrated to perform satisfactorily (and identically) and thus demonstrate their viability and benefits for practical applications using hexahedral-dominant meshing.

Dynamic modelling and natural characteristic analysis of cycloid ball transmission using lumped stiffness method

The vibration of robot joint reducer is the main factor that causes vibration or motion error of robot system. To improve the dynamic precision of robot system, the cycloid ball transmission used in robot joint is selected as study object in this paper. An efficient dynamic modelling method is presented—lumped stiffness method. Based on lumped stiffness method, a translational–torsional coupling dynamics model of cycloid ball transmission system is established. Mesh stiffness variation excitation, damping of system are all intrinsically considered in the model. The dynamic equation of system is derived by means of relative displacement relationship among different components. Then, the natural frequencies and vibration modes of the derivative system are presented by solving the associated eigenvalue problem. Finally, the influence of the main structural parameters on the natural frequency of the system is analysed. The present research can provide a new idea for dynamic analysis of robot joint reducer and provide a more simplify dynamic modelling method for robot system with joint reducer.

Sensitivity-Based Reliability Analysis of MEMS Acceleration Switch

MEMS acceleration switches have been used in many engineering applications. In this paper, the reliability of MEMS switch is evaluated under various uncertainties from materials and manufacturing process. First, the performance of MEMS switch is modeled using 1D mass-spring-damper-contact system. Different from conventional lumped element methods, the model includes the effect of geometric parameters as well as contact conditions. The parameters of 1D models are calibrated using a high-fidelity finite element model. For reliability assessment, four different methods are used in order to compare computational cost as well as accuracy in predicting reliability. It turned out that sensitivity-based reliability method has several benefits, such as computational time and identifying important parameters that contribute significantly to reliability. The sensitivity analysis showed that the cross-sectional height and the length of folded-beam contribute most significantly to the reliability of switch-on condition. After changing the length of the beam, the probability of failure was improved from 0.168 to 0.0003.

Molecular reconstruction model based on structure oriented lumping and group contribution methods

Abstract Molecular management is a promising technology to face challenges in the refining industry, such as more stringent requirements for product oil and heavier crude oil, and to maximize the value of every molecule in petroleum fractions. To achieve molecular management in refining processes, a novel model that is based on structure oriented lumping (SOL) and group contribution (GC) methods was proposed in this study. SOL method was applied to describe a petroleum fraction with structural increments, and GC method aimed to estimate molecular properties. The latter was achieved by associating rules between SOL structural increments and GC structures. A three-step reconstruction algorithm was developed to build a representative set of molecules from partial analytical data. First, structural distribution parameters were optimized with several properties. Then, a molecular library was created by using the optimized parameters. In the final step, maximum information entropy (MIE) method was applied to obtain a molecular fraction. Two industrial samples were used to validate the method, and the simulation results of the feedstock properties agreed well with the experimental data.

Design, modeling and experimental validation of a novel finned reciprocating compressor for Isothermal Compressed Air Energy Storage applications

Considering the need for a reliable and environmentally friendly energy storage solution for addressing renewable energy intermittency issue and following the developments on Isothermal Compressed Air Energy Storage (I-CAES) systems, a new finned piston compressor which is characterized by increased heat transfer area and coefficient has been designed, analyzed, manufactured and experimentally tested. This compressor includes two sets of concentric annular fins with different diameters: the mobile fins are pushed into the space between the stationary fins through a driver shaft and compress the air trapped in the interconnecting annular chambers while keeping the air temperature close to ambient. Modeling of heat transfer and fluid flow in such a complicated geometry with a transient, non-linear, multi-layer, multi-dimensional nature can be best done by equivalent electric analogies with variable resistances and capacitors and employing a lumped method. Using bond graph representation method and based on a previously developed model for a classic reciprocating compressor, energy conversion has been modeled using a conjugate heat transfer and fluid flow model. Results of the simulation are presented and have been validated using an experimental test bench and to provide contrast to current technology, compared to a classic reciprocating compressor. The heat transfer along one cycle has increased in the finned compressor by 32 times compared to a classic piston compressor. The results also reveal that however the volumetric efficiency is decreased slightly in the finned compressor (−8%), the exergetic efficiency has increased from 55.1% in a classic piston to 78.4% in the finned piston.

Froude-Stanton modeling of heat and mass transfer in large vertical spaces of high-rise buildings

Understanding physics of heat and mass transfer inside large vertical spaces is a major challenge for high-rise fire safety. Due to the size of a high-rise building, experimental studies based on sub-scaled models play an important role in high-rise heat and mass transfer research. Froude modeling method is probably the most common approach for sub-scaling. However, Froude modeling has been found incapable of obtaining accurate temperature predictions from the sub-scaled experiments, especially near building boundaries where there exists significant heat transfer between smoke and the boundaries. In this paper, a new modeling method, Froude-Stanton modeling, is developed for both mechanically-driven and naturally-driven thermal smoke spreads, in which heat transfer is taken into consideration in the energy balance equation. The flow resistance of the internal shaft structure is also considered using a lumped method. To verify the new method, series of experiments were conducted on three shafts with different sizes and material using both Froude and Froude-Stanton methods. The results, including temperature profile, relative neutral plane level and thermal smoke flow rate, are compared between the two modeling methods, and it was found that the new Froude-Stanton modeling method is more accurate.

Acoustic impact of the gradual glottal abduction degree on the production of fricatives: A numerical study.

The paper presents a numerical study about the acoustic impact of the gradual glottal opening on the production of fricatives. Sustained fricatives are simulated by using classic lumped circuit element methods to compute the propagation of the acoustic wave along the vocal tract. A recent glottis model is connected to the wave solver to simulate a partial abduction of the vocal folds during their self-oscillating cycles. Area functions of fricatives at the three places of articulation of French have been extracted from static MRI acquisitions. Simulations highlight the existence of three distinct regimes, named A, B, and C, depending on the degree of abduction of the glottis. They are characterized by the frication noise level: A exhibits a low frication noise level, B, which is a transitional unstable regime, is a mixed noise/voice signal, and C contains only frication noise. They have significant impacts on the first spectral moments. Simulations show that their boundaries depend on articulatory and glottal configurations. The transition regime B is shown to be unstable: it requires very specific configurations in comparison with other regimes, and acoustic features are very sensitive to small perturbations of the glottal configuration abduction in this regime.

Lumped finite elements for reaction–cross-diffusion systems on stationary surfaces

We consider a lumped surface finite element method (LSFEM) for the spatial approximation of reaction–diffusion equations on closed compact surfaces in R3 in the presence of cross-diffusion. We provide a fully-discrete scheme by applying the Implicit–Explicit (IMEX) Euler method. We provide sufficient conditions for the existence of polytopal invariant regions for the numerical solution after spatial and full discretisations. Furthermore, we prove optimal error bounds for the semi- and fully-discrete methods, that is the convergence rates are quadratic in the meshsize and linear in the timestep. To support our theoretical findings, we provide two numerical tests. The first test confirms that in the absence of lumping numerical solutions violate the invariant region leading to blow-up due to the nature of the kinetics. The second experiment is an example of Turing pattern formation in the presence of cross-diffusion on the sphere.

Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems.

Constructing Markov state models from large-scale molecular dynamics simulation trajectories is a promising approach to dissect the kinetic mechanisms of complex chemical and biological processes. Combined with transition path theory, Markov state models can be applied to identify all pathways connecting any conformational states of interest. However, the identified pathways can be too complex to comprehend, especially for multi-body processes where numerous parallel pathways with comparable flux probability often coexist. Here, we have developed a path lumping method to group these parallel pathways into metastable path channels for analysis. We define the similarity between two pathways as the intercrossing flux between them and then apply the spectral clustering algorithm to lump these pathways into groups. We demonstrate the power of our method by applying it to two systems: a 2D-potential consisting of four metastable energy channels and the hydrophobic collapse process of two hydrophobic molecules. In both cases, our algorithm successfully reveals the metastable path channels. We expect this path lumping algorithm to be a promising tool for revealing unprecedented insights into the kinetic mechanisms of complex multi-body processes.

Improving the linear flexibility distribution model to simultaneously account for gravity and lateral loads

There are two methods to model the plastification of members comprising lumped and distributed plasticity. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread from the joint interface resulting in a curvature distribution; therefore, the lumped plasticity methods assuming plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements, cannot model the actual behavior of reinforced concrete members. Some spread plasticity models including uniform, linear and recently power have been developed to take extended inelastic zone into account. In the aforementioned models, the extended inelastic zones in proximity of critical sections assumed close to connections are considered. Although the mentioned assumption is proper for the buildings simply imposed lateral loads, it is not appropriate for the gravity load effects. The gravity load effects can influence the inelastic zones in structural elements; therefore, the plasticity models presenting the flexibility distribution along the member merely based on lateral loads apart from the gravity load effects can bring about incorrect stiffness matrix for structure. In this study, the linear flexibility distribution model is improved to account for the distributed plasticity of members subjected to both gravity and lateral load effects. To do so, a new model in which, each member is taken as one structural element into account is proposed. Some numerical examples from previous studies are assessed and outcomes confirm the accuracy of proposed model. Also comparing the results of the proposed model with other spread plasticity models illustrates glaring error produced due to neglecting the gravity load effects.

Dynamics of fluid migration into porous solid matrix during high pressure treatment

A mathematical approach was used to describe the mechanism of pressure-driven flow during the holding period of high pressure processing (HPP). A lumped method was used for the estimation of mass transfer parameters using an analogy to Fick’s second law. In addition, a least squares optimization algorithm was introduced as inverse parameter estimators to obtain the associated mass diffusivity coefficients. The approach was verified using a model system involving liquid diffusion (1% w/w ascorbic acid solution) into a porous solid matrix (apple cubes) under HPP conditions (100–600MPa) with different holding times (0–30min). The associated fluid diffusivity values ranged 4.38×10−9–2.19×10−8m2s−1. Finally, a simple linear model was fitted to the experimental data at 100 and 600MPa which could be used to estimate the total porosity of the solid matrix. Thus, finite element numerical solutions combined with simple Fickian approach could be used to model the unsaturated liquid flow in to a porous solid matrix. The study also showed that the liquid in-flow decreased in blanched apples subjected to similar HPP confirming the need for a porous structure for the efficient liquid flow.

Flow field estimation analysis based on the Kalman filter FEM for selection of tidal stream power generator locations

In this paper, we present a shallow water flow field estimation analysis, based on the Kalman filter FEM, for locating the optimal positions for tidal stream power generation systems. In our flow field analysis, we adopt the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are employed as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carry out a flow estimation analysis for Tokyo Bay. The high estimation accuracy of the flow field estimation based on the Kalman filter FEM is confirmed by comparison with conventional FEM. The electric power generation potential is also computed using the estimated flow field.

東京湾における潮流発電ポテンシャル算定に対するカルマンフィルタFEMの適用

In recent years, tidal stream power generation is attracting attention as renewable energy. When a turbine submerged in the sea is rotated by a tidal current, kinetic energy is transformed to electric energy in this power generation method. In this paper, we present a flow field estimation analysis based on the Kalman filter FEM for locating the optimal positions for tidal stream power generation systems. We employed the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are used as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carried out a flow estimation analysis for Tokyo Bay and the electric power generation potential is calculated using the estimated flow field. It was confirmed that the estimation accuracy of the flow field estimation analysis by the Kalman filter FEM is higher than that by the conventional FEM.

Vapor-liquid phase boundaries and swelling factors of C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions

Techniques have been developed to determine vapor-liquid phase boundaries and swelling factors of CO2-heavy oil systems and C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions. Experimentally, a pure substance of CO2 and a gas mixture consisting of 27.7 mol% C3H8, 23.9 mol% n-C4H10, and 48.4 mol% CO2 are respectively introduced to dilute the highly viscous heavy oil. A pressure-volume-temperature (PVT) setup is used to measure vapor-liquid phase boundaries (i.e., saturation pressures) and swelling factors at high pressures up to 11.1 MPa and elevated temperatures up to 373.35 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) coupled with a recently modified alpha function is applied as the primary thermodynamic model to reproduce the experimental measurements. The heavy oil which is a complex mixture with unknown molecular structure is characterized as six pseudocomponents by using an exponential distribution splitting function and a logarithm-type lumping method. The optimal exponents in binary interaction parameter (BIP) correlations are obtained by best matching the measured saturation pressures. Subsequently, the comparisons have been performed between this work and a commercial simulator in terms of the overall prediction accuracy of saturation pressures for the quaternary C3H8-n-C4H10-CO2-heavy oil systems. It is found that the minimum absolute average relative deviation (AARD) of 6.7% is obtained by the methodology developed in this work, compared to the AARD of 35.6% obtained by running the commercial simulator.