Finite Accuracy Research Articles

On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

AbstractThe aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.

Disorder-dressed quantum evolution

The active harnessing of quantum resources in engineered quantum devices poses unprecedented requirements on device control. Besides the residual interaction with the environment, causing environment-induced decoherence, uncontrolled parameters in the system itself -- disorder -- remains as a substantial factor limiting the precision and thus the performance of devices. These perturbations may arise, for instance, due to imperfect sample production, stray fields, or finite accuracy of control electronics. Disorder-dressed quantum evolution means a unifying framework, based on quantum master equations, to analyze how these detrimental influences cause deviations from the desired system dynamics. This description may thus contribute to unveiling and mitigating disorder effects towards robust schemes. To demonstrate the broad scope of this framework, we evaluate two distinct scenarios: a central spin immersed in an isotropic spin bath, and a random mass Dirac particle. In the former scenario, we demonstrate how the disorder average reflects purity oscillations, indicating the time- and state-dependent severity of the disorder impact. In the latter scenario, we discuss disorder-induced backscattering and disorder-induced Zitterbewegung as consequences of the breakup of spin-momentum locking.

A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

Abstract The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements P k {P_{k}} and P m {P_{m}} ( k < m {k<m} ). Then we analyze the asymptotic relation between these two probabilistic laws when the difference m - k {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur.

Despite evidence of the biomechanical role of cortical bone, current state of the art finite element models of the proximal femur built from clinical CT data lack a subject-specific representation of the bone cortex. Our main research hypothesis is that the subject-specific modelling of cortical bone layer from CT images, through a deconvolution procedure known as Cortical Bone Mapping (CBM, validated for cortical thickness and density estimates) can improve the accuracy of CT-based FE models of the proximal femur, currently limited by partial volume artefacts. Our secondary hypothesis is that a careful choice of cortical-specific density-elasticity relationship may improve model accuracy. We therefore: (i) implemented a procedure to include subject-specific CBM estimates of both cortical thickness and density in CT-based FE models. (ii) defined alternative models that included CBM estimates and featured a cortical-specific or an independently optimised density-elasticity relationship. (iii) tested our hypotheses in terms of elastic strain estimates and failure load and location prediction, by comparing with a published cohort of 14 femurs, where strain and strength in stance and fall loading configuration were experimentally measured, and estimated through reference FE models that did not explicitly model the cortical compartment. Our findings support the main hypothesis: an explicit modelling of the proximal femur cortical bone layer including CBM estimates of cortical bone thickness and density increased the FE strains prediction, mostly by reducing peak errors (average error reduced by 30%, maximum error and 95th percentile of error distribution halved) and especially when focusing on the femoral neck locations (all error metrics at least halved). We instead rejected the secondary hypothesis: changes in cortical density-elasticity relationship could not improve validation performances. From these improved baseline strain estimates, further work is needed to achieve accurate strength predictions, as models incorporating cortical thickness and density produced worse estimates of failure load and equivalent estimates of failure location when compared to reference models. In summary, we recommend including local estimates of cortical thickness and density in FE models to estimate bone strains in physiological conditions, and especially when designing exercise studies to promote bone strength.

Dosimetric accuracy of delivering SBRT using dynamic arcs on Cyberknife.

PurposeSeveral studies have demonstrated potential improvements in treatment time through the use of dynamic arcs for delivery of stereotactic body radiation therapy (SBRT) on Cyberknife. However, the delivery system has a finite accuracy, so that potential exists for dosimetric uncertainties. This study estimates the expected dosimetric accuracy of dynamic delivery of SBRT, based on realistic estimates of the uncertainties in delivery parameters.MethodsFive SBRT patient cases (prostate A — conventional, prostate B — brachytherapy‐type, lung, liver, partial left breast) were retrospectively studied. Treatment plans were produced for a fixed arc trajectory using fluence optimization, segmentation, and direct aperture optimization. Dose rate uncertainty was modeled as a smoothly varying random fluctuation of ± 1.0%, ±2.0% or ± 5.0% over a time period of 10, 30 or 60 s. Multileaf collimator uncertainty was modeled as a lag in position of each leaf up to 0.25 or 0.5 mm. Robot pointing error was modeled as a shift of the target location, with the direction of the shift chosen as a random angle with respect to the multileaf collimator and with a random magnitude in the range 0.0–1.0 mm at the delivery nodes and with an additional random magnitude of 0.5–1.0 mm in between the delivery nodes. The impact of the errors was investigated using dose‐volume histograms.ResultsUncertainty in dose rate has the effect of varying the total monitor units delivered, which in turn produces a variation in mean dose to the planning target volume. The random sampling of dose rate error produces a distribution of mean doses with a standard deviation proportional to the magnitude of the dose rate uncertainty. A lag in multileaf collimator position of 0.25 or 0.5 mm produces a small impact on the delivered dose. In general, an increase in the PTV mean dose of around 1% is observed. An error in robot pointing of the order of 1 mm produces a small increase in dose inhomogeneity to the planning target volume, sometimes accompanied by an increase in mean dose by around 1%.ConclusionsBased upon the limited data available on the dose rate stability and geometric accuracy of the Cyberknife system, this study estimates that dynamic arc delivery can be accomplished with sufficient accuracy for clinical application. Dose rate variation produces a change in dose to the planning target volume according to the perturbation of total monitor units delivered, while multileaf collimator lag and robot pointing error typically increase the mean dose to the planning target volume by up to 1%.

Comparison and Analysis of Two Different Calculation Schemes of SLEVE- Hybrid Coordinate in GRAPES_MESO Model

The calculation scheme of the smoothed-level and hybrid (SLEVE-hybrid for short) coordinates in numerical forecasting model is not limited in number. It is divided into the semi-analytical scheme and the finite differential scheme in terms of the various differential methods of the coordinate deformation variables. Having compared the dynamic equation and the long-time batch simulation results of the two schemes, the present study draws the following conclusions. The first-order finite difference accuracy of the coordinate deformation variables in the finite differential scheme is theoretically lower than that in the semi-analytical scheme. The larger the vertical gradient of the layer thickness is, the larger the relative errors of the finite differential scheme are. The long-time batch simulation test in the GRAPES model dynamic core demonstrates that the bias of the temperature and the geopotential height in the semi-analytical scheme is smaller under the default layering, while the simulation difference of the two schemes is greatly reduced when the layering is more uniform.

Hand detection and segmentation using smart path tracking fingers as features and expert system classifier

Nowadays, hand gesture recognition (HGR) is getting popular due to several applications such as remote based control using a hand, and security for access control. One of the major problems of HGR is the accuracy lacking hand detection and segmentation. In this paper, a new algorithm of hand detection will be presented, which works by tracking fingers smartly based on the planned path. The tracking operation is accomplished by assuming a point at the top middle of the image containing the object then this point slides few pixels down to be a reference point then branching into two slopes: left and right. On these slopes, fingers will be scanned to extract flip-numbers, which are considered as features to be classified accordingly by utilizing the expert system. Experiments were conducted using 100 images for 10-individual containing hand inside a cluttered background by using Dataset of Leap Motion and Microsoft Kinect hand acquisitions. The recorded accuracy is depended on the complexity of the Flip-Number setting, which is achieved 96%, 84% and 81% in case 6, 7 and 8 Flip_Numbers respectively, in which this result reflects a high level of finite accuracy in comparing with existing techniques.

METHODS OF FACTORIAL CODING OF SPEECH SIGNALS

Context. The paper outlines the methods of factorial coding of speech signals using a factorial code to provide integrated information security and to maintain a receiver and transmitter clock phase. By integrated information security, for the methods proposed in this article, we mean data protection from effects of noise in communication channel and attempts of data unauthorized access in open multiple access telecommunication networks. Objective. The goal of the research is to provide integrated protection of real-time speech signals based on factorial coding. For this, the methods for factorial coding of speech signals and building speech codecs have been developed. These methods are based on the properties of factorial codes to keep synchronism with the working signal, to detect a significant part of errors caused by the action of noise, natural or created intentionally, to provide the ability to correct all detected errors with a finite accuracy, as well as to provide cryptographic protection against voice message unauthorized listening by hiding the law of converting speech signal samples into a permutation. Method. The main idea of the proposed methods is to choose permutations for information transferring with a specific set of properties and features that provide the ability to correct errors detected by code and to recover speech signal samples with a finite degree of accuracy (with a nonzero aperture). Results. The procedures for information coding/decoding have been determined. The results of the experimental evaluation of the model of such systems when working on a communication channel with both independent and multiple bit errors are presented. The magnitude of decoding noise due to the finite accuracy of speech signal samples recovery is determined as a function of bit error probability in a communication channel. Conclusions. The proposed methods of factorial coding of a speech signal provide integrated information security and recovery with finite accuracy of speech signal samples deformed by noise in communication channel. The requirements to the quality of communication channel (to the value of bit error probability) for comfortable speech perception are determined.

An Accurate and Efficient Time-domain Model for Simulating Wave Propagation in Half-space

The wave propagation in the unbounded domain is a hottest topic in engineering research. Based on the scaled boundary finite element method, an efficient and accuracy artificial boundary condition is proposed for the wave propagation in half space, and the shape of the artificial boundary can be arbitrary, such as ellipse and rectangle. A new continued fraction for solving the dynamic stiffness is derived, and by introducing auxiliary variables, it can be transformed into time domain conveniently. The dynamic stiffness of the artificial boundary condition in frequency domain in good agreement with the exact solution in high frequencies. The circle and ellipse artificial boundary condition is identical with the reference solution in time domain.

Research on Finite Element Model Modification of Carbon Fiber Reinforced Plastic (CFRP) Laminated Structures Based on Correlation Analysis and an Approximate Model.

Carbon fiber reinforced plastic (CFRP) laminated structures have been widely used in modern engineering due to their excellent material properties, especially in the aerospace and shipping industries. This requires a high-accuracy finite element model of CFRP laminated structures. However, it is difficult to master the mechanical properties of CFRP structures comprehensively and accurately due to influences from multiple aspects, such as dispersion of material properties, uncertainty of manufacturing technologies, etc. Therefore, a finite element model modification method of CFRP laminated structures based on correlation analysis and an approximate model was proposed. Aiming at minimizing the difference between the analysis model and the measured inherent frequency, the proposed method improves the finite element modeling accuracy of CFRP laminated structures, by iterative optimization based on a global optimization algorithm. In order to solve the problem of high spatial dimension and slow searching in modification of CFRP laminated structure models, the Pearson correlation analysis method was used to screen the material parameters which exert significant impacts on frequency characteristics to reconstruct the searching space. Based on significance parameters, an approximate response model of the CFRP laminated structural system was established. Meanwhile, the modeling accuracy of different orders of response surface models (RSM) and a radial basis function (RBF) neural network model was analyzed, and the best approximate modeling scheme was obtained. The approximate model was updated based on the multi-island genetic algorithm (MIGA) to modify the finite element model of the CFRP laminated structure model. The maximum error and mean error of the updated model are 1.47% and 0.45%. It was proved that the material parameters modified by the proposed method are applicable to simulation analysis of the CFRP laminated structure.

Efficient Implementation of Cluster Expansion Models in Surface Kinetic Monte Carlo Simulations with Lateral Interactions: Subtraction Schemes, Supersites, and the Supercluster Contraction.

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current kinetic Monte Carlo (KMC) algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate cluster expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: (1) representing the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, (2) employing the subtraction schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and (3) applying efficient search algorithms from a set of established methods (supersite approach). The cost of the resulting algorithm is fixed with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established variable step-size method by employing the supercluster, subtraction, and supersite algorithms (SSS-VSSM). © 2019 Wiley Periodicals, Inc.

Induction machine model with finite element accuracy for condition monitoring running in real time using hardware in the loop system

Most industrial processes are run by induction machines (IMs). Condition monitoring of IM assures their continuity of service, and it may avoid highly costly breakdowns. Among the methods for condition monitoring, on-line motor current signature analysis is being attracting a rising interest, because it is non-invasive, and it can identify a wide variety of faults at early stage. To favour the development of on-line fault diagnosis techniques, it is necessary to have real-time currents with which test the new techniques and devices. Models running in real time in hardware-in-the-loop (HIL) simulators are a suitable alternative to balance the drawbacks of test benches (costly, limited machines, faults and working conditions). These models must be accurate enough to reflect the effects of a fault and they must be running in real time. A promising technique based on the equivalent circuit parameters calculation of IM by finite element analysis (FEA) is attracting a rising interest due to its reliability, performance and the possibility of being run in a HIL. Nevertheless, prior to running in a HIL, it is necessary to compute the IM parameters using FEA, which requires long simulation times and high computing resources. Consequently, covering a whole range of degrees of a giving fault could be unaffordable. What is proposed in this paper is to apply the sparse subspace learning (SSL) in combination with the hierarchical Lagrangian interpolation (HLI) to obtain the parametric solutions of the faulty IM model that cover the whole range of severity of a given fault, with a reduced number of FEA simulations. By means of this approach it is possible not only to boost the computation speed but also to achieve a significant reduction of memory requirements while retaining reasonable accuracy compared to traditional FEA, so enabling the real-time simulation of predictive models.

A New Probabilistic Interpretation of the Bramble–Hilbert Lemma

Abstract The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size h goes to zero. Starting from a geometrical reading of the error estimate due to the Bramble–Hilbert lemma, we derive two probability distributions that estimate the relative accuracy, considered as a random variable, between two Lagrange finite elements P k {P_{k}} and P m {P_{m}} ( k < m {k<m} ). We establish mathematical properties of these probabilistic distributions and we get new insights which, among others, show that P k {P_{k}} or P m {P_{m}} is more likely accurate than the other, depending on the value of the mesh size h.

Numerical frequency analysis of skew sandwich layered composite shell structures under thermal environment including shear deformation effects

The numerical thermal frequency responses of the skew sandwich shell panels structure are investigated via a higher-order polynomial shear deformation theory including the thickness stretching effect. A customized MATLAB code is developed using the current mathematical model for the computational purpose. The finite element solution accuracy and consistency have been checked via solving different kinds of numerical benchmark examples taken from the literature. After confirming the standardization of the model, it is further extended to show the effect of different important geometrical parameters such as span-to-thickness ratios, aspect ratios, curvature ratios, core-to-face thickness ratios, skew angles, and support conditions on the frequencies of the sandwich composite flat/curved panel structure under elevated temperature environment.

Systematic Design of Bandgap Voltage Reference Using Precomputed Lookup Tables

Bandgap voltage references are indispensable in any analog/mixed-signal system. In this paper, we introduce a systematic gm/ID-based procedure to design a CMOS bandgap reference. The proposed iterative methodology relies on one-time-generated precomputed lookup tables (LUTs); thus, it does not require invoking a simulator in the loop. Despite the inherent finite accuracy of the LUT-based design approach, we demonstrate that a precision bandgap circuit can be designed with less than 1-ppm error. We verified the proposed procedure against the Spectre simulations and probed the design space using a symbolic circuit solver. Moreover, we demonstrated how variations and mismatch can be taken into account in the context of the proposed methodology. The results demonstrate that the proposed procedure can provide very accurate results in a short execution time, enabling the designer to explore the design space of key performance metrics, such as power-supply rejection (PSR) and noise.

$L_{1}$ Adaptive Control of a Dual-Rotor Tail-Sitter Unmanned Aerial Vehicle With Input Constraints During Hover Flight

The input constraints of control surfaces may lead to saturations, which could limit the achievable performance or even cause instability of vertical take-off and landing (VTOL) tail-sitter unmanned aerial vehicle (UAV). To improve flight safety and attitude tracking performance, a novel L 1 adaptive control architecture for attitude tracking of a tail sitter subjected to input constraints is proposed in this study. The imprecise mathematical model, low weight, and small size all present different challenges when designing a control system. In this work, a feedforward compensator is first used to narrow down the uncertain bounds with the consideration of finite accuracy from prior knowledge. Second, according to the linearized model, a baseline controller is designed to offer basic performance for a nominal system without uncertainty. Finally, the L 1 adaptive controller is developed to compensate for unmatched uncertainties based on the control system developed before. The stability and performance bounds of the closed-loop system are analyzed to illustrate the impact of input constraints. The numerical simulations and flight tests are carried out to verify the improved attitude tracking performance when input saturation exists.

The Influence of Finite Element Meshing Accuracy on a Welding Machine for Offshore Platform’S Modal Analysis

Abstract The purpose objective of this study was to investigate the influence of finite element meshing accuracy on modal analysis which is one of the basic factors affecting the accuracy of finite element analysis and mostly preoccupies the working staff in pre-processing finite element simulation models. In this paper, we established several finite element models of a welding machine for offshore platform, with the meshing accuracy as the variable and workbench software as the platform for modal analysis, as the same time, comparing the analysis results. The results indicated that for some specific structures and simulation types, mesh refinement alone does not achieve desired results, and the authors indicate that mesh refinement is rarely related to the equipment’s low-frequency modal analysis but it’s great related to the equipment’s high-frequency modal analysis. The findings of this study may serve as breaking the opinion that smaller mesh size means higher calculation precision and provides references for mesh division practices in low frequency modal analysis.

Practical Sample-and-Hold Stabilization of Nonlinear Systems Under Approximate Optimizers

It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even discontinuous feedbacks. In the latter case, the sample-and-hold framework is widely used, in which the control input is held constant during sampling periods. Consequently, only practical stability can be achieved at best. Existing approaches often require solving optimization problems for finding stabilizing control actions exactly. In practice, each optimization routine has a finite accuracy which might influence the state convergence. This work shows, what bounds on optimization accuracy are required to achieve prescribed stability margins. Simulation studies support the claim that optimization accuracy has high influence on the state convergence.

P149] Beam profile characteristic points designation for off-axis, wedged and FFF beams

Purpose The main aim of this work is the search of characteristic points of a beam profile and application of these points for the TPS commissioning purposes. The comparison between profiles during the commissioning of the treatment planning system is a very important procedure. It is impossible to designate a field size for the off-axis, wedged and FFF beams directly using the definition of the on-axis symmetric field size. This work demonstrates how to compute good indicators of the field size that can be used for commissioning and QA purposes. Methods The proposal is to use profile inflection points as the beam profile characteristic points. The comparison of distances between inflection points and between points of 50% intensity was done using a dedicated software. For the off-axis, wedged and FFF fields comparisons were done to the nominal field sizes. Results Distances between inflection points were smaller than 1 mm compared to nominal field sizes for all kinds of investigated beams. Conclusions With a finite accuracy, inflection points can be used for the off-axis, wedged and FFF field sizes comparison. The main advantage of inflection points for the beam sizes designation is their independence from the method of profile normalization.

Energy-speed-accuracy relation in complex networks for biological discrimination.

Discriminating between correct and incorrect substrates is a core process in biology, but how is energy apportioned between the conflicting demands of accuracy (μ), speed (σ), and total entropy production rate (P)? Previous studies have focused on biochemical networks with simple structure or relied on simplifying kinetic assumptions. Here, we use the linear framework for timescale separation to analytically examine steady-state probabilities away from thermodynamic equilibrium for networks of arbitrary complexity. We also introduce a method of scaling parameters that is inspired by Hopfield's treatment of kinetic proofreading. Scaling allows asymptotic exploration of high-dimensional parameter spaces. We identify in this way a broad class of complex networks and scalings for which the quantity σln(μ)/P remains asymptotically finite whenever accuracy improves from equilibrium, so that μ_{eq}/μ→0. Scalings exist, however, even for Hopfield's original network, for which σln(μ)/P is asymptotically infinite, illustrating the parametric complexity. Outside the asymptotic regime, numerical calculations suggest that, under more restrictive parametric assumptions, networks satisfy the bound, σln(μ/μ_{eq})/P<1, and we discuss the biological implications for discrimination by ribosomes and DNA polymerase. The methods introduced here may be more broadly useful for analyzing complex networks that implement other forms of cellular information processing.