Numerical Integration Method Research Articles

Dynamic Simulation Analysis of Carbon-Steel Hybrid Sucker Rod String in Vertical and Directional Wells

Carbon fiber composite continuous sucker rod string is more and more widely used in deep and ultradeep wells because of its light weight, high strength, and corrosion resistance. In order to analyze the dynamic problems of carbon fiber sucker rod string in actual oil wells, a transverse vibration simulation model of carbon fiber and steel (carbon-steel) hybrid rod string excited by buckling deformation in vertical wells is established with the compression buckling deformation of weighting rod. Considering the influence of wellbore trajectory and the constraint of tubing, the transverse vibration simulation model of carbon-steel hybrid rod string in directional wells under borehole trajectory excitation is also established in this paper. The finite difference method is used to discretize the well depth node, the numerical integration method (Newmark-β) is used to discretize the reciprocating periodic time node, and simulation methods for the contact and collision dynamics of rod-tubing in vertical wells and directional wells are formed. Through programming calculation, the distribution laws of transverse displacement, contact force, collision force, and bending stress of carbon-steel hybrid sucker rod string in vertical wells and directional wells along well depth are obtained. The simulation results in vertical wells show that the strong collision between the rod and tubing occurs near the bottom steel rod, while the upper load is small and the rod-tubing collision load of the upper rod of the carbon-steel hybrid rod string is much lower than that of the traditional steel rod string at the same position. Furthermore, the bending stress of the upper carbon fiber is also much less than that of the bottom steel rod. The simulation results in directional wells show that the collision phenomenon of the deflecting section and the bottom weighting rod compression section are the strongest and the rod-tubing contact pressure is also the largest. Second, the impact force of the upper carbon fiber rod is also much lower than that of the steel rod. Again, the maximum bending stress of the whole well occurs near the deviation section where the deviation angle changes suddenly. The transverse vibration mechanical model in directional wells in this paper lays a theoretical foundation and provides theoretical support for the optimal design of fracture and splitting prevention measures of carbon fiber sucker rod.

Feedback Gradient Descent: Efficient and Stable Optimization with Orthogonality for DNNs

The optimization with orthogonality has been shown useful in training deep neural networks (DNNs). To impose orthogonality on DNNs, both computational efficiency and stability are important. However, existing methods utilizing Riemannian optimization or hard constraints can only ensure stability while those using soft constraints can only improve efficiency. In this paper, we propose a novel method, named Feedback Gradient Descent (FGD), to our knowledge, the first work showing high efficiency and stability simultaneously. FGD induces orthogonality based on the simple yet indispensable Euler discretization of a continuous-time dynamical system on the tangent bundle of the Stiefel manifold. In particular, inspired by a numerical integration method on manifolds called Feedback Integrators, we propose to instantiate it on the tangent bundle of the Stiefel manifold for the first time. In our extensive image classification experiments, FGD comprehensively outperforms the existing state-of-the-art methods in terms of accuracy, efficiency, and stability.

High-order joint-smooth trajectory planning method considering tool-orientation constraints and singularity avoidance for robot surface machining

Compared with the traditional machine tools, robots are low-cost and flexible for the machining process. However, owing to the complex constraints in the operation space and the redundant degrees of freedom (DoFs), it is challenging to obtain a joint-smooth optimal trajectory for the robotic machining. This article develops a high-order smooth joint trajectory planning method for robot surface machining considering with the tool posture constraints (the collision avoidance and cutting angles limits) and the robot state limits (the singularity avoidance). In the proposed method, the whole trajectory of the tool posture is integrated by the optimized differential vector in steps. In every integrating step, the differential vector is optimized from the redundant DoFs with the combined and balanced optimization objective considering the joint-smooth requirements, tool orientation limits and robot state constraints. At the same time, the upper limit of the second-order differential is given to limit the change rate of the optimized differential vector and to smooth the generated trajectory further. As the drastic change of the feasible region and tool-tip path curve, the boundary of the feasible region should be smoothed in advance to compensate for the hysteresis of the numerical integration method. In the end, two cases of robot surface machining are provided to verify the method. In the experimental process, an UR-5 robot with Robot Operating System (ROS) controller is used and the complex curve is machined by the robot.

Construction of [formula omitted]- or [formula omitted]-symplectic general linear methods

We describe the construction of G- or G(ϵ)-symplectic, and parasitism free or ϵ-parasitism free general linear methods for numerical integration of Hamiltonian systems of differential equations. Examples of such methods are presented up to the order p=4 and stage order q=p−1. Numerical experiments confirm that all methods achieve the expected order of accuracy, and that these methods approximately preserve Hamiltonians as well as quadratic invariants of differential systems.

On the Choice of Methods for Numerically Integrating the Equations of Transients in Electric Power Systems

Algorithms for solving the system of differential-algebraic equations describing electromechanical transients in electric power systems are considered along with matters concerned with ensuring the reliability and required accuracy of the solution results. Classical explicit methods, methods for implicit numerical integration and simultaneous solution of differential-algebraic systems of equations are used to model dynamic processes in power systems. On the basis of the methods used, difference models of electric power system components are obtained. The equations of transients in electric power systems are written in a homogeneous coordinate basis with the use of nodal voltage equations. A comparative analysis of algorithms based on the explicit Runge-Kutta method and implicit methods of Euler, trapezoids, Euler with fitting coefficients is carried out. The analysis results have shown that in terms of stability and accuracy, the trapezoid method has the greatest advantages, which is not inferior to the 4th order Runge-Kutta method and allows calculations with a large integration step to be carried out. The effectiveness of the combined method is shown, in which the Euler method with fitting is used to solve the differential equations describing electromagnetic processes, and the trapezoid method is used to solve the equations of electromechanical motion.

Development of efficient hydrogen refueling station by process optimization and control

Development of efficient hydrogen refueling station (HRS) is highly desirable to reduce the hydrogen cost and hence the life cycle expense of fuel cell vehicles (FCVs), which is hindering the large scale application of hydrogen mobility. In this work, we demonstrate the optimization of gaseous HRS process and control method to perform fast and efficient refueling, with reduced energy consumption and increased daily fueling capacity. The HRS was modeled with thermodynamics using a numerical integration method and the accuracy for hydrogen refueling simulation was confirmed by experimental data, showing only 2 °C of temperature rise deviation. The refueling protocols for heavy duty FCVs were first optimized, demonstrating an average fueling rate of 2 kg/min and pre-cooling demand of less than 7 kW for 35 MPa type III tanks. Fast refueling of type IV tanks results in more significant temperature rise, and the required pre-cooling temperature is lowered by 20 K to achieve comparable fueling rate. The station process was also optimized to improve the daily fueling capacity. It is revealed that the hydrogen storage amount is cost-effective to be 25–30% that of the nominal daily refueling capacity, to enhance the refueling performance at peak time and minimize the start and stop cycles of compressor. A novel control method for cascade replenishment was developed by switching among the three banks in the order of decreased pressure, and results show that the daily refueling capacity of HRS is increased by 5%. Therefore, the refueling and station process optimization is effective to promote the efficiency of gaseous HRS.

In-situ γ-ray analysis of ground surface radioactivity using portable HPGe γ spectrometer.

As essential high-end equipment for nuclear emergency monitoring, the portable HPGe γ spectrometer currently lacks supporting in-situ measurement methods, limiting its role and value in emergency missions. For this practical problem, this paper studies the measurement of ground surface radioactivity by portable HPGe γ spectrometer in nuclear emergency monitoring in view of the particularity of nuclear emergency source items. Firstly, the detection efficiency of point sources at different horizontal distances when the spectrometer is installed at the height of 1 m from the center of the detector to the ground is calculated. Secondly, the concept of effective contribution distance is defined and analyzed. Thirdly, the point source detection efficiency is obtained using the numerical integration method of calculation. Integrate to calculate the detection efficiency of the surface source, and then calculate the radioactive surface activity of the surface. Finally, the effectiveness of the method is verified through experiments.

1123-P: Racial Differences in Glycemia and A1C in the Vitamin D and Diabetes (D2d) Study

Understanding the association between glycemia and A1c by race can improve screening for prediabetes and type 2 diabetes (T2D) . This association was examined cross-sectionally in 1016 Black and 2658 White persons screened for D2d (mean age 60; fasting glucose [FG] 1mg/dL; A1c 5.9%) . Of these, 22with at least 2-of-3 ADA glycemic criteria for prediabetes (mean age 60, FG 1mg/dL, A1c 5.9%, 28% Black) were followed longitudinally for median 2.5 years with annual OGTT and semi-annual FG and A1c. Numerical integration methods were used for the estimation of area under the OGTT-derived glucose curve (AUC) . Mean A1c was estimated for a given AUC quintile using linear regression for Whites, Blacks, and Asians. Adjusting for covariates, the A1c was higher by 0.2-0.25% among Black vs. White participants with similar glycemia in all AUC quintiles. During follow-up, Black participants were more likely to be diagnosed with T2D based on A1c; White participants were more likely to be diagnosed by FG. The absolute increase in A1c over time according to baseline AUC-glucose quintiles differed by race. Compared to White participants, Black participants in lower baseline AUC quintiles had greater increases in A1c over time, while A1c increased similarly in White and Black persons in the two highest baseline AUC quintiles. In summary, Black participants had higher A1c than White participants for similar degree of glycemia defined by AUC; the glycemic criteria contributing to the diagnosis of T2D differed by race; and there were AUC by racial interactions in A1c increase over time. Disclosure E.S.Leblanc: n/a. S.Dagogo-jack: Consultant; AstraZeneca, Bayer AG, Boehringer Ingelheim International GmbH, Janssen Pharmaceuticals, Inc., Medtronic, Merck & Co., Inc., Sanofi. J.P.Nelson: None. D.S.Hsia: None. D2d research group: n/a. A.G.Pittas: None. R.Chatterjee montgomery: Research Support; Bristol-Myers Squibb Company, Epigenomics AG. N.Rasouli: Advisory Panel; Eli Lilly and Company, Novo Nordisk, Sanofi, Research Support; Allergan, Eli Lilly and Company, Novo Nordisk. M.K.Rhee: Research Support; Kowa Company, Ltd. R.E.Pratley: Other Relationship; Bayer AG, Corcept Therapeutics, Dexcom, Inc., Hanmi Pharm. Co., Ltd., Merck & Co., Inc., Metavention, Novo Nordisk, Pfizer Inc., Poxel SA, Sanofi, Scohia Pharma Inc., Sun Pharmaceutical Industries Ltd. C.Desouza: Advisory Panel; AstraZeneca, Bayer AG, Novo Nordisk A/S, Consultant; Asahi Kasei Corporation. L.M.Neff: Employee; Eli Lilly and Company, Research Support; Amryt Pharma Plc, Novo Nordisk, Stock/Shareholder; Eli Lilly and Company. A.L.Peters: Advisory Panel; Abbott Diabetes, AstraZeneca, Eli Lilly and Company, Novo Nordisk, Shouti, Vertex Pharmaceuticals Incorporated, Zealand Pharma A/S, Other Relationship; Omada Health, Inc., Research Support; Abbott Diabetes, Dexcom, Inc., Insulet Corporation, Leona M. and Harry B. Helmsley Charitable Trust, Stock/Shareholder; Teladoc Health. Funding American Diabetes Association (1-14-D2d-01) ; National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases and Office of Dietary Supplements (U01DK098245)

Gauss-Hermite Cubature Method to estimate parameters of a multivariate GLMM

In this paper, the multivariate generalized linear mixed model (GLMM) was studied when there are three response variables, distributed as Normal, Bernoulli, and Poisson. And because there is a multiple integration in the likelihood function for the model under study, it is necessary to use mathematical methods to solve this integration, and because it is not possible to obtain the result of this integration by the well-known methods of integration, numerical methods have been used, the Gauss-Hermite Cubature (GHC) algorithm, which is one of the most common numerical integration methods. Then the estimates were obtained by maximizing the resulting likelihood function with respect to the parameters, and thus, estimates were obtained for the parameters. On the practical side, we have used real data representing the effect of potassium as a fixed effect, and referring patients were considered as a random effect on three response variables: calcium, creatinine, and urea as they follow Normal, Bernoulli, and Poisson distributions taken from the records of the Vajin Hospital in Dohuk city. The regression coefficients showed that the effect of potassium is positive on both calcium and urea because the values of the coefficients are positive, while its effect is negative on the creatinine because the value of the coefficient is negative. Based on the results, the researchers recommended several recommendations, including estimating the standard error of the estimates in their light, in order to construct hypotheses for a significance test about regression coefficients.

Numerical simulation method of SRC frame column based on FLPH model

In order to obtain the accurate numerical simulation of seismic performance for steel reinforced concrete (SRC) frame columns, a convenient and reliable numerical simulation method needs to be established. Based on the test results, a numerical simulation method of SRC frame column based on the finite length plastic hinge (FLPH) was proposed in this paper. The plastic hinge element model was obtained through analyzing the failure process of SRC column. The length of plastic hinge for SRC column was expressed by considering the contribution of bending effect and strain penetration effect in the plastic deformation of members furtherly. On the basis of the numerical integration method, the FLPH model suitable for SRC frame column was established by introducing the section stiffness correction coefficient at the integral point of the element. Finally, using the OpenSees finite element analysis platform, the test specimens were simulated by FLPH model established in this paper. The results shown that the hysteretic curves obtained by simulation are well with the experimental curves, indicated that the numerical simulation method for SRC frame column based on FLPH model can be well applied in SRC structures.

Construction and application of provable positive and exact cubature formulas

Abstract Many applications require multi-dimensional numerical integration, often in the form of a cubature formula (CF). These CFs are desired to be positive and exact for certain finite-dimensional function spaces (and weight functions). Although there are several efficient procedures to construct positive and exact CFs for many standard cases, it remains a challenge to do so in a more general setting. Here, we show how the method of least squares (LSs) can be used to derive provable positive and exact formulas in a general multi-dimensional setting. Thereby, the procedure only makes use of basic linear algebra operations, such as solving an LSs problem. In particular, it is proved that the resulting LSs CFs are ensured to be positive and exact if a sufficiently large number of equidistributed data points is used. We also discuss the application of provable positive and exact LSs CFs to construct nested stable high-order rules and positive interpolatory formulas. Finally, our findings shed new light on some existing methods for multi-variate numerical integration and under which restrictions these are ensured to be successful.

Nonlinear Dynamics of an Elastic Stop System and Its Application in a Rotor System

Impact dampers or vibration systems with gaps are common in engineering applications, and the impact effects introduced by the gaps make such systems strongly nonlinear. In this paper, a model with an elastic stop is established, considering the stiffness and damping characteristics of the stop, which is a novel kind of impact damper and can be applied in a rotor system. The amplitude–frequency and phase–frequency response of the system at different gaps are obtained by the harmonic balance method with the alternating frequency–time scheme (HBM-AFT). The stability of the periodic solution is analyzed by the Floquet theory, and the time history and frequency spectra of the unstable point are analyzed by the numerical integration method. In the results, there can be more than one steady-state response at unstable points for a given excitation frequency, and the jump phenomenon occurs. The elastic stop is effective in the vibration amplitude suppression if its stiffness has been designed properly. This study provides an insight into the dynamic responses and its applications of the system with gaps, which is guidance for the analysis of pedestal looseness faults and vibration suppress methods.

Aerodynamic Uncertainty Quantification for Tiltrotor Aircraft

The tiltrotor has unique flight dynamics due to the aerodynamic interference characteristics. Multiple aerodynamics calculation approaches, such as the CFD method, are utilised to characterise this feature. The calculation process is usually time-consuming, and the obtained results are generally varied from each other. Thus, the uncertainty quantification (UQ) method will be utilised in this research to identify the aerodynamic inaccuracy effect on the handling qualities of the tiltrotor aircraft. The study aims to quantify the influence of the aerodynamic interference on the tiltrotor flight dynamics in different flight states, such as forward speeds and nacelle tilting angles, which can guide the flight dynamics modelling simplification to improve the simulation efficiency. Therefore, uncertainty identification and full factorial numerical integration (FFNI) methods are introduced to scale these aerodynamic uncertainties. The eigenvalue and bandwidth and phase delay requirements are presented as the failure criteria. The UQ calculation indicates that the uncertainties of the aerodynamic calculation significantly affect the handling quality ratings in two flight ranges: the helicopter mode and the conversion and aeroplane modes with higher forward speed (close to the conversion envelope). Furthermore, a sensitivity analysis is performed to identify the mechanism behind these influences. The results demonstrate that aerodynamics affect the pitching attitude, the pitching damping, and the velocity and incidence stability derivatives. However, the effects of the velocity stability and the incidence stability are the reason causing the handling qualities’ degradation in the helicopter mode and high-speed mode, respectively.

An improved numerical integration method for prediction of milling stability using the Lagrange-Simpson interpolation scheme

An improved numerical integration method for prediction of milling stability using the Lagrange-Simpson interpolation scheme

An improved dynamic formulation for nonlinear response analysis of thin soft silicone plates with large deflection

This present paper develops an absolute nodal coordinate formulation (ANCF) improved lower-order plate element (ILOPE) for nonlinear dynamic response analysis of thin soft silicone plates with large deflection. Different from a common linear metallic plate which is modeled by combining linear constitutive model with original lower-order plate element (OLOPE), both material nonlinearity and geometric nonlinearity should be taken into account for this type of silicone plate. An improved dynamic formulation is developed for modeling and analyzing the soft deformable silicone plate based on Yeoh nonlinear constitutive model combined with ILOPE, meanwhile the stiffening effect problem is circumvented smoothly. By bringing in penalty function, and the elastic force and its derivative matrices of Yeoh model are deduced, and then a dynamic equations of motion for the silicone plate is founded in the frame of ANCF. The second order differential dynamic equation is solved by uniting Newton–Raphson iterative approach with Newmark numerical integral method. Dynamic free-falling motion process of a half-cantilevered silicone plate and a spherical hinge silicone plate only under the influence of gravitational force are simulated by adopting OLOPE and ILOPE, respectively. The comparison of the simulation results calculated by ILOPE with those obtained by the previously proposed reduced-order plate element and commercial software ANSYS demonstrates that the improved dynamic formulation is feasible and effective. Finally, the displacement nephograms of middle surface of two types of silicone plates are elaborated in terms of displacements and configuration variations, and the law of conservation of energy is elucidated from perspective of different energy variations.

Exact Run Length Computation on EWMA Control Chart for Stationary Moving Average Process with Exogenous Variables

The exponentially weighted moving average (EWMA) control chart is a popular tool used to monitor and identify slight unnatural variations in the manufacturing, industrial, and service processes. In general, control charts operate under the assumption of normality observation of the attention quality feature, but it is not easy to maintain this assumption in practice. In such situations, the data of random processes are correlated data, such as stock price in the economic field or air pollution data in the environment field. The characteristics and performance of the control chart are measured by the average run length (ARL). In this article, we present the new explicit formula of ARL for EWMA control chart based on MAX(q,r) process. The proposed explicit formula of ARL for the MAX(q,r) process is proved using the Fredholm integral equation technique. Moreover, ARL values are also assessed using the numerical integral equations method based on Gaussian, midpoint, and trapezoidal rules. Banach's fixed point theorem guarantees the existence and uniqueness of the solution. Furthermore, the accuracy of the proposed explicit formula is assessed in absolute percentage relative error compared with the numerical integral equations method. The results found that the explicit formula's ARL values are similar to those obtained using the numerical integral equation method; the absolute percentage relative errors are less than 0.0001 percent. As a result, the essential conclusion is that the explicit formula outperforms the numerical method in computational time. Consequently, the proposed explicit formula and the numerical integral equation have been the alternative approaches for computing ARL values of the EWMA control chart. They would be applied in various fields, including economics, environment, biology, engineering, and others.

Eigenmode-BLT-Based Method for Calculating the Coupling to Microstrip Antenna Inside a Cavity

The electromagnetic (EM) coupling effects of microstrip antennas have become increasingly prominent in complicated electric systems. In this article, a hybrid method is proposed based on the combination of cavity eigenmode theory and BLT equation. First, the internal electric field generated by the transmission lines inside the resonant cavity is obtained via cavity eigenmode theory. Then, the coupling mechanism between the electric field and microstrip antenna is established through radiation coupling interference. On this basis, the BLT equation and numerical integration method are applied to determine the induced voltage at the target microstrip antenna. Eventually, the proposed approach is validated by a full-wave simulation method and the impact of the microstrip antenna parameters on the coupling interference is discussed. This article provides an analytical method for calculating the coupling of a microstrip antenna. Compared with numerical simulation, this method has certain potential advantages in solving closed electrically large objects. Furthermore, duplicate modeling can be avoided in the same type of scenario.

Efficient Implementation of Continuous-Discrete Extended Kalman Filters for State and Parameter Estimation of Nonlinear Dynamic Systems

The extended Kalman filter (EKF), one of the most popular state estimators for nonlinear uncertain dynamic systems, is considered here in its continuous-discrete (CD) form. The CD version enhances the EKF's accuracy but requires robust and computationally efficient numerical integration methods. The purpose of this article is to present several new efficient integration methods suited to the implementation of the CD-EKF and to compare them to classical implementations such as the Dormand–Prince 4/5 and Euler methods. They are first applied on two proposed nonlinear parameter estimation testbenches and to the stiff Curtiss and Hirschfelder model for state and parameter estimation. Then, they are applied to the estimation of the iron losses of a high-speed permanent-magnet synchronous motor. The results show that for highly nonlinear dynamic systems or for a low to medium sampling frequency, the implicit implementation of the EKF provides a better accuracy and convergence safety. For less nonlinear functions and a higher sampling frequency, classical explicit methods obviously give similar results in a lower computation time.

A Blend of Analytical and Numerical Methods to Compute Orthogonal Image Moments over a Unit Disk

Accurate image moment computation is critical because they are used in a variety of fields, including image reconstruction and object recognition. Orthogonal polynomials are frequently used to compute moments due to their numerous intersecting and important theoretical properties. In polar coordinate systems, orthogonal polynomials such as the Polar Harmonic Fourier Transform (PHFT) and Polar Harmonic Transformation (PHT) are defined. However, the images are defined by a Cartesian coordinate system. To obtain image moments, a double integration over a unit circle over the product of the PHFT or PHT and the image function must be performed. The choice of double integration techniques and domain for the double integral has a significant effect on the precision of the computed moments. We have proposed a method for using the entire unit circle as an integration domain in this study, for image reconstruction. We used the PHFT and PHT to apply this technique to computing moments for the reconstruction. The proposed method outperforms other state-of-the-art methods, including Gaussian quadrature numerical integration method (GQM) and zeroth order approximation (ZOA) on variety of scenarios using three benchmarked image sets. We have demonstrated experimentally that this technique significantly improves the accuracy of image moments in higher order moments, as measured by reduced mean squared error (MSE). Additionally, the proposed method significantly improved the moment’s rotational (an improvement of 1-3% as compared to GQM and an improvement of 37-93% as compared to ZOA) and scaling invariance (an improvement of 0-500% as compared to GQM and an improvement of 3-7000% as compared to ZOA).

High order linearly implicit methods for evolution equations

This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs. The systematic design of these methods mixes the Runge–Kutta collocation formalism with collocation techniques, in such a way that the methods are linearly implicit and have high order. The fact that these methods are implicit allows to avoid CFL conditions when the large systems to integrate come from the space discretization of evolution PDEs. Moreover, these methods are expected to be efficient since they only require to solve one linear system of equations at each time step, and efficient techniques from the literature can be used to do so. After the introduction of the methods, we set suitable definitions of consistency and stability for these methods. This allows for a proof that arbitrarily high order linearly implicit methods exist and converge when applied to ODEs. Eventually, we perform numerical experiments on ODEs and PDEs that illustrate our theoretical results for ODEs, and compare our methods with standard methods for several evolution PDEs.