Simpson Integration Research Articles

Estimating carbon emissions from thermal power plants based on thermal characteristics

Carbon emissions from thermal power plants (TPPs) are a significant source of anthropogenic carbon and a priority for carbon reduction efforts. The accurate estimating of carbon emissions from TPPs is essential research in the field of carbon reduction. In this study, we take TPPs located in the United States as examples to discuss the relationship between the thermal characteristics of the power plant and its annual carbon emissions. Our data consists of land surface temperature (LST) product generated from Landsat 8 thermal data, LST product from ERA5-Land reanalysis dataset, and carbon emission data reported by the U.S. Energy Information Administration (EIA). Based on pertinent research of urban heat islands, we propose the concept of thermal characteristic index (TCI), which can provide a quantitative description of power plant thermal characteristics. Furthermore, we convert TCI to annual thermal characteristic index (A-TCI) by annual end-point interpolation and Simpson integration of the TCI series to match the annual carbon emission data and then establish a TCI-based annual carbon emission estimation model (TACEE-Model). Using the TACEE-Model, we predict the annual carbon emission values and evaluate the model’s performance. Experimental results indicate that the TACEE-Model exhibits great predictive capability, with the mean absolute percentage error (MAPE) of 0.0325, and the average prediction percentage error of 3.24%. The application of annual end-point interpolation and Simpson integration can significantly enhance the model’s prediction accuracy, resulting in a 51.42% reduction in MAPE. Overall, this research presents a new method for verifying annual carbon emissions from TPPs, which can contribute to the supervisory oversight of carbon emission reduction from TPPs.

A proposed numerical method for absolute efficiency calibration of α-spectrometers and its application for activity calculation

In this work, an absolute method to calibrate an α-spectrometer is proposed taking into account the Source-to-Detector, and lateral distances due to eccentric source distribution. An analytical formula to calibrate an α-spectrometer is derived and the Simpson's integration method was utilized to solve these equations in its integral form numerically using a written C computer code. The general Monte Carlo N-particle code, MCNP as well as experimental measurements for some standard α-emitters are used to benchmark the proposed method. An agreement was found between the efficiency results calculated by MC and the proposed method with a maximum relative difference of about 0.5%. While, experimental measurement of α-emitters activity employing the proposed method differs by about 1.65% from the certified values. Accounting for the man made error allows to accurately quantify the assayed sample. Therefore, the inaccuracy in the efficiency results due to non-accurate inputs pertained to the source, and detector radii, Source–Detector distances, and eccentric source distribution are investigated in the Source-to-Detector distance range of (4 to 44 mm). The results show that a difference of ±1% in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about ±2%, while a difference of ±50% in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than ±3% in the efficiency results.

Solar cell parameter extraction, with less than 10% percentage error, integrating the Co-Content function, using up to order 6 Simpson integration method, and 51 measured points per volt or less, in the case of a percentage noise of the maximum current

In this article, the solar cell parameters (within the one-diode solar cell model) are obtained with less than 10% error, integrating the Co-Content function using up to order 6 Simpson integration method, and as a function of the number of measured points per volt and a percentage noise of the maximum current. It is shown, that less than 10% error (in some cases around 1%) can be obtained, in case the percentage noise is as larger as 0.1%, using higher order Simpson integration than 1, the usually used trapezoidal integration method.

Time-dependent system reliability analysis for mechanical on-load tap-changer with multiple failure modes

To regulate voltage level, the mechanical on-load tap-changer is a crucial series system of the ultra-high-voltage converter transformer. Whether its motion is reliable throughout the whole process is vital for the safe operation of converter transformer. Therefore, the time-dependent system reliability analysis is carried on for the mechanical on-load tap-changer with multiple failure modes based on the first-passage method. First, the failure modes of the mechanical on-load tap-changer are comprehensively analyzed according to the safety requirement, and then, the output error of each failure mode related to the moving mechanism of the system is modeled based on the motion equation to establish the varied limit-state functions of the time intervals over the whole motion. Then, the first-passage method is leveraged to solve this time-dependent reliability problem with multiple failure modes, in which the analytical formula of the outcrossing rate, the crucial element of the first-passage method, is derived by introducing the first-order moment of the doubly truncated multivariate Gaussian distribution. On this basis, the time-dependent system kinematic reliability is calculated using the Simpson integration algorithm. Finally, a numerical case is studied first, and in what follows, the practical engineering application to the mechanical on-load tap-changer is showcased in detail to demonstrate the effectiveness and efficiency of the proposed method by comparison with previous methods.

Comparative Study of Numerical Methods for Solving the Fresnel Integral in Aperiodic Diffractive Lenses

In this work, we present a comparative analysis of different numerical methods to obtain the focusing properties of the zone plates based on Fibonacci and Cantor sequences. The Fresnel approximation was solved numerically in order to obtain the axial irradiance provided by these diffractive lenses. Two different methods were applied. The first one is based on numerical integration, specifically the Simpson integration method and the two-dimensional Gaussian quadrature. The second consisted in the implementation of the Fast Fourier Transform in both one and two dimensions. The axial irradiance of the lenses, the relative error with respect to the analytical solution, and the calculation time required by each method are analyzed and compared. From this analysis it was concluded that the Gauss method presents the best balance between accuracy and computation time. This analysis could be useful to decide the most convenient numerical method to be used for the study of more complex diffractive structures.

BiFold: A Python code for the calculation of double-folded (bifold) potentials with density-in/dependent nucleon-nucleon interactions

BiFold calculates the density-dependent (DDM3Yn, BDM3Yn, CDM3Yn) or independent double-folded potentials between two colliding spherical nuclei. It is written in a Python package form to give the ability to use the potentials directly in a nuclear reaction/structure code. In addition to using Woods-Saxon/Fermi or Gaussian functions, the code also allows the definition of nuclear matter densities using pre-calculated densities in a data file. The manuscript provides an overview of the double folding model and the use of the code. Program summaryProgram Title: BiFoldCPC Library link to program files:https://doi.org/10.17632/rmdx86p9dg.1Developer's repository link:https://github.com/mkarakoc/BiFoldCode Ocean capsule:https://codeocean.com/capsule/5286231Licensing provisions: GPLv3Programming language: Python 3.xNature of problem: BiFold calculates the real part of the nuclear potential between two colliding spherical nuclei by integrating a density-independent/dependent nucleon-nucleon (NN) interaction [1,2,3] over the nuclear matter densities of the two nuclei. The code is based on M3Y Reid/Paris NN interactions [1,2,3] by default, but it is possible to define custom NN interactions when necessary.Solution method: The code uses the Fourier transform method in spherical coordinates to calculate the potential. The method simplifies the sixfold integration [1] and makes the calculation significantly faster. The integration is done by default using Simpson's integration method, but Filon's integration method is also available.

Analytical and numerical study of diffusion and localization of cold atoms in 3D optical speckles.

This paper aims to study the diffusion and localization of cold atoms in three-dimensional (3D) optical speckles by using the theory of self-energy for N diffusers. In this paper, the Self-consistent Born approximation (SCBA) is used to study the diffusion and localization of cold atoms in an optical disordered speckles, while the spectral function is adopted to study the effect of the matter waves energy and the disorder amplitude on the behaviour of cold atoms. For this purpose, the models of SCBA and spectral function are computed by a numerical algorithm. The calculation of the latter quantity involves the application of Simpson’s integration methods. The diffusion and localization of a Bose–Einstein Condensate for First-order Born Approximation (FBA) and SCBA models are presented. In addition, the diffusion time and the mean free path between two diffusers are illustrated. Moreover, the effect of disorder amplitude and the scattering of matter waves in 3D disordered potentials are highlighted. In this study, the results show that the time response of cold atoms localization and metal–insulator transition in SCBA is faster and yields lower energy than the FBA approximation.

Application of Stabilized Numerical Integration Method in Acceleration Sensor Data Processing

It is necessary to perform a numerical or a quadratic integral calculation on the acceleration sensor data by rectangular integration, trapezoidal integration or Simpson integration, etc . to obtain the velocity or the displacement result in engineering practice. Since poles of transfer functions of these numerical integration systems are on the unit circle, when acceleration signals containing interference factors, such as random noise, are integrated, integration results are often divergent. Therefore, velocity and displacement results will have serious drift, which affects the accuracy of the follow-up attitude calculation and target positioning. In order to overcome acceleration integration drift, a method based on the stabilized numerical integration to obtain velocity and displacement is proposed in this paper, which makes improvements of the traditional numerical integration. The proposed method obtains accurate velocity and displacement through the acceleration integration by constructing a stable system to modify the transfer function of the integration system, and utilizes the characteristics of the stability system to effectively suppress the drift of the acceleration data multiple integration results. Experimental results show that compared with traditional acceleration integration methods, the quadratic integral displacement peak error, difference error, and absolute error of the proposed stabilized numerical integration method are 0.059, 0.0619 and 0.0084, respectively, which demonstrate that the proposed method is feasible that it can reduce the integration results drift error and improve the accuracy of the integration results.

The Calculation Method of PV Direct Current Energy Based on Modulated Broadband Mode Decomposition and Compound Simpson Integral Algorithm

The application of photovoltaic power is becoming more and more extensive presently, when the existing time-frequency analysis methods are used to analyze photovoltaic mutation signals such as transient rise and transient fall, the cornered signal will produce Gibbs phenomenon and leads to errors. Thus, the Broadband Mode Decomposition (BMD) method is proposed. The main idea of BMD is to search in the associated dictionary that contains the wideband and narrowband signals. However, the BMD algorithm may treat the wideband signal as several narrowband components, when applied to a wideband signal interfered by strong noise, because the relative bandwidth is not sufficiently small. Therefore, a modulated broadband modal decomposition (MBMD) based on the modulation differential operator is proposed. By multiplying a high-frequency single-frequency signal, the relative bandwidth of the effective wideband signal is much smaller than 1, and the wideband signal is processed as an approximate wideband signal. Meanwhile, because the errors of the traditional dot product sum algorithm in DC energy measurement cannot be positive and negative offset, while the compound Simpson integral algorithm has small error and high calculation accuracy. Therefore, a photovoltaic DC power calculation method based on the MBMD and compound Simpson integration is proposed.

DELINEATION OF TARGET VOLUME FOR BRAIN TUMORS IN RADIOTHERAPY USING ACTIVE CONTOUR SEGMENTATION AND SIMPSON INTEGRATION

This research conducts the delineation process for a brain tumor on the radio therapy. Delineation means the imaging process of target volume that is conducted in the beginning of Treatment Planning System (TPS). Target volume consists of gross tumor volume (GTV), clinical target volume (CTV), planning target volume (PTV), and Organ at Risk (OAR). This research aims to delineate target volume and measure the target volume axial brain tumor. The images that are used are Magnetic Resonance Imaging (MRI) including axial, coronal, and sagittal slice. Evaluation is only done with one patient affected by a brain tumor. Delineation process is performed by the active contour segmentation method and volume calculations using Simpson integration method. The delineation of target volume is conducted by segmenting each slice of images moreover they are reconstructed until the three dimension of visualized target volume is obtained. Having done this process, target area and target volume calculations are conducted. This research results range error rate for target area is 0.0006 to 0.0059 and target volume is 0.0001 to 0.0013

A Small Disturbance Model for Transonic Flow of Pure Steam With Condensation

A small-disturbance model to study transonic steady condensing flow of pure steam around a thin airfoil is developed. Water vapor thermodynamics is described by the perfect gas model and its dynamics by the compressible inviscid flow equations. Classical nucleation and droplet growth theory for homogeneous and nonequilibrium condensation is used to compute the condensate mass fraction. The model is derived from an asymptotic analysis of the flow and condensation equations in terms of the proximity of upstream flow Mach number to 1, the small thickness ratio of airfoil, the small quantity of condensate, and the small angle-of-attack. The flow field may be described by a nonhomogeneous and nonlinear partial differential equation along with a set of four ordinary differential equations for calculating condensate mass fraction. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme, which is composed of Murman and Cole's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction, is applied. The model is used to analyze the effects of heat release due to condensation on the aerodynamic performance of airfoils operating in steam at high temperatures and pressures near the vapor–liquid saturation dome.

Tradeoff Caching Strategy of the Outage Probability and Fronthaul Usage in a Cloud-RAN

In this paper, a tradeoff content caching strategy is proposed to jointly minimize the cell average outage probability and fronthaul usage in a cloud radio access network. At first, an accurate closed-form expression of the outage probability conditioned on the user's location is presented, and the cell average outage probability is obtained through the composite Simpson's integration. The caching strategy for jointly optimizing the cell average outage probability and fronthaul usage is then formulated as a weighted sum minimization problem, which is a nonlinear 0–1 integer problem. Two heuristic algorithms are proposed to solve the problem. First, a genetic algorithm (GA)-based approach is proposed. Numerical results show that the performance of the proposed GA-based approach with significantly reduced computational complexity is close to the optimal performance achieved by an exhaustive-search-based caching strategy, and the GA-based approach can improve the performance by up to 47.5% on average than the typical probabilistic caching strategy. Second, in order to further reduce the computational complexity, a mode selection approach is proposed. Numerical results show that this approach can achieve near-optimal performance over a wide range of weighting factors through a single computation.

SWRT: A package for semi-analytical solutions of surface wave propagation, including mode conversion, across transversely aligned vertical discontinuities

Abstract. We present a suite of programs that implement decades-old algorithms for computation of seismic surface wave reflection and transmission coefficients at a welded contact between two laterally homogeneous quarter-spaces. For Love as well as Rayleigh waves, the algorithms are shown to be capable of modelling multiple mode conversions at a lateral discontinuity, which was not shown in the original publications or in the subsequent literature. Only normal incidence at a lateral boundary is considered so there is no Love–Rayleigh coupling, but incidence of any mode and coupling to any (other) mode can be handled. The code is written in Python and makes use of SciPy's Simpson's rule integrator and NumPy's linear algebra solver for its core functionality. Transmission-side results from this code are found to be in good agreement with those from finite-difference simulations. In today's research environment of extensive computing power, the coded algorithms are arguably redundant but SWRT can be used as a valuable testing tool for the ever evolving numerical solvers of seismic wave propagation. SWRT is available via GitHub (https://github.com/arjundatta23/SWRT.git).

Non linear modeling of three-dimensional reinforced and fiber concrete structures

Under the effect of the ascending loading, the behavior of reinforced concrete structures is rather non linear. Research in industry and science aims to extend forward the use of non-linear calculation of fiber concrete for structural parts such as columns, veils and pious, as the fiber concrete is more ductile behavior then the classical concrete behavior. The formulation of the element has been established for modeling the nonlinear behavior of elastic structures in three dimensions, based on the displacement method. For the behavior of concrete and fiber concrete compressive and tensile strength (stress-strain) the uniaxial formulation is used. For steel bi-linear relationship is used. The approach is based on the discretization of the cross section trapezoidal tables. Forming the stiffness matrix of the section, the integral of the surface is calculated as the sum of the integrals on each of the cutting trapezoids. To integrate on the trapeze we have adopted the type of Simpson integration scheme.

Numerical estimation of photovoltaic–electrolyzer system performance on the basis of a weather database

ABSTRACTWe performed a numerical simulation to investigate the performance of a photovoltaic (PV)–electrolyzer on the basis of a simulated weather database during the summer solstice (SS), autumnal equinox (AE), and winter solstice (WS), and all year round. First, we selected a location in southern Taiwan (latitude: 22.65°N) to create a local weather simulation database that included daily solar radiation, wind speed, and ambient temperature. The I–V curves of a PV system and an electrolyzer were obtained numerically by using Simpson integration computation. Subsequently, the optimal configuration of a PV driving system comprising the electrolyzer and the PV panel was determined. The database of weather conditions was input into the numerical estimation model of the PV–electrolyzer system, and the hydrogen generation rates and hydrogen production volumes under both clear skies and changeable weather conditions were obtained.

How Much Is the Gap? Efficient Jump Risk-Adjusted Valuation of Leveraged Certificates

This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies on Monte Carlo simulations, which are not fast enough to be used in a market making environment. This is because issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model random jumps that occur at known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson's numerical integration rule. This yields a backward induction scheme which requires a significantly coarser spacial and time grid than finite difference methods. We confirm its robustness and accuracy through Monte Carlo simulations.

A simple and innovative way to measure ventricular volume in a mechanical mock of the left ventricle

Abstract Ongoing innovations in mechanical devices to improve the heart’s performance (e.g. left ventricular assist devices, LVAD) require numerical simulations and a bench validation before animal and clinical testing of the device. One of the major requirements of mechanical mocks of the cardiovascular system is the correct evaluation of the parameters of interest (pressure, volumes, flows). This paper presents a new optical method to measure the volume changes of a generic elastic camera through videos acquisition and analysis (using Simpson integration and Matlab software). We tested our proposal with a simple syringe mock of the cardiovascular system under different conditions of simulation dynamics and varying the stroke volumes (SV). We compared our results with those obtained with a standard electromagnetic flowmeter, in terms of instantaneous volume and total SV: the curves presented the same trends (squared Pearson’s coefficients greater than 0.9) with a mean difference less than 5%. The proposed optical method is simple and inexpensive and yields results comparable with those of a standard method.

Cyclotron resonant scattering feature simulations

Electron cyclotron resonant scattering features (CRSFs) are observed as absorption-like lines in the spectra of X-ray pulsars. A significant fraction of the computing time for Monte Carlo simulations of these quantum mechanical features is spent on the calculation of the mean free path for each individual photon before scattering, since it involves a complex numerical integration over the scattering cross section and the (thermal) velocity distribution of the scattering electrons. We aim to numerically calculate interpolation tables which can be used in CRSF simulations to sample the mean free path of the scattering photon and the momentum of the scattering electron. The tables also contain all the information required for sampling the scattering electron's final spin. The tables were calculated using an adaptive Simpson integration scheme. The energy and angle grids were refined until a prescribed accuracy is reached. The tables are used by our simulation code to produce artificial CRSF spectra. The electron momenta sampled during these simulations were analyzed and justified using theoretically determined boundaries. We present a complete set of tables suited for mean free path calculations of Monte Carlo simulations of the cyclotron scattering process for conditions expected in typical X-ray pulsar accretion columns (0.01<B/B_{crit}<=0.12, where B_{crit}=4.413x10^{13} G and 3keV<=kT<15keV). The sampling of the tables is chosen such that the results have an estimated relative error of at most 1/15 for all points in the grid. The tables are available online at http://www.sternwarte.uni-erlangen.de/research/cyclo.

Effect of the concentration on the kinetic model of the photo-degradation of 5-hydroxymethylfurfural by UV irradiation

The aim of this work was to study the effect of the initial concentration on the photo-degradation kinetics of 5-hydroxymethylfurfural (HMF) and develop different mathematical models for HMF photo-degradation related to the radiation absorbed by the solution. For this purpose, a mid-pressure mercury lamp with emission wavelengths between 250 and 740 nm was used. Aqueous solutions of 25 and 100 mg L−1 of HMF (pH 4) were irradiated at 12, 25, 35 and 45 °C. Then, aqueous solutions of 1 and 100 mg L−1 of HMF (pH 3, 4 and 5) were irradiated at 25 °C. The treatments were applied for 120 min. Aliquots were analysed to measure their HMF content and absorption spectra.The spectral radiant power absorbed by the solution was evaluated taking into account the linear spherical emission model and using the Simpson integration method. Its dependence on the HMF concentration was studied. Considering specific narrow ranges of concentrations, the function can be defined by linear equations.A three-stage degradation mechanism was proposed from which, considering different relations between the absorbed radiation and the concentration, three different kinetic models were obtained: first-order, zero-order and pseudo first-order.

Fast computation of seabed spherical-wave reflection coefficients in geoacoustic inversion.

This paper develops a fast numerical approach to computing spherical-wave reflection coefficients (SWRCs) for layered seabeds, which provides substantial savings in computation time when used as the forward model for geoacoustic inversion of broadband seabed reflectivity data. The approach exploits the Sommerfeld-integral representation of SWRCs as the Hankel transform of a function proportional to the plane-wave reflection coefficient (PWRC), and applies Levin integration to the rapidly oscillating integrand cast as the product of a (pre-computed) media-independent matrix and a vector involving PWRCs at a sparse sampling of integration angles. Compared to conventional Simpson's rule integration for computation of the SWRC, the Levin integration yields speed-up factors of an order of magnitude or more. Further, it results in reduced memory requirements for storage of pre-computed quantities, a desirable property when a graphics processing unit (GPU) is used for parallel computation of SWRCs. The paper applies trans-dimensional Bayesian inversion to investigate the impact of forward modeling in terms of PWRCs and SWRCs on the estimation of geoacoustic parameters and uncertainties. Model comparisons are quantified in simulated- and measured-data inversions by comparing the estimated geoacoustic parameters to the true parameters or core measurements, respectively, and by calculating the deviance information criterion for model selection.