Conventional Method Of Moments Research Articles

Frequency Analysis of Rainfall with Different Methods based on the Missing Data Processed by Random Forest Algorithm

Global warming is causing dramatic climate change, leading to rainfall that triggers a more severe risk of flooding. The conventional moment method and linear moment method’s basic theories for the design of flood frequency analyses were introduced and compared for frequency analysis of rainfall. The rainfall data from 149 long-series representative rainfall stations in Jiangsu Province were processed using the random forest (RF) algorithm to address the missing data encountered during the actual rainfall monitoring process. The frequency was calculated using conventional and linear moment methods, and the differences and advantages of the two methods were analyzed by comparing the calculation results of different sites under each method. The results show that under low design frequencies, both the conventional moment and linear moment methods exhibit minimal errors, rendering them suitable for calculating design rainfall. The linear moment method outperforms the conventional moment method in terms of the unbiasedness of the estimation process and for very large values, and that the parameters estimated by the linear moment method are more accurate. In practical hydrological frequency calculations, different computation methods can be chosen according to specific needs to enhance calculation accuracy.

Physics-informed Deep Learning to Solve 2D Electromagnetic Scattering Problems

The utilization of physics-informed deep learning (PI-DL) methodologies provides an approach to augment the predictive capabilities of deep learning (DL) models by constraining them with known physical principles. We utilize a PI-DL model called the deep operator network (DeepONet) to solve two-dimensional (2D) electromagnetic (EM) scattering problems. Numerical results demonstrate that the discrepancy between the DeepONet and conventional method of moments (MoM) is small, while maintaining computational efficiency.

Improved flood quantile estimation for South Africa

The performance of the most frequently used flood frequency probability distributions in South Africa (Log-Normal, Log Pearson3 and Generalised Extreme Value) were reviewed and all tend to perform poorly when lower exceedance probability frequency events are estimated, especially where outliers are present in the dataset. This can be attributed to the challenge when analysing very limited ‘samples’ of annual flood peak populations, which are an unknown. At present outliers are inadequately 'managed' by attempting to 'normalise' the flood peak dataset, which conceals the significance of the observed data. Thus, to adequately consider the outliers, this study was undertaken with the aim to improve the current statistical approach by developing a more stable and consistent methodology to estimate flood quantiles. The approach followed in the development of the new methodology, called IPZA, might be considered as unconventional, given that a multiple regression approach was used to accommodate the strongly skewed data, which are often associated with annual flood peak series. The main advantages of IPZA are consistency, the simplicity of application (only one set of frequency factors for every parameter, regardless of the skewness), the integrated handling of outliers and the use of conventional method of moments, thereby eliminating the need to adjust any moments. The performance of IPZA exceeded initial expectations. The results are more consistent and, by taking outliers into account, appear to be more sensible than existing probability distributions. It is recommended that IPZA should be used as a valuable addition to the existing set of decision-making tools for hydrologists/engineers performing flood frequency analyses.

Enhancing the accuracy of the scale of fluctuation estimating for tunnel surrounding rock mass properties

The scale of fluctuation (SOF) is used to evaluate the correlation between two locations of geotechnical parameter, which is important for mineral exploration and engineering construction. In this study, the performances of conventional moment methods are firstly estimated, and then the exponential autocorrelation function method that can achieve the best performance in estimating SOF is selected. After that, the Torque Penetration Index (TPI) and the Field Penetration Index (FPI) obtained from the Yinsong Water Diversion Project are used to detect the scale effect of SOF and to quantify the influences of rock types and surrounding rock mass grades on SOF. As the spatial scale increases, the SOF values increase, and the uncertainty in the SOF of the surrounding rock mass properties increases. The SOF calculated using TPI is slightly higher than using FPI. The mean values of SOF for granite, tuff, diorite, and limestone are quite close at the 50 m–200 m scales, with coefficients of variation (COVs) of SOF range from about 0.2 to 0.4. There are differences in SOF between grade III and grade IV surrounding rock masses at the 50 m–500 m scales. The mean values of SOF in grade III surrounding rock mass are about 4%–15% higher than that in grade IV surrounding rock mass, and this difference in general increases as scale increases. The rock mass with better conditions has a stronger spatial correlation. The COVs of SOF for the two rock grades reached about 0.3–0.5, owning to the inherent spatial variability.

Novel compressive sensing computing model used for analyzing electromagnetic scattering characteristics of three-dimensional electrically large objects

The method of moments is one of the most effective algorithms for solving electromagnetic scattering problems. However, the high computational complexity limits its application to electrically large problems. As an improved algorithm, the compressive sensing-based method of moments introduces the compressive sensing technique into the algorithmic structure, which avoids the inverse of the matrix equation and improves the computational efficiency. Using the underdetermined equation-based calculation model, this scheme is utilized to efficiently analyze the bistatic scattering of the objects. In this technique, the extracted few rows from the impedance matrix are used to construct the measurement matrix. Nevertheless, the results are unstable due to the random extraction utilized to build the measurement matrix. Furthermore, it is challenging task to provide an appropriate sparse basis for the induced currents of three-dimensional objects discretized by the Rao-Wilton-Glisson basis functions. To address the aforementioned issues, a novel compressive sensing calculation model that enhances measurement matrix building, sparse basis construction, and recovery is provided in this paper. First, several rows of the impedance matrix are uniformly extracted to produce consistent computation results, which is opposed to the randomly constructed measurement matrix in the conventional technique. The number of rows to be extracted is typically set to be 3–5 times the number of basis functions for high accuracy. Then, the characteristic basis functions based on the Foldy-Lax equation are employed to construct the sparse basis. Considering the prior knowledge that the lower order characteristic basis functions are dominant, the columns of the recovery matrix corresponding to some low-order characteristic functions are determined in advance as the columns that will be identified by the recovery algorithm, thus simplifying the recovery algorithm to a least-squares operation. Obviously, the matrix equation is reduced to an overdetermined equation instead of the underdetermined equation since only a few low-order basis functions are to be computed. Compared with the conventional compressive sensing-based method of moments with characteristic basis functions, the computation time is significantly reduced in terms of constructing the basis functions and recovering the current coefficients, while the accuracy is improved. Finally, both the suggested method and the conventional compressive sensing-based method of moments are used to simulate the bistatic radar cross sections of the perfect electrical conductor cube, cylinder, and missile model. The efficiency and accuracy of the proposed method are verified by the numerical results.

Composite Scattering from a PEC Object above Two-Layered Rough Soil Surfaces Based on an Efficient Bi-Iterative Model

In the study, an efficient bi-iterative physical optics (PO) electromagnetic model is used to analyze the composite scattering from a PEC object above two-layered rough soil surfaces for the first time. The PO method is applied to calculate the direct scattered fields from the object and the upper layer rough surface and to deal with the mutual coupling effect between the object and the two-layered rough surfaces. During the mutual coupling process, a bi-iterative strategy is considered to solve the coupling interaction between the object and the upper rough surface and the coupling interaction between the upper and lower rough surfaces. We assume a 2-D scattering problem. The result is validated by comparing it with that obtained from the conventional method of moments (MoM). Comparison results from different object types show that the scattered curves calculated using the proposed method resemble the ones obtained from MoM. The comparison of computer resources also shows the efficiency of our method. Meanwhile, the normalized radar cross-section of the composite model is analyzed under different parameters.

Relativistic second-order dissipative spin hydrodynamics from the method of moments

We derive relativistic second-order dissipative fluid-dynamical equations of motion for massive spin-1/2 particles from kinetic theory using the method of moments. Besides the usual conservation laws for charge, energy, and momentum, such a theory of relativistic dissipative spin hydrodynamics features an equation of motion for the rank-3 spin tensor, which follows from the conservation of total angular momentum. Extending the conventional method of moments for spin-0 particles, we expand the spin-dependent distribution function near local equilibrium in terms of moments of the momentum and spin variables. We work to next-to-leading order in the Planck constant $\hbar$. As shown in previous work, at this order in $\hbar$ the Boltzmann equation for spin-1/2 particles features a nonlocal collision term. From the Boltzmann equation, we then obtain an infinite set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local equilibrium. In order to close this system of moment equations, a truncation procedure is needed. We employ the "14+24-moment approximation", where "14" corresponds to the components of the charge current and the energy-momentum tensor and "24" to the components of the spin tensor, which completes the derivation of the equations of motion of second-order dissipative spin hydrodynamics. For applications to heavy-ion phenomenology, we also determine dissipative corrections to the Pauli-Lubanski vector.

An Improved RCS Calculation Method for Power Lines Combining Characteristic Mode with SMWA

The radar cross-section (RCS) of power lines has an important significance for detection of the power lines. The method of moments (MoM) can calculate the RCS of power lines. However, the efficiency of the MoM is limited by the time-consuming computing process, as well as the expensive storage overhead. In order to enhance the efficiency and reduce the storage of the RCS calculation of power lines, we propose an RCS calculation method that combines the characteristic mode (CM) with a Sherman–Morrison–Woodbury formula-based algorithm (SMWA), which is referred to as a CM-SMWA. CMs are used as the basis functions for reducing the dimension of the MoM impedance matrix, and the SMWA is applied to directly solve the CMs-reduced matrix equation, which can reduce the computational time and storage. The numerical results demonstrate that the proposed method can obtain the RCS of power lines, with different incident angles and different polarizations, at a higher efficiency. At 35 GHz, compared with the conventional MoM, for a typical LGJ50-8 power line with a length of 0.276 m, the computation time is reduced by 62.4% and the memory occupation is reduced by 96.4%.

Scattering From Fractal Surfaces Based on Decomposition and Reconstruction Theorem

A decomposition and reconstruction theorem (DRT) is introduced to advance computation and provide physical understanding for the scattering from fractal surfaces (FPs). The profile of FP is decomposed into test profiles (TPs), and the scattering of FP is reconstructed using the scattering of TPs to enhance the computational efficiency. A new method that applies DRT on the extended boundary condition method combined with the truncated singular value decomposition technique (TEBCM) is presented and referred to as TEBCM-DRT. The method of TEBCM-DRT is employed to solve the scattering from realistic soil surfaces, and the results are validated against other scattering models. Moreover, the efficiency of TEBCM-DRT and its validity range are investigated. The result shows that TEBCM-DRT improves computational efficiency to <inline-formula> <tex-math notation="LaTeX">$1.95\times 10^{5}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$7.35\times 10^{2}$ </tex-math></inline-formula> times, respectively, compared to TEBCM and the conventional method of moments for a wide range of roughness. In addition, TEBCM-DRT indicates that the amplitude and direction of propagation of scattering modes are dependent on deterministic TPs. This relationship benefits for obtaining the accurate height of an arbitrary point on the profile from bistatic scattering coefficients.

Mutual Impedance Computation of a Waveguide Slot-fed Arbitrary Patch Using Combined Conventional Moment Method and Equivalent Electric and Magnetic Dipole Method

Mutual Impedance Computation of a Waveguide Slot-fed Arbitrary Patch Using Combined Conventional Moment Method and Equivalent Electric and Magnetic Dipole Method

A hybrid sectional moment projection method for discrete population balance dynamics involving inception, growth, coagulation and fragmentation

A new and efficient sectional method is developed and presented in this work. This new method, namely hybrid sectional moment projection method, seeks to combine the techniques of moment projection method and sectional method in a flexible and accurate way. It adopts the concept of weighted particles from moment projection method to handle the particle population dynamics. Special treatment is made on the assignment of these weighted particles within each section so that the accumulation of particles at the smallest size can be better described. The performance of hybrid sectional moment projection method has been tested by comparing with the fixed pivot method and conventional sectional quadrature method of moments in handling a number of particle processes including inception, growth, coagulation and fragmentation. Results suggest that the proposed new method is highly robust and accurate. It is able to well predict the evolution of particle population under various conditions. Especially, it is superior to other sectional methods in the treatment of particle fragmentation process.

A Broadband Model-Based Parameter Estimation Method for Analyzing Multilayer Periodic Structures

A new model-based parameter estimation (MBPE) method for multilayer periodic EM surfaces is discussed in this article. By applying the proposed method to predict the generalized scattering matrix (GSM) of each unit layer section, the response of a composite structure can be determined by cascading GSMs while allowing the salient behavior of each section to be accurately captured. Based on the spectral properties of Green's functions with high-order wavenumbers and chosen basis functions, an advanced interpolation model is developed to estimate the broadband response of periodic structures in a robust and efficient manner. It needs fewer samples in the interpolation compared to the state of the art, and no restriction for the sample selection is required. Numerical analysis has been carried out for two types of multilayer structures, and a good agreement between the conventional periodic method of moments (PMM) and the proposed method has been obtained.

Alternative weighting schemes when performing matching-adjusted indirect comparisons.

Methods for indirect comparisons and network meta-analysis use aggregate level data from multiple studies. A very common, and closely related, scenario is where a company has individual patient data (IPD) from its own trial, but only has published aggregate data from a competitor's trial, and an indirect comparison of the treatments evaluated in these two trials is required. Matching-Adjusted Indirect Comparison (MAIC) has been developed for this situation, where we use the available IPD to adjust for between-trial imbalances in the distributions of observed baseline covariates between the two trials. We extend the current MAIC methodology, where we compute the weights that satisfy the conventional method of moments and result in the largest possible effective sample size (ESS). We show that the approach proposed by Zubizarreta in a previous study can be used for this purpose. We derive a new analytical result that shows why this alternative approach provides a larger ESS than a conventional MAIC. We also derive a new formula for the maximum ESS that can be achieved, even when permitting negative weights, when adjusting for one covariate. This can be used as an easily computed new metric that quantifies the difficulty in adjusting for covariates. What is already known: MAIC is an established way to perform population adjustment in the situation where IPD is available from one trial but only aggregate level data is available from another trial, and an indirect comparison is required. However the effective sample size (ESS) can be small after making the adjustment. What is new: We show that an alternative method can result in a larger ESS. We provide new analytical results showing why this is the case. We derive a new descriptive statistic that is based on maximising the ESS that quantifies the difficulties in adjusting for particular covariates. Potential impact for RSM readers outside the authors' field: Reweighting methods for population adjustment are becoming more commonly used and their implications for research synthesis methodology is now considerable. This paper provides important new links between the theoretical literature, and the more applied research synthesis methodology literature, relating to this topic.

Efficient calculation of interior scattering from cavities with partial IBC wall

The magnetic field integral equation based method of moments (MoM) with the Kirchhoff approximation can predict the interior scattering from cavities with impedance boundary condition (IBC) walls. However, if the IBC wall is a small part of the whole wall and is modified multiple times, the conventional MoM may be time-consuming due to the repeated and expensive lower–upper (LU) decompositions of impedance matrices. In this Letter, the Sherman–Morrison–Woodbury (SMW) formula is used to mitigate the problem. The authors only require to perform the LU decomposition of the cavity without IBC walls, and to efficiently obtain the solutions of the cavity with different IBC walls by reusing the LU decomposition and the SMW formula.

Surface–Volume–Surface EFIE Formulation for Fast Direct Solution of Scattering Problems on General 3-D Composite Metal–Dielectric Objects

A new formulation of the surface–volume–surface electric field integral equation (SVS-EFIE) combined with the regular EFIE is introduced for the electromagnetic analysis of the 3-D general composite structures of impenetrable metal and penetrable homogeneous dielectric objects. The proposed method introduces independent surface electric current densities on the boundary of each region which brings the benefit of the independent discretization of the regions according to their respective material properties and straightforward handling of the material junctions. This makes the algorithm more efficient and flexible for analysis of multiscale and large-scale composite structures in comparison with the traditional Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equation combined with the EFIE. The method of moment (MoM) solution of the new formulation is accelerated by the hierarchical ( $\mathcal H$ )-matrix framework. The numerical results are given to validate the new formulation. Also, the $\mathcal H$ -matrix acceleration of MoM solution of the new combined EFIE and SVS-EFIE formulation is shown to produce accurate results using only the small fraction of memory and total CPU time needed by conventional MoM.

Electromagnetic analysis of wires with joints using a hybrid meshless-moments technique

This paper presents a fast and accurate hybrid method to analyze radiation of and scattering from conducting wire structures. The proposed technique is based on meshless method (MlM) and method of moments (MoM). First, the electric field integral equation (EFIE) is broken into two parts, integral and differential parts. In this paper, we use smooth meshless basis functions in evaluating the differential part and conventionally employ pulse basis functions in estimation of the integral part, given by closed-form expressions. We call this new technique, advanced meshless method (AMM) and use it to analyze wire structures such as helix and straight dipole antennas. Next, we investigate structures that include two wires connecting at a joint point, such as a helical dipole antenna that is composed of a quarter-wavelength dipole, connected to two helical wires at both its ends and also a folded dipole antenna that has two half-wavelength dipoles connected by two small half ring wires. We propose a new hybrid meshless-moments technique (MMT) which treats separate wire parts like the helical wire, half ring wire, and straight dipole parts by the AMM and the joint or connection parts by the MoM. The interactions between different parts are then taken into account by calculation of the near-field integral equations. Various comparisons between AMM and MMT results with those of a conventional MoM confirm that while accuracy is fixed the AMM and MMT are at least 10 times faster than MoM. The main feature of the hybrid MMT method is its computational efficiency in analyzing electrically large problems. As an example, extinction cross section of a chaff cloud composed of a large number of randomly placed and oriented helical particles as a function of frequency is efficiently computed by the hybrid MMT to show its capability in fast and accurate calculation of a complex medium dispersion.

Use of loading devices with low stiffness may cause uncertainty in measuring the strength of cellular adhesion

ABSTRACT Cellular adhesion via the formation of molecular bond clusters is a fundamental biological phenomenon. Cell adhesion forces can be measured by various advanced techniques with adjustable probe stiffness. To quantitatively understand how the stiffness of a loading device may influence the measurement of these forces, we consider an idealized theoretical model of a cluster of molecular bonds that are subjected to an applied tensile load by a Hookean spring. In this model, the rebinding and rupture of individual molecular bonds are governed by stochastic master equations. By deriving an exact expression of the rebinding rate and directly solving the master equation, we find that the conventional moment method provides incorrect predictions for this problem. Moreover, the measured adhesion strength of a molecular bond cluster exhibits strong dependence on the stiffness of the loading device and the bond number when the stiffness value is close to or smaller than the effective stiffness of the bond cluster. Thus, an improper selection of the stiffness value of the loading device may lead to measurement uncertainty. Monte Carlo simulations are performed to verify the proposed analytical results.

Efficient Method of Moments for Numerical Analysis of Antennas With Variable Load Impedance

A computationally efficient method which is based on the method of moments (MoM) for numerical analysis of antennas with variable load impedance is proposed. The proposed method deals with both of the variable load impedance and its current as equivalent voltage source. Current distribution of antennas with the variable load impedance is obtained directly from their unloaded full-admittance matrix and the block impedance matrix corresponding to the variable load impedance. The proposed method is quite computationally efficient because inversion of the full-impedance matrix of the antennas is unnecessary when their load impedance varies. Moreover, the proposed method does not include any approximation and its result shows perfect agreement with that of the full-wave analysis. Numerical results of the proposed method are compared with those of conventional MoM using our in-house code and its performance is demonstrated.

A spectral domain integral equation technique for rough surface scattering problems

ABSTRACT In this paper, a novel formulation for scattering from one-dimensional (1D) rough surface problem has been presented. The formulation is based on the representation of the scattering field in spectral domain with an unknown spectral coefficient which is solved by applying Taylor series and Fourier Transforms techniques. It is also shown that forward–backward (FB) acceleration technique can be adapted to the spectral formulation to improve the effectiveness in a limited region of convergence. The obtained results are compared with the conventional method of moments (MoM) and the limitations of the formulation are analyzed in detail.

A Dipole-Moment-Based Formulation for Numerically Efficient Analysis of Scattering From Truncated Periodic Structures

Numerical analysis of truncated periodic structures by utilizing conventional method of moments (MoM) technique is challenging because the number of unknowns involved is often very large; hence, the computational cost is high. This letter presents a novel approach, based on the dipole moment (DM) method, for analyzing electromagnetic scattering from truncated periodic structures whose geometrical and/or material properties vary locally from those of a strictly doubly infinite periodic structure. The main advantage of using the DM method is that it provides convenient closed-form expressions for the scattered fields, facilitating the matrix computation in the context of the MoM much more efficiently than when the conventional Rao–Wilton–Glisson (RWG) type of basis functions are used for the same computation. Numerical results obtained by using the proposed approach are compared with those derived from a commercial MoM software package, and good agreement is found. The time advantage is clearly evident from this comparison.