Higher Order Method Of Moments Research Articles

Time-dependent seismic reliability analysis of rocking cold-formed steel frame based on improved HOMM

Cold-formed steel structures are particularly sensitive to seismic loads due to their relatively low ductility and limited energy dissipation capacity. Moreover, the small thickness of cold-formed steel structures makes them more susceptible to environmental influences, leading to corrosion and material degradation. Therefore, it is essential to quantitatively assess the seismic reliability of cold-formed steel structures from a lifecycle perspective. Current structural reliability design standards often focus on the ultimate strength at the component level while neglecting the global safety of structures. Additionally, it tends to neglect the time-variant characteristic of structural resistance due to the corrosion and degradation of materials. Therefore, the time-dependent seismic reliability analysis framework was proposed at the global structural level based on an improved high-order moment method (HOMM). It directly addresses the objective failure probabilities at the global structural level and takes into account the resistance degradation of structures in the design reference period. A comparative analysis of the time-dependent seismic reliability between rocking cold-formed steel frames and rigid cold-formed steel frames is conducted, focusing on load-bearing capacity limit states and deformation capacity limit states. The investigation indicates that the differences between time-dependent and time-independent seismic reliability indexes are substantial. For cold-formed steel structures subjected to prolonged exposure to the corrosive environment, it is recommended to consider the time-dependent degradation of structures.

Condition-based opportunistic maintenance strategy for multi-component wind turbines by using stochastic differential equations

The components of wind turbines are complex in structure and the working environment is harsh, which makes wind turbines face problems such as high failure rates and high maintenance costs. In this paper, the stochastic differential equation model has been established for the harsh operating environment of wind turbines, and used Brownian motion to simulate random disturbances; aiming at the problem of high failure rate of wind turbines, based on Weibull distribution, a new model has been established by combining operating time and equipment state to calculate the failure rate; in the analysis of monitoring data, the Higher-Order Moment method and Bayesian method were used to solve the parameters. The opportunity maintenance threshold curve and preventive maintenance threshold curve were obtained by analyzing Time-Based Maintenance and Condition-Based Maintenance. Therefore, the Condition-Based Opportunistic Maintenance strategy was obtained. The effectiveness of the proposed method was finally verified by arithmetic examples.

Plastic deformation-based rolling bearing reliability and sensitivity analysis under incomplete probability information

It is currently difficult to adequately characterize the probability distribution information of rolling bearings, and research on the reliability of rolling bearings based on plastic deformation is lacking. To address this problem, the Latin hypercube design, BP neural networks, and higher-order moment method are combined, fully considering the randomness of the load, geometry, and material parameters of the rolling bearing. The dynamics model of the rolling bearing was constructed by using the Hertz contact theory and Jones model, combined with a Latin hypercube design to obtain neural network training samples. Based on the rational construction of the neural network structure, the mapping relationship between the equivalent stress and the design variables is obtained. The state function of the rolling bearing is constructed according to the stress–strength interference model, and then, the reliability index and reliability of the rolling bearing are obtained using the higher-order moment method, followed by a reliability sensitivity analysis. Finally, the proposed method is applied to the reliability analysis of a certain type of angular contact ball bearing, and the calculation results are compared with the Monte Carlo method results to demonstrate the correctness and effectiveness of the proposed method.

Structural system reliability assessment using generalized factorized dimensional reduction method and iterative maximum entropy method

The system reliability analysis of complex engineering structures remains a challenge in the field of reliability. In this work, a high-order moment method using generalized factorized dimensional reduction method (GF-DRM) and iterative maximum entropy method (IMEM) is proposed for structural system reliability assessment. Firstly, the performance functions are described uniformly by equivalent description methods for various system reliability problems. Secondly, a novel point estimation method (PEM) based on GF-DRM is proposed for the high-order moments estimation of the equivalent performance function. Thirdly, the system failure probability of the structures is accurately determined by using the IMEM, which can automatically determine the order of moments. Finally, four examples, including numerical and engineering cases, are investigated to demonstrate the accuracy and efficiency of the proposed method, in which results obtained from the proposed method are compared with some other existing moment methods and Monte Carlo simulation (MCS) method. The results of the examples show the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and system reliability analysis.

Reliability of fully assembled precast concrete frame structures against progressive collapse

Although fully assembled precast concrete (PC) frame structures using dry connections have been widely promoted, limited studies have been carried out on anti-progressive collapse performance. This study presented a methodology to analyze and compare the reliabilities of entire structural systems between RC and fully assembled PC frame structures, which evaluates the risk and vulnerability of a structure when column failure occurs under accidental loads. First, based on the existing test results of three half-scale moment sub-structures, nonlinear finite element (FE) macro-models were established in OpenSEES software. The verified FE models were applied to three seven-story frame structures (one RC frame and two PC frames). To evaluate the progressive collapse resistance, nonlinear pushdown analysis was conducted on the frame structures using the alternate load path (ALP) approach. Combining the Nataf transformation-based point estimate method (i.e. the improved point estimate method (IPEM)) with the nonlinear analysis results, various load amplification factors (αmax) were estimated. Finally, the reliability indices of the intact and damaged frame structures were calculated using the Zhao-Ono high-order moment method (HOMM). The results revealed that the fully assembled PC frames had higher failure probability (2.1–6.6%) than the RC frame (0.2%) in a catastrophic event.

Reliability Assessment on Pile Foundation Bearing Capacity Based on the First Four Moments in High-Order Moment Method

In this paper, the high-order moment method (HOMM) was developed for estimating pile foundation bearing capacity reliability assessment. Firstly, after the performance function was established, the first four moments (viz. mean, variance, skewness, and kurtosis) were suggested to be determined by a point estimate method based on two-dimensional reduction integrations. Then, the probability distribution of the performance function for the pile foundation bearing capacity was then approximated by a four-parameter cubic normal distribution, in which its distribution parameters are the first four moments. Meanwhile, the quantile of the probability distribution for the performance function and its reliability index was capable to be obtained through this distribution. In order to examine the efficiency of this method in engineering application, four pile foundations with different length-diameter radios were investigated in detail. The results demonstrate that the reliability analysis based on HOMM is greatly improved to the computational efficiency without loss precision compared with Monte Carlo simulation (MCS) and does not require complex partial derivative solving, checking point sought, and large numbers of iteration comparing with first-order reliability method (FORM). Moreover, the probability distribution function (PDF) approximated by the four-parameter cubic normal distribution was found to be consistent with that obtained by MCS. Eventually, the effects of parameter sensitivity for relative soil layer of the certain pile on reliability index were illustrated using the above-mentioned method. It indicated that the HOMM is an effective and simple approach for reliability assessment of the pile foundation bearing capacity.

An Efficient Parallel Hybrid Method of FEM-MLFMA for Electromagnetic Radiation and Scattering Analysis of Separated Objects

In order to meet the rapidly increasing demand for accurate and efficient analysis of complex radiating or scattering structures in the presence of electrically large objects, a finite element method (FEM)-multilevel fast multipole algorithm (MLFMA) hybrid method that based on the Finite Element-Iterative Integral Equation Evaluation (FE-IIEE) mesh truncation technique is proposed in this paper. The present method makes use of FEM for the regions with small and complex features and MLFMA for the analysis of the electrically large objects, which ensure the accuracy and applicability of the method are better than most commonly adopted FEM-high frequency technique (HFT) hybrid method. The mutual interactions between regions are taken into account in a fully coupled way through iterative near filed computation process. In order to achieve an excellent performance, both algorithms have been implemented together from scratch, being able to run over multi CPU cores. An efficient parallel FEM domain decomposition method (DDM) solver with exploiting geometrical repetitions is included to drastically reduce memory requirements and computational time in the calculation of large array antenna. Also, the parallel MLFMA is adopted to expedite the near-field information exchange between regions. Through numerical example, the effect of distance between regions on the convergence of the proposed hybrid method is studied, and it is shown that the proposed method converge well even if the distance is equal to 0.05λ. Through comparisons with an in-house higher order method of moments (HOMoM) code and commercial software FEKO, the accuracy and effectiveness of the implemented parallel hybrid method are validated showing excellent performance.

Validation Strategy of Reduced-Order Two-Fluid Flow Models Based on a Hierarchy of Direct Numerical Simulations

Whereas direct numerical simulation (DNS) have reached a high level of description in the field of atomization processes, they are not yet able to cope with industrial needs since they lack resolution and are too costly. Predictive simulations relying on reduced order modeling have become mandatory for applications ranging from cryotechnic to aeronautic combustion chamber liquid injection. Two-fluid models provide a good basis in order to conduct such simulations, even if recent advances allow to refine subscale modeling using geometrical variables in order to reach a unified model including separate phases and disperse phase descriptions based on high order moment methods. The simulation of such models has to rely on dedicated numerical methods and still lacks assessment of its predictive capabilities. The present paper constitutes a building block of the investigation of a hierarchy of test-cases designed to be amenable to DNS while close enough to industrial configurations, for which we propose a comparison of two-fluid compressible simulations with DNS data-bases. We focus in the present contribution on an air-assisted water atomization using a planar liquid sheet injector. Qualitative and quantitative comparisons with incompressible DNS allow us to identify and analyze strength and weaknesses of the reduced-order modeling and numerical approach in this specific configuration and set a framework for more refined models since they already provide a very interesting level of comparison on averaged quantities.

An improved fourth-order moment reliability method for strongly skewed distributions

High-order statistical moment method uses only moments of random variable for reliability analysis and can widely address the problem of unknown probability distribution. However, for practical cases with strongly skewed distributions, the existing fourth-moment methods may produce large errors or result in instability in the analysis process. Thus, an improved expression of the fourth-order moment reliability index based on the fourth-moment standardization function for strongly skewed distributions is developed. First, the coefficients of the fourth-moment standardization function are modified for strongly skewed distributions by fitting the coefficients of the third-order polynomial transformation, and an improved fourth-moment standardization function is developed. Then, the accuracy of the improved model is demonstrated by analyzing the relative errors between the estimated moments and their target values. Furthermore, the complete reliability index formula is derived according to the monotonic expression of the third-order polynomial transformation. Finally, numerical examples show the improved accuracy achieved by the proposed method. It can be concluded that, compared to the original methods, the proposed method is more accurate and stable for reliability analysis in which the distribution is strongly skewed.

An improved high order moment-based saddlepoint approximation method for reliability analysis

Moment-based methods use only statistical moments of random variables for reliability analysis. The cumulative distribution function (CDF) or probability density function (PDF) of a performance function can be constructed from the perspective of the first few statistical moments, and the failure probability can be evaluated accordingly. However, existing moment-based methods may lead to large errors or instability. As such, the present paper focuses on the high order moment method for higher accuracy of reliability estimation by combining the common saddlepoint approximation technique, and an improved high order moment-based saddlepoint approximation (SPA) method for reliability analysis is presented. The approximated cumulant generating function (CGF) and the CDF of the performance function in terms of its first four statistical-moments are constructed. The developed method can be used for reliability evaluation of uncertain structures follow any types of distribution. Several numerical examples are given to demonstrate the efficacy and accuracy of the proposed method. Comparisons of the new method and several existing high order moment methods are also made on the reliability assessment.

Punch-Through Risk of Jack-Up Under the Dual Uncertainty of Structure and Foundation

Abstract The preload operation of Jack-up in complex multi-layered foundation requires an enhanced understanding of its behavior in punch-through accident and suitable safety analysis tools for the assessment of their reliability in a particular site. In order to evaluate punch-through risk, a risk-consistent method is proposed based on the model of foundation hazard and structural vulnerability. Besides, foundation bearing capacity is evaluated to quantify foundation hazard. Third, to improve the solution efficiency, higher-order moment method (HOMM)-Pushover method has been developed for assessing the structural vulnerability. In addition, case studies are presented to demonstrate the advantages of these techniques and important trends are highlighted by the results of parametric sensitivity studies. More specifically, failure probability analysis has been undertaken using improved method and the punch-through risk is evaluated quantitatively in different hazard levels. The results show that the dual uncertainty of both structure and foundation is crucial for assessment of foundation hazard and structural vulnerability. The randomness of foundation parameters is the dominant factor affecting the punch-through risk, and the risk increases with the increase of preload weight. The time-varying risk in the process of preload operation can be revealed using the risk analysis method mentioned in this paper.

HOMOM/PE Hybrid Algorithm Based Calculation on Ground-Wave of the HF Antennas over Irregular Terrain

The parabolic equation model usually uses a gaussian pattern to fit the actual antenna’s pattern in free space to set the initial field, and then uses the image theory to deal with the effect of ground on the antennas. However, this method of setting the initial field cannot consider the specific HF antenna, and the image theory is only applicable to the radio wave propagation of antennas working in the microwave bands and above. The HF antenna is erected low, and the irregular terrain or the buildings around the antenna and their media parameters will affect the current distribution on the antenna, resulting in a large difference with the radiation pattern in the free space. The traditional method of fitting the pattern is no longer accurate. Aiming at the problem of radio wave propagation of HF antennas in the actual installation environment by parabolic equation method, a hybrid algorithm based on higher order-method of moment and parabolic equation method (HOMOM-PE) is proposed. The hybrid algorithm divides the whole calculation region into two regions, which is the inner zone and the outer zone. The inner zone is the zone that has a great influence on the antenna current distribution. In this area, HOMOM is used to model the antenna and the terrain together, and the influence of the complex terrain near the antenna on the antenna is strictly calculated. The PE algorithm is used to calculate the long-distance propagation, and the initial field data is derived from the electromagnetic vector distribution calculated in the inner region. The hybrid algorithm combines the antenna radiation and the wave propagation directly, which solves the problem of the initial field setting of the actual HF antenna under the complicated terrain conditions.

Computing Mutual Impedance of Antennas by Spherical Harmonic Transform

The coupling of two antennas can be described with mutual impedance. This paper proposes computing the mutual impedance by reaction theorem, which involves integrating vector products of near fields over a sphere surrounding the second antenna. We express the near fields of both antennas by the vector spherical harmonic transform (SHT), evaluate the near fields of the first antenna on the eccentric sphere by a new fast Fourier transform (FFT)/interpolation method efficiently, and then obtain the mutual impedance by the reaction integrals. This new method has a computation complexity of $O(N^{3})$ , where N represents the truncation order in SHT. A comparison with the higher order moment method (HOMOM) indicates that the proposed method is a fast, accurate, stable, and universal method to analyze the coupling of any two antennas.

Higher order VIE method based on non‐conformal discretisation for EM scattering from anisotropic objects

This article presents a higher order method of moments (MoM) solution of the volume electric field integral equation (VEFIE) to model the electromagnetic (EM) scattering from anisotropic dielectric objects with arbitrary shape and inhomogeneity. This higher order solution is based on the higher order current modelling and higher order geometric modelling. Namely, the unknown electric flux density vector is discretised by the higher order hierarchical vector (HOHV) basis functions, and the geometric structure is discretised by the curved tetrahedral elements. Both kinds of higher order discretisation can reduce the number of mesh elements and the associated unknowns significantly. When the solution accuracy is on a comparable level, authors’ higher order VIE demands much less memory and CPU time than the conventional low-order volume integral (VIE). Moreover, authors’ scheme accommodates the non-conformal discretisation, because no divergence operator is imposed on the vectorial unknown. Numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of the proposed approach.

Fast coating analysis and modeling for RCS reduction of aircraft

In order to fast analyze the aircraft Radar Cross Section (RCS) and accurately reduce it with Radar Absorbing Materials (RAM), a comprehensive analysis method based on Higher-Order Method of Moments (HOMOM), termed Locally Coating Method (LCM), is proposed in this paper. There are two steps to fast analyze coatings for RCS reduction in this method: analyze the RCS of various parts before coating the aircraft; model a coating over the aircraft and analyze the wave absorbing effect of it. The aircraft RCS is calculated as a whole but analyzed in various parts by LCM, and thus the RCS contribution of different parts can be compared without disturbing the current continuity. A model expansion algorithm is also presented in LCM to model absorption coatings on specified aircraft parts for later stage RCS calculation of the coated aircraft.

The Influence of Buildings on the Radiation Performance of Shortwave Antenna

Based on practical erection environment of shortwave antenna, this paper simulates and analyzes the radiation performance of common shortwave antenna that erected on roof, different distance and orientation front of buildings according to Higher Order-Method of Moment (HO-MoM), and proposes suggestions on using.

The effect of microwave on the crystallization process of magnesium carbonate from aqueous solutions

The effect of microwave on reactive crystallization is investigated with magnesium carbonate as the working substance. In the experiments, magnesium carbonate is precipitated by mixing aqueous magnesium sulfate and sodium carbonate solutions in a MSMPR crystallizer located in a microwave reactor. A population balance model along with crystallization kinetics is formulated to assess the influence of microwave energy input on nucleation, growth, agglomeration and breakage during crystallization process. A general high order moment method of classes (HMMC) framework is applied to solve the model numerically. The results show that crystallization kinetics parameters, including the nucleation rate constant (kn), the growth rate constant (kg), the exponent of growth rate (g) and the collision efficiency (Ψag) change significantly due to mass transfer enhancement in microwave field. Meanwhile, the exponent of nucleation (n) and the breakage rate constant (kbr) remain constant or only change slightly. It is further discovered that the crystal suspension attenuates the microwave effect during crystallization process.

An Efficient Matrix Equation Parallel Direct Solver for Higher-Order Method of Moments in Solution of Complex Electromagnetic Problems

An efficient parallel direct solver with a new pivoting scheme is presented for solving impedance matrix equations generated by the higher-order method of moments in high-frequency electromagnetic computation. Given the diagonal dominance characteristic of the dense complex impedance matrices, a local-block pivoted parallel LU decomposition algorithm is developed in the solver, which requires less communication time than the Intel math kernel library and the communication avoiding LU solver, because the pivoting operations execute in local blocks of the processes. To demonstrate the stability and performance of the algorithm, electromagnetic radiation and scattering from complex models containing metallic and dielectric structures are computed. When up to 1200 CPU cores are used, numerical results show that the solving time of the proposed LU solver is significantly reduced.

High Order Moment Model for Polydisperse Evaporating Sprays towards Interfacial Geometry Description

In this paper we propose a new Eulerian modeling and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model is its capacity to describe some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. For this purpose, we use fractional size-moments, where the size variable is taken as the droplet surface. In order to evaluate the evaporation of the polydisperse spray, we use a smooth reconstruction which maximizes the Shannon entropy. However, the use of fractional moments introduces some theoretical and numerical difficulties, which need to be tackled. First, relying on a study of the moment space, we extend the Maximum Entropy (ME) reconstruction of the size distribution to the case of fractional moments. Then, we propose a new accurate and realizable algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. This algorithm is based on a mathematical analysis of the kinetic evolution due to evaporation, where it shown that the evolution of some negative order fractional moments have to be properly predicted, a peculiarity related to the use of fractional moments. The present model and numerical schemes yield an accurate and stable evaluationof the moment dynamics with minimal number of variables, as well as a minimal computational cost as with the EMSM model, but with the very interesting additional capacity of coupling with diffuse interface model and transport equation of averaged geometrical interface variables, which are essential in oder to describe atomization.

New Higher Order Method of Moments for Accurate Inductance Extraction in Transmission Lines of Complex Cross Sections

A new higher order (HO) method of moments is proposed for high accuracy extraction of the resistance and inductance matrices in the multiconductor transmission lines (MTLs) of complex cross sections. The computational framework is based on the numerical solution of a surface–volume–surface electric field integral equation of magnetostatics. In order to achieve an exponentially efficient reduction in the error of the solution, HO geometrical representation of the conductor cross sections is accompanied with the discretization of the unknown field quantities on the conductor boundaries and cross sections with 1-D and 2-D HO polynomial basis functions, respectively. The methodology allows for extraction of the network parameters in broad ranges of frequencies for which resistive and inductive contributions to the impedance matrix vary within a wide dynamic range. Comparison of numerically computed currents to the currents obtained analytically for canonical transmission line configurations is performed. Solutions of the extraction problem for MTLs with complex cross sections are compared against the finite-element method solutions to demonstrate the efficiency of the proposed methodology.