An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Mathematical modelling of a biofilm: The Adomian decomposition method

A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement.

Restarted Adomian Decomposition Method for Solving Volterra’s Population Model

In this paper, we used an efficient algorithm to obtain an analytic approximation for Volterra’s model for population growth of a species within a closed system, called the Restarted Adomian decomposition method (RADM) to solve the model. The numerical results illustrate that RADM has the good accuracy.

The proper orthogonal decomposition method for the Navier-Stokes equations

The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.

Reaction Rate Models for the Thermal Decomposition of Ibuprofen Crystals

Kinetics of the decomposition of racemic ibuprofen crystals were studied by non-isothermal analysis. Thermogravimetric analysis revealed that ibuprofen is thermally stable up to 152.6°C and the initial loss of mass was due to evaporation only. Activation energy, pre-exponential factor, activation entropy and Gibbs free energy for the decomposition of ibuprofen were determined using the integral method of Coats-Redfern (CR). Geometrical contraction models were found to be the best fits. The Arrheinus equation for the thermal decomposition of ibuprofen is k = (1.1 × 107) e–79125/RT sec–1.

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

Exponentially Convergent Multiscale Finite Element Method

We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation.The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions.Unlike most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity functions.In general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence.Indeed,there are online and offline parts in the function representation provided by the ExpMsFEM.The online part depends on the right-hand side locally and can be computed in parallel efficiently.The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

Reaction pathway and kinetics of CdO nanoparticles prepared from CdCO_3 precursor using thermal decomposition method

The non-isothermal kinetics of CdO nanoparticles prepared from CdCO3 precursor using thermal decomposition method was investigated. A model-fitting Malek approach and a model-free advanced isoconversional method of Vyazovkin were applied to the analysis of the DSC and TGA data. The results showed that CdO nanoparticles prepared from CdCO3 followed an autocatalytic reaction. Sestak–Berggren model could favorably describe the studied reaction process. Moreover, the apparent activation energy of CdCO3 decomposition was calculated to be (119.19±9.97) kJ/mol and the explicit rate equation form of CdCO3 decomposition was established.

Analytical Expressions for Steady-State Concentrations of Substrate and Product in an Amperometric Biosensor with the Substrate Inhibition—The Adomian Decomposition Method

A mathematical model of an amperometric biosensor with the substrate inhibition for steady-state condition is discussed. The model is based on the system of non-stationary diffusion equation containing a non-linear term related to non-Michaelis–Menten kinetics of the enzymatic reaction. This paper presents the analytical expression of concentrations and current for all values of parameters φ2s φ2s α and β . Here the Adomian decomposition method (ADM) is used to find the analytical expressions for substrate, product concentration and current. A comparison of the analytical approximation and numerical simulation is also presented. A good agreement between theoretical predictions and numerical results is observed.

Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled KdV. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

Multi-scale Decomposition of Co-seismic Deformation from High Resolution DEMs:a Case Study of the 2004 Mid-Niigata Earthquake

Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.

Ab Initio and RRKM Study of the Unimolecular Decomposition of Five-membered Ring Heterocyclic (X:O,S,N-H)

Quantum mechanical and Rice-Ramsperger-Kassel-Marcus （RRKM） calculations are carried out to study the thermal unimolecular decomposition of 2,5-dihydrofuran （1）,2,5dihydrothiophene （2）,and 3-pyrroline （3） at the MPW1PW91/6-31＋＋G level of theory,and the results are in good agreement with the experimental values.The predicted high pressure limit rate constants （k（T）） in various states of activation energy and pre-exponential （S1：（A（calc.）,E a（calc.））,S2：（A （calc.）,E a（exp.））,and S3：（A （exp.）,E a（calc.））） for the thermal decomposition processes 1-3 were evaluated.Also,the fall-off pressures （P1/2） for compounds 1-3 in the states 1-3 are found to be （1.24×10-2,1.09×10-3,and 4.19×10-2mmHg）,（1.24×10-2,1.63×10-3,and 2.79×10-2mmHg）,and （1.24×10-2,1.63×10-3,and 4.19×10-2 mmHg）,respectively.As the fall-off pressure of thermal decomposition process of compounds 1-3 is in the following order：P1/2（3）〉 P1/2（1）〉 P1/2 （2）,the decomposition rates are as below：rate（3） 〈rate（1）〈rate（2）.

Methods in Model Order Reduction(MOR) field

Nowadays,the modeling of systems may be quite large,even up to tens of thousands orders.In spite of the increasing computational powers,direct simulation of these large-scale systems may be impractical.Thus,to industry requirements,analytically tractable and computationally cheap models must be designed.This is the essence task of Model Order Reduction(MOR).This article describes the basics of MOR optimization,various way of designing MOR,and gives the conclusion about existing methods.In addition,it proposed some heuristic footpath.

基于有限差分低秩分解策略的黏声各向异性纯qP波正演模拟方法

地下介质的黏弹性和各向异性特征会导致地震波出现相位频散和振幅衰减,如果在地震数据处理中忽略这些影响,那么成像结果会出现同相轴畸变和偏移假象。常规黏声TTI介质拟声波方程可用于模拟地震波在黏声各向异性介质中的传播特征,但存在伪横波干扰和受模型参数限制(各向异性参数ε必须大于δ)等问题。为了解决上述问题,将基于声学近似的纯qP波频散关系与常Q衰减模型相结合,推导了一种黏声TTI介质纯qP波方程。该方程包含解耦的相位频散和振幅衰减项,便于实现衰减补偿逆时偏移。基于新推导的方程,发展了有限差分低秩分解求解策略,实现了黏声TTI介质纯qP波正演模拟。数值模拟结果表明,该方程克服了黏声TTI介质拟声波方程的局限,可较为准确且稳定地模拟地震波在黏声各向异性介质中的传播过程。同时,该有限差分低秩分解求解策略继承了有限差分求解方法高效的优势,相比于传统低秩分解法具有更高的计算效率。

基于Twin Builder的110kV油浸式变压器3维磁场降阶模型及损耗分析

为解决3维变压器磁场有限元仿真计算效率低的问题,提出基于本征正交分解法的磁场降阶模型与基于二次多项式的损耗响应面模型。以1台110 kV变压器为算例,首先建立了考虑绕组涡流损耗的变压器磁场仿真模型,通过仿真分析了其在额定工况下的磁场及损耗分布;其次,通过仿真试验设计获取了多组工况下的磁场与损耗数据,在Twin Builder中训练得到变压器磁场的各降阶模块;最后,搭建面向数字孪生应用的变压器3维磁场降阶模型,实现了变压器磁场损耗的快速计算与云图分布的可视化。与计算单数据相比,仿真结果考虑了涡流效应的绕组损耗在靠近端部时有明显升高,最大值分别出现在高、低压绕组两端,约为绕组中部损耗的1.3~1.65倍。基于该磁场结果建立的降阶模型在计算效率方面较全阶模型有显著提升,将实际仿真时间缩短至0.76s,可满足数字孪生应用场景下的磁场快速计算需求。

基于层次分解、主成分分析和高斯混合模型的火成岩岩性识别——以惠州26洼古潜山为例

火成岩油气成藏规律复杂,受到火山运动、强构造运动以及风化剥蚀等叠加影响,火成岩的化学成分和结构构造复杂多样,非均质性极强,采用常规岩性识别方法难以一次性将所有岩性准确识别。借鉴层次分解思路,以惠州26洼古潜山为例,提出了一种火成岩岩性测井识别分类方法:综合考虑火成岩地质分类原则和测井响应特征来确定岩性识别层级,基于这种层次性的分类原则,在每一层次定量优选岩性识别敏感参数,建立研究区岩性识别优选层级;在明确岩性识别优选层级的基础上,逐级逐次使用主成分分析(PCA)和高斯混合模型(GMM)对岩性进行判别并确定其计算函数,建立分级优选岩性识别模型,最终达到整体岩性区分的目的。研究结果表明,研究区辉绿岩和闪长岩识别正确率分别为87.31%和84.32%,未分级未优选辉绿岩和闪长岩识别正确率为60.45%和54.88%,分级未优选其岩性识别正确率为69.61%和67.04%,有效提高了研究区的复杂岩性识别精度。该方法的提出对提高火成岩岩性识别精度提供了一种思路,也为研究区古潜山火成岩岩性精确识别提供了参考依据。

面向数字孪生模型应用的油浸式变压器绕组温度POD-RBFLP降阶计算方法

了解油浸式电力变压器绕组的温度情况是保证其运行稳定性的关键,也是当前针对油浸式变压器数字孪生分析的必然需求。为了快速地获得变压器绕组的稳态温度,该文提出一种基于本征正交分解(proper orthogonal decomposition,POD)和包含线性多项式的径向基函数响应面法(radial basis function response surface method including linear polynomial,RBFLP)的降阶计算模型。首先,讨论POD方法的降阶特性,并设计一种基于留一法交叉验证的自适应获得快照矩阵方法,以提高计算精度及效率;其次,采用响应面方法建立POD模态系数与绕组工况的相关关系,旨在实现通过绕组工况快速获得POD模态系数,从而跳过对降阶模型的复杂非线性计算,进而高效重构绕组温度场。相关算例表明,该方法具有较好的计算精度和效率,在50组测试工况下,与全阶计算相比,误差不超过2.5 K,且总计算时间仅为1.45 s;最后,基于110 kV变压器绕组搭建温升试验平台,试验结果表明,降阶计算结果相较于试验结果,平均计算误差不超过2 K,且单步计算时间仅为0.03 s,相较于同等规模的全阶计算,计算效率有较大幅度地提升。

Accurate simulations of pure-viscoacoustic wave propagation in tilted transversely isotropic media

Forward modeling of seismic wave propagation is crucial for the realization of reverse time migration(RTM) and full waveform inversion(FWI) in attenuating transversely isotropic media. To describe the attenuation and anisotropy properties of subsurface media, the pure-viscoacoustic anisotropic wave equations are established for wavefield simulations, because they can provide clear and stable wavefields. However, due to the use of several approximations in deriving the wave equation and the introduction of a fractional Laplacian approximation in solving the derived equation, the wavefields simulated by the previous pure-viscoacoustic tilted transversely isotropic(TTI) wave equations has low accuracy. To accurately simulate wavefields in media with velocity anisotropy and attenuation anisotropy, we first derive a new pure-viscoacoustic TTI wave equation from the exact complex-valued dispersion formula in viscoelastic vertical transversely isotropic(VTI) media. Then, we present the hybrid finite-difference and low-rank decomposition(HFDLRD) method to accurately solve our proposed pure-viscoacoustic TTI wave equation. Theoretical analysis and numerical examples suggest that our pure-viscoacoustic TTI wave equation has higher accuracy than previous pure-viscoacoustic TTI wave equations in describing q P-wave kinematic and attenuation characteristics. Additionally, the numerical experiment in a simple two-layer model shows that the HFDLRD technique outperforms the hybrid finite-difference and pseudo-spectral(HFDPS) method in terms of accuracy of wavefield modeling.

基于SVM-STL-LSTM的区域短期电力负荷预测研究

针对区域电力负荷的时间序列数据随机性强、预测精度低及单一模型的数据特征提取能力差等问题,提出了一种支持向量机(SVM)、STL时序分解法、长短期记忆神经网络(LSTM)组合的电力负荷预测模型。该模型利用SVM对时间序列的电力负荷数据进行初始预测,并通过STL时序分解法对残差序列进行时序分解,从而提高残差序列的稳定性,减小其随机性,最后用LSTM对SVM的预测误差进行修正。试验结果证明,该方法利用误差修正可有效处理随机性强的数据,有利于预测结果的稳定性,提高预测精度。

基于CEEMDAN-GMDH-ARIMA的大坝变形预测模型研究

为提高大坝变形预测精度,针对大坝变形数据的复杂性和非线性等特征,基于自适应噪声完备集成经验模态分解(CEEMDAN)、数据处理群集法(GMDH)和差分自回归移动平均模型算法(ARIMA)进行大坝变形预测研究。采用CEEMDAN将大坝变形原始数据分解为高频随机分量、中频周期分量和低频趋势分量,再分别采用GMDH模型、ARIMA模型对高中频分量、低频分量进行预测,建立基于CEEMDAN-GMDH-ARIMA的大坝变形预测模型。以江西上犹江水电站为例,将该模型预测结果与反向传播(BP)、径向基函数(RBF)、GMDH和CEEMDAN-GMDH模型的预测结果进行对比分析。结果表明:CEEMDAN-GMDH-ARIMA模型的均方根误差(E_(RMS))、平均绝对误差(E_(MA))、相关系数(r)分别为0.048 mm、0.035 mm、0.994,均优于BP、RBF、GMDH、CEEMDAN-GMDH模型,模型预测效果最好,能够很好地体现监测点水平位移变化趋势。