Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties

This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.

Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

Bayesian Prediction of Future Generalized Order Statistics from a Class of Finite Mixture Distributions

This article is concerned with the problem of prediction for the future generalized order statistics from a mixture of two general components based on doubly?type II censored sample. We consider the one sample prediction and two sample prediction techniques. Bayesian prediction intervals for the median of future sample of generalized order statistics having odd and even sizes are obtained. Our results are specialized to ordinary order statistics and ordinary upper record values. A mixture of two Gompertz components model is given as an application. Numerical computations are given to illustrate the procedures.

基于分数阶的空气弹簧建模及电动汽车主动悬架控制研究

电控空气悬架系统(electrically controlled air suspension, ECAS)具有调节悬架刚度和车身高度的功能,可有效改善车辆乘坐舒适性和操纵稳定性。以某乘用车ECAS为对象,利用分数阶理论描述橡胶气囊的黏弹性阻尼特性,考虑等效阻尼及滞回特性对其热力学模型进行了优化,结果与实验数据吻合良好,验证了优化后的空气弹簧模型的精确性。在此基础上,考虑车辆纵横向动力学特性与Dugoff轮胎模型,建立14自由度整车ECAS动力学模型,提出模型预测(model predictive control, MPC)主动悬架控制方法,以可测变量为控制器输入,实现直线及转向行驶工况下的主动控制。仿真与整车台架实验研究表明,分数阶修正模型可以很好地反映ECAS变刚度特性,基于MPC的主动悬架控制策略能实时调整空气弹簧刚度,控制车身姿态,有效改善电动汽车行驶时的平顺性与稳定性。论文的研究方法为车辆悬架系统建模及主动控制提供了一种新思路。

分数阶Boost变换器的混沌控制研究

基于电容电感均为分数阶的事实,对分数阶连续导通模式Boost变换器的非线性动力学特性进行分析,提出了基于优化参数共振微扰法的分数阶Boost变换器混沌控制策略。首先,采用预估-校正算法建立了峰值电流控制分数阶Boost变换器的预估-校正模型,通过分岔图详细分析了电路参数对变换器非线性动力学特性的影响。然后,采用优化参数共振微扰法对变换器进行混沌控制,推导了系统的稳定判据,计算了扰动信号的最优幅值与相位。最后,在MATLAB/Simulink中进行仿真实验。研究表明,选择合理的扰动信号,能够有效抑制变换器的混沌现象,使变换器由混沌回归稳定状态。与参数共振微扰法相比,优化后的控制策略提高了系统的鲁棒性。仿真结果验证了所提策略的有效性。

基于节点相似性的二阶链路预测方法

复杂网络中基于节点相似性的链路预测算法通常根据两个节点之间的相似度,预测节点对之间是否存在链路。提出基于节点相似性的二阶链路预测方法,判别节点对之间是否存在未连接的节点,并补全节点对之间的二阶链路。同时,提出二阶链路预测指标,计算已知节点与其他并不存在链路的节点之间的相似性,并构建二阶可达网络保留原始网络中的二阶链路信息。实验结果表明,该方法能够在真实的网络数据中找到节点对之间的缺失节点,并补全可能存在的二阶链路。不同的链路预测指标在4个不同网络中的性能表现有所不同,所有实验中的最佳精确率达83.7%。

间歇性循环荷载下冻融风积土变形特性及分数阶预测模型

列车运营对路基的长期作用由振动加载、荷载间歇交替组成,已往研究多只考虑振动加载周期对路基土体强度和变形特性的影响,而忽略了间歇期的影响。为研究间歇性循环荷载作用下风积土路基变形特性,利用GDS DYNTTS冻土动三轴仪,开展不同有效固结围压σ_(3c)、冻融循环次数FT、动应力幅值σ_(d)^(ampl)和振动频率f的间歇性循环荷载下风积土动三轴试验,研究间歇性循环荷载下冻融风积土变形特性及其影响因素。试验结果表明:间歇性循环荷载作用下风积土累积塑性应变曲线呈稳定型、发展型和破坏型三种形态。间歇阶段能够在较大程度上削弱土体的应变累积,从而使其较连续荷载作用下变形减小。基于极差方法,确定动应力幅值是影响风积土累积塑性应变的最重要因素,其余依次为有效固结围压、冻融循环次数、振动频率。采用双Abel黏壶建立考虑间歇性循环荷载作用的冻融风积土分数阶累积塑性应变预测模型,并与试验结果进行了对比分析,二者吻合度较高,说明该文建立的分数阶累积塑性应变数学模型可合理预测间歇性循环荷载作用下风积土路基长期变形特性。研究成果可为季节性冻土地区路基工程设计和灾害防治提供科学依据。

基于弱化算子的黑龙江省人口老龄化灰色预测

近年来,黑龙江省人口老龄化率高于全国,老龄人口规模持续上升,对医疗保障体系、劳动力资源结构以及养老服务体系等产生影响,因此,研究黑龙江省人口老龄化的预测问题具有十分重要的现实意义。针对黑龙江省人口老龄化的灰色特性,提出一种结合一阶弱化算子优化的均值GM(1,1)预测模型,对黑龙江省老龄人口发展趋势进行预报。以2006—2021年间的黑龙江省老龄人口原始数据为样本,构建基于一阶弱化算子均值GM(1,1)的黑龙江省人口老龄化预测模型,并与基于均值GM(1,1)的黑龙江省人口老龄化预测模型精度进行对比分析。结果表明:黑龙江省老龄人口的一阶弱化算子均值GM(1,1)预测模型精度高于传统的均值GM(1,1)模型,说明一阶弱化算子的均值GM(1,1)模型能够提高黑龙江省老龄人口预报精度。

k阶采样和图注意力网络的知识图谱表示模型

知识图谱表示(KGE)旨在将知识图谱中的实体和关系映射到低维度向量空间而获得其向量表示。现有的KGE模型只考虑一阶近邻,这影响了知识图谱中推理和预测任务的准确性。为了解决这一问题,提出了一种基于k阶采样算法和图注意力网络的KGE模型。k阶采样算法通过聚集剪枝子图中的k阶邻域来获取中心实体的邻居特征。引入图注意力网络来学习中心实体邻居的注意力值,通过邻居特征加权和得到新的实体向量表示。利用ConvKB作为解码器来分析三元组的全局表示特征。在WN18RR、FB15k-237、NELL-995、Kinship数据集上的评价实验表明,该模型在链接预测任务上的性能明显优于最新的模型。此外,还讨论了阶数k和采样系数b的改变对模型命中率的影响。

基于SMD与WaOA-CNN-LSTM的短期光伏功率预测

针对当前光伏功率预测模型所面临因数据的复杂性、信号处理过程的噪声干扰、非线性特征难以提取等问题而导致的预测精度低、稳定性差等多方面挑战,提出了一种融合二次模态分解(SMD)和基于海象算法(WaOA)优化CNN-LSTM神经网络的组合预测模型。首先,利用完全自适应噪声集合经验模态分解(CEEMDAN)对光伏数据进行分解,并结合K均值聚类算法(K-means)将多个子序列重构成低频、中频以及高频序列;其次,将含有残余噪声的高频序列采用变分模态分解(VMD)进行二次分解处理;最后,对各分量分别构建CNN-LSTM模型,并利用WaOA算法对网络参数进行寻优,将各分量的预测结果进行叠加,得到最终预测结果。SMD处理方法解决了传统数据处理方法模态混叠、低频分量过多和高频分量噪声残余等问题,CNN-LSTM模型能够捕捉数据中的空间关系和长期依赖关系,WaOA算法对模型参数的优化提高了模型的性能和效率。选取陕西某地光伏电站数据进行测试,通过多组对比实验进行验证,结果表明:所提方法具有更高的预测精度。

单输入单输出系统分数阶预测函数控制

基于分数阶微积分理论和预测函数控制理论,针对一类单输入单输出分数阶线性系统提出了一种分数阶预测函数控制方法。用Oustaloup近似法对分数阶系统近似的整数阶系统建立预测输出模型,并根据GL定义在代价函数中引入分数阶算子。该控制方法通过将控制输入结构化简化了控制器设计,引入分数阶算子增加了控制器的自由度。仿真结果表明:与传统预测控制器相比,分数阶预测函数控制器具有调节时间短、抗干扰能力强及鲁棒性强等优点,在模型失配的情况下也有较好的跟踪效果。

永磁同步电机无模型自适应滑模补偿预测控制

针对在永磁同步电机矢量控制系统中应用模型预测控制方法设计控制器时依赖电机数学模型参数,当电机运行过程中参数变化时,引起控制器参数与电机参数失配,导致系统控制性能降低。提出一种无模型自适应预测控制方法,利用系统输入输出数据和时变的伪偏导数建立预测模型;又由于无模型自适应预测控制方法没有反馈校正环节,易受外部扰动的影响,设计一种新型高阶滑模补偿器作为校正部分,以提高控制系统的鲁棒性且抑制滑模自身的抖振,最后MATLAB仿真验证了无模型自适应高阶滑模补偿预测控制方法的优越性。

基于直流电流瞬时微分的特高压直流分层接入系统非故障层换相失败预防控制策略

在特高压直流分层接入系统中,由于层间耦合作用,某一层交流系统发生故障可能导致非故障层换流器发生换相失败。为此,考虑到故障过程直流电流的变化,提出一种基于直流电流瞬时微分的换相失败预防控制策略。该策略基于故障后直流电流的变化特性,得到换相电流时间面积控制中触发角修正量,代替原有换相失败预防控制,提高非故障层换相失败预防控制的启动精度;同时基于电流预测量和等效直流输入电阻动态调整低压限流控制器的指令值,提高其响应速度。在PSCAD/EMTDC中搭建仿真模型对不同工况下所提控制策略进行验证。结果表明,该策略可降低高低端换流器同时发生换相失败的风险,改善故障后系统的运行性能。

基于二阶滑模扰动观测的PMSM电流预测控制研究

针对无差拍电流预测控制(DPCC)对电机参数的依赖性,系统性能尤其易受电感参数影响的问题,研究基于二阶滑模扰动观测的永磁同步电机(PMSM)电流预测控制方法。首先,根据滑模控制原理分析电感参数失配对系统参数鲁棒性的影响,及传统滑模控制的不连续函数导致的系统“抖振”;然后,在DPCC中引入一种基于二阶趋近律的滑模扰动观测器(SMDO),实时补偿电感参数失配造成的扰动,同时通过二阶趋近律加速扰动误差的收敛;最后,将该方法与DPCC、SMDO+DPCC进行对比仿真实验。实验结果表明,在电感参数失配的情况下,该方法降低了电流稳态误差,提高了系统参数的鲁棒性,减少了传统滑模控制带来的系统“抖振”现象。

利用长短期记忆神经网络的改进POD-Galerkin降阶模型及其在流场预测中的应用

针对标准POD-Galerkin降阶模型在流场快速预测中存在误差而导致精度不高的问题,提出了一种利用长短期记忆神经网络的改进POD-Galerkin降阶模型。使用本征正交分解对流场进行降维,投影得到低维降阶模型,引入两个长短期记忆神经网络,建立从POD-Galerkin降阶模型到实际POD模态时间系数之间的修正映射、低阶模态时间系数与高阶模态时间系数之间的扩展映射,分别用于消除标准POD-Galerkin降阶模型的误差累积和扩展降阶模型的阶数,从而实现物理驱动与数据驱动混合的流动降阶模型的构建。将改进POD-Galerkin降阶模型应用于二维圆柱绕流的流场预测,通过与原始标准POD-Galerkin降阶模型的对比,分析了所提模型的精度和计算速度。结果表明:添加神经网络修正项后的降阶模型相较于标准POD-Galerkin降阶模型,有效提升了降阶模型的精度,预测各阶模态时间系数的均方根误差能够减小1~2个数量级,预测的流场更接近原始流场;在预测相同阶数的情况下,计算时间显著减小,基于4阶和6阶扩展的8阶改进降阶模型相较于原始8阶POD-Galerkin降阶模型预测速度分别提高了约56%和25%。