The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

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).

海水淡化厂与区域水-能耦合系统的协同调度

海水淡化厂具有能量密集、运行灵活的特点,是理想的电力需求响应资源。然而,现有关于淡化厂与电网协同运行的研究大多关注电网和淡化厂的一体化调度、无法适应双方自主决策的工程场景,对淡化厂运行约束的刻画也比较粗糙。该文研究反渗透淡化厂与区域水-能耦合系统(waterenergy nexus,WEN)的协同运行方法。首先,考虑淡化厂的生产流程、调节特性和运行约束,分别建立传统及新能源淡化厂的水-能管理模型;其次,在保障两类淡化厂和区域WEN自主决策和信息隐私的条件下,提出以双方调度计划互动为载体的“激励型”和“价格型”两种协同运行机制及调度模型,并提出基于二阶锥松弛和McCormick包络的求解方法。用算例验证所提协同运行机制、调度模型及求解方法的有效性。

基于HPPC-FFRLS的锂电池等效模型参数在线辨识

目的为了实现锂离子动力电池的高精度状态监测与分析,方法针对锂离子动力电池二阶RC等效电路模型的参数在线辨识展开研究。搭建锂离子动力电池二阶RC等效电路模型;利用开路电压法与安-时积分算法相结合的方式进行电池荷电状态(SOC)评估;通过HPPC测试实验数据进行等效电路模型的离线参数辨识;以离线辨识结果作为系统状态初值,结合带遗忘因子的递推最小二乘算法(FFRLS)对锂离子动力电池二阶RC等效电路模型参数进行在线辨识;利用Simulink搭建电池状态监测和充放电控制仿真系统,对基于在线辨识参数的模型进行仿真测试;利用可编程电源和电子负载搭建实验平台。结果对比在线辨识参数的系统仿真输出、离线辨识参数的系统仿真输出和实验数据,结果表明:基于HPPC-FFRLS在线辨识的模型仿真输出的误差相对于HPPC实验法减小了50%;在线辨识策略克服了环境温度、电池老化、充放电倍率等因素对参数的影响;仿真初期系统波动明显减小,等效模型系统动态跟踪具有更高的精度,鲁棒性更好。结论基于HPPC-FFRLS的锂电池等效模型在线辨识保证了模型参数的有效性,简化运算量的同时提高了模型精度。

S-ZVI处理亚甲基蓝染料废水的好氧实验研究

采用零价铁与Na2S在厌氧条件下制备硫化零价铁(S-ZVI)颗粒,并对其处理亚甲基蓝废水影响因素进行研究。结果表明S-ZVI表面粗糙附有硫化物薄膜,具有壳核结构;S-ZVI颗粒对亚甲基蓝的去除率随着S/Fe比的增加先增加后下降,当S/Fe比为0.025时对亚甲基蓝的去除效果最好,去除率为98.02%,整体反应在150 min基本达吸附平衡,且遵循伪二级动力学反应;在应用S-ZVI去除亚甲基蓝废水时最佳pH在6~8之间。好氧条件对亚甲基蓝的去除率为厌氧的1.46倍,氧的存在有助于提高S-ZVI对亚甲基蓝的去除效果。

计及电-气双向耦合的综合能源配电网优化重构

综合能源系统是实现电网、气网以及热网等多种能源系统深度融合,利用能量耦合互补等优势提升整个系统能源利用效率的有效形式。为提升综合能源系统优化运行能力,文章首先基于电转气技术与天然气发电技术,构建了的电-气双向耦合综合能源系统总体模型。进而考虑配电网重构技术(Distribution Network Reconfiguration Technology,DNR)中拓扑结构灵活可控这一特性,在配电子系统中引入开关变量、系统运行总费用最低这一目标函数及网络辐射状拓扑结构等约束,建立了配电子系统重构模型。从降低模型求解复杂性的角度,应用二阶锥松弛、乘积变量线性化及分段线性化等方法,将原始综合能源配电网重构非凸非线性模型转化为混合整数二阶锥规划(Mixed Integer Second-Order Cone Programming,MISOCP)问题求解。仿真结果表明,在电-气双向耦合的综合能源系统中应用配电网重构技术,能够降低综合能源系统运行费用,同时有效支撑了配电子系统电压与配气子系统气压。

考虑电压-无功调节的台区互联装置规划方法

伴随分布式能源广泛接入低压配电网,其对配电网运行灵活性和消纳能力的要求不断提高。利用低压柔性互联装置将独立运行的低压配电台区分区互联,避免传统电压调节和无功补偿装置频繁动作。考虑到柔性互联装置造价昂贵,协同传统电压-无功调节装置,文中提出低压柔性互联装置的选址定容规划方法。首先,分析低压柔性互联装置拓扑和运行方式,建立其潮流模型。其次,建立低压柔性互联装置优化配置的双层规划模型,上层规划以年综合费用最小为目标,下层规划考虑电压-无功协调控制时间序列模型,以运行成本和电压偏差最小为目标,基于粒子群优化算法和混合整数二阶锥规划算法交替求解,得出配电系统最优柔性互联方案和最优运行方式。最后,在IEEE 33节点系统上进行实例分析,验证该双层规划算法的有效性。结果表明,所提方法能有效减少柔性互联装置的过度布置,同时减少由分布式能源频繁波动造成的运行成本。将模型凸化并线性化的方法明显提高了求解效率。

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。

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.

Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function

By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.

Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots

Target tracking control for wheeled mobile robot （WMR） need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.

Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations

Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.