Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2nd-CASAM)” for the efficient and exact computation of 1st- and 2nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (i.e., model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N2/2 + 3 N/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2nd-LASS requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1st-LASS and 2nd-LASS requires the same computational solvers as needed for solving (i.e., “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1st-LASS and the 2nd-LASS. Since neither the 1st-LASS nor the 2nd-LASS involves any differentials of the operators underlying the original system, the 1st-LASS is designated as a “first-level” (as opposed to a “first-order”) adjoint sensitivity system, while the 2nd-LASS is designated as a “second-level” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2nd-LASS that involve the imprecisely known boundary parameters. Notably, the 2nd-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.

Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

Second-order sensitivity of eigenpairs in multiple parameter structures

This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method.

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。

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

SQUEEZE FLOW OF A SECOND-ORDER FLUID BETWEEN TWO PARALLEL DISKS OR TWO SPHERES

The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

二阶Radon-Fourier变换与遗传算法结合的快速相参积累算法

针对匀加速运动的高速目标,可以用二阶Radon-Fourier变换(Second-order Radon-Fourier Transform,SRFT)完成对回波信号的相参积累。SRFT算法的原理是通过“速度-加速度”联合搜索来实现目标的运动参数估计,其计算量较大,不满足实时检测的需求。针对这个问题,提出一种基于遗传算法(Genetic Algorithm,GA)的快速实现方法。首先对运动参数集进行编码,设置初始群体;然后通过遗传算法对群体更新迭代,使其能够自发快速地逼近全局最优解,减少不必要的搜索路径;最终快速实现待检测目标的相参积累。仿真结果表明,在保证检测性能的前提下,算法计算量得到有效改善,运算次数减少大约一个量级。

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

基于二阶ETP解析解的空调-建筑电热耦合系统辨识方法

对空调-建筑电热耦合系统进行建模是挖掘空调调节潜力的基础。为解决当前基于二阶等效热参数(ETP)建模研究中存在的拟合精度有限、电热耦合特性考虑不足等问题,文中首先推导了二阶ETP模型解析递推形式,具有高拟合精度、递推值有界、步长灵活可调的优势,可提高模型的准确性、可靠性以及对多样化数据采集技术的适应性。然后,采用平均能效比刻画空调电热转化过程,提出考虑平均能效比的空调-建筑电热耦合解析化模型参数辨识方法,综合利用室内气温拟合机制和制热量拟合机制进行参数寻优。最后,搭建实际测试环境对所提方法性能进行验证。结果表明,该方法能在现有基础上显著提升参数辨识的准确率,从而为能源系统仿真、空调负荷调控等应用提供更加准确可靠的模型基础。

基于EKF-PF算法的退役动力锂电池SOC估计

为准确估计退役动力锂电池的荷电状态(SOC),避免其在储能系统中因放电容量不一致导致运行效果不佳,保障储能系统安全运行,提出了利用扩展卡尔曼粒子滤波算法(EKF-PF)与二阶Thevenin等效电路模型相结合的方法估计退役动力锂电池的荷电状态。该方法首先采用二阶Thevenin等效电路构建退役动力锂电池的等效电路模型,写出观测方程与状态方程;其次利用含遗忘因子的递推最小二乘法(FFRLS)对建立的等效电路模型进行参数辨识;最终通过EKF-PF算法在城市道路循环(UDDS)工况下对退役动力锂电池进行在线SOC估计,并与粒子滤波(PF)算法做对比。实验结果表明,EKFPF算法在估计退役动力电池SOC时能将其平均误差控制在1.23%以内,最大误差控制在3.37%以内,优于PF算法的估计结果。证明了EKF-PF算法在估计退役动力锂电池SOC时具有更高的精度和应用价值。

单相整流器二次纹波抑制的有源功率解耦控制算法

为了解决单相整流器中LC谐振回路频率适应性差的问题,引入有源功率解耦电路代替LC谐振回路抑制母线电压二次纹波,选择直流母线电容分裂拓扑有利于减小支撑电容容值。首先,对有源功率解耦电路的工作模态进行分析,建立了单相整流器和分裂电容有源功率解耦回路数学模型。其次,传统解耦控制算法间接计算解耦参考电压,为提高功率解耦效果,采用二阶广义积分器直接提取电压纹波作为电压参考,并提出一种基于滑模观测器的无电流传感器控制策略,滑模观测器降低了解耦电路成本,提高了抗干扰能力。然后,根据整流器性能指标和功率解耦要求,给出了有源功率解耦回路电感和电容设计依据。最后,对不同拓扑结构的单相整流器进行了稳态和动态实验对比,实验结果证明了控制算法的有效性。

磷酸铁锂电池二阶可变阻容的模型研究

精确的电池模型是动力电池荷电状态(State of Charge,SOC)估计的基础,提高模型精度可从电池内部特性出发。提出二阶阻容可变参数等效电路模型,能够反映电池内部双极化效应,同时用可变的参数描述电池内部动态变化过程。通过对锂离子电池充放电实验和HPPC测试,结合MATLAB拟合工具,辨识出不同SOC下各参数的值,基于SIMULINK搭建仿真模型。对比仿真结果,所建立模型的端电压平均误差为12.36mV,相比于固定参数传统模型的31.50mV,精度提高了60.76%,更能准确描述锂离子电池内部的静动态特性。

不同分数导数下Maxwell杂化纳米流体流动和传热变化的灵敏度分析

研究多孔介质中垂直拉伸板引起的分数阶Maxwell杂化纳米流体流动与传热现象,并考虑二阶滑移边界条件.利用分数阶剪应力和分数阶Fourier定律构建边界层控制方程.然后采用有限差分结合L1算法进行数值求解,并详细讨论分数导数参数增大时,各物理参数对该流体流动与传热影响的灵敏度变化.结果表明,Darcy数和滑移参数对平均表面摩擦系数的影响,以及滑移参数对平均Nusselt数的影响,对速度分数导数比对温度分数导数更敏感.Darcy数对平均Nusselt数的影响只对温度分数导数敏感,与速度分数导数几乎无关.此外,一阶滑移参数比二阶滑移参数对流动和传热的影响更大.

基于改进EKF算法的锂离子电池SOC在线估计

锂离子电池因其能量密度高、自放电率低、污染小等优势,已经在储能电站领域得到广泛应用。针对锂离子电池各项状态预测,首先搭建二阶RC等效电路模型,然后采用带遗忘因子的递推最小二乘法(FFRLS)对模型参数进行辨识,提出一种基于自适应扩展卡尔曼滤波(AEKF)算法的SOC-SOH联合估计方法。在不同电池工况下进行对比验证,结果表明,与扩展卡尔曼滤波(EKF)和无迹卡尔曼滤波(UKF)相比,所提方法预测SOC和SOH的精确度和计算效率均有所提高,具有一定的实用价值。

基于负二阶广义积分正交信号发生器反馈并网电流有源阻尼方法研究

LCL滤波器反馈状态变量实现有源阻尼需要高精度传感器才能具有较好的灵活性和鲁棒性,基于此,提出负二阶广义积分正交信号发生器反馈并网电流的有源阻尼方法,在抑制谐振尖峰的同时,也减少网侧电压背景谐波对并网电流的影响,同时减少传感器的个数,增加系统可靠性。采用极点配置法,围绕系统的稳定裕度设计负二阶广义积分正交信号发生器参数,探讨在该有源阻尼控制系统下LCL参数和电网阻抗变化时系统的鲁棒性。仿真结果表明,所提策略在各方面均有更好效果。

基于λ-PDF和一次二阶矩的不确定性反求方法

为了有效评价测量响应中不确定性对结构参量识别结果的影响,提出一种基于λ概率密度函数(Probability distribution function,PDF)和一次二阶矩的不确定性计算反求方法。采用二次衍生λ-PDF对待识不确定性参量的PDF进行建模。内层通过对参量呈λ-PDF的功能函数采用一次二阶矩法进行正问题求解,得到计算响应的概率分布;外层通过最小化测量响应与计算响应之间的概率分布特征量将不确定性反问题转化为确定性的最优化问题,并用隔代映射遗传算法识别未知参量λ-PDF的参数。本方法不仅有效地实现了结构未知参量PDF的估计,而且与传统基于抽样的统计方法相比,计算效率较高。数值算例和工程应用验证了本方法的可行性和有效性。

基于高阶EKF的锂电池SOC测算精度研究

锂电池荷电状态是电池管理系统运行的前提和核心任务,为能够准确跟踪测算电池SOC值,以18650-20R型锂电池为主要研究对象,建立二阶Thevenin等效电路模型,经脉冲特性实验对电路模型参数进行辨识,在恒流、脉冲放电及Fuds工况下验证模型的准确性,并在此基础上实现了利用一阶、二阶及高阶EKF算法对电池荷电状态的估计。最后通过Matlab仿真结果验证,高阶EKF在锂离子电池动静态SOC测算时均具有更高的测算精度。

基于R-SOBI的结构模态参数辨识方法

提出了一种基于稳健SOBI算法提取结构/系统的频率、阻尼比及模态振型的方法。运用该法提取系统/结构模态参数的步骤为:首先利用稳健SOBI的盲源分离方法采集的信号进行分离,然后将分离矩阵作为结构/系统的模态振型矩阵,最后再对各个分离后的单自由度信号提取频率、阻尼比参数。研究结果表明,提出的方法可以准确提取出结构/系统的模态参数,尤其是即使噪声环境下仍然能准确提取出系统的模态振型矩阵。

基于二阶振荡粒子群算法的铝合金Y-U硬化模型参数反演

针对铝合金的Y-U硬化模型在标定过程中参数的迭代求解特点,采用二阶振荡粒子群算法(PSO)对参数进行了反演分析求解。首先,建立参数反演的数学模型与残差目标函数;然后,基于图解法的参数近似解确定部分参数取值,对选定的5个待反演参数进行求解域标定;最后,采用具有跳出局部最优解特性的二阶振荡粒子群算法进行目标函数的优化求解。结合7075-O铝合金的拉压循环实验数据,实现了Y-U硬化模型参数的反演寻优。研究结果表明:二阶振荡粒子群算法前期渐进收敛,强化全局搜索,快速逼近最优解;后期振荡收敛,跳出局部最优,提高反演精度。

斜拉-自锚式悬索组合体系桥梁结构参数变化对活荷载效应影响

基于线性二阶和非线性理论对一座多塔斜拉-自锚式悬索组合体系桥梁的活载效应进行对比分析,来确定合理的活载计算分析方法;在活荷载作用下,通过考虑不同的主梁、桥塔及主缆刚度等结构参数,来分析研究结构主要部件的控制截面受力情况。分析结果表明:采用线性二阶和非线性理论对比分析后,主跨160 m的斜拉-自锚式悬索组合体系桥梁的活载效应计算误差在5%以内,在工程中可采用线性二阶理论进行活载作用分析;在活载作用下,副塔及主塔刚度对结构受力性能影响较小,主梁和主缆刚度对结构受力性能影响较大,在同类桥梁设计中应给予足够重视。