Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response

This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1st- and 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.

Illustrative Application of the 2^nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.

UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities

This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.

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.

一种带2阶补偿的高精度带隙基准源

介绍了一种采用2阶补偿技术的高精度带隙基准电路。通过增加预基准电路,提高了电源抑制比。通过PTAT2电路补偿VBE的2阶项,改善了基准电压的温度特性。Hspice仿真结果表明,在-55℃~125℃范围内,温度系数为4.3×10-6V/℃,低频时PSRR为114 dB。

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.

Stochastic ordering of medians in exchangeable trivariate normal vectors

In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.

Optimized Pump Power Ratio on 2nd Order Pumping Discrete Raman Amplifier

By optimizing pump power ratio between 1st order backward pump and 2nd order forward pump on discrete Raman amplifier, we demonstrated over 2dB noise figure improvement without excessive non-linearity degradation.

基于Volterra滤波器的参量阵扬声器互调失真补偿研究

针对单边带调制方法预处理的参量阵扬声器系统在复杂信号输入情况下存在明显互调失真的问题,引入Volterra滤波器模型和简化的一维Volterra滤波器模拟了其互调失真。设计了相应的逆滤波器,并对其抑制系统互调失真的性能进行了实验对比。结果表明,所设计的逆滤波器都能有效降低系统的互调失真,而后者具有较低的计算复杂度。

随路遥泵系统二阶泵浦方式泵浦性能分析与优化

为了解决随路遥泵系统采用传统二阶泵浦方式时出现自激的问题,提出了基于滤波隔离技术的降低多径干扰方案和基于混合型光纤技术的降低非线性系数方案.滤波隔离技术通过将滤波隔离单元放置于光纤线路中来有效改善多径干扰现象;混合型光纤技术通过采用大的有效面积光纤和普通光纤混合结构降低非线性效应.理论分析表明减少泵浦光的多次反射可减弱多径干涉;增加光纤有效面积可以降低非线性系数.实验结果表明:采用由波分复用器和隔离器组成的滤波隔离单元,进入远程增益单元的泵浦功率可提高1.2dB;采用20km EX2000和80km G.652混合型光纤结构,进入远程增益单元的泵浦功率可提高1dB.该研究对降低自激影响的随路二阶泵浦的研制和应用具有一定意义.

对梅森素数分布规律的一种猜想

提出了关于梅森素数分布规律的一种猜想：梅森素数的指数ｐ的二阶差分序列每１０项中都有６项非负值与４项负值

SRTM基线测量中的非线性滤波方法

基线测量精度对于SRTM高程测量精度影响很大,SRTM基线测量的关键是CCD相机对副天线上的LED灯进行质心定位,其结果含有的误差在后期干涉处理时需进一步滤除。鉴于LED运动呈非线性,本文对无迹RTS平滑,粒子滤波,无迹粒子滤波3种非线性滤波进行了研究,使用依赖于幅度的刚性模型叠加不同标准差的加性噪声模拟测量值,改进状态空间模型与滤波器参数设置,分别在有/无加速度计辅助测量的条件下进行仿真,结果表明无迹粒子滤波的效果优于其他方法,使用加速度计对于滤波精度普遍有所提高。

优序融资理论推论二在我国上市公司的验证研究

美国财务学家斯蒂芬.罗斯(Ross)根据优序融资理论提出了三大推论,这些推论在我国上市公司是否有效?本文以第二推论为分析对象,以我国制造业盈利上市公司为研究样本,从负债率的多角度用统计分析的方法进行研究,结果显示企业的盈利能力与企业的有息负债率负相关,从而证实了优序融资理论推论二在我国上市公司的实证有效性。

巡航导弹高度跟踪制导律研究

针对巡航导弹弹道对飞行高度的控制需求,提出了两种实现导弹高度跟踪的制导律模型,一种将高度控制回路转化为经典控制理论中的二阶无静差系统,通过调节系统稳定性实现高度跟踪;另一种引入速度补偿项,构建了期望高度规律与期望过载之间的非线性关系,实现高度跟踪。建立了导弹运动模型,利用典型高度规律,对所设计制导律进行数值仿真,对比分析了各自的特点。所设计的制导律已得到工程应用验证。

Contribution in Information Signal Processing for Solving State Space Nonlinear Estimation Problems

In this paper, comprehensive methods to apply several formulations of nonlinear estimators to integrated navigation problems are considered and developed. The problem of linear and nonlinear filters such as Kalman Filter (KF) and Extended Kalman Filter (EKF) is stated. Analog solution which is based on fisher information matrix propagation for linear and nonlinear filtering is also developed. Additionally, the idea of iterations is included through the update step both for Kalman filters and Information filters in order to improve accuracy. Through this development, two new formulations of High order Kalman filters and High order Information filters are presented. Finally, in order to compare these different nonlinear filters, special applications are analyzed by using the proposed techniques to estimate two well-known mathematical state space models, which are based on nonlinear time series used to apply these estimation algorithms. A criterion used for comparison is the root mean square error RMSE and several simulations under specific conditions are illustrated.

Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Expressions and CPU-Time Comparisons for Computing 1^st-, 2^nd- and 3^rd-Order Sensitivities

This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 7477 imprecisely known (uncertain) model parameters which have nonzero values. These parameters are as follows: 180 microscopic total cross sections;7101 microscopic scattering sections;60 microscopic fission cross sections;60 parameters that characterize the average number of neutrons per fission;60 parameters that characterize the fission spectrum;10 parameters that characterize the fission source;and 6 parameters that characterize the isotope number densities. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 7477 first-order and 27,956,503 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters. These works showed that largest response sensitivities involve the total microscopic cross sections, which motivated the recent computation of all of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. It turned out that some of these 3rd-order cross sections were far larger than the corresponding 2nd-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4th-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4th-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross section and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.

用琼斯传输矩阵法研究二阶偏振模色散的统计特性

利用琼斯传输矩阵法研究了二阶偏振模色散的统计特性。对数值模拟中出现的偏振模色散随步长变化的问题做了相应的修正 ,利用修正后的模型得到了偏振模色散矢量的频率相关特性 ;模拟了偏振模色散值为 2 5ps时二阶偏振模色散的几率分布 ,所得结果与理论结果能够很好地吻合 ;简单地分析了脉宽为 8ps的高斯脉冲在此条件下的展宽情况 ,指出了高阶补偿的必要性。

A matrix-perturbation-theory-based optimal strategy for small-signal stability analysis of large-scale power grid

In this paper,a sensitivity matrix based approach is proposed to improve the minimum damping ratio.The proposed method also avoids burdensome deviation calculations of damping ratio of large-scale power grids when compared to the Small-Signal-Stability Constrained Optimal Power Flow(SSSC-OPF)approach.This is achieved using the Matrix Perturbation Theory(MPT)to deal with the 2nd order sensitivity matrices,and the establishment of an optimal corrective control model to regulate the output power of generating units to improve the minimum damping ratio of power grids.Finally,simulation results on the IEEE 9-bus,IEEE 39-bus and a China 634-bus systems show that the proposed approach can significantly reduce the burden of deviation calculation,while enhancing power system stability and ensuring calculation accuracy.