The error distribution testing plays an important role in linear regression as distribution misspecification seriously affects the validity and efficiency of regression analysis. The least squares (OLS) residuals are often used to construct test statistics; in order to overcome the non-independent and identically residuals, the best linear unbiased scale (BLUS) residuals are applied in this paper, which, unlike OLS residuals, the residuals vector is identically and independently distributed. Based on the BLUS residuals, a new test statistic is constructed by using the sample random distance between sample quantile and quasi sample quantile derived from the null distribution, and the goodness-of-fit test of error distribution in the linear model is studied. The powers of the new tests under certain alternatives are examined. They are more powerful tests for the hypotheses concerned.

This paper studies simultaneous confidence intervals (SCIs) for the ratios of means of zero-heavy log-normal populations. We propose four SCIs by using the Bonferroni adjustment principle. Specifically, we integrate the fiducial generalized pivotal quantity (FGPQ) with the other two statistics to have two FGPQ-based methods and incorporate the variance estimates recovery (MOVER) with FGPQ to have two MOVER-based methods. We develop expedient algorithms to implement the methods, and conduct extensive simulation studies to evaluate and compare the performance of the four methods, which show that our methods perform well. We also apply the methods to analyse a real data set as an illustration.

针对新形势下国防和军队建设对铸魂育人提出的"四有"新要求,通过梳理"有血性"的本质内涵,提出在军校教育训练中,不仅要有体力"马拉松"式的血性训练,而且要有脑力"马拉松"式的血性训练.利用数学隐性教育的功能,剖析了数学教育对脑力"马拉松"式的血性训练的可行性和基本措施.

针对运动声源无源测距问题,给出了目标方位、多普勒频移和距离特征量作为测量信息来估计目标初始距离的方法.通过伪线性化的处理方法,构造了一个异方差的线性模型.在声呐平台直航条件下,证明了非径向运动的声源目标,利用3个目标方位、2个多普勒频移和2个距离特征量的观测信息,可以唯一地确定目标的距离、速度和航向,而仅利用目标方位和距离特征量的观测信息,系统是不可观测的.蒙特卡洛数值模拟表明:对于初始距离5 nm(海里)的情形,三维信息测量方法比参考方法的目标距离的平均收敛时间要少200 s左右,收敛时间标准差要少40 s左右.随着初始距离的增加,两种方法收敛时间差有变大的趋势,这意味着三维信息构造的方法的稳健性优于参考方法.实验数据也进一步验证了在300 8左右,目标距离的估计逐渐趋于收敛.因此,该方法可以在稳定的干涉结构条件下,实现运动声源的无源定位.

论文分析了数学素养的内涵、构成要素以及其行为表现,比较了传统的课堂教学与数学素养视域下的课堂教学的不同,概括出数学素养视域下的课堂教学的三个主要特征:一是重视培养观念成分数学素养中的整体观素养,加强知识结构的系统性,引导学生从整体性上认识数学的内容;二是重视知识成分数学素养中的关联性和策略性知识教学,加强数学的思想性教学和数学思维的培养;三是重视精神成分的数学素养中的文化价值,加强数学教育的育人性.论文以此为指导,对正项级数的比值审敛法的课堂教学进行了教学设计,突出了该次教学内容中蕴含的化归和类比数学思想方法以及辩证思维的设计,收到了满意的教学效果.

针对水中运动声源定位问题,建立了一种基于声场干涉结构谱向量相似度匹配的目标运动参数估计方法.结合声场干涉结构水平纵向相关特性,利用目标辐射噪声LOFAR谱图中不同频率的谱值序列,基于两方位-两距离目标运动要素计算方法获取的目标距离解向量,构造声场干涉结构谱向量相似度匹配代价因子,实现目标运动参数估计.仿真数据与试验数据验证结果表明:在绘制的目标运动要素解算结果可视化分布图中可清晰呈现出目标初距、航向和速度结果.该算法实现过程简单、解算效率高,对目标方位误差有较好的鲁棒性.

以海洋内波流场和密度场数值模拟结果作为外部驱动数据,提出基于数据驱动的潜体受内波影响的仿真分析方法,利用六自由度运动方程计算了潜体以不同潜深和初始速度通过模拟内波区时的运动响应,并根据运动响应的定量分析结果和非线性内波特点,给出了潜体水下航行安全及操纵的初步建议,该研究对于潜体水下航行安全具有重要应用价值.

本文针对在浅海环境中声呐作用距离估计不准确这一问题,利用Kraken模型研究了4类声速剖面不同结构变化对声呐作用距离的影响.研究结果显示,对于不同的均匀层声速剖面,相差2m/s的声速剖面对声呐作用距离有影响.对于负梯度声速剖面和正梯度声速剖面,声速剖面结构变化对声呐作用距离影响较大,进一步揭示了声速剖面曲线的凹凸性结构对于声呐作用距离也有较大影响.对于负跃层声速剖面,在跃层厚度不变的情形下,温度梯度变化率和跃层以上均匀层声速对声呐作用距离有影响.因此,在声呐的实际工作中,需要考虑声速剖面的结构变化带来的不确定影响,不仅要给出某个声呐作用距离,还要明确某个置信区间.

目前,集合预报方法是解决单一预报结果不确定性问题的一种有效方法,其中初始扰动的生成是集合预报的关键技术之一.利用高分辨率的ROMS区域海洋模式,基于增长模繁殖(BGM)的思想,研究了海洋集合预报中,初始随机扰动的生成及其在繁殖循环过程中随时间的发展特征.结果表明:初始扰动的发展与背景流场结构有一定联系,而BGM型初始扰动表现为良好的动力学结构,在对预报结果的影响方面,BGM型扰动发展强区内初始扰动的影响大于扰动发展弱区内初始扰动的影响;初始扰动发展强区内具有BGM型结构的初始扰动的影响要大于无明确结构的初始扰动的影响.

The shape estimation of vector towed array is investigated by using attitude data and the depth data of a single sensor in 2-dimensional domain under the condition which the array shape is parabola.By researching the relationship between the attitude angle data and the directional derivative of tangent line on one hydrophone position of the array,a nonlinear model with equal constrains is established by least squared method,and by using parameter transform,the analytic algorithm of the model is presented.The related numerical simulations demonstrate that the shape estimation of towed array,which supposed parabola shape,can be obtained by using depth data of single sensor and attitude data of some hydrophones.Under the same numbers of hydrophone,the larger the error of attitude data,the larger the error of array estimation.For the identical distribution of the error of attitude data,the more the numbers of hydrophone,the less the error of shape estimation.

Bearings-only target tracking is a representative nonlinear problem,pseudo linear target tracking filter is a sort of important method solving this problem in theory and engineering. To the observability question of system,which produced by pseudo linearizing the measured model of bearings-only,a new method solving target elements is presented which using time-varying optimal condition number. In theory,the optimal multiplier factor is obtained to improve the observability of system. The new method is better than the classical pseudo-linear method,which verified using results of both numerical simulation and sea experiment in system condition number and convergence probability of parameter estimators.

Focusing on the rapid prediction of acoustic field uncertainty in environment with temporal and spatial sound speed perturbation, evolvement of sound speed structure over time is predicted based on the ocean-acoustic coupled model to obtain the uncertainty distribution of the vertical structure of sound speed. Further, a method combining the arbitrary polynomial chaos expansion with the empirical orthogonal function is proposed to reduce the dimensionality of uncertain parameters and to obtain the uncertainty distribution of the acoustic field. Simulations have shown that the computational complexity can be reduced by 2 orders of magnitude compared to the conventional polynomial chaos expansion while ensures the same precision. Moreover, the computational complexity is not influenced by the complexity of the sound speed profile. The acoustic field and uncertainty predicted in uncertain environment by proposed method also have been tested with the experimental data.

The estimation of target elements using least square method are not optimal unbiased estimates as the pseudo linear target tracking filter based on non-correlation errors of model and equal variance.In order to solve the question,a heteroscedastic pseudo-linear model was established by using new parameter variables,based on the model,a weighted method for target motion analysis was presented.The heteroscedastic part of error of the pseudo-linear model was considered.Firstly,the ratio of instantaneous distance and initial distance were esti-mated by using bearings and the estimate of the heteroscedastic part of model error was obtained,then,By using the weighted least squared method,the optimal unbiased estimates of target elements were obtained in theory. Numerical simulation results showed that the new method was better than the classical pseudo-linear methodt.

Considering the filter properties of the long horizontal line array (HLA) to the sound field modes,we established an adaptive optimal method to design HLA weights,which can change the filter pass band with the frequency.Using the normal modes theory and combining with the feature of the sound field HLA beam forming,and analyzing the differences of definition and slope in the LOFAR (Low Frequency Analysis Recording) spectrogram between the singlehydrophone and the beam former,a frequency adaptive optimal estimate was obtained by solving a quadratic optimization model with linear equality constraint.The numerical simulation and the experimental data analysis indicated that we can obtain the beam former signal with the designed optimal array weight which was made up by the Surface-Reflected Bottom-Reflected modes or Non-Surface-Reflected Bottom-Reflected modes.The slope of striations in the signal spectrogram fitted well with the theoretical analysis.

研究了一种高频水声信号的滤波问题,提出了一种改进的经验模态分解加小波阈值滤波方法.首先对信号进行带通滤波处理,再进行经验模态分解,将分解得到的各个模态转换为频域信号,采用小波软阈值方法对这些频域信号进行滤波,最后对信号进行重构,并转换为时域信号.经数值仿真与试验数据验证表明此方法是可行有效的,与原基于经验模态分解的小波阈值滤波方法相比,本方法滤波效果较好:对不同输入信噪比的仿真信号进行滤波后,本方法的输出信噪比最大提高17.41 dB,滤波后所得信号与加噪前纯信号的相关系数最大提高0.90;对实验数据进行滤波后,不同时间段信号的相关系数最大提高0.62.

This work studies a method for filtering intermediate and high frequency underwater acoustic signal based on the ensemble empirical mode decomposition (EEMD) and the wavelet soft threshold (WST) methods. Firstly, the band-pass filter is used to denoise the signal with noise. Secondly, the EEMD method is used to process the signal, then the intrinsic mode functions (IMFs) are transformed to signals in frequency domain, respectively. Thirdly, the IMFs in frequency domain are filtered by using the WST method. Finally, the IMFs are added to reconstruct the signal in frequency domain, and then the signal in time domain is obtained. This method and the original WST method are used to filter the underwater acoustic signal with different frequencies respectively. The following acquaintances can be observed: When the frequency of the underwater acoustic signal is less than 800Hz, the original filtering method can obtain better result. However, when the frequency is more than 800Hz, the new method can get better result. In order to obtain the satisfied filtering result, the filtering method should be chosen based on the frequency of the underwater acoustic signal.

A method of applying target bearings and Doppler frequency shift of line spectrum to estimate the motion parameters of a constant velocity target is presented in this paper. The method is also valid to target motion analysis without observer maneuver. First, two kinds measurement information of target is linearized and two linear models are constructed. Then using least squared method, two pseudo linear filters are obtained, the arithmetic of target elements estimation is obtained by fusion method. The main advantages of this method comparing with the former results are as follows: 1) Two linear estimators are two-dimensional systems, so the observability of them is enhanced. 2) It doesn’t necessary to estimate the original signal of line spectrum in Doppler frequency shift estimator. Numerical simulations are made to show the performance of arithmetic under different measurement errors, and the effectiveness of the proposed method is verified by experiment results.

针对声纳探测性能预报的需求,建立了海洋-声学-探测模型,实现了并行计算.该模型将海洋数值预报模式、声学模式与海洋观测资源进行整合,辅以战术需求,实现了对水声环境和声纳探测性能的动态预报和估计.同时,结合高性能计算机系统,设计并实现了模型的并行算法,结果表明,该程序具有较高的并行性能,较好地满足了声纳探测性能预报对实效性的要求,为形成业务化海洋水声环境预报能力打下了良好的基础.

考虑到海洋环境的时空变化对水声环境不确定性的影响,建立了海洋声学耦合数值模式,实现了并行计算.该模式将声学计算纳入到运动的海洋中,从而实现了对水声环境的动态预报和估计.同时,采用集合预报方法对典型断面的温度垂直结构、实验海区声速剖面和传播损失进行预报,并给出了声速剖面的预报误差、不同深度与频率下,传播损失90％的概率区间以及声速、传播损失、声呐作用距离的不确定性直方图.结果反映了海洋时空变化对水声环境不确定性的影响,量化了水声环境中不确定性的大小.实验结果表明该方法可以刻画海洋动态变化引起的水声环境不确定性,并对其进行了量化和描述.

地声参数的不确定性对水声传播具有重要的影响.通过贝叶斯理论建立水声环境不确定性推理模型,理论推导了地声参数的似然函数以及地声参数和传播损失的后验概率密度,并采用MCMC(Markov Chain Monte Carlo)进行了仿真计算,给出了地声参数的二维后验联合概率密度和一维边缘概率密度,在此基础上对传播损失的不确定性进行了估计,得到了传播损失80％的可信区间.仿真和实验结果表明,该方法适用于地声参数反演和不确定性估计,并能获取因地声参数不确定性导致的传播损失不确定性估计.