Optimization of Well Position and Sampling Frequency for Groundwater Monitoring and Inverse Identification of Contamination Source Conditions Using Bayes’Theorem

Coupling Bayes’Theorem with a two-dimensional(2D)groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity(M),release location(0 X,0 Y)and release time(0 T),based on monitoring well data.To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters,a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy.To demonstrate how the model works,an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed.The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index.The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events.Based on the optimized monitoring well position and sampling frequency,the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach.The case study results show that the following parameters were obtained:1)the optimal monitoring well position(D)is at(445,200);and 2)the optimal monitoring frequency(Δt)is 7,providing that the monitoring events is set as 5 times.Employing the optimized monitoring well position and frequency,the mean errors of inverse modeling results in source parameters(M,X0,Y0,T0)were 9.20%,0.25%,0.0061%,and 0.33%,respectively.The optimized monitoring well position and sampling frequency canIt was also learnt that the improved Metropolis-Hastings algorithm(a Markov chain Monte Carlo method)can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization,which significantly improved the accuracy and numerical stability of the inverse modeling results.

EXACT EVALUATIONS OF FINITE TRIGONOMETRIC SUMS BY SAMPLING THEOREMS

We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli＇s numbers play a role similar to that of Euler＇s in the old ones. Our technique differs from that of Byrne-Smith （1997） and Berndt-Yeap （2002）.

Sampling theorem for multiwavelet subspaces

Unlike scalar wavelets, multiscaling functions can be orthogonal, regular and symmetrical, and have compact support and high order of approximation simultaneously. For this reason, even if multiscaling functions are not cardinal, they still hold for perfect A/D and D/A. We generalize the Walter＇s sampling theorem to multiwavelet subspaces based on reproducing kernel Hilbert space. The reconstruction function can be expressed by multiwavelet function using the Zak transform. The general case of irregular sampling is also discussed and the irregular sampling theorem for multiwavelet subspaces established. Examples are presented.

APPROXIMATE SAMPLING THEOREM FOR BIVARIATE CONTINUOUS FUNCTION

An approximate solution of the refinement equation was given by its mask, and the approximate sampling theorem for bivariate continuous function was proved by applying the approximate solution . The approximate sampling function defined uniquely by the mask of the refinement equation is the approximate solution of the equation , a piece-wise linear function , and posseses an explicit computation formula . Therefore the mask of the refinement equation is selected according to one' s requirement, so that one may controll the decay speed of the approximate sampling function .

Vector sampling theorem for wavelet subspaces

The vector sampling theorem has been investigated and widely used by multi-channel deconvolution, multi-source separation and multi-input multi-output （MIh40） systems. Commonly, for most of the results on MIMO systems, the input signals are supposed to be band-limited. In this paper, we study the vector sampling theorem for the wavelet subspaces with reproducing kernel. The case of uniform sampling is discussed, and the necessary and sufficient conditions for reconstruction are given. Examples axe also presented.

基于ARCS模型的翻转课堂教学设计

以“取样定理”为例,提出采用ARCS模型进行翻转课堂教学设计的案例。教学内容设计注重核心价值观的传播,从取样定理形成的历史脉络引出课程思政;运用多种教学手段,提升学生注意力;重视学习内容的关联设计,学生端倚重信息技术应用,及时反馈,提升学生自信度;学习评价注重应用性,提升学习满意度。教学实施结果表明,该教学设计能调动学生的课堂热情,师生满意度高。

从奈奎斯特采样到压缩感知拓展教学方法

从“信号与系统”到“数字信号处理”,采样定理都是重要的教学内容。但是在工程应用中,产生大量数据造成存储空间的极大浪费,而压缩感知突破奈奎斯特采样定理的限制,能够实现远低于奈奎斯特频率的采样。为适应新工科背景下的教学改革,让学生接触前沿研究成果,压缩感知被引入作为传统奈奎斯特采样定理教学的补充和拓展,取得良好的教学效果。

融入课程思政的“抽样定理”教学案例设计与实践

课程思政是实现高校立德树人根本任务的重要举措,该文以“信号与系统”课程中的“抽样定理”为例,挖掘课程思政元素,探索案例式教学的设计与实践。深入分析课程特点,重塑课程教学内容,以先进的教学手段和教学资源建设为载体,设计思政教育融入教学的全过程,培养学生勇于探索的科学精神,增强学生科学报国的决心。课程思政的探索实践,对优化课程思政建设、提升学生工程实践能力、培养学生爱国精神有重要意义。

局部平均随机过程随机场采样定理

随机信号采样定理的相关研究几十年来一直是采样定理主流方向之一,在理论和实际应用两方面都受到信息领域和数学领域的广泛关注。近年来,采样理论在随机过程和随机场的局部平均采样方面得出了一系列研究成果。首先,分析了采样定理在应用中的缺陷和局限性。其次,对近几年在随机过程、高维随机过程、随机场、时空随机场局部平均采样定理方面的发展和相关结论做了系统介绍。最后,对基于混合范数的时空随机场采样逼近、采样形式、信号形式、范数形式等问题进行了展望。结果表明:局部平均的采样方式提高了采样的精度和逼近效果,随机场局部平均采样理论在海浪参数反演和海洋污染监测方面有重要应用。特别是基于混合范数的时空随机场采样理论的研究不仅具有重要的理论价值,而且对于工程领域也有应用价值。

基于压缩感知的可见光通信定位一体化系统性能分析

为了降低到达时间(time of arrival, TOA)算法的接收信号采样率需求,基于正交频分复用(orthogonal frequency division multiplexing, OFDM)系统中信号具有频谱稀疏性的特点,提出了基于压缩感知算法的可见光通信定位一体化系统。仿真结果表明,采用压缩感知算法后,通信系统仅需原始采样率为100 MHz时数据量的60%即可使误码率降至10-3以下,定位系统仅需原始采样率为800 MHz时数据量的2.1%即可准确估计收发端距离,远低于采样定理所需数据量,证明了所提算法的优越性。此外,在引入噪声后,通过提高压缩感知算法的测量数据比例,一体化系统仍能在奈奎斯特采样率以下保持良好的通信与定位性能。

Computing Recomposition of Maps with a New Sampling Asymptotic Formula

The aim of the present paper is to state an asymptotic property &#929 of Shannon’s sampling theorem type, based on normalized cardinal sines, and keeping constant the sampling frequency of a not necessarilly band- limited signal. It generalizes in the limit the results stated by Marvasti et al. [7] and Agud et al. [1]. We show that &#929 is fulfilled for any constant signal working for every given sampling frequency. Moreover, we conjecture that Gaussian maps of the form e-&#923t2 ,&#923&#8712R+, hold &#929. We support this conjecture by proving the equality given by for the three first coefficients of the power series representation of e-&#923t2 .

Truncation and aliasing errors for Whittaker-Kotelnikov-Shannon sampling expansion

Let B^pΩ, 1 ≤ p 〈 ∞, be the space of all bounded functions from Lp（R） which can be extended to entire functions of exponential type Ω. The uniform error bounds for truncated Whittaker-Kotelnikov-Shannon series based on local sampling are derived for functions f ∈ B^pΩ without decay assumption at infinity. Then the optimal bounds of the aliasing error and truncation error of Whittaker-Kotelnikov-Shannon expansion for non-bandlimited functions from Sobolev classes L/（Wp（R）） are determined up to a logarithmic factor.

ON TRUNCATION ERROR BOUND FOR MULTIDIMENSIONAL SAMPLING EXPANSION LAPLACE TRANSFORM

The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.

Optimizing the atmospheric sampling sites using fuzzy mathe-matic methods

A new approach applying fuzzy mathematic theorems, including the Primary Matrix Element Theorem and the Fisher Classification Method, was established to solve the optimization problem of atmospheric environmental sampling sites. According to its basis, an application in the optimization of sampling sites in the atmospheric environmental monitoring was discussed. The method was proven to be suitable and effective. The results were admitted and applied by the Environmental Protection Bureau (EPB) of many cities of China. A set of computer software of this approach was also completely compiled and used.

瞬变电磁勘探中采样率与地电结构重建的必要条件

提高瞬变电磁法的探测精度,不仅需要加密测点还需要加密时窗。然主流瞬变电磁仪为保持各测量窗口的样本数基本不变,使采样率随发射频率的降低而降低,所增加的时窗数以减少参与统计平均的样本量为代价降低了原有的信噪比。论文以Phoenix Geophysics的V8仪器为例,分析了瞬变电磁仪信号检测的主要步骤,以Wiener-Khnchin大数定律为依据,提出了在增加时窗的同时,不减少参加每个时窗统计平均的样本数,形成固定高采样率接收机方案。从Nyquist采样定理出发,给出了以长度为量纲的探测精度的定义,根据重建地电结构的必要条件,确定了点线距和时窗间隔与地电信号频谱最小周期的关系式。以大同达子沟煤矿多层积水采空区的探测为例,展现了在地球物理前提存在的情况下,因欠采样造成的混叠和通过附加条件获得的精细地电剖面。地电结构重建的必要条件说明,满足Nyquist采样定理不一定能够重建地电结构,但不满足这个定理则一定不能完整地重建。

采样理论中的正交变换问题

采样理论是信号处理教学的重要内容,从信号空间及投影角度出发,论证了采样定理与傅里叶变换类似,都属于信号的正交变换过程,基于信号先验知识,采用不同内插函数的模数转换扩展了采样理论的应用范围,有助于加深对采样理论抽象概念的理解与掌握。

关于非齐次树上马氏双链的一个强偏差定理

该文研究了非齐次树上马氏双链的一个强偏差定理.首先给出了非齐次树上马氏双链的定义和样本散度的概念,然后利用构造非负鞅的方法,给出了关于非齐次树上马氏双链的一个强偏差定理.

非齐次树上马氏双链转移矩阵的一个强偏差定理

该文研究非齐次树上马氏双链转移矩阵的一个强偏差定理.首先给出非齐次树上马氏双链的定义和样本散度的概念,然后利用构造非负辅助鞅的方法,给出了关于非齐次树上马氏双链转移矩阵的一个强偏差定理.

关于树指标马氏双链随机矩阵的一个强偏差定理

本文研究树指标马氏双链随机矩阵的一个强偏差定理.首先给出非齐次树指标马氏双链样本相对熵率的概念,然后利用构造非负辅助鞅的方法,给出关于非齐次树指标马氏双链随机矩阵的一个强偏差定理.

软硬件结合的声音抽样与恢复实验

时域抽样是“信号与系统”课程及其工程应用中重要知识点,但课堂教学内容注重理论分析,难以提高学生的学习兴趣。通过设计“敲琴声音抽样”实验,利用计算机声卡中的A/D、D/A转换芯片和Simulink软件,软、硬件结合,实现系统调试、数据录取与数据分析,实现抽样频率可调的实际抽样与恢复实验。通过实验设计、调试以及对实验数据的时频域分析,可加深学生对时域抽样定理的理解,进一步培养其创新精神和实践能力。