【SOEE3250】Inverse Theory

这篇具有很好参考价值的文章主要介绍了【SOEE3250】Inverse Theory。希望对大家有所帮助。如果存在错误或未考虑完全的地方,请大家不吝赐教,您也可以点击"举报违法"按钮提交疑问。

Q1. A racing car needs to be assessed for performance. In a time trial, measurements are made of its position at a series of times. Assuming that the car has (unknown) constant acceleration a  and (unknown) initial speed u and (known) zero initial position, the task is to fit the mathematical model x = ut + ½ at2, where x is the distance travelled at time t.

  1. For the inverse problem, write down the model and data vectors.  [2]
  2. Write down the matrix G that connects the data and model vectors.    [3]
  3. Ignoring the uncertainty (assuming accurate measurements of distance), write down in matrix form the equation giving the least squares estimate of the model vector. You should write in numbers whereever possible, but there is no need to actually calculate the resulting vector.    [4]
  4.  Write down the covariance matrix Qdd for the observations and include the units. [2]
  5. Write down the model vector estimate using the best linear unbiased estimator in matrix form, substituting numbers wherever possible. There is no need to actually calculate the resulting vector.  [3]
  6.  Explain each of the four terms in a single sentence: best linear unbiased estimator.

(Write 4 sentences, one for each term).    [4]

  1. How might you quantify the uncertainty of your estimate using the BLUE of the model parameter a using bootstrapping?    [3]
  2. A colleague suggests that the model needs to be revised: they believe that a better model is of the form x = ut + bsin(t π/40) + ce(t/10) 

for unknown constants u, b and c.

Ignoring uncertainty, write down the new model vector and the new matrix G that connects the data and model vector. [4]

 Four measurements, d1 – d4, are made of the volume at times: t = 0, 1, 2, 3 days, from which you would like to infer the unknown parameters using an unweighted least squares method.

  1. Is this inverse problem linear or nonlinear? [1]
  2. If the volume V is measured in m3 and time is measured in days, what is the unit of each of the model parameters? [2]
  3. You now assert a guess of the four model parameters. What is the update of the model vector that leads to an improved estimation of the unweighted least squares solution?  There is no need to multiply out any matrices in your answer, but you should include as many numeric matrix entries as possible.  [8]
  4. Describe how you might implement this in an iterative scheme             [4]
  5. You find an answer that is converged. What confidence can you place in your answer? [2]
  6. Describe how you might check your answer using the neighbourhood algorithm. [8]

Q3.  The figure below shows a 2-D seismic tomography experiment carried out in a laboratory on a piece of rock measuring 30 cm by 20 cm.  The lines with arrows represent the paths of five seismic rays through the rock, the measured travel times for each of which is given below:

Ray Number 1 2   3     4        5        

Time (ms) 440 615     525       817      545     

In the model set-up, the rock is divided into six 10x10 cm blocks, as shown, and the goal is to determine the slowness of each of the blocks, assumed constant in each block. The model vector m should describe the slowness in each block taken in alphabetical order.

 

  1. For each block, write down whether it is under, exactly or over determined.  [6]
  2. Write down the system d = Gm for this problem, specifying each of d, G and m using numerical values where possible. [6]
  3. A student computes the singular values of the matrix G, producing the vector

[2.37607898 1.84775907 1.41421356 0.76536686 0.59518794].

What does this tell you about the existence of model and data null spaces and the numbers of spanning vectors (i.e. their dimension)? [3]

d) The measurements of ray 5 is now judged to be too much in error, and ray 5 is now ignored.  What will change in terms of the data and model null spaces?   [4]

e) Write down the new spanning vector that appears and specify which of the null spaces it lies in.        [3]

f) Ray 5 is now replaced by a different measurement (see below).  What will change in terms of the data and model null spaces ? [3]文章来源地址https://www.toymoban.com/news/detail-812206.html

到了这里,关于【SOEE3250】Inverse Theory的文章就介绍完了。如果您还想了解更多内容,请在右上角搜索TOY模板网以前的文章或继续浏览下面的相关文章,希望大家以后多多支持TOY模板网!

本文来自互联网用户投稿,该文观点仅代表作者本人,不代表本站立场。本站仅提供信息存储空间服务,不拥有所有权,不承担相关法律责任。如若转载,请注明出处: 如若内容造成侵权/违法违规/事实不符,请点击违法举报进行投诉反馈,一经查实,立即删除!

领支付宝红包 赞助服务器费用

相关文章

  • 鸿沟理论(The Chasm Theory)介绍

    鸿沟理论由Jeffery Moore(杰弗里 摩尔)于1991年提出,距今已有 30 年时间,但该理论至今依然奏效,另外该理论也在 CNCF 项目的成熟度划分中得到应用。本文将介绍”鸿沟理论“相关的一些知识,希望能够引发大家对技术选型、新技术推广的一些思考。更多“鸿沟理论”相关知识

    2024年02月05日
    浏览(42)
  • 创宇区块链|Inverse Finance 安全事件分析

    北京时间 2022 年 4 月 2 日晚,Inverse Finance 借贷协议遭到攻击,损失约 1560 万美元。知道创宇区块链安全实验室第一时间跟踪本次事件并分析。 基础信息 攻击tx1:0x20a6dcff06a791a7f8be9f423053ce8caee3f9eecc31df32445fc98d4ccd8365 攻击tx2:0x600373f67521324c8068cfd025f121a0843d57ec813411661b07edc5ff781842 攻

    2023年04月08日
    浏览(38)
  • 乘法逆元(inverse element)及四大相关求法详解(含证明)

    知识的补缺是老生常谈的一大问题,随着自身学习进程的推进,越发觉着逆元知识的重要,故此我站在网上各路大牛的肩膀上,对此知识进行一定程度上的系统梳理。如有不足之处,还请大家指出,大家共同进步,互利共赢 !! 先呈上菜: 很明显,上述式子只有一条不成立

    2023年04月15日
    浏览(33)
  • 【论文笔记】A theory of learning from different domains

    防盗 https://www.cnblogs.com/setdong/p/17756127.html domain adaptation 领域理论方向的重要论文. 这篇笔记主要是推导文章中的定理, 还有分析定理的直观解释. 笔记中的章节号与论文中的保持一致. domain adaptation 的设定介绍: 有两个域, source domain 与 target domain. source domain: 一组从 source dist. 采

    2024年02月05日
    浏览(42)
  • [移动通讯]【Carrier Aggregation in LTE】【 Theory + Log analysis-1】

    CA:       Carrrier Aggregation PCC:     Primary Component Carrier SCC:    SCC Secondary Component Carrier 目录:     背景介绍     PCC SCC     聚合方式     Precondition for CA 一 背景介绍      在没有CA 技术前,手机和基站以单子载波的方式,收发数据。 对应子载波称为:   Primary Component Car

    2024年02月11日
    浏览(41)
  • MATLAB - 机器人逆运动学设计器(Inverse Kinematics Designer APP)

          通过逆运动学设计器,您可以为 URDF 机器人模型设计逆运动学求解器。您可以调整逆运动学求解器并添加约束条件,以实现所需的行为。使用该程序,您可以 从 URDF 文件或 MATLAB 工作区导入 URDF 机器人模型。 调整逆运动学求解器和约束条件。 创建关节配置并导出航点

    2024年04月14日
    浏览(29)
  • Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models

    论文链接:https://arxiv.org/abs/2211.10655 GitHub链接:https://github.com/HJ-harry/DiffusionMBIR 【score-MRI作者】 扩散模型已成为具有高质量样本的新的艺术生成模型,具有模式覆盖和高灵活性等有趣的特性。它们也被证明是有效的逆问题求解器,充当分布的先验,而正演模型的信息可以在采

    2024年02月09日
    浏览(42)
  • 机器人——正向运动学(Forward Kinematics)与逆向运动学(Inverse Kinematics)

    正向运动学和反向运动学分别是什么意思 正向运动学是指从机器人的关节运动推导出末端执行器的运动的过程,也就是从机器人的关节坐标计算出末端执行器的位置和姿态信息的过程。反向运动学则是指从末端执行器的位置和姿态信息推导出机器人的关节坐标的过程。简单来

    2024年02月16日
    浏览(44)
  • 【反渲染高斯】GS-IR: 3D Gaussian Splatting for Inverse Rendering

    会有自己的理解PS,不保证正确,欢迎评论中指出错误。 我们提出了一种基于3D高斯溅射(GS)的新型反向渲染方法GS-IR,它利用前向映射体渲染forward mapping volume rendering来实现逼真的新视图合成和重照明结果。与先前使用隐式神经表征和体绘制(例如NeRF)的工作不同,这些工作具有

    2024年02月19日
    浏览(36)
  • MinMaxScaler 中scaler.inverse_transform不能反归一化正确的数据

    参考代码[时间序列预测]基于BP、RNN、LSTM、CNN-LSTM算法多特征(多影响因素)用电负荷预测[保姆级手把手教学] 他的源代码部分: 我的代码仿写部分: 其中的 np.concatenate 就是拼接,按列拼接。 我拿个demo来解释一下: 也就是从demo理解了我把y列加在了x上,并且是在最后列。

    2023年04月22日
    浏览(35)

觉得文章有用就打赏一下文章作者

支付宝扫一扫打赏

博客赞助

微信扫一扫打赏

请作者喝杯咖啡吧~博客赞助

支付宝扫一扫领取红包,优惠每天领

二维码1

领取红包

二维码2

领红包