Depth dependence of verticalplunging force in granular medium

The future of agriculture is poised for significant changes that will revolutionize the way we grow,harvest,and distribute food.As the global population continues to grow, the need for sustainable and efficient agricultural practices becomes increasingly important.Here are some key areas where we can expect to see major transformations in the coming years:1.Technological Advancements:The integration of technology in agriculture is set to increase exponentially.This includes the use of drones for crop monitoring,precision farming tools that optimize the use of water and fertilizers,and data analytics to predict crop yields and manage resources more effectively.2.Sustainable Practices:With climate change being a pressing issue,sustainable farming practices will become more prevalent.This includes organic farming,regenerative agriculture,and the use of renewable energy sources to power agricultural operations.3.Vertical Farming:Urbanization is leading to a decrease in available farmland.Vertical farming,which involves growing crops in vertically stacked layers,will allow for the efficient use of space and reduce the need for arable land.4.Genetic Modification:Advances in genetic engineering will enable the development of crops that are more resistant to pests,diseases,and changing climate conditions.This could lead to higher yields and more resilient food sources.5.Agricultural Robotics:Robots will play a larger role in agriculture,performing tasks such as planting,harvesting,and weeding.This will not only increase efficiency but also reduce the need for manual labor.6.Aquaculture and Insect Farming:As traditional livestock farming faces challenges related to environmental impact and resource use,alternative protein sources like aquaculture fish farming and insect farming will gain popularity.7.Precision Livestock Farming:Similar to precision farming for crops,precision livestock farming will use technology to monitor the health and wellbeing of animals, ensuring optimal growth conditions and reducing the need for antibiotics.8.Food Waste Reduction:Innovations in storage,transportation,and packaging will help to minimize food waste.This includes the development of new materials that prolong the shelf life of produce and the use of smart systems that track and manage inventory.9.Blockchain in Agriculture:The use of blockchain technology will improve traceabilityand transparency in the food supply chain,allowing consumers to know the origin of their food and ensuring quality and safety standards are met.10.ClimateSmart Agriculture:Farmers will adopt practices that help to mitigate the effects of climate change,such as carbon sequestration in soils,water conservation techniques,and the use of cover crops to improve soil health.cation and Training:There will be a greater emphasis on educating farmers about new technologies and practices.This will involve partnerships between educational institutions,government agencies,and the agricultural industry.12.Policy and Regulation:Governments will play a crucial role in shaping the future of agriculture through policies that encourage innovation,support sustainable practices,and ensure food security.In conclusion,the future of agriculture is one that will be characterized by innovation, sustainability,and a focus on meeting the needs of a growing global population.By embracing these changes,we can work towards a more efficient and environmentally friendly food system.。

第3期王寅等:基于深度强化学习与旋量法的机械臂路径规划517及其衍生算法、PRM(probabilistic road maps)[8]及其衍生算法、退火算法[9]等都是基于采样的,环境发生改变后需要重新采样才能得到可行路径,难以适用于多变的机械臂工作场景.因此,如何提高机械臂在复杂环境的泛化性能成为了机械臂路径规划中的一个难点.深度强化学习(deep reinforcement learning,DR-L)[10–11],将深度学习的感知能力和强化学习的决策能力相结合,近年来被广泛运用在包括机械臂路径规划的各领域中.文献[12]将深度强化学习与机器人逆运动学融合实现了无碰撞的路径规划;文献[13]提出了一种基于SAC(soft actor-critic)算法的多臂机器人周期运动障碍物路径规划算法;文献[14]采用了一种基于DRL的混合控制算法,并通过了真实机械臂进行的测试;文献[15]使用了一种无模型深度强化学习算法进行训练;文献[16]提出通过深度强化学习让机器人具有自主获取进行复杂装配的能力,证明了通过DRL 模型可以提高机器人的智能水平;文献[17]提出了一种面向果园复杂环境的基于深度强化学习的快速、鲁棒的无碰撞路径规划方法;文献[18]提出使用深度强化学习方法来学习机械臂的控制器,即通过机械臂的控制器的反馈数据进行训练,将机械臂引导到目标地点;文献[19]通过奖励函数的设计来解决面向路径规划的DRL算法在障碍物环境中性能差的现象;文献[20]提出一种基于六自由度机械臂运动规划的改进DRL算法,通过添加成功经验池和碰撞经验池、改进奖励函数、优先训练前三轴等方法提升了训练效率和模型性能.这些研究通过DRL进行机械臂的路径规划研究,并通过经验池改进、奖励函数改进等方法使DRL更适用于机械臂,但仍然存在明显的获取样本成本过高问题,且随着机械臂轴数增多、环境复杂程度增大,样本获取成本将成指数式增长.因而,提升样本利用率对于深度强化学习在机械臂领域的应用有着不可忽视的作用.利用学习过程中不断生成的自然轨迹作为实际示例来进行训练,是目前机械臂训练过程中获取样本的常见方法,但样本获取成本大,且常存在样本利用效率过低的问题.文献[21]提出经验回放方法,将与环境交互所得样本存储至重放缓冲区,使样本多次用于训练.深度学习中的数据增强方法,是在已有样本集的基础上进行样本的扩充,但由于强化学习的样本是在探索过程中即时得到,故对强化学习并不适用,但可以通过数据增强的思路对样本进行有效扩充.例如HER(hindsight experience replay)算法[22],此算法将采集所得智能体的状态作为该轨迹的新目标,以此生成有效人工轨迹.除此以外还有HER的衍生算法、对称等扩充样本的方法,但这些方法只通过改变智能体状态的方式进行样本扩充,提升样本利用率.本文基于数据增强的思想提出了一种面向机械臂领域的离线策略强化学习通用算法:DRL与旋量法的融合算法(screw method in DRL,SMIDRL).具体贡献如下:1)通过旋量法[23]对机械臂与环境交互得到的自然轨迹进行有效扩充,从而使得样本利用率得到了更高效的提升,总体流程如图1所示.因为SMIDRL需要将即时采集到的轨迹进行扩充再存入回放经验池,故只能局限于离线策略DRL算法;2)SMIDRL在扩充轨迹的同时还可以通过改变障碍物等物体姿态的方式对交互环境进行同步改变,从而提升智能体对动态复杂环境的应对能力;3)SMIDRL可以与HER算法这类样本扩充算法进行结合,这样可以使样本利用率和训练效率得到更显著提升.图1旋量法与离线策略DRL的融合算法Fig.1Fusion algorithm of screw method and off-policy DRL 本文的组织结构如下:第1部分介绍了DRL在机械臂路径规划领域的研究现状以及提升样本利用率的必要性;第2部分介绍了深度强化学习算法在机械臂路径规划中的应用;第3部分介绍了SMIDRL理论;第4部分在OpenAI Gym[24]的Mujoco平台下,通过Fe-tch机械臂[25]和UR5机械臂的仿真环境,使用DDPG (deep deterministic policy gradient)算法[26]进行实验分析,证明本算法不仅可以提高模型训练效率,还能提高机械臂在复杂动态环境的泛化能力;第5部分进行了总结.2DRL在机械臂路径规划中的应用2.1马尔可夫决策过程马尔可夫决策过程(Markov decision process,MD-P)[27]是强化学习的基础,用于系统状态具有马尔可夫性质的环境,模拟智能体可实现的随机性策略与回报.给定一个随机过程的当前状态和所有过去状态,如果未来状态的条件概率分布且仅与当前状态有关,则称该随机过程具有马尔可夫性质.本文考虑将连续状态和动作空间模拟为多目标马尔可夫决策过程,即{S,A,G,T,R,p,γ}.其中:S是连续的状态空间;A指的是一个连续的动作空间;G是一组目标;T:S×A×S→[0,1]代表描述环境动态的未知转换函数;R{s,a,s′,g}是当智能体目标为g∈G时,执行动作a∈A后从状态s∈S达到状态s′∈S 所得到的即时奖励;γ∈[0,1]是折扣因子.在该框架518控制理论与应用第40卷下的机械臂学习目的是获得一个策略π:S ×G ∈A ,使预期折扣奖励的总和对于任何给定的目标都能达到最大化.2.2DDPG 与机械臂路径规划基于DDPG 的机械臂路径规划方法如图2所示.行动者当前网络负责机械臂动作选择策略的更新,评判家当前网络负责对机械臂所执行动作评判策略的更新.两个目标网络则是借鉴了DDQN (double deep Q-learning)算法[28]的双网络框架模式,通过目标框架评判当前框架的方式解决单个网络框架收敛慢、算法不稳定的问题.经验回放将机械臂与环境交互所得转移样本(s,a,r,s ′)存放到经验池中,训练时再从经验池中随机采样,以此将采集样本碎片化存储,避免了样本之间的相关性,同时也提高了样本利用率.图2基于DDPG 的机械臂路径规划方法[26]Fig.2Path planning method of manipulator based on DDPG [26]3DRL 与旋量法的融合旋量法是一种基于李群的解决机械臂运动学的方法.SMIDRL 算法如图1所示,即通过旋量法将机械臂探索过程中收集到的自然轨迹进行复制、筛选,以此得到廉价的可行人工轨迹,在不进行额外探索的前提下得到更多的训练样本,达到提高样本利用率的目的.每次转换得到的人工轨迹必须通过自然轨迹生成,否则可能会使训练结果有很大偏差.3.1旋量法进行旋量运算需要参数ξ和θ,其中θ为旋转角度,ξ=[νω]T ∈se (3)⊂R 6为旋量系数,ν=−ω×q ,ω=[w 1w 2w 3]T ∈so (3)⊂R 3表示旋转轴(如z 轴为旋转轴时ω=[001]T ),q ∈R 3为旋转体到旋转轴的垂直向量.ξ和θ对应的旋量矩阵g (ξ,θ)表示为g (ξ,θ)=[e ˆωθ(I −e ˆωθ)(ω×ν)01]∈SE (3),(1)其中:ˆω=0−ω3ω2ω30−ω1−ω2ω10,(2)e ˆωθ=I +ˆωsin θ+ˆω2(1−cos θ)∈SO (3),(3)其中:SO (n )⊂R n ×n 为n 维的特殊正交群,SE (n )⊂R (n +1)×(n +1)为系统位形空间R n 与SO (n )的乘积空间,so (n ),se (n )为李群SO (n ),SE (n )的李代数.3.2机械臂参数本文所使用机械臂仿真环境参数如下:1)状态空间s =(s f ,s ob ,s ob2g ,s obs ),其中:s f 包含夹具位置(x f ,y f ,z f ),线速度(x ′f ,y ′f ,z ′f ),手指的相对距离d f 和相对速率d ′f ;s ob 包括可移动物体的位姿(x ob ,y ob ,z ob ,αob ,βob ,γob ),线速度和角速度(x ′ob ,y ′ob ,z ′ob ,α′ob ,β′ob ,γ′ob );s ob2g 表示可移动物体与目标的距离差(x ob2g ,y ob2g ,z ob2g );s obs 表示障碍物的位姿(x obs ,y obs ,z obs ,αobs ,βobs ,γobs ),若环境中无障碍物,则s obs 为空集;2)动作空间a =(x a ,y a ,z a ,d f ),其中:d f 为夹爪手指的相对距离,(x a ,y a ,z a )表示机械臂下一步将运动到的位置;3)目标g =(x g ,y g ,z g )表示目标位置;4)奖励函数R 如式(4)所示,未完成任务则给予惩第3期王寅等:基于深度强化学习与旋量法的机械臂路径规划519罚“−1”,反之反馈值为“0”.R =−1,d (ob ,g ) ϵ,0,d (ob ,g )>ϵ,(4)其中:d (ob ,g )为可移动物体与目标之间的距离标量;ϵ为距离阈值,d (ob ,g ) ϵ时判定任务完成.3.3自然轨迹与人工轨迹的映射假定一条长度为h 的轨迹τ={g,(s 0,a 1,r 1,s 1,a 2,r 2,s 2,···,s h )},g ∈G ,s 0∈S ,∀i =1,2,···,h ,s i ∈S ,a i ∈A ,r i =R (s i −1,a i ,s i ,g ).假定所有在真实存在的机械臂中的轨迹的长度不大于H ∈N (即每个操作长度有限),则所有轨迹集合为L =H ∪h =1G ×S ×(A ×R ×S )h .所有可行轨迹集合为L ⊆L .对于τ∈L ,都有T (s i −1,a i ,s i ),则判定τ∈L .对于τ∈L ,若满足条件R (τ)>R min 或r i >R min ,则判定τ为成功轨迹.其中:R (τ)=h ∑i =1γi −1R (s i −1,a i ,s i ,g ),R min 为阈值.本文中的成功条件为r i >R min ,阈值为R min =−1.成功轨迹集合为L +⊆L .定义可行轨迹L 的映射为f :L →L ,使得f (L ,θ)=L ,其中f (L ,θ)={τ∈L|∃τ′∈L ,f (τ′,−θ)=τ}(下文将f (L ,θ)简化为f (L )表示).对于任意轨迹τ∈L 进行映射f 时,其元素也存在映射f G :G →G ,f S :S →S ,f A :A →A .换言之,状态、动作和奖励都可进行单独映射,即对于任意τ∈L 都存在f (τ)=τ′∈L .定义自然轨迹为τ={g,(s 0,a 1,r 1,s 1,a 2,r 2,s 2,···,s h )},所得人工轨迹为τ′={g ′,(s ′0,a ′1,r ′1,s ′1,a ′2,r ′2,s ′2,···,s ′h )},则τ与τ′中的元素满足以下映射关系:g ′=f G (g ),s ′0=f S (s 0),∀i =1,2,···,h ,a ′i =f A (a i ),s ′i =f S (s i ),r ′i =R (f S (s i −1),f A (a i ),f S (s i ),f G ).在SMIDRL 算法中,对于任意τ∈L 通过映射f 得到的人工轨迹τ′∈L ,其内部元素之间的相对距离并未改变(例如机械臂末端相对于目标的距离并未改变,即d (ob ,g )=d (f S (ob),f G (g ))),因此自然轨迹τ映射得到人工轨迹τ′后奖励值不变,即r ′i =r i .所有成功轨迹L +⊆L 同样适用可行轨迹L 的映射关系.3.4SMIDRL 算法旋量法的本质是旋转,通过旋量法对轨迹映射(简称为旋量映射)后,可能会生成工作区外的无效轨迹,因此设置参数θmax 来提高生成轨迹的有效性.SMIDRL 算法将机械臂与环境交互得到的自然轨迹通过旋量法进行扩充得到人工轨迹,在加以筛选后,与自然轨迹共同放入到经验回放库中.需通过旋量法进行映射的轨迹元素包括第3.2节中介绍的状态、动作、目标,其中包括位置矢量、线速度矢量、欧拉角、角速度以及夹具相对距离和相对速度等元素.夹具相对距离和相对速度是刚体内的元素,在经过旋量映射以后并不会被改变,因此不对其进行映射.在仿真环境中,因为机械臂底座坐标系未与世界坐标系重合,故需将机械臂底座坐标系简单转换至世界坐标系,接下来的介绍将默认已进行转换.每条自然轨迹可同时进行多次映射,在此定义每条自然轨迹进行旋量映射次数的参数n tw ,具体如下所示:Θ={θj |θj ∼(0,θmax ],j =1,2,···,n tw },(5)其中Θ表示在(0,θmax ]采样n tw 次所得角度的集合.每次旋量映射除了旋量参数ξ和角度θ以外并无改变,接下来仅介绍单次旋量映射.为了方便介绍,下文所有位置和线速度皆以(x,y,z )表示,所有弧度和角速度皆以(α,β,γ)表示.首先,将对应的(x,y,z )和(α,β,γ)(如障碍物的位置和姿态、可移动物体的线速度和角速度定义为对应)转换为以下SE (3)矩阵形式:g 0=[R 0p 001],(6)其中:R 0=Eul(α,β,γ),p 0=[x y z ]T .再根据式(1)得到该轨迹参数ξ,θ对应的旋量矩阵g (ξ,θ),则可得(x ′,y ′,z ′)和(α′,β′,γ′)的SE (3)矩阵g =g (ξ,θ)g 0=[R ′p′01],(7)从而可得到映射后的(x ′,y ′,z ′)和(α′,β′,γ′):[x ′,y ′,z ′]=(p ′)T ,(8)[α′,β′,γ′]=Eul −1(R ′),(9)其中:Eul(·)为将欧拉角映射为旋转矩阵SO (3)的运算,Eul −1(·)为Eul(·)的逆运算.以上为单次旋量映射的过程,下文将由Sc 表示,如将状态s 映射为s ′,可用s ′←Sc (s )表示.旋量映射完成后,需通过生成轨迹是否在工作空间内等条件来判断该轨迹是否有效,如有效才可存放至经验池.SMIDRL 算法的伪代码见算法1所示.SMIDRL 算法将已得到的自然轨迹进行复制扩充,在不进行额外探索的情况下获得更多廉价的有效人工轨迹,从而提高样本利用率和学习效率;在复制轨迹的同时,对障碍物等环境元素进行同步改变,以此提升机械臂对随机环境的泛化性能.4实验与验证4.1实验环境实验环境如下:仿真环境为Mujoco 平台中具有双指平行夹具的模拟7自由度Fetch 机械臂和6自由度520控制理论与应用第40卷UR5机械臂;深度强化学习算法为DDPG 算法;神经网络框架为Pytorch;显卡为GeForce GTX 2080Ti;CPU 为Intel(R)Core(TM)i9-9900X CPU @3.50GHz;操作系统为Ubuntu16.04;GPU 为32G.算法1:DRL 与旋量法的融合算法(SMIDL)Input :离线策略DRL 算法D ,容量为N 的经验回放库R ,回合数(episode)M ,每回合步数T ,采样样本数m ,最大角度θmax ,旋量参数ξ,旋量映射次数n tw .1初始化离线策略DRL 算法D 和经验回放库R 2for episode =1,2,···,M do3获得目标g 和初始状态s 1.4for t =1,2,···,T do5通过算法D 获得动作a t 并执行;6到达下一状态s t +1,计算得奖励值r t ;7将转移样本(s t ,a t ,r t ,s t +1)存入R ;8end9for j =1,2,···,n tw do10采样获得角度θj ∼(0,θmax ];11根据θj 和ξ映射g 和s 1:12g ′←Sc (g ),s ′1←Sc (s 1);13for t =1,2,···,T do14根据θj 和ξ映射a t 和s t +1:a ′t ←Sc (a ′),s ′t +1←Sc (s t +1);15if 该人工轨迹为有效轨迹then16将(s ′i ,a ′i ,r i ,s ′t +1)存入R 17end18end19end20for t =1,2,···,T do21从R 进行随机采样m 个转移样本(s,a,r,s ′);22使用算法D 和采样转移样本进行优化23end 24end仿真环境包括如图3–5所示的Fetch 机械臂仿真环境以及如图6所示的UR5机械臂仿真环境.Fetch 机械臂仿真环境包括推动、滑动、拾取和放置任务,UR5机械臂仿真环境为拾取和放置任务.在所有任务中,每一回合都会使可移动物体和障碍物在桌上进行随机初始化.图3–6中可移动物体为黑色方块,预设目标为红色球体,障碍物为黄色方块.状态、动作及奖励函数等如第3.2节定义.1)推动:该任务通过机械臂末端将物体推动至桌上的预设位置.2)拾取和放置:该任务先使用机械臂末端的夹爪将物体拾取,再将物体放置到工作空间中的预设位置.3)滑动:该任务通过机械臂末端对物体施加一个力,使物体在存在摩擦力的前提下滑动到桌子上的预设位置(目标位置在机械臂的工作区之外).(a)无障碍物任务(b)有障碍物任务图3推动任务的环境Fig.3Environment of the pushingtask(a)无障碍物任务(b)有障碍物任务图4拾取与放置任务的环境Fig.4Environment of the pick-and-placement task第3期王寅等:基于深度强化学习与旋量法的机械臂路径规划521(a)无障碍物任务(b)有障碍物任务图5滑动任务的环境Fig.5Environment of slidingtask图6UR5机械臂的拾取与放置任务环境Fig.6Pick-and-placement task environment of UR5manipulator4.2神经网络超参数设置在本文实验所使用的算法中,其网络框架超参数设置如表1所示,除非有特殊说明,否则超参数值不做改变.4.3算法评判标准在强化学习中,一回合(epoch)由固定大小的连续步(episode)组成,因此可以通过计算每回合(即每迭代一次)中成功的步数来计算该回合的成功率.以此为基础,在本文实验中,算法每次更新完成后,都会通过当前的训练模型控制机械臂执行10次任务并求得其平均成功率,该平均成功率则为当前时刻的训练模型优劣性的评判标准.表1神经网络框架超参数Table 1Hyperparameter of neural networkframework超参数符号超参数名称具体数值α策略网络学习率0.001β评价网络学习率0.001τ目标网络软更新参数0.1γ衰减因子0.98m 小批量采样样本数128N 经验回放池容量1×106M 回合数200T每回合步数504.4实验与分析本文实验中,分别给推动、拾取和放置任务8倍加速,由于滑动任务更加困难,因此给它24倍加速.前文提到SMIDRL 与HER 算法融合后可使样本利用率提升更高,接下来将使用HER 算法中效果最好的“未来策略”进行验证,HER 算法的使用次数为4.为了更好介绍SMIDRL 算法的性能,本文将通过无障碍情况下有无HER 算法、不同次数的旋量映射、存在障碍物情况这3种情况进行实验对比并验证.同时为了证明SMIDRL 的通用性,本文通过solidworks 导出的UR5机械臂模型,保存UR5机械臂的物理参数,在存在障碍物环境下让该UR5机械臂进行“拾取与放置”实验.本实验中所展示数据图皆截取至Tensor-board,为方便对比已用Tensorboard 自带插件进行拟合,其中被虚化部分为原始数据,实体部分为拟合后数据.4.4.1无障碍情况下有无HER 算法的性能比较本实验将通过DRL,SMIDRL,DRL+HER 以及S-MIDRL+HER 这4种情况进行对比,来验证SMIDRL 算法提升性能的有效性,且与HER 算法融合后性能可使提升更高.其中推动任务、拾取与放置任务进行旋量映射的次数n tw =16,滑动任务进行旋量映射的次数n tw =24.实验结果如图7所示,实验分析如下:1)在推动任务中,DRL 算法的成功率呈微下降趋势;SMIDRL 算法的成功率在160回合开始上升,最高达到30%;HER+DRL 算法的成功率于60回合开始上升;HER+SMIDRL 算法在60回合时成功率就达到90%以上,并于80回合左右达到峰值且大致平稳;2)在拾取与放置任务中,DRL 算法的效果较差,成功率无上升趋势且均低于10%;SMIDRL 算法在100回合处成功率开始上升;HER+DRL 算法的成功率522控制理论与应用第40卷虽有增长,但相对缓慢,200回合时成功率都未高于90%;HER+SMIDRL 算法在120回合左右成功率就已达到峰值,并大致保持平稳;3)滑动任务相对其他两个任务更为困难,相对于HER+DRL 算法,HER+SMIDRL 算法仅得到微弱的提升;但在未融入HER 算法的情况下,SMIDRL 算法对比DRL 算法的优势较为明显:DRL 算法成功率无上升趋势,而SMIDRL 算法在130回合后成功率开始增高.(a)拾取与放置任务(b)滑动任务(c)推动任务图7无障碍任务下SMIDRL 算法的性能Fig.7Performance of SMIDRL without obstacle综上,在无障碍情况下,SMIDRL 算法的效率明显高于DRL 算法,且融入HER 算法后SMIDRL 算法提升更为显著.4.4.2不同次数旋量法对性能的影响本实验将通过进行不同次数旋量映射的实验,来比较在无障碍物的情况下不同次数旋量映射对算法性能的影响.在此次实验中,将在HER+SMIDRL 算法的基础上,通过0次、1次、8次、16次及32次旋量映射来进行比较.实验结果如图8所示,实验分析如下:1)在推动任务中,单次旋量映射的算法与未进行旋量映射的相比,训练效率得到大幅提升;而n tw =1到n tw =32的区别不大,在训练前期(60回合前)随着旋量映射次数增多成功率提升越快,在60回合左右达到最高值;2)拾取与放置任务与推动任务相似,n tw =1相对于n tw =0,其算法性能提升明显:n tw =0的成功率均低于90%,而n tw =1的成功率于140回合左右达到峰值;而n tw =1到n tw =32虽对算法的训练效率虽有提升,但提升幅度随着旋量映射次数的增加而减少;3)滑动任务相对更为复杂,随着旋量映射次数增多,训练效率虽能得到提升,但提升幅度降小.(a)拾取与放置任务(b)滑动任务(c)推动任务图8无障碍环境下进行不同次数旋量映射的比较Fig.8Comparison of screw-mapping with different times inbarrier-free environments在这3个任务中,在一定的旋量映射次数范围内,随着旋量映射的次数增加,成功率随之升高,但提升第3期王寅等:基于深度强化学习与旋量法的机械臂路径规划523效果逐渐降低.4.4.3存在障碍物情况的性能比较本实验将在仿真环境中加入障碍物,以此验证SMIDRL 算法在障碍物环境中也是可行有效的.为了方便对比,本实验将融入HER 算法,即通过HER+DRL 算法与HER+SMIDRL 算法进行对比分析.实验结果如图9所示,由于障碍物的加入使环境变得复杂,导致HER+DRL 的训练模型成功率均处于较低的状态.实验分析如下:1)在推动任务中,HER+DRL 算法成功率低于10%,但HER+SMIDRL 算法成功率逐步上升,在90回合开始成功率保持在90%以上;2)在拾取与放置任务中,HER+DRL 算法的成功率上升缓慢,在130回合处才开始有明显上升趋势;HER+SMIDRL 算法的成功率在40回合左右开始稳步上升,在120回合后保持在90%左右;3)由于滑动任务相对其他两个任务难度更大,故仅有小幅度的性能提升.(a)拾取与放置任务(b)滑动任务(c)推动任务图9存在障碍任务下SMIDRL 算法的性能Fig.9Performance of SMIDRL with obstacle综上,SMIDRL 算法在存在障碍物的非结构化下同样具备提升样本利用率和模型泛化性能的能力.4.4.4UR5机械臂的性能验证前3个实验已经验证SMIDRL 在Fetch 机械臂环境中的可行性,本实验将通过UR5机械臂在障碍物环境下进行拾取与放置实验,验证SMIDRL 的通用性以及在现实环境的可行性.在本实验中,旋量映射参数n tw 设置为16,为了方便对比观察,此实验都将融入HER 算法,即通过HER+DRL 与HER+SMIDRL 进行分析.实验结果如图10所示.由于UR5机械臂为六自由度,在障碍物环境中运动受限,因而成功率较低.HER+DRL 算法成功率低于10%,而HER+SMIDRL 算法在130回合左右将成功率稳定在42%左右.图10UR5机械臂下的SMIDRL 性能验证Fig.10SMIDRL performance verification in UR5manipulator5结论针对深度强化学习在机械臂路径规划的应用中仍面临的样本需求量大和获取成本高的问题,本文提出了SMIDRL 算法,并通过Fetch 机械臂和UR5机械臂在非结构化环境下的仿真实验进行了验证.SMIDRL 算法通过旋量法与DRL 算法的融合,在同样的探索次数下,能够复制更多的有效轨迹并投入训练,使训练效率得到提升;并且在进行轨迹扩充的同时,通过对目标、障碍物等环境元素进行同步复制的方式,对交互环境进行相应改变,从而提高了机械臂在复杂随机环境中的适应能力,提高训练模型的泛化性能.实验结果表明,在未融入HER 算法的情况下,旋量法对训练模型有质的提升;在与HER 算法结合后,加快了在推动、拾取与放置任务中的学习速度,大幅提高了机械臂的成功率.在滑动任务中也有一定的性能提升,且在有障碍物的复杂环境中,采用SMIDRL 算法的性能提升效率更为明显.参考文献:[1]YANG C,ZENG C,CONG Y ,et al.A learning framework of adap-tive manipulative skills from human to robot.IEEE Transactions on Industrial Informatics ,2018,15(2):1153–1161.524控制理论与应用第40卷[2]YANG C,WU H,LI Z,et al.Mind control of a robotic arm with vi-sual fusion technology.IEEE Transactions on Industrial Informatics, 2017,14(9):3822–3830.[3]NUBERT J,KOHLER J,BERENZ V,et al.Safe and fast 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Robotics and Biomimetics.Kuala Lumpur:IEEE,2018: 1755–1760.[20]LI Z,MA H,DING Y,et al.Motion planning of six-dof arm robotbased on improved DDPG algorithm.The39th Chinese Control Con-ference IEEE.Shenyang:IEEE,2020:3954–3959.[21]LIN L J.Self-improving reactive agents based on reinforcementlearning,planning and Teaching.Machine Learning,1992,8(3/4): 293–321.[22]ANDRYCHOWICZ M,WOLSKI F,RAY A,et al.Hindsight experi-ence replay.The31th Conference on Neural Information Processing Systems(NIPS2017),Long Beach,CA,USA:2017,30:5048–5058.[23]MURRAY,RICHARD M,ZEXIANG LI,et al.A Mathematical In-troduction to Robotic Manipulation.Boca Raton:CRC press,2017: 61–66.[24]BROCKMAN G,CHEUNG V,PETTERSSON L,et al.OpenAIGym.arXiv Preprint,2016:1606.0154OVI.[25]PLAPPERT M,ANDRYCHOWICZ M,RAY A,et al.Multi-goalreinforcement learning:Challenging robotics environments and request for research.ArXiv Preprint,2018:arXiv:1802.09464.[26]LILLICRAP T P,HUNT J J,PRITZEL A,et al.Continuous con-trol with deep reinforcement learning.International Conference on Learning Representations(Poster).Santiago:ICLR,2015.[27]SCHAUL T,HORGAN D,GREGOR K,et al.Universal value func-tion approximators.International Conference on Machine Learning.Lile:ICML,2015:1312–1320.[28]V AN HASSELT H,GUEZ A,SILVER D.Deep reinforcementlearning with double q-learning.Proceedings of the AAAI Conference on Artificial Intelligence.Texas:AAAI,2016,30(1):2094–2100.作者简介:王寅硕士研究生,目前研究方向为深度强化学习、串联机械臂、路径规划,E-mail:*********************;王永华副教授,博士,目前研究方向为信号处理、机器学习、智能测控,E-mail:********************.cn;尹泽中硕士研究生,目前研究方向为移动机械臂、深度强化学习、运动规划,E-mail:*********************;万频教授,博士,目前研究方向为智能测控技术、信号处理、物联网,E-mail:***************.第40卷第3期2023年3月控制理论与应用Control Theory&ApplicationsV ol.40No.3Mar.2023基于双边闭环函数的网络化采样控制系统稳定性分析曾红兵,颜俊杰,肖会芹†(湖南工业大学电气与信息工程学院,湖南株洲412007)摘要:考虑数据通信时延不确定环境下网络化采样控制系统的稳定性问题.首先基于输入时滞方法,建立包含采样周期信息的网络化采样控制系统的数学模型,在此基础上,采用双边闭环函数方法和自由矩阵积分不等式技术,得到网络传输时滞变化区间依赖稳定性新准则,并进一步讨论了网络化采样控制系统中网络时延与采样周期之间的关系.仿真结果表明减小采周期可以增强网络控制系统对网络通信时延的鲁棒性.关键词:网络控制系统;双边闭环函数;自由矩阵积分不等式;不确定数据传输时滞引用格式:曾红兵,颜俊杰,肖会芹.基于双边闭环函数的网络化采样控制系统稳定性分析.控制理论与应用, 2023,40(3):525–530DOI:10.7641/CTA.2022.11008Stability analysis of networked control system based ontwo-sided looped functionalsZENG Hong-bing,YAN Jun-jie,XIAO Hui-qin†(School of Electrical and Information Engineering,Hunan University of Technology,Zhuzhou Hunan412007,China) Abstract:The stability of a class of networked sampled-data control systems with data transmission delay is studied. Firstly,based on the input delay method,a model of networked control systems with periodic sampling is established.On this basis,a new stability criterion with uncertain transmission delay is obtained by using the two-sided looped function method and the free matrix integral inequality technique.Furthermore,the relationship of uncertain data transmission delay and the sampling period in networked sampled-data control system is investigated.Simulation results show that reducing the sampling period can improve the robustness of networked control system.Key words:networked control system;two-sided looped-functionals;free-matrix-based integral inequality;uncertain delayCitation:ZENG Hongbing,YAN Junjie,XIAO Huiqin.Stability analysis of networked control system based on two-sided looped functionals.Control Theory&Applications,2023,40(3):525–5301引言伴随着计算机和网络通讯技术的迅速发展,网络控制系统(networked control system,NCS)得到了广泛的关注[1].在网络控制系统中,采样作为信息处理的前端,在网络通讯、数据传输的过程中起着重要作用.增大采样周期可以降低信息的传输量,从而有效的节约网络通讯资源.此外,系统元件执行的速度和网络带宽是有限的,在信号的采集和传输中不可避免的会产生拥堵,从而导致数据传输时滞.因此,在具有数据传输时滞的网络环境下研究不确定时滞与保证系统稳定允许的最大采样周期之间的关系对实际网络控制系统的设计具有指导意义.目前,采样控制系统已经被学者们广泛研究并取得了许多重要成果[2–6].针对采样控制系统问题的稳定性问题,主要采用以下3种方法:1)离散时间系统方法[3],此方法主要应用于确定采样区间,它将采样系统构建为一个离散的时间系统模型,并基于离散时间系统理论进行分析;2)脉冲系统方法[4],此方法将采样系统建立成一个脉冲系统进行分析;3)输入时滞方法[5–6],此方法是将采样系统转化为具有输入时滞的连续时间系统,并基于连续时间系统理论进行分析.2012年,针对采样控制系统的稳定性问题,文献收稿日期:2021−10−21;录用日期:2022−07−27.†通信作者.E-mail:xiaohq***********;Tel.:+86731-22183270.本文责任编委:施阳.国家自然科学基金项目(62173136),湖南省自然科学基金项目(2020JJ2013,2021JJ50047)资助.Supported by the National Natural Science Foundation of China(62173136)and the National Natural Science Foundation of Hunan Province (2020JJ2013,2021JJ50047).。

2024届山东中学联盟高三下学期5月预测热身卷英语试题+详细解析注意事项:1. 答卷前，考生务必将自己的姓名、考生号等填写在答题卡和试卷指定位置。

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ASmall Ways You Can Donate Money To CharityThere are plenty of innovative ways that you can help people in need, even when money is tight. Here are just a few unique ways to give.Food Angel, Hong KongFood insecurity has become a global problem for families. In Hong Kong, the people behind the Food Angel program collect 45 tonnes of edible surplus food each week that grocery stores, restaurants and individuals would otherwise dispose of. That includes fresh fruits and vegetables and other perishables (易腐烂的食物) that aren’t normally accepted in food-donation boxes.The impact is significant: Volunteers make and serve around 20,000 meals and distribute more than 11,000 other meals and food packs every day.Frigos Solidaires, FranceImagine if those in need could help themselves to food with anonymity (匿名) and dignity. Frigos Solidaires, or Solidarity Fridges, was started with that aim by Dounia Mebtoul, a young restaurateur in Paris. Now, 130 fridges installed in front of places such as shops and schools offer free food to the hungry across France.Stuff A Bus, CanadaIn Edmonton, the transit service parks vehicles in front of supermarkets for its annual “Stuff a Bus” campaign each November. Volunteers collect food and cash donations from shoppers to fill buses bound for food banks. Since its start in 1995, the campaign has collected 553,000 kilograms of food and roughly half a million dollars.Rice Bucket Challenge, IndiaHeard of the Ice Bucket Challenge? You take a video of yourself dumping a bucket of ice water over your head, then nominate (指定) three more people to do the same. In some versions, the participant donates $100 if they don’t complete the challenge.“I thought it was an amazing way to raise awareness of ALS and raise funds,” recall s Manju Kalanidhi, a journalist in Hyderabad, India. But it didn’t make sense in her country, where water is too precious to waste, even for a good cause. Then in 2014, it hit her: Why not make it a Rice Bucket Challenge to fight hunger? “I gave a bucket o f rice to someone in need and clicked a photo. I shared it on Facebook and said, ‘This is a Rice Bucket Challenge.Why don’t you do it, too?’” Participants donate a bucket of rice to an individual or family —no, it’s not dumped — take a photo and post it on social media with a message encouraging others to do the same.1. Which one can help people in need get food without hurting their pride?A. Food Angel, Hong KongB. Frigos Solidaires, FranceC. Stuff A Bus, CanadaD. Rice Bucket Challenge, India2. What do you know about Rice Bucket Challenge in India?A. It is an amazing way to raise awareness of ALS.B. It was inspired by the Ice Bucket Challenge.C. A bucket of rice is given and dumped.D. A bucket of water is donated for a good cause.3. What’s the p urpose of the text?A. To explain how important to help people in need.B. To inspire readers to start a non-profit organization.C. To introduce some creative ways to give away.D. To appeal to readers to donate money to charity.【答案】1. B 2. B 3. C【解析】【导语】本文是一篇说明文。

Bed-Load Sediment Transport on Large Slopes:Model Formulation and Implementation within a RANS SolverDavid D.Apsley 1and Peter K.Stansby 2Abstract:Standard bed-load sediment-transport formulas are extended using basic mechanical principles to include gravitational influ-ence on large slopes of arbitrary orientation.The resulting sediment fluxes are then incorporated into a morphodynamics model in a general-purpose,three-dimensional,finite-volume,Reynolds-averaged Navier–Stokes ͑RANS ͒code.Major features are:͑1͒the down-slope component of weight is combined with the fluid stress to form an effective bed stress ͑similar to the work of Wu in 2004͒;͑2͒the critical effective stress is reduced in proportion to the component of gravity normal to the slope;͑3͒a simple flux-based model for avalanching is implemented as a numerical means of preventing the local slope from exceeding the angle of repose;͑4͒an entirely vectorial formulation of bed-load transport is developed to account for arbitrary surface orientation;and ͑5͒methods for reducing numerical instability in the morphodynamics equation are described.Sample computations are shown for scour and accretion in a channel bend and for the movement of sand mounds on erodible and nonerodible bases.DOI:10.1061/͑ASCE ͒0733-9429͑2008͒134:10͑1440͒CE Database subject headings:Sediment transport;Slopes;Bed loads;Morphology;Channel bends;Computational fluid dynamics .IntroductionThe movement of sediment by fluids is an important natural pro-cess.Siltation reduces the storage capacity of reservoirs and ob-structs the free passage of water in irrigation or drainage channels.Scour may undermine the foundations of hydraulic structures,coastal defences,and the piers or abutments of bridges.The landscape has been shaped by erosion processes in air and water,whereas dunes and sandbanks provide a degree of natural protection at coastlines.The advent of powerful computers has led to the extensive use of sediment-transport formulas in numerical models—initially to establish the sediment-carrying capacity of predefined waterways under steady flow,and then to predict evolving surface morphol-ogy ͑Wu et al.2000;Wu 2004;Liang et al.2005͒.Sediment in motion may be divided into two components:that which rolls or slides along the bed ͑bed load ͒and that which is carried along in the moving fluid ͑suspended load ͒.This paper focuses on the former.A number of predictive formulas for sedi-ment flux are in widespread use.Some of these are listed in Table 1and are used in this paper.Most bed-load sediment-transport formulas are derived and calibrated for rivers of small slope.͑Where slopes do appear theyare part of the normal-flow relation used to predict the bed-shear stress.͒The intention of this work is to extend these formulas using basic mechanical principles to include gravitational influ-ence on large slopes and to implement them in a three-dimensional,finite-volume Reynolds-averaged Navier–Stokes ͑RANS ͒flow solver coupled with a surface-movement algorithm.Other authors have extended bed-load sediment-transport for-mulas to include gravitational influence on slopes.Sekine and Parker ͑1992͒employed a stochastic model of saltating grains to deduce a formula for the ratio of cross stream to streamwise bed-load transport on a lateral slope.Kovacs and Parker ͑1994͒pro-posed a vectorial ͑and hence arbitrary slope ͒formulation for bed-load sediment transport.Assuming equilibrium between fluid drag,slope-tangential component of weight,and coulombic fric-tion,they derived an expression for the ratio of critical stress on arbitrary slopes to that on a flat bed in a similar manner ͑although in very different notation ͒to our own.By contrast with our model,however,they adopted a very specific,Bagnold-type hy-pothesis for the bed load.With this they were able to demonstrate,numerically,the evolution of a straight channel with trapezoidal cross section to one with a fully developed equilibrium shape.An empirical adjustment of the Meyer-Peter and Müller ͑1948͒bed-load transport model for longitudinal slope was proposed by Damgaard et al.͑1997͒.There is a standard adjustment to the critical stress for incipient motion and an additional enhancement factor for downslope flow.Note that this model is still couched in terms of the fluid stress ␶alone.By contrast,Wu ͑2004͒com-bined fluid drag and the downslope component of weight into an effective bed stress ␶eff ,although—at least as presented in that paper ͑his equations 31–33͒—not for an arbitrary vectorial align-ment of these forces.The model was incorporated in a depth-averaged hydrodynamic solver,with a nonequilibrium approach for total ͑suspended+bed-load ͒sediment transport.Ortiz and Smolarkiewicz ͑2006͒simulated the evolution of sand dunes in severe winds.Arbitrary slopes were incorporated in a modified critical stress,but not in the subsequent direction of transport,which was always assumed aligned with the local flow.1Lecturer,School of Mechanical,Aerospace and Civil Engineering,Univ.of Manchester,PO Box 88,Manchester M601QD,U.K.E-mail:d.apsley@ 2Professor of Hydrodynamics,School of Mechanical,Aerospace and Civil Engineering and Tyndall Centre for Climate-Change Research,Univ.of Manchester,PO Box 88,Manchester M601QD,U.K.E-mail:peter.k.stansby@Note.Discussion open until March 1,2009.Separate discussions must be submitted for individual papers.The manuscript for this paper was submitted for review and possible publication on January 19,2007;ap-proved on January 30,2008.This paper is part of the Journal of Hydrau-lic Engineering ,V ol.134,No.10,October 1,2008.©ASCE,ISSN 0733-9429/2008/10-1440–1451/$25.00.D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .They noted that sand avalanches acted as a natural slope limiterand simulated ͑the slope-limiting effect of ͒an avalanche flux by a slope-dependent diffusivity.As in Wu ͑2004͒we have chosen to absorb the additional downslope gravitational force into an effective bed stress,allow-ing the user to continue using standard bed-load transport models.The handling of critical conditions for incipient motion is,how-ever,different to that of Wu.Our formulation is given in a vec-torial form,independent of any underlying coordinate system and slope alignment.The present paper also deals with the integration of sediment transport and morphology into a general-purpose three-dimensional ͑3D ͒flow model.This solves the full RANS equations rather than the depth-averaged flow equations;conse-quently the bed stress can be determined from the near-bed flow properties,rather than from a depth/slope/roughness parameter-ization such as Chézy or Manning’s formula.The structure of the rest of the paper is as follows.The next section summarizes existing bed-load transport formulas suitable for the computational model,whereas the subsequent section de-scribes their extension for large slopes of arbitrary orientation.These extensions are “natural”in the sense that they require no additional empirical input ͑other than the angle of repose ͒.This is followed by details of how the surface-height equation is coupled with a general-purpose 3D flow solver.The application of this to the generation of the equilibrium bed profile in a channel bend and to the time-dependent motion of isolated sand mounds is then shown.Finally,the paper concludes with a summary of the main features of the computational model and suggests directions for future work.Existing Formulas for Bed-Load TransportBed-load transport of sediment is quantified by the bed-load flux q b —the volume of nonsuspended sediment crossing unit length of surface per unit time.On horizontal beds the tendency of bed particles to move is determined by the drag imposed by the fluid flow and countered by the particle weight ͑reduced by buoyancy ͒,so that q b may be taken as a function of the bed-shear stress ␶b ,reduced gravity ͑s −1͒g ͑where s =␳s /␳͒,particle diameter d ,and the fluid density ␳,and kinematic viscosity ␯.A formal dimen-sional analysis ͑six variables,three independent dimensions ͒dic-tates that there is a relationship between three nondimensional groups,conveniently taken asq *=q bͱ͑s −1͒gd 3͑dimensionless bed-load flux ͒͑1a ͒␶*=␶b␳͑s −1͒gd͑dimensionless shear stress or Shields stress ͒͑1b ͒d *=dͫ͑s −1͒g␯2ͬ1/3͑dimensionless particle diameter ͒͑1c ͒We have tried to maintain a consistent and meaningful nota-tion in this paper.Note,however,that elsewhere in the literature q *is often denoted by ⌽and ␶*by ␪or 1/⌿.Note also that variables such as bed-load flux and bed-shear stress are vector quantities;when their direction is important they will be written in bold type.In practice,sediment moves only after a certain critical shear stress ␶crit is exceeded.Various analytic approximations to Shields’original data have been proposed.Expressed in dimen-sionless terms,two convenient formulas ͑which differ only at very small values of d *͒are those of Van Rijn ͑1984͒and Soulsby ͑1997͒.The latter is␶crit*=0.301+1.2d *+0.055͓1−exp ͑−0.020d *͔͒͑2͒and is used in all calculations presented here.Extensive lists of sediment-transport formulas may be found in,e.g.,the textbooks of Soulsby ͑1997͒and Raudkivi ͑1998͒.Table 1lists some of those more commonly used in conjunction with computational fluid dynamics ͑CFD ͒.Most of the models have parameter restrictions,for which one must refer to the origi-nal papers.Table mon Bed-Load Transport Formulas ReferenceFormulaCommentsMeyer-Peter and Müller ͑1948͒q *=8͑␶*−␶crit*͒3/2The original paper assumed ␶crit*=0.047Einstein-Brown ͑Brown 1950͒q *=͕K exp ͑−0.391/␶*͒0.465,␶*Ͻ0.18240K ␶*3,␶*ജ0.182K =ͱ23+36d*3−ͱ36d *3Yalin ͑1963͒q *=0.635r ͱ␶*͓1−1␴rln ͑1+␴r ͔͒r =␶*␶crit*−1,␴=2.45ͱ␶crit*s 0.4Van Rijn ͑1984͒q *=0.053d *0.3͑␶*␶crit*−1͒2.1Nielsen ͑1992͒q *=12͑␶*−␶crit*͒ͱ␶*D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I V E R S I T Y o n 09/28/13. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .Proposed Modifications for Slopes Main FeaturesThe main modifications to sediment-transport formulas for large slopes are:1.Existing bed-load models are retained,but with bed stress ␶replaced by the effective stress ␶eff formed by the vector ad-dition of ␶and the downslope component of particle weight;2.The critical effective stress is reduced in proportion to thecomponent of gravity normal to the slope;i.e.,as the cosine of the slope angle;3.An “avalanche”flux is added when the slope angle exceedsthe angle of repose;and4.the flux divergence from any vertical column depends onslope orientation and is computed as a line integral of the outward bed-load flux around cell perimeters;the computa-tional implementation,together with a numerical smoothing technique,is described after the sediment-transport models.Although calculations in this paper were performed using the Meyer-Peter–Müller and Van Rijn models,the modifications de-scribed may be applied to any model in Table 1and,in general,to any bed-load transport models that can be written in the dimen-sionless formq b*=f ͑␶*,d *͒͑3͒An additional benefit of the modifications is that they introduce anatural diffusion-like term into the morphodynamics equation which aids numerical stability.Effective StressThe orientation of the surface is completely determined by thelocal unit normal vector nˆ͑Fig.1͒.In particular,the angle ␤made by the slope with the horizontal is the same as the angle made by nˆwith the vertical.If a Cartesian coordinate system is adopted,with z vertical and z b ͑x ,y ͒the height of the bed,thennˆ=1ͱ1+͉١z b ͉2ͩ−ץz b ץx ,−ץz bץy ,1ͪ͑4͒cos ␤=n z ,sin ␤=ͱn x2+n y2=ͱ1−n z2͑5͒On sloping beds,particle motion is influenced by the compo-nent of weight down the slope.A unit vector bˆdown the line of maximum slope may be found by normalizing ͑eˆz ϫn ˆ͒ϫn ˆ,where eˆz =unit vector in the vertical direction and a vector cross product is used to generate a vector perpendicular to two given vectors.Thensin ␤b ˆ=−n z 2١z b −͑1−n z 2͒e ˆz =͑n x n z ,n y n z ,n z 2−1͒͑6͒The in-slope forces affecting the motion of a particle along thebed are ͑see Fig.2͒:•Fluid force ␶A s in the direction of flow,where A s ϭrepresentative area of a sediment particle;•Component of ͑buoyancy-reduced ͒weight down the slope,W Јsin ␤bˆ;and •Resistance force with maximum magnitude ␮ϫnormal reaction =␮W Јcos ␤.Here,␮may ͑somewhat loosely ͒be termed a coefficient of fric-tion,and is given by␮=tan ␾͑7͒where ␾=angle of repose—the angle at which particles begin to avalanche in the absence of flow.The first two forces may be combined to give a single effective stress ␶eff ,such that␶eff A s =␶A s +W Јsin ␤bˆ͑8͒The “friction”force always acts in the diametrically opposed di-rection to this combination.The nondimensional effective stressis found by dividing by ͑s −1͒␳gdA s ,noting that the reduced weight W Јis ͑s −1͒␳Vg ,with V the particle volume␶eff ͑s −1͒␳gd =␶͑s −1͒␳gd +V A s dsin ␤b ˆor␶eff *=␶*+D 0sin ␤b ˆ͑9͒where D 0=particle shape parameter ͑V /A s d ͒whose value is inde-pendent of slope and flow .On slopes,the component of particle weight normal to the bed ͑which is what determines the normal reaction from the surface ͒is reduced by a factor cos ␤,and hence it is logical that the critical effective stress needed to initiate particle movement should be reduced by the same factor;i.e.␶eff,crit *=␶crit,0*cos ␤͑10͒where ␶crit,0*=dimensionless critical stress on horizontal beds.This provides a means of deducing D 0,as,in the absence of flow,incipient motion under gravity alone occurs when ␤equals the angle of repose ␾,whence Eqs.͑9͒and ͑10͒giveFig.1.Local unit vectors onthe slopeFig.2.Forces on a particle in a plane locally tangential to the surfaceD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .D 0sin ␾=␶crit,0*cos ␾HenceD 0=␶crit,0*tan ␾͑11͒For typical values ␶crit,0*=0.055and ␾=32°,this would give D 0=0.09.Finally,we substitute Eq.͑6͒for the downslope vector into Eq.͑9͒to give␶eff *=␶*−D 0n z 2١z b −D 0͑1−n z 2͒e ˆz͑12͒As the formulas ͑Table 1͒for bed-load flux vector q b typicallycontain a factor ␶eff −␶eff,crit ,the underlined term in Eq.͑12͒pro-vides a gradient-diffusion-like term in the morphodynamics equa-tion;this aids numerical stability,especially if the morphodynamics equation is solved implicitly.The last term in Eq.͑12͒simply ensures that the effective stress is parallel to the slope.Avalanche ModelThe avalanche model makes no pretension to modeling the inter-mittent ͑and somewhat probabilistic ͒slippages on real slopes.Here,it is simply a numerical artifice to prevent the slope angle ␤significantly exceeding the angle of repose ␾.It does so in a conservative fashion ͑i.e.,by adjusting the flux ͒;specifically,it isimplemented by the addition of a further contribution q aval bˆto the bed-load flux vector.Referring to Fig.3,if tan ␤exceeds tan ␾then a volume 1/2L ϫL ͑tan ␤−tan ␾͒per unit width is transferred from one side of the midpoint to the other in the course of a time step ⌬t ,corresponding to an additional ͑in-surface,rather than horizontal ͒flux per unit width ofq aval =͑1−p ͒12L 2͑tan␤−tan ␾͒cos ␤⌬tif tan ␤Ͼtan ␾͑13͓͒where p =porosity—see Eq.͑20͒later ͔directed along the line ofmaximum slope bˆ.In practice,the multiplier ͑i.e.,the definition of length L ͒need not be too precise,the sole purpose of the additional flux being to redistribute sediment rapidly if the slope exceeds the angle of repose.Calculations in this paper employed as L the maximum horizontal dimension ͑a diagonal ͒of the adjacent surface cell faces.Summary of Bed-Load Flux ModificationsIn summary,the modifications necessary to account for significant slopes are:•Replacement of dimensionless bed stress by an effective stress—Eqs.͑9͒or ͑12͒;•Reduction of the critical effective stress—Eq.͑10͒;•The value of D 0—Eq.͑11͒;and•At slopes larger than the angle of repose,an additional ava-lanche flux—Eq.͑13͒.Coordinate-dependent quantities ͑if required ͒are given in Eqs.͑4͒–͑6͒.Model in ContextFirst,we note that there is an important distinction between thecritical effective stress and the critical fluid stress for incipient particle motion.The first is obtained simply by multiplying the zero-slope value by the cosine of the slope ͓Eq.͑10͔͒.The latter is more complicated and may be found by combining Eqs.͑9͒and ͑10͒such that͉␶crit *+D 0sin ␤b ˆ͉=␶crit,0*cos ␤͑14͒Resolving the fluid stress into components along and perpendicu-lar to the line of maximum slope ͑see Fig.2for the definition of angle ␺͒,substituting for D 0,squaring Eq.͑14͒and solving aquadratic equation for ␶crit*gives ␶crit*=sin ␤cos ␺+ͱcos 2␤tan 2␾−sin 2␤sin 2␺tan ␾␶crit,0*͑15͒This is a formula given by,e.g.,Soulsby ͑1997͒and Ortiz and Smolarkiewicz ͑2006͒,but its origin is considerably older.Comparison with other models may be affected by considering the special cases of longitudinal and lateral slopes.For longitudi-nal slopes fluid and gravitational forces on sediment particles are aligned and our model gives,for the excess effective stress ͑␶eff ͒in terms of the excess fluid stress ͑␶͒Upslope flow ͑␺=0°͒:␶eff*−␶eff,crit*=␶*−sin ͑␾+␤͒sin ␾␶crit,0*͑16a ͒Downslope flow ͑␺=180°͒:␶eff*−␶eff,crit*=␶*−sin ͑␾−␤͒sin ␾␶crit,0*͑16b ͒The critical fluid stress is modified in exactly the same way as in Damgaard et al.͑1997͒.If the underlying bed-load model is as-sumed to be that of Meyer-Peter and Müller then the two models are exactly the same for upslope flow,but our model does not contain the empirical enhancing slope factor f slope for downslope flow that is suggested in Damgaard et al.͑1997͒.For lateral slopes ͑␺=90°͒,the critical fluid stress is,accord-ing to Eq.͑15͒␶crit*=␶crit,0*cos ␤ͱ1−tan 2␤tan 2␾͑17͒which is consistent with other authors.The assumption in our model that the bed-load flux vector remains in the direction of the effective stress after the onset of motion leads to a ratio of cross-stream ͑n ͒to streamwise ͑s ͒components given,up to the angle of repose,byFig.3.Defining the avalanche fluxD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .q nq s =1ͱtan 2␾−tan 2␤␶crit *␶*tan ␤͑18͒compared with,say,Sekine and Parker ͑1992͒q nq s =0.75ͩ␶crit *␶*ͪ1/4tan ␤͑19͒Numerical ImplementationFlow SolverFlow calculations were performed with an in-house researchcode,STREAM:a general-purpose,two-or three-dimensional,finite-volume,RANS solver.The integral equations of fluid mo-tion are solved on multiblock,boundary-conforming,curvilinear meshes.The code permits the use of surface-conforming moving meshes.The code features an extensive repertoire of turbulence models ͑Leschziner and Apsley 2001͒,but the standard k –␧model ͑Launder and Spalding 1974͒is used in all calculations here.The bed-shear stress ␶b is provided by the flow solver,using wall functions for arbitrarily rough surfaces ͑Apsley 2007͒.The Ni-kuradse roughness height k s is required;for sand roughness in controlled laboratory experiments,this is taken ask s =d 50where d 50=median grain size.For natural bodies of water k s can be increased to account for bed forms and surface irregularities contributing to a more generalized unresolvable roughness—a common value is k s =2.5d 50͑Raudkivi 1998͒.Variable storage is cell-centered and collocated and the code uses the standard SIMPLE pressure-correction algorithm,with Rhie-Chow interpolation for advective velocities on cell faces to eliminate “odd-even”pressure decoupling on collocated meshes.Bed MorphodynamicsThe flow calculation is coupled to an equation for the moving bed.“Conservation of sand”leads to an equation for the time variation of the bed height z b ͑x ,y ͒͑1−p ͒ץz bץt=−١h ·q h ͑20͒where p =porosity ͑here taken as 0.4͒and ٌh denotes the horizon-tal divergence operator.q h =rate of horizontal transport of sand per unit horizontal length of bed and is different to the bed-load flux vector q b when there are slopes because:͑1͒the actual length of the bed exceeds the projected horizontal length when there are lateral slopes and ͑2͒the horizontal projection of the bed-flux vector is less than its magnitude if there are streamwise slopes.These orientation features are often ignored in depth-averaged solvers,leading to errors in the net flux for large slopes.In our code the bed height equation is coded in an integral form as͑1−p ͒A h⌬z b⌬t=−ͶץAq b ·d s ϫnˆ͑21͒where the line integral is taken around the boundary of a cell face on the bed ͑Fig.4͒and gives the net outward volume flux ofsediment across the cell face edges irrespective of surface orien-tation.A h =horizontal projected area of a cell face;z b =height of a cell-face-center control point with ⌬z b =height swept out over a time step.Note thatA h ⌬z b =A ⌬n͑22͒where A =sloping area of bed for this cell face and ⌬n =distance moved normal to this slope.Both sides of Eq.͑22͒represent,to leading order,the volume swept out by a cell face in one time step.Control volumes in the flow are defined by their vertices,but the topography of both bed and free surface is defined by control points ͓Fig.5͑a ͔͒whose horizontal positions coincide with cell-face centers.The vertices on the bed and free surface are deter-mined by interpolation from adjacent control points.The mesh moves—albeit slowly—in response to the time evolution of the bed and/or free surface,with cells between bed and free surface being stretched to maintain the same constant fractions of local water depth.Finite-volume moving-mesh and free-surface tech-niques have been described by Apsley and Hu ͑2003͒.The surface orientation is everywhere determined by the unitnormal vector nˆ.At cell-face centers this is determined by nor-malizing the vector area of that cell face ͑which is routinely com-puted from its vertices ͒.At cell edges nˆedge is found by normalizing ⌬x ϫ⌬s ,where ⌬x=vector joining control points ei-ther side of the edge ⌬s .Fig.4.Geometry of a cell face on the bedFig.5.Control points and cell vertices:͑a ͒arrangement;͑b ͒constantcurvature ͑in two dimensions ͒;and ͑c ͒“sawtooth”patternD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .The procedure for moving cell-face-center control points ver-tically is as follows.Note that,in a conservative formulation,flux vectors are required on cell edges .In STREAM this is accom-plished by first interpolating the fluid stress to the cell edges and then forming the bed-load flux vector.Interpolation of the stress vector to cell edges requires care because the surface is curved:simple interpolation of Cartesian components would underesti-mate the magnitude and produce a stress vector that was not tangential to the surface.1.The fluid stress is determined ͑from a wall function ͒at cell-face centers on the bed.This is then split into two in-surface components in the x –z and y –z planes;͑note:not Cartesian components ͒.2.Linear interpolation of the in-surface components is used toreconstruct the fluid stress vector using the in-surface unit vectors on a cell edge.This is then combined vectorially with the downslope component of weight ͓Eq.͑9͔͒to form thedimensionless effective stress ␶eff*on each cell edge.3.The magnitude of the bed-load flux vector q b is computed oncell edges by using one of the models in Table 1,but with ␶*and ␶crit *replaced by ␶eff *and ␶eff,crit*,respectively.The direc-tion of the bed-load flux vector is that of ␶eff*.For slopes exceeding the angle of repose,the bed-load flux vector is supplemented by an avalanche component directly down the slope.4.The net flux of sediment out of each surface cell is computed by integrating the flux across cell edges ⌬sDIV ͑q b ͒ϵͶq ·d s ϫnˆ→͚edgesq b ,edge ·⌬s ϫn ˆedge ͑23͒͑Upper-case DIV signifies the integral divergence from thecell rather than the vector differential operator.͒5.Eq.͑21͒is stepped forward in time using a fully implicit ͑first-order,backward-differencing ͒scheme.The height of the control point z b on each surface cell face evolvesasFig.6.Channel bend:surface morphology and near-surface flowD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .z b n +1=z b n −⌬t͑1−p ͒A hDIV ͑q b ͒n +1͑24͒This equation is solved iteratively at each time step in con-junction with the flow equations—typically,a number of it-erations of the flow solver followed by one or more iterations of the bed control points ͑and consequent change in the com-putational mesh ͒.Iteration stops only when both mesh and flow equations have converged.If necessary,the bed move-ment can be under-relaxed at each iteration.As q b contains a diffusive component proportional to −ٌz b we have found that numerical stability can be enhanced if Eq.͑24͒is solved implicitly for simultaneous incremental corrections ͕␦z b ͖to all control points,rather than as a predictor–corrector-type formula for individual control points.Bed SmoothingTo evaluate the integrated fluxes in Eq.͑23͒requires q b at cell-face edges .How the flux vector is evaluated there depends on the specific node/vertex/cell geometry of individual computer codes.In STREAM the fluid stress is first interpolated to cell edges and then the bed-load flux vector is constructed on those edges.For coarse grids no additional bed smoothing is required.However,our experience is that on finer grids some numerical smoothing is often necessary.To ensure that this is still conservative—i.e.,does not change the overall sediment budget–this must be accomplished by changes to the flux vector.In STREAM,the surface is defined by intermediate control points ͓Fig.5͑a ͔͒,with bed vertices obtained from them by inter-polation.A “sawtooth”pattern of control points can be identified by examining changes to the difference z b −z ¯b ,where z b =height of a control point and z ¯b =average height of adjacent vertices at the same horizontal location.This difference is inversely propor-tional to the radius of curvature.On flat or uniformly-sloping beds it would be zero.On beds with constant curvature it would be a constant ͓Fig.5͑b ͔͒.However,if the control points were to adopt a sawtooth pattern this would alternate in sign ͓Fig.5͑c ͔͒.To prevent the growth of oscillatory wiggles,but to have no effect on beds with constant curvature,a diffusion-like term proportional to the change in z b −z ¯b can be added to the bed-load flux vector.A suitable modification was found to beq b →q b +10͉q b ͉⌬lϫ͓͑z b −z ¯b ͒L −͑z b −z ¯b ͒R ͔͑25͒where q b =component of the bed-load flux vector from left ͑L ͒to right ͑R ͒nodes on either side of a cell edge and ⌬l is the distance between these nodes.The correction vanishes when there is no sediment transport ͑q b =0͒,or on surfaces of constant slope or constant curvature;in general,it is proportional to the derivative of the radius of curvature ͑in this coordinate direction ͒.Calcula-tions for the channel bend ͑see later ͒with successive values of 2,5,and 10for the numerical factor in Eq.͑25͒gave no discernible difference in final surface profiles;however,the calculation was more difficult to initiate with the smaller numbers.Nonerodible BasesAlthough the majority of natural applications are for deep beds of sediment,comparison with laboratory experiments sometimes in-volves cases where sediment is swept away to expose a nonerod-ible base.In these circumstances a crude but effective flux limiter was employed whereby the integrated flux through one cell edge was limited by that required to deplete the upstream column by half its sediment content in one time step.Once again we note that overall sediment conservation requires that any adjustment for nonerodible bases must be made by modifying the flux,not by limiting bed heights directly.ApplicationsSediment Transport in a 90°Channel BendKawai and Julien ͑1996͒reported experimental measurements of bed scour in a 90°channel bend.͓Numerical simulations of this case have also been performed by Rüther and Olsen ͑1995͒.͔The channel width was 0.2m and the centerline radius of the bend was 0.6m.Two grades of bed material were used,but only the coarser type ͑0.6mm sand ͒is considered here.The initial longi-tudinal slope was 1/300.A steady flow of water ͑Q =4L s −1͒and sediment discharge ͑Q s =1.44cm 3s −1͒were maintained for 200min,after which the channel bed was observed to have reached a steady state.The initial water depth ͑0.041m ͒was close to the normal depth for this channel.During the experiment secondary currents in the bend ͑outward flow at the free surface,inward flow at the bed ͒led to substantial scour on the outside of the bend and deposition on the inside.Our time-dependent nu-merical simulations suggest that the inner-bank structure forms first.Numerical simulations were conducted on coarse,intermediate and fine meshes of 90ϫ20ϫ12,135ϫ30ϫ18,and 185ϫ45ϫ18cells,respectively;only minor differences in bed profile were found on the intermediate and fine meshes.V olume fluxes of water and sediment were fixed at inlet and the water level was fixed at outlet.The inflow velocity profile was taken from an initial fully developed-flow calculation and was scaled during the full simulation to maintain a constant volume flux as the free surface and bed evolved.As our code actually solves for piezo-metric pressure,p *=p +␳g ͑z −z ref ͒,the downstream height con-dition was implemented by setting z ref to the downstream water level and p *=0on the exit boundary.The motion of both the free surface and the mobile bed was followed,with the mesh evolving to conform to them.As a final steady state was anticipated,a larger time step was used fortheFig.7.Channel bend:bed-height changes at banksD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y X I 'A N J I A O T O N G U N I VE R S I T Y o n 09/28/13. C o p y r i g h t A S C E .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

WHEN IS A MAXIMAL INV ARIANT HYPOTHESIS TEST BETTER THAN THE GLRT?Hyung Soo Kim and Alfred O.HeroDepartment of Electrical Engineering and Computer ScienceUniversity of Michigan,Ann Arbor,MI48109-2122ABSTRACTThere has been considerable recent interest in applying max-imal invariant(MI)hypothesis testing as an alternative tothe generalized likelihood ratio test(GLRT).This interesthas been motivated by several attractive theoretical prop-erties of MI tests including:exact robustness to variationof nuisance parameters,finite-sample min-max optimality(in some cases),and distributional robustness,i.e.insensi-tivity to changes in the underlying probability distributionover a particular class.Furthermore,in some importantcases the MI test gives a reasonable test while the GLRThas worse performance than the trivial coinflip decision rule[1].However,in other cases,like the deep hide target detec-tion problem,there are regimes(SNR,number of wirelessusers,coherence bandwidth)for which either of the MI andthe GLRT can outperform the other.We will discuss con-ditions under which the MI tests can be expected to outper-form the GLRT in the context of a radar imaging and targetdetection application.1.INTRODUCTIONIn automatic target recognition,the most important issue isreliable detection which is robust to target and clutter vari-ability,yet maintains the highest possible discrimination ca-pability.In the past,most adaptive radar and array detectionproblems have been formulated under the general assump-tion that the target has known form but unknown ampli-tude in Gaussian noise whose covariance matrix is totallyunknown or unstructured.The nature of this assumptionled to the application of the general multivariate analysis ofvariance(GMANOV A)model[2]to the measurements,andthe subsequent development of many detection algorithms.With this assumption and the GMANOV A model,Kelly[3]derived the constant false alarm rate(CFAR)test using thegeneralized likelihood ratio(GLR)principle.However,when a prior structure of the clutter covari-ance matrix exists,one can expect an improvement in per-formance by exploiting this a priori structure.Also whencatenating these vectors we obtain the measurement:whereis the target location vector,and,thefirst column,and Here the subscripts denote the two different regions A andB.denote pixels in the chip which is being tested for containing the target.As described in[2],the MI test is constructed by apply-ing the likelihood ratio test to a statistic called the maximal invariant.The maximal invariant is the lowest dimension statistic summarizing the data yet preserving target vs.clut-ter discrimination capability for the specific parameter ing the maximal invariant approach,Bose andLog GLR:????outperforms GLRT2for low.These observations also hold for mismatched cases:between MI test1and GLRT1in Case2/3(Figs.3/4),and between MI test2and GLRT2in Case1(Figs.2).For Case3(Fig.4),the ROC curve forGLRT2approaches that of the matched GLRT3since largenumber of pixels()provide sufficiently ac-curate estimates of the variance in region B.In Figs.5and7,ROC curves are compared with dif-ferent ratios of from those of Figs.2-4.Kelly’stest for Case1and Bose and Steinhardt’s test for Case2areshown to be more sensitive to the dimensional parameters and.The relative advantages of MI vs.GLR tests are moreclosely investigated in Fig.6and8.In(a)of bothfigures,we increased whilefixing SNR.Note that the GLR andMI tests have ROCs which are virtually indistinguishablefor large.In(b),however,by increasing SNR whilefixing ,the positions of the crossings of the ROCs for the GLR and MI tests decreased.In particular,if onefixes a level of false alarm,say,then note from Fig.6 (b)that the GLR test dominates the MI test for SNR=19dB while the reverse is true for SNR=7dB.Next,we consider an application to real SAR imageryin Fig.1.The image shown is a rural scene near RedstoneArsenal at Huntsville,Alabama,reproduced from the datacollected using the Sandia National Laboratories Twin Ot-ter SAR sensor payload operating at X band.The bound-ary was hand extracted and a SLICY target extracted from Fig.9(e)was inserted so that it straddles the bound-ary.The images in Fig.9correspond to the same target but viewed at different pose angles of azimuth.The data from which these images are reproduced was downloaded from the MSTAR SAR database at the Center for Imaging Sci-ence().With the realigned image in Fig. 10,structured Kelly’s test,MI test1,and GLRT1statistics are calculated and maximized over each possible location along the boundary.Table3shows the minimum magnitude of amplitude required for each test to detect the target at the correct location.In this experiment both the GLR and MI tests perform as good as the structured Kelly’s test.TestTable3.Amplitudes required in magnitude for detection ofthe target at the correct location.Finally,we maximized the test statistics over the differ-ent target poses in Fig.9as well as over all possible loca-tions along the boundary.Only the peak values for9target signatures are plotted in Fig.11,and all the tests success-fully picked the signature at the true pose and location.4.CONCLUSIONThe deep hide scenario considered in this paper complicates the design of optimal target detectors.This scenario gives rise to block diagonal constraints imposed by the clutter co-variance structure.Both GLR and MI tests can be derived under these constraints.Numerical results indicate that nei-ther GLR nor MI tests dominate the other in terms of ROC performance.The GLRT outperforms the MI test only when high estimator accuracy is attainable,e.g.for a large num-ber of samples,but otherwise MI test is better especially in low.Therefore,MI test not only plays an important role as an alternative to GLRT,but also has the desirable property of reliable performance in low with a small number of snapshots.The results in this paper are general-izable to other applications where invariance principle can be applied.5.REFERENCES[1] E.L.Lehmann,Testing Statistical Hypotheses,Wiley,NewYork,1959.[2]T.Kariya and B.K.Sinha,Robustness of Statistical Tests,Academic Press,San Diego,1989.[3] E.J.Kelly,“An adaptive detection algorithm,”IEEE Trans.Aerosp.Electron.Syst.,vol.AES-22,pp.115-127,Mar.1986.[4]S.Bose and A.O.Steinhardt,“A maximal invariant frame-work for adaptive detection with structured and unstructured covariance matrices,”IEEE Trans.Sig.Proc.,vol.43,no.9, pp.2164-2175,Sep.1995.[5] A.O.Hero and C.Guillouet,“Robust detection of SAR/IRtargets via invariance,”1997ICIP,Santa Barbara,CA,vol.3, pp.472-475,Oct.1997.2004006008001000 50100150200250300350Region ARegion BFig.1.SAR clutter image with SLICY target in the bound-ary at column305.PFAP DFig.2.ROC curves for Case 1with SNR =22dB ().Fig.3.ROC curves for Case 2with SNR =10dB ().Fig.4.ROC curves for Case 3with SNR =10dB ().Fig.5.ROC curves for Case 1with SNR =19dB ().(a)SNR =7dB(b)parison of GLR and MI tests for Case 1by (a)varying with fixed SNR and (b)increasing SNR withsmall ().PFAPDFig.7.ROC curves for Case 2with SNR =10dB ().(a)SNR=10dB(b)parison of GLR and MI tests for Case 2by (a)varying with fixed SNR and (b)increasing SNR with small ().(a)(b)(c)(d)(e)(f)(g)(h)(i)Fig.9.SLICY canonical target images at elevation and different azimuth angles.Image in (e)is inserted in Fig.1.2004006008001000102030405060708090100chip1 targetchip2Fig.10.Image realigned along the extracted boundary.SL-ICY target is located at column 305with .Fig.11.Peak values obtained for 9different target images.。

托福阅读真题第185篇DistributionofSeaweeds（答案文章最后）Distribution of SeaweedsParagraph 1: Seaweeds are multicellular algae that inhabit the oceans. Despite their evolutionary distance from each other, seaweeds — such as brown algae, red algae, and green algae —have in common many aspects of their biology and contributions to the ecology of the seas.Paragraph 2: Most species of seaweed are benthic (living on the seafloor); they grow on rock, sand, mud, and coral on the sea bottom. Other species live on other organisms and as part of fouling communities (plants and animals that live on pilings, boat bottoms, and other artificial surfaces). Some seaweeds attach to very specific surfaces, whereas other seaweeds are rather nonselective. In general, seaweeds inhabit about 2 percent of the seafloor. The presence of benthic seaweeds defines the inner continental shelf, where the marine community largely depends on the food and protection that seaweeds provide. Life on the outer continental shelf and in the deep sea is quite different in the absence of seaweeds. The distinction between the inner and outer shelves is based on the compensation depth of algae. The compensation depth is the depth of water at which there is just enough light for algae to survive. At that depth all the oxygen produced by photosynthesis is consumed by the algae’s respiration, so that no further growth can occur.1. What can be inferred from paragraph 2 about the outer continental shelf?O The outer continental shelf contains more benthic seaweeds than the deep sea does.O The outer continental shelf lacks enough sunlight to support the growth of algae.O The outer continental shelf has a compensation depth that is about the same as that of the inner continental shelf.O The outer continental shelf has a greater variety of marine life than does the inner continental shelf.2. According to paragraph 2, all of the following are true of seaweeds EXCEPT:O Seaweeds provide food and protection for other organisms.O Seaweeds can grow on both living and nonliving things.O Some seaweeds select specific surfaces to attach to, while others are not selective.O Two percent of seaweed species live on the ocean floor.Paragraph 3: The environmental factors that are most influential in governing the distribution of seaweeds are light and temperature. Some other abiotic (nonliving) factors critical in governing the distribution of seaweeds are duration of tidal exposure and desiccation (drying out), wave action and surge, salinity, and availability of mineral nutrients. The areas of the world most favorable to seaweed diversity include both sides of the North Pacific Ocean, Australia, southwestern Africa, and the Mediterranean Sea.Paragraph 4: The vertical and horizontal distributions of seaweeds are limited in part by the availability of sunlight and, therefore, vary by depth, latitude, sea conditions, and season. It was once thought that the vertical distribution of red, brown, and green algae could be explained by their accessory photosynthetic pigments (photosynthetic pigments other than chlorophyll), the presence of which gives the seaweeds theircharacteristic colors, a concept known as chromatic adaptation. Because green light penetrates deepest in coastal waters and the accessory pigments of red algae absorb mostly green wavelengths, red algae were thought to extend to the greatest depth. It followed that green algae, which have pigments absorbing mostly blue and red wavelengths that are diminished rapidly in seawater, should be found at the shallowest depths. Because accessory pigments of brown algae absorb intermediate wavelengths of light, brown algae would be expected to be most abundant at intermediate depths. Indeed, some recent evidence would seem to support the hypothesis of chromatic adaptation because the depth record (295 meters, or 973 feet) for seaweeds is held by a yet undescribed species of red algae from the Bahamas. However, the green alga Rhipiliopsis profunda is close behind this record at 268 meters (884 feet).3. According to the concept of chromatic adaptation explained in paragraph 4, which of the following types of algae should be found closest to the ocean’s surface?O Red algaeO Blue algaeO Green algaeO Brown algae4. Why does the author mention “a yet undescribed species of red algae from the Bahamas”?O To suggest that the concept of chromatic adaptation applies only to algae living in deep watersO To argue that location is more important than chromatic adaptation in determining the vertical distribution of algae O To emphasize the difficulty of testing the concept of chromatic adaptation in deep watersO To provide information that may confirm the idea that chromatic adaptation is responsible for the vertical distribution of algae5. What can be inferred from the author’s discussion of the green algae Rhipiliopsis profunda in paragraph 4?O Chromatic adaptation may not be an adequate explanation for the vertical distribution of algae.O All types of algae share the same accessory photosynthetic pigments.O Chromatic adaptation is responsible for the distribution of red algae but not for the distribution of green algae.O Both red and green algae absorb red wavelengths.Paragraph 5: The concept of chromatic adaptation was proposed in 1883, and the hypothesis was accepted for about 100 years, until it was realized that such zonation did not necessarily occur and that the distribution of seaweeds depended more on herbivory (the consumption of plant material), competition, varying concentration of the specialized pigments, and the ability of seaweeds to alter their forms of growth.6. Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leave out essential information.O For about 100 years, chromatic adaptation was thought to have a greater impact on seaweed distribution than various other factors such as herbivory and competition.O The hypothesis of chromatic adaptation was accepted for about 100 years until it was concluded that other factors could explain the distribution of seaweeds.O About 100 years after the concept of chromatic adaptation was developed, it was realized that seaweed zonation occurred even in the absence of chromatic adaptation.O Until the hypothesis of chromatic adaptation became widely accepted 100 years after it was proposed, various other factors were thought to determine the distribution of seaweeds.Paragraph 6: Temperature affects the distribution of seaweeds. The greatest diversity of algal species is in tropical waters. Farther north or south of the equator, the number of species decreases, and the species themselves are different. Many marine algae in colder latitudes are perennials, meaning that they live longer than two years. During the colder seasons only part of the alga remains alive, sometimes only a few cells, but most often a mass of stemlike structures. When the temperature warms up in the spring, this body part initiates new growth. Temperature is not usually a limiting factor for algae that live in tropical and subtropical seas, although temperatures in intertidal areas (those areas between high and low tides) may become too warm and contribute to seasonal mass mortality of many seaweeds and the animals they shelter. At high latitudes, freezing and scouring by ice may eliminate seaweeds from the intertidal and shallow subtidal zones.7. What is the author’s purpose in discussing “temperatures in intertidal areas”?O To emphasize the idea that warm temperatures can be just as dangerous to algae as cold temperaturesO To identify a limiting factor for algae common to both tropical seas and waters at higher latitudesO To compare the causes of seaweed mortality in tropical seas and in seas at higher latitudesO To note an exception to the idea that temperature does not limit the growth of algae in tropical and subtropical waters8. According to paragraph 6, all of the following are true of perennials EXCEPT:O Perennials live for more than two years.O Only part of a perennial remains alive during the winter.O A large number of the marine algae found in cold latitudes are perennials.O Species in the tropics are more sensitive to temperature than are species in colder latitudes.Paragraph 2: Most species of seaweed are benthic (living on the seafloor); they grow on rock, sand, mud, and coral on the sea bottom. Other species live on other organisms and as part of fouling communities (plants and animals that live on pilings, boat bottoms, and other artificial surfaces). ■Some seaweeds attach to very specific surfaces, whereas other seaweeds are rather nonselective. In general, seaweeds inhabit about 2 percent of the seafloor. ■The presence of benthic seaweeds defines the i nner continental shelf, where the marine community largely depends on the food and protection that seaweeds provide. ■Life on the outer continental shelf and in the deep sea is quite different in the absence of seaweeds. ■The distinction between the inner and outer shelves is based on the compensation depth of algae. The compensation depth is the depth of water at which there is just enough light for algae to survive. At that depth all the oxygen produced by photosynthesis is consumed by the algae’s respiration, so that no further growth can occur.9. Look at the four squares [■] that indicate where the following sentence could be added to the passage.They are most prevalent on the part of the sea bottomknown as the continental shelf.Where would the sente nce best fit? Click on a square [■] to add the sentence to the passage.10. Directions: An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in the passage. Some answer choices do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points. Drag your choices to the spaces where they belong. To review the passage, click on View Text.Seaweeds are multicellular algae living in the oceans.Answer ChoicesO Seaweeds are limited to areas with enough light for them to survive, with most living on the seafloor and more species inhabiting warm waters than colder waters.O Some recent evidence shows that the color of any species of seaweed is determined by the amount of chlorophyll contained in its accessory pigments.O The greatest diversity of seaweed is found in warm waters, and seaweed cannot survive when the temperature is either too hot or too cold.O Seaweeds are distributed most evenly over areas of ocean that experience changing tides, strong waves, a dry climate, and high concentrations of salt and minerals.O The chromatic-adaptation hypothesis was long thought to explain the vertical distribution of seaweed, but current belief is that distribution is better explained by other factors.O Temperature extremes in tropical and subtropical areas as well as at high latitudes cause seaweeds to abandon the intertidalareas for the subtidal zones of the seafloor.。

海洋物种濒临灭绝的现状考研英语阅读shifting baselineThe Current State of Endangered Marine Species: A Shifting Baseline PerspectiveThe vast expanse of the world's oceans has long been perceived as an endless source of resources, a realm teeming with diverse and resilient life. However, the harsh reality is that many marine species are facing an unprecedented threat of extinction, a crisis that demands urgent attention and concerted action. As we grapple with the shifting baseline syndrome, understanding the current state of endangered marine species and the underlying factors driving their decline becomes crucial for safeguarding the delicate balance of our oceanic ecosystems.One of the primary concerns regarding endangered marine species is the alarming rate at which their populations are dwindling. According to the International Union for Conservation of Nature (IUCN), a staggering 27% of the world's sharks and rays are now threatened with extinction. This includes iconic species such as the great white shark, the hammerhead shark, and the manta ray, all ofwhich play vital roles in maintaining the health and balance of marine ecosystems. The decline of these apex predators can have cascading effects, disrupting the intricate food webs and leading to further imbalances in the delicate web of life beneath the waves.In addition to sharks and rays, numerous other marine species are also facing similar threats. The vaquita, a small porpoise found only in the Gulf of California, is on the brink of extinction, with fewer than 20 individuals remaining. The Hawaiian monk seal, once abundant in the Hawaiian Archipelago, has seen its population plummet to just a few hundred individuals due to a combination of factors, including entanglement in fishing gear, habitat loss, and human disturbance. The plight of these charismatic species serves as a sobering reminder of the fragility of our marine ecosystems and the urgent need for comprehensive conservation efforts.The underlying causes of this marine biodiversity crisis are multifaceted and complex. Overfishing, a persistent and widespread issue, has depleted the populations of many commercially valuable species, often through the use of unsustainable fishing practices. The bycatch of non-target species, such as sea turtles, dolphins, and seabirds, further exacerbates the problem, as these animals are often unintentionally caught and killed in the pursuit of other fisheries.Climate change and ocean acidification pose additional threats tomarine species. Rising sea temperatures and changing ocean currents can disrupt the delicate balance of marine ecosystems, causing shifts in species distribution and altering the availability of critical resources. Ocean acidification, a consequence of increased carbon dioxide absorption by the oceans, can have detrimental effects on organisms with calcium-based structures, such as coral reefs and shellfish, further destabilizing the foundation of marine food webs.Habitat destruction and degradation also contribute significantly to the decline of endangered marine species. Coastal development, pollution, and the destruction of critical habitats like mangrove forests, seagrass beds, and coral reefs can have devastating impacts on the species that rely on these ecosystems for survival. The loss of these vital habitats not only threatens the species that directly depend on them but also disrupts the broader functioning of marine ecosystems.The shifting baseline syndrome, a phenomenon where each generation perceives the current state of the environment as the "normal" or "natural" condition, further complicates the understanding and appreciation of the severity of the marine biodiversity crisis. As successive generations become accustomed to a progressively degraded environment, the baseline for what is considered a healthy, thriving marine ecosystem shifts, making itincreasingly difficult to recognize and address the true scale of the problem.Addressing the plight of endangered marine species requires a multifaceted approach that combines scientific research, effective policies, and collaborative efforts among various stakeholders. Strengthening international treaties and regulations, such as the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES), can help curb the illegal trade and exploitation of endangered marine species. Implementing robust fisheries management strategies, including the establishment of marine protected areas and the adoption of sustainable fishing practices, can help rebuild depleted populations and restore the balance of marine ecosystems.Additionally, investing in habitat restoration and conservation initiatives can play a crucial role in safeguarding the critical environments that support endangered marine species. Coral reef restoration projects, mangrove reforestation efforts, and the protection of seagrass beds and other coastal habitats can help mitigate the impacts of habitat loss and degradation.Engaging local communities and indigenous populations in conservation efforts is also essential, as these groups often possess invaluable traditional ecological knowledge and can serve asstewards of the marine environment. Empowering these stakeholders to participate in decision-making processes and to become active agents of change can lead to more effective and sustainable conservation outcomes.Ultimately, addressing the crisis of endangered marine species requires a holistic approach that addresses the multifaceted challenges facing our oceans. By combining scientific research, effective policies, and collaborative efforts, we can work towards a future where the diversity and resilience of marine life are preserved for generations to come. As we confront the shifting baseline syndrome and strive to restore the true abundance and vitality of our oceans, we must recognize the intrinsic value of these ecosystems and the crucial role they play in sustaining life on our planet.。

临界深度英语The Critical DepthThe vast expanse of the ocean has long captivated the human imagination, its depths concealing a world of mysteries and untold wonders. One such enigma that has intrigued scientists and adventurers alike is the concept of the critical depth, a threshold that marks the boundary between the familiar and the unknown.Beneath the shimmering surface, the ocean's depths descend into a realm of immense pressure, darkness, and extreme conditions that challenge the very limits of human exploration. As one delves deeper, the weight of the water above bears down, exerting a force that can crush even the sturdiest of vessels. This critical depth, where the pressure becomes too great for most conventional diving equipment, represents a formidable barrier that separates the accessible from the inaccessible.It is at this critical depth that the true nature of the ocean's mysteries begins to unfold. The abyssal zone, the deepest and most remote region of the ocean, is a realm where light rarely penetrates, and the creatures that inhabit this alien landscape have evolved in ways thatdefy our understanding. Here, bizarre and otherworldly lifeforms thrive, adapted to the crushing pressures and total darkness that characterize this extreme environment.The quest to explore and unravel the secrets of the critical depth has driven countless expeditions and technological advancements. From the pioneering dives of early deep-sea explorers to the development of sophisticated submersibles and remotely operated vehicles, the human drive to push the boundaries of our understanding has been a constant driving force.One of the most significant breakthroughs in this pursuit was the development of the Trieste, a unique deep-sea research vessel capable of reaching depths previously thought inaccessible. In 1960, the Trieste made a historic descent to the Challenger Deep, the deepest point in the world's oceans, located in the Mariana Trench. This remarkable feat, achieved by Swiss oceanographer Jacques Piccard and U.S. Navy lieutenant Don Walsh, marked a pivotal moment in the exploration of the critical depth, demonstrating that even the most extreme environments could be accessed and studied.Since that groundbreaking dive, the quest to explore the critical depth has continued, with new technologies and techniques pushing the boundaries of what is possible. The development of autonomous underwater vehicles (AUVs) and remotely operated vehicles (ROVs)has allowed scientists to venture deeper and gather more comprehensive data about the abyssal zone, revealing a wealth of information about the unique ecosystems and geological features that exist in these extreme environments.One of the most intriguing aspects of the critical depth is the way it challenges our understanding of life itself. The creatures that thrive in the crushing pressures and total darkness of the abyssal zone have evolved remarkable adaptations, from bioluminescent organs that produce their own light to specialized sensory systems that allow them to navigate and hunt in the absence of sunlight.These deep-sea denizens, often referred to as "extremophiles," have captured the imagination of scientists and the public alike, as they represent a testament to the resilience and adaptability of life on our planet. By studying these remarkable organisms, we can gain insights into the fundamental processes that govern the evolution of life, and perhaps even uncover clues about the potential for life on other worlds.As we continue to explore the critical depth, we are also confronted with the sobering reality of the fragility of the ocean's ecosystems. The deep sea, long considered a remote and untouched realm, is increasingly under threat from human activities such as overfishing, deep-sea mining, and the accumulation of plastic pollution.Understanding the critical depth and the delicate balance of the abyssal zone is crucial if we are to protect these precious and irreplaceable habitats.In conclusion, the critical depth represents a threshold that challenges our understanding of the ocean and the limits of human exploration. From the crushing pressures to the bizarre and otherworldly creatures that thrive in these extreme environments, the critical depth continues to captivate and inspire us, driving us to push the boundaries of our knowledge and technology. As we delve deeper into this mysterious realm, we uncover not only the secrets of the ocean but also the profound lessons about the resilience and adaptability of life on our planet. The quest to explore the critical depth is a testament to the human spirit, a journey of discovery that promises to reveal the wonders and complexities of the natural world.。