-
摘要: 近年来, 基于卷积神经网络的目标检测研究发展十分迅速, 各种检测模型的改进方法层出不穷. 本文主要对近几年内目标检测领域中一些具有借鉴价值的研究工作进行了整理归纳. 首先, 对基于卷积神经网络的主要目标检测框架进行了梳理和对比. 其次, 对目标检测框架中主干网络、颈部连接层、锚点等子模块的设计优化方法进行归纳, 给出了各个模块设计优化的基本原则和思路. 接着, 在COCO数据集上对各类目标检测模型进行测试对比, 并根据测试结果分析总结了不同子模块对模型检测性能的影响. 最后, 对目标检测领域未来的研究方向进行了展望.Abstract: In recent years, research on object detection based on convolutional neural network has developed rapidly, and various improved algorithms and models have emerged one after another. This paper mainly summarizes some recent valuable research work in the field of object detection. Firstly, main object detection framework based on convolutional neural network is analyzed and compared. Secondly, the optimization methods of backbone, neck, anchors and other sub-modules are summarized, and the basic principles and ideas for the design and optimization of each modules are given. Thirdly, various objection detection models are tested and compared on the COCO dataset, effects of different sub-modules on the detector performance were analyzed according to the test results. Finally, future research direction in object detection is prospected.
-
Key words:
- Convolutional neural network /
- object detection /
- sub-module optimization
-
战机在空战中近距格斗不可避免, 大迎角下精准且快速的机头指向能力是空战胜败的关键因素[1]. 当战机进行大迎角机动时, 机体附近的气流从附着流变为不稳定的分裂流, 使得气动力和气动力矩表现出强烈的非线性, 同时导致气动操纵面舵效降低和通道间产生强耦合性[2]. 推力矢量发动机能够直接改变飞行器的推力大小和推力方向, 是发挥现代飞行器高机动性能的重要技术. 因此, 设计推力矢量战机大迎角机动协同控制方法, 对增强其战斗能力和生存能力具有重要意义. 如何设计控制方法克服飞机大迎角机动时的强非线性和强耦合性, 并合理分配到气动舵面和推力矢量上, 是飞机大迎角机动控制的核心问题.
围绕大迎角的机动控制问题, 发展出了多种有效的控制方法. 利用小扰动线性化模型, 增益调度[3]、多平衡点自适应切换[4]和鲁棒控制[5]等经典控制方法得以应用, 然而基于线性模型的控制方法难以覆盖大迎角机动飞行包线. 针对大迎角飞行导致的强非线性, 广义逆方法[6]利用非线性模型信息实现控制解耦, 通过反馈线性化的方式设计逆控制器, 并可与容错控制[7]、模糊控制[8]和自适应动态规划[9]等方法结合. 广义逆方法克服了线性控制器的局限性, 但依赖于精确的模型信息, 难以应对战机大迎角机动时表现的强非线性与模型不确定.
针对战机在大迎角状态下动力学不确定的处理方法大致可分为三种: 第一种方法是设计鲁棒控制策略抵抗不确定的影响, 文献[10]利用滑模控制的鲁棒和抗扰性能, 设计了战机大迎角机动和侧滑角抗扰控制律. 文献[11]针对输入受限下飞行器力矩计算的不确定性, 设计了神经网络滑模姿态跟踪控制律, 有效减少了系统颤振. 第二种方法是设计状态观测器对模型不确定进行估计, 文献[12]基于自抗扰控制方法, 利用扩张状态观测器对模型不确定性进行估计和补偿, 并实现了气动舵面和推力矢量的协同控制. 文献[13]考虑过失速机动时输入饱和的影响, 设计了非线性有限时间观测器实现对飞行器模型中非稳态气动扰动的实时估计, 提高了姿态控制的精度. 文献[14]考虑风扰动对飞行器动力学的干扰, 设计了基于扰动观测器的自适应控制器, 实现了对未知扰动和不确定的有效估计. 第三种方法是通过智能方法对模型不确定进行在线估计和补偿. 基于反步法的控制框架, 将状态变量作为虚拟控制递归设计控制器, 便于精细处理级联子系统的不确定[15], 同时具有与其他方法整合灵活[16-17]的特点. 文献[18]将未知气动函数转化为线性参数化的形式, 设计自适应更新律对未知气动参数进行估计. 文献[19-20]针对战机建模误差和外部干扰等模型不确定, 提出了基于反步法的鲁棒自适应控制方案, 保证了闭环系统的全局稳定. 文献[21-22]基于神经网络智能学习方法, 对反步框架下的级联子系统不确定进行估计, 有效提升了系统非线性学习性能和控制精度. 文献[23]进一步构建离线有限时间复合学习律存储训练数据, 有效减少了计算负荷.
基于以上分析, 战机大迎角模型呈现大范围非线性、气动不确定及强耦合特性, 要求飞控系统消除非线性影响, 使控制系统具备较好的操稳特性. 大迎角机动时飞机没有典型配平状态, 已有平衡点小扰动线性化和传统增益预置控制失效, 而自抗扰等非线性控制方法利用鲁棒观测处理集总未知, 仅面向闭环稳定, 难以实现集总干扰的精细估计与补偿. 本文通过将通道耦合作用和模型强非线性视为集总扰动, 将动力学模型解耦为迎角、侧滑角和滚转角速率子系统. 通过平行估计系统构建表征干扰不确定学习性能的预测误差信号, 设计复合学习更新律对集总未知进行有效估计和补偿, 并基于估计信息设计智能自适应控制律. 最后基于串接链控制分配方案, 实现气动舵面与推力矢量的协同控制. 仿真测试表明所提方法能够实现大迎角机动指令的有效跟踪, 且跟踪精度更高、学习性能更好.
1. 问题描述
1.1 六自由度非线性模型
考虑战机动力学模型[12]为
$$ \begin{split} \dot \alpha =\; & q - \tan \beta (p\cos \alpha + r \sin \alpha )\;+\\ & \frac{1}{{mV\cos \beta }}( - L + mg\cos \gamma \cos \mu )\; +\\ & \frac{1}{{mV\cos \beta }}( - {T_x}\sin \alpha + {T_z}\cos \alpha ) \end{split} $$ (1) $$ \begin{split} \dot \beta = \;& - r\cos \alpha + p\sin \alpha + \frac{1}{{m V}} Y\cos \beta\; +\\ & \frac{1}{{m V}}( mg\cos \gamma \sin \mu - {T_x}\sin \beta \cos \alpha )\;+ \\ & \frac{1}{{m V}}( {T_y}\cos \beta - {T_z}\sin \beta \sin \alpha ) \end{split} $$ (2) $$ \begin{split} \dot p = \;& \frac{{{I_{zz}}({l_a} + {l_T}) + {I_{xz}}({n_a} + {n_T})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}\; +\\ & \frac{{{I_{xz}}({I_{xx}} - {I_{yy}} + {I_{zz}})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}pq \;+\\ & \frac{{{I_{zz}}({I_{yy}} - {I_{zz}}) - I_{xz}^2}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}qr \end{split} $$ (3) $$ \begin{split} \dot q =\; & \frac{m_a+m_T}{I_{yy}} + \frac{I_{zz}pr - I_{xx}pr}{I_{yy}}\;+ \\ &\frac{I_{xz}r^2 -I_{xz}p^2}{I_{yy}} \end{split} $$ (4) $$ \begin{split} \dot r = \;& \frac{{{I_{xz}}({l_a} + {l_T}) + {I_{xx}}({n_a} + {n_T})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}} \;+\\ & \frac{{{I_{xx}}({I_{xx}} - {I_{yy}}) + I_{zz}^2}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}pq \;-\\ & \frac{{{I_{xz}}({I_{xx}} - {I_{yy}} + {I_{zz}})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}qr \end{split} $$ (5) 该模型状态量为${\boldsymbol{x}} = [\alpha , \beta , p, q, r]^{\rm{T}}$, $ \alpha $和$ \beta $分别表示迎角和侧滑角, $ p $, $ q $和$ r $分别表示滚转角速率、俯仰角速率和偏航角速率. 控制输入为${\boldsymbol{u}} = [{\delta _e},{\delta _a}, {\delta _r},{\delta _x},{\delta _y},{\delta _z}]^{\rm{T}}$, $ \delta_e $, $ \delta_a $和$ \delta_r $分别表示升降舵、副翼和方向舵偏角, $ \delta_x $, $ \delta_y $和$ \delta_z $分别表示滚转、偏航和俯仰方向的推力矢量喷管偏角. $ V $, $ \gamma $, $ \chi $和$ \mu $分别表示速度、航迹倾斜角、航迹方位角和航迹滚转角, $ T_x $, $ T_y $和$ T_z $分别表示推力矢量产生的力在机体轴的分量, $ l_T $, $ m_T $和$ n_T $分别表示推力矢量产生的三轴力矩, $ m $表示战机质量, $ g $表示重力加速度, $ I_{ij} $$( i = x,y,z$, $j = x,y,z)$表示惯性矩. $ D $, $ Y $和$ L $分别表示阻力、侧力和升力, $ l_a $, $ m_a $和$ n_a $分别表示滚转力矩、俯仰力矩和偏航气动力矩, 表达式分别为
$$ \begin{split}& D = \bar qS( - {C_{xtot}}\cos \alpha\cos \beta -{C_{ytot}} \sin \beta \;-\\ &\qquad {C_{ztot}}\sin \alpha \cos \beta )\\& Y = \bar qS( - {C_{xtot}} \cos \alpha \sin \beta + {C_{ytot}}\cos \beta \;-\\ &\qquad {C_{ztot}}\sin \alpha \sin \beta )\\ &L = \bar qS({C_{xtot}}\sin \alpha - {C_{ztot}}\cos \beta )\\ &{l_a} = \bar qSb{C_{ltot}}\\ &{m_a} = \bar qS\bar c{C_{mtot}}\\ &{n_a} = \bar qSb{C_{ntot}} \end{split} $$ 其中,
$$ \begin{split} &C_{xtot} = {C_{x0}} + {C_{x,q}}\frac{{\bar cq}}{{2V}}\\ & {C_{ytot}} = {C_{y0}} + {C_{y,{\delta _a}}}{{\bar \delta }_a} + {C_{y,{\delta _r}}}{{\bar \delta }_r} + {C_{y,r}}\frac{{br}}{{2V}} + {C_{y,p}}\frac{{bp}}{{2V}}\\ & {C_{ztot}} = {C_{z0}} + {C_{z,q}}\frac{{\bar cq}}{{2V}}\\ & {C_{ltot}} = {C_{l0}} + {C_{l,{\delta _a}}}{{\bar \delta }_a} + {C_{l,{\delta _r}}}{{\bar \delta }_r} + {C_{l,r}}\frac{{br}}{{2V}}\;+ \\ &\qquad\;\; {C_{l,p}}\frac{{bp}}{{2V}} + d{C_{l,\beta }}\beta \\ &{C_{mtot}} = {C_{m0}} + {C_{ztot}}({x_{cgr}} - {x_{cg}}) + {C_{m,q}}\frac{{\bar cq}}{{2V}}\\ &{C_{ntot}} = {C_{n0}} + \frac{{\bar c}}{b}{C_{ytot}}({x_{cgr}} - {x_{cg}}) + {C_{n,{\delta _a}}}{{\bar \delta }_a}\;+ \\ &\;\;\qquad {C_{n,{\delta _r}}}{{\bar \delta }_r} + {C_{n,r}}\frac{{br}}{{2V}} + {C_{n,p}}\frac{{bp}}{{2V}} + d{C_{n,\beta }}\beta \end{split} $$ 式中, $ \bar q = 0.5\rho V^2 $, $ \rho $表示空气密度, $ S $表示气动参考面积, $ \bar c $表示平均气动弦长, $ b $表示机翼展长, $ x_{cgr} $表示参考重心位置, $ x_{cg} $表示重心位置, $ \bar \delta_a = \delta_a /21.5 $, $ \bar \delta_r = \delta_r /30 $, $ {C_{x0}} $, $ C_{y0} $, $ C_{z0} $, $ C_{l0} $, $ C_{m0} $, $ C_{n0} $, $ C_{x,q} $, $ C_{z,q} $, $ C_{m,q} $, $ C_{y,r} $, $ C_{l,r} $, $ C_{n,r} $, $ C_{y,p} $, $ C_{l,p} $, $C_{n,p} $, $ C_{y,\delta_a} $, $ C_{l,\delta_a} $, $ C_{n,\delta_a} $, $ C_{y,\delta_r} $, $ C_{l,\delta_r} $, $ C_{n,\delta_r} $, $ dC_{l,\beta} $和$ dC_{n,\beta} $为气动参数.
注 1. 战机动力学模型存在较强的耦合特性, 在俯仰、滚转和偏航三通道的表达式中包含另外两个通道中的状态, 同时三通道气动参数均为各通道变量、升降舵、副翼和方向舵的非线性函数.
1.2 推力矢量发动机模型
飞机尾部对称安装的两台推力矢量发动机提供额外的控制力矩. 定义推矢喷管的上下偏转角为$\delta_{zi}\,(i = l,f)$, 其中$ l $和$f$分别表示左右推矢喷管, 向下偏转为正. 定义推矢喷管的左右偏转角为$\delta_{yi}\,(i = l,f)$, 向左偏转为正. 两台发动机的上下偏转提供俯仰力矩, 俯仰通道的推矢偏角为$\delta_z = (\delta_{zl}+\delta_{zf})/2$. 两台发动机的左右偏转提供偏航力矩, 偏航通道的推矢偏角为$\delta_y = (\delta_{yl}+\delta_{yf})/2$. 两台发动机差动偏转提供飞机的滚转力矩, 滚转通道的推矢偏角为$\delta_x = (-\delta_{zl}+\delta_{zf})/2$.
假设两台发动机的推力大小和左右偏转角均相等, 即$\delta_{yl} = \delta_{yf} = \delta_y$. 在喷管偏角小于$ 20^\circ $的限制下, 推力矢量产生的推力在机体系三轴的分量为
$$ \begin{align} \begin{bmatrix} T_x \\ T_y\\T_z \end{bmatrix} = &\;\zeta _f T\begin{bmatrix} \cos {\delta _x}\cos {\delta _y}\cos {\delta _z}\\ \sin {\delta _y}\\ - \cos {\delta _x}\cos {\delta _y}\sin {\delta _z}\end{bmatrix} \end{align} $$ (6) 式中, $ T $表示发动机推力, $ \zeta_f $表示推力系数.
令$ x_T $, $ y_T $和$ z_T $表示推力在机体系三轴上作用点的位置, 则推力矢量产生的推力力矩为
$$ \begin{align} \begin{bmatrix} {l_T}\\ {m_T}\\ {n_T}\end{bmatrix} = \begin{bmatrix} {x_T}\\ {y_T}\\ {z_T}\end{bmatrix}\times \begin{bmatrix} {T_x}\\ {T_y}\\ {T_z} \end{bmatrix} \end{align} $$ (7) 1.3 动力学模型变换
根据式(1)和(4), 可得迎角子系统
$$ \begin{cases} \dot \alpha = q + {f_\alpha }\\ \dot q = {b_{0\alpha }}{v_1} + {f_q} \end{cases} $$ (8) 式中, $ b_{0\alpha} $表示俯仰控制系数, $ v_1 $表示俯仰操纵力矩, $ f_\alpha $和$ f_q $表达式分别为
$$ \begin{split} {f_\alpha } =\;& - \tan \beta (p\cos \alpha + r\sin \alpha)\;+ \\ & \frac{1}{{mV\cos \beta }}( - L + mg\cos \gamma \cos \mu )\;+\\ & \frac{1}{{mV\cos \beta }}( - {T_x}\sin \alpha + {T_z}\cos \alpha )\\ {f_q} = \;&\frac{{({m_a} + {m_T}) + ({I_{zz}} - {I_{xx}})pr }}{{{I_{yy}}}}\;+ \\ &\frac{{I_{xz}}({r^2} - {p^2})}{I_{yy}}- {b_{0\alpha }}{v_1} \end{split} $$ 根据式(2)和(5), 可得侧滑角子系统
$$ \begin{cases} \dot \beta = {r_x}\\ {{\dot r}_x} = {b_{0\beta }}{v_2} + {f_r} \end{cases} $$ (9) 式中, $ b_{0\beta} $表示偏航控制系数, $ v_2 $表示偏航操纵力矩, $ f_r $表达式为
$$ \begin{split} {f_r} = \;&- \frac{{{I_{xx}}({I_{xx}} - {I_{yy}}) + I_{xz}^2}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}pq\cos \alpha \;+\\ & \frac{{{I_{xz}}({I_{xx}} - {I_{yy}} + {I_{zz}})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}qr\cos \alpha + r\dot \alpha \sin \alpha + {{\dot f}_\beta }\;-\\ & \frac{I_{xx}(n_a + n_T) + I_{xz} (l_a+l_T )} {I_{xx}I_{zz} - I_{xz}^2} \cos \alpha - {b_{0\beta }}{v_2} \end{split} $$ $$ \begin{split} f_\beta = & \frac{1}{mV} (Y\cos\beta + mg\cos\gamma\sin\mu - T_x \sin\beta\cos\alpha\; + \\ &T_y\cos\beta - T_z\sin\beta\sin\alpha)\end{split} $$ 根据式(3), 可得滚转角速率子系统
$$ \dot p = {b_{0p}}{v_3} + {f_p} $$ (10) 式中, $ b_{0p} $表示滚转控制系数, $ v_3 $表示滚转操纵力矩, $ f_p $表达式为
$$ \begin{split} {f_p} =\;& \frac{{{I_{xz}}({I_{xx}} - {I_{yy}} + {I_{zz}})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}pq + \frac{{{I_{zz}}({I_{yy}} - {I_{zz}}) - I_{xz}^2}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}}qr \;+\\ & \frac{{{I_{xz}}({n_a} + {n_T})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}} + \frac{{{I_{zz}}({l_a} + {l_T})}}{{{I_{xx}}{I_{zz}} - I_{xz}^2}} - {b_{0p}}{v_3} \end{split} $$ 引理 1. 对于紧子集$\Omega \in {\bf{R}}$上的未知平滑非线性函数, 采用径向基神经网络[21] 进行估计, 可得
$$ f({\boldsymbol{\xi}}) = {{\boldsymbol{W }}^{\rm{T}}} {\boldsymbol{\vartheta }} ({\boldsymbol{\xi}}) + {\boldsymbol{\varepsilon }} $$ (11) 式中, $ {\boldsymbol{\xi}} \in \Omega $表示输入向量; ${\boldsymbol{W }} \in {{\bf{R}}^l}$表示最优权重向量, $ l>1 $; $ {\boldsymbol{\varepsilon }} $表示神经网络的逼近误差, 满足$ \left\| {\boldsymbol{\varepsilon }} \right\| \le {\varepsilon _M} $, 其中$ {\varepsilon _M}>0 $表示逼近误差上界; ${\boldsymbol{\vartheta }} ({\boldsymbol{\xi}} ) = [{\vartheta _1}({\boldsymbol{\xi}}), {\vartheta _2}({\boldsymbol{\xi}}),\, \cdots ,{\vartheta _l}({\boldsymbol{\xi}})]^{\rm{T}}$表示基函数向量, 一般选择高斯函数作为径向基函数, 表达式为
$$ {\vartheta _j}({\boldsymbol{\xi}}) = \frac{1}{{\sqrt {2\pi {{\bar \sigma }_j}} }}\exp \left[ { - \frac{{{{({\boldsymbol{\xi}} - {{\boldsymbol{\varrho}}_j})}^{\rm{T}}}({\boldsymbol{\xi}} - {{\boldsymbol{\varrho}}_j})}}{{2{{\bar \sigma }^2}_j}}} \right] $$ (12) 式中, $ j = 1,2, \cdots ,l $; ${{\boldsymbol{\varrho}}_j} = {[{\varrho_{j1}},{\varrho_{j2}},\, \cdots ,{\varrho_{jD}}]^{\rm{T}}}$表示吸引域中心, $ D>1 $; $ {\bar \sigma _j} $表示高斯函数的标准差.
1.4 控制目标
考虑解耦后的迎角子系统(8)、侧滑角子系统(9)和滚转角速率子系统(10), 本文的控制目标是设计基于复合学习的智能自适应控制方法获取期望操纵力矩, 在此基础上设计串接链分配方法获取气动舵面和推力矢量偏角, 实现大迎角机动指令的有效跟踪.
2. 控制器设计
针对解耦后的子系统, 采用神经网络估计未知气动函数, 构建预测误差对学习性能进行评价, 结合气动估计信息对模型非线性进行补偿, 设计自适应控制器获取期望控制力矩, 保证机动指令的有效跟踪. 以迎角子系统为例, 控制结构如图1所示.
2.1 迎角子系统设计
步骤 1. 考虑迎角动力学, 采用神经网络逼近未知气动函数$ f_\alpha $, 可得
$$ \dot \alpha = q + {\boldsymbol{\omega }}_{{f_\alpha }}^{*{\rm{T}}}{{\boldsymbol{\theta }}_{{f_\alpha }}}( \bar {{\boldsymbol{x}}}_\alpha ) + \varepsilon _\alpha $$ (13) 式中, $ {\boldsymbol{\omega }}_{{f_\alpha }}^* $表示神经网络的最优权重, $ {{\boldsymbol{\theta }}_{{f_\alpha }}}({\bar{\boldsymbol{x}}}_\alpha) $表示基函数向量, ${\bar{\boldsymbol{x}}}_\alpha = [V, \alpha, \gamma]^{\rm{T}}$, $ {\varepsilon _\alpha} $表示逼近误差.
定义迎角跟踪误差$ e_\alpha = \alpha-\alpha_d $, $ \alpha_d $表示迎角指令. 设计俯仰角速率虚拟控制量为
$$ {q_c} = - {k_\alpha }{e_\alpha } - {\hat f_\alpha } + {\dot \alpha _d} $$ (14) 式中, $ k_\alpha $表示控制参数, ${\hat f_\alpha } = \hat {\boldsymbol{\omega }}_{{f_\alpha }}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_\alpha }}}({{\bar{\boldsymbol{x}}}_\alpha})$表示$ f_\alpha $的估计值, $ \hat {\boldsymbol{\omega }}_{f_\alpha} $表示最优权重$ {\boldsymbol{\omega }}_{{f_\alpha }}^* $的估计值.
引入一阶滤波器为
$$ {\sigma _\alpha }{\dot q_d} + {q_d} = {q_c},\quad{q_d}(0) = {q_c}(0) $$ (15) 式中, $ \sigma_\alpha $表示滤波参数, $ q_d $表示$ q_c $经过一阶滤波器后获得的信号.
定义俯仰角速率跟踪误差$ e_q = q-q_d $. 迎角跟踪误差的导数为
$$ \begin{split} {{\dot e}_\alpha } = \tilde {\boldsymbol{\omega }}_{{f_\alpha }}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_\alpha }}}({\bar{\boldsymbol{x}}}_\alpha) + {\varepsilon _\alpha } - {k_\alpha }{e_\alpha } + {e_q} + {q_d} - {q_c} \end{split} $$ (16) 式中, $ \tilde {\boldsymbol{\omega }}_{{f_\alpha }}^{} = {\boldsymbol{\omega }}_{{f_\alpha }}^* - \hat {\boldsymbol{\omega }}_{{f_\alpha }}^{} $.
设计滤波补偿信号为
$$ {\dot c_\alpha } = - {k_\alpha }{c_\alpha } + {c_q} + {q_d} - {q_c},\;{c_\alpha }(0) = 0 $$ (17) 式中, 补偿信号$ c_q $在下一步给出.
定义补偿后的迎角跟踪误差为
$$ \tilde \alpha = {e_\alpha } - {c_\alpha } $$ (18) 定义预测误差为
$$ \begin{cases} {z_\alpha } = \alpha - \hat \alpha \\ \dot {\hat {\alpha} } = q + {{\hat f}_\alpha } + {\lambda _\alpha }{z_\alpha } \end{cases} $$ (19) 式中, $ \lambda_\alpha $表示设计参数.
设计复合学习更新律为
$$ {{\dot {\hat {\boldsymbol{\omega}} }}_{{f_\alpha }}} = {\Gamma _\alpha }\left[ {\left( {{\tilde \alpha } + {\Gamma _{z\alpha }}{z_\alpha }} \right){{\boldsymbol{\theta }}_{{f_\alpha }}}({\bar{\boldsymbol{x}}}_\alpha) - {\delta _{{f_\alpha }}}{{\hat {\boldsymbol{\omega }}}_{{f_\alpha }}}} \right] $$ (20) 式中, $ \Gamma_\alpha $, $ \Gamma_{z\alpha} $和$ \delta_{f\alpha} $表示设计参数.
步骤 2. 考虑俯仰角速率动力学, 采用神经网络逼近未知气动函数$ f_q $, 可得
$$ \dot q = {b_{0\alpha }}{v_1} + {\boldsymbol{\omega }}_{{f_q}}^{*{\rm{T}}}{{\boldsymbol{\theta }}_{{f_q}}}({\bar{\boldsymbol{x}}}_q) + {\varepsilon _q} $$ (21) 式中, $ {\boldsymbol{\omega }}_{{f_q}}^* $表示神经网络的最优权重, $ {{\boldsymbol{\theta }}_{{f_q}}}({\bar{\boldsymbol{x}}}_q) $表示基函数向量, ${\bar{\boldsymbol{x}}}_q = [V, \alpha, q, \gamma]^{\rm{T}}$, $ {\varepsilon _q} $表示逼近误差.
设计俯仰操纵力矩为
$$ {v_1} = b_{0\alpha }^{ - 1}\left( { - {k_q}{e_q} - {e_\alpha } - {{\hat f}_q} + {{\dot q}_d}} \right) $$ (22) 式中, $ k_q $表示控制参数, ${\hat f_q} = \hat {\boldsymbol{\omega }}_{{f_q}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_q}}}({\bar{\boldsymbol{x}}}_q)$表示$ f_q $的估计值, $ {\hat {\boldsymbol{\omega }}_{{f_q}}} $表示最优权重$ {\boldsymbol{\omega }}_{{f_q}}^* $的估计值.
俯仰角速率跟踪误差的导数为
$$ \begin{split} {{\dot e}_q} = \tilde {\boldsymbol{\omega }}_{{f_q}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_q}}}({\bar{\boldsymbol{x}}}_q) + {\varepsilon _q} - {k_q}{e_q} - {e_\alpha } \end{split} $$ (23) 式中, $ \tilde {\boldsymbol{\omega }}_{{f_q}}^{} = {\boldsymbol{\omega }}_{{f_q}}^* - \hat {\boldsymbol{\omega }}_{{f_q}}^{} $.
设计滤波补偿信号为
$$ {\dot c_q} = - {k_q}{c_q} - {c_\alpha },\;{c_q}(0) = 0 $$ (24) 定义补偿后的俯仰角速率跟踪误差为
$$ \tilde q = {e_q} - {c_q} $$ (25) 定义预测误差为
$$ \begin{cases} {z_q} = q - \hat q\\ \dot {\hat {q}} = {b_{0\alpha }}{v_1} + {{\hat f}_q} + {\lambda _q}{z_q} \end{cases} $$ (26) 式中, $ \lambda_q $表示设计参数.
设计复合学习更新律为
$$ {{{{\dot {\hat {\boldsymbol{\omega}} }}}}_{{f_q}}} = {\Gamma _q}\left[ {\left( {{\tilde q} + {\Gamma _{zq}}{z_q}} \right){{\boldsymbol{\theta }}_{{f_q}}}({\bar{\boldsymbol{x}}}_q) - {\delta _{{f_q}}}{{\hat {\boldsymbol{\omega }}}_{{f_q}}}} \right] $$ (27) 式中, $ \Gamma_q $, $ \Gamma_{zq} $和$ \delta_{f_q} $表示设计参数.
2.2 侧滑角子系统设计
步骤 1. 考虑侧滑角动力学, 定义侧滑角跟踪误差$ e_\beta = \beta-\beta_d $, $ \beta_d $ 表示侧滑角参考指令. 设计$ r_{xc} $为
$$ r_{xc} = -k_\beta e_\beta+\dot{\beta_d} $$ (28) 式中, $ k_\beta $表示控制参数.
引入一阶滤波器为
$$ {\sigma _r}{\dot r_{xd}} + {r_{xd}} = {r_{xc}},\quad{r_{xd}}(0) = {r_{xc}}(0) $$ (29) 式中, $ \sigma_r $表示滤波参数, $ r_{xd} $为$ r_{xc} $经过一阶滤波器后获得的信号.
定义偏航角速率跟踪误差为$ e_r = r_x-r_{xd} $. 侧滑角跟踪误差的导数为
$$ \begin{split} {{\dot e}_\beta } & = - {k_\beta }{e_\beta } + {e_r} + {r_{xd}} - {r_{xc}} \end{split} $$ (30) 设计滤波补偿信号为
$$ {\dot c_\beta } = - {k_\beta }{c_\beta } + {c_r} + {r_{xd}} - {r_{xc}} ,\;{c_\beta }(0) = 0 $$ (31) 式中, 补偿信号$ c_r $在下一步给出.
定义补偿后的侧滑角跟踪误差为
$$ \tilde \beta = {e_\beta } - {c_\beta } $$ (32) 步骤 2. 考虑偏航角速率动力学, 采用神经网络逼近未知气动函数$ f_r $, 可得
$$ {\dot r_x} = {b_{0\beta }}{v_2} + {\boldsymbol{\omega }}_{{f_r}}^{*{\rm{T}}}{{\boldsymbol{\theta }}_{{f_r}}}({\bar{\boldsymbol{x}}}_r) + {\varepsilon _r} $$ (33) 式中, $ {\boldsymbol{\omega }}_{{f_r}}^* $表示神经网络的最优权重, $ {{\boldsymbol{\theta }}_{{f_r}}}({\bar{\boldsymbol{x}}}_r) $表示基函数向量, ${\bar{\boldsymbol{x}}}_r = [\mu, \alpha,\beta, p, r]^{\rm{T}}$, $ {\varepsilon _r} $表示逼近误差.
设计偏航操纵力矩为
$$ {v_2} = b_{0\beta }^{ - 1}\left( { - {k_r}{e_r} - {e_\beta } - {{\hat f}_r} + {{\dot r}_{xd}}} \right) $$ (34) 式中, $ k_r $表示控制参数, ${\hat f_r} = \hat {\boldsymbol{\omega }}_{{f_r}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_r}}}({\bar{\boldsymbol{x}}}_r)$表示$ f_r $的估计值, $ {\hat {\boldsymbol{\omega }}_{{f_r}}} $表示最优权重$ {\boldsymbol{\omega }}_{{f_r}}^* $的估计值.
偏航角速率跟踪误差的导数为
$$ \begin{split} {{\dot e}_r} = \tilde {\boldsymbol{\omega }}_{{f_r}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_r}}}({\bar{\boldsymbol{x}}}_r) + {\varepsilon _r} - {k_r}{e_r} - {e_\beta } \end{split} $$ (35) 式中, $ \tilde {\boldsymbol{\omega }}_{{f_r}}^{} = {\boldsymbol{\omega }}_{{f_r}}^* - \hat {\boldsymbol{\omega }}_{{f_r}}^{} $.
设计滤波补偿信号为
$$ {\dot c_r} = - {k_r}{c_r} - {c_\beta },\;{c_r}(0) = 0 $$ (36) 定义补偿后的偏航角速率跟踪误差为
$$ \tilde r = {e_r} - {c_r} $$ (37) 定义预测误差为
$$ \begin{cases} {z_r} = {r_x} - {{\hat r}_x}\\ {\dot {\hat{r}}_x} = {b_{0\beta }}{v_2} + {{\hat f}_r} + {\lambda _r}{z_r} \end{cases} $$ (38) 式中, $ \lambda_r $表示设计参数.
设计复合学习更新律为
$$ {{\dot {\hat {\boldsymbol{\omega}} }}_{{f_r}}} = {\Gamma _r}\left[ {\left( {{\tilde r} + {\Gamma _{zr}}{z_r}} \right){{\boldsymbol{\theta }}_{{f_r}}}({\bar{\boldsymbol{x}}}_r) - {\delta _{{f_r}}}{{\hat {\boldsymbol{\omega }}}_{{f_r}}}} \right] $$ (39) 式中, $ \Gamma_r $, $ \Gamma_{zr} $和$ \delta_{f_r} $表示设计参数.
2.3 滚转角速率子系统控制
考虑滚转角速率动力学, 采用神经网络逼近未知气动函数$ f_p $, 可得
$$ \dot p = {b_{0p}}{v_3} + {\boldsymbol{\omega }}_{{f_p}}^{*{\rm{T}}}{{\boldsymbol{\theta }}_{{f_p}}}({\bar{\boldsymbol{x}}}_p) + {\varepsilon _p} $$ (40) 式中, $ {\boldsymbol{\omega }}_{{f_p}}^* $表示神经网络的最优权重, $ {{\boldsymbol{\theta }}_{{f_p}}}({\bar{\boldsymbol{x}}}_p) $表示基函数向量, ${\bar{\boldsymbol{x}}}_p = [\beta, p,q, r]^{\rm{T}}$, $ {\varepsilon _p} $表示逼近误差.
定义滚转角速率跟踪误差$ e_p = p-p_d $, $ p_d $表示滚转角速率指令. 设计滚转操纵力矩为
$$ {v_3} = b_{0p}^{ - 1}\left( { - {k_p}{e_p} - {{\hat f}_p} + {{\dot p}_d}} \right) $$ (41) 式中, $ k_p $表示控制参数, ${\hat f_p} = \hat {\boldsymbol{\omega }}_{{f_p}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_p}}}({\bar{\boldsymbol{x}}}_p)$表示$ f_p $的估计值, $ {\hat {\boldsymbol{\omega }}_{{f_p}}} $表示最优权重$ {\boldsymbol{\omega }}_{{f_p}}^* $的估计值.
滚转角速率跟踪误差的导数为
$$ \begin{split} {{\dot e}_p} = \tilde {\boldsymbol{\omega }}_{{f_p}}^{\rm{T}}{{\boldsymbol{\theta }}_{{f_p}}}({\bar{\boldsymbol{x}}}_p) + {\varepsilon _p} - {k_p}{e_p} \end{split} $$ (42) 式中, $ \tilde {\boldsymbol{\omega }}_{{f_p}}^{} = {\boldsymbol{\omega }}_{{f_p}}^* - \hat {\boldsymbol{\omega }}_{{f_p}}^{} $.
定义预测误差为
$$ \begin{cases} {z_p} = p - \hat p\\ \dot {\hat p} = {b_{0p}}{v_3} + {{\hat f}_p} + {\lambda _p}{z_p} \end{cases} $$ (43) 式中, $ \lambda_p $表示设计参数.
设计复合学习更新律为
$$ {{{\dot {\hat {\boldsymbol{\omega}} }}}_{{f_p}}} = {\Gamma _p}\left[ {\left( {e_p + {\Gamma _{zp}}{z_p}} \right){{\boldsymbol{\theta }}_{{f_p}}}({\bar{\boldsymbol{x}}}_p) - {\delta _{{f_p}}}{{\hat {\boldsymbol{\omega }}}_{{f_p}}}} \right] $$ (44) 式中, $ \Gamma_p $, $ \Gamma_{zp} $和$ \delta_{f_p} $表示设计参数.
2.4 控制分配
控制分配问题可以描述为: 对于给定的虚拟控制量与控制输入, 存在映射关系${\boldsymbol{G}}({{\boldsymbol{x}}}):{{\bf{R}}^6} \to {{\bf{R}}^3}$, 在控制输入满足期望指标的约束下求解不定方程
$$ {\boldsymbol{v}} = {\boldsymbol{G}}({{\boldsymbol{x}}}){{\boldsymbol{u}}} $$ (45) 式中, ${\boldsymbol{v}} = {[{v_1},{v_2},{v_3}]^{\rm{T}}} \in {{\bf{R}}^3}$表示期望操纵力矩, ${{\boldsymbol{u}}} \in {{\bf{R}}^6}$表示控制输入, ${\boldsymbol{G}}({{\boldsymbol{x}}}) = [{\boldsymbol{G}}_{aero} \quad{{\boldsymbol{G}}_{tv}}]$表示控制能效矩阵, 表达式为
$$ \begin{align} {\boldsymbol{G}}_{aero} = \begin{bmatrix} g_{\delta_e}^{m}({\boldsymbol{x}})&g_{\delta_a}^{m}({\boldsymbol{x}})&g_{\delta_r}^{m}({\boldsymbol{x}})\\ g_{\delta_e}^{n}({\boldsymbol{x}})&g_{\delta_a}^{n}({\boldsymbol{x}})&g_{\delta_r}^{n}({\boldsymbol{x}})\\ g_{\delta_e}^{l}({\boldsymbol{x}})&g_{\delta_a}^{l}({\boldsymbol{x}})&g_{\delta_r}^{l}({\boldsymbol{x}}) \end{bmatrix} \end{align} $$ (46) $$ \begin{align} {\boldsymbol{G}}_{tv} = \begin{bmatrix} g_{\delta_x}^{m}({\boldsymbol{x}})&g_{\delta_y}^{m}({\boldsymbol{x}})&g_{\delta_z}^{m}({\boldsymbol{x}})\\ g_{\delta_x}^{n}({\boldsymbol{x}})&g_{\delta_y}^{n}({\boldsymbol{x}})&g_{\delta_z}^{n}({\boldsymbol{x}})\\ g_{\delta_x}^{l}({\boldsymbol{x}})&g_{\delta_y}^{l}({\boldsymbol{x}})&g_{\delta_z}^{l}({\boldsymbol{x}}) \end{bmatrix} \end{align} $$ (47) 式中, $ g_{{\delta _j}}^i({{\boldsymbol{x}}}) $表示在状态$ {\boldsymbol{x}} $下操纵面$\delta _j \,(j = e,a,r, x,y,z)$对应通道的操纵力矩导数.
控制输入约束为
$$ \Omega = \{ {{{\boldsymbol{u}}}_{\min}} \le {{\boldsymbol{u}}} \le {{{\boldsymbol{u}}}_{\max}},\;\;{{\boldsymbol{\Gamma }}_{\min}} \le {\dot{\boldsymbol{ u}}} \le {{\boldsymbol{\Gamma }}_{\max}}\} $$ (48) 式中, $ {\boldsymbol{u}}_{\min} $和$ {\boldsymbol{u}}_{\max} $表示舵面偏转幅度限制, $ {\boldsymbol{\Gamma}}_{\min} $和$ {\boldsymbol{\Gamma}}_{\max} $表示舵面偏转的速度限制.
定义${{\boldsymbol{u}}_{aero}} = [\delta_e,\delta_a,\delta_r]^{\rm{T}}$和 ${{\boldsymbol{u}}_{tv}} = [\delta_x,\delta_y,\delta_z]^{\rm{T }}$, 气动舵面和推力矢量对应的操纵导数矩阵分别为$ {\boldsymbol{G}}_{aero} $和$ {\boldsymbol{G}}_{tv} $, 其广义逆矩阵分别为$ {\boldsymbol{P}}_{aero} = {\boldsymbol{G}}_{aero}^{-1} $和$ {\boldsymbol{P}}_{tv} = {\boldsymbol{G}}_{tv}^{-1} $. 串接链分配方法在分配过程中优先使用气动舵面, 即优先满足
$$ {\boldsymbol{v}} = {{\boldsymbol{G}}_{aero}}{{\boldsymbol{u}}} $$ (49) 对式(49)求解得
$$ {{{\boldsymbol{u}}}_{aero}} = {{\boldsymbol{P}}_{aero}}{\boldsymbol{v}} $$ (50) 若$ {{\boldsymbol{u}}}_{aero} $均在位置和速率限制内, 则分配完成; 若达到气动舵面饱和, 推力矢量喷管发生偏转来补偿剩余分配力矩, 推力矢量偏角表达式为
$$ {{{\boldsymbol{u}}}_{tv}} = \text{sat}({{\boldsymbol{P}}_{tv}}{\boldsymbol{E}}) $$ (51) 式中, $ {\boldsymbol{E}} = {\boldsymbol{v}} - {{\boldsymbol{G}}_{aero}}\text{sat}({{{\boldsymbol{u}}}_{aero}}) $表示待补偿的控制力矩, $ {\rm{sat}}( \cdot ) $为饱和函数.
3. 稳定性分析
3.1 迎角子系统稳定性
定理 1. 考虑迎角子系统(8), 设计俯仰操纵力矩(22), 复合学习更新律(20)和(27), 则李雅普诺夫函数(52)中的误差信号$ \tilde \alpha $, $ \tilde q $, $ z_{\alpha} $, $ z_q $, $ \tilde {\boldsymbol{\omega }}_{{f_\alpha }}^{} $和$ \tilde {\boldsymbol{\omega }}_{{f_q }}^{} $是一致终值有界的.
证明. 选择李雅普诺夫函数$ V_\alpha $为
$$ V_\alpha = V_1 + V_2 $$ (52) 式中,
$$ \begin{split} &V_1 = \frac{1}{2} ( \tilde \alpha ^2+ \Gamma_{z\alpha}z_\alpha^2 + {\tilde {\boldsymbol{\omega }}}_{{f_\alpha }}^{\rm{T}}\Gamma _\alpha ^{ - 1}\tilde {\boldsymbol{\omega }}_{{f_\alpha }} )\\ &V_2 = \frac{1}{2} ( \tilde q ^2 + \Gamma_{zq}z_q^2 + {\tilde {\boldsymbol{\omega }}}_{{f_q }}^{\rm{T}}\Gamma _q ^{ - 1}\tilde {\boldsymbol{\omega }}_{{f_q }} ) \end{split} $$ 对$ V_1 $和$ V_2 $求导, 可得
$$ \begin{split} \dot V_1 = \;& -k_\alpha \tilde \alpha ^2 + \tilde \alpha {\varepsilon _\alpha } - {\Gamma _{z\alpha }}{\lambda _\alpha }z_\alpha ^2 + {\Gamma _{z\alpha }}{z_\alpha }{\varepsilon _\alpha }\;+\\ &{\delta _{{f_\alpha }}}\tilde {\boldsymbol{\omega }}_{{f_\alpha }}^{\rm{T}} ( -{\tilde {\boldsymbol{\omega}}}_{f_\alpha} + {\boldsymbol{ \omega}}^*_{f_\alpha} )+\tilde \alpha \tilde q \end{split} $$ (53) $$ \begin{split} \dot V_2 =\; & -k_q\tilde q^2 + \tilde q{\varepsilon _q} - {\Gamma _{zq}}{\lambda _q}z_q^2 + {\Gamma _{zq}}{z_q}{\varepsilon _q}\;+\\ & {\delta _{{f_q}}}\tilde {\boldsymbol{\omega }}_{{f_q}}^{\rm{T}} ( -{\tilde {\boldsymbol{\omega}}}_{f_q} + {\boldsymbol{ \omega}}^*_{f_q} )-\tilde \alpha \tilde q \end{split} $$ (54) 考虑如下不等式
$$ \begin{align} \tilde \alpha \varepsilon_\alpha &\le \frac{1}{2}\tilde \alpha^2 + \frac{1}{2}\varepsilon^2_\alpha \end{align} $$ (55) $$ \begin{align} z_\alpha \varepsilon_\alpha &\le \frac{1}{2}z_\alpha^2 + \frac{1}{2}\varepsilon^2_\alpha \end{align} $$ (56) $$ \begin{align} \tilde {\boldsymbol{\omega }}_{f_\alpha}^{\rm{T}} (-\tilde {\boldsymbol{\omega }}_{f_\alpha} +{\boldsymbol{\omega }}_{f_\alpha}^*) &\le -\frac{1}{2}\tilde {\boldsymbol{\omega }}_{f_\alpha}^{\rm{T}} \tilde {\boldsymbol{\omega }}_{f_\alpha} +\frac{1}{2}\Vert {\boldsymbol{ \omega }}_{f_\alpha}^* \Vert ^2 \end{align} $$ (57) $ \dot V_2 $的放缩与$ \dot V_1 $类似, 进一步可得
$$ \begin{split} \dot V_\alpha \le\;& -\left(k_\alpha-\frac{1}{2} \right) \tilde \alpha ^2-\left(k_q-\frac{1}{2} \right) \tilde q ^2 \;-\\ &\left(\lambda_\alpha-\frac{1}{2}\right) \Gamma_{z\alpha } z_\alpha^2-\left(\lambda_q-\frac{1}{2}\right) \Gamma_{zq} z_q^2\;-\\ & \frac{1}{2}\delta_{f_\alpha}\tilde {\boldsymbol{\omega }}_{f_\alpha}^{\rm{T}} \tilde {\boldsymbol{\omega }}_{f_\alpha} -\frac{1}{2}\delta_{f_q}\tilde {\boldsymbol{\omega }}_{f_q}^{\rm{T}} \tilde {\boldsymbol{\omega }}_{f_q} +\Xi_\alpha \end{split} $$ (58) 式中,
$$ \begin{split} \Xi_\alpha =\;& \frac{1}{2}\delta_{f_\alpha}\Vert {\boldsymbol{ \omega }}_{f_\alpha}^* \Vert ^2 + \frac{1}{2} \left(\Gamma_{z\alpha}+1\right)\varepsilon_\alpha^2\;+\\ & \frac{1}{2}\delta_{f_q}\Vert {\boldsymbol{ \omega }}_{f_q}^* \Vert ^2 + \frac{1}{2} (\Gamma_{zq}+1)\varepsilon_q^2 \end{split} $$ 选择控制参数$ k_\alpha>\frac{1}{2} $, $ k_q>\frac{1}{2} $, $ \lambda_\alpha>\frac{1}{2} $和$ \lambda_q> \frac{1}{2} $, 可得
$$ \begin{align} \dot V_\alpha \le -\varpi_\alpha V_\alpha+\Xi_\alpha \end{align} $$ (59) 式中, $\varpi_\alpha = \min\{2k_\alpha-1, 2k_q-1, 2\lambda_\alpha-1, 2\lambda_q-1, \delta_{f_\alpha} \Gamma_\alpha, \delta_{f_q}\Gamma_q \}$, 进一步可得
$$ \begin{align} 0 \le V_\alpha \le \frac{\Xi_\alpha}{\varpi_\alpha} + \left[V_\alpha(0)-\frac{\Xi_\alpha}{\varpi_\alpha}\right]{\rm{e}}^{-\varpi_\alpha t} \end{align} $$ (60) 由此可证, $ \tilde \alpha $, $ \tilde q $, $ z_{\alpha} $, $ z_q $, $ \tilde {\boldsymbol{\omega }}_{{f_\alpha }}^{} $和$ \tilde {\boldsymbol{\omega }}_{{f_q }} $一致终值有界.
□ 3.2 侧滑角子系统稳定性
定理 2. 考虑侧滑角子系统(9), 设计偏航操纵力矩(34), 自适应复合学习更新律(39), 则李雅普诺夫函数(61)中的误差信号$ \tilde \beta $, $ \tilde r $, $ z_r $和$ \tilde{\boldsymbol{\omega}}_{f_r} $是一致终值有界的.
证明. 选择李雅普诺夫函数$ V_\beta $为
$$ \begin{align} V_\beta = \frac{1}{2}(\tilde \beta^2 + \tilde r^2 + \Gamma_{zr}z_r^2 + {\tilde {\boldsymbol{\omega }}}_{{f_r }}^{\rm{T}}\Gamma _r ^{ - 1}\tilde {\boldsymbol{\omega }}_{{f_r }} ) \end{align} $$ (61) 对$ V_\beta $求导可得
$$ \begin{split} \dot V_\beta =\; & -k_\beta \tilde \beta ^2 -k_r\tilde r^2 + \tilde r{\varepsilon _r} - {\Gamma _{zr}}{\lambda _r}z_r^2 \;+\\ & {\Gamma _{zr}}{z_r}{\varepsilon _r} + {\delta _{{f_r}}}\tilde {\boldsymbol{\omega }}_{{f_r}}^{\rm{T}}( -{\tilde {\boldsymbol{\omega}}}_{f_r} + {\boldsymbol{ \omega}}^*_{f_r} ) \end{split} $$ (62) $ \dot V_\beta $的放缩与$ \dot V_1 $类似, 进一步可得
$$ \begin{split} \dot V_\beta \le\;& -k_\beta \tilde \beta -\left(k_r-\frac{1}{2} \right) \tilde r ^2 -\left(\lambda_r-\frac{1}{2}\right) \Gamma_{zr} z_r^2 \;-\\ & \frac{1}{2}\delta_{f_r}\tilde {\boldsymbol{\omega }}_{f_r}^{\rm{T}} \tilde {\boldsymbol{\omega }}_{f_r} +\Xi_\beta\\[-15pt] \end{split} $$ (63) 式中, $ \Xi_\beta = \frac{1}{2}\delta_{f_r}\Vert {\boldsymbol{ \omega }}_{f_r}^* \Vert ^2 + \frac{1}{2} (\Gamma_{zr}+1)\varepsilon_r^2 $.
选择控制参数$ k_r>\frac{1}{2} $和$ \lambda_r>\frac{1}{2} $, 可得
$$ \begin{align} \dot V_\beta \le -\varpi_\beta V_\beta+\Xi_\beta \end{align} $$ (64) 式中, $ \varpi_\beta = \min\{2k_\beta, 2k_r-1, 2\lambda_r-1, \delta_{f_r}\Gamma_r \} $, 进一步可得
$$ \begin{align} 0 \le V_\beta \le \frac{\Xi_\beta}{\varpi_\beta} + \left[V_\beta(0)-\frac{\Xi_\beta}{\varpi_\beta}\right]{\rm{e}}^{-\varpi_\beta t} \end{align} $$ (65) 由此可证, $ \tilde \beta $, $ \tilde r $, $ z_r $和$ \tilde{\boldsymbol{\omega}}_{f_r} $是一致终值有界的.
□ 3.3 滚转角速率子系统稳定性
定理 3. 考虑滚转角速率子系统(10), 设计滚转操纵力矩(41), 复合学习更新律(44), 则李雅普诺夫函数(66)中的误差信号$ e_p $, $ z_p $和$ \tilde{\boldsymbol{\omega}}_{f_p} $一致终值有界.
证明. 选择李雅普诺夫函数$ V_p $为
$$ \begin{align} V_p = \frac{1}{2}( e_p^2 + \Gamma_{zp}z_p^2 + {\tilde {\boldsymbol{\omega }}}_{{f_p }}^{\rm{T}}\Gamma _p ^{ - 1}\tilde {\boldsymbol{\omega }}_{{f_p }} ) \end{align} $$ (66) 对$ V_p $求导可得
$$ \begin{split} \dot V_p = \;& k_p e_p^2 +{\tilde p} {\varepsilon _p} - {\Gamma _{zp}}{\lambda _p}z_p^2 \;+\\ & {\Gamma _{zp}}{z_p}{\varepsilon _p} + {\delta _{{f_p}}}\tilde {\boldsymbol{\omega }}_{{f_p}}^{\rm{T}}( -{\tilde {\boldsymbol{\omega}}}_{f_p} + {\boldsymbol{ \omega}}^*_{f_p} ) \end{split} $$ (67) $ \dot V_p $的放缩与$ \dot V_1 $类似, 进一步可得
$$ \begin{split} \dot V_p\le \;&-\left(k_p-\frac{1}{2} \right) e_p ^2 -\left(\lambda_p-\frac{1}{2}\right) \Gamma_{zp} z_p^2 \;-\\ & \frac{1}{2}\delta_{f_p}\tilde {\boldsymbol{\omega }}_{f_p}^{\rm{T}} \tilde {\boldsymbol{\omega }}_{f_p} +\Xi_p \end{split} $$ (68) 式中, $ \Xi_p = \frac{1}{2}\delta_{f_p}\Vert {\boldsymbol{ \omega }}_{f_p}^* \Vert ^2 + \frac{1}{2} (\Gamma_{zp}+1)\varepsilon_p^2 $.
选择控制参数$ k_p>\frac{1}{2} $和$ \lambda_p>\frac{1}{2} $, 可得
$$ \begin{align} \dot V_p \le -\varpi_p V_p+\Xi_p \end{align} $$ (69) 式中, $\varpi_p = \min\{2k_p-1, 2\lambda_p-1, \delta_{f_p}\Gamma_p \}$, 进一步得
$$ \begin{align} 0 \le V_p \le \frac{\Xi_p}{\varpi_p} + \left[V_p(0)-\frac{\Xi_p}{\varpi_p}\right]{\rm{e}}^{-\varpi_p t} \end{align} $$ (70) 由此可证, $ e_p $, $ z_p $和$ \tilde{\boldsymbol{\omega}}_{f_p} $是一致终值有界的.
□ 注 2. 根据李雅普诺夫稳定性定理, 需选择控制增益$k_i\,(i = \alpha,q,\beta,r,p)$和自适应参数$\lambda_k, \delta_{fk}, \Gamma_k, \Gamma_{zk} \,(k = \alpha,q,r,p)$, 使得$ \varpi_\alpha>0 $, $ \varpi_\beta>0 $, $ \varpi_p>0 $. 在实际参数整定中, 首先调整参数$ k_i $和$ \lambda_k $使系统满足基本控制性能, 之后调整参数$ \delta_{fk},\Gamma_k $和$ \Gamma_{zk} $提高系统的跟踪精度和不确定学习效果.
4. 仿真分析
设定飞机的初始迎角为10°, 飞行高度1 200 m, 初始飞行速度90 m/s, 飞行过程中保持恒定发动机推力90 kN. 仿真步长和仿真周期分别设置为$ t_s $ = 0.001 s和$ T $ = 16 s. 对于迎角子系统, 控制器参数设置为$ b_{0\alpha} = 1 $, $ k_\alpha = 15 $, $ k_q = 15 $, $ \lambda_\alpha = 5 $, $ \lambda_q = 1 $, $ \sigma_\alpha = 0.005 $, $ \Gamma_\alpha = 0.2 $, $ \Gamma_{z\alpha} = 3 $, $ \delta_{f_\alpha} = 0.3 $, $ \Gamma_q = 0.2 $, $ \Gamma_{zq} = 0.1 $和$ \delta_{fq} = 0.3 $. 对于侧滑角子系统, 控制器参数设置为$ b_{0\beta} = -10 $, $ k_\beta = 0.1 $, $ k_r = 0.6 $, $ \lambda_r = 1.4 $, $ \sigma_r = 0.005 $, $ \Gamma_r = 2.6 $, $ \Gamma_{zr} = 1 $和$ \delta_{fp} = 1 $. 对于滚转角速率子系统, 控制器参数设置为$ b_{0p} = 10 $, $ k_p = 5\; 000 $, $ \lambda_p = 5 $, $ \Gamma_p = 2 $, $ \Gamma_{zp} = 1 $和$ \delta_{fp} = 3 $. 针对未知函数$ f_\alpha $, $ f_q $, $ f_r $和$ f_p $, 神经网络节点数分别设置为$ N_\alpha = 729 $, $N_q = 2\,401$, $N_r = 3\,125$和$N_p = 2\,401$. 估计误差分别定义为$ e_{f_\alpha} = f_\alpha-\hat f_\alpha $, $ e_{f_q} = f_q-\hat f_q $, $ e_{f_r} = f_r-\hat f_r $和$ e_{f_p} = f_p-\hat f_p $. 本文提出的复合学习控制方法记为“NN-CL”, 无预测误差的经典神经网络控制方法记为“NN”. 为验证所提方法的有效性, 对两者进行仿真对比.
眼镜蛇机动是典型的过失速机动, 是验证飞机大迎角飞行控制律的基本动作之一. 眼镜蛇机动的迎角指令跟踪结果如图2所示, 迎角在2 s内达到70°, 随后迅速改出, 回到初始配平状态. 图3为未知气动函数$ f_\alpha $的估计及误差曲线, 图4为升降舵和推力矢量的偏转角. 由仿真结果可知, 所提控制方法对眼镜蛇机动指令的跟踪精度更高、学习效果更好.
图 2 眼镜蛇机动迎角跟踪((a) 指令跟踪; (b) 跟踪误差)Fig. 2 Angle of attack tracking under Cobra maneuver ((a) Command tracking; (b) Tracking error)
图 3 眼镜蛇机动$f_\alpha$的估计值((a) 基于NN-CL的$\hat f_\alpha$;(b) 基于NN的$\hat f_\alpha$; (c) 估计误差)Fig. 3 Estimation of $f_\alpha$ under Cobra maneuver ((a) $\hat f_\alpha$ under NN-CL; (b) $\hat f_\alpha$ under NN; (c) Estimation error)
图 4 眼镜蛇机动的操纵偏转量((a) 升降舵; (b) 俯仰推矢偏角)Fig. 4 Control surface deflection under Cobra maneuver ((a) Elevator; (b) Pitch thrust vector deflection angle)赫伯斯特机动[19]是指飞机进入大迎角状态的同时机身滚转迅速改变机头方向的一种机动方式. 赫伯斯特机动指令的迎角跟踪和滚转角速率跟踪及相应的跟踪误差如图5、图6所示, 由仿真结果可知, 基于所提的大迎角控制方法, 迎角和滚转角速率的跟踪误差几乎为0, 并且基本无滞后, 取得了较好的机动指令跟踪控制效果. 战机的飞行状态和轨迹如图7、图8所示, 飞行速度由初始90 m/s减小到了40 m/s左右, 在40 m/s ~ 60 m/s之间飞机绕速度轴进行滚转, 整个大迎角低速度阶段持续了10 s左右; 侧滑角实现了快速稳定; 在机动过程中航迹方位角发生了180° 变化, 实现了飞行速度的快速减小和快速转弯, 转弯半径小于70 m, 高度变化小于400 m.
图 5 赫伯斯特机动迎角跟踪((a) 指令跟踪; (b) 跟踪误差)Fig. 5 Angle of attack tracking under Herbst maneuver ((a) Command tracking; (b) Tracking error)
图 6 赫伯斯特机动滚转角速率跟踪((a) 指令跟踪; (b) 跟踪误差)Fig. 6 Roll angle rate tracking under Herbst maneuver ((a) Command tracking; (b) Tracking error)
图 7 赫伯斯特机动飞行状态((a) 侧滑角;(b) 速度; (c) 航迹方位角)Fig. 7 Flight states under Herbst maneuver ((a) Sideslip angle; (b) Speed; (c) Flight path azimuth angle)图9、图10为战机的操纵偏转量, 在赫伯斯特机动过程中, 常规气动舵面在整个机动过程中出现了较长时间的饱和状态, 推力矢量偏角高达20°, 以满足长时间大迎角过失速机动的操纵能力要求. 图11 ~ 图14为未知气动函数$ f_\alpha $, $ f_q $, $ f_r $和$ f_p $的估计结果, 所提出的复合学习方法能保证集总扰动的有效估计, 实现了非线性、不确定和耦合干扰的精确补偿, 进而提升了机动指令的跟踪效果. 图15为神经网络权重的估计曲线.
图 9 赫伯斯特机动气动操纵舵面偏转((a) 升降舵; (b) 副翼; (c) 方向舵)Fig. 9 Aerodynamic control surfaces deflection under Herbst maneuver ((a) Elevator; (b) Aileron; (c) Rudder)
图 10 赫伯斯特机动推力矢量偏转((a)滚转推矢偏角; (b)偏航推矢偏角; (c)俯仰推矢偏角)Fig. 10 Thrust vector nozzles deflection under Herbst maneuver ((a) Roll thrust vector deflection angle; (b) Yaw thrust vector deflection angle; (c) Pitch thrust vector deflection angle)
图 11 赫伯斯特机动$f_\alpha$的估计值((a) 基于NN-CL的$\hat f_\alpha$; (b) 基于NN的$\hat f_\alpha$; (c) 估计误差)Fig. 11 Estimation of $f_\alpha$ under Herbst maneuver ((a) $\hat f_\alpha$ under NN-CL; (b) $\hat f_\alpha$ under NN; (c) Estimation error)
图 14 赫伯斯特机动$f_p$的估计值((a) 基于NN-CL的$\hat f_p$; (b) 基于NN的$\hat f_p$; (c) 估计误差)Fig. 14 Estimation of $f_p$ under Herbst maneuver ((a) $\hat f_p$ under NN-CL; (b) $\hat f_p$ under NN; (c) Estimation error)
图 15 神经网络权重估计值 ((a) $\|\hat{{\boldsymbol{\omega}}}_{f_\alpha}\|$; (b) $\|\hat{{\boldsymbol{\omega}}}_{f_q}\|$; (c) $\|\hat{{\boldsymbol{\omega}}}_{f_r}\|$; (d) $\|\hat{{\boldsymbol{\omega}}}_{f_p}\|$)Fig. 15 Estimation of NN weights ((a) $\|\hat{{\boldsymbol{\omega}}}_{f_\alpha}\|$; (b) $\|\hat{{\boldsymbol{\omega}}}_{f_q}\|$; (c) $\|\hat{{\boldsymbol{\omega}}}_{f_r}\|$; (d) $\|\hat{{\boldsymbol{\omega}}}_{f_p}\|$)考虑飞行过程中受到外部干扰和气动参数摄动的影响, 在三通道加入扰动力矩${D_q} = 1 \times {10^4}\sin (2t \;+ 0.1)$N·m, ${D_r} = 5 \times {10^6}\sin (2t + 0.1)$N·m, ${D_p} = 5\; \times {10^6}\sin (2t + 0.1)$N·m, 同时气动参数拉偏范围$ \pm30\% $. 图16为鲁棒验证仿真结果, 迎角和滚转角速率指令的最大跟踪误差分别为0.210° 和0.053°/s, 侧滑角控制在7° 以内, 表明所设计控制方法对外部扰动和参数摄动表现出较高的鲁棒性.
图 16 鲁棒测试((a) 迎角; (b) 侧滑角; (c) 滚转角速率)Fig. 16 Robustness verification ((a) Angle of attack; (b) Sideslip angle; (c) Roll angle rate)
图 12 赫伯斯特机动$f_q$的估计值((a) 基于NN-CL的$\hat f_q$; (b) 基于NN的$\hat f_q$; (c) 估计误差)Fig. 12 Estimation of $f_q$ under Herbst maneuver ((a) $\hat f_q$ under NN-CL; (b) $\hat f_q$ under NN; (c) Estimation error)
图 13 赫伯斯特机动$f_r$的估计值((a) 基于NN-CL的$\hat f_r$; (b) 基于NN的$\hat f_r$; (c) 估计误差)Fig. 13 Estimation of $f_r$ under Herbst maneuver ((a) $\hat f_r$ under NN-CL; (b) $\hat f_r$ under NN; (c) Estimation error)综上所述, 通过气动舵面与推力矢量的协同操纵, 所设计的复合学习智能自适应控制方法实现了大迎角机动指令的有效跟踪和集总干扰的高效学习, 对参数摄动和外部扰动具备自适应和干扰抑制能力.
5. 结论
本文针对战机大迎角机动进行了复合学习智能控制方法研究. 首先将六自由度非线性动力学解耦为迎角、侧滑角和滚转角速率子系统, 针对分解后的子系统基于预测误差构建神经网络复合学习律, 对未知气动函数进行估计和补偿, 据此设计了智能自适应控制律获取操纵力矩, 并基于串接链分配方法实现气动舵面与推力矢量的协同分配控制. 通过李雅普诺夫稳定性分析证明了闭环系统的一致最终有界. 典型大迎角机动仿真测试和参数拉偏测试表明所提方法具有更高的指令跟踪精度和不确定学习性能, 同时对参数摄动和外界干扰表现出较强的鲁棒性.
在未来研究工作中可进一步考虑飞机舵面故障, 研究控制分配与自适应容错控制方法. 除此之外, 将边界保护技术引入现有控制框架中, 对保证大迎角机动的安全性和鲁棒性具有重要意义.
-
图 3 典型目标检测算法速度−准确率对比
Fig. 3 Speed-accuracy comparison of typical object detection algorithms
图 31 基于注意力机制RPN与多关系头部的少样本检测
Fig. 31 Attention-RPN and multi-relation head based few-shot detection
表 1 各检测模型的性能对比
Table 1 Performance comparison of different object detection models
模型 主干网络 AP AP50 AP75 APS APM APL Faster R-CNN VGG-16 21.9 42.7 — — — — Faster R-CNN R-101* 29.1 48.4 30.7 12.9 35.5 50.9 Faster R-CNN R-101-CBAM 30.8 50.5 32.6 — — — Faster R-CNN++ R-101-FPN 36.2 59.1 39.0 18.2 39.0 48.2 Faster R-CNN++ HR-W32 39.5 61.0 43.1 23.6 42.9 51.0 Faster-DCR V2 R-101 34.3 57.7 35.8 13.8 36.7 51.1 OHEM VGG-16 22.6 42.5 22.2 5.0 23.7 37.9 SIN VGG-16 23.2 44.5 22.0 7.3 24.5 36.3 ION VGG-16 23.6 43.2 22.6 6.4 24.1 38.3 Mask R-CNN R-101-FPN 38.2 60.3 41.7 20.1 41.1 50.2 Mask R-CNN HR-32 40.7 61.8 44.7 25.2 44.4 51.8 Mask R-CNN R-101-FPN+GC 40.8 62.1 45.5 24.4 43.7 51.9 SN-Mask R-CNN R-101-FPN 40.4 58.7 42.5 — — — IN-Mask R-CNN R-101-FPN 40.6 59.4 43.6 24.3 43.9 52.6 R-FCN R-101 29.9 51.9 — 10.8 32.8 45.0 CoupleNet R-101 34.4 54.8 37.2 13.4 38.1 50.8 Cascade R-CNN R-101 42.8 62.1 46.3 23.7 45.5 55.2 Libra R-CNN R-101-FPN 41.1 62.1 44.7 23.4 43.7 52.5 Grid R-CNN[100] X-101* 43.2 63.0 46.6 25.1 46.5 55.2 Light-Head R-CNN R-101 38.2 60.9 41.0 20.9 42.2 52.8 M2Det800 VGG-16 41.0 59.7 45.0 22.1 46.5 53.8 SSD512 VGG-16 28.8 48.5 30.3 10.9 31.8 43.5 GHM SSD X-101 41.6 62.8 44.2 22.3 45.1 55.3 YOLOV3 D-53* 33.0 57.9 34.4 18.3 35.4 41.9 YOLOV3 D-53 34.3 — 36.2 — — — RetinaNet X-101-FPN 39.0 59.4 41.7 22.6 43.4 50.9 GA-RetinaNet X-101-FPN 40.3 60.9 43.5 23.5 44.9 53.5 RefineDet512++ R-101-FPN 41.8 62.9 45.7 25.6 45.1 55.3 FCOS X-101-FPN 42.1 62.1 45.2 25.6 44.9 52.0 FoveaBox X-101-FPN 42.1 61.9 45.2 24.9 46.8 55.6 FSFA X-101-FPN 42.9 63.8 46.3 26.6 46.2 52.7 CornerNet HG-104* 40.5 56.5 43.1 19.4 42.7 53.9 ExtremeNet HG-104 40.2 55.5 43.2 20.4 43.2 53.1 CenterNet HG-104 42.1 61.1 45.9 24.1 45.5 52.8 RepPoints R-101 41.0 62.9 44.3 23.6 44.1 51.7 SNIP++ R-101 43.1 65.3 48.1 26.1 45.9 55.2 SNIPER++ R-101 46.1 67.0 51.6 29.6 48.9 58.1 TridentNet R-101 42.7 63.6 46.5 23.9 46.6 56.6 *注: R-ResNet, X-ResNeXt, HR-HRNet, D-DarkNet, HG-Hourglass. ++表示使用了多尺度、水平翻转等策略 
下载: 导出CSV
表 2 部分检测模型的速度、显存消耗、参数量与计算量对比(基于Titan Xp)
Table 2 Speed, VRAM consumption, parameters and computation comparison of some object detection models (on Titan Xp)
模型 主干网络 训练速度 (s/iter) 显存消耗 (GB) 推理速度 (fps) 参数量 运算次数 Faster R-CNN++ R-101-FPN 0.465 5.7 11.9 60.52×106 283.14×109 Faster R-CNN++ HR-W32 0.593 5.9 8.5 45.0×106 245.3×109 Mask R-CNN R-101-FPN 0.571 5.8 9.4 62.81×106 351.65×109 Mask R-CNN x-101-FPN 0.759 7.1 8.3 63.17×106 355.4×109 Mask R-CNN R-101-FPN+GC 0.731 7.0 8.6 82.13×106 352.8×109 R-FCN R-101 0.400 5.6 14.6 — — Cascade R-CNN R-101-FPN 0.584 6.0 10.3 87.8×106 310.78×109 Cascade R-CNN X-101-FPN 0.770 8.4 8.9 88.16×106 314.53×109 Libra R-CNN R-101-FPN 0.495 6.0 10.4 60.79×106 284.19×109 Grid R-CNN X-101-FPN 1.214 6.7 10.0 82.95×106 409.19×109 M2Det800 VGG-16 — — 11.8 — — SSD512 VGG-16 0.412 7.6 20.7 36.04×106 386.02×109 GHM RetinaNet X-101-FPN 0.818 7.0 7.6 56.74×106 319.14×109 RetinaNet X-101-FPN 0.632 6.7 9.3 56.37×106 319.04×109 GA-RetinaNet X-101-FPN 0.870 6.7 7.5 56.01×106 283.13×109 FCOS R-101-FPN 0.558 9.4 11.6 50.96×106 276.53×109 CornerNet HG$-104^*$ — — 4.9 — — ExtremeNet HG-104 — — 3.1 — — CenterNet HG-104 — 11.91 8.5 — — RepPoints R-101 0.558 5.6 10.9 55.62×106 266.23×109 SNIP++ R-101 — — < 1.0 — — SNIPER++ R-101 — — 4.8 — — TridentNet R-101 0.985 6.6 2.1 — — *注: R-ResNet, X-ResNeXt, HR-HRNet, D-DarkNet, HG-Hourglass. ++表示使用了多尺度、水平翻转等策略
下载: 导出CSV
-
[1] Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision, 2004, 60(2): 91−110 doi: 10.1023/B:VISI.0000029664.99615.94 [2] Viola P, Jones M. Rapid object detection using a boosted cascade of simple features. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). Kauai, HI, USA: IEEE, 2001. I−511−I−518 [3] Dalal N, Triggs B. Histograms of oriented gradients for human detection. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). San Diego, CA, USA: IEEE, 2005. 886−893 [4] Girshick R, Donahue J, Darrell T, Malik J. Region-based convolutional networks for accurate object detection and segmentation. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2016, 38(1): 142−158 [5] Girshick R. Fast R-CNN. In: Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV). Santiago, Chile: IEEE, 2015. 1440−1448 [6] Ren S Q, He K M, Girshick R, Sun J. Faster R-CNN: Towards real-time object detection with region proposal networks. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2017, 39(6): 1137−1149 [7] Liu W, Anguelov D, Erhan D, Szegedy C, Reed S, Fu C Y, et al. SSD: Single shot MultiBox detector. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, 2016. 21−37 [8] Redmon J, Divvala S, Girshick R, Farhadi A. You only look once: Unified, real-time object detection. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 779−788 [9] Redmon J, Farhadi A. YOLO9000: Better, faster, stronger. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 6517−6525 [10] Redmon J, Farhadi A. YOLOv3: An incremental improvement. arXiv: 1804.02767, 2018 [11] Law H, Deng J. CornerNet: Detecting objects as paired keypoints. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer, 2018. 765−781 [12] Zhou X Y, Zhuo J C, Krähenbühl P. Bottom-up object detection by grouping extreme and center points. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 850−859 [13] Zhou X Y, Wang D Q, Krähenbühl P. Objects as points. arXiv: 1904.07850, 2019 [14] Yang Z, Liu S H, Hu H, Wang L W, Lin S. RepPoints: Point set representation for object detection. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 9656−9665 [15] Zhang S F, Wen L Y, Bian X, Lei Z, Li S Z. Single-shot refinement neural network for object detection. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 4203−4212 [16] Chi C, Zhang S F, Xing J L, Lei Z, Li S Z, Zou X D. Selective refinement network for high performance face detection. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). Honolulu, Hawaii, USA: AAAI, 2019. 8231−8238 [17] Li Z M, Peng C, Yu G, Zhang X Y, Deng Y D, Sun J. Light-head R-CNN: In defense of two-stage object detector. arXiv: 1711.07264, 2017 [18] Simonyan K, Zisseman A. Very deep convolutional networks for large-scale image recognition. arXiv: 1409.1556, 2014 [19] He K M, Zhang X Y, Ren S Q, Sun J. Deep residual learning for image recognition. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 770−778 [20] Xie S N, Girshick R, Dollár P, Tu Z W, He K M. Aggregated residual transformations for deep neural networks. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 5987−5995 [21] Szegedy C, Liu W, Jia Y Q, Sermanet P, Reed S, Anguelov D, et al. Going deeper with convolutions. In: Proceedings of the 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Boston, MA, USA: IEEE, 2015. 1−9 [22] Hu J, Shen L, Sun G. Squeeze-and-excitation networks. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 7132−7141 [23] Wang X L, Girshick R, Gupta A, He K M. Non-local neural networks. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 7794−7803 [24] Cao Y, Xu J R, Lin S, Wei F Y, Hu H. GCNet: Non-local networks meet squeeze-excitation networks and beyond. arXiv: 1904.11492, 2019 [25] Woo S, Park J, Lee J Y, So Kweon I. CBAM: Convolutional block attention module. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer, 2018. 3−19 [26] Lin T Y, Dollár P, Girshick R, He K M, Hariharan B, Belongie S. Feature pyramid networks for object detection. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 936−944 [27] Pan J M, Chen K, Shi J P, Feng H J, Ouyang W N, Lin D H. Libra R-CNN: Towards balanced learning for object detection. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 821−830 [28] Liu S, Qi L, Qin H F, Shi J P, Jia J Y. Path aggregation network for instance segmentation. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 8759−8768 [29] Zhao Q J, Sheng T, Wang Y T, Tang Z, Chen Y, Cai L, et al. M2det: A single-shot object detector based on multi-level feature pyramid network. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). Honolulu, Hawaii, USA: AAAI, 2019. 9259−9266 [30] Tan M X, Pang R M, Le Q V. EfficientDet: Scalable and efficient object detection. arXiv: 1911.09070, 2020 [31] Newell A, Yang K Y, Deng J. Stacked hourglass networks for human pose estimation. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, Cham, 2016. 483−499 [32] Sun K, Xiao B, Liu D, Wang J D. Deep high-resolution representation learning for human pose estimation. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 5686−5696 [33] Yu F, Koltun V. Multi-scale context aggregation by dilated convolutions. arXiv: 1511.07122, 2016 [34] Zhu C C, Tao R, Luu K, Savvides M. Seeing small faces from robust anchor＇ s perspective. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 5127−5136 [35] Xie L L, Liu Y L, Jin L W, Xie Z C. DeRPN: Taking a further step toward more general object detection. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). Honolulu, Hawaii, USA: AAAI, 2019. 9046−9053 [36] Zhong Y Y, Wang J F, Peng J, Zhang L. Anchor box optimization for object detection. arXiv: 1812.00469, 2020 [37] Wang J Q, Chen K, Yang S, Loy C C, Lin D H. Region proposal by guided anchoring. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 2960−2969 [38] Dai J F, Qi H Z, Xiong Y W, Zhang G D, Hu H, Wei Y C. Deformable convolutional networks. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 764−773 [39] Zhu X Z, Hu H, Lin S, Dai J F. Deformable ConvNets V2: More deformable, better results. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 9300−9308 [40] Tian Z, Shen C H, Chen H, He T. FCOS: Fully convolutional one-stage object detection. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 9626−9635 [41] Kong T, Sun F C, Liu H P, Jiang Y N, Li L, Shi J B. FoveaBox: Beyond anchor-based object detector. arXiv: 1904.03797, 2020 [42] Zhu C C, He Y H, Savvides M. Feature selective anchor-free module for single-shot object detection. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 840−849 [43] Zhu C C, Chen F Y, Shen Z Q, Savvides M. Soft anchor-point object detection. arXiv: 1911.12448, 2020 [44] Bodla N, Singh B, Chellappa R, Davis L S. Soft-NMS-improving object detection with one line of code. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICVV). Venice, Italy: IEEE, 2017. 5562−5570 [45] He Y H, Zhang X Y, Savvides M, Kitani K. Softer-NMS: Rethinking bounding box regression for accurate object detection. arXiv: 1809.08545, 2019 [46] Jiang B R, Luo R X, Mao J Y, Xiao T T, Jiang Y N. Acquisition of localization confidence for accurate object detection. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer, 2018. 816−832 [47] Liu Y, Liu L Q, Rezatofighi H, Do T T, Shi Q F, Reid I. Learning pairwise relationship for multi-object detection in crowded scenes. arXiv: 1901.03796, 2019 [48] Rezatofighi H, Tsoi N, Gwak J Y, Sadeghian A, Reid L, Savarese S. Generalized intersection over union: A metric and a loss for bounding box regression. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 658−666 [49] Cai Z W, Vasconcelos N. Cascade R-CNN: Delving into high quality object detection. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 6154−6162 [50] Shrivastava A, Gupta A, Girshick R. Training region-based object detectors with online hard example mining. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 761−769 [51] Yu H, Zhang Z N, Qin Z, Wu H, Li D S, Zhao J, et al. Loss Rank Mining: A general hard example mining method for real-time detectors. In: Proceedings of the 2018 International Joint Conference on Neural Networks (IJCNN). Rio de Janeiro, Brazil: IEEE, 2018. 1−8 [52] He K M, Gkioxari G, Dollár P, Girshick R. Mask R-CNN. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2020, 42(2): 386−397 [53] Dai J F, Li Y, He K M, Sun J. R-FCN: Object detection via region-based fully convolutional networks. In: Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS). Barcelona, Spain: Curran Associates Inc., 2016. 379−387 [54] Zhu Y S, Zhao C Y, Wang J Q, Zhao X, Wu Y, Lu H Q. CoupleNet: Coupling global structure with local parts for object detection. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 4146−4154 [55] Zhai Y, Fu J J, Lu Y, Li H Q. Feature selective networks for object detection. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 4139−4147 [56] Chen Y T, Han C X, Wang N Y, Zhang Z X. Revisiting feature alignment for one-stage object detection. arXiv: 1908.01570, 2019 [57] Cheng B W, Wei Y C, Shi H H, Feris R, Xiong J J, Huang T. Revisiting RCNN: On awakening the classification power of faster RCNN. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer. 2018. 473−490 [58] Cheng B W, Wei Y C, Feris R, Xiong J J, Hwu W M, Huang T, et al. Decoupled classification refinement: Hard false positive suppression for object detection. arXiv: 1810.04002, 2020 [59] Bell S, Zitnick C L, Bala K, Girshick R. Inside-outside net: Detecting objects in context with skip pooling and recurrent neural networks. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 2874−2883 [60] Ouyang W L, Luo P, Zeng X Y, Qiu S, Tian Y L, Li H S, et al. DeepID-Net: Multi-stage and deformable deep convolutional neural networks for object detection. arXiv: 1409.3505, 2014 [61] Chen X L, Gupta A. Spatial memory for context reasoning in object detection. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 4106−4116 [62] Liu Y, Wang R P, Shan S G, Chen X L. Structure inference net: Object detection using scene-level context and instance-level relationships. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 6985−6994 [63] Hu H, Gu J Y, Zhang Z, Dai J F, Wei Y C. Relation networks for object detection. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 3588−3597 [64] Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez A N, et al. Attention is all you need. In: Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS). Long Beach, California, USA: Curran Associates Inc., 2017. 6000−6010 [65] Gidaris S, Komodakis N. Object detection via a multi-region and semantic segmentation-aware CNN model. In: Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV). Santiago, Chile: IEEE, 2015. 1134−1142 [66] Zeng X Y, Ouyang W L, Yang B, Yan J J, Wang X G. Gated bi-directional CNN for object detection. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, 2016. 354−369 [67] Luo W J, Li Y J, Urtasun R, Zemek R. Understanding the effective receptive field in deep convolutional neural networks. In: Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS). Barcelona, Spain: Curran Associates Inc., 2016. 4905−4913 [68] Lin T Y, Goyal P, Girshick R, He K M, Dollár P. Focal loss for dense object detection. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 2999−3007 [69] Cai Z W, Fan Q F, Feris R S, Vasconcelos N. A unified multi-scale deep convolutional neural network for fast object detection. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, 2016. 354−370 [70] Yang F, Choi W, Lin Y Q. Exploit all the layers: Fast and accurate CNN object detector with scale dependent pooling and cascaded rejection classifiers. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 2129−2137 [71] Singh B, Davis L S. An analysis of scale invariance in object detection - SNIP. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 3578−3587 [72] Singh B, Najibi M, Davis L S. SNIPER: Efficient multi-scale training. In: Proceedings of the 32nd International Conference on Neural Information Processing Systems (NIPS). Montreal, Canada: Curran Associates Inc., 2018. 9333−9343 [73] Najibi M, Singh B, Davis L S. AutoFocus: Efficient multi-scale inference. arXiv: 1812.01600, 2018 [74] Li Y H, Chen Y T, Wang N Y, Zhang Z X. Scale-aware trident networks for object detection. arXiv: 1901.01892, 2019 [75] Chen L C, Papandreou G, Schroff F, Adam H. Rethinking atrous convolution for semantic image segmentation. arXiv: 1706.05587, 2017 [76] Chen K, Li J G, Lin W Y, See J, Wang J, Duan L Y, et al. Towards accurate one-stage object detection with AP-Loss. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 5114−5122 [77] Li B Y, Liu Y, Wang X G. Gradient harmonized single-stage detector. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). Honolulu, Hawaii, USA: AAAI, 2019. 8577−8584 [78] Wang X L, Xiao T T, Jiang Y N, Shao S, Sun J, Shen C H. Repulsion loss: Detecting pedestrians in a crowd. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 7774−7783 [79] Yu J H, Jiang Y N, Wang Z Y, Cao Z M, Huang T. UnitBox: An advanced object detection network. In: Proceedings of the 24th ACM International Conference on Multimedia. Amsterdam, The Netherlands: ACM, 2016. 516−520 [80] Tychsen-Smith L, Petersson L. Improving object localization with fitness NMS and bounded IoU loss. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 6877−6885 [81] Ma J Q, Shao W Y, Ye H, Wang L, Wang H, Zheng Y B, et al. Arbitrary-oriented scene text detection via rotation proposals. IEEE Transactions on Multimedia, 2018, 20(11): 3111−3122 doi: 10.1109/TMM.2018.2818020 [82] Liao M H, Shi B G, Bai X. TextBoxes++: A single-shot oriented scene text detector. IEEE Transactions on Image Processing, 2018, 27(8): 3676−3690 doi: 10.1109/TIP.2018.2825107 [83] Zhou X Y, Yao C, Wen H, Wang Y Z, Zhou S C, He W R, et al. EAST: An efficient and accurate scene text detector. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 2642−2651 [84] Huang L C, Yang Y, Deng Y F, Yu Y N. DenseBox: Unifying landmark localization with end to end object detection. arXiv: 1509.04874, 2015 [85] Deng D, Liu H F, Li X L, Cai D. PixelLink: Detecting scene text via instance segmentation. arXiv: 1801.01315, 2018 [86] Xie E Z, Zang Y H, Shao S, Yu G, Yao C, Li G Y. Scene text detection with supervised pyramid context network. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI). Honolulu, Hawaii, USA: AAAI, 2019. 9038−9045 [87] Wang W H, Xie E Z, Li X, Hou W B, Lu T, Yu G, et al. Shape robust text detection with progressive scale expansion network. arXiv: 1903.12473, 2019 [88] Xia G S, Bai X, Ding J, Zhu Z, Belongie S, Luo J B, et al. DOTA: A large-scale dataset for object detection in aerial image. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 3974−3983 [89] Li K, Wan G, Cheng G, Meng L Q, Han J W. Object detection in optical remote sensing images: A survey and a new benchmark. ISPRS Journal of Photogrammetry and Remote Sensing, 2020, 159: 296−307 doi: 10.1016/j.isprsjprs.2019.11.023 [90] Yang F, Fan H, Chu P, Blasch E, Ling H B. Clustered object detection in aerial images. arXiv: 1904.08008, 2019 [91] Ding J, Xue N, Long Y, Xia G S, Lu Q K. Learning RoI transformer for oriented object detection in aerial images. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 2844−2853 [92] Qian W, Yang X, Peng S L, Guo Y, Yan J C. Learning modulated loss for rotated object detection. arXiv: 1911.08299, 2019 [93] Zhu Y X, Wu X Q, Du J. Adaptive period embedding for representing oriented objects in aerial images. arXiv: 1906.09447, 2019 [94] Zhang S S, Benenson R, Schiele B. CityPersons: A diverse dataset for pedestrian detection. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 4457−4465 [95] Shao S, Zhao Z J, Li B X, Xiao T T, Yu G, Zhang X Y, et al. CrowdHuman: A benchmark for detecting human in a crowd. arXiv: 1805.00123, 2018 [96] Pang Y W, Xie J, Khan M H, Anwer R M, Khan F S, Shao L. Mask-guided attention network for occluded pedestrian detection. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 4966−4974 [97] Zhang S F, Wen L Y, Bian X, Lei Z, Li S Z. Occlusion-aware R-CNN: Detecting pedestrians in a crowd. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer, 2018. 657−674 [98] Liu T R, Luo W H, Ma L, Huang J J, Stathaki T, Dai T H. Coupled network for robust pedestrian detection with gated multi-layer feature extraction and deformable occlusion handling. arXiv: 1912.08661, 2019 [99] Liu S T, Huang D, Wang Y H. Adaptive NMS: Refining pedestrian detection in a crowd. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 6452−6461 [100] Lu X, Li B Y, Yue Y X, Li Q Q, Yan J J. Grid R-CNN. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 7355−7364 [101] Zoph B, Vasudevan V, Shlens J, Le Q V. Learning transferable architectures for scalable image recognition. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 8697−8710 [102] Chen Y K, Yang T, Zhang X Y, Meng G F, Xiao X Y, Sun J. DetNAS: Backbone search for object detection. In: Proceedings of the 33rd Conference on Neural Information Processing Systems (NIPS). Vancouver, Canada: Margan Kaufmann Publishers, 2019. 6638−6648 [103] Ghiasi G, Lin T Y, Le Q V. NAS-FPN: Learning scalable feature pyramid architecture for object detection. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 7029−7038 [104] Wang N, Gao Y, Chen H, Wang P, Tian Z, Shen C H, et al. NAS-FCOS: Fast neural architecture search for object detection. arXiv: 1906.04423, 2020 [105] Fang J M, Sun Y Z, Peng K J, Zhang Q, Li Y, Liu W Y, et al. Fast neural network adaptation via parameter remapping and architecture search. arXiv: 2001.02525, 2020 [106] Karlinsky L, Shtok J, Harary S, Schwartz E, Aides A, Feris R, et al. RepMet: Representative-based metric learning for classification and few-shot object detection. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 5192−5201 [107] Fan Q, Zhuo W, Tang C K, Tai Y W. Few-shot object detection with attention-RPN and multi-relation detector. arXiv: 1908.01998, 2020 [108] Wang T, Zhang X P, Yuan L, Feng J S. Few-shot adaptive faster R-CNN. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 7166−7175 [109] Yan X P, Chen Z L, Xu A N, Wang X X, Liang X D, Lin L. Meta R-CNN: Towards general solver for instance-level low-shot learning. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 9576−9585 [110] Kang B Y, Liu Z, Wang X, Yu F, Feng J S, Darrell T. Few-shot object detection via feature reweighting. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 8419−8428 [111] Inoue N, Furuta R, Yamasaki T, Aizawa K. Cross-domain weakly-supervised object detection through progressive domain adaptation. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 5001−5009 [112] RoyChowdhury A, Chakrabarty P, Singh A, Jin S Y, Jiang H Z, Cao L L, et al. Automatic adaptation of object detectors to new domains using self-training. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 780−790 [113] Kim S, Choi J, Kim T, Kim C. Self-training and adversarial background regularization for unsupervised domain adaptive one-stage object detection. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 6091−6100 [114] Chen Y H, Li W, Sakaridis C, Dai D X, van Gool L. Domain adaptive faster R-CNN for object detection in the wild. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 3339−3348 [115] Saito K, Ushiku Y, Harada T, Saenko K. Strong-Weak distribution alignment for adaptive object detection. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 6949−6958 [116] Zhu X G, Pang J M, Yang C Y, Shi J P, Lin D H. Adapting object detectors via selective cross-domain alignment. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 687−696 [117] Zhu J Y, Park T, Isola P, Efros A A. Unpaired image-to-image translation using cycle-consistent adversarial networks. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 2242−2251 [118] Howard A G, Zhu M L, Chen B, Kalenichenko D, Wang W J, Weyand T, et al. MobileNets: Efficient convolutional neural networks for mobile vision applications. arXiv: 1704.04861, 2017 [119] Sandler M, Howard A, Zhu M L, Zhmoginov A, Chen L C. MobileNetV2: Inverted residuals and linear bottlenecks. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 4510−4520 [120] Howard A, Sandler M, Chen B, Wang W J, Chen L C, Tan M X, et al. Searching for MobileNetV3. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 1314−1324 [121] Zhang X Y, Zhou X Y, Lin M X, Sun J. ShuffleNet: An extremely efficient convolutional neural network for mobile devices. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 6848−6856 [122] Ma N N, Zhang X Y, Zheng H T, Sun J. ShuffleNet V2: Practical guidelines for efficient CNN architecture design. In: Proceedings of the 2018 European Conference on Computer Vision (ECCV). Munich, Germany: Springer, 2018. 122−138 [123] Zhang T, Qi G J, Xiao B, Wang J D. Interleaved group convolutions. In: Proceedings of the 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy: IEEE, 2017. 4383−4392 [124] Qin Z, Li Z M, Zhang Z N, Bao Y P, Yu G, Peng Y X, et al. ThunderNet: Towards real-time generic object detection on mobile devices. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 6717−6726 [125] Zhang P Y, Zhong Y X, Li X Q. SlimYOLOv3: Narrower, faster and better for real-time UAV applications. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW). Seoul, Korea: IEEE, 2019. 37−45 [126] Bilen H, Vedaldi A. Weakly supervised deep detection networks. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 2846−2854 [127] Kantorov V, Oquab M, Cho M, Laptev I. ContextLocNet: Context-aware deep network models for weakly supervised localization. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, 2016. 350−365 [128] Tang P, Wang X G, Bai S, Shen W, Bai X, Liu W Y, et al. PCL: Proposal cluster learning for weakly supervised object detection. IEEE Transactions on Pattern Analysis & Machine Intelligence, 2020, 42(1): 176−191 [129] Diba A, Sharma V, Pazandeh A, Pirsiavash H, van Gool L. Weakly supervised cascaded convolutional networks. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Honolulu, HI, USA: IEEE, 2017. 5131−5139 [130] Li Y, Liu L Q, Shen C H, van den Hengel A. Image co-localization by mimicking a good detector＇ s confidence score distribution. In: Proceedings of the 2016 European Conference on Computer Vision (ECCV). Amsterdam, The Netherlands: Springer, 2016. 19−34 [131] Yang K, Li D S, Dou Y. Towards precise end-to-end weakly supervised object detection network. In: Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV). Seoul, Korea: IEEE, 2019. 8371−8380 [132] Wan F, Wei P X, Jiao J B, Han Z J, Ye Q X. Min-entropy latent model for weakly supervised object detection. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 1297−1306 [133] Zhou B L, Khosla A, Lapedriza A, Oliva A, Torralba A. Learning deep features for discriminative localization. In: Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016. 2921−2929 [134] Zhang X L, Wei Y C, Feng J S, Yang Y, Huang T. Adversarial complementary learning for weakly supervised object localization. In: Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Salt Lake City, Utah, USA: IEEE, 2018. 1325−1334 [135] Choe J, Shim H. Attention-based dropout layer for weakly supervised object localization. In: Proceedings of the 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). Long Beach, CA, USA: IEEE, 2019. 2214−222 期刊类型引用(36)
1. 张俊斌，景春阳，王希阔，蒋弘毅，王永娟. 基于人体骨架点的有生目标检测和行为预估. 兵器装备工程学报. 2025(01): 221-229 . 
百度学术2. 吴庆涛，朱军龙，葛泉波，张明川. 一种基于条件梯度的加速分布式在线学习算法. 自动化学报. 2024(02): 386-402 . 本站查看3. 黄荣，宋俊杰，周树波，刘浩. 基于自监督视觉Transformer的图像美学质量评价方法. 计算机应用. 2024(04): 1269-1276 . 百度学术4. 王铁铮，任博瀚，辛锋，潘焜. 基于实时视频的工业园区出入控制系统. 自动化技术与应用. 2024(05): 182-188 . 百度学术5. 刘以，邱军海，张嘉星，张小峰，王桦，张彩明. 基于权衡因子和多维空间度量的高鲁棒性图像分割算法. 图学学报. 2024(03): 482-494 . 百度学术6. 王旭，巩晓雯，黄其帅，陈炳瑞，杨世强，杨旭，张延杰. 基于深度机器视觉的香炉山隧洞钻孔多维特征精准定位. 清华大学学报(自然科学版). 2024(07): 1278-1292 . 百度学术7. 陈悦，罗逸豪，李锦. 基于多模态感知的水下目标检测应用构想. 数字海洋与水下攻防. 2024(03): 334-341 . 百度学术8. 郑舒志. 关于目标分类与目标检测任务中各类网络模型梳理及可改进方向与应用前景探究. 中国信息界. 2024(04): 243-246 . 百度学术9. 郑英子，魏东川，王蓓，曾景兴. 基于YOLOv8的安全帽佩戴检测研究. 无线互联科技. 2024(17): 27-30 . 百度学术10. 龙莹莹，余华云，杨武，殷俊凯. 基于改进的YOLOv5小目标检测SAR船只方法. 湖南邮电职业技术学院学报. 2024(03): 56-60 . 百度学术11. 周鼎，何涛，周杰，黄亮，杨国林. 基于迁移学习方法的架空配电线路无人机精准定位及拍摄技术研究. 供用电. 2024(10): 68-74+83 . 百度学术12. 邴政，周良将，董书航，温智磊. 一种基于微多普勒和机器学习的无人机目标分类识别技术. 雷达科学与技术. 2024(05): 549-556+568 . 百度学术13. 姜天，樊佳庆，宋慧慧. 空间感知与多注意力加权融合的无锚目标检测网络. 计算机与数字工程. 2024(10): 2941-2948+2990 . 百度学术14. 苟军年，杜愫愫，刘力. 基于改进掩膜区域卷积神经网络的输电线路绝缘子自爆检测. 电工技术学报. 2023(01): 47-59 . 百度学术15. 肖进胜，赵陶，周剑，乐秋平，杨力衡. 基于上下文增强和特征提纯的小目标检测网络. 计算机研究与发展. 2023(02): 465-474 . 百度学术16. 张帆，葛世荣. 矿山数字孪生构建方法与演化机理. 煤炭学报. 2023(01): 510-522 . 百度学术17. 李功，赵巍，刘鹏，唐降龙. 一种用于目标跟踪边界框回归的光滑IoU损失. 自动化学报. 2023(02): 288-306 . 本站查看18. 汪威，李琴锋，王冲，胡新宇. 基于旋转框的电子元器件检测. 仪表技术与传感器. 2023(03): 33-38+49 . 百度学术19. 周逸云，万新军，胡伏原，陈昊. 基于联合注意与特征关联的实例分割算法. 计算机工程. 2023(06): 217-226 . 百度学术20. 聂志勇，阴宇薇，汤佳欣，涂志刚. 一种基于边界框关键点距离的框回归算法. 计算机工程. 2023(07): 65-75 . 百度学术21. 万琴，李智，李伊康，葛柱，王耀南，吴迪. 基于改进YOLOX的移动机器人目标跟随方法. 自动化学报. 2023(07): 1558-1572 . 本站查看22. 赵亮，周继开. 基于重组性高斯自注意力的视觉Transformer. 自动化学报. 2023(09): 1976-1988 . 本站查看23. 姜淙文，金立左. Vehicle-YOLO——一种基于航拍影像的车辆检测模型. 微型电脑应用. 2023(09): 134-137 . 百度学术24. 杨学，严骏驰. 基于特征对齐和高斯表征的视觉有向目标检测. 中国科学:信息科学. 2023(11): 2250-2265 . 百度学术25. 谢斌红，张鹏举，张睿. 结合Graph-FPN与稳健优化的开放世界目标检测. 计算机科学与探索. 2023(12): 2954-2966 . 百度学术26. 戴云峰，冯兴明，丁亚杰，王瀚，王庆华. 单阶段目标检测网络的实例分割方法. 应用科技. 2023(06): 42-47 . 百度学术27. 文载道，王佳蕊，王小旭，潘泉. 解耦表征学习综述. 自动化学报. 2022(02): 351-374 . 本站查看28. 刘青茹，李刚，赵创，顾广华，赵耀. 基于多重注意结构的图像密集描述生成方法研究. 自动化学报. 2022(10): 2537-2548 . 本站查看29. 郑晗，储珺. 目标检测中的特征融合方法. 南昌航空大学学报(自然科学版). 2022(04): 59-67 . 百度学术30. 陈悦，石英，周申培，林朝俊，陈卓. 面向无人驾驶道路场景的FCOS改进算法. 武汉理工大学学报. 2022(12): 97-104 . 百度学术31. 赵俊杰，王金伟. 基于SmsGAN的对抗样本修复. 郑州大学学报(工学版). 2021(01): 50-55 . 百度学术32. 王宪保，朱啸咏，姚明海. 基于改进Faster RCNN的目标检测方法. 高技术通讯. 2021(05): 489-499 . 百度学术33. 张学军，黄爽，靳伟，鄢金山，史增录，周鑫城，张朝书. 基于改进Faster R-CNN的农田残膜识别方法. 湖南大学学报(自然科学版). 2021(08): 161-168 . 百度学术34. 刘凯旋，黄操军，李亚鹏，佟尚谕. 一种基于级联R-CNN的水稻害虫检测算法. 黑龙江八一农垦大学学报. 2021(05): 106-111+134 . 百度学术35. 包俊，刘宏哲，褚文博. 环视鱼眼图像处理深度学习研究进展. 中国图象图形学报. 2021(12): 2778-2799 . 百度学术36. 王新，李喆，张宏立. 一种迭代聚合的高分辨率网络Anchor-free目标检测方法. 北京航空航天大学学报. 2021(12): 2533-2541 . 百度学术其他类型引用(65)
-
下载:
计量
- 文章访问数: 3208
- HTML全文浏览量: 3308
- PDF下载量: 1623
- 被引次数: 101
