海洋资源勘探拖缆动力特性与姿态控制研究
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摘要
海洋油气资源是我国能源安全战略的核心，海洋油气资源勘探开发又是我国能源战略的重点。作为传统的地质勘探技术，地震波勘探是目前全球进行海洋资源勘探开发活动中应用最广泛、效率最高的地球物理技术。为了提高勘探作业的效率，控制勘探阵列的深度和水平间距，防止拖曳阵列之间的缠绕，需要仔细研究拖曳阵列动力学特性，准确预报勘探阵列的姿态，提出有效的勘探拖缆姿态控制策略。
本文在对国内外学者关于勘探拖曳系统的研究进行了比较系统的回顾与总结的基础上，建立了勘探拖缆的三维非线性动力学模型，通过数值和实验的方法研究了勘探拖缆的动力学特性，研制了嵌入式勘探拖缆控制器，设计了鲁棒自适应勘探拖缆姿态控制策略。
本文首先在拉格朗日坐标系下，考虑拖缆的弯曲刚度，分析作用在拖缆上的各种外载荷，使用微元法建立了各拖缆的三维动力学方程。经简化处理，同时给出了不考虑弯曲刚度的张紧拖缆的动力学方程。
鉴于有限差分Box method在求解拖缆非线性方程上的不稳定性及其对拖缆初值的强依赖性，本文在拖缆的数值求解中，在时域上采用广义算法。在一阶非线性系统上应用广义算法，分析了广义算法的精度。并通过谱半径法分别分析了中心差分Box method、向后差分算法、广义梯形算法以及值不同时广义算法的稳定性。采用相同权重法计算复杂的非线性动力学方程的平均系数矩阵，当广义算法运用到多自由度的非线性动力系统时，在空间上使用Box method的离散方法，在时间上使用广义算法。
编写了求解拖缆三维非线性动力学方程的计算程序Sjtu-tow。采用New-Raphson法求解微分方程的两点边值问题。由于拖缆可能出现局部变量变化较快的特性，在计算程序中，采用了一种基于变分法的自适应空间网格方法以减少计算时间，提高计算效率。在时域上，同样采用了自适应时间步长的方法以防止强非线性引起时域不收敛性。通过对勘探拖缆的实际算例的计算，与其他已有的算法进行了比较研究。
通过在拖曳水池进行拖缆的拖曳实验研究了拖缆动力学特性。在0.55m/s、1.01m/s、1.5m/s三种拖曳速度下研究了拖缆的稳态和瞬态动力学响应，测量了拖缆顶端和距离自由端1米处的张力和剪力。为了考查拖车振动的影响，测量了拖曳过程中拖车振动的加速度信号。在数值与实验的比较研究中，采用非一致网格处理顶端固定处的快速的张力和剪力变化。采用增强的水动力学系数，计算拖缆的稳态响应。同时，采用变阻力系数和定阻力系数两种方法研究了拖缆的瞬态动力学响应。
勘探拖缆的运动控制与姿态优化是现代地震勘探技术发展的重点和趋势。为了对海洋资源勘探拖曳阵列进行有效地控制，本文研制了嵌入式海洋资源勘探拖缆控制器—Sjtu-bird。首先进行了机械结构，通信和控制模块的设计，为满足性能指标的要求，特别的研制了一种高精度，抗干扰能力强的压力传感器。设计了椭圆形三维水翼，用以减少流动噪声，提高升阻比。根据总体设计要求，进行了水翼水动力性能试验、压力传感器精度及抗干扰性能试验、耐压及密封性能试验、转动摩擦阻力矩的测量试验。
勘探拖缆的运动是降低勘探效率，引起勘探拖缆缠绕的主要原因。勘探拖缆被水鸟分为两部分：一部分是控制段，即低应力段，另一部分是未控段，即高应力段。本文利用哈密尔顿原理建立了勘探拖缆和水鸟的耦合动力学模型，包括描述勘探拖缆线性化的变系数的双曲偏微分方程和描述水鸟动力学的常微分方程。基于李雅普诺夫方法，在勘探拖缆的精确模型下，设计了基于精确模型的鲁棒控制规律。然后考虑到实际勘探作业时系统的不确定参数，在基于精确模型的控制规律的基础上，设计了鲁棒自适应规律。两种控制规律用于隔离由勘探船的偏航引起的运动，自适应规律还能在线更新勘探拖缆密度的变化和水鸟处的张力变化。理论上分别证明了两种控制算法的稳定性，通过数值仿真研究了确定边界扰动和不确定边界扰动下，两种控制规律的有效性。
通过以上的研究得出了以下主要的结论：
1)理论分析表明当广义算法应用到简单一阶非线性系统时，该方法具有二阶精度。谱半径法分析结果表明当的取值范围为：[-0.3,-0.7]时，广义算法求解稳定性较好。与向后差分、有限差分Box method、广义梯形法的对比仿真实验表明，本文开发的计算程序Sjtu-tow不仅求解精度高，而且仿真运算求解时间短。
2)低频加速度信号的频谱分析表明，三种拖曳速度下拖车自身振动的频段和拖缆的低阶固有频率不在同一频段范围，因此拖车自身的振动对稳态工况下拖缆的响应影响不大。稳态拖曳速度下，拖曳点处和距尾端1米处的张力和剪力的变化及其FFT变换表明了拖缆拖曳过程中存在复杂的涡击振动现象和拖曳点处弯矩在拖缆动力学响应中所起到的主要作用。采用增强的水动力学系数计算拖缆的稳态响应能够与实验结果保持较好的一致性。采用变阻力系法计算的拖缆瞬态动力学响应与实验结果吻合较好。
3)水翼水动力性能试验、压力传感器精度及抗干扰性能试验、耐压及密封性能试验、转动摩擦阻力矩的测量试验的试验结果表明，各试验技术指标能完全满足恶劣海况作业时的要求。
4)基于精确模型的控制规律和鲁棒自适应规律分别能指数和渐进的驱使勘探拖缆的位移到零。鲁棒自适应控制规律能够在不牺牲隔振性能的前提下，改进系统的阻尼性能。在水鸟上没有外界扰动作用时，鲁棒自适应控制规律能有效的隔离船舶偏航引起的拖缆的运动，在水鸟上有外界扰动作用时，控制规律能够将外界的扰动控制在一个较小的界内。
5)所提出的鲁棒自适应控制规律能够在线更新勘探拖缆及水鸟的不确定性参数，同时所提出的控制规律具有鲁棒性，能够抵抗建模误差、参数不确定性、未知扰动等不确定性。所提出的控制规律只需要拖缆水鸟处的斜率和速度做为反馈，并不需要实际作业中难以测量的位移。勘探拖缆的斜率可以很容易的通过倾角传感器测量得到，因此本文所提出的控制规律在实际工程中是很容易实施的。所提出的控制规律不但能够用于勘探拖缆水平振动的控制，同时也可以扩展到勘探拖缆深度方向的控制。
Marine seismic exploration is now the most popular and effectiveapplication of the geophysical techniques. During the practical process ofsurvey, the stability and validity of signals ask for a certain requirement to thecontrol of towed seismic streamers both in depth and horizon, which is noteasy for the underwater towed cable in several kilometers long. The crux ofsolving this problem is to find a way to forecast the attitude of towed seismicstreamers accurately and master the dynamic characteristics of towed seismicstreamers.
Based on the review and summary of towed seismic streamer system inthe recent decades, in this thesis, three-dimensional nonlinear dynamic modelof towed cable was built up, dynamic performance of the towed cable wasstudied through numerical and experimental method respectively, embeddedcontroller of towed cable was designed and robust adaptive attitude controlstrategy was studied.
Considering bending rigidity of towed cable, this thesis analyzedexternal loads of towed cable and deduced its motion equation of each cableby differential element method under Lagrange-coordinate system. Asimplified approach was carried out to study the motion equation withoutconsidering bending rigidity.
Using Box method to solve nonlinear equation of towed cables wasunstable and depended heavily on initial value. In view of that, generalized
method was employed for temporal discretization in numerical calculationprocess.
The accuracy of generalized method was demonstrated when thegeneralized method was applied in simple nonlinear problem. Also, usingspectral radius method, the stability of Box method, backward differentiationformulae, generalized trapezoidal algorithm and generalized method wereresearched respectively.
Mean coefficient matrix of complex nonlinear dynamic equations werecalculated by adopting same weighted method. Generalized method wasemployed to solve complex nonlinear dynamic equations. Box method wasused in spatial discretization and generalized method was used intemporal discretization.
New-Rahpson method was adopted to solve two–point boundary valueproblems in calculation program of tree-dimensional nonlinear dynamicequations. In this calculation program, based on variation method, an adaptivespatial meshing method was deduced to reduce computational time andimprove calculation efficiency. In the time domain, adaptive time step methodwas used to improve non-convergence caused by strong nonlinear. Throughpractical calculation of towed cable, a comparative analysis was made withother algorithms.
We edited the calculation program of the low-tension cable. Theadvantages were verified by comparative analysis of classical examples.Experimental research of the cable dynamic performance was carried out intowing tank. In the experiment, the velocity of the cable were set as0.55m/s,1.01m/s,1.5m/s, respectively, to study the dynamic response of thelow-tension cable. Cable tension and shear forces were measured at the topend and the middle span. Acceleration was measured at the fixed end of thecable for the effect of towed carriage vibration. The tension and shear forcewere measured at the top end and the point about one meter from the free end.Strengthened coefficient method was used to carry out steady state simulation.
Both variable resistance coefficient method and constant resistancecoefficient method were used to study transient dynamic response of towedcable.
Motion control and attitude optimization of towed cable are hot pointsand trends of seismic exploration technology. In order to control the towedarray effectively, this thesis designed an embedded controller of towed cable(SJTU-bird). Firstly, the mechanical structure, communication and controlmode were designed and a kind of pressure sensor with high precision andanti-jamming ability was developed to meet design requirement. To decreaseflow-induced noise and increase lift-drag ratio, the shape of hydrofoil wasdesign as ellipse. Also, dynamic performance of hydrofoil test, precision andanti-jamming ability performance of pressure sensor test, pressure integritytest and pivoting friction torque measurement test were carried out,respectively.
The vibration of towed seismic streamers is a main reason for efficiencyreduction of the seismic survey and tail tangling. A vibration suppressionscheme of towed seismic streamers was investigated in this paper. The towedseismic streamer is divided into two spans, a controlled span, i.e., the lowtension span, and an uncontrolled span, i.e., the high tension span, by acontroller. Usually, the controller is called bird. The system model includes ahyperbolic partial differential equation with variable coefficient describing thetowed seismic streamers, and an ordinary differential equation describing thedynamic of bird. Robust based-model knowledge and adaptive controllers,based on the Lyapunov method, were designed to isolate the vibration oftowed seismic streamers caused by the course deviations of towing vessel，thevariations of towing vessel velocity and the variations of towed seismicstreamer density. The stability analysis of the whole system was carried outunder the action of robust based-model knowledge and robust adaptivecontrollers respectively. The finite difference scheme was used to validate theefficiency of the control law under different external disturbances.
The conclusions from the researches above are gained as following:
1)Theoretical analysis showed that generalized method has secondorder accurate and has good computational stability when the value rangeof is-0.7to-0.3. Spectral analysis results show that, compared with Box method, backward differentiation formulae and generalized trapezoidalalgorithm, generalized method that used in calculation program can notonly improve accuracy of solution, but also decrease computational time.
2)The FFT spectrum analysis of low frequency accelerometer shows thatthe low order natural frequencies of carriage are not the same as that of thetowed cable. The fluctuation and FFT spectrum of the tension and shear forceunder steady towed velocity demonstrate the effect of vortex shedding and themain role of moment at the top end. The comparative analysis of numericaland experimental results shows that strengthened coefficient method hasbetter agrrement at steady state simulation.
3)The results of dynamic performance of hydrofoil test, precision andanti-jamming ability performance of pressure sensor test, pressure integritytest and pivoting friction torque measurement test verified that all kinds oftechnical indexes can satisfy requirements under extreme sea conditions.
4)The robust based-model knowledge and adaptive controllersexponentially and asymptotically drive the controlled span-towed seismicstreamer displacement to zero, respectively. The robust adaptive controllerprovides improved damping but not sacrifice isolation performance. Therobust adaptive controller can isolate the vibration from the vessel when theperiod external disturbance does not act on the controller. The robust adaptivecontroller can control the streamer under a small bound when the periodexternal disturbance acts on the controller.
5)The adaptive scheme can tolerate the lack of knowledge of someuncertain parameters and directly execute the online adjustment of theparameters. Meanwhile, the proposed control law is robust and can resist themodel uncertainty due to parameter incertitude, model error and unknowndisturbance and so on. The control law only includes the velocity and slope,while it does not need the displacement which is difficult to measure inpractical operations. Thus it is easy to implement. The proposed control lawsare not only used in horizontal control, but also in depth control.
本文在对国内外学者关于勘探拖曳系统的研究进行了比较系统的回顾与总结的基础上，建立了勘探拖缆的三维非线性动力学模型，通过数值和实验的方法研究了勘探拖缆的动力学特性，研制了嵌入式勘探拖缆控制器，设计了鲁棒自适应勘探拖缆姿态控制策略。
本文首先在拉格朗日坐标系下，考虑拖缆的弯曲刚度，分析作用在拖缆上的各种外载荷，使用微元法建立了各拖缆的三维动力学方程。经简化处理，同时给出了不考虑弯曲刚度的张紧拖缆的动力学方程。
鉴于有限差分Box method在求解拖缆非线性方程上的不稳定性及其对拖缆初值的强依赖性，本文在拖缆的数值求解中，在时域上采用广义算法。在一阶非线性系统上应用广义算法，分析了广义算法的精度。并通过谱半径法分别分析了中心差分Box method、向后差分算法、广义梯形算法以及值不同时广义算法的稳定性。采用相同权重法计算复杂的非线性动力学方程的平均系数矩阵，当广义算法运用到多自由度的非线性动力系统时，在空间上使用Box method的离散方法，在时间上使用广义算法。
编写了求解拖缆三维非线性动力学方程的计算程序Sjtu-tow。采用New-Raphson法求解微分方程的两点边值问题。由于拖缆可能出现局部变量变化较快的特性，在计算程序中，采用了一种基于变分法的自适应空间网格方法以减少计算时间，提高计算效率。在时域上，同样采用了自适应时间步长的方法以防止强非线性引起时域不收敛性。通过对勘探拖缆的实际算例的计算，与其他已有的算法进行了比较研究。
通过在拖曳水池进行拖缆的拖曳实验研究了拖缆动力学特性。在0.55m/s、1.01m/s、1.5m/s三种拖曳速度下研究了拖缆的稳态和瞬态动力学响应，测量了拖缆顶端和距离自由端1米处的张力和剪力。为了考查拖车振动的影响，测量了拖曳过程中拖车振动的加速度信号。在数值与实验的比较研究中，采用非一致网格处理顶端固定处的快速的张力和剪力变化。采用增强的水动力学系数，计算拖缆的稳态响应。同时，采用变阻力系数和定阻力系数两种方法研究了拖缆的瞬态动力学响应。
勘探拖缆的运动控制与姿态优化是现代地震勘探技术发展的重点和趋势。为了对海洋资源勘探拖曳阵列进行有效地控制，本文研制了嵌入式海洋资源勘探拖缆控制器—Sjtu-bird。首先进行了机械结构，通信和控制模块的设计，为满足性能指标的要求，特别的研制了一种高精度，抗干扰能力强的压力传感器。设计了椭圆形三维水翼，用以减少流动噪声，提高升阻比。根据总体设计要求，进行了水翼水动力性能试验、压力传感器精度及抗干扰性能试验、耐压及密封性能试验、转动摩擦阻力矩的测量试验。
勘探拖缆的运动是降低勘探效率，引起勘探拖缆缠绕的主要原因。勘探拖缆被水鸟分为两部分：一部分是控制段，即低应力段，另一部分是未控段，即高应力段。本文利用哈密尔顿原理建立了勘探拖缆和水鸟的耦合动力学模型，包括描述勘探拖缆线性化的变系数的双曲偏微分方程和描述水鸟动力学的常微分方程。基于李雅普诺夫方法，在勘探拖缆的精确模型下，设计了基于精确模型的鲁棒控制规律。然后考虑到实际勘探作业时系统的不确定参数，在基于精确模型的控制规律的基础上，设计了鲁棒自适应规律。两种控制规律用于隔离由勘探船的偏航引起的运动，自适应规律还能在线更新勘探拖缆密度的变化和水鸟处的张力变化。理论上分别证明了两种控制算法的稳定性，通过数值仿真研究了确定边界扰动和不确定边界扰动下，两种控制规律的有效性。
通过以上的研究得出了以下主要的结论：
1)理论分析表明当广义算法应用到简单一阶非线性系统时，该方法具有二阶精度。谱半径法分析结果表明当的取值范围为：[-0.3,-0.7]时，广义算法求解稳定性较好。与向后差分、有限差分Box method、广义梯形法的对比仿真实验表明，本文开发的计算程序Sjtu-tow不仅求解精度高，而且仿真运算求解时间短。
2)低频加速度信号的频谱分析表明，三种拖曳速度下拖车自身振动的频段和拖缆的低阶固有频率不在同一频段范围，因此拖车自身的振动对稳态工况下拖缆的响应影响不大。稳态拖曳速度下，拖曳点处和距尾端1米处的张力和剪力的变化及其FFT变换表明了拖缆拖曳过程中存在复杂的涡击振动现象和拖曳点处弯矩在拖缆动力学响应中所起到的主要作用。采用增强的水动力学系数计算拖缆的稳态响应能够与实验结果保持较好的一致性。采用变阻力系法计算的拖缆瞬态动力学响应与实验结果吻合较好。
3)水翼水动力性能试验、压力传感器精度及抗干扰性能试验、耐压及密封性能试验、转动摩擦阻力矩的测量试验的试验结果表明，各试验技术指标能完全满足恶劣海况作业时的要求。
4)基于精确模型的控制规律和鲁棒自适应规律分别能指数和渐进的驱使勘探拖缆的位移到零。鲁棒自适应控制规律能够在不牺牲隔振性能的前提下，改进系统的阻尼性能。在水鸟上没有外界扰动作用时，鲁棒自适应控制规律能有效的隔离船舶偏航引起的拖缆的运动，在水鸟上有外界扰动作用时，控制规律能够将外界的扰动控制在一个较小的界内。
5)所提出的鲁棒自适应控制规律能够在线更新勘探拖缆及水鸟的不确定性参数，同时所提出的控制规律具有鲁棒性，能够抵抗建模误差、参数不确定性、未知扰动等不确定性。所提出的控制规律只需要拖缆水鸟处的斜率和速度做为反馈，并不需要实际作业中难以测量的位移。勘探拖缆的斜率可以很容易的通过倾角传感器测量得到，因此本文所提出的控制规律在实际工程中是很容易实施的。所提出的控制规律不但能够用于勘探拖缆水平振动的控制，同时也可以扩展到勘探拖缆深度方向的控制。
Marine seismic exploration is now the most popular and effectiveapplication of the geophysical techniques. During the practical process ofsurvey, the stability and validity of signals ask for a certain requirement to thecontrol of towed seismic streamers both in depth and horizon, which is noteasy for the underwater towed cable in several kilometers long. The crux ofsolving this problem is to find a way to forecast the attitude of towed seismicstreamers accurately and master the dynamic characteristics of towed seismicstreamers.
Based on the review and summary of towed seismic streamer system inthe recent decades, in this thesis, three-dimensional nonlinear dynamic modelof towed cable was built up, dynamic performance of the towed cable wasstudied through numerical and experimental method respectively, embeddedcontroller of towed cable was designed and robust adaptive attitude controlstrategy was studied.
Considering bending rigidity of towed cable, this thesis analyzedexternal loads of towed cable and deduced its motion equation of each cableby differential element method under Lagrange-coordinate system. Asimplified approach was carried out to study the motion equation withoutconsidering bending rigidity.
Using Box method to solve nonlinear equation of towed cables wasunstable and depended heavily on initial value. In view of that, generalized
method was employed for temporal discretization in numerical calculationprocess.
The accuracy of generalized method was demonstrated when thegeneralized method was applied in simple nonlinear problem. Also, usingspectral radius method, the stability of Box method, backward differentiationformulae, generalized trapezoidal algorithm and generalized method wereresearched respectively.
Mean coefficient matrix of complex nonlinear dynamic equations werecalculated by adopting same weighted method. Generalized method wasemployed to solve complex nonlinear dynamic equations. Box method wasused in spatial discretization and generalized method was used intemporal discretization.
New-Rahpson method was adopted to solve two–point boundary valueproblems in calculation program of tree-dimensional nonlinear dynamicequations. In this calculation program, based on variation method, an adaptivespatial meshing method was deduced to reduce computational time andimprove calculation efficiency. In the time domain, adaptive time step methodwas used to improve non-convergence caused by strong nonlinear. Throughpractical calculation of towed cable, a comparative analysis was made withother algorithms.
We edited the calculation program of the low-tension cable. Theadvantages were verified by comparative analysis of classical examples.Experimental research of the cable dynamic performance was carried out intowing tank. In the experiment, the velocity of the cable were set as0.55m/s,1.01m/s,1.5m/s, respectively, to study the dynamic response of thelow-tension cable. Cable tension and shear forces were measured at the topend and the middle span. Acceleration was measured at the fixed end of thecable for the effect of towed carriage vibration. The tension and shear forcewere measured at the top end and the point about one meter from the free end.Strengthened coefficient method was used to carry out steady state simulation.
Both variable resistance coefficient method and constant resistancecoefficient method were used to study transient dynamic response of towedcable.
Motion control and attitude optimization of towed cable are hot pointsand trends of seismic exploration technology. In order to control the towedarray effectively, this thesis designed an embedded controller of towed cable(SJTU-bird). Firstly, the mechanical structure, communication and controlmode were designed and a kind of pressure sensor with high precision andanti-jamming ability was developed to meet design requirement. To decreaseflow-induced noise and increase lift-drag ratio, the shape of hydrofoil wasdesign as ellipse. Also, dynamic performance of hydrofoil test, precision andanti-jamming ability performance of pressure sensor test, pressure integritytest and pivoting friction torque measurement test were carried out,respectively.
The vibration of towed seismic streamers is a main reason for efficiencyreduction of the seismic survey and tail tangling. A vibration suppressionscheme of towed seismic streamers was investigated in this paper. The towedseismic streamer is divided into two spans, a controlled span, i.e., the lowtension span, and an uncontrolled span, i.e., the high tension span, by acontroller. Usually, the controller is called bird. The system model includes ahyperbolic partial differential equation with variable coefficient describing thetowed seismic streamers, and an ordinary differential equation describing thedynamic of bird. Robust based-model knowledge and adaptive controllers,based on the Lyapunov method, were designed to isolate the vibration oftowed seismic streamers caused by the course deviations of towing vessel，thevariations of towing vessel velocity and the variations of towed seismicstreamer density. The stability analysis of the whole system was carried outunder the action of robust based-model knowledge and robust adaptivecontrollers respectively. The finite difference scheme was used to validate theefficiency of the control law under different external disturbances.
The conclusions from the researches above are gained as following:
1)Theoretical analysis showed that generalized method has secondorder accurate and has good computational stability when the value rangeof is-0.7to-0.3. Spectral analysis results show that, compared with Box method, backward differentiation formulae and generalized trapezoidalalgorithm, generalized method that used in calculation program can notonly improve accuracy of solution, but also decrease computational time.
2)The FFT spectrum analysis of low frequency accelerometer shows thatthe low order natural frequencies of carriage are not the same as that of thetowed cable. The fluctuation and FFT spectrum of the tension and shear forceunder steady towed velocity demonstrate the effect of vortex shedding and themain role of moment at the top end. The comparative analysis of numericaland experimental results shows that strengthened coefficient method hasbetter agrrement at steady state simulation.
3)The results of dynamic performance of hydrofoil test, precision andanti-jamming ability performance of pressure sensor test, pressure integritytest and pivoting friction torque measurement test verified that all kinds oftechnical indexes can satisfy requirements under extreme sea conditions.
4)The robust based-model knowledge and adaptive controllersexponentially and asymptotically drive the controlled span-towed seismicstreamer displacement to zero, respectively. The robust adaptive controllerprovides improved damping but not sacrifice isolation performance. Therobust adaptive controller can isolate the vibration from the vessel when theperiod external disturbance does not act on the controller. The robust adaptivecontroller can control the streamer under a small bound when the periodexternal disturbance acts on the controller.
5)The adaptive scheme can tolerate the lack of knowledge of someuncertain parameters and directly execute the online adjustment of theparameters. Meanwhile, the proposed control law is robust and can resist themodel uncertainty due to parameter incertitude, model error and unknowndisturbance and so on. The control law only includes the velocity and slope,while it does not need the displacement which is difficult to measure inpractical operations. Thus it is easy to implement. The proposed control lawsare not only used in horizontal control, but also in depth control.
引文
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