Dynamic evaluation of the matching degree and utilization condition of generalized agricultural water and arable land resources in China
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摘要:
作为农业发展的核心要素，水土资源匹配态势与利用程度决定着中国农业可持续发展及食物安全。为优化中国农业水土资源配置，该研究基于2000—2020年31个省市的统计数据，采用基尼系数评价农业水土匹配状况，提出广义农业水土匹配系数揭示各省农业水土资源匹配状况及配比程度，联合匹配特征与水土利用状况确定各省农业水土资源利用类型区。结果表明：1）研究期内，中国灌溉水与耕地分布差距较大（基尼系数均值0.424），匹配情况变差；广义农业水资源与耕地资源分布相对合理（基尼系数均值为0.360），无显著变化趋势。地理区及省际间农业水土匹配程度存在较大差异。华北、西北和东北地区匹配状况为“土多水少”，华东、华中和西南地区匹配状况为“水多土少”，广东（广义农业水土匹配系数均值为2.06）和云南（广义农业水土匹配系数均值为1.02）匹配程度分别为各省市最低和最高，匹配状况均为“水多土少”；2）农业水土资源利用程度空间异质性明显，垦殖率东南高西北低，农业水资源利用程度北高南低；3）吉林、新疆、江苏水土资源配置情况变差（转为低匹配高开发区），北京水土资源配置情况有所好转（转为高匹配低开发区）。研究结果能够为国家农业水土资源优化配置相关决策提供支撑，对实现国家食物安全及农业可持续发展具有重要意义。
Abstract:Water and land resources are the core elements of agricultural development, and their matching situation and degree of utilization determine agricultural sustainability and food security in China. In order to promote the optimal allocation of agricultural water and land resources in China, based on the statistical data for the 31 provinces in the mainland of China from 2000 to 2020, this study dynamically evaluated the matching degree of agricultural water and arable land resources according to the generalized agricultural water and land resources matching index and Gini index, determined the agricultural water and land resources zoning by integrating their matching degree and the utilization condition. The results showed that: 1) During the study period, there was a large gap between the distribution of irrigation water and arable land in China, with the mean Gini index calculated as 0.424, and the matching situation had deteriorated. The distribution of generalized agricultural water resources and arable land resources was relatively reasonable, with the mean Gini index calculated as 0.360, and the change was relatively stable. Great differences on the matching degree existed between provinces and geographic areas. The matching conditions in North China, Northeast and Northwest were "more land and less water", and the matching conditions in East China, Central China and Southwest were "more water and less land". The average values of the generalized agricultural water and land resources matching index were 2.06 for Guangdong and 1.02 for Yunnan, presenting the lowest and highest matching degrees among the provinces, respectively. The variation in the generalized agricultural water and land resources matching index increased with the value of the matching index, and the values of the matching index were related to the share of precipitation, showing a first increasing and then decreasing trend with the increase of the share of precipitation. 2) The utilization degree of agricultural water resources fluctuated with the abundance and decline of water resources from 2000 to 2020.The spatial heterogeneity of agricultural water and land resources utilization was obvious, with the reclamation rate generally "high in the southeast and low in the northwest" and the utilization degree of agricultural water resources "high in the north and low in the South". Especially, the reclamation rates in Henan and Shandong were more than 40%, while those in the northwest were less than 10%. And the utilization degrees of agricultural water resources in Tianjin (78%) and Hebei (74%) were higher than the development and utilization limit in 2020. 3) The agricultural water and land resources zoning in 11 provinces had changed from 2000 to 2020. The allocation of water and land resources in Jilin, Xinjiang and Jiangsu provinces deteriorated to the type of low matching high utilization zoning, while the allocation of water and land resources in Beijing improved to the type of high matching low utilization zoning. The main reason for the zoning changes was the change of matching degree for Xinjiang and Jiangsu and the changes in the utilization degree of water and land resources for Beijing and Jilin. As of 2020, 5 provinces, including Hebei, Shanxi, Jiangsu, Jilin and Xinjiang, belonged to the type of low matching and high utilization zoning, presenting the worst allocation of water and land resources, while 8 provinces, such as Beijing, Shaanxi, Sichuan and Qinghai, belonged to the type of high matching and low utilization, presenting good allocation of water and land resources. The results can provide support for the relevant decision making of the optimal allocation of agricultural water and land resources in China and are of great significance to achieve national food security and agricultural sustainable development.
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0. 引 言
中国甘薯种植面积和出口量均居世界首位[1]，具有区域广、跨度大等特点。针对不同作业场景，农艺专家们探索了多种甘薯种植生产模式[2]。丘陵山地甘薯生产量占全国总量的62.8%[3]，甘薯覆膜垄作栽培是北方薯区丘陵山地区域的主要种植模式，具有增加土壤有效积温，改善膜内土壤结构与墒情等作用，可显著提高甘薯产量[4-5]，有利于缓解人口增加与粮食短缺的矛盾[6-7]。甘薯裸苗（薯苗）膜上扦插是覆膜垄作栽培模式的重要环节，需要满足茎蔓种植、浅栽、多埋节等复杂农艺要求。目前中国丘陵山地薯苗膜上扦插主要依靠人工作业，劳动强度大、效率低，各穴种植姿态一致性差[8]。丘陵山地甘薯移栽机短缺是提升甘薯生产机械化水平的短板和卡点[9]。
目前旱地作物覆膜栽培生产方式主要用于膜上播种或移栽。其中膜上播种包括花生[10]、棉花[11]、马铃薯[12]、小麦[13]、玉米[14]等多种作物，主要通过研究速度补偿机构、凸轮与曲柄组合机构、平行四杆机构等控制鸭嘴成穴器，使其减弱入土-出土播种期间的水平移动，从而缓解撕膜、挑膜、错位等现象导致的漏播问题。意大利FORIGO公司[15]和侯守印等[16]通过膜上侧向开穴解决覆膜播种时膜孔尺寸大、形状不规则、播种质量差等问题。膜上移栽则主要通过机械装置剪切、挤压等动作，实现垄体膜上开穴、膜下土壤运移和回填，以满足移栽苗位姿需求[17]。许春林等[18]设计了步行式水稻钵苗膜上开孔移栽机构，实现了水稻钵苗膜上栽植，在秸秆纤维地膜和塑料地膜上其开孔刀开出的膜孔宽度和长度皆满足设计需求。LIU等[19]和金鑫等[20]分别采用五连杆机构和滑块机构控制鸭嘴栽植器动作，解决膜上移栽穴口大、直立度低、穴口地膜破损等问题。YANG等[21]指出在相同种植频率下，吊杯式移栽机采用锥形杯的破膜大小、地膜破损程度和成孔性能均优于多边形杯。胡飞等[22]采用复合曲柄摇杆配合鸭嘴栽植器实现蔬菜膜上双行栽植。韩长杰等[23]开展了半自动压缩基质型西瓜钵苗移栽机的成穴器参数优化研究，发现成穴深度是影响穴口上部纵长的主要因素。
上述研究主要针对钵苗膜上直立栽种，而甘薯膜上移栽需要采用裸苗进行浅栽、多埋节种植，以增加产量[24]。现有机具主要有荷兰MICHIGAN和意大利CHECCHI&MAGLI公司生产的MT移栽机和OTMA移栽机[25-27]、胡良龙等[28]设计的甘薯裸苗复式栽植机。这些机器主要用于无覆膜垄体的甘薯移栽，通过开沟投苗覆土方式种植裸苗。针对甘薯膜上移栽模式，朱斌彬等[29]进行了指夹式栽植机构的运动轨迹理论分析。PAN等[30]研制了用于大田作业的甘薯膜上多行复式移栽机，可实现薯苗膜上船底形栽插姿态。日本井关农机株式会社[31]则研发了PVH型带夹送苗式手扶移栽机，通过棘轮棘爪控制送苗装置跟随植苗部件运动，可实现精准间歇送苗，但采用棘轮棘爪也限制了作业速度的提升。LIU等[32]设计了一种履带式甘薯移植机，该机器可以完成水平、垂直等多种栽植轨迹并进行自动补苗作业，由于采用电力驱动，连续作业时间有限。上述研究主要以膜上栽种姿态为设计目标，忽略了破膜孔尺寸的问题，会影响保温保墒效果[33]。
针对北方丘陵山地甘薯膜上机械化移栽这一产业难题，本文基于PVH1系列蔬菜移栽机传动及行走系统，根据丘陵山地甘薯膜上扦插农艺需求，设计了丘陵山地仿形扦插甘薯移栽机，重点研究并联传动式薯苗栽植单元结构参数和工作参数等，并对不同速度下整机的薯苗穴内形态、栽植质量等性能进行田间试验。
1. 丘陵山地仿形扦插甘薯移栽机结构及工作原理
1.1 作业农艺需求及难点分析
北方薯苗人工膜上扦插常采用斜插、船底形插和水平插等方式，以实现“浅栽、多埋节”的复杂农艺需求[34]。其中船底形插法具备水平插法入土节位多和斜插法抗旱力强、易发根的优点，结薯多而大小均匀，因此本研究中选定船底形插法为机具的实现目标。采用此法扦插时，适用壮苗（棚内拔苗、根部较直、节间长度短）密植，苗长25～35 cm左右，苗粗5 mm左右，入土4～5节，露出覆膜垄体1～2节，将头尾翘起如船底形，埋入膜下5～10 cm深，薯苗扦插角为30°～60°。根据薯苗品种不同，则船底扦插埋入土下薯节长度约为10～20 cm。同时，根据土壤肥力及品种特性不同，移栽株距多为18～30 cm。
薯苗膜上扦插的难点在于，保证船底形态的同时，减少对地膜的破坏。而丘陵山地膜上扦插，由于地势不平、垄体不均匀等问题，其机械化生产还需具备整机调平和垄面仿形等功能，以满足扦插深度。
针对甘薯膜上船底形插农艺需求，构建图1所示坐标系，机械扦插时，扦插轨迹E（x，y）沿移栽入土方向依次经过破膜入土点H，船栽苗最深点M，船栽苗最远点N和出土点Q，并存在如下几何关系：
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图 1 薯苗机械化船底形插模型注：H为破膜入土点；Q为出土点；M为最深点；N为最远点；η为薯苗与地面夹角，（°）； XOY为坐标系，X轴与前进方向平行且相反，Y轴垂直地面向下；Z2为破膜穴口长度，mm；E(x,y)为扦插轨迹；h为扦插深度，mm。Figure 1. Mechanical transplanting model of sweet potato seedlings with boat-bottom placementNote: H is the soil penetration point; Q is the excavation point; M is the deepest point; N is the farthest point; η is the angle between the slip and the ground, (°); XOY is the coordinate, X axis is parallel and opposite to the forward direction, Y axis is vertical and downward to the ground; Z2 is the length of the cavity of the mulched ridge, mm; E(x,y) is transplanting trajectory; h is the transplanting depth, mm.{h=yM−yHZ1≈|MN| + |MH| = √(xM−xH)2+h2+√(xM−xN)2+(yM−yN)2η = arctan˙yH˙xHZ2=xQ−xH (1) 式中Z1为膜下薯苗长度，mm；Z2为破膜穴口长度，mm；xH为破膜入土点H的横坐标，mm；yH为点H的纵坐标mm；xM为点M的横坐标，mm；yM为点M的纵坐标，mm；xN为点N的横坐标，mm；yN为点N的纵坐标，mm。
1.2 整机结构及工作原理
丘陵山地仿形扦插甘薯移栽机由手扶式底盘、行走装置、送苗装置、植苗装置、垄面仿形系统、动力并联传动系统等组成（图2）。
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图 2 丘陵山地仿形扦插甘薯移栽机1.手扶式底盘 2.垄体导向装置 3.行走装置 4.垄面仿形系统 5.送苗装置 6.植苗装置 7.机架 8.动力并联传动系统 9.置苗架Figure 2. Profiling transplanter for sweet potato in hilly and mountainous region1.Handheld chassis 2.Ridge guiding device 3.Walking device 4.Ridge surface profiling system 5.Seedling delivery device 6.Seedling planting device 7.Frame 8.Power parallel transmission system 9.Seedling rack丘陵山地薯苗扦插覆膜垄体垄高为25～30 cm，垄距为80～90 cm。垄体左右侧受丘陵山地坡度影响存在偏差。丘陵山地仿形扦插甘薯移栽机作业时，先根据垄面坡度通过手扶式底盘进行整机左右调平，保证植苗装置位于垄面中央，同时根据垄面高度，调整垄面仿形系统仿形装置位置，保证扦插深度。随后动力经发动机底盘经过并联传动系统分别传至行走装置、送苗装置和植苗装置。送苗装置和植苗装置配合，实现薯苗扦插。整机参数如表1所示。
表 1 丘陵山地仿形扦插甘薯移栽机主要参数Table 1. Main parameters of sweet potato seedlings profiling transplanter for hilly and mountainous region参数 Parameters 数值 Value 整机尺寸（长×宽×高）
Machine demensions (length×width×height)/mm×mm×mm1800×1200×1200 整机质量 Weight of machine/kg 210 作业幅宽 Working width/mm 650～800 扦插株距 Transplanting spacing/mm 180～300 扦插深度 Transplanting depth/mm 40～100 作业速度 Working speed/(km·h−1) 0.6～0.75 2. 关键部件设计
2.1 薯苗栽植单元
2.1.1 植苗装置
植苗装置采用指夹模拟人手进行薯苗扦插，是实现船底形插的关键，由植苗杆件及夹苗组件构成（图3），其中植苗杆件由机架、曲柄、连杆、摇杆等组成，夹苗组件由驱动凸轮、夹指、导轨等组成，并通过旋转轴和支架安装在连杆上，从而随连杆运动。植苗装置作业时，通过曲柄逆时针旋转，带动连杆及其上夹苗组件沿船底形栽苗轨迹运动入土，夹苗组件在经过最近点R时，夹指I和夹指II在驱动凸轮作用下闭合取苗，随后运移经过H、M、N等点。在经过N点时，夹指张开放苗，随后继续运移经过Q点出土。其中夹指I和夹指II可绕安装在支架上的旋转轴转动，实现剪刀式开合。当两夹指与驱动凸轮高点配合时指夹张嘴，与凸轮机构低点配合时指夹闭合。同时，指夹开合过程有导轨和弹簧约束，保证其在垂直于连杆方向上的稳定运动，不发生空间上的偏移。
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图 3 植苗装置结构及工作原理示意图1.机架 2.摇杆 3.连杆 4.曲柄 5.夹苗组件 6.导轨 7.弹簧 8.夹指I 9.薯苗 10.栽插轨迹 11.垄体 12.驱动凸轮 13.支架 14.夹指II1.Frame 2.Rocker 3.Connecting rod 4.Crank 5.Seedling clamping component 6.Guide rail 7.Spring 8. Finger I 9.Sweet potato seedlings 10.Transplanting trajectory 11.Ridge 12.Drive cam 13.Support frame 14.Finger II注：P、R分别为指夹扦插轨迹最高点和最近点。Note: P and R are the highest point and closest point of the trajectory.Figure 3. Structure and working principle diagram of planting mechanism构建与甘薯膜上船底形插农艺相同的坐标系XOY如图4所示。根据解析法[35]，确定连杆上E点运动轨迹即植苗轨迹E(x，y)为
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图 4 植苗装置机构简图注：A为曲柄旋转中心；B为曲柄与连杆铰接点；C为连杆与摇杆铰接点；D为摇杆与机架铰接点；E为指夹夹持点；l1为曲柄长度，mm；l2为连杆长度，mm；l3为摇杆长度，mm；l4为机架长度，mm；l5为|BE|长度，mm；θ为连杆BC与BE夹角，(°)；φ0为机架AD与X轴方向夹角，(°)；φ为曲柄转角，(°); δ为BC与AD夹角，(°)；β为BD与AD夹角，(°)。Figure 4. Schematic diagram of planting mechanismNote: A is the rotation center of the crank; B is the hinge point between the crank and connecting rod; C is the hinge point between the connecting rod and the rocker; D is the hinge point between the rocker and the frame; E is the clamping point of the upper finger; l1 is the length of the crank, mm; l2 is the length of the connecting rod, mm; l3 is the length of rocker, mm; l4 is the length of the frame, mm; l5 is the length of |BE|, mm; θ is the angle between the connection rods BC and BE, (°); φ0 is the angle between the frame AD and X-axis direction, (°); φ is the crank angle, (°); δ is the angle between BC and AD, (°); β is the angle between BD and AD, (°).{Ex=xA+l1cos(φ0+φ)+l5cos(θ+φ0+δ),φ∈[0,2π)Ey=yA+l1sin(φ0+φ)+l5sin(θ+φ0+δ),φ∈[0,2π)δ=arccosl22+d2−l322l2d−ββ=arcsinl1sinφdd=√l12+l42−2l1l4cosφ (2) 式中xA为点A横坐标，mm；yA为点A纵坐标，mm。A点与坐标系O点重合，则xA=0，yA=0。
由于夹指在导轨上平行于连杆BC运动，则θ=0°。假定曲柄长度l1已知，则决策变量为l2、l3、l4、l5和φ0，根据曲柄摇杆成立条件[35]可得约束条件如下：
{g1(l2,l3,l4,l5,φ0)=l1+l4−l2−l3⩽ (3) 植苗装置进行船底形插时，夹苗指轨迹E( x，y )应形成不重合的回路，以防止因机构扰动而影响已放置薯苗的位姿；轨迹E(x，y)不能过扁，即纵向高度|yM-yP|与横向长度|xN-xR|相差不能过大，以同时满足扦插入土深度与取苗扦插位置；植苗夹指关联尺寸l5不宜过长；具有船形弧线。基于此，以四连杆机构分析图谱[36]为基础，初步选定满足上述要求的l1:l2:l3:l4:l5为1:2.0:2.0:2.5:3.5等多组轨迹，并对各比例取并集（式（4）），在此并集内求解可实现膜下船底形扦插姿态的最优解。
\begin{split} l_{1}:l_{2}:l_{3}:l_{4}:l_{5}=&1:(2.0～2.5):(1.5～4.0):\\&(2.5～4.5):(2.0～4.0) \end{split} (4) 曲柄长度l1=100 mm，为寻求满足扦插农艺需求的较优解，根据式（2），可得扦插轨迹E(x，y)关于曲柄旋转角度φ的一阶导数为
\left\{\begin{array}{l}\stackrel{·}{{E}{_x}}={l}_{5}\left(\dfrac{\dfrac{{l}_{1}{l}_{4}\mathrm{sin}\varphi }{d{l}_{2}}-\dfrac{{l}_{1}{l}_{4}e\mathrm{sin}\varphi }{2{d}^{3}{l}_{2}}}{\sqrt{1-\dfrac{{e}^{2}}{4{d}^{2}{l}_{2}{}^{2}}}}+\dfrac{\dfrac{{l}_{1}\mathrm{cos}\varphi }{d}-\dfrac{{l}_{1}{}^{2}{l}_{4}{\mathrm{sin}}^{2}\varphi }{{d}^{3}}}{\sqrt{1-\dfrac{{l}_{1}{}^{2}{\mathrm{sin}}^{2}\varphi }{{d}^{2}}}}\right)\\ \begin{array}{cc}& \end{array}\cdot \mathrm{sin}\left(\theta +\mathrm{arccos}\left(\dfrac{e}{2d{l}_{2}}\right)-\mathrm{arcsin}\left(\dfrac{{l}_{1}\mathrm{sin}\varphi }{d}\right)\right)-{l}_{1}\mathrm{sin}\varphi \\ \stackrel{·}{{E}{_y}}={l}_{1}\mathrm{cos}\varphi +{l}_{5}\mathrm{cos}\left(\theta +\mathrm{arccos}\left(\dfrac{e}{2d{l}_{2}}\right)-\mathrm{arcsin}\left(\dfrac{{l}_{1}\mathrm{sin}\varphi }{d}\right)\right)\\ \begin{array}{cc}& \end{array}\cdot \left(-\dfrac{\dfrac{{l}_{1}{l}_{4}\mathrm{sin}\varphi }{d{l}_{2}}-\dfrac{{l}_{1}{l}_{4}e\mathrm{sin}\varphi }{2{d}^{3}{l}_{2}}}{\sqrt{1-\dfrac{{e}^{2}}{4{d}^{2}{l}_{2}{}^{2}}}}-\dfrac{\dfrac{{l}_{1}\mathrm{cos}\varphi }{d}-\dfrac{{l}_{1}{}^{2}{l}_{4}{\mathrm{sin}}^{2}\varphi }{{d}^{3}}}{\sqrt{1-\dfrac{{l}_{1}{}^{2}{\mathrm{sin}}^{2}\varphi }{{d}^{2}}}}\right)\\ e={l}_{1}{}^{2}+{l}_{2}{}^{2}-{l}_{3}{}^{2}+{l}_{4}{}^{2}-2{l}_{1}{l}_{4}\;\mathrm{cos}\varphi ={l}_{2}{}^{2}-{l}_{3}{}^{2}+{d}^{2}\end{array} \right. (5) 取苗点为指夹扦插轨迹最近点R，否则植苗装置与供苗装置发生干涉，且在入土前完成取苗，则植苗装置夹苗组件长度应大于连杆，摇杆铰接点C轨迹不能触碰地面，约束条件如下：
\left\{ \begin{gathered} {{{g}} _6}({{{l}}_2}{{,}}{{{l}}_3}{{,}}{{{l}}_4}{{,}}{{{l}}_5}{{,}}{\varphi _0}){{ = }}{{{x}}_R}{{ - }}{{{x}}_{{H}}} < 0 \\ {{{g}} _7}({{{l}}_2}{{,}}{{{l}}_3}{{,}}{{{l}}_4}{{,}}{{{l}}_5}{{,}}{\varphi _0}){{ = }}{{{l}}_5}{{ - }}{{{l}}_2} > h \\ {{{g}} _8}({{{l}}_2}{{,}}{{{l}}_3}{{,}}{{{l}}_4}{{,}}{{{l}}_5}{{,}}{\varphi _0}){{ = }}{{{l}}_4}\sin {\varphi _0}{{ + }}{{{l}}_3}{{ - }}{{{y}}_M}{{ - }}h < 0 \\ {{{x}}_{\rm{R}}}{{ = }}{{{x}}_{\min }}({{E}}({{x,y}})) \\ {{{y}}_{\rm{M}}}{{ = }}{{{y}}_{\max }}({{E}}({{x,y}})) \\ \end{gathered} \right. (6) 根据式（5），当植苗轨迹横坐标Ex导数为0时，可得扦插最远点N、扦插最近点R的坐标及极坐标参数。当植苗轨迹纵坐标Ey导数为0时，可得扦插最上点P、扦插最深点M的坐标及极坐标参数。已知yM后，结合农艺需求的栽插深度h，可得扦插入土点H、出土点Q的坐标及极坐标参数。
根据四连杆图谱轨迹，确定杆件l2～l5的求解区间，结合曲柄摇杆基本条件（式（3））和实际工作需求（式（6）），根据农艺指标，进行决策变量求解。求得植苗装置结构参数对静轨迹的影响规律如图5所示。由图5分析可知，l2影响扦插轨迹的整体形状，l4影响扦插轨迹包围区域，并与扦插姿态和穴口长度直接相关，l3和l5也对扦插轨迹存在一定影响。
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图 5 结构参数对扦插轨迹的影响Figure 5. Effects of structural parameters on transplanting trajectory针对扦插形态指标的重要性，确定本试验权重分配集P1=[0.1 0.45 0.35 0.1]，即栽深h、膜下薯苗长度Z1、扦插夹角η、穴口尺寸Z2的权重分别为0.1、0.45、0.35、0.1。通过建立指标隶属度模型（式（7）），构成模糊关系矩阵Rr（式（8））。由模糊矩阵Rr与权重P确定模糊综合评价值集W（式（9））。
\begin{split} {{r}}_{{{i}{j}}}=\frac{{{Y}}_{{{i}{j}}}-{{Y}}_{{i}\rm{{{m}{i}{n}}}}}{{{Y}}_{{i}\rm{{{m}{a}{x}}}}-{{Y}}_{{i}\rm{{{m}{i}{n}}}}} {,}\;{i}=1,2,3,4;\;j=1,2,3,\cdot \end{split} (7) \mathop {{{\boldsymbol{R}}}}\nolimits_r = \left[ \begin{gathered} \begin{array}{*{20}{c}} {\mathop r\nolimits_{11} }&{\mathop r\nolimits_{12} }&{...}&{...} \end{array} \\ \begin{array}{*{20}{c}} {\mathop r\nolimits_{21} }&{\mathop r\nolimits_{22} }&{...}&{...} \end{array} \\ \begin{array}{*{20}{c}} {\mathop r\nolimits_{31} }&{\mathop r\nolimits_{32} }&{...}&{...} \end{array} \\ \begin{array}{*{20}{c}} {\mathop r\nolimits_{41} }&{\mathop r\nolimits_{42} }&{...}&{...} \end{array} \\ \end{gathered} \right] (8) {{W}}={{P}}\cdot{{R}}_{r} (9) 式中rij为指标Yi第j个决策变量解对应的指标值获得的隶属度值；Yij为指标Yi第j个决策变量解对应的指标值；Yimax为指标Yi的最优值；Yimin为指标Yi的最差值。
最终根据模糊综合评价得分W，确定各杆长度为l2=2.0 l1，l3=2.0 l1，l4=2.5 l1，l5=2.75 l1，φ0=0°。此时，薯苗栽植后与地面夹角η为55°，栽植深度h=65 mm，膜下薯苗长度Z1=195 mm，穴口长度Z2=80 mm，满足北方膜上船底形插的农艺需求。
2.1.2 薯苗栽植单元送苗机构
植苗装置曲柄旋转中心A与坐标系O点重合，则在薯苗栽植单元中坐标系XOY如图6所示。由于φ0=0°，则X轴平行机架AD且与机具前行方向相反。薯苗栽植单元由植苗装置和送苗装置组成，通过并联传动系统相互配合，实现薯苗膜上扦插。送苗装置由摆苗板、夹苗刷、送苗支架、传动装置等组成，为实现植苗装置可靠夹持薯苗，送苗装置应在R点处为植苗装置供苗，植苗装置每运动1圈，送苗装置刚好在供苗点供苗1株。
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图 6 薯苗栽植单元Figure 6. Planting unit of sweet potato seedlings1.送苗装置 2.并联传动系统 3.摆苗板 4. 夹苗刷 5.机架 6.植苗装置 7.送苗支架 8.薯苗1.Seedling delivery device 2.Parallel transmission system 3.Seedling placing plate 4.Seedling holding brush 5.Frame 6.Seedling planting device 7.Frame of the seedling delivery device 8.Sweet potato seedling注：h1为夹苗刷放苗位置底部离植苗装置曲柄旋转中心的垂直距离，mm；h2为夹苗刷放苗后植苗装置持苗部位置距离曲柄旋转中心的水平距离，mm；ld为植苗装置运动轨迹离送苗装置的最近水平距离，mm。Note: h1 is the vertical distance from the bottom surface of the seedling holding brush to the center of the crank shaft, mm; h2 is the horizontal distance from the outer surface of the seedling holding brush to the center of the crank shaft, mm; ld is the nearest horizontal distance from the transplanting trajectory to the seedling delivery device, mm.送苗装置与植苗装置的相对位置是保证在R点供苗的前提，夹苗刷夹持苗株后，应满足以下关系：
\left\{ \begin{aligned}& h_1 = y_{\rm{R}} \\ &h_2 = x_{\rm{R}} - {{l}}_{\rm{d}} \\ \end{aligned} \right. (10) 为保证夹苗指与送苗装置不干涉，则有
{{{l}}_{\rm{d}}} \geqslant {{{l}}_{\rm{Z}}}/2 (11) 式中lZ为植苗装置夹指宽度，mm。
且为保证薯苗与指夹的接触，薯苗摆放后，其伸出板刷尾部的长度应满足：
{X_{\rm{L}}} \geqslant {l_{\rm{d}}} + {l_{\rm{Z}}}/2 (12) 式中XL为薯苗摆放后其伸出板刷尾部的长度，mm。且|ld-lZ/2|越小，夹苗越靠近根部，越容易成功。因此，根据连杆参数设计，最终确定ld=lZ/2=10 mm，h1=267 mm，h2=141 mm，XL≥20 mm。
假设植苗装置转速为n1（r/min），送苗装置转速为n2（r/min），夹苗刷安装间距为Z1个链齿节距，送苗装置所用链轮齿数为Z2，要求植苗装置每运动一圈，刚好下一夹苗刷到达R点为植苗装置供苗，则有：
\frac{{\mathop n\nolimits_1 }}{{\mathop n\nolimits_2 }} = \frac{{\mathop Z\nolimits_2 }}{{\mathop Z\nolimits_1 }} (13) 2.2 并联传动系统
株距是甘薯种植的重要农艺参数，根据甘薯移栽农艺需求，对于鲜食薯和工业薯，移栽株距约为18～30 cm不等。自走式甘薯移栽机株距及行进速度为
{d}_{z}=\frac{\pi {d}_{轮}}{\Pi }=\frac{\pi {d}_{轮}}{{n}_{1}/{n}_{地}} (14) v=\pi {d}_{轮}{n}_{地} (15) 式中dz为移栽株距，m；d轮为地轮直径，m；Π为植苗装置曲柄转速n1与地轮转速n地的比值；v为机器前进速度，m/min。其中，根据机具底盘特性可知d轮=500 mm，工作时机器前进速度v=0.6～0.75 km/h，可通过增加油门实现变速。当移栽株距为18～30 cm时，Π为5.2～8.7。
根据上述参数及PVH1蔬菜移栽机动力底盘传动特点设计并联传动系统如图7所示。其中动力经发动机到达第I级减速箱，并由此传给地轮，驱动其工作。随后传递给手动变速箱、横向减速箱，并传给左侧侧边齿轮箱传动系统、链传动II、驱动植苗装置，同时传给万向传动轴、链传动I并驱动送苗装置。通过可调速齿轮箱调节，传动比变化范围为5.5～7.8，移栽株距调节范围约为20～28 cm。
2.3 垄面仿形系统
垄面仿形系统主要由液压缸、可调节流阀、液压控制阀、仿形装置、溢流阀、齿轮泵等组成（图8）。
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图 8 垄面仿形系统1.液压缸 2.可调节流阀 3.液压控制阀 4.仿形装置 5.溢流阀 6.齿轮泵 7.栽植单元铰接点 8.机架Figure 8. Ridge surface profiling system1.Hydraulic cylinder 2.Adjustable flow valve 3.Hydraulic control valve 4.Profile apparatus 5.Relief valve 6.Gear pump 7.Hinge point of planting unit 8.Frame仿形装置位于薯苗栽植单元前方，作业时仿形装置与垄面实时紧密贴合。随着机具前行作业，丘陵山区垄面起伏，仿形装置随之高低变化，拉动液压控制阀阀芯操作杆，进而带动控制阀动作。薯苗栽植单元机架与底盘铰接，液压缸推杆与薯苗栽植单元分布在机架铰接点两侧。如图8所示，根据杠杆原理，系统液压缸随着控制阀动作实时伸缩，带动铰接点另一侧的薯苗栽植单元以5.8倍距离升降，实现仿形。
垄面仿形系统采用油泵马达总成式齿轮泵为液压系统动力源，型号为VOITH-IPVP-3，为压力补偿控制式变量泵，在1500 r/min额定转速下的流量为7.8 L/min，系统额定工作压力为33 MPa。
薯苗扦插时，在液压缸的作用下，薯苗栽植单元在垄面的上下运动由液压缸支撑，则有：
{F_{\text{T}}} = \dfrac{\pi }{4}D_{\text{T}}^2{P_1} \geqslant {m_{\text{T}}}g (16) 式中FT为液压缸推力，N；DT为活塞直径，mm；P1为液压缸最大液压压力，取33 MPa；mT为栽植单体质量，kg；g为重力加速度，取9.8 N/kg。其中栽植单元质量为55 kg，则仿形系统液压缸推力在540 N以上，DT≥4.6 mm。结合系统压力，初步选定液压缸型号为YUKEN Mini型液压缸。
根据薯苗栽植单元关键参数与结构设计，仿形装置触地点与植苗装置最低点在X轴方向水平距离为400 mm，自走底盘可实现的最大作业速度为0.75 km/h，则液压缸必须在1.92 s内实现植苗装置到达垄面凸起或凹陷处。液压缸提升速度为
{V_{\text{L}}} = \dfrac{{{Q_{\text{L}}}}}{{{Z_{\text{L}}}\pi [{{({D_{\text{T}}}/2)}^2} - {{({d_{\text{T}}}/2)}^2}] \times {{10}^{ - 3}}}} (17) 式中VL为液压缸提升速度，m/min；QL为液压缸额定流量，取7.8 L/min；ZL为液压缸数量，取1；dT为活塞杆直径，取20 mm。取活塞直径DT为40 mm，计算得VL为8.3 m/min。根据扦插深度，假定仿形量为100 mm，则液压缸对应仿形行程为17.2 mm，提升时间为0.12 s，满足仿形速度要求。
3. 室内取苗试验
田间种植的薯苗品种不同，其形态特征各异。为验证薯苗栽植单元对不同薯苗的取苗效果，根据《甘薯机械化生产技术规范》（DB37/T 3355-2018），选用5种黄淮海地区常用的基部较直立的甘薯拔苗（长25～35 cm）进行室内取苗试验。所选薯苗品种包括：济薯26（即板栗薯）、龙薯9号、烟薯25、普薯32（即西瓜红）、紫薯新引1号（即紫罗兰）（图9）。
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图 9 栽植单元室内取苗试验Figure 9. Indoor test of sweet potato seedlings taking by using planting unit室内取苗试验时，在40～50 r/min植苗速度下，给送苗装置供给上述5种薯苗，检验栽植单元植苗装置取苗成功率，每种薯苗分别连续供苗300株，取苗过程通过高速摄像系统（Photron FASTCAM MiniUX50 型）进行拍摄记录，拍摄速度为250 帧/s。室内试验结果表明（表2），在40、50 r/min植苗速度下，5种薯苗的取苗成功率均不低于99%，满足移栽需求。
表 2 室内取苗试验结果Table 2. The results of indoor test of taking sweet potato seedlings品种
Varieties薯苗基部参数*
Parameters of sweet
potato seedling bases取苗成功率
Seedling picking
success rate/%直立程度
Verticality
level /mm直径
Diameter/mm叶片数
Number of leaves40 r·min−1 50 r·min−1 济薯26
Jishu268.1 4-5 3-4 100.0 99.7 龙薯9号
Longshu 910.3 3-4 3-4 100.0 100.0 烟薯25
Yanshu 2514.3 4-5 3-4 100.0 99.7 普薯32
Pushu 3213.6 4-5 3-4 100.0 100.0 紫罗兰
Zhiluolan16.8 2-3 4-5 99.3 99.0 注：*薯苗基部是指薯苗从根部往上8 cm内的范围，直立程度则表示薯苗基部弯曲后宽度。 Note: *The base of the sweet potato seedlings is the range from the bottom to the upwards within 8 cm, and the verticality level indicates the width of the base of the sweet potato seedlings stem. 同时，针对未被成功取到的苗株，通过调取高速录像进行分析发现，基部薯苗叶片数较多，且苗株叶片较长时，植苗装置已成功夹取基部并沿船底形轨迹运移薯苗，但长叶片仍被夹苗刷夹持，导致薯苗叶片挂在夹苗刷上；薯苗筛选时未排查特别弯曲的植株个体，导致其基部偏离取苗点较远，不在夹指夹取范围内。综上可知，取苗效果与苗株特性有关，保证薯苗基部的直立度在夹指张开后的取苗范围内是取苗成功的关键。根据植苗装置参数及室内试验结果可得， R 点上下约15 mm以内，左右约20 cm以内时，指夹取苗成功率高。
4. 田间试验
4.1 试验条件
2022年5月初，在山东省济宁市泗水县圣水峪镇进行丘陵山地仿形扦插甘薯移栽机的田间试验（图10）。试验根据《甘薯机械化生产技术规范》（DB37/T 3355-2018）和《旱地栽植机械》标准（JB/T10291-2013），采用长280～320 mm，茎粗约4 mm的薯苗进行作业，作业品种为济薯26（鲜食型甘薯品种）。
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图 10 丘陵山地仿形扦插甘薯移栽机田间试验Figure 10. Field test of profiling transplanter for sweet potato in hilly and mountainous area4.2 作业参数正交试验
4.2.1 试验方法
根据覆膜栽培实际需求和当地土壤肥力情况，设定扦插株距24 cm，以作业速度XV、薯苗基部特征XT、薯苗伸出夹苗刷长度XL为因子进行三因素三水平（表3）田间移栽正交试验。
表 3 田间正交试验因素及水平Table 3. Factors and levels of field orthogonal test水平
Level作业速度
Working velocity
XV/(km·h−1)薯苗基部特征*
Characteristics of
sweet potato seedling
bases XT薯苗伸出长度
Length of
extended brush part
XL/mm1 0.5 优 20 2 0.6 良 40 3 0.7 中 60 注：*薯苗基部直立度≤8 mm为优，8 mm<直立度≤12 mm为良，12 mm<直立度≤16 mm为中。 Note: * the seedling base is optimal, good and moderate when the width of the seedling base within 8 cm from the root of the sweet potato seedling base is ≤ 8 mm, 8-12 mm, 12-16 mm, respectively. 根据当地春薯种植初期保温及作物生长期抑制杂草生长的需求，选用0.01 mm黑膜进行覆膜，共9组试验。每组试验分别移栽200 m，试验后每组选取60 m长度，测量种植成功的每穴薯苗平均长度Y1、栽深合格率Y2和漏苗率Y3。移栽一周后，待薯苗生根，以垄面为基准线，剖开土壤纵截面，测量甘薯的种植深度，并以薯苗与垄面交汇点为基点，扯出薯苗，测量膜下薯苗长度等参数。统计漏苗率、株距变异系数、栽深合格率等移栽质量评价指标，计算方法如下：
{Y_1} = \dfrac{{\displaystyle\sum\limits_{k = 1}^n {{L_k}} }}{{{n_k}}} (18) {Y_2} = \dfrac{{{N_h}}}{n} \times 100\text{%} (19) {Y_3} = \frac{{{N_{{LZ} }}}}{{N'}} \times 100\text{%} (20) 式中Lk为膜下薯苗长度，mm；nk为扦插成功的薯苗株数；Nh为栽植深度合格的薯苗总株数；n为测定的总株数；NLZ为漏栽薯苗株数；N′为测试长度内的理论扦插株数。
4.2.2 作业参数试验结果及分析
丘陵山地仿形扦插甘薯移栽机膜上扦插正交试验田间试验结果见表4。分析可知，平均膜下薯苗长度Y1为216.9 mm，平均栽深合格率Y2为97.3%，平均漏苗率Y3为4.1%，满足薯苗膜下浅栽、多埋节的农艺需求。
表 4 田间试验方案与结果Table 4. Field test scheme and results试验序号
Test No.XV XT XL 膜下薯苗长度
Length of seedlings
under film/mm栽深合格率
Transplanting
depth qualified rate/%漏苗率
Leakage rate /%1 1 1 1 196.2 96.7 0.20 2 1 2 2 214.5 97.2 0.10 3 1 3 3 235.6 96.3 4.85 4 2 1 2 218.1 98.4 0.90 5 2 2 3 232.6 98.5 2.70 6 2 3 1 200.1 96.9 6.40 7 3 1 3 237.5 97.6 4.00 8 3 2 1 198.6 95.9 8.00 9 3 3 3 219.2 98.1 10.00 对田间试验结果进行多因素方差分析（表5），结果表明，各因素对膜下薯苗平均长度Y1的影响大小顺序为薯苗伸出长度XL、作业速度XV、薯苗基部形态XT，对栽深合格率Y2的影响大小顺序为薯苗伸出长度XL、作业速度XV和薯苗基部形态XT，对漏苗率Y3的影响大小顺序为作业速度XV、薯苗基部形态XT、薯苗伸出长度XL。其中，作业速度和基部特征对漏苗率影响显著，这主要是因为薯苗基部形态直接影响了薯苗夹持段是否经过取苗点，同时作业速度过快，会影响人工摆苗质量，使得薯苗不在夹指取苗范围内。同时，薯苗伸出长度对膜下薯苗长度影响显著，这主要是因为薯苗伸出长度多，则夹指取苗入土后，多伸出的薯苗全部入土，且薯苗伸出长度三个水平皆大于等于设计值，因此膜下薯苗长度在不同水平下大于等于理论设计值。
表 5 多因素方差分析结果Table 5. Results of multivariate analysis of variance源
Source指标
Index平方和
Sum of squares均方
Mean squareP XV Y1 13.500 13.500 0.149 Y2 0.327 0.327 0.554 Y3 47.320 47.320 0.005 XT Y1 1.602 1.602 0.572 Y2 0.327 0.327 0.554 Y3 43.470 43.470 0.006 XL Y1 2046.607 1023.303 0.000 Y2 3.082 1.541 0.254 Y3 2.507 1.254 0.497 注：P<0.05表示影响显著，P≥0.05表示影响不显著。 Note: P<0.05 means the effect is significant, and P≥0.05 means the effect is non-significant. 4.2.3 最优作业参数求解
为分析作业速度、薯苗基部特征和伸出长度对丘陵山地仿形扦插甘薯移栽机膜上扦插作业质量的综合影响效果，应用模糊综合评价法对正交试验结果进行优化求解（式（9）），找出最佳参数组合。根据田间试验栽植性能指标的重要性，确定本试验权重分配集P2=[0.30 0.15 0.55]，即每穴薯苗平均埋节数Y1、栽深合格率Y2和漏苗率Y3的权重分别为0.35、0.15、0.5。由模糊矩阵（式（7）～（8））与权重分配集P2确定模糊综合评价，评价结果见表6。
表 6 模糊综合评价结果Table 6. Results of fuzzy comprehensive evaluation试验号
Test No.指标隶属度值
Indicator value rij综合评分
Composite score WY1 Y2 Y3 1 0 0.05 0.53 0.58 2 0.13 0.08 0.54 0.75 3 0.29 0.02 0.28 0.59 4 0.16 0.14 0.50 0.80 5 0.26 0.15 0.40 0.81 6 0.03 0.06 0.20 0.28 7 0.30 0.10 0.33 0.72 8 0.02 0 0.11 0.13 9 0.17 0.13 0 0.29 将各因素按综合评分进行极差分析，求得作业速度XV、薯苗基部特征XT、薯苗伸出夹苗刷长度XL等因子在权重P2下的不同水平下的试验结果综合得分总值及各因素对综合得分影响优劣的极差值，分析结果表明（见表7）。影响薯苗栽植指标综合评分的主次因素为：薯苗伸出夹苗刷长度XL、薯苗基部特征XT、作业速度XV，最优工作参数组合为作业速度XV为水平S、薯苗基部特征XT为水平S、薯苗伸出夹苗刷长度XL为水平U时，即作业速度0.5 km/h，薯苗基部形态优，薯苗伸出长度60 mm时，作业漏苗率、株距稳定性及栽深合格率等移栽质量较好。
表 7 模糊综合评价结果极差分析Table 7. Range analysis of fuzzy comprehensive evaluation results水平 Level XV XT XL 1 1.92 2.10 0.38 2 1.89 1.69 0.88 3 1.15 1.17 2.17 极差Range 0.26 0.31 0.60 4.3 扦插结果验证
在最佳参数组合下进行田间验证试验。连续作业1333 m2，随机选取3段60 m长度，如图11所示，测量薯苗扦插深度、膜下薯苗长度、破膜穴口长度、薯苗扦插角和漏苗率。
最终测量结果表明，平均薯苗扦插深度为73.6 mm，膜下薯苗平均长度为205.4 mm，平均穴口长度为76.5 mm，薯苗栽植后与地面平均夹角为53.8°，满足北方膜上船底形插的农艺需求，且与理论设计值相近。同时，扦插株距变异系数为8.9%，栽深合格率为93.7%，漏苗率为3.5%，扦插效果好。
5. 结 论
1）针对北方薯区丘陵山地甘薯膜上机械化移栽这一产业难题，设计了丘陵山地仿形扦插甘薯移栽机，重点研究了薯苗栽植单元、并联传动系统、垄面仿形系统等关键部件参数：以栽深、膜下薯苗长度、扦插夹角、穴口尺寸的最优综合得分为目标，确定各杆长度关系为1:2.0:2.0:2.5:2.75；根据空间配合需求，确定了送苗装置与植苗装置的相对位置和传动参数；根据农艺株距需求和底盘特征，确定传动比为5.2～8.7。
2）对丘陵山地仿形扦插甘薯移栽机薯苗栽植单元进行室内取苗试验，结果表明在40～50 r/min植苗速度下，栽植单元对黄淮海地区常用薯苗品种取苗效果较好，取苗成功率皆在99%以上，满足田间作业需求。
3）以作业速度、薯苗基部形态、薯苗伸出板刷长度为影响因素，薯苗平均埋节数Y1、栽深合格率Y2和漏苗率Y3为指标，进行田间移栽正交试验，结果表明，影响薯苗栽植指标综合评分的主次因素为：薯苗伸出夹苗刷长度 、薯苗基部特征 、作业速度，最优参数组合为作业速度0.5 km/h，薯苗基部形态优，薯苗伸出长度60 mm。验证试验结果表明，最优参数组合下，平均薯苗扦插深度为73.6 mm，膜下薯苗平均长度为205.4 mm，平均穴口长度为76.5 mm，薯苗栽植后与地面平均夹角为53.8°，扦插株距变异系数为8.9%，栽深合格率为93.7%，漏苗率为3.5%，扦插效果良好，满足北方膜上船底形插的农艺需求。
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图 1 农业水土资源利用分区示意图
注：M为广义农业水土匹配系数；U为农业水土资源利用程度。M0为界限值。
Figure 1. Schematic diagram of agricultural water and land resources utilization zoning
Note: M is generalized agricultural water and land resources matching index; U is utilization degree of agricultural water and land resources.M0 is limit value
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图 2 2000—2020年中国农业水土资源基尼曲线及基尼系数
注：图a中y1、y2、y3分别表示累计占比为40%的灌溉水、降水和广义农业水资源所对应的耕地面积累计占比。
Figure 2. Gini Curve and Gini index of China's agricultural water and land resources from 2000 to 2020
Note: In figure a, y1, y2, and y3 respectively represent the cumulative share of cultivated land area corresponding to 40% cumulative share of irrigation water, precipitation, and generalized agricultural water resources.
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图 3 2000—2020年各省份广义农业水土匹配系数
Figure 3. Generalized agricultural water and land matching index in each province from 2000 to 2020
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图 4 2000—2020年广义农业水土匹配系数与降水占比的空间分布及其间关系
注：图a中A和W分别为“土多水少”和“水多土少”；图c中***代表P<0.001，N为拟合的散点数量。
Figure 4. Spatial distribution and relationship between generalized agricultural water and land matching index and share of precipitation from 2000 to 2020
Note: In figure a, A and W are "more land and less water" and "more water and less land", respectively; *** in figure c represents P<0.001, N is the number of fitted scatters.
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图 5 2000—2020年农业水资源利用程度（UW）和垦殖率（UK）
Figure 5. Utilization degree of agricultural water resources (UW ) and reclamation rate (UK) from 2000 to 2020
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