摘要:我国庞大的用电人口导致输电线路极其复杂, 无人机巡检技术的出现, 能综合考虑现有巡检因素,优化输电线路巡检方案,是解决目前实际输电线路巡检高要求与班组承载力不足矛盾的有效方法,但无人机日常巡检依然会耗费大量人力去执行部分机械操作,本文将简单探讨基于遗传算法输电线路的巡检路径规划方法,以此弥补目前无人机巡检中依然存在的大量固定、机械操作。
关键词:遗传算法;输电线路;无人机;巡检路径规划
0、前言
目前,为了满足目前巡检的需要,无人机通过其特殊的巡检方法,在线路巡检中被越来越广泛使用。要使无人机实现自主飞行巡检,必须事先巡检无人机巡检路径并导入导航系统。巡检路径包括作业起飞点、降落点、目标点经纬度、高度、云台信息及相机参数等。现在,一般使用的巡检路径计划的方法是操作员按点计算飞行路径,手动将这些数据输入到无人机的导航系统中。计算要求非常准确,计算错误会带来安全隐患。遗传算法对于无人机提示路径具有优秀的全局搜索功能,能够从路径空间快速检索最适合的无人机提示路径。巡检过程中,机器的工作效率决定巡检效率。在无人机巡检过程中,需要事先规划巡检路径。输电线路无人机巡检方法主要分为手动巡检和自动巡检,手动巡检面临着庞大的工作量,同时输电线路一般存在地理环境恶劣、横穿湖山等自然条件,从而导致无法进行无人机手动巡检。因此,使用无人机自主巡检可以极大的提升巡检效率。
1、输电线路无人机巡检路径
多个对象的路径规划使用遗传算法。由于初始路径是随机生成的,因此初始化过程中会产生更多具有代表性的初始群体,从而提高算法的复杂性和速度。本文使用极坐标对监视对象点进行编码,解决最大路径偏转角、最小步长、最大路径节点数的限制,有效提高无人机巡检的效率和安全性。固定翼无人机进行传输线巡检时,其路径计划受到包括巡检任务和无人机性能参数在内的各种制约的影响。这些限制允许找到安全、适当、有效的传输线无人机巡检。传输线路的无人机巡检路径计划中需要考虑的约束是最大范围、最小步长和最大路径偏移角。路线检测路径规划是找到符合设定空间约束条件的飞行路径。可以使用一系列预设空间的路径节点来计算路径。所有相邻的两个路径节点都通过线段连接。遗传算法是从随机生成的初始群体开始的。初始群体由一定数目的个体组成。在无人机飞行的开始点S和结束点E之间,S和E通过一系列随机的连续折线连接。各个体(染色体)表示选择、交叉、突变的路径作为基本算子。通过选择操作,父代个体(优化路径)以高概率被子代继承。优化后的路径会发生交叉变化。通过交换路径信息来变更巡检路径的基本信息,运用时的巡检路径会更加合适。进化过程结束后,最适合的最大符合值路径将成为无人机飞行路径的最佳解决方案。常规二进制编码由0个字符和1个字符组成。编码、解码和实现相对简单,但搜索路径的灵活性降低,限制了本地搜索最佳路径的功能。极坐标编码方法用于编码巡检路径全体的监视点(节点),构建染色体,建立数学模型。使用无人飞机巡检输电线路的话,工作效率会提高。现在一般使用的无人飞机是四旋翼无人机。四旋翼无人机稍显突出,无负荷时的重量仅为9kg。电池续航约2小时,比其他无人机长。重负荷可以运送20kg,是目前负重最大的无人机类型、,高速巡航速度最快达到60km/h。无人机巡检的高分辨率图像收集装置和无线图像发送装置达成了远程发送和信息收集的目标。
2、无人机巡检路径规划问题描述
2.1飞行姿态
传输线路的状态是静态的,为了有效地巡检线路,无人机的飞行姿势非常重要。可以以正确的飞行姿势顺利地取得图像。妨碍无人机飞行姿势的主要原因是空气流动、风向和操作能力等。想要确保正确的飞行姿势,控制人员需要进行正确的控制,可以应对各种紧急情况和突发情况。
2.2图像预处理和优化技术
为规划输电线路无人机巡检路径的遗传算法主要包括三个遗传运算符:选择算子、交叉算子及变异算子。从路径段种群中选择适当的子路径段,选择不适合突然变异操作的子路径段。交叉算子作用于公共节点的相邻路径段,在节点选择过程中,也可以交换公共节点的路径段信息。无人机巡检技术的核心是,通过搭载在无人机上的图像设备收集传输线的状态,通过传输设备返回控制中心,控制中心进行调查和处理。在整个过程中,收集高品质图像并预处理图像的方法是检验成功的重要因素。图像模糊的原因有各种各样的,如果返回的图像数据模糊的话,有可能会忽略问题。因此,在分析和判断无人机收集的图像信息时,应用合理的图像处理方法非常重要。
3、基于遗传算法的输电线路无人机巡检路径规划
3.1约束条件
城际间的传输线、城际内的传输线、从发电站到变电站的传输线等,因为有很多种类的传输线,所以由于传输线复杂的环境,无人机的巡检路径受到很多因素的影响。很难找到实际巡检的途径。传输线所面临的限制有无人机的航程、最小步长和最大路径偏移角(图1所示)。
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)
3.2目标函数
为寻找最优巡检路线,在巡检路线规划时利用函数原理,在空间中寻找符合约束条件的空间点,将空间点连在起义可找到一条巡检路线。在寻找巡检路线时,用S代表一组巡检路线,用D1,D2,…,Dn-1,E序列点来表示,其中S是起始点,E是终点,D1,D2,…,Dn-1是中间路径节点,如图2所示。
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAm0AAADdCAYAAADpXkXiAAAgAElEQVR4nO2dd3hUZf72M33SCAm9SkdIKGJH7BRXd0FUVFYEdW2Iov4UdhVhEcsCiggWEAQVEJTOUuRFEURBlK4ihE4ghRRSppfkfv/Y63n2OScTigtJTub+XNe50iaZmZOZcz7n+3xLjMfjQU3dfvjhhyp/DNy4cePGjRs3bpG28/WUmPT0dNTUbenSpVX+GLhx48aNGzdu3CJt5+spMajBbN++vaofAiGEEEJIRM7XUyhthBBCCCFVAKVNgdJGCCGEkOoKpU2B0kYIIYSQ6orhpG379u3nvMXExJzX7efOnVvVT48QQgghJCJz5849Pw+q6gd8PsTEGOrhEkIIIYRcMAxlQZQ2QgghhEQrhrIgShshhBBCohVDWRCljRBCCCHRiqEsiNJGCCGEkGjFUBZEaSOEEEJItGIoC6K0EUIIISRaMZQFUdoIIYQQEq0YyoIobYQQQgiJVgxlQZQ2QgghhEQrhrIgShshF5aysjIAQGlpKUKhEEpLSxEIBBAKhRAMBhEIBFBaWorS0lKEw2GEw2F5u1AohEAggHA4jNLSUgSDQYTDYQQCAZSVlWk2Qggh/zuGsiBKGyEXFlWsAoGAFC8hYX6/Hz6fD8FgEEVFRXC5XHC5XPB4PCgpKYHX64XP54Pb7UY4HIbL5YLP50NZWZn8O5Q2Qgi5MBjKgihthFxYysrKUFpaCgBS0kKhENxuNwKBAIqLi7Ft2zYMHz4cTZo0gcVigdlshtVqhdVqRZ06ddCjRw/MmjULJSUlUvxENI4QQsiFw1AWRGkj5MIipE18FMuifr8fGRkZmDp1Klq3bg273Q6r1QqbzSalTf2YkJCAhx9+GOnp6XLJNBwOc3mUEEIuIIayIEobIRcWdXk0HA7LPLZDhw7hySefhMlkgtVqhclkQkxMDEwmE8xms9xExM1sNsNms6FHjx7YuHGjlEAujxJCyIXDUBZEaSPkwqIKmxAtt9uNF198EfHx8VLOYmJiYLVaERMTIzez2SxlTtzObrejS5cuyMrKksuk6lZaWipz3oTQ+Xw+jeBxWZUQQiJjKAuitBFyYRGCJOSttLQUX331Fdq2bQuz2QyLxaKJsonPxdfio4i2Cbl7+OGHEQwGZUGD1+uVX4vP1cpTdSOEEBIZQ1kQpY2QC4sqa+FwGMXFxRg+fDhsNpuMrOllLVKkTYibKFRo27Yttm/fDp/PJ+XM7/fLQgURhfP5fDIKxygbIYScGUNZEKWNkAuLukwZDAZx6NAh9OrVS0bY9JE2vbipeW7i9jExMWjcuDEWLlyI06dPo7i4GMXFxTLCFgqF4Pf7ZQ6d+CgeB3PgCCEkMoayIEobIRcWdXk0HA7j4MGD+NOf/gSHwyGjZmLZM5K46QsT1KibzWZDvXr10LNnTwwePBhTpkzBu+++i6VLl+K7777Dvn37kJOTU64ZbzgcruK9Qggh1RNDWRCljZDzRy9Efr8fwWAQHo8HoVBITjnw+XxIT0/HDTfcAIvFApvNVmF0TS9sNptNSp7D4UB8fDwGDBiAESNG4IorrkDHjh3RqFEjNGnSBPXr10fjxo3Rpk0bdO7cGVdeeSUGDRqEN954A8uWLcMvv/yCY8eO4cSJE5rJDOJxinYiIl9OLO2KViXiZ2Kag5o3pxZcqJ+rkyHON9KnLjGrf1tMh1AnTKiPRb1tKBSC1+uVz0ksGavPVf0dfS4iISQ6MJQFUdoIOX/UE72QAZFrporb0aNH8cgjjyAlJaVcO49IkTZ1WVR8FL9z6aWX4rfffpPNeouLi7F792588803mDZtGkaPHo37778ft956KxwOh6w8tVqtcDqduOSSS9CrVy+MGDECr732GhYvXowNGzbg8OHD5STO6/XC6/VqvqfKmpAl8TzF98SmCtcfESB1/4r7CQQCGoEUAhcMBpGXl4eff/4Za9euxddff41vv/0WX3/9tZw+IWTT7/fLx6Q2LFYfJ6WNkOjCUBZEaSPk/FEjQaq8CcnJzMzE+PHj0aFDBzidTqSlpaFhw4ZwOp1SyCoSNlEtarVaYbfbZeTt73//u6bgQESMRDTM7/cjLy8P+fn5OHToEPbs2YNPPvkEEyZMwK233oprr70Wl156KWrXrg2bzYZatWohJSUFTZs2xSWXXIK//OUveO6557B8+XJ8//332LdvHw4ePKiJSqkFEGpEUTwGdbZqpKjb+exffRRM3G84HIbb7UZeXh6+//573H///WjatCnq1KmD5ORkpKSkoHbt2khJSUGHDh3w1FNP4eeff5YyLfaffparKm+UNkKiB0NZEKWNkPNHPcmry3bBYBC7d+/GzTffjPj4eMTGxmLixIn49ddfMX/+fDRo0EBTISqKDNTNYrHA6XTKpVGLxYKbb74ZmZmZUpyEeAiJE49BPA7xuaguDYfDyM3NxY4dO7BixQrMmjULL7zwAvr27YsePXrIKlWHwwGHw4HExERceuml6NGjB5588kmMHDkSn3zyCXbs2AGXyyXvX0S/1MeiRt/+l1mp6j5Wo38+nw+nTp3Cyy+/jCZNmkjBVfeXzWaTy8sWiwVt2rTB22+/relrpz62SPJGCIkODGVBlDZCzh+1ea5Yajty5AgmT56M2NhY1KpVC/fffz82btyoEZgxY8agTp06MqKmVpKqrUBMJhOcTicSEhJw33334ejRo3IJVjTOFXIkHouasyXEThVLMaReiJbH45Gi5Xa7cfz4cSxZsgSjRo3CkCFD0KNHD6SlpaFWrVoaEXI6nWjWrBn69OmD559/Hp9//jlWrFiBnTt34sCBAwgEAnC73f9T1EovbKqQHj9+HHfccYdc/hWiJj6K5WeTyYTExES5xOxwODBs2DAUFBRo9lWkKBuljZDowVAWRGkj5L8Spl+SE0t9ak6XiGyJfmjFxcX49ttv0atXL8TFxaFjx46YN28esrOzNc1uw+EwPB4Pli1bhr59+yIuLk6Km9p012QyITY2Fs2aNcM//vEPnDx5En6/X5M4X9FynjrvVB89Ej/Xj8OKlPRfWlqKzMxM7N+/H5s2bcKqVavw0ksvYciQIejatSsaN26MWrVqISEhAQ6HAwkJCWjXrh26deuG3r174+mnn8b06dOxdu1a5OTkoKioCC6XS8qkEDARoROPQc09E3KqjgLzeDzo16+flLVI/e0iLTuLr+vUqYOPPvoIbrdbiptazBDts10jvR7EPhHvAfV1o+YE6gtTzlTwEa37l1RPDGVBlDZCtCerYDAohUycYLxeL8rKymROlRCOXbt2YdiwYTL/rGfPnjhw4IBcOlSjReoSYn5+PpYtW4aHH34YN954I6677jrceOON6N69OwYMGIBJkybh119/lf3XRBXk/7Lc+Ef3iVo5KpZcfT4f1q1bh+XLl+P111/H//3f/6F3797o2LEjUlJS4HQ6ZdVrbGwsbrjhBtx55514+eWX8fbbb2P9+vXYvHkzjhw5opE48RxdLpfcZ+o+37x5s6ysFbl+ai7g2Taz2YxLL70UO3bskJFH8X8NhUIAUOGyaTRsesES0Vr14kXImPhcXFCIvErxOhHvkVAoBI/HoxE5ShupThjKgihthJRv4SFOWOLEo+aHeTweHDx4EB999BG6dOmClJQUXH/99Zg2bRoyMjLg8/lkUr5+nJSafyaWEbOyspCRkYGcnBwcP34cBQUFUhpFewv9bNHKOOmp9yUiZOqJWHwufpadnY2jR49i9+7d2LVrF8aOHYunn34aPXr0QMeOHdG6dWs0btwY9evXR8uWLdGkSRN06NABXbt2xZNPPokpU6Zg06ZN2LVrFw4fPoxjx47h0KFDOH36tLyPN998UzPiS+SsnamNihp5ExW848eP10SB9FWk0bxFiqSprVaEnJ0+fRo5OTlIT0/H4cOHcfDgQWRlZaGgoADBYBDFxcWyaER9L1TW65eQc8VQFkRpI6T86Cl9XzDx+alTp/Diiy+iW7duMJlM6NevH+bNm4fCwkJNxEEVAfVvqUtNaosMEU1Sc9PUSQcej6fc37jYqBEX8ZgDgQC8Xq+malXNnwsEAjJKVlpaCo/HA5/Ph5ycHBw4cAA//PADli5dio8//hhvv/02Ro4cif79+6NDhw5yzFdSUhJat26Nyy+/HH/+85/Rv39/jBw5EhMmTECfPn1gt9ths9nK5QCeSdjUwg+73Y7HHntM04/uTLlt0bqpFxplZWXyQmLv3r2YOHEiBg4ciFtuuQXt2rVDamoqUlNTcfPNN+Oee+7BpEmTkJ2dLdutqMv7jLSR6oahLIjSRgg0UQAxjF0IlIgqTJo0Ca1atYLNZsNll12GmTNnIjMzU0Ye1OiYiLQJeVEjOeLvis+FsIn7VgVI5MGJ5VH1pFrZ+0U8Br/fD7fbremZJiRTfa76ZU9VksR+DQQCKCwsRH5+PjIyMrB69Wq8//77GDx4MG6//XZ07twZbdu2RWJiImw2GxwOh6wUVQsOzhZpUwXObrejf//++PXXX7Fv3z6kp6fj999/R3p6Og4cOID9+/cjPT2dm7Lt3bsX+/btw7x583DVVVdp+g3q5+XGx8cjLi4OPXv2xJo1a1BUVKSJMDOnjVQ3DGVBlDYSTegjCaLZakWJ/iKi9Mwzz6BevXqIi4vDY489hm3btpVb7hQipgpapH5g+k19bOr9qxGJin6nsveZ+rj0ien6Brxqjlik34+0JKd//ocPH8bOnTuxcuVKzJ07F1dffbVsk3ImWRN5b+qSqLi91WpFrVq10KlTJ3Tu3BldunRBWloa0tLS0KlTJ/m5iB5F06buA7FvOnfujNTUVFx22WVISUmRy9FnahAtlq0vueQSfPrpp3C5XOUKec70XiCkMjGUBVHaSDQhZED06lJFQb9UWVBQgJkzZ6JNmzZwOp3485//jJUrV8LlcsHlcslmrfrkbZ58LgxqLqCI1s2YMUPOYNXPaFUbFqv92pxOp6aXW0pKCtq1a4fLL78cXbp0Qbdu3dC1a1dcdtll6NKlS9RvYl907doVV155Ja677jrUr19fLi+rOYSRpFnsf7G/bTYb1q5dq6nSFe/D/6UBMyEXCkNZEKWNRAv6iI5aZKA2ifX7/Vi5ciUGDBiAunXrolGjRhg8eDBEpaOa1yV+h930LyxqTpUQ7GAwiGPHjiElJUWO51LlQb+JClYhDhaLBYmJiXj44Yexfft2HDx4EIcOHcLBgwdx+PBhHDp0CIcPH4767ciRIzh06JDcN//+979x+eWXayRZjVzqxU2VZrPZjJSUFHTt2hWnTp3SRGEryh8kpLIxlAVR2ki0oC55CuEqLi6WQhAKhbBz5068/PLLSEhIQHx8PHr16oUffvhBJtiL5R0150x85InnwiH2o5oTWFhYiGAwiGXLlqFOnToaYYj0UUTjxHKd3W5H165dsX37ds3/TZ2vqlaURvsmXuczZ86U+Wt2u/2M0zz0kTbxP4iPj8f7778vixoCgYAmv1P9nxNS2RjKgihtJJoQIqDOyvR4PMjLy8Nrr72Gyy+/HHa7HV26dMHrr7+OU6dOoaSkRPZuC4fDMiFfRN3UyQM86VwY1GXsUCgEt9st97XX68XcuXPRoUMHGflRBUIvbgkJCUhKSsKtt96K7777rtx8VCFu+py6aN3U5f6srCw89thjsgBE5ApardazLo+KSFtcXBysVisGDBigmUIhqqQZpSZVjaEsiNJGajr6vDU1GT4cDmPHjh0YNGgQrFYrkpOT8cgjj+Cnn37SnMD0URh9bg5POhcHdf+qRR2lpaX4+eef8dRTT6Fhw4YVjgIzm81o3749/vWvf+HQoUOywjeSoPB/+B/U13dOTg7uvPNOKccOh0NGzyqaPCEimyKnTWx9+/bVTKAQ1cPMaSNVjaEsiNJGahpqkrM4Sag5a+LE/c033+DZZ59Fu3bt0LZtW4wbNw67du1CSUkJc2+qKapoiaXq3Nxc/Pzzz5g+fTrGjh2LN998E+PGjcPHH3+M3bt3o6ioSDMuS+13R7QIORainJ+fj6eeekrTZkWtHo00iUJE2MRtxFi2oUOHatrE6Cu1+b4iVYWhLIjSRmoa+uhMaWmpbE4bDAZx6NAhTJw4EY0aNYLT6cS1116LDRs2lGu2qs9V059oSOUj9r1aeahOsBDfF5XA6igxdcSS+H8SLep7RqQELFq0CA0bNpQRM1GJG0nW9JWjIuqWnJyMefPmyQIe9SKKy6OkqjGUBVHaSE1Df/Uuqg/dbjemTZuGa665BhaLBW3atMGECRNQUFCgyVETy6gVdcknVYdeoPUTJLxer6wAVudeikITdboFI23l0b/e/X4/jh8/jr59+8qIWaRZr+qYMDGxwmKxwOFwwGKxoGfPnigrK9OMZFObT/P9RaoSQ1kQpY3UNNQTgJh9uGHDBvz1r39FUlIS6tevj1tvvRW7du3C6dOnNZ3axYleRBzEST5S7hOpfNTcNvH/Uf83QuL0S6hCwlVJYKStPKoQi/dDIBDA5s2bkZqaCqvVCrvdrumJp35UJ1WI21osFrz22mtyeoj6v4jUZJeQysZQFkRpI9WdMx3IxUFfXfZSo2QnT57Eyy+/jBYtWsDhcOCmm27CqlWr4PF4yuXXiMhLRcnpPKlUD/T/B/G/i1QFqd5WvR0T3yOj33fqBc3SpUvRrl07jbDp266I5VAxjSIlJQVJSUlwOp247LLL8NZbbyEvL09TkCDuTx9140USqSwMZUGUNlLdEQdscSAXV+lqfy2xtFlSUgKv1wuXy4WdO3eia9eusNlsaNWqFd544w3k5+drThbihEQI+Q968RVNqEOhENavX497770XiYmJmjw2IWoOhwN2ux21atXC008/jS1btmDJkiXo2bMnmjVrhqSkJDRr1gwvv/wydu7cCa/Xq2lyLd6Poq2OWulLyMXCUBZEaSPVHfWArZ5Q9HM/RY5MXl4exo8fj9atWyMpKQkPPvggtm3bpplmoM7J5EmBkP+iCpt6cSTyBI8fP45FixbhpZdewpVXXiknTyQlJaFbt24YNWoUli5disLCQk3F9qZNmzB48GAkJibCbrejWbNm+Mc//oHc3Fz53hVL2SLaDQCBQKCK9wip6RjKgihtpLoTKdKmJjEHAgEEAgEUFBRg3rx5aNOmDRwOB+rWrYuFCxfKZdBgMAiXywWfzyev5NWlUEKI9sJIXSIV+YNqHqHX64Xf75fpBuK9Fg6H5aQRn88nK3c9Hg8OHDiAkSNH4uqrr0ZiYiJiY2MxYcIE7NixA263W1Z78/1JKgtDWRCljVR3VGnTJ0oHg0GcOHECK1aswH333Yc6deqgU6dOeOWVV/DNN99oqgtF1EBNhlajbYREO2rUWX+RpL9Y0o/8UqNxapGImCQi3ot+vx9erxcHDhzAlClT0KNHD9SpUwcdO3bEnXfeiU8++QTZ2dnw+/2UNlIpGMqCKG2kOnCmpH+1D5d68giHw1iwYAGuvPJK2Gw2tGnTBiNGjMDJkyc1sw1LS0vlCUDt26X2cyOEaNHnfOqLE/S9C8VtxNeq3KkpDADk+1H8/R9//BFDhw5Fw4YNYTab0bRpUwwdOhSrVq0ql8qg3o94bCwuIf8LhrIgShupDuhPAGrPNHGlLq7g/X4/du7ciQceeADJyclITk7GwIEDsXLlSnlbdR6ogAUHhFQP1FxS8d4uKCjAnj178Oqrr6JNmzaIi4tD3bp18eSTT2LHjh0oLi6WkTtx0RYIBFBcXKwpLlKrUAk5FwxlQZQ2Uh2IlEcjBE1cqYu8mNWrV6Nz586wWCzo0KED5s2bJ0dPqVVo+oM2D+KEVA/UPnDBYFDmxYkcuZMnT2LixIno0aMHHA4HGjVqhEGDBuHnn3+G3++XjX9FPquacyf+Pt/v5FwxlAVR2kh1QJ+vJirOxFW12+3G/v370b9/f9StWxctW7bEyJEjcfz4cY3cqS0CKG2EVE/UBsdqzqmaD+fz+ZCTk4Mvv/wSaWlpcDqdSE5Oxr333ouFCxfi6NGjshI8EAjI2bIcNUfOF0NZEKWNVAf0DTXF+KFwOCxbeKSmpiIuLg5t2rTBunXr4PV65W30HfArGvROCKl69I2OxWgrt9stK05FlXcwGER6ejpmzpyJ7t27w2azoVatWujRowcWL16sicbrp5cQci4YyoIobeR80EfDAGgOlGpV5549e7B7927s2rULv/32m0xCVq+y1Sa36sdQKIT8/HwsWrQInTp1gs1mQ7NmzfDiiy/KvyHy1kRSs340Ea+6Came6CdViAstQJvvJt7D6uir2bNn44477kC9evVgMpnQtGlTjB07Fr///rvmOBCpoEn/M7WQgceI6MVQFkRpI2cj0oFOHbAuBnIXFhbi559/xpgxY/CnP/0Jbdu2Rfv27dGqVSu0b98eDzzwAN577z0cPnwYhYWFcllTrQoVB+bt27fj0UcfRd26dREXF4c+ffrg//2//6dpH8CDLCHRQVlZmaZPXG5uLr766ivce++9SElJQe3atZGWloY333wT2dnZMmJXUlIiI3ci31WkUIhJDKwiJ4ayIEobORf0RQJqCw6Px4Pt27fj8ccfR8uWLRETE4PY2Fg5NNpms8ku6FarFc2bN8cLL7yAvXv3yoHuotAgMzMTEydORNOmTZGQkIAbbrgBc+bM0fR9Ynk/IdFFpEIlsay6efNmjBkzBr169YLT6URaWhrGjx+P1atXIycnR8qa2mRbPzaLkbboxlAWRGkjZ0OVJHWwczAYhNfrxezZs9GhQwdYrVZYLBZYLBY52kbMJrTZbJrZhDabDampqfj000/hdruRmZmJd999F1dccQXq1KmDe++9F5s2bUJOTo6mMoxDpAmJPvRRfrVSXETs8/Ly8OWXX+L2229H48aN0bBhQ3Tq1AkTJ07E/v37ZeNfVdr0y7AkOjGUBVHayLkQ6So3FArh999/R/fu3eFwOKScCXmLiYmR4iY2m80Gk8kkb9uyZUtMmzYNPXv2RGJiIurUqYOPPvoI+fn5sjJMbD6fTzNEmhASPejzacVkBf20hpKSEnz77bcYOHAgLBYLzGYz2rdvj2effRZbtmzRtBZRc2lJ9GIoC6K0kXNBf0UqckJmzJiBuLg4KWcxMTFSyoS8mc1mmEwmGXUzmUxwOp1S6mJjY5GYmIg77rgDW7Zs0eSsqeOm9Hl1FDdidNTXcKT3mHgPREqwjxQpEn+vpkWi9ReN+uInEf0Xn4fDYXi9XuzevRvPP/88mjdvDovFgoYNG2L48OH4/vvv5X4Vfd70kx7OFtGvafs4mjGUBVHayLminhxCoRAKCwtx9dVXSymLiYk56yZkLiYmBlarFXa7HXa7HePHj0dWVpZMGNZLGiE1DfU1Hg6H8csvv2DhwoVYsGAB5s+fjwULFuDzzz/HokWLsHTpUsybNw8//fQTXC4XCgsLZWNZcQEVSThqOvpcN/2orXA4jIKCApn31q5dO9jtdrRq1QpvvfUWjh49Co/HIyN0ot+bEDpxLBIiWJPFOJoxlAVR2sjZiHRgDAaDyMnJ0UTThJSdq7yJjxaLBQsWLJAFCWq+Cau6SE1F/346fPgwli5dihEjRqBevXpITEzEiBEjsGTJEixZsgTLly/HBx98gF69euGvf/0rtmzZIquv1QsdNQJX09Hn2+ovLNVpCR6PB4WFhZg6dSq6dOmC2rVro1atWrjrrrvwxRdfaKL6oiJeFDBEEuFo2cfRgKEsiNJGzoZe2sSSTU5OjlwWFdJ2Ppv6u7Nnz5al+epJh8ugpKZSVlYm8zPVvM3XX38ddrsdLVq0QE5OjpwKIhpJ5+TkYPTo0bjqqqukuKm9zPTv1ZpMRUvK+sIFdRnU4/HgwIEDePPNN9G9e3fExsaiTp06uPvuu7F8+XJkZWWVG6HHSFvNxlAWRGkj54o+MpCbm4uGDRvK5VGxnWukTWxmsxkrV64sVyHKKBupyegrsn0+H06ePIkBAwbAbDbjvvvug8fjkbIh5M3r9eLUqVNwOp14/PHHkZubK8VNbXodDVKhPkf98UmVLDUPTvRnEzNOZ86cidtvvx1msxl2ux2dOnXCrFmzkJ+fr6k01UfbomH/RguGsiBKGzkX9MsQ4or1iSeegNVq1UTahLiJ3DURVVOlTv26SZMmsgpMDI/WJ1sTUtNQK7GFbG3evBnNmjWDxWLBunXr5M9E1EdUTLpcLvTr1w+JiYlYvHixplF1NLXFUZ+jesEX6XO1ka44hokoWmFhIdatW4e+ffuiffv2qF+/Pnr06IGPPvoI6enpcLlcmkKFP7KR6ouhLIjSRs4FfZKvOOj98MMPaNWqFeLi4jSVomazGU6nUzbXFWInKkhFpanFYsGnn34qTzhqtC2acnNI9KGPtLndbvzzn/+ExWJBkyZNUFBQoIkMqQ2t8/LykJqaCovFgkcffRSnT5+WbS/0BQlES6QlVCFvHo8He/fuxezZs9GlSxeYzWakpaXhsccew5w5c1BQUCDFWG0MLtoRqceuSHNQ+f+onhjKgiht5GxUVKHl9/vhcrnw6quvolatWjCbzbDZbFLORENdk8mEhIQEOJ1O+bXFYkGdOnUwceJEFBQUyAo4MSiaV6mkpqNGkktLS1FUVITevXvDZDLh3nvvRW5urkbC1IT4nJwc+T4aNGiQHNsUKa+LaKnoeCZkS8hxdnY2Pv/8c9x1112wWq1wOp1o0aIFpk+fjgMHDsjop8vlkk179dFT/f+B/4/qiaEsiNJGzob+IKd2Ii8tLUVWVhaGDx+O2rVry2pSIW8i4qZOSrBarWjcuDEmTZqEU6dOaWaPikIEsZTBEw+pyagn+JMnT8LpdMLpdOLVV1+VkTZR/agKxeLFi+X768EHH5SzfMV7kpG2itFLlNoeRH9sC4fDOH36ND777DPcfPPNSEpKgsPhQNeuXfHaa6/h+PHjCAQC5YoWIs1q5rGs+k9QhiYAACAASURBVGIoC6K0kXNFrRwVV/9iObO4uBhbt27FAw88gGbNmsklUYfDAYvFgtjYWFitVrRq1QpDhgzBgQMH5LKP6I2kj7TplxYIqWmIE7zP58NHH30kJ4UsWbKk3Kgldej5s88+C6vVCqvVig8//FDmgkZb9egfQS9t6rKm2I/ieCQiaOJnP/74IwYOHIimTZvCbDajRYsWGDt2LNLT0zVirYqb/r5J9cNQFkRpI2dDfxLQJ08HAgF4vV6UlpbC7XZj586d6NWrF6xWK1JSUtChQwe88MILeOedd5Ceng6v1yujB+Igqc9jUw+kZzrQ6Su5zjUhmInDpDI422tOzQ+98cYbYbFYcOWVV2Lnzp0akVCX7vLy8tCpUyfYbDY0b94cGzdu1Ix7q2hZjgnz/0G/NKrvC6nmuImLUrXfW35+Pn788UeMGTMGl112GeLj43HFFVdg/Pjx2Llzp2zNUtFQ+or+L5FuEy3/k6rGUBZEaSPngv7AouZviLJ4kUy9fPlyNGrUCHXr1sXEiRNlsm4wGLygj0lfISYGQqsl+uJ7IidIiKK6DKIuaVR00iPkj6C+hvSJ6qo0/P7772jVqhViYmLwyCOPIC8vT9N/TV0mff/992UqwkMPPSRTDERkSC8g6n2KaJ1aaaoKIV/vkdGLtpC5jIwMDB8+HJdccgksFgsaNWqEoUOHYtOmTbJBr/gfq58LmRMXu+J/ItJP1PSQ0lIOsr/YGMqCKG3kbOhzM/RLAOIgFAgE8Ntvv+GWW26B3W7Hiy++CJfLJQXvQg96Vx+XOAnpWyOIz4W8iROTuvQhHp/f79cszVLayP/KmZbi1FSDDz/8EMnJyUhMTMSkSZPg9Xo1/dlCoRC8Xi+OHj2Kv/zlL7DZbLjkkkvw5ZdfysrFM0V19O8TNa1Bn4dFyiPEST3+ieOKy+XCnj178N577+G6666D1WpF3bp1cfvtt2PZsmU4duyYHFAvLho9Ho/suyfGkYmInn7lgVx8DGVBlDZyNvQnHrVJpYgEBAIB5OTk4K677oLJZEL79u2Rm5srTz5C7C7041KjFuqgaBH1E49PRPrUk5aamyfkTY1UiAMnIX8U9QJAfK1GasrKylBcXIy7775b5nx+9dVXmgsKtVDns88+Q506deBwOPDQQw+hoKBAE7nRDz7XX2yJOZvi7zOqc27oo6XieCOES1wg/vLLL5g6dSquuOIKmcvbp08ffPHFF1i+fDn27t0rj0niOCUEUC/0/H9UHoayIEobORv6q3X1pCAO/rm5uXj00UfhdDpx/fXXIz09XdO7SM0VuZCoj8Pn88l8kmAwiGXLlmH27NmYPXs25syZg88++wwLFizA3LlzMW/ePMybNw8bN27EsWPHZDSDfa7IhSRStEtd0g+FQli5ciVatmwJq9WKBx54QF5YlJSUyAuMsrIyfPjhh2jTpg0uueQSvPXWW/L1LiJykXLa9J+L1/iRI0ewaNEijB49WgqkeI+S8uj/j/plaFWyA4EAfv31VwwcOBAJCQmyol5sdrsdrVu3Rp8+ffDee+/h6NGjmrw5VgBXPoayIEobORuRTjqiNYcoPnjzzTcRHx+Pzp07Y9WqVZqGoGp07mI9LhG9EFswGMSmTZswe/ZspKamwmq1onnz5li7di3Wrl2LNWvWYNWqVXjjjTdwzz334IsvvtAsobJylVwIKio+EFGavLw8vP3227Db7UhOTsaECRNQVFSEoqIiFBQUoKCgACdPnsT48ePRtGlT9OvXD+vXr5dV1kIUxElfjeBFkjZxwZWdnY13330XDRo0YEuKc0B//FP3pdjE/p81axYuvfRSxMbGwm63yypf0VhctGoRLZB69+6N1atXa6bCMK+2cjGUBVHayNlQD/4iiiXEyOfz4ZNPPkGLFi1Qt25dLFy4UB7ELvYA64oqrdTHumHDBjgcDjgcDjzxxBPlZgmGQiFs27YNrVu3xttvv438/PyLFhUk0Ye6xCXeE0KwfvnlF4wdOxa33XYbunfvjptuuglDhgzBuHHj8Oqrr2LUqFF47rnn8NRTT2HkyJHYvHmzjOioy/tqqxxVJtRlVZFHJb4Oh8NYuXIlmjVrRkE4ByqKmOor6d999105BUadAKOO+VNH/YlRfvXr18eSJUs0DZRZHFJ5GMqCKG3kbKgRAn1u2L59+9C7d284HA4899xzKCkpkQcefb7MxZQ2/dVvKBRCUVER3nnnHdhsNsTFxWH58uWy2EA8xkAgAJfLhe7du6NRo0b48MMP4fV6uTRBLgiRomziPeRyuZCVlSW3zMxMZGZm4tSpU8jOzkZWVhZOnjyJ4uJiFBUVlRMyNSH+9OnTGD9+PP7v//4Pc+fOxTvvvINXXnlFVm6L173awFpI28V6f9YkzrTELY4nc+fORdOmTREbGyuFLTY2VgqaKmv6mcwWiwWtW7fGgQMHNCsUoVCoqp96VGAoC6K0kbMhTjZqXowoMPjss8/gcDjQv39/nDp1SnNiEAeciy1A6tKPGkUrLi7Ggw8+CLvdjq5duyInJ6dcArY4+Y0aNQqxsbH4y1/+guPHj/MkRi4I+oIW0dpBVDmL11+kVAJ1EoL6mhVLq/o8qjlz5uDRRx9Fbm4uvvzySwwZMgSFhYV46623MHz4cLz//vvIzMyU7801a9agefPmjLSdA+p+0VfQl5WVYf/+/ejZsycSEhKkrKlCpkbWhLCpc5hjY2MRHx+PSZMmsUFyFWAoC6K0kbOhX3IsK/tPe4wNGzYgMTER3bp1w/bt2zVLMfo+aBfrABSpSELcp8fjQYcOHWCz2fD888/D7XbLn4lZjaJw4YUXXoDFYpEROUbayIVA//pUlzVVWVNbP+j7q6kFBuoUEXFbt9uNvLw8PPfcc1i9ejVCoRCefvppTJ06FXl5eZg1axY++eQTrFixArm5uVwe/QNU1EZFHAsXL16M+Ph4KWJiGozNZpPfqyjiZrFYZGSub9++mqgs/yeVg6EsiNJGVCo6MOmLEE6ePIkuXbqgbt26mDZtmpQgsYlIgj7J+WItjwLaK+BgMIji4mJ5MFywYIH8uThpqtGOrl27yoPokiVLNAdNQv4okZZH9blQajW2uOBRhU18VCNvop+XqCxNT0/HwIEDkZ6ejlAohKuvvhpz587F1q1by/UeFK/5FStWoHnz5vJvnum9H+3o94X+/7lgwQIZWROi5nQ6pcCp0qaXN/E7VqsVvXv3Llc5yv1/8TGUBVHaiIo4UKh5a+o4l1AohIyMDDz55JNITEzEwIEDkZ+fL5cJKrO3WUUnGHESfOutt2Cz2XDjjTfit99+03QlV/vMZWdnIy0tTVZ5LVmyhFe5pNqhf42rS/wlJSXYsmWL/N6KFSuwZ88e+RpXo9ClpaU4duwYFi9ejOXLl+Orr75CZmamZsqJKpZ8D5xZ2srKyjB//nxYLBbExMTAZrNp5EzIXKRImyhasFgssNlsuO222zQSz/1fORjKgihtREXIl7gaF00jRTl6ZmYmhg0bhsTERFx++eXYunWrZlB1ZbfKiJQcHAqFUFJSgjvvvBMOhwNDhw5FcXFxuaUnEb3YtGkT2rVrB6vVijZt2uDbb79lpI1UOyJFvtVqbnWgvJpzpV+O1fd0U8crRUpnYMTtzMujpaWlWLx4MRITE2U7D7FVJG1C3CwWi4zEWa1W3HHHHRGb7JKLi6EsiNJGVFQBEicFIWyhUAijR4+GxWJB06ZN8cMPP2iSoqsypC/uW5x4Nm/ejBYtWqBx48aYP3++pgGmOFmJvLe33noLtWvXhtlsxsCBA5GTk8MTFal2REpVEJ+rhQqiolSVNf3FimjXI5ZX1dsILmZqg9FQn7u+EKG0tBQHDx7EbbfdBrPZLHuy6WVNL20xMTGw2+3ydxwOB8aMGaP5v1bWqkW0YygLorQRgXqgEFfwoho0FAphwYIFiI+PR4MGDfDJJ5+goKBAcyKoCmlTIw5qNGH8+PGIj4/HFVdcgSNHjshogtoqIRAIoKioCIMGDZIiOn/+/HI5JYRUByItz6nCJXLXxEWU+p5UlzrFz0QzaX1Daf1UBf19RyMVCbPaAumDDz5A06ZNpaiJ5dKKpE1Inci7bd68OY4cOSKPYeK+yMXHUBZEaSMC/bKL1+uVn2/btg2pqalITEzESy+9BJfLVe5AX1URNjXKFgwGkZ+fj0GDBsFms6F///6ayJoacSsrK8OSJUvQsGFDWCwW3HXXXcjNza30JV5CzgV90Y0qDuprWwiZEDR90YP6uSpxkaJyQhoobZGLslTJPXXqFJ577jnY7fazSpsQOxFls1qtmDlzZjnBjvb9XlkYyoIobUSgPyiJDuu///47brvtNthsNvTt2xdHjx6VzWmrMmlZfwAV0YbvvvsO7dq1g9PpxOuvv16uH5aIROTl5ckoW/fu3WXlndpaQc19ixSBIKSyqCjSVtH3z+V3zvT7fJ1rqWi/qceMrKwsjBw5Eg0aNIDdbpc5a2LuqDoZwWKxwOFwIDU1FVOmTNG0JKK0VS6GsiBKGxHoo1ZerxfFxcUYN24cEhIS0LFjRxw+fFhG1c7WKqAyH7M42Hm9XkyfPh12ux2xsbFYtWqVXBYVy73i46JFi5CUlIS0tDRs3bpVs9Th8Xhw4sQJrFixArNnz8bJkycpbYQQDWrETRSEFBUVYdWqVRg4cCBSUlLkVAQ1383hcCApKQkvvvgifvrpJ7hcLtnGRZU25rVVDoayIEobEYilFiFloVAI06ZNg9PpRHJyMpYtW1auXYagKpKWIy1TZGRk4M4774TZbIbD4UBOTo48GIrb5OfnY/LkyYiPj8dtt92GTZs2IRAIwOv1yjyfU6dO4eGHH8bQoUPx0EMPoUWLFti0aROvfgkhEjXSplbxlpX9p23SwYMHMWPGDAwbNgxPPfUUhg4dihEjRuDzzz9HXl4evF5vuVnI+gpecvExlAVR2ohAzWcLBAI4ePAgGjdujISEBLz55ptwuVzlkpb1oXzxdypL2lTRXL9+PcaOHYu2bduiQYMGqF+/PmbNmoXZs2dj5syZmDVrFsaMGYMBAwbg7rvvxvz583Hw4EHN2C1ReLFmzRocO3ZM9sB67LHHMGfOHHmQ5sGUEKKuTqhFIGJihWibJBohCyHTV7Gr1b9cHq18DGVBlDaiIhKRi4uL8cwzz6BWrVoYNmwYTp8+LQsT1EadVZ20rD6erVu3YsuWLfj666/x3XffYd26ddi4cSO++eYbfP3111i/fj02b96M/Px8TdNgsSSqznZUCxtKS0vx6KOPYseOHVweJYRIVGHTL5UKGVMjaKLFiv4Yqr8dUzEqF0NZEKUt+tAfYNTN6/XC7XZj1KhRcDgcePzxx1FSUiKjb+oBpzokLav3fbZRPGfb1AOuWLZwuVwYNWoUNm3aVK49AiEkujlbYYc+YvZHN3JxMZQFUdqiD33Zv9o8NxAI4IsvvkCTJk1Qv3597Nu3T9POQ60QrUniIqQvHA7D5XIhHA4jNzcXn376KWbPng2Px4P8/HyNIBJCCDE+hrIgSlv0ofZ3UsvVfT4ftm7dihYtWqBWrVr44IMP4PF4NHlu+khbTUEtZgiFQti9ezcGDx6MtLQ03HXXXRg8eDA+/PBDzbguQgghxsdQFkRpiz5UaSstLYXH45E9hm644QbYbDbcd999OHbsmOzVpjanVXM4agpqk8xwOIysrCysXLkSK1euxJo1a7BixQocOXKkRj53QgiJZgxlQZS26ENtiCuKC4qKivDMM88gPj4e3bp1w08//ST7makyU1NzLfTSplaDiSijmp9CaSOEkJqBoSyI0laz0Sfaq6XlonLJ7Xbj008/RZMmTdCgQQP8+OOP5SYeRGrpUZOkTRUx/T7T5/LVpOdNCCHRjqEsiNJWc9FXVopImSg8EHlsq1evRosWLeB0OvHSSy+VG01FCCGE1FQMZUGUtpqLXtrEiBTRf8zn8+HYsWPo1KkTkpOTMXToUOTk5NTYvDVCCCFEj6EsiNJWc1GX9dTCA5/Ph0AggP379+POO++E1WrFgAEDkJ2drWn0yPYWhBBCajqGsiBKW81En5clImyBQAAejwfZ2dkYMmQI7HY7evTogePHj8vpAGq1KPO3CCGE1GQMZUGUtpqJXtqEsPl8PrjdbkyYMAHJyclISEjAv//973LDirk8SgghJBowlAVR2mom6limsrIy+P1+2b5j48aNqFOnDho2bIhp06bJOXn6th5AzZp6QAghhOgxlAVR2mom+skFQsry8/Nx9913w+FwYOjQocjLy9P0IVOXRxlpI4QQUtMxlAVR2mom+h5jYrLB7NmzUatWLdx0002auaLqGCc2kSWEEBItGMqCKG01F1W8/H4/NmzYgNTUVHTs2BH79++XvdtEkUJZWZlmODyljRBCSE3HUBZEaTM++ipR/RYKhfDbb7/hhhtugNlsxogRI+B2uzVFB/rO/zVx6gEhhPwRKqrGFxe64ms1HUWkmoifqVNmIl0c81hbdRjKgihtNQO1SlQscfp8Pni9Xhw7dgx33HEHLBYLHn74YRQWFiIcDsPlcslcNh40CCEkMupFrWhUHgqF5MWvy+WSohYMBuXcYnFMFt93uVyyybmYa0xpq3oMZUGUNuOj5qSJq7jS0lIEAgHk5+fj8ccfl/3YfvnlF/h8Pk01qfhdLoUSQkh51KiY3+9HMBiE3++H1+uF2+3Gb7/9hn379mH//v1IT0/Hvn37kJ6ejv379+PAgQP4/fff8euvvyI9PR179+7F4cOH4XK5yuURk6rBUBZEaTM++oHw6lzRN954AwkJCWjbti2++eYbBAIBeL1e+P1+Ga5npI0QQipG30LJ4/EgFArB5/OhoKAAr7/+Oh588EHUq1cPVqsVl19+OV577TWMGzcOY8eOxauvvophw4bh0ksvhclkwrXXXosDBw7I5VUef6sWQ1kQpc3Y6PMixBWgx+PBggUL5CD4t99+G263W14l6qNsIseCEEKIFnUJU1wYB4NBTT7bSy+9hNjYWCQlJWHKlCkIBAKan3s8HuzZswdXXHEFnn32WRQWFspjN4+/VYuhLIjSVv1QRSwYDMrvC8lS23Soia8idyIcDuPXX39Fhw4dYDab8eSTT5YrNNB/JIQQEhn1WBkOh+H1emVxQSAQQEZGBvr27Qun04lWrVrhxx9/lFInjtc+nw+nTp1C37598d577/EYXI0wlAVR2qoXahheJKp6vV54vV4ZHVOTWEXyqzqC6tSpU+jfvz+sVituvfVWZGZmlqsSJYQQcm6olfTiOCu2QCCAjRs3om3btrDb7bjjjjvg8Xg0S6jieF1QUIAZM2Zg8+bNrNSvRhjKgiht1Qf1zSsOBsXFxXJuqKhYKigoQHZ2NlatWoXp06fjgw8+wOLFi3Hq1CkUFhbin//8J5KSktCtWzesXLkSfr+/XDsPQggh50aklh8+n0+mo8yaNQt2ux1OpxMTJkyQohYIBLB//35s27YNwWAQXq8XeXl58Hg8EVsskarBUBZEaas+RLqaE/lnwWAQWVlZmDx5Mm666SbEx8fDZDLBbrfDbDbDbDYjMTER3bp1Q0pKCho0aICFCxfC6/Vqig0YaSOEkPNDvzwq0lLE0uiAAQPgcDhgs9lw9OhReZvCwkLcfffd+Pbbb6Xoeb3ecu0+eFyuWgxlQZS26oP+DSySXT0eD5YuXYq0tDQ4nU44HA44nU7ExMRIYbNarXKzWCxo1KgR5s6di9OnT8sRVsyfIISQ80e/CiJWP0KhEPbu3Yt69erBZrOhW7du2Lp1KzZv3owvvvgC99xzD/r06YPc3FwZoRO/p0bueFyuWgxlQZS26oM6NkpUgnq9XqxatQqtW7eWchYTE4OYmBiYTCaYTCb5ffG5GnmbPn06vF6vZsmVBwtCCDl39Euj4vgcDoexZMkSeUx+8sknMW7cOAwZMgTNmzdHXFwcJk6cqMk5VkcLciJC9cBQFkRpqz7o38CBQACbN2/GtddeC4fDoRE1k8kkDxTqJsTNYrHAbDYjOTkZGzduhM/nk528ReieibCEEHJ29Be66sjAESNGwGazoV69erJqtKCgAO+88w6aNm0Kl8slc9xEuosabePFc9VjKAuitFUf9AJVXFyMV155BRaLBTabTQqZEDbxdUXSZjKZkJSUhGuuuUYz4kp/xUhpI4SQM6Muj6qtlq6//nrY7Xb86U9/wuHDh+XP58+fj2HDhsnjrmgPIiRNrIBQ2qoeQ1kQpa36oL+Sy8zMxLXXXgu73Y74+HhYrVY4nU5YLJaIUTZV2kRum9lsRu3atfH7779rQvP6aBshhJDIqMdItT9mTk4OGjZsCIvFgkmTJsmKUbFKsmLFCk1Lpl9++UX2eBMzSsXfIlWHoSyI0lZ90F91paenw2azwWq1IjY2FiaTSUbQ1KXSMy2PxsfHIyEhAXPnzpXNeStaHiWEEFIecXzUr1IsXrwYdevWRevWrbFixQq43W7NEqhaeLBmzRr069dPRtnUfm+8eK5aDGVBlLbqg17ajhw5IqNmYllUyFhFOW2iolRtBZKSkoI5c+bIqidxdadOV+ABgxBCIqOXNlGE8Pjjj8NiseCmm26SrT6E1KkzRY8fP47u3btj1qxZsisAc4qrD4ayIEpb9UHfwDEzMxNpaWky2qbPX4u0ifw3i8UiW4AkJiZiz549su9baWmppg0IDxiEEFIxatqKKOY6ePAgbr75ZjgcDjzzzDPy2KoWewWDQZw8eRIvvvgiGjdujBMnTsjom9/vZyumaoKhLIjSVr0QV2kAUFxcjH/84x8wmUyaHmxnirCJJVKHwyEjbddee61mwLF6YKG0EULImVGlzePxYM6cORg5ciRatmyJuLg4PPHEE5g5cyZmzpyJOXPm4OOPP8b777+PF154ATfeeCPsdjtGjRqFkpISuFwuzRhC5rRVPYayIEpb9UKNtIVCIaSnp+Puu++G3W6PWC0qJE0VN7GEarPZkJaWhl27dpWreNIvxVLcCCEkMvqm53l5eSgoKEB+fj6ys7NRWFiIoqIiFBUVobCwEMXFxfLz3Nxc5ObmwuVyySpSr9crI22sHq16DGVBlLbqgypPImfixIkTGDZsGOLi4jRyFqkIQRU6m80mpyIUFBSUG0Qfae4dDxqEEFIetWJUrFSINBNVxMRxu6ysTK5qBAIBOYowFArJYgWR/8aZ0FWPoSyI0la1qJVIoppIfL5//370798fJpMJbdu2RWpqqoyiqRE29aPFYoHdbkfPnj2xZs0aTcKr+LviQKH2bDvTAUMvdpFET/xN9faM5BFCagL6C2r1uK1PNVGPe+q8UlE1qjbnVQsceHysOgxlQZS2ykc/EkX07BF5Dm63Gz///DOuvvpqxMbGIjU1FevWrcOePXvw97//HR06dEBKSgocDocsUEhISEBKSgquu+46TJw4ERkZGfLgopep8z04qL+ntg2JdHDST3XgsHpCCCHVGUNZEKWt8lHzysTg4UAgALfbjZMnT2Ly5Mlo3rw5EhIS8OCDD2Lnzp0yDB8KhZCVlYVNmzbh/fffx9ixY/HKK6/gnXfewfr165GVlaVZ/hQRNXG/f1TaVEnTJ9CqvYbUiKH6e6yQIoQQUh0xlAVR2iofVZ7C4bBMSt29ezeuu+46JCQkoHXr1li2bBkKCgrg9/vl7FCfz6fJnRCbuI2QO1Wa9NL2Rx+vGk3Th/j1S69iZIvaB47SRgghpLphKAuitFU++uXDYDCINWvWoGvXrjCbzbj++uuxYcMGKWper1f2/CkqKpJJsCJCJ8RMiJLoAwRASp243/9F2vTCpuZriCigOrJF/Rnz2gghhFRHDGVBlLaLS6R8L3VpNDs7G+PGjUPdunVRu3ZtDB8+HCdOnJCDhYX0eDweKWDiZ+rfUwcRVxTduhCRtoMHD2LQoEG45557UK9ePSQkJOCqq67CkCFDMGjQIDz88MN49tln8eqrr2L69OnYtm2b5rFFKmKgzBFCCKkqDGVBlLaLhz6aJpY3Q6EQfD4ftm/fjgceeABJSUm49dZbsXz5chQVFcnb6IWvqtBH2ILBIL7++ms0atQISUlJmDZtmma5tLi4GAcOHMDUqVNx2WWXYcqUKXC5XOUidGw3QgghpKoxlAVR2i4eIpomImRi+dDj8eCzzz5D27ZtUbt2bYwfPx5FRUUyN01UkoocMSFwVfk8xHMRJe/Dhg1DQkIC2rRpg/Xr12ty7kTV6uHDh9GzZ08kJyfj22+/1RQxUNgIIYRUBwxlQZS2i4caoRJVoqdPn8Yrr7yCJk2aIDExEZMnT9aMNSkpKZGROH1bjap+HkK2Tpw4gZ49e8JkMqFHjx44ceKEFLJgMAi/3w+/3w+Xy4UxY8bAYrHgqaeeitgGhOJGCCGkKjGUBVHaLi6icjMQCODEiRN47LHHYLfbUbduXYwePVpT7SkKDsTH6tTfTH08a9asQcuWLWGz2TB06FBNdFAMQg6FQiguLsaYMWMQGxuLli1blmsbQmkjhBBS1RjKgiht58+ZpgPoG86WlpaisLAQq1atws0334zk5GTceOONWLhwIXw+X7neZmeaD1pVz0t9DH6/H+PHj5cNfZctW6apGlVbkRw/fhy33347zGYz6tWrJ6ONHFRPCCGkumAoC6K0nRuqYKgRMLUnmsj38vv9KC4uljlqw4cPR61atWCz2fDSSy8hKysLLpdLtu6oLgJTUVsPtRdcTk4O7rvvPhktPH36tGw3okYJfT4f9u3bh7S0NNjtdjRo0KCc1FWn504IISQ6MZQFUdrOjUgtKvQRMZHT5Xa7ZXXorbfeCovFgvbt22P+/Pnw+XyaWXX6hrXV4TlGaqArqka3b9+Ohg0bwmq14v7775fz9ERvNvHcSktLsWHDBlgsFphMJlx99dVS1oTYiudbHZZ/CSGERCeGsiBKwCiUdAAADupJREFU27lR0XKh+FpUe4bDYbhcLmzbtg29e/dGbGwsrrrqKqxbtw65ubmyyEBUWVanaQGRpE3ImBCxBQsWwG63w2w24+OPP9ZE4tTxWaFQCC+99BLMZjPsdjv+9re/yaVR9e8y0kYIIaQqMZQFUdrOjUhiISJtQr4CgQAyMjLw+uuvo2vXrujevTveeOMNFBcXywibOmpKtMaoTuKilza13UcoFMI111wDs9mMLl26ICMjQ47gUtuBBINBZGRkICUlBXa7HVarFStWrJBLrOq0BDX/jxBCCKlsDGVBlLbInK3YQC0cELlcP/30E2655RY4nU50794dmzdvhtvt1jTYVdt/RGp9UZ2es+gtJ55jTk4ObDYbLBYLHn30UeTn58vbiHmjQkaff/55WCwWWK1W3HPPPcjLy5Pip84srU7CSgghJPowlAVR2rREyudS889EJEkscwaDQfh8PixcuBAdO3ZETEwMrrnmGnz//ffweDyaIerVRc4qQl/1WlJSohG3ESNGICYmBiaTCfPmzZP7wuPxyFw+v9+PvXv3IjU1FRaLBVdeeSW2b98ul07V3Df1/qrrPiGEEFKzMZQFUdq06JcG9Yn4QsJEP7K8vDy8/fbbSEhIQEJCAgYPHozc3FzN4HYRYVMlsDoilnjVKJsQs4KCAlx//fWwWCy46qqrsHPnTlmAIPL5gsEgjh07hoEDB8LhcOC6667DgQMHZKNgIWoFBQXYu3cvdu3aVa33ByGEkJqPoSyI0laeipZCRc6WkJTVq1ejX79+iI+PR9euXfHJJ58gPz9f5q15PB6NtKnVptWRSBFG0aJjw4YNaNmyJcxmMwYNGoTc3Fy43W5N5OzkyZMYOHAgateujccffxw//fSTjESqVaOrV69G7969MXjwYLlPmdNGCCGkKjCUBVHayqNPwBeRNhE983g8ePfdd9GkSRPYbDbce++9OHz4cLk+ZG63W0qb2ki3ugqKGl0MhUJwu904deoUZsyYgQceeAAJCQmIjY1Fnz59MHPmTMyYMQMzZszA9OnT8fe//x0DBgzA448/jq+++kqO5hKSKyJ3IkI5atQo/O1vf9PkzxFCCCGVjaEsKFql7WyFBmqzXDWHraioCLNnz0bt2rURHx+PZ599FpmZmfB6vbK4QCwDqqKn/7vVEX3fuUAggOLiYnz33XfYuHEjvvnmG2zcuFGzie/9+OOPOHbsmMyDKysr0/Rv0xc1PPvss3j00Ucj5rVV531ECCGkZmEoC6K0lW89IfLW1KiZEJgpU6agQYMGaNSoEd5//32cPn1a3k58pHSU37/qvgyHw3j++ecxZMgQTfuPSOOtuC8JIYRcTAxlQdEqbfr+aPqGryKvy+/3o6CgAPPmzcMtt9yCFi1a4N5775XVoW63W0bj1Ny16roEWlmoUTsRqRQtQUpLS/H0009jyJAh5ZZP9VW2lDZCCCEXE0NZULRKmyprQhiENKjtPLKzs/HCCy/AarWidu3aGDFiBPLz8zUTEEQkTl0WpbT9t6hBiJnIcfP7/fj73/+OBx98sJzYqcuolDVCCCEXG0NZUDRLm34outrWIxAI4IcffkCvXr1gsVjQuXNnfPnll/B6vXLCgc/nkyIiihAYHfoP+uVRUWnq8/mwceNGfP7551i4cCG+++47nD59WoqvXti4LwkhhFxMDGVBRpO2MxUQ/C+bkDYx3eCrr75CWloarFYrOnfujC1btsDv98uIkTqSiTlt5VGXR/UTE0QLECFp+kkJ4nMKMCGEkIuNoSzIqNImIjKiYlOc+IU4qU1wQ6GQnJEpvlb/hliyC4VCSE9Px/Dhw5GQkIDGjRtj3LhxOHnyZMScNUoFIYQQYmwMZUFGkjZ9ZEyd3+n3+zW5U36/H36/HydOnMB3332Hd955B2+++SYmT56MmTNnYuvWrSgoKNCI2+bNm9G9e3c4HA506NABGzZskCOahAhWFKkjhBBCiPEwjgXBWNKmn40pomOiAEAsvQUCAezcuRMTJ07EpZdeCqvVCrPZDLPZDJvNBqvVitjYWPz5z3/Ge++9h8OHD+PQoUPo3LkzLBYLbrvtNuzevRter7ecrAHQSBqljRBCCDEuxrEgGEva9M1vxfJnIBCQy58lJSWYNWsWUlNTYbfbYbVaYbFYYLVa4XA4YDabpcRZLBbEx8fj8ssvR5s2bZCUlIRnnnkGR48e1UTthAzqixaA/4okIYQQQoyHcSwIxpI24L+SJMRJnX0ZDAYxfPhw1K1bV0qZxWKBzWaDxWKRwmYymeTXJpMJVqsVtWrVwrBhw5CXlwefz6fpGaZ+rpc2RtoIIYQQ42IoC7qQ0qZWYIrN6/Xi8OHDWLp0Kb799lusX78eGzZskIn9hYWF8Hg8GjmqSIIqGjclIm7/+te/YLPZYDKZ5BYTE3PWzWQywWaz4aqrrsKxY8c0/dcijbZix35CCCGkZhCV0iZkTRWcgoICLFiwAK+++iqWLl2KLVu24Pvvv8fkyZPx0EMP4Z///CdGjhyJ48ePl5OjSFQ0wSAcDmPnzp3o1q0bbDabFLFzkTXx0Ww2IyEhAZMnT5YtKdT8OYoZIYQQUvOISmkTXe2FTPn9fnzxxReYMGECiouL4ff7ZcWnz+fD7NmzYbFYMHr0aHg8nnLJ/hXdh3obEWHz+/3417/+haSkJFit1nOKrunlTYjb/fffj6ysrIitPQghhBBSs4haaVPzzXJyctCpUycsWrRIilUwGJSTBA4cOIDGjRtj1qxZ5XLGzjXSpk4xGDlyJCwWiybCdrZom7qEKnLcrrvuOuzZs0fT8JXSRgghhNRMolba1B5qU6dORcuWLbF27Vr4/X54vV45HsrtduPUqVMYPXo0Nm/efM4d8CNJm6jyfPnll2Vbj/NZHhVFCTExMTCbzbj++uvxyy+/aHLauDxKCCGE1EyiVtrU6sopU6YgNjYWffr0kU1qRfsM0fi2uLgYXq9XM7PzbIKkipQYJVVaWorPPvsMDRo0kBEzUTkqlj1Fpahe1vTSdv/99yMzM1PT5kPcHyGEEEJqFlEvbaFQCF999RViYmLgcDjQtm1bjB49GkePHpXtNNSKUf2g9TNF2oREieicKETYsWMHunbtCovFArvdDqfTqenLplaVCqEToia2hg0bYvbs2fKxqc+HkTZCCCGk5hG10qYOTQ+FQnjkkUeQmJgIs9mMuLg4xMfH44knnsCvv/4qo2Tid8TfOJelSFUQ1RYjH330ERo3bozY2FhZRep0OmVETfRoU3PYbDab/NivXz9kZGQgFAqhoKBAs2QbDocvyH4ihBBCSPUhKqVNFRyRZ5adnY1ly5ahT58+SExMlI1uU1NTMX36dBnR8vv95xxp0xc8qOJWWFiId955B/Xq1YPT6YTVapVTEcQUBBFd0y+dNmnSBPv379cMnXe5XPJ+GGkjhBBCah5RKW36KQVq+49gMIgPP/wQt99+O5KTk2Gz2dCwYUMsWrQIwWBQStvZKjX1s0fFfQjJEu1E1q5di169eiEhIUFKm5g5qi6PmkwmJCcn4+6778a2bdtksYSYaapKIXPaCCGEkJpHjZY2/bB0sRQqImZCntSWGUKuCgoK8O6776JRo0awWCx44okn5GSEc5E2fTROX7EqJCsQCCArKwvTpk3DVVddhfbt2yMhIUFG3ho1aoT27dvjrrvuwpo1a1BUVKTpE1fRRgghhJCaRY2WNhVVlsLhsJwkoC4xBgIBjUwVFRVh4MCBsNlsGDJkiLydKl/nK0j63DbRWqS0tBQejwf79+/HZ599hqlTp+KDDz7AN998g6NHj6KkpERzn+JvEEIIISQ6iAppU6Ns4mNBQQGGDx+OGTNmSFlTl0zLysrg9/sxY8YM1K9fH0899ZT8HvBf+TpfadMXJojInihyEE19xfeE1JWVlSEQCMhIH3PXCCGEkOgiqqRNSFEoFEJGRgauueYaTJ06VfY5U3PDxGSEV155Bc2bN8e6des0QvdHG9nqh8er+XQi4qY+FlEooYqlOpWBEEIIIdFBjZY2VajUQoNQKIS9e/fCYrGgX79+OHbsmJQgr9crxej48ePo0aMHJk2apBE+dYnzj0hbpCII8beErOlFU3yuRtkYaSOEEEKih6iQNv0EhHA4jPT0dDRr1gypqal44oknkJWVhYyMDGRkZOD48eM4ePAgXnnlFbzxxhvIz8+X0bdIRQDnS6TCgUhD3/UD5zkYnhBCCIlearS0CfTzP4PBINxuN44ePQqXy4W1a9di0aJFmDNnDhYuXIgvv/wSX3zxBXbt2gWPxwOv1wu/3y+XLylOhBBCCKlsarS06SNtajGCyBMTQhYMBuH1euHxeBAOh+X3xe29Xq8mUsdiAEIIIYRUJlEhbcB/lxdFor/o1SZyysTEA1G9GQgE4Ha7UVJSoikUUJvYMtJGCCGEkMoiKqRNJPirg9vVthpqEYBYBhWbKD5QZ5VyeZQQQgghlU2NljaBWoigNsbVf098rRYbRJI0VQYpbYQQQgipDKJC2gghhBBCjI6hLIjSRgghhJBoxVAWRGkjhBBCSLRiKAuitBFCCCEkWjGUBVHaCKk89BM5zjZ3V1+kI35PzMj9XyeJRLqvyigEijSdxMij5PSPW19oJYq09N8X1ffq3zDi8yfEyBjKgihthBBCCIlWDGVBlDZCCCGERCuGsiBKGyGEEEKiFUNZEKWNEEIIIdGKoSyI0kYIIYSQaMVQFkRpI4QQQki0YigLorQRQgghJFoxlAVR2gghhBASrRjKgihthBBCCIlWaEGEEEIIIQaA0kYIIYQQYgAobYQQQgghBoDSRgghhBBiAChthBBCCCEGgNJGCCGEEGIAKG2EEEIIIQaA0kYIIYQQYgAobYQQQgghBoDSRgghhBBiAChthBBCCCEGgNJGCCGEEGIAKG2EEEIIIQaA0kYIIYQQYgAobYQQQgghBoDSRgghhBBiAChthBBCCCEGgNJGCCGEEGIAKG2EEEIIIQaA0kYIIYQQYgAobYQQQgghBoDSRgghhBBiAChthBBCCCEGgNJGCCGEEGIAKG2EEEIIIQaA0kYIIYQQYgAobYQQQgghBuD/A43ED2kgMTKxAAAAAElFTkSuQmCC)
利用遗传算法对输电线路无人机巡检进行路径规划,遗传算法运算流程如图3所示。
3.3实际的应用
在实际应用中,无人机需要注意几个方面:首先,必须正规化无人机巡检,使用无人机巡检技术建立定期巡检系统。在巡检过程中,可以巡检线路,也可以巡检输电线路的地形并收集数据,主要是利用技术参数对一些较为特殊化的情况和较为特殊化的区域进行实时巡检,另外也要辅助工作人员进行工程的放线操作以及区域内异物的处理工作。
4、结束语
综上所述,无人机技术应用于传输线路的巡检,大大提高了巡检效率,强化了日常巡检能力,延长了传输设备的使用年限。建立巡检算法的数学模型,使用遗传算法规划无人机巡检路径,通过组合无人机性能参数的限制和实际巡检要求,设计适当的函数,基于路径偏转角的编码方式,并计划更合理的无人机飞行路线。实现了无人机输电线路巡回巡检路径的计划,通过模拟验证了算法的有效性,提高了循环巡检的品质和效率,确保了循环巡检的安全性,计算出了实用性高的路径。随着无人机技术的不断进步,无人机可以应对复杂的状况,制约也越来越少,这种新技术被广泛推进以提高电力公司的效率。
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