Research Progress of Memristor-based Neuromorphic Synapses
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摘要: 大脑之所以能够控制人和动物的复杂生命活动，使生物体在多变的自然环境得以生存，得益于大规模神经网络中高效、快速、精准的信息传递。神经突触作为神经元之间信息传递的重要机构，保证了神经网络的高效运转，因此构建具有神经突触功能的电子突触是研究仿生系统和类脑神经网络的必经之路。研究人员尝试各种电子元件对神经突触进行模拟，其中忆阻器由于其独特的器件结构和具有“记忆特性”的电学性能，成为构建类脑神经突触的最佳选择。文章全面概述近年来忆阻器模拟神经突触的研究进展，包括忆阻器模拟神经突触的可塑性、再可塑性、非联想学习、联想学习等功能，总结了忆阻器神经突触在人工神经网络中的应用、存在的问题和挑战，并对忆阻器神经突触的研究进行展望。Abstract: The efficient, fast and accurate information transmission in the large-scale neural network in the brain is the exact origin that the brain can control the complex life activities of humans and animals and enable organisms to survive in the changeable natural environment. As an important medium for information transmission between neurons, the synapses ensure the efficient operation of neural networks. Therefore, to build electronic synapses with synaptic functions is one essential way to study bionic systems and brain-like neural networks. Researchers have previously tried to simulate synaptic functions with various electronic devices, among which memristor has become one good candidate to build neuromorphic synapses due to its unique device structure and memory characteristics. The researches of memristor-based synapses in recent years are comprehensively summarized in this article, including the synaptic plasticity, metaplasticity, non-associative learning, associative learning and other functions. It also summarizes the application, problems and challenges in artificial neural networks, as well as the research prospects of memristor-based synapses.
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Keywords:
- memristor /
- synapse /
- plasticity /
- neural network
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当前，我国对能源需求越来越大，在大力发展传统化石能源的基础上，也需要积极拓展其他能源形式。在“十三五”能源规划中，我国计划今后要大力开发清洁可再生能源，以满足能源需求，并实现节能减排的战略目标，“十四五”期间，习近平总书记提出并不断深化低碳经济发展战略，使得新能源相关技术及产业获得了进一步发展。为保障我国能源安全，地热资源因其清洁、高效、储量巨大且可持续发展等特点愈发凸显其优势，有望成为我国能源续接的重要路径。根据国土资源部2015年统计数据，我国中深层(200~4 000 m)中低温资源量合13 700亿吨标准煤当量、高温资源发电潜力为8 466 MW，深层(3~10 km)干热岩资源总计为2.09×1025 J，合860万亿吨标准煤，约为2014年全国能源消耗总量的26万倍，但截至2015年底我国仅实现年替代标煤290万吨[1-3]。因此，加快干热岩等深部地热资源的高效开发和利用，对改善我国能源战略布局、优化能源结构及促进转型发展具有重大政治、经济意义。但是干热岩地层，尤其是最典型的火成岩-花岗岩地层，所处地层环境复杂，具有温度高、硬度大、抗压强度高、研磨性强、钻头难以吃入地层等特征，普通钻井技术不能实现其高效钻进。
为有效推进干热岩地热资源的开发利用，明确超高温作用下的岩石力学性质演化规律尤为重要。围绕花岗岩这一干热岩常见岩性，前人研究结果表明，当花岗岩所处温度升高时，除了外观(如颜色等)的显著差异，岩石体积膨胀，骨架密度逐渐下降，内部水分不断蒸发，在岩石加热过程中岩石微裂纹开始产生并逐渐沟通形成宏观裂纹，岩石矿物骨架遭到破坏，且随着岩石损伤的不断增强，其宏观刚度和强度等力学指标显著降低，蠕变特征和塑性变形趋于明显，岩石的脆性降低，且存在阈值温度使得岩石力学、物理及化学指标(如单轴抗压强度、弹性模量等)发生明显改变[4-9]。同时，岩石颗粒尺寸差异越大，其阈值温度也就越低，岩石强度变化愈明显[10]。另外，加热源类型、升温速率、外界温差、循环次数等作业参数对花岗岩损伤效果、阈值温度和峰值强度具有显著影响[9, 11-14]。但目前开展的高温作用下干热岩力学性质研究多集中于花岗岩室内特性测试，对高温作用下岩石受载荷的应力场分布特征和裂纹延展机制尚缺乏理论研究，且干热岩室内力学实验对加热极限温度和实验设备要求较高，导致实验研究难度较大，干热岩破碎机理亟需进一步研究。
为揭示干热岩破碎机理，以干热岩地层常见的花岗岩为研究对象，本研究提出超高温条件下花岗岩力学性质演化规律研究，建立高温花岗岩巴西圆盘劈裂数值模型，通过预置硬质花岗岩的岩石力学参数和温度参数，探究硬质花岗岩在温度-载荷联合作用下岩石应力场分布特征与扰动机制，从而揭示温度对岩石单轴抗拉强度影响规律和岩石在超高温作用下裂缝延展机制，为温度作用下花岗岩力学性质演化规律和深层干热岩资源的高效开发提供理论依据。
1. 有限元破岩模型构建
为揭示巴西劈裂过程中干热岩破碎机制，基于岩石力学、断裂力学等学科基础理论，参照干热岩与温度相关力学参数，利用Abaqus有限元模拟平台，建立温度-载荷联合作用下的硬质花岗岩巴西劈裂圆盘数值模型(图 1)。
鉴于花岗岩脆性破坏模式，定义岩石破碎本构关系为Drucker-Prager准则且设定其硬化特征，并以黏聚力单元定义岩石破坏模式，巴西劈裂过程中，将上下承压板视为刚体部件，为模拟实际岩石破碎过程，设定载荷过程中上下承压板均以1 mm/s压缩岩石，持续压缩时间为1 s(包含40个等时间隔，间隔0.025 s)。由于加热过程中岩石密度与体积变化相对较小，模拟过程中统一岩石密度和泊松比分别为2.7 g/mm3和0.200，且以室温(25 ℃)条件下岩石强度作为参照对象，模拟岩石所处温度范围为150~650 ℃。
为进行超高温条件下花岗岩力学损伤性质的模拟，表 1中数据包括文章调研数据和必要插值，具体数据详见文献[15]~[18]。岩石与承压板三棱形切削齿的接触形式采用通用显式接触，切向摩擦系数设置为0.3，并定义岩石与承压板接触面的接触关系为“硬接触”。通过观测岩石破碎过程中承压板受到的反作用力可以获得岩石在巴西劈裂过程中的受压载荷，而应力场动态分布特征则可帮助揭示干热岩裂纹延展机制。
表 1 巴西劈裂圆盘材料主要物性参数Table 1. The main material parameters of Brazilian test modelling材料 温度/℃ 密度/(g·mm-3) 弹性模量/GPa 泊松比 单轴抗压强度/MPa 承压板 — 7.8 210.00 0.077 — 花岗岩 25 2.7 39.30 0.200 90.42 150 2.7 32.26 0.200 87.73 200 2.7 29.22 0.200 86.35 300 2.7 27.43 0.200 79.36 400 2.7 18.97 0.200 83.77 500 2.7 20.99 0.200 68.20 600 2.7 19.87 0.200 69.56 650 2.7 16.16 0.200 59.83 2. 有限元模拟结果分析
以25 ℃花岗岩模拟岩样作为参照，本模拟研究重点阐述超高温作用下花岗岩巴西劈裂圆盘的岩石应力场分布特征、裂纹延展特征和巴西劈裂拉伸强度特征。
2.1 超高温作用下岩石应力场分布特征
为明确干热岩应力场分布特征，本节模拟未考虑裂缝等非均质性影响因素，通过定义岩石在不同温度下的强度参数，可以获得花岗岩巴西劈裂圆盘在横向和纵向上的应力分布(图 2、图 3)，其中暖色(如红色)表示拉伸效应，冷色(如蓝色)表示压缩效应。通过观察不同加热处理样品的应力图谱分布，可以得到岩石的应力场分布特征。为对比不同温度处理下的花岗岩巴西劈裂圆盘应力场分布特征，需要对各模拟结果作统一图例处理，以便更加直观、高效地观察花岗岩圆盘各处实时应力大小与受力状态。
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图 2 花岗岩巴西劈裂圆盘横向应力分布Figure 2. The horizontal stress distribution of granite Brazilian disk![]()
图 3 花岗岩巴西劈裂圆盘纵向应力分布Figure 3. The vertical stress distribution of granite Brazilian disk从横向(x轴方向)应力分布图(图 2)来看，若统一横向应力图谱显示图例为-1.00~1.00 MPa，岩石最大横向拉伸应力发生在圆盘中心处，沿x轴方向向外逐渐递减，但在靠近载荷的y轴纵向方向呈不断减小趋势并逐渐减小至0，在载荷施加处及其附近区域横向拉伸应力转变为压缩应力，载荷位置附近压缩效应显著且呈对称状扇形分布，且随着压缩时间的增大而越发明显。随着岩石处理温度从25 ℃升高至650 ℃，花岗岩巴西劈裂圆盘各处横向应力显著降低，圆盘中心横向拉伸效应减弱，两端载荷位置附近区域压缩效应亦显著减弱，表明超高温作用可以削弱岩石在横向的应力分布。
从纵向(y轴方向)应力分布图(图 3)来看，若统一纵向应力图谱显示图例为-5.00~5.00 MPa，岩石最大纵向压缩应力发生在圆盘载荷施加处，沿y轴方向向圆心逐渐递减，越靠近施加载荷初，载荷纵向压缩应力越大，相较于x轴方向压缩应力分布，沿载荷方向纵向压缩效应显著，且随着压缩时间的增大而越发明显。模拟发现，圆盘纵向拉伸效应微弱，拉伸应力可以忽略。随着岩石处理温度从25 ℃升高至650 ℃，花岗岩巴西劈裂圆盘各处压缩应力显著降低，圆盘两端载荷位置附近区域压缩效应显著减弱，圆盘中心纵向压缩效应呈现不断减小趋势，表明超高温作用可以削弱岩石纵向的应力分布。
在花岗岩圆盘巴西劈裂过程中，岩心各处沿x轴(横向)和y轴(纵向)应力分布的差异明显，故作x-y平面内剪切应力图谱分析如图 4所示。若统一剪切应力图谱显示图例为-3.00~3.00 MPa，巴西劈裂圆盘载荷施加处剪切效应显著，其他位置(如圆心附近)剪切力可以忽略。从局部看，左部圆盘和右部圆盘靠近同一载荷施加位置分别呈现拉伸效应与压缩效应，其数值大小相等且较y轴呈对称分布；上部圆盘和下部圆盘靠近两端载荷施加位置分别呈现拉伸效应与压缩效应，其数值大小相等且较x轴呈对称分布；从整体上看，圆盘剪切应力图谱呈中心对称分布。随着岩石处理温度从25 ℃升高至650 ℃，花岗岩巴西劈裂圆盘各处剪切应力显著降低，表明超高温作用可以削弱岩石在载荷施加位置处的剪切应力分布。
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图 4 t=0.025 s时刻花岗岩巴西劈裂圆盘剪切应力分布Figure 4. The shear stress distribution of granite Brazilian disk at t=0.025 s2.2 温度-载荷联合作用下岩石裂纹延展机制
基于超高温作用下岩石应力场分布特征，向花岗岩巴西劈裂圆盘全局网格添加cohesive粘结单元并设置粘结拉伸破坏属性。以25 ℃下巴西劈裂圆盘模拟数据为例，取第1(t=0.025 s)、第5(t=0.125 s)、第15(t=0.375 s)、第25(t=0.625 s)、第40(t=1.000 s)分析间隔数据作为参照，实现巴西劈裂过程中花岗岩模拟裂缝的动态捕捉(图 5)。若统一米塞斯(Mises)应力图谱显示图例为0.0~100.0 MPa，由图 5可知，25 ℃处理的花岗岩在t=0.025 s时刻载荷施加位置出现明显的应力集中现象。由于剪切效应(图 3)的存在，使得载荷施加位置逐渐产生微裂缝，并逐渐向岩石圆盘中部延展，在0.125 s时在两端载荷位置形成裂纹簇。裂纹簇中沿载荷施加方向径向裂纹具有优势传播方向，在0.375 s时延展形成裂纹网状结构，进一步延展沟通，在0.625 s时刻显示为径向宏观裂纹。在载荷继续作用1.000 s时形成最终网状纹络结构，圆盘中心损伤效果显著。相较于25 ℃的花岗岩，在同一劈裂时刻下，600 ℃花岗岩受压损伤区域相对较小，裂缝沟通过程中岩石应力释放较为明显。
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图 5 25 ℃和600 ℃下花岗岩巴西劈裂圆盘裂缝延展机制Figure 5. The fracture dynamics comparison of granite Brazilian disks between 25 ℃ and 600 ℃为进一步揭示温度-载荷联合作用下岩石裂纹的延展机制，将不同温度处理下花岗岩巴西劈裂圆盘在t=1.000 s时形成的最终裂纹汇总于图 6。可以发现，随着温度的升高，花岗岩圆盘沿载荷方向中央裂纹密度显著减小，裂纹沟通难度降低，表明温度升高后岩石横轴方向的应力较小，沿径向张开较为容易，超高温作用可以削弱岩石在横轴方向上的应力分布，与未添加粘结单元时模拟数据支撑结论一致(图 2)；同时，花岗岩圆盘横向裂纹延展性显著增强，裂纹沟通较好，表明温度升高后岩石纵轴方向的应力较小，沿横向张开较为容易，超高温作用可以削弱岩石在纵轴方向上的应力分布，与未添加粘结单元时的模拟数据支撑结论一致(图 3)。另外，当温度从25 ℃升高至650 ℃，花岗岩两端载荷位置的裂纹簇规模显著减小，破碎区域较小且裂纹数目减少，表明载荷位置的剪切效应被显著削弱，超高温作用可以削弱岩石在载荷施加位置的剪切应力分布，与未添加粘结单元时的模拟数据支撑结论一致(图 4)。
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图 6 不同温度作用下花岗岩巴西劈裂圆盘裂缝延展机制Figure 6. The fracture dynamics of granite Brazilian disks under various temperature conditions在巴西劈裂过程中，花岗岩圆盘应力分布特征与裂纹延展机制互为印证，表明数值模型的有效性与准确性，该模型可被用于模拟花岗岩圆盘在超高温作用下的损伤破坏效果，因此可计算其在不同温度条件下的巴西劈裂强度。根据巴西劈裂数值模型模拟数据，由于超高温作用对花岗岩圆盘横向应力、纵向应力和剪切应力的削弱作用，在温度从25 ℃升高至650 ℃的过程中，温度的升高使得岩石沿圆盘中央方向的裂纹沟通更容易，载荷施加位置的裂纹簇规模显著减小，圆盘裂纹密度显著降低，岩石损伤效果更为明显，表明相较于低温度范围处理的岩石，超高温作用下岩石在巴西劈裂过程中受到单轴径向压缩载荷越容易产生拉伸破坏。
2.3 温度对岩石巴西劈裂强度的影响规律
根据岩石模拟破裂过程中的载荷曲线，选取最大载荷计算硬质花岗岩在超高温作用下的巴西劈裂抗拉强度，具体计算方法依据国际通用测量标准(ASTM)执行：
σt=2PπDL (1) 式中，P为施载过程中最大载荷(N)，D为岩石的直径(mm)，L为岩石的厚度(mm)。
花岗岩巴西劈裂圆盘的破坏过程中受力载荷可以通过收集承压板受到的反作用力获得。如表 2所示，在温度从25 ℃升高至650 ℃的过程中，施载过程中最大载荷不断减小，25 ℃花岗岩在压碎过程中的最大载荷为621.77 N，而650 ℃高温作用下花岗岩的最大载荷下降至122.71 N，降幅达80%。该结果表明：在超高温作用下，花岗岩的巴西劈裂抗拉强度显著降低。
表 2 花岗岩的巴西劈裂圆盘的抗拉强度模拟结果Table 2. The numerical results of Brazilian tensile strength of granite discs温度/℃ 弹性模量/GPa 单轴抗压强度/MPa 最大载荷/N 巴西劈裂强度/MPa 25 39.30 90.42 621.77 13.19 150 32.26 87.73 532.13 11.29 200 29.22 86.35 494.11 10.49 300 27.43 79.36 474.93 10.08 400 18.97 83.77 374.06 7.94 500 20.99 68.20 382.35 8.11 600 19.87 69.56 140.66 2.99 650 16.16 59.83 122.71 2.60 将巴西圆盘劈裂过程中最大载荷带入式(1)求解可知，在25、150、200、300、400、500、600、650 ℃温度作用下，花岗岩圆盘破坏过程中受到的巴西劈裂抗拉强度分别为13.19、11.29、10.49、10.08、7.94、8.11、2.98、2.60 MPa(图 7)。
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图 7 不同温度下花岗岩巴西劈裂圆盘的抗拉强度Figure 7. The tensile strength of granite Brazilian disk under various temperature conditions随着岩石温度的升高，岩石的劈裂强度不断降低，且存在温度阈值约500 ℃，可使岩石的拉伸强度发生显著变化，岩样强度显著下降。相较于25 ℃处理岩样的抗拉强度(13.19 MPa)，600 ℃处理所得岩样的劈裂强度下降至2.60 MPa，降幅达80%，仅为原有强度的20%，表明超高温作用下花岗岩巴西劈裂抗拉强度显著降低。
3. 结论
为揭示超高温作用下花岗岩破碎特性，利用Abaqus有限元分析建立了高温花岗岩巴西圆盘劈裂数值模型，探究了硬质花岗岩在温度-载荷联合作用下岩石的应力场分布特征、裂纹延展机制和劈裂强度。数值模拟数据结果表明：当花岗岩温度从25 ℃升高至650 ℃，超高温作用可以显著削弱岩石圆盘的应力分布，扰动原有应力场分布特征，尤其是削弱圆盘中心沿横轴方向的拉伸效应、两端载荷施加位置附近的压缩效应和剪切效应；伴随着岩石应力的削弱，岩石沿圆盘中央方向裂纹沟通更为容易，载荷施加位置的裂纹簇规模显著减小，岩石损伤效果更为明显；根据模拟数据分析，进一步处理载荷数据发现，超高温作用下岩石的劈裂拉伸强度降幅达80%，且存在阈值温度约500 ℃使得岩石拉伸强度发生显著变化。
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图 12 忆阻器模拟神经突触非联想学习功能
Figure 12. The memristor simulates non associative learning of synapse
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表 1 忆阻器与生物神经突触的比较
Table 1 The comparison diagram of memristor and biological nerve synapse
忆阻器 神经突触 结构 顶电极-阻变层-底电极 突触前膜-间隙-后膜 性质 非易失性(阻态依赖特性) 可塑性 工作原理 离子迁移 神经递质迁移 主要参数 电导 突触权重 
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