| Citation: | SUN Jianping, YANG Pengtao, LIU Shaobo, ZHOU Fang, DONG Xiaoli, WEN Haihu, CHENG Jinguang. Pressure Effects on the Tetragonal FeS Superconductor[J]. Chinese Journal of High Pressure Physics, 2022, 36(6): 060101. doi: 10.11858/gywlxb.20220677
|
军事工程中, 混凝土材料可以作为抵御武器破坏和恐怖爆炸的天然屏障, 因此关于动能弹对混凝土材料的侵彻效应的研究对于地下防护工程建设和武器战斗部设计有着重要的意义[1]。动能弹对混凝土侵彻深度的计算和预测是防护工程的重要研究内容之一。目前, 国内外关于侵彻深度的研究越来越多, 已建立了多种确定侵彻深度的方法, 包括经验公式法、数值计算法和其他方法。经验公式法主要基于大量实测数据建立侵彻深度经验公式, 包括纯经验公式和半经验半理论公式, 种类不下40种[2], 并且各公式千差万别, 有着各自的应用范围和条件, 应用较广的主要有Young公式、Bernard公式、别列赞公式及Forrestal公式等[3-6]。由于侵彻效应的机理不清楚, 且影响因素较多, 因此经验公式法的预测误差相对较大。数值计算法[7-8]主要基于数值分析软件建立数值模型进行计算, 目前多采用有限元法、有限差分法、离散元法等, 其计算结果的准确性与数值模型参数选取是否合理密切相关, 通常需要根据实测数据多次计算、修正模型参数, 否则会导致计算结果不够准确。
近年来, 灰色理论、神经网络等方法被越来越多地应用于对混凝土靶体侵彻深度的预测[9-11]。灰色理论针对含有不确定因素的系统, 通过累加、累减等方法生成新数据, 建立生成数据模型, 具有需求样本量较少、原理相对简单的优点, 但也存在明显的理论缺陷。虽然引入灰导数和背景值的概念简化了计算, 但由于不是采用对应于同一点的函数值和导数值去辨识微分方程中的参数, 导致了较大的预测误差[12]; 此外, 解微分方程时将第一个原始数据作为其生成数据的预测值也会引起明显的系统误差[13]。神经网络智能方法基于实测数据进行不断学习训练得到合适的模型参数, 进而建立预测模型, 往往需要大量训练样本, 实际中样本数量很难满足要求, 使得预测误差相对较大。
随着计算机技术的不断进步, 基于统计学习理论, 适合于小样本学习、可解决非线性及高维数等问题的支持向量机(Support Vector Machine, SVM)方法受到了国内外研究者的广泛关注, 并逐步应用于模式识别和函数拟合[14-16]。SVM具有的优势可解决实际工程中侵彻问题的机理复杂、影响因素多、测试数据有限等问题。文献[17]率先提出了以弹头长径比作为主要影响因素之一预测混凝土靶体侵彻深度的SVM方法, 使预测精度大为提高。已有的研究表明, 弹头长径比并不是影响动能弹侵彻深度的主要因素, 而动能弹长径比才是主要因素[18]; 此外, 文献[17]中选取的影响因素较多, 需要的训练样本量也大, 易产生“过拟合”现象, 且模型参数未利用样本数据进行优化选取, 其预测精度有待提高。本研究将粒子群优化算法(Particle Swarm Optimization, PSO)与SVM相结合(PSO-SVM), 进行动能弹侵彻混凝土靶体深度的预测研究, 并分析训练样本数量对预测相对误差的影响。
SVM是一种基于统计学习理论的新型机器学习方法, 由Vapnik等于20世纪90年代首次提出。与传统的机器学习理论相比, 统计学习理论采用结构风险最小化原理, 并考虑了经验风险和置信范围, 其推广性能良好, 着重于解决小样本(有限样本)、非线性、高维数和局部极小点等实际问题。SVM主要应用于模式识别和回归分析, 其核心是支持向量。回归分析的基本思想是:定义最优回归超平面, 并把寻找最优回归超平面的问题归结为求解一个二次凸规划问题, 再根据最优化理论获得全局最优解; 进而基于Mercer核展开定理, 通过非线性映射, 把样本空间映射到一个高维特征空间(即Hilbert空间), 使在特征空间中可以应用线性学习机的方法解决样本空间中的高度非线性问题。简言之, 即实现升维和线性化, 该算法的基本形式可以参考文献[14-16]。
对于非线性回归, 一般通过非线性映射Ψ(x)把样本x映射到高维特征空间中, 然后在高维特征空间中求解最优回归函数, 这样高维特征空间中的线性回归就对应低维特征空间中的非线性回归。因此, 采用适当的核函数K(xi, x)代替高维空间中的内积运算Ψ(xi)·Ψ(x)即可实现非线性变换, 但却没有增加计算的复杂度。
在高维特征空间中建立线性回归函数
| f(x)=w⋅Ψ(x)+b | (1) |
拟合数据为{xi, yi}(xi∈Rn, yi∈R; i=1, 2, …, k; k为训练样本个数), 考虑到允许拟合误差ε的情况, 引入松弛因子ξi和ξi*, 则优化问题转化为
| minΦ(w)=12‖ | (2) |
约束条件为
| \left\{ \begin{array}{l} {y_i} - \mathit{\boldsymbol{w}}\;\mathit{\boldsymbol{\cdot}}\;\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}({\mathit{\boldsymbol{x}}_i}) - b \le \varepsilon + {\xi _i}\\ \mathit{\boldsymbol{w}}\;\mathit{\boldsymbol{\cdot}}\;\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}({\mathit{\boldsymbol{x}}_i}) + b - {y_i} \le \varepsilon + {\xi _i}^*\\ {\xi _i} \ge 0,\;\;\;\;{\xi _i}^* \ge 0,\;\;\;\;C > 0 \end{array} \right. | (3) |
式中:C为惩罚因子, 表示对超出误差ε样本的惩罚程度; ε规定了回归函数的误差要求。
根据最优化理论, 将上述优化问题转化为其对偶问题
| \begin{array}{l} {\rm{max}}\;W(\alpha, {\alpha ^*}) =-\varepsilon \sum\limits_{i = 1}^k {({\alpha _i} + {\alpha _i}^*)} + \sum\limits_{i = 1}^k {{y_i}({\alpha _i}-{\alpha _i}^*)} \\ -\frac{1}{2}\sum\limits_{i, j = 1}^k {({\alpha _i} - {\alpha _i}^*)({\alpha _j} - {\alpha _j}^*)K({\mathit{\boldsymbol{x}}_i}, {\mathit{\boldsymbol{x}}_j})} \end{array} | (4) |
约束条件为
| \left\{ \begin{array}{l} \sum\limits_{i = 1}^k {\left( {{\alpha _i}-{\alpha _i}^*} \right) = 0} \\ 0 \le {\alpha _i} \le C, 0 \le {\alpha _i}^* \le C \end{array} \right. | (5) |
式中:αi、αi*为Lagrange乘子, 通常系数(αi-αi*)只有一小部分不为零, 其对应的样本为支持向量。
通过求解(4)式和(5)式可以得到最优解为α=[α1, α2, …, αk], α*=[α1*, α2*, …, αk*], 进而可以求出w的最优值为
| {\mathit{\boldsymbol{w}}^*} = \sum\limits_{i = 1}^k {({\alpha _i}-{\alpha _i}^*)\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}({\mathit{\boldsymbol{x}}_i})} | (6) |
根据Karush-Kuhn-Tucker定理, 偏置b的最优值为
| \begin{array}{l} {b^*} = \frac{1}{{{N_{{\rm{n}}\;{\rm{sv}}}}}}\\ \left\{ {\sum\limits_{0 < {\alpha _i} < C} {\left[{{y_i}-\sum\limits_{{\mathit{\boldsymbol{x}}_i} \in \mathit{\boldsymbol{S}}} {\left( {{\alpha _i}-{\alpha _i}^*} \right)} K\left( {{\mathit{\boldsymbol{x}}_i}, {\mathit{\boldsymbol{x}}_j}} \right)-\varepsilon } \right]} \\ + \sum\limits_{0 < {\alpha _i}^* < C} {\left[{{y_i}-\sum\limits_{{\mathit{\boldsymbol{x}}_j} \in \mathit{\boldsymbol{S}}} {\left( {{\alpha _j}-{\alpha _j}^*} \right)} K\left( {{\mathit{\boldsymbol{x}}_i}, {\mathit{\boldsymbol{x}}_j}} \right) + \varepsilon } \right]} } \right\} \end{array} | (7) |
式中:Nnsv为支持向量个数, S为支持向量的集合。由此可得回归函数为
| \begin{array}{l} f\left( \mathit{\boldsymbol{x}} \right) = {\mathit{\boldsymbol{w}}^*}\mathit{\boldsymbol{\cdot}}\;\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}\left( \mathit{\boldsymbol{x}} \right) + {b^*} = \sum\limits_{i = 1}^k {({\alpha _i} - {\alpha _i}^*)\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}({\mathit{\boldsymbol{x}}_i})\mathit{\boldsymbol{ \boldsymbol{\varPsi} }}\left( \mathit{\boldsymbol{x}} \right) + {b^*}} \\ = \sum\limits_{i = 1}^k {({\alpha _i} - {\alpha _i}^*)} K({\mathit{\boldsymbol{x}}_i},\mathit{\boldsymbol{x}}) + {b^*} \end{array} | (8) |
目前, 为解决高维问题引入的核函数主要有以下几种常用类型:
| \begin{array}{*{20}{c}} {\left( 1 \right)\;\;{\rm{多项式核函数}}\;\;\;\;\;\;\;\;\;}&{\;\;\;\;K\left( {{\mathit{\boldsymbol{x}}_i},\mathit{\boldsymbol{x}}} \right) = {{\left( {{\mathit{\boldsymbol{x}}_i}\cdot\mathit{\boldsymbol{x}} + 1} \right)}^q}}&{\left( {q = 1,2, \ldots ,n} \right)} \end{array} | (9) |
| \begin{array}{*{20}{c}} {\left( 2 \right)\;\;{\rm{径向基核函数}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;}&{K({\mathit{\boldsymbol{x}}_i},\mathit{\boldsymbol{x}}) = {\rm{exp}}( - \gamma {{\left\| {{\mathit{\boldsymbol{x}}_i} - \mathit{\boldsymbol{x}}} \right\|}^2})} \end{array} | (10) |
| \begin{array}{*{20}{c}} {\left( 3 \right)\;\;{\rm{Sigmoid \;函数}}\;\;\;\;\;\;}&{\;K({\mathit{\boldsymbol{x}}_i},\mathit{\boldsymbol{x}}) = {\rm{tan}}\;{\rm{h}}\left[ {\varphi ({\mathit{\boldsymbol{x}}_i}\mathit{\boldsymbol{\cdot x}}) + \theta } \right]} \end{array} | (11) |
PSO算法是1995年Kennedy和Eberhart受人工生命研究成果的启发, 通过模拟鸟群觅食过程中的迁徙和群聚行为而提出的一种基于群体智能的全局随机搜索算法[15]。
PSO算法中, 每个粒子都代表问题的一个潜在解, 并对应一个由被优化函数决定的适应值, 同时每个粒子还有一个由速度决定的飞翔方向和距离, 速度随自身及其他粒子的移动经验进行动态调整, 从而实现个体在可解空间中寻优。PSO首先初始化为一群随机粒子(随机解), 然后通过迭代寻找到最优解。在每一次迭代中, 粒子通过跟踪个体极值(Pbest)和群体极值(Gbest)进行更新。
假设D维搜索空间中, 由n个粒子组成的种群为X=(X1, X2, …, Xn), 其中D维向量Xi表示第i个粒子在D维搜索空间中的位置, 也表示问题的一个潜在解, 满足Xi=(Xi1, Xi2, …, XiD)T。根据目标函数可以计算出每个粒子位置Xi对应的适应度。第i个粒子的速度为Vi=(Vi1, Vi2, …, ViD)T, 其个体极值为Pi=(Pi1, Pi2, …, PiD)T, 种群的群体极值为Pg=(Pg1, Pg2, …, PgD)T。
在每次迭代中, 粒子通过个体极值和群体极值更新自身的速度和位置, 即
| \begin{array}{l} V_{id}^{k + 1} = \omega V_{id}^k + {c_1}{r_1}\left( {P_{id}^k-X_{id}^k} \right) + {c_2}{r_2}\left( {P_{gd}^k-X_{id}^k} \right)\\ \;X_{id}^{k + 1} = X_{id}^k + V_{id}^{k + 1} \end{array} | (12) |
式中:d=1, 2, …, D; i=1, 2, …, n; k为当前迭代次数; Vid为粒子速度; Xid为粒子当前位置; ω为惯性权重; c1、c2为加速度因子; r1、r2为分布于(0, 1)之间的随机数。
影响侵彻深度的因素较多, 主要包括混凝土靶体参数、动能弹着靶条件、动能弹参数、实验系统参数。为了减小计算量, 降低参数实验误差的影响, 提高预测精度及效率, 一般取同类型实验数据进行分析, 以减少影响因素的数量(同类型实验中很多影响因素是不变的, 可不考虑相同影响因素对系统特征行为的影响[9])。本研究主要针对动能弹参数、实验系统参数、混凝土靶体尺寸参数及动能弹着靶方式相同条件下, 而着靶速度和混凝土强度不同时侵彻深度的预测。
首先对测试数据进行归一化处理, 其次利用PSO算法快速地寻找全局最优参数, 最后将优化参数赋予SVM, 不断训练及验证得到预测模型。预测模型PSO-SVM构建流程见图 1, 具体建模步骤如下:(1)选取不同混凝土强度及不同着靶速度下样本n个, 从中选取n1个样本作为训练样本, 其余n2个作为测试样本(n1+n2=n), 调用scaleForSVM函数对数据进行归一化处理; (2)选择核函数类型, 通常选取径向基核函数, 同时采用PSO算法, 调用psoSVMcgForRegress函数, 选择初始参数(种群数量、迭代次数等)不断进行迭代计算, 搜索最优的模型相关参数, 即惩罚因子C及核函数中的核参数γ; (3)通过优化后的参数调用svmtrain函数进行样本训练, 获得支持向量、不为零的系数(αi-αi*)以及偏置常数b的数值, 由此建立PSO-SVM预测模型, 即建立侵彻深度与混凝土强度及着靶速度之间的非线性关系式; (4)通过训练建立的PSO-SVM预测模型, 调用svmpredict函数对测试样本(同时也对训练样本)进行预测, 再调用反归一化函数进行结果对比, 观测该模型是否满足精度要求, 若达不到精度, 可转到步骤(2)改变PSO的初始参数重新优化或改变核函数类型重新计算, 直到满足精度要求为止; (5)针对上述所建立满足精度要求的PSO-SVM预测模型, 根据svmtrain函数返回的model提供的信息, 应用MATLAB软件编写程序得到预测函数的非线性关系式, 以对同类型或相似类型中其他条件下的侵彻深度进行预测。
动能弹冲击混凝土靶体后, 对靶体产生侵彻作用。动能弹对靶体的侵彻过程中, 会对周围的混凝土产生径向压缩和切向拉伸等作用, 使其产生径向裂隙; 由于冲击面的存在, 侵彻过程还伴随着斜向剪切作用, 从而使混凝土形成不规则漏斗状破坏。实验中采用单轴抗压强度为76.6 MPa的素混凝土制成高度为584 mm、直径为600 mm的圆柱体。采用材料为高强度钢、重约250 g的卵形弹头以216 m/s的着靶速度进行正冲击, 其宏观破坏结果如图 2所示[19]。
由图 2明显可以看出, 混凝土靶体的侵彻深度一般由2部分构成, 一部分为漏斗状成坑深度, 另一部分为残孔深度。
以下援引中国工程物理研究院的实测数据对PSO-SVM预测模型进行验证[20]。为了与灰色模型(Grey Model, GM)预测结果[9, 18]对比分析, 选取1号~7号实测数据为训练样本(建模数据), 8号~14号为测试样本(验证数据), 应用MATLAB软件编制PSO-SVM程序进行训练与预测, 选用径向基核函数优化出参数C=355.5和γ=0.007 7, 然后通过不断训练得到4个支持向量、4个不为零的系数(αi-αi*)以及偏置常数b=-0.886 5, 由此可建立预测函数非线性关系式。各样本的实测值及预测值如表 1所示, 其中σc为混凝土的抗压强度, v为动能弹着靶速度, s为实测侵彻深度, s1和s2分别为采用GM和PSO-SVM方法预测的侵彻深度, δ1和δ2为GM和PSO-SVM预测值相对于实测侵彻深度的相对误差。
| Samples | No. | σc/MPa | v/(m·s-1) | s/m | s1/m | δ1/% | s2/m | δ2/% |
| Training samples | 1 | 45 | 510 | 0.597 | 0.597 | 0 | 0.592 | 0.84 |
| 2 | 23 | 510 | 0.834 | 0.742 | 11.03 | 0.839 | -0.60 | |
| 3 | 45 | 612 | 0.716 | 0.816 | -13.97 | 0.716 | 0 | |
| 4 | 23 | 612 | 1.001 | 1.089 | -8.79 | 1.001 | 0 | |
| 5 | 45 | 680 | 0.795 | 0.791 | 0.50 | 0.799 | -0.50 | |
| 6 | 23 | 680 | 1.113 | 1.129 | -1.44 | 1.107 | 0.54 | |
| 7 | 45 | 748 | 0.875 | 0.856 | 2.17 | 0.880 | -0.57 | |
| Testing samples | 8 | 23 | 748 | 1.224 | 1.204 | 1.63 | 1.213 | 0.90 |
| 9 | 45 | 850 | 0.994 | 0.971 | 2.31 | 1.001 | -0.70 | |
| 10 | 23 | 850 | 1.391 | 1.320 | 5.10 | 1.368 | 1.65 | |
| 11 | 45 | 918 | 1.074 | 1.049 | 2.33 | 1.080 | -0.56 | |
| 12 | 23 | 918 | 1.502 | 1.398 | 6.92 | 1.469 | 2.20 | |
| 13 | 45 | 1020 | 1.193 | 1.166 | 2.26 | 1.194 | -0.08 | |
| 14 | 23 | 1020 | 1.669 | 1.514 | 9.29 | 1.616 | 3.18 |
为更加形象直观地对比PSO-SVM和GM两种预测方法的预测性能, 将表 2中混凝土侵彻深度的实测值、GM预测值及PSO-SVM预测值绘制折线图, 如图 3所示。由表 1和图 3可知, 对于测试样本而言, GM预测的最大相对误差为9.29%, PSO-SVM预测的最大相对误差为3.18%。由此可见, 相对于GM预测, PSO-SVM预测的准确性相对较高, 可满足防护工程建设和设计的工程要求, 同时对混凝土侵彻效应研究具有指导意义与参考价值。此外, 采用PSO可以实现全局寻优, 能够有效解决预测模型相关参数难以确定的问题, 优化后的参数可满足预测精度的要求。
| Training samples | Testing samples | Maximum relative error/% |
| 4 (No.1-No.4) | 10 (No.5-No.14) | 10.02 |
| 6 (No.1-No.6) | 8 (No.7-No.14) | 5.43 |
| 7 (No.1-No.7) | 7 (No.8-No.14) | 3.18 |
| 8 (No.1-No.8) | 6 (No.9-No.14) | 2.85 |
| 10 (No.1-No.10) | 4 (No.11-No.14) | 1.18 |
通过支持向量数目可以看出, 训练样本中只有一部分为支持向量, 其余的为非支持向量。预测函数由支持向量确定, 与非支持向量无关, 从而避免了“维数灾难”。SVM针对小样本预测效果较好且具有较好的泛化能力, 在实际工程中样本数量总是有限的甚至很少, 因此, SVM相对于传统预测方法具有独特的优势。
采用PSO-SVM方法进行两个主要影响因素7组训练样本的预测, 其最大相对误差为3.18%;文献[17]中进行5个影响因素21组训练样本的预测, 其最大相对误差为5.5%。因此, 影响因素及训练样本的数量、内容均会对预测效果产生影响。
现按照表 1中的数据顺序选择不同的样本组合以分析训练样本数量对预测效果的影响, 其结果列于表 2中。从表 2可以看出, 随着训练样本数量增多, 最大相对误差逐渐减小, 且减小的幅度逐渐变缓直至并不明显, 但计算量逐渐增大, 因此, 在满足精度控制要求时, 选择合适的训练样本数量, 可以提高效率及节省成本。训练样本数量的确定主要与影响因素的数量、预测精度控制要求等有关, 目前还没有统一的标准, 一般需要通过反复试算才可以确定。
PSO-SVM预测模型适用于小样本情况, 其预测效果与PSO初始参数、影响因素、训练样本及核函数选取等有关。此外, 其建立的非线性关系式相对复杂, 实际工程应用时需借助编程实现。
(1) 采用同类型实验条件下两个主要影响因素7组训练样本所建立的PSO-SVM预测模型, 其预测的最大相对误差为3.18%, 可满足防护工程建设与设计的要求。PSO-SVM算法应用于动能弹侵彻混凝土靶体的深度预测合理可行。
(2) PSO-SVM预测的最大相对误差为3.18%, GM预测的最大相对误差为9.29%, 相比于GM预测, PSO-SVM预测的相对误差较小, 其预测性能明显优于GM预测, 而且PSO全局寻优可以搜索出满足精度要求的最优参数值。对于PSO-SVM预测, 选择合适的训练样本数量既可获得良好的预测效果, 又可以提高预测效率及节省成本。
(3) SVM方法的实际应用以小样本采集为先决条件, 但是具有严密理论基础的SVM方法在解决小样本、非线性、局部极小点以及高维数等实际问题中具有独特的优势, 且具有较好的应用前景, 是一种新型智能预测方法。
| [1] |
WU W, CHENG J G, MATSUBAYASHI K, et al. Superconductivity in the vicinity of antiferromagnetic order in CrAs [J]. Nature Communications, 2014, 5: 5508. doi: 10.1038/ncomms6508
|
| [2] |
CHENG J G, MATSUBAYASHI K, WU W, et al. Pressure induced superconductivity on the border of magnetic order in MnP [J]. Physical Review Letters, 2015, 114(11): 117001. doi: 10.1103/PhysRevLett.114.117001
|
| [3] |
SUN J P, MATSUURA K, YE G Z, et al. Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe [J]. Nature Communications, 2016, 7: 12146. doi: 10.1038/ncomms12146
|
| [4] |
LI Y, SUN Z, CAI J W, et al. Pressure-induced charge-order melting and reentrant charge carrier localization in the mixed-valent Pb3Rh7O15 [J]. Chinese Physics Letters, 2017, 34(8): 087201. doi: 10.1088/0256-307X/34/8/087201
|
| [5] |
ZHANG C, SUN J P, LIU F L, et al. Evidence for pressure-induced node-pair annihilation in Cd3As2 [J]. Physical Review B, 2017, 96(15): 155205. doi: 10.1103/physrevb.96.155205
|
| [6] |
MATSUDA M, LIN F K, YU R, et al. Evolution of magnetic double helix and quantum criticality near a dome of superconductivity in CrAs [J]. Physical Review X, 2018, 8(3): 031017. doi: 10.1103/PhysRevX.8.031017
|
| [7] |
SUN J P, JIAO Y Y, YI C J, et al. Magnetic-competition-induced colossal magnetoresistance in n-type HgCr2Se4 under high pressure [J]. Physical Review Letters, 2019, 123(4): 047201. doi: 10.1103/PhysRevLett.123.047201
|
| [8] |
LIU Z Y, ZHANG T, XU S X, et al. Pressure effect on the anomalous Hall effect of ferromagnetic Weyl semimetal Co3Sn2S2 [J]. Physical Review Materials, 2020, 4(4): 044203. doi: 10.1103/physrevmaterials.4.044203
|
| [9] |
CHEN K Y, WANG N N, YIN Q W, et al. Double superconducting dome and triple enhancement of Tc in the Kagome superconductor CsV3Sb5 under high pressure [J]. Physical Review Letters, 2021, 126(24): 247001. doi: 10.1103/PhysRevLett.126.247001
|
| [10] |
WANG N N, CHEN K Y, YIN Q W, et al. Competition between charge-density-wave and superconductivity in the kagome metal RbV3Sb5 [J]. Physical Review Research, 2021, 3(4): 043018. doi: 10.1103/PHYSREVRESEARCH.3.043018
|
| [11] |
YUAN H Q, GROSCHE F M, DEPPE M, et al. Observation of two distinct superconducting phases in CeCu2Si2 [J]. Science, 2003, 302(5653): 2104–2107. doi: 10.1126/science.1091648
|
| [12] |
孙建平, 王铂森, 程金光. FeSe单晶的高压研究进展 [J]. 科学通报, 2017, 62(34): 3925–3934. doi: 10.1360/N972017-00713
SUN J P, WANG B S, CHENG J G. Recent progress on the high-pressure studies of FeSe single crystal [J]. Chinese Science Bulletin, 2017, 62(34): 3925–3934. doi: 10.1360/N972017-00713
|
| [13] |
SUN J P, YE G Z, SHAHI P, et al. High-Tc superconductivity in FeSe at high pressure: dominant hole carriers and enhanced spin fluctuations [J]. Physical Review Letters, 2017, 118(14): 147004. doi: 10.1103/PhysRevLett.118.147004
|
| [14] |
SHAHI P, SUN J P, WANG S H, et al. High-Tc superconductivity up to 55 K under high pressure in a heavily electron doped Li0.36(NH3) yFe2Se2 single crystal [J]. Physical Review B, 2018, 97(2): 020508. doi: 10.1103/physrevb.97.020508
|
| [15] |
孙建平, SHAHI P, 周花雪, 等. 插层FeSe高温超导体的高压研究进展 [J]. 物理学报, 2018, 67(20): 207404. doi: 10.7498/aps.67.20181319
SUN J P, SHAHI P, ZHOU H X, et al. Effect of high pressure on intercalated FeSe high-Tc superconductors [J]. Acta Physica Sinica, 2018, 67(20): 207404. doi: 10.7498/aps.67.20181319
|
| [16] |
SUN J P, SHAHI P, ZHOU H X, et al. Reemergence of high-Tc superconductivity in the (Li1- xFe x)OHFe1- ySe under high pressure [J]. Nature Communications, 2018, 9(1): 380. doi: 10.1038/s41467-018-02843-7
|
| [17] |
LIU Z Y, DONG Q X, SHAN P F, et al. Pressure-induced metallization and structural phase transition in the quasi-one-dimensional TlFeSe2 [J]. Chinese Physical Letters, 2020, 37(4): 047102. doi: 10.1088/0256-307X/37/4/047102
|
| [18] |
SUN J P, SHI M Z, LEI B, et al. Pressure-induced second high-Tc superconducting phase in the organic-ion-intercalated (CTA)0.3FeSe single crystal [J]. Europhysics Letters, 2020, 130(6): 67004. doi: 10.1209/0295-5075/130/67004
|
| [19] |
程金光, 孙建平. 铁硒基超导体的高压研究进展 [J]. 中国科学: 物理学 力学 天文学, 2021, 51(4): 047403. doi: 10.1360/SSPMA-2020-0414
CHENG J G, SUN J P. Pressure effects on the FeSe-based superconductors [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2021, 51(4): 047403. doi: 10.1360/SSPMA-2020-0414
|
| [20] |
HSU F C, LUO J Y, YEH K W, et al. Superconductivity in the PbO-type structure α-FeSe [J]. Proceedings of the National Academy of Sciences of the United States of America, 2008, 105(38): 14262–14264. doi: 10.1073/pnas.0807325105
|
| [21] |
MEDVEDEV S, MCQUEEN T M, TROYAN I A, et al. Electronic and magnetic phase diagram of β-Fe1.01Se with superconductivity at 36.7 K under pressure [J]. Nature Materials, 2009, 8(8): 630–633. doi: 10.1038/nmat2491
|
| [22] |
HOLENSTEIN S, PACHMAYR U, GUGUCHIA Z, et al. Coexistence of low-moment magnetism and superconductivity in tetragonal FeS and suppression of Tc under pressure [J]. Physical Review B, 2016, 93(14): 140506. doi: 10.1103/PhysRevB.93.140506
|
| [23] |
LAI X F, LIU Y, LÜ X J, et al. Suppression of superconductivity and structural phase transitions under pressure in tetragonal FeS [J]. Scientific Reports, 2016, 6: 31077. doi: 10.1038/srep31077
|
| [24] |
ZHANG J, LIU F L, YING T P, et al. Observation of two superconducting domes under pressure in tetragonal FeS [J]. NPJ Quantum Materials, 2017, 2(1): 49. doi: 10.1038/s41535-017-0050-7
|
| [25] |
SHIMIZU M, TAKEMORI N, GUTERDING D, et al. Two-dome superconductivity in FeS induced by a lifshitz transition [J]. Physical Review Letters, 2018, 121(13): 137001. doi: 10.1103/PhysRevLett.121.137001
|
| [26] |
LAI X F, ZHANG H, WANG Y Q, et al. Observation of superconductivity in tetragonal FeS [J]. Journal of the American Chemical Society, 2015, 137(32): 10148–10151. doi: 10.1021/jacs.5b06687
|
| [27] |
LIN H, LI Y F, DENG Q, et al. Multiband superconductivity and large anisotropy in FeS crystals [J]. Physical Review B, 2016, 93(14): 144505. doi: 10.1103/PhysRevB.93.144505
|
| [28] |
CHENG J G, MATSUBAYASHI K, NAGASAKI S, et al. Integrated-fin gasket for palm cubic-anvil high pressure apparatus [J]. Review of Scientific Instruments, 2014, 85(9): 093907. doi: 10.1063/1.4896473
|
| [29] |
CHENG J G, WANG B S, SUN J P, et al. Cubic anvil cell apparatus for high-pressure and low-temperature physical property measurements [J]. Chinese Physics B, 2018, 27(7): 077403. doi: 10.1088/1674-1056/27/7/077403
|
| [30] |
YING T P, LAI X F, HONG X C, et al. Nodal superconductivity in FeS: evidence from quasiparticle heat transport [J]. Physical Review B, 2016, 94(10): 100504. doi: 10.1103/PhysRevB.94.100504
|
| [31] |
TERASHIMA T, KIKUGAWA N, LIN H, et al. Upper critical field and quantum oscillations in tetragonal superconducting FeS [J]. Physical Review B, 2016, 94(10): 100503. doi: 10.1103/PhysRevB.94.100503
|
| [32] |
BORG C K H, ZHOU X Q, ECKBERG C, et al. Strong anisotropy in nearly ideal tetrahedral superconducting FeS single crystals [J]. Physical Review B, 2016, 93(9): 094522. doi: 10.1103/PhysRevB.93.094522
|
| [33] |
LUO X G, CHEN X H. Crystal structure and phase diagrams of iron-based superconductors [J]. Science China Materials, 2015, 58(1): 77–89. doi: 10.1007/s40843-015-0022-9
|
| [34] |
MIZUGUCHI Y, TOMIOKA F, TSUDA S, et al. Substitution effects on FeSe superconductor [J]. Journal of the Physical Society of Japan, 2009, 78(7): 074712. doi: 10.1143/JPSJ.78.074712
|
| [35] |
MAN H R, GUO J G, ZHANG R, et al. Spin excitations and the Fermi surface of superconducting FeS [J]. NPJ Quantum Materials, 2017, 2(1): 14. doi: 10.1038/s41535-017-0019-6
|
| [36] |
BAUM A, MILOSAVLJEVIĆ A, LAZAREVIĆ N, et al. Phonon anomalies in FeS [J]. Physical Review B, 2018, 97(5): 054306. doi: 10.1103/PhysRevB.97.054306
|
| [37] |
TAKELE S, HEARNE G R. Electrical transport, magnetism, and spin-state configurations of high-pressure phases of FeS [J]. Physical Review B, 1999, 60(7): 4401–4403. doi: 10.1103/PhysRevB.60.4401
|
| [1] | CHEN Yinqi, WANG Hongbo. Hydrogen-Rich Superconductors with High Critical Temperature under High Pressure[J]. Chinese Journal of High Pressure Physics, 2024, 38(2): 020103. doi: 10.11858/gywlxb.20230842 |
| [3] | WANG Ningning, SHAN Pengfei, CUI Qi, WANG Gang, CHENG Jinguang. Synthesis and High-Pressure Regulation of Hexagonal ReO3[J]. Chinese Journal of High Pressure Physics, 2024, 38(5): 050105. doi: 10.11858/gywlxb.20240843 |
| [4] | FA Zhixiang, WANG Wendan, LI Ao, YU Shaonan, WANG Liping. Compression Behavior of Tetragonal PbTeO3 Crystals under High Pressure[J]. Chinese Journal of High Pressure Physics, 2023, 37(1): 011102. doi: 10.11858/gywlxb.20220646 |
| [5] | GUO Jing, SUN Liling. High Pressure Studies on Superconductivity of Strongly Correlated Electron Systems[J]. Chinese Journal of High Pressure Physics, 2022, 36(1): 010101. doi: 10.11858/gywlxb.20210889 |
| [6] | ZHAO Wendi, DUAN Defang, CUI Tian. New Developments of Hydrogen-Based High-Temperature Superconductors under High Pressure[J]. Chinese Journal of High Pressure Physics, 2021, 35(2): 020101. doi: 10.11858/gywlxb.20210727 |
| [7] | XIE Yafei, JIANG Changguo, LUO Xingli, TAN Dayong, XIAO Wansheng. Synthesis of 6H-Type Hexagonal Perovskite Phase of BaGeO3 at High Temperature and High Pressure[J]. Chinese Journal of High Pressure Physics, 2021, 35(5): 051201. doi: 10.11858/gywlxb.20210761 |
| [8] | SHI Zhentian, YANG Xujia, WANG Haoyang, QIAO Li. Superconducting Transition of Nb3Sn Single Crystal under High-Pressure[J]. Chinese Journal of High Pressure Physics, 2021, 35(2): 021102. doi: 10.11858/gywlxb.20200615 |
| [9] | DONG Bingshun, WANG Haikuo, TONG Feifei, HOU Zhiqiang, LI Zhen, LIU Tong, ZANG Jinhao, YANG Xigui. Fabrication of Submicron Tetragonal Polycrystalline ZrO2 by the Transformation of Micro Monoclinic ZrO2 under High Pressure[J]. Chinese Journal of High Pressure Physics, 2019, 33(2): 020104. doi: 10.11858/gywlxb.20190709 |
| [10] | GUO Chun-Hai, ZHANG Wen-Wu, RU Hao-Lei. Numerical Simulation of High Pressure Micro Water Jet Modulation with the Constraint of Gas Flow[J]. Chinese Journal of High Pressure Physics, 2017, 31(5): 585-592. doi: 10.11858/gywlxb.2017.05.012 |
| [11] | JIN Chang-Qing. The High Pressure Synthesis and Properties of Apical Oxygen Doped High Tc Superconductors[J]. Chinese Journal of High Pressure Physics, 2004, 18(1): 4-9 . doi: 10.11858/gywlxb.2004.01.002 |
| [12] | LI Shao-Chun, ZHU Jia-Lin, YU Ri-Cheng, LI Feng-Ying, LIU Zhen-Xing, JIN Chang-Qing. High Pressure Synthesis of Bulk MgB2 Superconductor[J]. Chinese Journal of High Pressure Physics, 2001, 15(3): 226-228 . doi: 10.11858/gywlxb.2001.03.010 |
| [13] | YAO Yu-Shu, HUANG Xin-Ming, WU Bing-Qing, JIN Chang-Qing, WANG Wen-Kui. High Density Bi-System Superconductor Prepared under High Pressure[J]. Chinese Journal of High Pressure Physics, 1991, 5(2): 112-117 . doi: 10.11858/gywlxb.1991.02.005 |
| [14] | WU Bing-Qing, JIN Chang-Qing, WANG Wen-Kui, YAO Yu-Shu. Microstructures of Superconducting BiPbSrCaCuO Ceramics Treated by High Pressure[J]. Chinese Journal of High Pressure Physics, 1991, 5(2): 104-111 . doi: 10.11858/gywlxb.1991.02.004 |
| [15] | CUI De-Liang, LIU Hong-Jian, WANG Yi-Feng, LI Li-Ping, SU Wen-Hui. Effects of High Pressure Treatment on the Superconductivity of BiSrCaCu2Oy[J]. Chinese Journal of High Pressure Physics, 1991, 5(1): 20-26 . doi: 10.11858/gywlxb.1991.01.004 |
| [16] | HAN Cui-Ying. Properties of High-Tc Superconductors under High Pressure and Low Temperature[J]. Chinese Journal of High Pressure Physics, 1991, 5(1): 35-45 . doi: 10.11858/gywlxb.1991.01.006 |
| [17] | WANG Huai-Yu, ZHANG Li-Yuan, LIU Fu-Sui, WANG En-Ge. The Electronic Structure of High Temperature Superconducting Material YBa2Cu3O7 under High Pressure[J]. Chinese Journal of High Pressure Physics, 1990, 4(3): 194-203 . doi: 10.11858/gywlxb.1990.03.005 |
| [18] | ZHANG Jin-Long, LIU Yong, CUI Chang-Geng, YANG Qian-Sheng. Behavior of Two Oxide Superconductors under High Pressure[J]. Chinese Journal of High Pressure Physics, 1989, 3(4): 298-301 . doi: 10.11858/gywlxb.1989.04.006 |
| [19] | HUANG Xin-Ming, CUI Chang-Geng, CHEN Hong, XU Xiao-Ping, HE Shou-An, WANG Wen-Kui. Heat Treatment and Sinter of Oxide Superconductors under High Pressure[J]. Chinese Journal of High Pressure Physics, 1988, 2(2): 159-164 . doi: 10.11858/gywlxb.1988.02.010 |
| [20] | HUANG Xin-Ming, HE Shou-An, WANG Wen-Kui. Superconductivity of Crystallized Phases from Amorphous La80Al20[J]. Chinese Journal of High Pressure Physics, 1987, 1(2): 130-137 . doi: 10.11858/gywlxb.1987.02.005 |
Figures(4)
Supported by: Beijing Renhe Information Technology Co. Ltd support:
info@rhhz.net
PAN Qiang, ZHANG Jichun, XIAO Qinghua, ZOU Xinkuan, SHI Hongchao. Prediction of Penetration Depth of Projectiles into Concrete Targets Based on PSO-SVM[J]. Chinese Journal of High Pressure Physics, 2018, 32(2): 025102. doi: 10.11858/gywlxb.20170577
| Samples | No. | σc/MPa | v/(m·s-1) | s/m | s1/m | δ1/% | s2/m | δ2/% |
| Training samples | 1 | 45 | 510 | 0.597 | 0.597 | 0 | 0.592 | 0.84 |
| 2 | 23 | 510 | 0.834 | 0.742 | 11.03 | 0.839 | -0.60 | |
| 3 | 45 | 612 | 0.716 | 0.816 | -13.97 | 0.716 | 0 | |
| 4 | 23 | 612 | 1.001 | 1.089 | -8.79 | 1.001 | 0 | |
| 5 | 45 | 680 | 0.795 | 0.791 | 0.50 | 0.799 | -0.50 | |
| 6 | 23 | 680 | 1.113 | 1.129 | -1.44 | 1.107 | 0.54 | |
| 7 | 45 | 748 | 0.875 | 0.856 | 2.17 | 0.880 | -0.57 | |
| Testing samples | 8 | 23 | 748 | 1.224 | 1.204 | 1.63 | 1.213 | 0.90 |
| 9 | 45 | 850 | 0.994 | 0.971 | 2.31 | 1.001 | -0.70 | |
| 10 | 23 | 850 | 1.391 | 1.320 | 5.10 | 1.368 | 1.65 | |
| 11 | 45 | 918 | 1.074 | 1.049 | 2.33 | 1.080 | -0.56 | |
| 12 | 23 | 918 | 1.502 | 1.398 | 6.92 | 1.469 | 2.20 | |
| 13 | 45 | 1020 | 1.193 | 1.166 | 2.26 | 1.194 | -0.08 | |
| 14 | 23 | 1020 | 1.669 | 1.514 | 9.29 | 1.616 | 3.18 |
| Training samples | Testing samples | Maximum relative error/% |
| 4 (No.1-No.4) | 10 (No.5-No.14) | 10.02 |
| 6 (No.1-No.6) | 8 (No.7-No.14) | 5.43 |
| 7 (No.1-No.7) | 7 (No.8-No.14) | 3.18 |
| 8 (No.1-No.8) | 6 (No.9-No.14) | 2.85 |
| 10 (No.1-No.10) | 4 (No.11-No.14) | 1.18 |
| Samples | No. | σc/MPa | v/(m·s-1) | s/m | s1/m | δ1/% | s2/m | δ2/% |
| Training samples | 1 | 45 | 510 | 0.597 | 0.597 | 0 | 0.592 | 0.84 |
| 2 | 23 | 510 | 0.834 | 0.742 | 11.03 | 0.839 | -0.60 | |
| 3 | 45 | 612 | 0.716 | 0.816 | -13.97 | 0.716 | 0 | |
| 4 | 23 | 612 | 1.001 | 1.089 | -8.79 | 1.001 | 0 | |
| 5 | 45 | 680 | 0.795 | 0.791 | 0.50 | 0.799 | -0.50 | |
| 6 | 23 | 680 | 1.113 | 1.129 | -1.44 | 1.107 | 0.54 | |
| 7 | 45 | 748 | 0.875 | 0.856 | 2.17 | 0.880 | -0.57 | |
| Testing samples | 8 | 23 | 748 | 1.224 | 1.204 | 1.63 | 1.213 | 0.90 |
| 9 | 45 | 850 | 0.994 | 0.971 | 2.31 | 1.001 | -0.70 | |
| 10 | 23 | 850 | 1.391 | 1.320 | 5.10 | 1.368 | 1.65 | |
| 11 | 45 | 918 | 1.074 | 1.049 | 2.33 | 1.080 | -0.56 | |
| 12 | 23 | 918 | 1.502 | 1.398 | 6.92 | 1.469 | 2.20 | |
| 13 | 45 | 1020 | 1.193 | 1.166 | 2.26 | 1.194 | -0.08 | |
| 14 | 23 | 1020 | 1.669 | 1.514 | 9.29 | 1.616 | 3.18 |
| Training samples | Testing samples | Maximum relative error/% |
| 4 (No.1-No.4) | 10 (No.5-No.14) | 10.02 |
| 6 (No.1-No.6) | 8 (No.7-No.14) | 5.43 |
| 7 (No.1-No.7) | 7 (No.8-No.14) | 3.18 |
| 8 (No.1-No.8) | 6 (No.9-No.14) | 2.85 |
| 10 (No.1-No.10) | 4 (No.11-No.14) | 1.18 |
下载:
DownLoad:
