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基于事件触发的全信息粒子群优化器及其应用

王闯 韩非 申雨轩 李学贵 董宏丽

王闯, 韩非, 申雨轩, 李学贵, 董宏丽. 基于事件触发的全信息粒子群优化器及其应用. 自动化学报, 2020, 45(x): 1−13 doi: 10.16383/j.aas.c200621
引用本文: 王闯, 韩非, 申雨轩, 李学贵, 董宏丽. 基于事件触发的全信息粒子群优化器及其应用. 自动化学报, 2020, 45(x): 1−13 doi: 10.16383/j.aas.c200621
Wang Chuang, Han Fei, Shen Yu-Xuan, LI Xue-Gui, Dong Hong-Li. Full-Information particle swarm optimizer based on event-triggering strategy and its applications. Acta Automatica Sinica, 2020, 45(x): 1−13 doi: 10.16383/j.aas.c200621
Citation: Wang Chuang, Han Fei, Shen Yu-Xuan, LI Xue-Gui, Dong Hong-Li. Full-Information particle swarm optimizer based on event-triggering strategy and its applications. Acta Automatica Sinica, 2020, 45(x): 1−13 doi: 10.16383/j.aas.c200621

基于事件触发的全信息粒子群优化器及其应用

doi: 10.16383/j.aas.c200621
基金项目: 国家自然科学基金(61873058, 61933007, 62073070), 黑龙江省自然科学基金重点项目(ZD2019F001), 中国博士后科学基金资助项目(2017M621242, 2020T130092)资助
详细信息
    作者简介:

    王闯:东北石油大学博士研究生. 主要研究方向为深度学习与管道完整性分析. E-mail: wangchuang64@126.com

    韩非:东北石油大学人工智能能源研究院副教授. 2017年获得上海理工大学系统分析与集成专业博士学位. 主要研究方向为分布式滤波与控制, 深度学习和强化学习. E-mail: tomcumt@126.com

    申雨轩:东北石油大学人工智能能源研究院讲师. 2020年获得东华大学控制科学与工程专业博士学位. 主要研究方向为网络化系统的滤波与控制. E-mail: shenyuxuan5973@163.com

    李学贵:东北石油大学计算机与信息技术学院副教授. 2017年获得东北石油大学地质资源与地质工程专业博士学位. 主要研究方向为深度学习与大数据分析, 微地震监测技术. E-mail: lixg82@163.com

    董宏丽:东北石油大学人工智能能源研究院教授. 2012年获得哈尔滨工业大学控制科学与工程专业博士学位. 主要研究方向为网络化控制系统, 智能控制, 传感器网络信息处理. 本文通讯作者. E-mail: shiningdhl@gmail.com

Full-Information Particle Swarm Optimizer Based on Event-Triggering Strategy and its Applications

Funds: Supported by the National Natural Science Foundation of China (61873058, 61933007, 62073070), the Key Project of Natural Science Foundation of Heilongjiang Province of China(ZD2019F001), the Postdoctoral Science Foundation of China (2017M621242, 2020T130092)
  • 摘要: 针对标准粒子群优化算法存在早熟收敛和容易陷入局部最优的问题, 本文提出了一种基于事件触发的全信息粒子群优化算法(Event-Triggering-Based Full-Information Particle Swarm Optimization, EFPSO). 首先, 引入一类基于粒子空间特性的事件触发策略实现粒子群优化算法(Particle Swarm Optimization, PSO) 的模态切换, 更好地维持了算法搜索和收敛能力之间的动态平衡. 然后, 鉴于引入历史信息能够降低算法陷入局部最优的可能性, 提出一种全信息策略来克服PSO算法搜索能力不足的缺陷. 数值仿真实验表明, EFPSO算法在种群多样性、收敛率、成功率方面是优于其它改进的PSO算法. 最后, 应用EFPSO算法对变分模态分解(Variational Mode Decomposition, VMD)去噪算法进行改进, 并在现场管道信号去噪取得了很好的效果.
  • 图  1  PSO算法寻优过程

    Fig.  1  Optimization process of the PSO algorithm

    图  2  EFPSO算法流程图

    Fig.  2  The flowchart of the EFPSO algorithm

    图  5  Rastrigin函数收敛特性

    Fig.  5  Convergence characteristics of Rastrigin

    图  6  Schwefel 2.22函数收敛特性

    Fig.  6  Convergence characteristics of Schwefel 2.22

    图  7  Schwefel 1.2函数收敛特性

    Fig.  7  Convergence characteristics of Schwefel 1.2

    图  8  Griewank函数收敛特性

    Fig.  8  Convergence characteristics of Griewank

    图  9  Penalized 1函数收敛特性

    Fig.  9  Convergence characteristics of Penalized 1

    图  3  Sphere函数收敛特性

    Fig.  3  Convergence characteristics of Sphere

    图  10  Step 函数收敛特性

    Fig.  10  Convergence characteristics of Step

    图  4  Ackley函数收敛特性

    Fig.  4  Convergence characteristics of Ackley

    图  11  原始现场管道信号

    Fig.  11  Signal of original pipeline

    图  13  VMD算法去噪后的现场管道信号

    Fig.  13  Pipeline signal denoised by VMD algorithm

    图  14  PSO-VMD算法去噪后的现场管道信号

    Fig.  14  Pipeline signal denoised by PSO-VMD algorithm

    图  16  EFPSO优化的VMD去噪算法适应度函数收敛曲线

    Fig.  16  Convergence curve of the EFPSO optimized VMD denoising algorithm

    图  12  EMD算法去噪后的现场管道信号

    Fig.  12  Pipeline signal denoised by EMD algorithm

    图  15  EFPSO-VMD算法去噪后的现场管道信号

    Fig.  15  Pipeline signal denoised by EFPSO-VMD algorithm

    表  1  基准函数配置

    Table  1  The benchmark function configuration

    函数 名称 搜索范围 维数 阈值 最优值
    $f_{1}(x)$ Sphere [−100 100] 20 0.01 0
    $f_{2}(x)$ Ackley [−32 32] 20 0.01 0
    $f_{3}(x)$ Rastrigin [−5.12 5.12] 20 50 0
    $f_{4}(x)$ Schwefel 2.22 [−10 10] 20 0.01 0
    $f_{5}(x)$ Schwefel 1.2 [−100 100] 20 0.01 0
    $f_{6}(x)$ Griewank [−600 600] 20 0.01 0
    $f_{7}(x)$ Penalized 1 [−100 100] 20 0.01 0
    $f_{8}(x)$ Step [−100 100] 20 0.01 0
    下载: 导出CSV

    表  2  六种PSO算法测试结果统计

    Table  2  Six PSO algorithms test results statistics

    PSO-LDIW PSO-TVAC PSO-CK SDPSO MDPSO EFPSO
    $f_{1}(x)$ Min $2.44\times10^{-202}$ $8.44\times10^{-152}$ 0 $6.85\times10^{-13}$ $7.57\times10^{-68}$ $1.60\times10^{-139}$
    Mean $1.90\times10^{-188}$ $3.49\times10^{-58}$ 0 $4.26\times10^{-9}$ $2.99\times10^{-46}$ $1.63\times10^{-75}$
    Std.Dev 0 $2.47\times10^{-57}$ 0 $9.72\times10^{-9}$ $1.89\times10^{-45}$ $7.32\times10^{-75}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{2}(x)$ Min $2.66\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $4.09\times10^{-7}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$
    Mean $5.15\times10^{-15}$ $5.50\times10^{-15}$ $2.72$ $7.14\times10^{-6}$ $8.06\times10^{-15}$ $5.50\times10^{-15}$
    Std.Dev $1.64\times10^{-15}$ $1.43\times10^{-15}$ $4.00$ $5.89\times10^{-6}$ $3.22\times10^{-15}$ $1.45\times10^{-15}$
    Ratio 100% 100% 20% 100% 100% 100%
    $f_{3}(x)$ Min $3.97$ $2.98$ $20.8$ $3.99$ $5.96$ $4.97$
    Mean $17.1$ $10.2$ $56.3$ $19.5$ $21.1$ $ 9.50$
    Std.Dev $15.3$ $4.10$ $22.6$ $12.7$ $12.3$ $2.44$
    Ratio 96% 100% 50% 94% 98% 100%
    $f_{4}(x)$ Min $5.09\times10^{-119}$ $1.07\times10^{-37}$ $6.60\times10^{-65}$ $2.46\times10^{-8}$ $4.37\times10^{-34}$ $1.99\times10^{-32}$
    Mean $12.6$ $6.00\times10^{-1}$ $3.11\times10^{-3}$ $3.00$ $1.40$ $2.96\times10^{-18}$
    Std.Dev $11.9$ $2.39$ $8.40$ $5.05$ $3.50$ $1.32\times10^{-17}$
    Ratio 28% 94% 44% 72% 86% 100%
    $f_{5}(x)$ Min $4.31\times10^{-27}$ $4.15\times10^{-33}$ $2.70\times10^{-104}$ $9.40\times10^{-2}$ $1.92\times10^{-21}$ $6.56\times10^{-26}$
    Mean $2.56\times10^{3}$ 133 $1.33\times10^{3}$ 204 533 $3.32\times10^{-15}$
    Std.Dev $3.91\times10^{3}$ 942 $2.49\times10^{3}$ 988 $1.63\times10^{3}$ $1.12\times10^{-14}$
    Ratio 64% 98% 76% 0% 90% 100%
    $f_{6}(x)$ Min 0 0 0 $2.98\times10^{-13}$ 0 0
    Mean $1.84$ $3.69\times10^{-2}$ $1.82$ $2.43\times10^{-2}$ $2.82\times10^{-2}$ $2.03\times10^{-2}$
    Std.Dev $12.7$ $2.92\times10^{-2}$ $12.7$ $2.08\times10^{-2}$ $2.80\times10^{-2}$ $2.35\times10^{-2}$
    Ratio 12% 14% 28% 34% 36% 40%
    $f_{7}(x)$ Min $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $3.77\times10^{-16}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$
    Mean $2.35\times10^{-32}$ $2.43\times10^{-32}$ $2.60\times10^{-1}$ $3.46\times10^{-9}$ $2.37\times10^{-32}$ $ 2.35\times10^{-32}$
    Std.Dev $2.73\times10^{-34}$ $4.49\times10^{-33}$ $5.17\times10^{-1}$ $1.70\times10^{-8}$ $1.09\times10^{-33}$ $2.80\times10^{-48}$
    Ratio 100% 100% 52% 100% 100% 100%
    $f_{8}(x)$ Min 0 0 0 0 0 0
    Mean 200 0 401 0 0 0
    Std.Dev $1.41\times10^{3}$ 0 $1.97\times10^{3}$ 0 0 0
    Ratio 98% 100% 62% 100% 100% 100%
    下载: 导出CSV

    表  3  不同$\gamma_i(k)$的EFPSO算法统计结果比较

    Table  3  The statistical results of the EFPSO algorithm with different $\gamma_i(k)$ are compared

    $\gamma_i(k)=0.2$ $\gamma_i(k)=0.3$ $\gamma_i(k)=0.4$ $\gamma_i(k)=0.5$ $\gamma_i(k)=0.6$ $\gamma_i(k)=0.7$
    $f_{1}(x)$ Min $1.42\times10^{-25}$ $2.31\times10^{-101}$ $1.69\times10^{-139}$ $6.03\times10^{-90}$ $7.91\times10^{-53}$ $5.14\times10^{-30}$
    Mean $5.14\times10^{-35}$ $3.34\times10^{-60}$ $1.63\times10^{-75}$ $4.32\times10^{-65}$ $2.24\times10^{-32}$ $7.98\times10^{-7}$
    Std.Dev $3.21\times10^{-35}$ $3.95\times10^{-60}$ $7.32\times10^{-75}$ $3.98\times10^{-65}$ $3.41\times10^{-32}$ $5.31\times10^{-7}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{2}(x)$ Min $2.60\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $3.45\times10^{-12}$ $2.97\times10^{-7}$
    Mean $3.91\times10^{-14}$ $6.29\times10^{-15}$ $5.50\times10^{-15}$ $7.14\times10^{-14}$ $3.63\times10^{-10}$ $5.48\times10^{-7}$
    Std.Dev $4.32\times10^{-14}$ $8.91\times10^{-15}$ $1.45\times10^{-15}$ $8.93\times10^{-14}$ $2.97\times10^{-10}$ $6.92\times10^{-7}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{3}(x)$ Min $9.01$ $12.6$ $4.97$ $9.12$ $13.1$ $11.1$
    Mean $18.3$ $17.2$ $9.50$ $12.9$ $20.0$ $13.8$
    Std.Dev $6.59$ $3.33$ $2.44$ $3.39$ $8.18$ $2.23$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{4}(x)$ Min $1.69\times10^{-24}$ $1.59\times10^{-24}$ $1.99\times10^{-32}$ $2.24\times10^{-40}$ $2.41\times10^{-35}$ $5.71\times10^{-20}$
    Mean $5.38\times10^{-16}$ $1.78\times10^{-16}$ $2.96\times10^{-18}$ $2.56\times10^{-32}$ $7.98\times10^{-22}$ $6.94\times10^{-7}$
    Std.Dev $7.69\times10^{-17}$ $0.97\times10^{-16}$ $1.32\times10^{-17}$ $1.68\times10^{-32}$ $6.54\times10^{-22}$ $3.89\times10^{-7}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{5}(x)$ Min $2.31\times10^{-28}$ $7.34\times10^{-30}$ $6.56\times10^{-26}$ $7.19\times10^{-20}$ $5.34\times10^{-20}$ $1.53\times10^{-9}$
    Mean $5.46\times10^{-15}$ $3.84\times10^{-15}$ $3.32\times10^{-15}$ $7.34\times10^{-9}$ $8.91\times10^{-9}$ $8.72\times10^{-5}$
    Std.Dev $2.49\times10^{-15}$ $2.96\times10^{-15}$ $1.12\times10^{-14}$ $1.36\times10^{-9}$ $6.37\times10^{-9}$ $6.54\times10^{-5}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{6}(x)$ Min $2.72\times10^{-7}$ $1.31\times10^{-7}$ 0 $5.18\times10^{-7}$ $9.07\times10^{-7}$ $1.01\times10^{-6}$
    Mean $1.54\times10^{-2}$ $1.19\times10^{-2}$ $2.03\times10^{-2}$ $4.45\times10^{-3}$ $1.03\times10^{-2}$ $2.40\times10^{-2}$
    Std.Dev $3.04\times10^{-2}$ $9.57\times10^{-3}$ $2.35\times10^{-2}$ $6.16\times10^{-3}$ $1.05\times10^{-2}$ $3.15\times10^{-2}$
    Ratio 30% 40% 40% 42% 38% 36%
    $f_{7}(x)$ Min $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $4.67\times10^{-20}$ $2.37\times10^{-16}$
    Mean $2.43\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $8.96\times10^{-20}$ $ 8.91\times10^{-9}$
    Std.Dev $3.71\times10^{-34}$ $3.69\times10^{-33}$ $2.80\times10^{-48}$ $4.96\times10^{-33}$ $7.69\times10^{-20}$ $7.34\times10^{-8}$
    Ratio 100% 100% 100% 100% 100% 100%
    $f_{8}(x)$ Min 0 0 0 0 0 0
    Mean 0 0 0 0 0 0
    Std.Dev 0 0 0 0 0 0
    Ratio 100% 100% 100% 100% 100% 100%
    下载: 导出CSV

    表  4  测试算法的信噪比和均方误差

    Table  4  SNR and MSE of test algorithm

    算法 信噪比(SNR) 均方误差(MSE)
    EMD 28.3163 0.2429
    VMD 28.4436 0.2394
    PSO-VMD 28.4799 0.2384
    本文算法 28.6010 0.2351
    下载: 导出CSV
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  • 收稿日期:  2020-08-05
  • 录用日期:  2020-12-01
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