Full-information Particle Swarm Optimizer Based on Event-triggering Strategy and Its Applications
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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、成功率方面优于其他改进的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.Abstract: In this paper, an event-triggering-based full-information particle swarm optimization algorithm (EFPSO) is proposed with the purpose of decreasing the possibility of premature convergence and local optimization. First of all, an event-triggering strategy is employed to achieve the mode switching of the particle swarm optimization (PSO) algorithms in terms of the spatial properties of the particles, which better maintains a dynamic balance between the convergence and population diversity. Next, a full-information strategy is introduced to overcome the defect, i.e., the poor exploration ability of the PSO algorithm, where the historical information is considered to reduce the possibility of falling into the local optimum. Experiment results demonstrate the superiority of the proposed EFPSO algorithm over existing popular PSO algorithms in terms of population diversity, convergence rate, and success ratio. Finally, an EFPSO-optimized variational mode decomposition (VMD) denoising algorithm is designed and applied successfully in the field pipeline signal denoising.
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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
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 $f_{4}(x)$ Schwefe 2.22 [−10 10] 20 0.01 0 $f_{5}(x)$ Schwefe 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 
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表 2 6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 $f_{1}(x)$ 最小值 $2.44\times10^{-202}$ $8.44\times10^{-152}$ 0 $6.85\times10^{-13}$ $7.57\times10^{-68}$ $1.60\times10^{-139}$ 均值 $1.90\times10^{-188}$ $3.49\times10^{-58}$ 0 $4.26\times10^{-9}$ $2.99\times10^{-46}$ $1.63\times10^{-75}$ 标准差 0 $2.47\times10^{-57}$ 0 $9.72\times10^{-9}$ $1.89\times10^{-45}$ $7.32\times10^{-75}$ 成功率(%) 100 100 100 100 100 100 $f_{2}(x)$ 最小值 $2.66\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $4.09\times10^{-7}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ 均值 $5.15\times10^{-15}$ $5.50\times10^{-15}$ $2.72$ $7.14\times10^{-6}$ $8.06\times10^{-15}$ $5.50\times10^{-15}$ 标准差 $1.64\times10^{-15}$ $1.43\times10^{-15}$ $4.00$ $5.89\times10^{-6}$ $3.22\times10^{-15}$ $1.45\times10^{-15}$ 成功率(%) 100 100 20 100 100 100 $f_{3}(x)$ 最小值 $3.97$ $2.98$ $20.8$ $3.99$ $5.96$ $4.97$ 均值 $17.1$ $10.2$ $56.3$ $19.5$ $21.1$ $ 9.50$ 标准差 $15.3$ $4.10$ $22.6$ $12.7$ $12.3$ $2.44$ 成功率(%) 96 100 50 94 98 100 $f_{4}(x)$ 最小值 $5.09\times10^{-119}$ $1.07\times10^{-37}$ $6.60\times10^{-65}$ $2.46\times10^{-8}$ $4.37\times10^{-34}$ $1.99\times10^{-32}$ 均值 $12.6$ $6.00\times10^{-1}$ $3.11\times10^{-3}$ $3.00$ $1.40$ $2.96\times10^{-18}$ 标准差 $11.9$ $2.39$ $8.40$ $5.05$ $3.50$ $1.32\times10^{-17}$ 成功率(%) 28 94 44 72 86 100 $f_{5}(x)$ 最小值 $4.31\times10^{-27}$ $4.15\times10^{-33}$ $2.70\times10^{-104}$ $9.40\times10^{-2}$ $1.92\times10^{-21}$ $6.56\times10^{-26}$ 均值 $2.56\times10^{3}$ 133 $1.33\times10^{3}$ 204 533 $3.32\times10^{-15}$ 标准差 $3.91\times10^{3}$ 942 $2.49\times10^{3}$ 988 $1.63\times10^{3}$ $1.12\times10^{-14}$ 成功率(%) 64 98 76 0 90 100 $f_{6}(x)$ 最小值 0 0 0 $2.98\times10^{-13}$ 0 0 均值 $1.84$ $3.69\times10^{-2}$ $1.82$ $2.43\times10^{-2}$ $2.82\times10^{-2}$ $2.03\times10^{-2}$ 标准差 $12.7$ $2.92\times10^{-2}$ $12.7$ $2.08\times10^{-2}$ $2.80\times10^{-2}$ $2.35\times10^{-2}$ 成功率(%) 12 14 28 34 36 40 $f_{7}(x)$ 最小值 $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $3.77\times10^{-16}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ 均值 $2.35\times10^{-32}$ $2.43\times10^{-32}$ $2.60\times10^{-1}$ $3.46\times10^{-9}$ $2.37\times10^{-32}$ $ 2.35\times10^{-32}$ 标准差 $2.73\times10^{-34}$ $4.49\times10^{-33}$ $5.17\times10^{-1}$ $1.70\times10^{-8}$ $1.09\times10^{-33}$ $2.80\times10^{-48}$ 成功率(%) 100 100 52 100 100 100 $f_{8}(x)$ 最小值 0 0 0 0 0 0 均值 200 0 401 0 0 0 标准差 $1.41\times10^{3}$ 0 $1.97\times10^{3}$ 0 0 0 成功率(%) 98 100 62 100 100 100
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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$\gamma_i(k)=0.2$ $\gamma_i(k)=0.3$ $\gamma_i(k)=0.4$ $\gamma_i(k)=0.5$ $\gamma_i(k)=0.6$ $\gamma_i(k)=0.7$ $f_{1}(x)$ 最小值 $1.42\times10^{-25}$ $2.31\times10^{-101}$ $1.69\times10^{-139}$ $6.03\times10^{-90}$ $7.91\times10^{-53}$ $5.14\times10^{-30}$ 均值 $5.14\times10^{-35}$ $3.34\times10^{-60}$ $1.63\times10^{-75}$ $4.32\times10^{-65}$ $2.24\times10^{-32}$ $7.98\times10^{-7}$ 标准差 $3.21\times10^{-35}$ $3.95\times10^{-60}$ $7.32\times10^{-75}$ $3.98\times10^{-65}$ $3.41\times10^{-32}$ $5.31\times10^{-7}$ 成功率(%) 100 100 100 100 100 100 $f_{2}(x)$ 最小值 $2.60\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $2.66\times10^{-15}$ $3.45\times10^{-12}$ $2.97\times10^{-7}$ 均值 $3.91\times10^{-14}$ $6.29\times10^{-15}$ $5.50\times10^{-15}$ $7.14\times10^{-14}$ $3.63\times10^{-10}$ $5.48\times10^{-7}$ 标准差 $4.32\times10^{-14}$ $8.91\times10^{-15}$ $1.45\times10^{-15}$ $8.93\times10^{-14}$ $2.97\times10^{-10}$ $6.92\times10^{-7}$ 成功率(%) 100 100 100 100 100 100 $f_{3}(x)$ 最小值 $9.01$ $12.6$ $4.97$ $9.12$ $13.1$ $11.1$ 均值 $18.3$ $17.2$ $9.50$ $12.9$ $20.0$ $13.8$ 标准差 $6.59$ $3.33$ $2.44$ $3.39$ $8.18$ $2.23$ 成功率(%) 100 100 100 100 100 100 $f_{4}(x)$ 最小值 $1.69\times10^{-24}$ $1.59\times10^{-24}$ $1.99\times10^{-32}$ $2.24\times10^{-40}$ $2.41\times10^{-35}$ $5.71\times10^{-20}$ 均值 $5.38\times10^{-16}$ $1.78\times10^{-16}$ $2.96\times10^{-18}$ $2.56\times10^{-32}$ $7.98\times10^{-22}$ $6.94\times10^{-7}$ 标准差 $7.69\times10^{-17}$ $0.97\times10^{-16}$ $1.32\times10^{-17}$ $1.68\times10^{-32}$ $6.54\times10^{-22}$ $3.89\times10^{-7}$ 成功率(%) 100 100 100 100 100 100 $f_{5}(x)$ 最小值 $2.31\times10^{-28}$ $7.34\times10^{-30}$ $6.56\times10^{-26}$ $7.19\times10^{-20}$ $5.34\times10^{-20}$ $1.53\times10^{-9}$ 均值 $5.46\times10^{-15}$ $3.84\times10^{-15}$ $3.32\times10^{-15}$ $7.34\times10^{-9}$ $8.91\times10^{-9}$ $8.72\times10^{-5}$ 标准差 $2.49\times10^{-15}$ $2.96\times10^{-15}$ $1.12\times10^{-14}$ $1.36\times10^{-9}$ $6.37\times10^{-9}$ $6.54\times10^{-5}$ 成功率(%) 100 100 100 100 100 100 $f_{6}(x)$ 最小值 $2.72\times10^{-7}$ $1.31\times10^{-7}$ 0 $5.18\times10^{-7}$ $9.07\times10^{-7}$ $1.01\times10^{-6}$ 均值 $1.54\times10^{-2}$ $1.19\times10^{-2}$ $2.03\times10^{-2}$ $4.45\times10^{-3}$ $1.03\times10^{-2}$ $2.40\times10^{-2}$ 标准差 $3.04\times10^{-2}$ $9.57\times10^{-3}$ $2.35\times10^{-2}$ $6.16\times10^{-3}$ $1.05\times10^{-2}$ $3.15\times10^{-2}$ 成功率(%) 30 40 40 42 38 36 $f_{7}(x)$ 最小值 $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $4.67\times10^{-20}$ $2.37\times10^{-16}$ 均值 $2.43\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $2.35\times10^{-32}$ $8.96\times10^{-20}$ $ 8.91\times10^{-9}$ 标准差 $3.71\times10^{-34}$ $3.69\times10^{-33}$ $2.80\times10^{-48}$ $4.96\times10^{-33}$ $7.69\times10^{-20}$ $7.34\times10^{-8}$ 成功率(%) 100 100 100 100 100 100 $f_{8}(x)$ 最小值 0 0 0 0 0 0 均值 0 0 0 0 0 0 标准差 0 0 0 0 0 0 成功率(%) 100 100 100 100 100 100
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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 (dB) 均方误差 EMD 28.3163 0.2429 VMD 28.4436 0.2394 PSO-VMD 28.4799 0.2384 本文算法 28.6010 0.2351
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