Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (3): 842-847.DOI: 10.11772/j.issn.1001-9081.2022010122
Special Issue: 先进计算
• Advanced computing • Previous Articles Next Articles
Received:
2022-02-08
Revised:
2022-04-21
Accepted:
2022-04-25
Online:
2022-05-07
Published:
2023-03-10
Contact:
Hanping HU
About author:
YIN Cong, born in 1995, M. S. candidate. His research interests include chaos theory, machine learning.
Supported by:
通讯作者:
胡汉平
作者简介:
尹聪(1995—),男,河北沧州人,硕士研究生,主要研究方向:混沌理论、机器学习基金资助:
CLC Number:
Cong YIN, Hanping HU. Parameter identification model for time-delay chaotic systems based on temporal attention mechanism[J]. Journal of Computer Applications, 2023, 43(3): 842-847.
尹聪, 胡汉平. 基于时间注意力机制的时滞混沌系统参数辨识模型[J]. 《计算机应用》唯一官方网站, 2023, 43(3): 842-847.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2022010122
混沌系统 | θ1 | θ2 | τ |
---|---|---|---|
时滞Logistic方程 | [ | [40,80] | [0,2] |
Ikeda微分方程 | [0,5] | [0,80] | [0,5] |
Mackey-Glass混沌系统 | [0,1] | [0,1] | [0,100] |
Tab.1 Value ranges of parameters and time delay
混沌系统 | θ1 | θ2 | τ |
---|---|---|---|
时滞Logistic方程 | [ | [40,80] | [0,2] |
Ikeda微分方程 | [0,5] | [0,80] | [0,5] |
Mackey-Glass混沌系统 | [0,1] | [0,1] | [0,100] |
混沌系统 | 注意力网络训练集 | 求根网络 训练集 | 测试集 |
---|---|---|---|
时滞Logistic方程 | 4 966 | 4 604 | 1 237 |
Ikeda微分方程 | 45 202 | 9 050 | 1 635 |
Mackey-Glass混沌系统 | 12 622 | 16 173 | 1 567 |
Tab.2 Number of parameter-time delay groups of each chaotic system
混沌系统 | 注意力网络训练集 | 求根网络 训练集 | 测试集 |
---|---|---|---|
时滞Logistic方程 | 4 966 | 4 604 | 1 237 |
Ikeda微分方程 | 45 202 | 9 050 | 1 635 |
Mackey-Glass混沌系统 | 12 622 | 16 173 | 1 567 |
神经网络模块 | 模块组成 | 神经元配置 |
---|---|---|
注意力网络 | BiLSTM | BiLSTM(2层,每层50个神经元) |
FFNNq | 全连接层(50),Tanh激活函数,全连接层(50) | |
FFNNk | 全连接层(50),Tanh激活函数,全连接层(50) | |
时滞辨识 | FFNN τ | 全连接层(M),Tanh激活函数,全连接层(1) |
求根网络 | LSTM θ | LSTM(2层,每层150个神经元) |
FFNN θ | Tanh激活函数,全连接层(dim( θ )) |
Tab.3 Settings of neurons
神经网络模块 | 模块组成 | 神经元配置 |
---|---|---|
注意力网络 | BiLSTM | BiLSTM(2层,每层50个神经元) |
FFNNq | 全连接层(50),Tanh激活函数,全连接层(50) | |
FFNNk | 全连接层(50),Tanh激活函数,全连接层(50) | |
时滞辨识 | FFNN τ | 全连接层(M),Tanh激活函数,全连接层(1) |
求根网络 | LSTM θ | LSTM(2层,每层150个神经元) |
FFNN θ | Tanh激活函数,全连接层(dim( θ )) |
算法 | 参数 | 参数取值 |
---|---|---|
ARA | 种群规模 | 256.0 |
迭代轮数 | 100.0 | |
最优个体对雨滴流动方向的影响权值 | 0.8 | |
次优个体对雨滴流动方向的影响权值 | 0.2 | |
GFPA | 种群规模 | 256.0 |
迭代轮数 | 100.0 | |
HCS | 种群规模 | 40.0 |
迭代轮数 | 100.0 | |
CWA | 种群规模 | 36.0 |
迭代轮数 | 100.0 | |
元胞自动机搜索邻域规模 | C9 |
Tab.4 Parameter setting of each intelligent search algorithm
算法 | 参数 | 参数取值 |
---|---|---|
ARA | 种群规模 | 256.0 |
迭代轮数 | 100.0 | |
最优个体对雨滴流动方向的影响权值 | 0.8 | |
次优个体对雨滴流动方向的影响权值 | 0.2 | |
GFPA | 种群规模 | 256.0 |
迭代轮数 | 100.0 | |
HCS | 种群规模 | 40.0 |
迭代轮数 | 100.0 | |
CWA | 种群规模 | 36.0 |
迭代轮数 | 100.0 | |
元胞自动机搜索邻域规模 | C9 |
时滞混沌 系统 | 辨识方法 | RMSE | 平均辨识 耗时/ms | ||
---|---|---|---|---|---|
θ1 | θ2 | τ | |||
时滞 Logistic 方程 | ARA | 2.591 8 | 10.049 2 | 0.254 4 | 12 167.17 |
GFPA | 4.765 0 | 17.923 6 | 0.363 9 | 4 936.86 | |
HCS | 3.752 5 | 14.423 5 | 0.346 2 | 643.53 | |
CWA | 3.321 1 | 12.863 7 | 0.369 3 | 1 724.11 | |
PINN-TA | 0.211 0 | 0.648 7 | 0.004 4 | 18.59 | |
Ikeda 微分 方程 | ARA | 1.649 2 | 29.399 9 | 0.909 6 | 12 887.46 |
GFPA | 2.101 7 | 28.115 2 | 0.798 5 | 4 816.49 | |
HCS | 1.728 1 | 28.792 4 | 0.969 4 | 609.28 | |
CWA | 1.828 3 | 27.205 9 | 0.698 3 | 2 345.99 | |
PINN-TA | 0.151 6 | 0.399 0 | 0.051 9 | 19.43 | |
Mackey- Glass 混沌系统 | ARA | 0.619 2 | 0.638 7 | 20.741 0 | 13 193.81 |
GFPA | 0.643 0 | 0.520 1 | 36.720 4 | 4 870.81 | |
HCS | 0.630 4 | 0.513 7 | 32.293 2 | 628.35 | |
CWA | 0.622 7 | 0.522 5 | 34.042 0 | 1 642.45 | |
PINN-TA | 0.005 4 | 0.004 1 | 2.008 4 | 19.42 |
Tab. 5 Identification results of typical time-delay chaotic systems obtained from PINN-TA and different intelligent search algorithms
时滞混沌 系统 | 辨识方法 | RMSE | 平均辨识 耗时/ms | ||
---|---|---|---|---|---|
θ1 | θ2 | τ | |||
时滞 Logistic 方程 | ARA | 2.591 8 | 10.049 2 | 0.254 4 | 12 167.17 |
GFPA | 4.765 0 | 17.923 6 | 0.363 9 | 4 936.86 | |
HCS | 3.752 5 | 14.423 5 | 0.346 2 | 643.53 | |
CWA | 3.321 1 | 12.863 7 | 0.369 3 | 1 724.11 | |
PINN-TA | 0.211 0 | 0.648 7 | 0.004 4 | 18.59 | |
Ikeda 微分 方程 | ARA | 1.649 2 | 29.399 9 | 0.909 6 | 12 887.46 |
GFPA | 2.101 7 | 28.115 2 | 0.798 5 | 4 816.49 | |
HCS | 1.728 1 | 28.792 4 | 0.969 4 | 609.28 | |
CWA | 1.828 3 | 27.205 9 | 0.698 3 | 2 345.99 | |
PINN-TA | 0.151 6 | 0.399 0 | 0.051 9 | 19.43 | |
Mackey- Glass 混沌系统 | ARA | 0.619 2 | 0.638 7 | 20.741 0 | 13 193.81 |
GFPA | 0.643 0 | 0.520 1 | 36.720 4 | 4 870.81 | |
HCS | 0.630 4 | 0.513 7 | 32.293 2 | 628.35 | |
CWA | 0.622 7 | 0.522 5 | 34.042 0 | 1 642.45 | |
PINN-TA | 0.005 4 | 0.004 1 | 2.008 4 | 19.42 |
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