混沌策略和非线性收敛因子的核参数寻优算法

问轲; 林晶; 张学昌; 刘永跃

doi:10.13433/j.cnki.1003-8728.20220097

混沌策略和非线性收敛因子的核参数寻优算法

doi: 10.13433/j.cnki.1003-8728.20220097

问轲^{1, 2,},
林晶¹,
张学昌^2, ,,
刘永跃³

1.
哈尔滨商业大学轻工学院，哈尔滨　150028
2.
浙大宁波理工学院机能学院，浙江宁波　315100
3.
宁波合力模具科技股份有限公司，浙江宁波　315700

基金项目: 宁波市科技创新2025重大专项（2019B10099）与黑龙江省属高校科技成果研发项目（TSTAU-R2018009）

详细信息

作者简介:
问轲（1996−），硕士研究生，研究方向为机器学习、图像处理算法，wenke961208@163.com

通讯作者:
张学昌，教授，硕士生导师，zz_zxc@163.com

中图分类号: TH16;TP181
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- 文章访问数: 119
- HTML全文浏览量: 55
- PDF下载量: 12
- 被引次数: 0
出版历程
- 收稿日期: 2021-08-03
- 刊出日期: 2023-09-30

Kernel Parameter Optimization Algorithm for Chaotic Strategy and Nonlinear Convergence Factor

WEN Ke^{1, 2
,},
LIN Jing¹,
ZHANG Xuechang^{2
, ,},
LIU Yongyue³

1.
School of Light Industry, Harbin University of Commerce, Harbin 150028, China
2.
School of Electromechanical and Energy, Ningbo Institute of Technology, Ningbo 315100, Zhejiang, China
3.
Ningbo Heli Mould Technology Co., Ltd., Ningbo 315700, Zhejiang, China

摘要

摘要: 为有效地解决SVM核参数寻优问题，提出了一种基于Fuch混沌策略协同非线性收敛因子的灰狼优化算法(FGWO)。在算法的3个阶段分别引入Fuch混沌反向学习策略、动态非线性控制参数、双权重因子策略和胜劣汰选择策略，为平衡全局探索和局部开发性能提供了新机制，增强了算法的收敛速度和收敛精度；以FGWO为新策略，构建一种FGWO-SVM分类模型，实现铝铸件表面缺陷识别。为验证算法的性能，引入10个标准测试函数，采用本文FGWO与其他算法相比较。结果表明，FGWO可以有效地解决函数优化问题；将FGWO-SVM模型应用于缺陷识别问题上，该模型对缺陷类型的平均识别率为96.6%，优于其他分类器。
- 灰狼优化算法 /
- Fuch映射 /
- 收敛因子 /
- 支持向量机 /
- 缺陷分类
Abstract: In order to effectively solve the optimization problem of SVM kernel parameters, a gray wolf optimization algorithm (FGWO) based on Fuch chaos strategy and nonlinear convergence factor is proposed in this paper. This method introduces Fuch chaos reverse learning strategy, dynamic nonlinear control parameters, dual weight factor strategy and survival of the fittest selection strategy, respectively in the three stages of the algorithm. The purpose is to provide a new mechanism for balancing the performance of global exploration and local development, and to enhance the convergence speed and accuracy of the algorithm. Secondly, using FGWO as a new strategy, FGWO-SVM classification model is constructed to realize the identification of surface defects of aluminum castings. In order to verify the performance of the algorithm, on the basis of 10 standard test functions, the FGWO algorithmof this paper is compared with other algorithms. The results show that FGWO can effectively solve the function optimization problem, andwhenthe FGWO-SVM model is applied to the defect recognition problem,its average recognition rate of the defect type is 96.6%, which is better than other classifiers.
- GWO algorithm /
- Fuch mapping /
- convergence factor /
- SVM /
- defect classification

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图 1 FGWO算法流程图

Figure 1. Flowchart of the FGWO algorithm

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图 2 10个标准函数收敛曲线图（Dim = 100）

Figure 2. Convergence curves of 10 standard functions (Dim = 100)

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图 3 不同类型逐渐缺陷图像

Figure 3. Different types of gradually defective images

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图 4 FGWO-SVM 流程图

Figure 4. Flowchart of FGWO-SVM

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图 5 优化SVM识别效果

Figure 5. Optimization of SVM recognition performance

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表 1 标准的测试函数

Table 1. Test functions

表达式f(x)	范围	$ {f_{\min }} $	Dim	收敛精度
$ {f_1}(x) = \displaystyle\sum\limits_{i = 1}^d {x_i^2} $	[−100,100]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_2}(x) = \displaystyle\sum\limits_{i = 1}^d {\|{x_i}\|} + \prod\limits_{i = 1}^d {\|{x_i}\|} $	[−10,10]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_3}(x) = {\displaystyle\sum\limits_{i = 1}^d {\left(\displaystyle\sum\limits_{j = 1}^i {{x_j}} \right)} ^2} $	[−100,100]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_4}(x) = \max \left\{ {\|{x_i}\|,1 \leqslant {x_i} \leqslant d} \right\} $	[−100,100]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_5}(x) = \displaystyle\sum\limits_{i = 1}^d {[100{{({x_{(i + 1)}} - x_i^2)}^2} + {{({x_i} - 1)}^2}]} $	[−5,10]	0	30 100 500	$1 \times {10^{ + 0} }$
$ {f_6}(x) = {\displaystyle\sum\limits_{i = 1}^n {\left( {\|{x_i} + 0.5\|} \right)} ^2} $	[−100,100]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_7}(x) = \displaystyle\sum\limits_{i = 1}^d {ix_i^4 + {\rm{rand}}(0,1)} $	[−1.28,1.28]	0	30 100 500	$ 1 \times {10^{ - 4}} $
${f_8}(x) = \displaystyle\sum\limits_{i = 1}^d {[x_i^2 - 10\cos (2{\text{π}} {x_i}) + 10]}$	[−5.12,5.12]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$\begin{gathered} {f_9}(x) = - 20\exp \left( - 0.2\sqrt {\dfrac{1}{d} }{\displaystyle\sum\limits_{i = 1}^d {x_i^2} } \right) \\ - \exp \left[\dfrac{1}{d}\displaystyle\sum\limits_{i = 1}^d {\cos (2{\text{π}} {x_i})} \right] + 20 + e \\ \end{gathered}$	[−32,32]	0	30 100 500	$ 1 \times {10^{ - 8}} $
$ {f_{10}}(x) = \dfrac{1}{{4\;000}}\displaystyle\sum\limits_{i = 1}^d {x_i^2} - \prod\limits_{i = 1}^d {\cos \left(\dfrac{{{x_i}}}{{\sqrt i }}\right)} + 1 $	[−600,600]	0	30 100 500	$ 1 \times {10^{ - 8}} $

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表 2 FGWO与传统寻优算法比较结果

Table 2. Comparison results between FGWO and traditional optimization algorithms

f_(x)	Dim	FGWO			GWO			PSO
f_(x)	Dim	Mean	Std	SR/%	Mean	Std	SR/%	Mean	Std	SR/%
f₍₁₎	30	0	0	100	9.97 × 10⁻²⁹	1.24 × 10⁻²⁹	100	4.08 × 10⁻⁵	6.45 × 10⁻⁵	0
	100	0	0	100	1.62 × 10⁻¹²	3.54 × 10⁻¹²	100	1.76 × 10¹	4.66 × 10⁰	0
	500	0	0	100	9.70 × 10⁻³	2.79 × 10⁻³	0	3.03 × 10⁴	5.73 × 10⁴	0
f₍₂₎	30	0	0	100	3.61 × 10⁻¹⁷	4.56 × 10⁻¹⁷	100	6.73 × 10⁻²	5.44 × 10⁻²	0
	100	0	0	100	4.53 × 10⁻⁸	5.36 × 10⁻⁹	0	3.81 × 10¹	3.65 × 10¹	0
	500	0	0	100	1.10 × 10⁻²	3.74 × 10⁻²	0	1.41 × 10³	2.45 × 10³	0
f₍₃₎	30	0	0	100	1.06 × 10⁻⁷	5.27 × 10⁻⁷	0	8.29 × 10¹	2.67 × 10¹	0
	100	0	0	100	7.97 × 10²	6.95 × 10²	0	1.35 × 10⁴	6.78 × 10³	0
	500	0	0	100	3.73 × 10⁵	1.34 × 10⁵	0	4.86 × 10⁵	7.38 × 10⁵	0
f₍₄₎	30	0	0	100	4.55 × 10⁻⁷	1.53 × 10⁻⁷	0	1.10 × 10⁰	8.56 × 10⁻¹	0
	100	0	0	100	1.39 × 10⁰	1.17 × 10⁰	0	1.19 × 10¹	5.34 × 10⁰	0
	500	0	0	100	6.44 × 10¹	4.59 × 10⁰	0	2.84 × 10¹	4.76 × 10¹	0
f₍₅₎	30	2.82 × 10¹	6.38 × 10⁻¹	0	2.79 × 10¹	1.02 × 10⁰	0	7.46 × 10¹	6.34 × 10¹	0
	100	9.87 × 10¹	6.63 × 10⁻³	0	9.71 × 10¹	7.01 × 10⁻¹	0	1.10 × 10⁴	1.21 × 10³	0
	500	4.98 × 10²	3.94 × 10⁻²	0	4.97 × 10²	1.16 × 10⁻¹	0	6.29 × 10⁶	6.34 × 10⁶	0
f₍₆₎	30	2.24 × 10⁰	4.84 × 10⁻¹	0	7.28 × 10⁻¹	3.21 × 10⁰	0	1.24 × 10⁻⁶	6.13 × 10⁻⁶	0
	100	1.74 × 10¹	1.08 × 10⁰	0	9.34 × 10⁰	2.74 × 10¹	0	1.81 × 10¹	3.21 × 10¹	0
	500	1.14 × 10²	1.92 × 10⁰	0	9.26 × 10¹	4.37 × 10⁰	0	6.38 × 10³	7.54 × 10³	0
f₍₇₎	30	1.79 × 10⁻⁵	1.89 × 10⁻⁵	100	6.84 × 10⁻²	5.43 × 10⁻²	0	1.63 × 10⁻¹	8.44 × 10⁰	0
	100	8.92 × 10⁻⁵	3.64 × 10⁻⁵	100	7.30 × 10⁻³	6.28 × 10⁻³	0	1.64 × 10³	1.26 × 10³	0
	500	4.28 × 10⁻⁶	3.10 × 10⁻⁶	100	5.26 × 10⁻²	1.37 × 10⁻²	0	5.61 × 10⁴	3.32 × 10³	0
f₍₈₎	30	0	0	100	6.23 × 10⁻¹³	3.25 × 10⁻¹³	100	5.78 × 10¹	6.09 × 10¹	0
	100	0	0	100	5.68 × 10⁰	2.56 × 10⁰	0	6.75 × 10²	1.78 × 10²	0
	500	0	0	100	1.09 × 10²	5.78 × 10²	0	5.95 × 10³	8.36 × 10²	0
f₍₉₎	30	8.81 × 10⁻¹⁶	0	100	9.53 × 10⁻¹⁴	3.77 × 10⁻¹⁵	100	6.77 × 10⁻¹	1.78 × 10⁻¹	0
	100	8.88 × 10⁻¹⁶	0	100	9.80 × 10⁻⁸	2.67 × 10⁻⁸	0	3.77 × 10⁰	6.64 × 10⁰	0
	500	8.88 × 10⁻¹⁶	0	100	1.08 × 10⁻⁷	7.86 × 10⁻⁷	0	3.71 × 10⁰	8.56 × 10⁰	0
f₍₁₀₎	30	0	0	100	2.34 × 10⁻³	4.34 × 10⁻⁴	0	7.20 × 10⁻³	5.67 × 10⁻⁴	0
	100	0	0	100	1.98 × 10⁻³	7.83 × 10⁻³	0	6.07 × 10³	1.03 × 10³	0
	500	0	0	100	2.25 × 10⁻⁴	4.79 × 10⁻⁴	0	9.55 × 10¹	6.87 × 10¹	0

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续表
f_(x)	Dim	SSA			SCA
f_(x)	Dim	Mean	Std	SR/%	Mean	Std	SR/%
f₍₁₎	30	2.45 × 10⁻⁷	6.84 × 10⁻⁸	0	3.05 × 10⁰	2.16 × 10¹	0
	100	1.76 × 10³	3.85 × 10³	0	1.49 × 10⁴	4.37 × 10⁴	0
	500	7.66 × 10⁴	1.74 × 10⁴	0	9.77 × 10⁵	4.88 × 10⁵	0
f₍₂₎	30	1.74 × 10⁰	5.33 × 10⁰	0	1.58 × 10⁻²	1.20 × 10⁻³	0
	100	4.77 × 10¹	6.56 × 10¹	0	9.86 × 10⁰	4.56 × 10⁰	0
	500	5.33 × 10²	7.55 × 10²	0	1.21 × 10²	5.19 × 10²	0
f₍₃₎	30	1.68 × 10³	4.37 × 10³	0	8.26 × 10³	2.45 × 10²	0
	100	6.63 × 10⁴	3.32 × 10⁴	0	2.49 × 10⁵	7.45 × 10⁵	0
	500	1.75 × 10⁶	7.56 × 10⁶	0	7.27 × 10⁶	5.34 × 10⁶	0
f₍₄₎	30	1.27 × 10¹	6,79 × 10⁰	0	2.50 × 10¹	5.45 × 10⁰	0
	100	2.99 × 10¹	3.47 × 10¹	0	8.96 × 10¹	1.86 × 10¹	0
	500	4.18 × 10¹	2.87 × 10¹	0	9.91 × 10¹	4.12 × 10¹	0
f₍₅₎	30	1.12 × 10²	4.76 × 10²	0	1.09 × 10²	5.76 × 10²	0
	100	1.40 × 10⁴	1.67 × 10³	0	2.23 × 10⁵	5.44 × 10⁴	0
	500	1.82 × 10⁶	7.55 × 10⁶	0	8.56 × 10⁶	3.25 × 10⁶	0
f₍₆₎	30	1.90 × 10⁻⁷	7.88 × 10⁻⁷	0	1.21 × 10¹	7.02 × 10⁰	0
	100	1.31 × 10³	2.18 × 10²	0	1.69 × 10⁴	1.78 × 10⁴	0
	500	1.03 × 10⁵	1.32 × 10⁰	0	1.24 × 10³	5.30 × 10⁻¹	0
f₍₇₎	30	1.25 × 10⁻¹	3.95 × 10⁻¹	0	1.55 × 10⁻¹	7.67 × 10⁻¹	0
	100	2.58 × 10⁰	3.94 × 10⁰	0	7.16 × 10¹	1.17 × 10⁰	0
	500	2.77 × 10²	8.46 × 10²	0	1.86 × 10⁴	2.18 × 10⁴	0
f₍₈₎	30	5.24 × 10¹	3.28 × 10¹	0	5.62 × 10¹	1.08 × 10¹	0
	100	2.26 × 10²	5.39 × 10²	0	2.49 × 10²	5.54 × 10¹	0
	500	3.03 × 10³	2.42 × 10³	0	5.82 × 10²	8.37 × 10²	0
f₍₉₎	30	2.63 × 10⁰	1.03 × 10⁰	0	1.58 × 10¹	7.40 × 10⁰	0
	100	1.63 × 10¹	3.19 × 10⁰	0	8.82 × 10²	2.26 × 10²	0
	500	8.07 × 10⁰	7.02 × 10⁰	0	2.06 × 10¹	3.29 × 10¹	0
f₍₁₀₎	30	5.66 × 10⁻³	6.12 × 10⁻²	0	5.83 × 10⁰	1.63 × 10⁰	0
	100	1.63 × 10¹	3.11 × 10¹	0	8.82 × 10¹	7.62 × 10¹	0
	500	9.15 × 10²	1.30 × 10²	0	8.92 × 10²	8.91 × 10¹	0

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表 3 FGWO与改进GWO的比较结果（Dim=30）

Table 3. Comparison results between FGWO and improved GWO (Dim=30)

$ {f_{(x)}} $	评价指标	FGWO	MGWO	CGWO	GWOepd
f₁	Mean	0	6.44 × 10⁻²⁰⁵	－	1.10 × 10⁻⁹²
	Std	0	0		5.90 × 10⁻⁹²
	Rank	1	2		3
f₂	Mean	0	3.34 × 10⁻¹¹⁹	1.16 × 10⁻²¹	5.46 × 10⁻⁶¹
	Std	0	4.95 × 10⁻¹¹⁹	1.98 × 10⁻²²	8.09 × 10⁻⁶¹
	Rank	1	2	4	3
f₃	Mean	0	2.74 × 10⁻⁵²	3.17 × 10⁻⁴²	2.30 × 10⁻⁸
	Std	0	1.19 × 10⁻⁵¹	1.04 × 10⁻⁴¹	1.22 × 10⁻⁷
	Rank	1	2	3	4
f₄	Mean	0	1.20 × 10⁻⁵¹	1.02 × 10⁻²²	－
	Std	0	4.25 × 10⁻⁵¹	1.93 × 10⁻²³
	Rank	1	2	3
f₅	Mean	2.82 × 10¹	2.69 × 10¹	7.31 × 10⁻⁷	4.72 × 10¹
	Std	6.38 × 10⁻¹	8.52 × 10¹	6.25 × 10⁻⁶	7.78 × 10¹
	Rank	3	2	1	4
f₆	Mean	2.24 × 10⁰	7.86 × 10¹	－	－
	Std	4.84 × 10⁻¹	2.44 × 10¹
	Rank	1	2
f₇	Mean	1.79 × 10⁻⁵	2.60 × 10⁻⁴	1.32 × 10⁻⁶	－
	Std	1.89 × 10⁻⁵	1.76 × 10⁻⁴	2.05 × 10⁻⁵
	Rank	2	3	1
f₈	Mean	0	0	0	6.83 × 10⁻²
	Std	0	0	0	3.74 × 10⁻¹
	Rank	1	1	1	2
f₉	Mean	8.81 × 10⁻¹⁶	7.82 × 10⁻¹⁵	－	1.23 × 10⁻¹⁴
	Std	0	7.94 × 10⁻¹⁶		2.27 × 10⁻¹⁵
	Rank	1	2		3
f₁₀	Mean	0	0	0	3.71 × 10⁻⁴
	Std	0	0	0	2.03 × 10⁻³
	Rank	1	1	1	2

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表 4 FGWO不同参数取值比较结果（Dim=30）

Table 4. Comparison results for FGWO with different parameter values (Dim=30)

$ {f_{(x)}} $	评价指标	${ {{A} }_{\min } }{\text{ = 0} }{\text{.5} },\;{ {{A} }_{\max } }{\text{ = 1} }$	${ {{A} }_{\min } }{\text{ = 0} }{\text{.5} },\;{ {{A} }_{\max } }{\text{ = 2} }$	${ {{A} }_{\min } }{\text{ = 1} }{\text{.5} },\;{ {{A} }_{\max } }{\text{ = 3} }$	${ {{A} }_{\min } }{\text{ = 1} }{\text{.5} },\;{ {{A} }_{\max } }{\text{ = 4} }$
f₁	Mean	0	0	0	0
f₁	Std	0	0	0	0
f₂	Mean	0	0	0	0
f₂	Std	0	0	0	0
f₃	Mean	0	0	0	0
f₃	Std	0	0	0	0
f₄	Mean	0	0	0	0
f₄	Std	0	0	0	0
f₅	Mean	2.82 × 10¹	2.88 × 10¹	2.88 × 10¹	2.88 × 10¹
f₅	Std	6.38 × 10⁻¹	3.60 × 10⁻²	4.19 × 10⁻²	2.18 × 10⁻²
f₆	Mean	2.24 × 10⁰	2.00 × 10⁰	1.76 × 10⁰	1.33 × 10⁰
f₆	Std	4.84 × 10⁻¹	5.88 × 10⁻¹	2.23 × 10⁻¹	6.67 × 10⁻²
f₇	Mean	1.79 × 10⁻⁵	6.95 × 10⁻⁵	1.12 × 10⁻⁴	1.65 × 10⁻⁴
f₇	Std	1.89 × 10⁻⁵	4.26 × 10⁻⁵	3.34 × 10⁻⁵	5.87 × 10⁻⁵
f₈	Mean	0	0	0	0
f₈	Std	0	0	0	0
f₉	Mean	8.81 × 10⁻¹⁶	8.81 × 10⁻¹⁶	8.81 × 10⁻¹⁶	8.81 × 10⁻¹⁶
f₉	Std	0	0	0	0
f₁₀	Mean	0	0	0	0
f₁₀	Std	0	0	0	0

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表 5 缺陷分类结果对比

Table 5. Comparison results fordefect classification

算法模型	R/%	FGWO-SVM	GWO-SVM	PSO-SVM	GA-SVM
“一对多”分类器	最高识别率	116	116	106	108
	最低识别率	115	108	106	106
	平均识别率	115.7	113.7	106	106.8
	标准差	0.45	3.74	0	0.74
	Rank	1	2	4	3

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表 6 SVM与BP神经网络分类对比结果

Table 6. Comparison results between SVM and BP neural network classification

分类器	缺陷类型	划伤	黑斑	孔洞类	识别率/%
FGWO-SVM分类器模型	划伤	40	0	0	100
	黑斑	3	37	0	92.50
	孔洞类	0	1	39	97.50
BP神经网络	划伤	38	1	1	95
	黑斑	4	36	0	90
	孔洞类	1	4	35	88
FGWO-SVM平均识别		正确识别样本数：116		平均识别率：96.6%
BP神经网络平均识别		正确识别样本数：109		平均识别率：90%

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参考文献(19)

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